%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN481-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:17 AM UTC 2025
% Result : Unsatisfiable 1.31s 1.49s
% Output : Proof 1.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN481-1 : TPTP v9.0.0. Released v2.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:38:27 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.31/1.49 % SZS status Unsatisfiable
% 1.31/1.49 % SZS output start Proof
% 1.31/1.49 tff(c2_1_type, type, (
% 1.31/1.49 c2_1: $i > $o)).
% 1.31/1.49 tff(a1650_type, type, (
% 1.31/1.49 a1650: $i)).
% 1.31/1.49 tff(c3_1_type, type, (
% 1.31/1.49 c3_1: $i > $o)).
% 1.31/1.49 tff(a1636_type, type, (
% 1.31/1.49 a1636: $i)).
% 1.31/1.49 tff(c1_1_type, type, (
% 1.31/1.49 c1_1: $i > $o)).
% 1.31/1.49 tff(c0_1_type, type, (
% 1.31/1.49 c0_1: $i > $o)).
% 1.31/1.49 tff(ndr1_0_type, type, (
% 1.31/1.49 ndr1_0: $o)).
% 1.31/1.49 tff(hskp3_type, type, (
% 1.31/1.49 hskp3: $o)).
% 1.31/1.49 tff(hskp1_type, type, (
% 1.31/1.49 hskp1: $o)).
% 1.31/1.49 tff(a1637_type, type, (
% 1.31/1.49 a1637: $i)).
% 1.31/1.49 tff(a1634_type, type, (
% 1.31/1.49 a1634: $i)).
% 1.31/1.49 tff(hskp0_type, type, (
% 1.31/1.49 hskp0: $o)).
% 1.31/1.49 tff(a1638_type, type, (
% 1.31/1.49 a1638: $i)).
% 1.31/1.49 tff(hskp11_type, type, (
% 1.31/1.49 hskp11: $o)).
% 1.31/1.49 tff(a1680_type, type, (
% 1.31/1.49 a1680: $i)).
% 1.31/1.49 tff(a1646_type, type, (
% 1.31/1.49 a1646: $i)).
% 1.31/1.49 tff(a1643_type, type, (
% 1.31/1.49 a1643: $i)).
% 1.31/1.49 tff(hskp8_type, type, (
% 1.31/1.49 hskp8: $o)).
% 1.31/1.49 tff(a1648_type, type, (
% 1.31/1.49 a1648: $i)).
% 1.31/1.49 tff(hskp10_type, type, (
% 1.31/1.49 hskp10: $o)).
% 1.31/1.49 tff(a1640_type, type, (
% 1.31/1.49 a1640: $i)).
% 1.31/1.49 tff(hskp22_type, type, (
% 1.31/1.49 hskp22: $o)).
% 1.31/1.49 tff(hskp15_type, type, (
% 1.31/1.49 hskp15: $o)).
% 1.31/1.49 tff(hskp2_type, type, (
% 1.31/1.49 hskp2: $o)).
% 1.31/1.49 tff(hskp28_type, type, (
% 1.31/1.49 hskp28: $o)).
% 1.31/1.49 tff(hskp18_type, type, (
% 1.31/1.49 hskp18: $o)).
% 1.31/1.49 tff(hskp20_type, type, (
% 1.31/1.49 hskp20: $o)).
% 1.31/1.49 tff(hskp30_type, type, (
% 1.31/1.49 hskp30: $o)).
% 1.31/1.49 tff(hskp27_type, type, (
% 1.31/1.49 hskp27: $o)).
% 1.31/1.49 tff(a1737_type, type, (
% 1.31/1.49 a1737: $i)).
% 1.31/1.49 tff(a1642_type, type, (
% 1.31/1.49 a1642: $i)).
% 1.31/1.49 tff(hskp26_type, type, (
% 1.31/1.49 hskp26: $o)).
% 1.31/1.49 tff(a1664_type, type, (
% 1.31/1.49 a1664: $i)).
% 1.31/1.49 tff(hskp7_type, type, (
% 1.31/1.49 hskp7: $o)).
% 1.31/1.49 tff(a1675_type, type, (
% 1.31/1.49 a1675: $i)).
% 1.31/1.49 tff(hskp17_type, type, (
% 1.31/1.49 hskp17: $o)).
% 1.31/1.49 tff(hskp19_type, type, (
% 1.31/1.49 hskp19: $o)).
% 1.31/1.49 tff(hskp9_type, type, (
% 1.31/1.49 hskp9: $o)).
% 1.31/1.49 tff(a1644_type, type, (
% 1.31/1.49 a1644: $i)).
% 1.31/1.49 tff(a1682_type, type, (
% 1.31/1.49 a1682: $i)).
% 1.31/1.49 tff(hskp5_type, type, (
% 1.31/1.49 hskp5: $o)).
% 1.31/1.49 tff(hskp21_type, type, (
% 1.31/1.49 hskp21: $o)).
% 1.31/1.49 tff(a1691_type, type, (
% 1.31/1.49 a1691: $i)).
% 1.31/1.49 tff(a1639_type, type, (
% 1.31/1.49 a1639: $i)).
% 1.31/1.49 tff(hskp4_type, type, (
% 1.31/1.49 hskp4: $o)).
% 1.31/1.49 tff(a1667_type, type, (
% 1.31/1.49 a1667: $i)).
% 1.31/1.49 tff(hskp16_type, type, (
% 1.31/1.49 hskp16: $o)).
% 1.31/1.49 tff(a1689_type, type, (
% 1.31/1.49 a1689: $i)).
% 1.31/1.49 tff(hskp14_type, type, (
% 1.31/1.49 hskp14: $o)).
% 1.31/1.49 tff(a1661_type, type, (
% 1.31/1.49 a1661: $i)).
% 1.31/1.49 tff(a1647_type, type, (
% 1.31/1.49 a1647: $i)).
% 1.31/1.49 tff(hskp29_type, type, (
% 1.31/1.49 hskp29: $o)).
% 1.31/1.49 tff(a1697_type, type, (
% 1.31/1.49 a1697: $i)).
% 1.31/1.49 tff(a1658_type, type, (
% 1.31/1.49 a1658: $i)).
% 1.31/1.49 tff(hskp13_type, type, (
% 1.31/1.49 hskp13: $o)).
% 1.31/1.49 tff(a1635_type, type, (
% 1.31/1.49 a1635: $i)).
% 1.31/1.49 tff(hskp12_type, type, (
% 1.31/1.49 hskp12: $o)).
% 1.31/1.49 tff(a1653_type, type, (
% 1.31/1.49 a1653: $i)).
% 1.31/1.49 tff(hskp24_type, type, (
% 1.31/1.49 hskp24: $o)).
% 1.31/1.49 tff(hskp25_type, type, (
% 1.31/1.49 hskp25: $o)).
% 1.31/1.49 tff(a1709_type, type, (
% 1.31/1.49 a1709: $i)).
% 1.31/1.49 tff(a1701_type, type, (
% 1.31/1.49 a1701: $i)).
% 1.31/1.49 tff(1,plain,
% 1.31/1.49 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(2,plain,
% 1.31/1.49 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[1])).
% 1.31/1.49 tff(3,plain,
% 1.31/1.49 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(4,plain,
% 1.31/1.49 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V)))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp3))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(5,plain,
% 1.31/1.49 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[4])).
% 1.31/1.49 tff(6,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 1.31/1.49 tff(7,plain,
% 1.31/1.49 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.31/1.49 tff(8,plain,
% 1.31/1.49 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.31/1.49 tff(9,plain,(
% 1.31/1.49 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.31/1.49 inference(skolemize,[status(sab)],[8])).
% 1.31/1.49 tff(10,plain,
% 1.31/1.49 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.31/1.49 tff(11,plain,
% 1.31/1.49 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(12,plain,
% 1.31/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[11])).
% 1.31/1.49 tff(13,plain,
% 1.31/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(14,plain,
% 1.31/1.49 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(15,plain,
% 1.31/1.49 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[14])).
% 1.31/1.49 tff(16,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause199')).
% 1.31/1.49 tff(17,plain,
% 1.31/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.31/1.49 tff(18,plain,
% 1.31/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[17, 13])).
% 1.31/1.49 tff(19,plain,(
% 1.31/1.49 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 1.31/1.49 inference(skolemize,[status(sab)],[18])).
% 1.31/1.49 tff(20,plain,
% 1.31/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[19, 12])).
% 1.31/1.49 tff(21,assumption,(~hskp1), introduced(assumption)).
% 1.31/1.49 tff(22,assumption,(~c0_1(a1638)), introduced(assumption)).
% 1.31/1.49 tff(23,plain,
% 1.31/1.49 (^[U: $i] : refl((hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(24,plain,
% 1.31/1.49 (![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[23])).
% 1.31/1.49 tff(25,plain,
% 1.31/1.49 (![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(26,plain,
% 1.31/1.49 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp8) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp8))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp8) | hskp1) <=> ((hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp1))), rewrite(((hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp1) <=> (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp8) | hskp1) <=> (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(27,plain,
% 1.31/1.49 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp8) | hskp1) <=> ![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[26])).
% 1.31/1.49 tff(28,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp8) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause160')).
% 1.31/1.49 tff(29,plain,
% 1.31/1.49 (![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[28, 27])).
% 1.31/1.49 tff(30,plain,
% 1.31/1.49 (![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[29, 25])).
% 1.31/1.49 tff(31,plain,(
% 1.31/1.49 ![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.31/1.49 inference(skolemize,[status(sab)],[30])).
% 1.31/1.49 tff(32,plain,
% 1.31/1.49 (![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[31, 24])).
% 1.31/1.49 tff(33,assumption,(~hskp0), introduced(assumption)).
% 1.31/1.49 tff(34,assumption,(c2_1(a1650)), introduced(assumption)).
% 1.31/1.49 tff(35,plain,
% 1.31/1.49 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(36,plain,
% 1.31/1.49 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[35])).
% 1.31/1.49 tff(37,plain,
% 1.31/1.49 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(38,plain,
% 1.31/1.49 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp22) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp22))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(39,plain,
% 1.31/1.50 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[38])).
% 1.31/1.50 tff(40,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause190')).
% 1.31/1.50 tff(41,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[40, 39])).
% 1.31/1.50 tff(42,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[41, 37])).
% 1.31/1.50 tff(43,plain,(
% 1.31/1.50 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.31/1.50 inference(skolemize,[status(sab)],[42])).
% 1.31/1.50 tff(44,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[43, 36])).
% 1.31/1.50 tff(45,assumption,(~hskp11), introduced(assumption)).
% 1.31/1.50 tff(46,plain,
% 1.31/1.50 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(47,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[46])).
% 1.31/1.50 tff(48,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(49,plain,
% 1.31/1.50 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp11))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(50,plain,
% 1.31/1.50 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[49])).
% 1.31/1.50 tff(51,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 1.31/1.50 tff(52,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[51, 50])).
% 1.31/1.50 tff(53,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[52, 48])).
% 1.31/1.50 tff(54,plain,(
% 1.31/1.50 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.50 inference(skolemize,[status(sab)],[53])).
% 1.31/1.50 tff(55,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[54, 47])).
% 1.31/1.50 tff(56,assumption,(~hskp10), introduced(assumption)).
% 1.31/1.50 tff(57,plain,
% 1.31/1.50 ((hskp18 | hskp11 | hskp10) <=> (hskp18 | hskp11 | hskp10)),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(58,plain,
% 1.31/1.50 (((hskp10 | hskp18) | hskp11) <=> (hskp18 | hskp11 | hskp10)),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(59,axiom,((hskp10 | hskp18) | hskp11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 1.31/1.50 tff(60,plain,
% 1.31/1.50 (hskp18 | hskp11 | hskp10),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[59, 58])).
% 1.31/1.50 tff(61,plain,
% 1.31/1.50 (hskp18 | hskp11 | hskp10),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[60, 57])).
% 1.31/1.50 tff(62,plain,
% 1.31/1.50 (hskp18 | hskp11 | hskp10),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[61, 57])).
% 1.31/1.50 tff(63,plain,
% 1.31/1.50 (hskp18 | hskp11 | hskp10),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[62, 57])).
% 1.31/1.50 tff(64,plain,
% 1.31/1.50 (hskp18 | hskp11 | hskp10),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[63, 57])).
% 1.31/1.50 tff(65,plain,
% 1.31/1.50 (hskp18),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[64, 45, 56])).
% 1.31/1.50 tff(66,plain,
% 1.31/1.50 (((~hskp18) | (~c2_1(a1680))) <=> ((~hskp18) | (~c2_1(a1680)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(67,plain,
% 1.31/1.50 (((~c2_1(a1680)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a1680)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(68,axiom,((~c2_1(a1680)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 1.31/1.50 tff(69,plain,
% 1.31/1.50 ((~hskp18) | (~c2_1(a1680))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[68, 67])).
% 1.31/1.50 tff(70,plain,
% 1.31/1.50 ((~hskp18) | (~c2_1(a1680))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[69, 66])).
% 1.31/1.50 tff(71,plain,
% 1.31/1.50 (~c2_1(a1680)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[70, 65])).
% 1.31/1.50 tff(72,plain,
% 1.31/1.50 (((~hskp18) | (~c0_1(a1680))) <=> ((~hskp18) | (~c0_1(a1680)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(73,plain,
% 1.31/1.50 (((~c0_1(a1680)) | (~hskp18)) <=> ((~hskp18) | (~c0_1(a1680)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(74,axiom,((~c0_1(a1680)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 1.31/1.50 tff(75,plain,
% 1.31/1.50 ((~hskp18) | (~c0_1(a1680))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[74, 73])).
% 1.31/1.50 tff(76,plain,
% 1.31/1.50 ((~hskp18) | (~c0_1(a1680))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[75, 72])).
% 1.31/1.50 tff(77,plain,
% 1.31/1.50 (~c0_1(a1680)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[76, 65])).
% 1.31/1.50 tff(78,plain,
% 1.31/1.50 (((~hskp18) | c1_1(a1680)) <=> ((~hskp18) | c1_1(a1680))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(79,axiom,((~hskp18) | c1_1(a1680)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 1.31/1.50 tff(80,plain,
% 1.31/1.50 ((~hskp18) | c1_1(a1680)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[79, 78])).
% 1.31/1.50 tff(81,plain,
% 1.31/1.50 ((~hskp18) | c1_1(a1680)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[80, 78])).
% 1.31/1.50 tff(82,plain,
% 1.31/1.50 ((~hskp18) | c1_1(a1680)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[81, 78])).
% 1.31/1.50 tff(83,plain,
% 1.31/1.50 ((~hskp18) | c1_1(a1680)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[82, 78])).
% 1.31/1.50 tff(84,plain,
% 1.31/1.50 ((~hskp18) | c1_1(a1680)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[83, 78])).
% 1.31/1.50 tff(85,plain,
% 1.31/1.50 (c1_1(a1680)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[84, 65])).
% 1.31/1.50 tff(86,assumption,(~ndr1_0), introduced(assumption)).
% 1.31/1.50 tff(87,plain,
% 1.31/1.50 ((ndr1_0 | (~hskp20)) <=> (ndr1_0 | (~hskp20))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(88,plain,
% 1.31/1.50 (((~hskp20) | ndr1_0) <=> (ndr1_0 | (~hskp20))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(89,axiom,((~hskp20) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause12')).
% 1.31/1.50 tff(90,plain,
% 1.31/1.50 (ndr1_0 | (~hskp20)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[89, 88])).
% 1.31/1.50 tff(91,plain,
% 1.31/1.50 (ndr1_0 | (~hskp20)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[90, 87])).
% 1.31/1.50 tff(92,plain,
% 1.31/1.50 (~hskp20),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[91, 86])).
% 1.31/1.50 tff(93,plain,
% 1.31/1.50 (((~hskp30) | ndr1_0) <=> ((~hskp30) | ndr1_0)),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(94,axiom,((~hskp30) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 1.31/1.50 tff(95,plain,
% 1.31/1.50 ((~hskp30) | ndr1_0),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[94, 93])).
% 1.31/1.50 tff(96,plain,
% 1.31/1.50 ((~hskp30) | ndr1_0),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[95, 93])).
% 1.31/1.50 tff(97,plain,
% 1.31/1.50 ((~hskp30) | ndr1_0),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[96, 93])).
% 1.31/1.50 tff(98,plain,
% 1.31/1.50 ((~hskp30) | ndr1_0),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[97, 93])).
% 1.31/1.50 tff(99,plain,
% 1.31/1.50 ((~hskp30) | ndr1_0),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[98, 93])).
% 1.31/1.50 tff(100,plain,
% 1.31/1.50 (~hskp30),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[99, 86])).
% 1.31/1.50 tff(101,plain,
% 1.31/1.50 ((ndr1_0 | (~hskp27)) <=> (ndr1_0 | (~hskp27))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(102,plain,
% 1.31/1.50 (((~hskp27) | ndr1_0) <=> (ndr1_0 | (~hskp27))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(103,axiom,((~hskp27) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause5')).
% 1.31/1.50 tff(104,plain,
% 1.31/1.50 (ndr1_0 | (~hskp27)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[103, 102])).
% 1.31/1.50 tff(105,plain,
% 1.31/1.50 (ndr1_0 | (~hskp27)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[104, 101])).
% 1.31/1.50 tff(106,plain,
% 1.31/1.50 (~hskp27),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[105, 86])).
% 1.31/1.50 tff(107,plain,
% 1.31/1.50 ((hskp20 | hskp30 | hskp27) <=> (hskp20 | hskp30 | hskp27)),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(108,plain,
% 1.31/1.50 (((hskp20 | hskp27) | hskp30) <=> (hskp20 | hskp30 | hskp27)),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(109,plain,
% 1.31/1.50 ((hskp27 | hskp20) <=> (hskp20 | hskp27)),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(110,plain,
% 1.31/1.50 (((hskp27 | hskp20) | hskp30) <=> ((hskp20 | hskp27) | hskp30)),
% 1.31/1.50 inference(monotonicity,[status(thm)],[109])).
% 1.31/1.50 tff(111,plain,
% 1.31/1.50 (((hskp27 | hskp20) | hskp30) <=> (hskp20 | hskp30 | hskp27)),
% 1.31/1.50 inference(transitivity,[status(thm)],[110, 108])).
% 1.31/1.50 tff(112,axiom,((hskp27 | hskp20) | hskp30), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 1.31/1.50 tff(113,plain,
% 1.31/1.50 (hskp20 | hskp30 | hskp27),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[112, 111])).
% 1.31/1.50 tff(114,plain,
% 1.31/1.50 (hskp20 | hskp30 | hskp27),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[113, 107])).
% 1.31/1.50 tff(115,plain,
% 1.31/1.50 (hskp20 | hskp30 | hskp27),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[114, 107])).
% 1.31/1.50 tff(116,plain,
% 1.31/1.50 (hskp20 | hskp30 | hskp27),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[115, 107])).
% 1.31/1.50 tff(117,plain,
% 1.31/1.50 (hskp20 | hskp30 | hskp27),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[116, 107])).
% 1.31/1.50 tff(118,plain,
% 1.31/1.50 ($false),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[117, 106, 100, 92])).
% 1.31/1.50 tff(119,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.31/1.50 tff(120,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a1680) | c2_1(a1680) | (~ndr1_0) | (~c3_1(a1680)) | (~c1_1(a1680)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a1680) | c2_1(a1680) | (~ndr1_0) | (~c3_1(a1680)) | (~c1_1(a1680)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(121,plain,
% 1.31/1.50 ((hskp11 | (~ndr1_0) | c0_1(a1680) | (~c3_1(a1680)) | (~c1_1(a1680)) | c2_1(a1680) | c0_1(a1680) | (~c3_1(a1680))) <=> (hskp11 | c0_1(a1680) | c2_1(a1680) | (~ndr1_0) | (~c3_1(a1680)) | (~c1_1(a1680)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(122,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a1680) | (~c3_1(a1680)) | (~c1_1(a1680)) | c2_1(a1680) | c0_1(a1680) | (~c3_1(a1680)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a1680) | c2_1(a1680) | (~ndr1_0) | (~c3_1(a1680)) | (~c1_1(a1680))))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[121])).
% 1.31/1.50 tff(123,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a1680) | (~c3_1(a1680)) | (~c1_1(a1680)) | c2_1(a1680) | c0_1(a1680) | (~c3_1(a1680)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a1680) | c2_1(a1680) | (~ndr1_0) | (~c3_1(a1680)) | (~c1_1(a1680)))),
% 1.31/1.50 inference(transitivity,[status(thm)],[122, 120])).
% 1.31/1.50 tff(124,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a1680) | (~c3_1(a1680)) | (~c1_1(a1680)) | c2_1(a1680) | c0_1(a1680) | (~c3_1(a1680)))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(125,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a1680) | c2_1(a1680) | (~ndr1_0) | (~c3_1(a1680)) | (~c1_1(a1680))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[124, 123])).
% 1.31/1.50 tff(126,plain,
% 1.31/1.50 (~c3_1(a1680)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[125, 119, 45, 85, 77, 71, 55])).
% 1.31/1.50 tff(127,plain,
% 1.31/1.50 (^[U: $i] : refl((hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(128,plain,
% 1.31/1.50 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[127])).
% 1.31/1.50 tff(129,plain,
% 1.31/1.50 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(130,plain,
% 1.31/1.50 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp10) | hskp1) <=> ((hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp1))), rewrite(((hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp1) <=> (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp10) | hskp1) <=> (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(131,plain,
% 1.31/1.50 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp10) | hskp1) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[130])).
% 1.31/1.50 tff(132,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp10) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 1.31/1.50 tff(133,plain,
% 1.31/1.50 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[132, 131])).
% 1.31/1.50 tff(134,plain,
% 1.31/1.50 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[133, 129])).
% 1.31/1.50 tff(135,plain,(
% 1.31/1.50 ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.31/1.50 inference(skolemize,[status(sab)],[134])).
% 1.31/1.50 tff(136,plain,
% 1.31/1.50 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[135, 128])).
% 1.31/1.50 tff(137,plain,
% 1.31/1.50 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp1 | c0_1(a1680) | c2_1(a1680) | (~ndr1_0) | c3_1(a1680))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp1 | c0_1(a1680) | c2_1(a1680) | (~ndr1_0) | c3_1(a1680))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(138,plain,
% 1.31/1.50 ((hskp10 | hskp1 | (~ndr1_0) | c2_1(a1680) | c0_1(a1680) | c3_1(a1680)) <=> (hskp10 | hskp1 | c0_1(a1680) | c2_1(a1680) | (~ndr1_0) | c3_1(a1680))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(139,plain,
% 1.31/1.50 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a1680) | c0_1(a1680) | c3_1(a1680))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp1 | c0_1(a1680) | c2_1(a1680) | (~ndr1_0) | c3_1(a1680)))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[138])).
% 1.31/1.50 tff(140,plain,
% 1.31/1.50 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a1680) | c0_1(a1680) | c3_1(a1680))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp1 | c0_1(a1680) | c2_1(a1680) | (~ndr1_0) | c3_1(a1680))),
% 1.31/1.50 inference(transitivity,[status(thm)],[139, 137])).
% 1.31/1.50 tff(141,plain,
% 1.31/1.50 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a1680) | c0_1(a1680) | c3_1(a1680))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(142,plain,
% 1.31/1.50 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp1 | c0_1(a1680) | c2_1(a1680) | (~ndr1_0) | c3_1(a1680)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[141, 140])).
% 1.31/1.50 tff(143,plain,
% 1.31/1.50 ($false),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[142, 119, 56, 21, 77, 71, 136, 126])).
% 1.31/1.50 tff(144,plain,(hskp11 | hskp10 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.31/1.50 tff(145,plain,
% 1.31/1.50 (hskp10),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[144, 45, 21])).
% 1.31/1.50 tff(146,plain,
% 1.31/1.50 (((~hskp10) | (~c3_1(a1648))) <=> ((~hskp10) | (~c3_1(a1648)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(147,plain,
% 1.31/1.50 (((~c3_1(a1648)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a1648)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(148,axiom,((~c3_1(a1648)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 1.31/1.50 tff(149,plain,
% 1.31/1.50 ((~hskp10) | (~c3_1(a1648))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[148, 147])).
% 1.31/1.50 tff(150,plain,
% 1.31/1.50 ((~hskp10) | (~c3_1(a1648))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[149, 146])).
% 1.31/1.50 tff(151,plain,
% 1.31/1.50 (~c3_1(a1648)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[150, 145])).
% 1.31/1.50 tff(152,plain,
% 1.31/1.50 (((~hskp10) | c0_1(a1648)) <=> ((~hskp10) | c0_1(a1648))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(153,axiom,((~hskp10) | c0_1(a1648)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 1.31/1.50 tff(154,plain,
% 1.31/1.50 ((~hskp10) | c0_1(a1648)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[153, 152])).
% 1.31/1.50 tff(155,plain,
% 1.31/1.50 ((~hskp10) | c0_1(a1648)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[154, 152])).
% 1.31/1.50 tff(156,plain,
% 1.31/1.50 ((~hskp10) | c0_1(a1648)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[155, 152])).
% 1.31/1.50 tff(157,plain,
% 1.31/1.50 ((~hskp10) | c0_1(a1648)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[156, 152])).
% 1.31/1.50 tff(158,plain,
% 1.31/1.50 ((~hskp10) | c0_1(a1648)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[157, 152])).
% 1.31/1.50 tff(159,plain,
% 1.31/1.50 (c0_1(a1648)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[158, 145])).
% 1.31/1.50 tff(160,plain,
% 1.31/1.50 (((~hskp10) | c2_1(a1648)) <=> ((~hskp10) | c2_1(a1648))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(161,axiom,((~hskp10) | c2_1(a1648)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 1.31/1.50 tff(162,plain,
% 1.31/1.50 ((~hskp10) | c2_1(a1648)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[161, 160])).
% 1.31/1.50 tff(163,plain,
% 1.31/1.50 ((~hskp10) | c2_1(a1648)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[162, 160])).
% 1.31/1.50 tff(164,plain,
% 1.31/1.50 ((~hskp10) | c2_1(a1648)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[163, 160])).
% 1.31/1.50 tff(165,plain,
% 1.31/1.50 ((~hskp10) | c2_1(a1648)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[164, 160])).
% 1.31/1.50 tff(166,plain,
% 1.31/1.50 ((~hskp10) | c2_1(a1648)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[165, 160])).
% 1.31/1.50 tff(167,plain,
% 1.31/1.50 (c2_1(a1648)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[166, 145])).
% 1.31/1.50 tff(168,assumption,(~c3_1(a1648)), introduced(assumption)).
% 1.31/1.50 tff(169,assumption,(c2_1(a1648)), introduced(assumption)).
% 1.31/1.50 tff(170,assumption,(c0_1(a1648)), introduced(assumption)).
% 1.31/1.50 tff(171,plain,
% 1.31/1.50 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp8 | hskp1 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp8 | hskp1 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(172,plain,
% 1.31/1.50 ((hskp8 | hskp1 | (~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648))) <=> (hskp8 | hskp1 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(173,plain,
% 1.31/1.50 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp8 | hskp1 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648))))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[172])).
% 1.31/1.50 tff(174,plain,
% 1.31/1.50 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp8 | hskp1 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)))),
% 1.31/1.50 inference(transitivity,[status(thm)],[173, 171])).
% 1.31/1.50 tff(175,plain,
% 1.31/1.50 ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(176,plain,
% 1.31/1.50 ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp8 | hskp1 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[175, 174])).
% 1.31/1.50 tff(177,plain,
% 1.31/1.50 (hskp8),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[176, 119, 21, 170, 169, 168, 32])).
% 1.31/1.50 tff(178,plain,
% 1.31/1.50 (((~hskp8) | (~c2_1(a1643))) <=> ((~hskp8) | (~c2_1(a1643)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(179,plain,
% 1.31/1.50 (((~c2_1(a1643)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a1643)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(180,axiom,((~c2_1(a1643)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 1.31/1.50 tff(181,plain,
% 1.31/1.50 ((~hskp8) | (~c2_1(a1643))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[180, 179])).
% 1.31/1.50 tff(182,plain,
% 1.31/1.50 ((~hskp8) | (~c2_1(a1643))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[181, 178])).
% 1.31/1.50 tff(183,plain,
% 1.31/1.50 (~c2_1(a1643)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[182, 177])).
% 1.31/1.50 tff(184,plain,
% 1.31/1.50 (^[U: $i] : refl((hskp28 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp28 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(185,plain,
% 1.31/1.50 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[184])).
% 1.31/1.50 tff(186,plain,
% 1.31/1.50 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(187,plain,
% 1.31/1.50 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp0))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) | hskp28) <=> ((hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp28))), rewrite(((hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp28) <=> (hskp28 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) | hskp28) <=> (hskp28 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(188,plain,
% 1.31/1.50 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) | hskp28) <=> ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[187])).
% 1.31/1.50 tff(189,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 1.31/1.50 tff(190,plain,
% 1.31/1.50 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[189, 188])).
% 1.31/1.50 tff(191,plain,
% 1.31/1.50 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[190, 186])).
% 1.31/1.50 tff(192,plain,(
% 1.31/1.50 ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.31/1.50 inference(skolemize,[status(sab)],[191])).
% 1.31/1.50 tff(193,plain,
% 1.31/1.50 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[192, 185])).
% 1.31/1.50 tff(194,plain,
% 1.31/1.50 ((hskp26 | hskp1 | hskp0) <=> (hskp26 | hskp1 | hskp0)),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(195,plain,
% 1.31/1.50 (((hskp0 | hskp26) | hskp1) <=> (hskp26 | hskp1 | hskp0)),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(196,axiom,((hskp0 | hskp26) | hskp1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 1.31/1.50 tff(197,plain,
% 1.31/1.50 (hskp26 | hskp1 | hskp0),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[196, 195])).
% 1.31/1.50 tff(198,plain,
% 1.31/1.50 (hskp26 | hskp1 | hskp0),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[197, 194])).
% 1.31/1.50 tff(199,plain,
% 1.31/1.50 (hskp26 | hskp1 | hskp0),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[198, 194])).
% 1.31/1.50 tff(200,plain,
% 1.31/1.50 (hskp26 | hskp1 | hskp0),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[199, 194])).
% 1.31/1.50 tff(201,plain,
% 1.31/1.50 (hskp26 | hskp1 | hskp0),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[200, 194])).
% 1.31/1.50 tff(202,plain,
% 1.31/1.50 (hskp26),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[201, 33, 21])).
% 1.31/1.50 tff(203,plain,
% 1.31/1.50 (((~hskp26) | (~c0_1(a1737))) <=> ((~hskp26) | (~c0_1(a1737)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(204,plain,
% 1.31/1.50 (((~c0_1(a1737)) | (~hskp26)) <=> ((~hskp26) | (~c0_1(a1737)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(205,axiom,((~c0_1(a1737)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 1.31/1.50 tff(206,plain,
% 1.31/1.50 ((~hskp26) | (~c0_1(a1737))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[205, 204])).
% 1.31/1.50 tff(207,plain,
% 1.31/1.50 ((~hskp26) | (~c0_1(a1737))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[206, 203])).
% 1.31/1.50 tff(208,plain,
% 1.31/1.50 (~c0_1(a1737)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[207, 202])).
% 1.31/1.50 tff(209,plain,
% 1.31/1.50 (((~hskp26) | c3_1(a1737)) <=> ((~hskp26) | c3_1(a1737))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(210,axiom,((~hskp26) | c3_1(a1737)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 1.31/1.50 tff(211,plain,
% 1.31/1.50 ((~hskp26) | c3_1(a1737)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[210, 209])).
% 1.31/1.50 tff(212,plain,
% 1.31/1.50 ((~hskp26) | c3_1(a1737)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[211, 209])).
% 1.31/1.50 tff(213,plain,
% 1.31/1.50 ((~hskp26) | c3_1(a1737)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[212, 209])).
% 1.31/1.50 tff(214,plain,
% 1.31/1.50 ((~hskp26) | c3_1(a1737)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[213, 209])).
% 1.31/1.50 tff(215,plain,
% 1.31/1.50 ((~hskp26) | c3_1(a1737)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[214, 209])).
% 1.31/1.50 tff(216,plain,
% 1.31/1.50 (c3_1(a1737)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[215, 202])).
% 1.31/1.50 tff(217,plain,
% 1.31/1.50 (((~hskp26) | c2_1(a1737)) <=> ((~hskp26) | c2_1(a1737))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(218,axiom,((~hskp26) | c2_1(a1737)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 1.31/1.50 tff(219,plain,
% 1.31/1.50 ((~hskp26) | c2_1(a1737)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[218, 217])).
% 1.31/1.50 tff(220,plain,
% 1.31/1.50 ((~hskp26) | c2_1(a1737)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[219, 217])).
% 1.31/1.50 tff(221,plain,
% 1.31/1.50 ((~hskp26) | c2_1(a1737)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[220, 217])).
% 1.31/1.50 tff(222,plain,
% 1.31/1.50 ((~hskp26) | c2_1(a1737)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[221, 217])).
% 1.31/1.50 tff(223,plain,
% 1.31/1.50 ((~hskp26) | c2_1(a1737)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[222, 217])).
% 1.31/1.50 tff(224,plain,
% 1.31/1.50 (c2_1(a1737)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[223, 202])).
% 1.31/1.50 tff(225,plain,
% 1.31/1.50 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp28 | hskp0 | c0_1(a1737) | (~ndr1_0) | (~c3_1(a1737)) | (~c2_1(a1737)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp28 | hskp0 | c0_1(a1737) | (~ndr1_0) | (~c3_1(a1737)) | (~c2_1(a1737)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(226,plain,
% 1.31/1.50 ((hskp28 | hskp0 | (~ndr1_0) | c0_1(a1737) | (~c2_1(a1737)) | (~c3_1(a1737))) <=> (hskp28 | hskp0 | c0_1(a1737) | (~ndr1_0) | (~c3_1(a1737)) | (~c2_1(a1737)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(227,plain,
% 1.31/1.50 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c0_1(a1737) | (~c2_1(a1737)) | (~c3_1(a1737)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp28 | hskp0 | c0_1(a1737) | (~ndr1_0) | (~c3_1(a1737)) | (~c2_1(a1737))))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[226])).
% 1.31/1.50 tff(228,plain,
% 1.31/1.50 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c0_1(a1737) | (~c2_1(a1737)) | (~c3_1(a1737)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp28 | hskp0 | c0_1(a1737) | (~ndr1_0) | (~c3_1(a1737)) | (~c2_1(a1737)))),
% 1.31/1.50 inference(transitivity,[status(thm)],[227, 225])).
% 1.31/1.50 tff(229,plain,
% 1.31/1.50 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c0_1(a1737) | (~c2_1(a1737)) | (~c3_1(a1737)))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(230,plain,
% 1.31/1.50 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp28 | hskp0 | c0_1(a1737) | (~ndr1_0) | (~c3_1(a1737)) | (~c2_1(a1737))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[229, 228])).
% 1.31/1.50 tff(231,plain,
% 1.31/1.50 (hskp28),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[230, 119, 33, 224, 216, 208, 193])).
% 1.31/1.50 tff(232,plain,
% 1.31/1.50 (((~hskp28) | c2_1(a1646)) <=> ((~hskp28) | c2_1(a1646))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(233,axiom,((~hskp28) | c2_1(a1646)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 1.31/1.50 tff(234,plain,
% 1.31/1.50 ((~hskp28) | c2_1(a1646)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[233, 232])).
% 1.31/1.50 tff(235,plain,
% 1.31/1.50 ((~hskp28) | c2_1(a1646)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[234, 232])).
% 1.31/1.50 tff(236,plain,
% 1.31/1.50 ((~hskp28) | c2_1(a1646)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[235, 232])).
% 1.31/1.50 tff(237,plain,
% 1.31/1.50 ((~hskp28) | c2_1(a1646)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[236, 232])).
% 1.31/1.50 tff(238,plain,
% 1.31/1.50 ((~hskp28) | c2_1(a1646)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[237, 232])).
% 1.31/1.50 tff(239,plain,
% 1.31/1.50 (c2_1(a1646)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[238, 231])).
% 1.31/1.50 tff(240,plain,
% 1.31/1.50 (((~hskp8) | (~c3_1(a1643))) <=> ((~hskp8) | (~c3_1(a1643)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(241,plain,
% 1.31/1.50 (((~c3_1(a1643)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a1643)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(242,axiom,((~c3_1(a1643)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 1.31/1.50 tff(243,plain,
% 1.31/1.50 ((~hskp8) | (~c3_1(a1643))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[242, 241])).
% 1.31/1.50 tff(244,plain,
% 1.31/1.50 ((~hskp8) | (~c3_1(a1643))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[243, 240])).
% 1.31/1.50 tff(245,plain,
% 1.31/1.50 (~c3_1(a1643)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[244, 177])).
% 1.31/1.50 tff(246,plain,
% 1.31/1.50 (((~hskp8) | c1_1(a1643)) <=> ((~hskp8) | c1_1(a1643))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(247,axiom,((~hskp8) | c1_1(a1643)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 1.31/1.50 tff(248,plain,
% 1.31/1.50 ((~hskp8) | c1_1(a1643)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[247, 246])).
% 1.31/1.50 tff(249,plain,
% 1.31/1.50 ((~hskp8) | c1_1(a1643)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[248, 246])).
% 1.31/1.50 tff(250,plain,
% 1.31/1.50 ((~hskp8) | c1_1(a1643)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[249, 246])).
% 1.31/1.50 tff(251,plain,
% 1.31/1.50 ((~hskp8) | c1_1(a1643)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[250, 246])).
% 1.31/1.50 tff(252,plain,
% 1.31/1.50 ((~hskp8) | c1_1(a1643)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[251, 246])).
% 1.31/1.50 tff(253,plain,
% 1.31/1.50 (c1_1(a1643)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[252, 177])).
% 1.31/1.50 tff(254,plain,
% 1.31/1.50 (((~hskp28) | c1_1(a1646)) <=> ((~hskp28) | c1_1(a1646))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(255,axiom,((~hskp28) | c1_1(a1646)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 1.31/1.50 tff(256,plain,
% 1.31/1.50 ((~hskp28) | c1_1(a1646)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[255, 254])).
% 1.31/1.50 tff(257,plain,
% 1.31/1.50 ((~hskp28) | c1_1(a1646)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[256, 254])).
% 1.31/1.50 tff(258,plain,
% 1.31/1.50 ((~hskp28) | c1_1(a1646)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[257, 254])).
% 1.31/1.50 tff(259,plain,
% 1.31/1.50 ((~hskp28) | c1_1(a1646)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[258, 254])).
% 1.31/1.50 tff(260,plain,
% 1.31/1.50 ((~hskp28) | c1_1(a1646)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[259, 254])).
% 1.31/1.50 tff(261,plain,
% 1.31/1.50 (c1_1(a1646)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[260, 231])).
% 1.31/1.50 tff(262,plain,
% 1.31/1.50 (((~hskp28) | c3_1(a1646)) <=> ((~hskp28) | c3_1(a1646))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(263,axiom,((~hskp28) | c3_1(a1646)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 1.31/1.50 tff(264,plain,
% 1.31/1.50 ((~hskp28) | c3_1(a1646)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[263, 262])).
% 1.31/1.50 tff(265,plain,
% 1.31/1.50 ((~hskp28) | c3_1(a1646)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[264, 262])).
% 1.31/1.50 tff(266,plain,
% 1.31/1.50 ((~hskp28) | c3_1(a1646)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[265, 262])).
% 1.31/1.50 tff(267,plain,
% 1.31/1.50 ((~hskp28) | c3_1(a1646)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[266, 262])).
% 1.31/1.50 tff(268,plain,
% 1.31/1.50 ((~hskp28) | c3_1(a1646)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[267, 262])).
% 1.31/1.50 tff(269,plain,
% 1.31/1.50 (c3_1(a1646)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[268, 231])).
% 1.31/1.50 tff(270,assumption,(~c0_1(a1646)), introduced(assumption)).
% 1.31/1.50 tff(271,plain,
% 1.31/1.50 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(272,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[271])).
% 1.31/1.50 tff(273,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(274,plain,
% 1.31/1.50 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp11) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp11))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.31/1.51 inference(bind,[status(th)],[])).
% 1.31/1.51 tff(275,plain,
% 1.31/1.51 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.31/1.51 inference(quant_intro,[status(thm)],[274])).
% 1.31/1.51 tff(276,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 1.31/1.51 tff(277,plain,
% 1.31/1.51 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[276, 275])).
% 1.31/1.51 tff(278,plain,
% 1.31/1.51 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[277, 273])).
% 1.31/1.51 tff(279,plain,(
% 1.31/1.51 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.31/1.51 inference(skolemize,[status(sab)],[278])).
% 1.31/1.51 tff(280,plain,
% 1.31/1.51 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[279, 272])).
% 1.31/1.51 tff(281,assumption,(~c3_1(a1643)), introduced(assumption)).
% 1.31/1.51 tff(282,assumption,(~c2_1(a1643)), introduced(assumption)).
% 1.31/1.51 tff(283,assumption,(c1_1(a1646)), introduced(assumption)).
% 1.31/1.51 tff(284,assumption,(c2_1(a1646)), introduced(assumption)).
% 1.31/1.51 tff(285,assumption,(~c0_1(a1643)), introduced(assumption)).
% 1.31/1.51 tff(286,plain,
% 1.31/1.51 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 1.31/1.51 inference(bind,[status(th)],[])).
% 1.31/1.51 tff(287,plain,
% 1.31/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.31/1.51 inference(quant_intro,[status(thm)],[286])).
% 1.31/1.51 tff(288,plain,
% 1.31/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(289,plain,
% 1.31/1.51 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 1.34/1.51 inference(bind,[status(th)],[])).
% 1.34/1.51 tff(290,plain,
% 1.34/1.51 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.34/1.51 inference(quant_intro,[status(thm)],[289])).
% 1.34/1.51 tff(291,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause194')).
% 1.34/1.51 tff(292,plain,
% 1.34/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[291, 290])).
% 1.34/1.51 tff(293,plain,
% 1.34/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[292, 288])).
% 1.34/1.51 tff(294,plain,(
% 1.34/1.51 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.34/1.51 inference(skolemize,[status(sab)],[293])).
% 1.34/1.51 tff(295,plain,
% 1.34/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[294, 287])).
% 1.34/1.51 tff(296,assumption,(ndr1_0), introduced(assumption)).
% 1.34/1.51 tff(297,plain,
% 1.34/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(298,plain,
% 1.34/1.51 (((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1646) | (~c1_1(a1646)) | (~c2_1(a1646)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643)) <=> (c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(299,plain,
% 1.34/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1646) | (~c1_1(a1646)) | (~c2_1(a1646)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[298])).
% 1.34/1.51 tff(300,plain,
% 1.34/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1646) | (~c1_1(a1646)) | (~c2_1(a1646)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646)))),
% 1.34/1.51 inference(transitivity,[status(thm)],[299, 297])).
% 1.34/1.51 tff(301,plain,
% 1.34/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1646) | (~c1_1(a1646)) | (~c2_1(a1646)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(302,plain,
% 1.34/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[301, 300])).
% 1.34/1.51 tff(303,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[302, 296, 283, 284, 170, 169, 168, 282, 281, 295, 270, 285])).
% 1.34/1.51 tff(304,plain,(c0_1(a1646) | (~ndr1_0) | (~c1_1(a1646)) | (~c2_1(a1646)) | (~c0_1(a1648)) | (~c2_1(a1648)) | c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | c0_1(a1643)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(305,plain,
% 1.34/1.51 (c0_1(a1646) | (~c1_1(a1646)) | (~c2_1(a1646)) | (~c0_1(a1648)) | (~c2_1(a1648)) | c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | c0_1(a1643)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[304, 119])).
% 1.34/1.51 tff(306,plain,
% 1.34/1.51 (c0_1(a1643)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[305, 270, 170, 284, 283, 169, 168, 282, 281])).
% 1.34/1.51 tff(307,plain,
% 1.34/1.51 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.34/1.51 inference(bind,[status(th)],[])).
% 1.34/1.51 tff(308,plain,
% 1.34/1.51 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.34/1.51 inference(quant_intro,[status(thm)],[307])).
% 1.34/1.51 tff(309,plain,
% 1.34/1.51 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(310,plain,
% 1.34/1.51 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp15) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp15))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.34/1.51 inference(bind,[status(th)],[])).
% 1.34/1.51 tff(311,plain,
% 1.34/1.51 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.34/1.51 inference(quant_intro,[status(thm)],[310])).
% 1.34/1.51 tff(312,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 1.34/1.51 tff(313,plain,
% 1.34/1.51 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[312, 311])).
% 1.34/1.51 tff(314,plain,
% 1.34/1.51 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[313, 309])).
% 1.34/1.51 tff(315,plain,(
% 1.34/1.51 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.34/1.51 inference(skolemize,[status(sab)],[314])).
% 1.34/1.51 tff(316,plain,
% 1.34/1.51 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[315, 308])).
% 1.34/1.51 tff(317,assumption,(~c0_1(a1737)), introduced(assumption)).
% 1.34/1.51 tff(318,assumption,(c1_1(a1643)), introduced(assumption)).
% 1.34/1.51 tff(319,assumption,(c3_1(a1737)), introduced(assumption)).
% 1.34/1.51 tff(320,assumption,(c2_1(a1737)), introduced(assumption)).
% 1.34/1.51 tff(321,plain,
% 1.34/1.51 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c0_1(a1737) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c3_1(a1737)) | (~c2_1(a1737)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c0_1(a1737) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c3_1(a1737)) | (~c2_1(a1737)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(322,plain,
% 1.34/1.51 ((hskp15 | (~ndr1_0) | c3_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c0_1(a1737) | (~c3_1(a1737)) | (~c2_1(a1737))) <=> (hskp15 | c0_1(a1737) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c3_1(a1737)) | (~c2_1(a1737)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(323,plain,
% 1.34/1.51 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c0_1(a1737) | (~c3_1(a1737)) | (~c2_1(a1737)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c0_1(a1737) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c3_1(a1737)) | (~c2_1(a1737))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[322])).
% 1.34/1.51 tff(324,plain,
% 1.34/1.51 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c0_1(a1737) | (~c3_1(a1737)) | (~c2_1(a1737)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c0_1(a1737) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c3_1(a1737)) | (~c2_1(a1737)))),
% 1.34/1.51 inference(transitivity,[status(thm)],[323, 321])).
% 1.34/1.51 tff(325,plain,
% 1.34/1.51 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c0_1(a1737) | (~c3_1(a1737)) | (~c2_1(a1737)))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(326,plain,
% 1.34/1.51 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c0_1(a1737) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c3_1(a1737)) | (~c2_1(a1737))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[325, 324])).
% 1.34/1.51 tff(327,plain,
% 1.34/1.51 (hskp15 | (~c0_1(a1643))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[326, 119, 320, 319, 318, 317, 281, 316])).
% 1.34/1.51 tff(328,plain,
% 1.34/1.51 (hskp15),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[327, 306])).
% 1.34/1.51 tff(329,plain,
% 1.34/1.51 (((~hskp15) | (~c2_1(a1664))) <=> ((~hskp15) | (~c2_1(a1664)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(330,plain,
% 1.34/1.51 (((~c2_1(a1664)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a1664)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(331,axiom,((~c2_1(a1664)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 1.34/1.51 tff(332,plain,
% 1.34/1.51 ((~hskp15) | (~c2_1(a1664))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[331, 330])).
% 1.34/1.51 tff(333,plain,
% 1.34/1.51 ((~hskp15) | (~c2_1(a1664))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[332, 329])).
% 1.34/1.51 tff(334,plain,
% 1.34/1.51 (~c2_1(a1664)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[333, 328])).
% 1.34/1.51 tff(335,plain,
% 1.34/1.51 (((~hskp15) | (~c1_1(a1664))) <=> ((~hskp15) | (~c1_1(a1664)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(336,plain,
% 1.34/1.51 (((~c1_1(a1664)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a1664)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(337,axiom,((~c1_1(a1664)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 1.34/1.51 tff(338,plain,
% 1.34/1.51 ((~hskp15) | (~c1_1(a1664))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[337, 336])).
% 1.34/1.51 tff(339,plain,
% 1.34/1.51 ((~hskp15) | (~c1_1(a1664))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[338, 335])).
% 1.34/1.51 tff(340,plain,
% 1.34/1.51 (~c1_1(a1664)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[339, 328])).
% 1.34/1.51 tff(341,plain,
% 1.34/1.51 (((~hskp15) | c0_1(a1664)) <=> ((~hskp15) | c0_1(a1664))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(342,axiom,((~hskp15) | c0_1(a1664)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 1.34/1.51 tff(343,plain,
% 1.34/1.51 ((~hskp15) | c0_1(a1664)),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[342, 341])).
% 1.34/1.51 tff(344,plain,
% 1.34/1.51 ((~hskp15) | c0_1(a1664)),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[343, 341])).
% 1.34/1.51 tff(345,plain,
% 1.34/1.51 ((~hskp15) | c0_1(a1664)),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[344, 341])).
% 1.34/1.51 tff(346,plain,
% 1.34/1.51 ((~hskp15) | c0_1(a1664)),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[345, 341])).
% 1.34/1.51 tff(347,plain,
% 1.34/1.51 ((~hskp15) | c0_1(a1664)),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[346, 341])).
% 1.34/1.51 tff(348,plain,
% 1.34/1.51 (c0_1(a1664)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[347, 328])).
% 1.34/1.51 tff(349,assumption,(c3_1(a1646)), introduced(assumption)).
% 1.34/1.51 tff(350,plain,
% 1.34/1.51 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(351,plain,
% 1.34/1.51 ((hskp11 | (~ndr1_0) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c0_1(a1646) | (~c3_1(a1646)) | (~c1_1(a1646))) <=> (hskp11 | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(352,plain,
% 1.34/1.51 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c0_1(a1646) | (~c3_1(a1646)) | (~c1_1(a1646)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[351])).
% 1.34/1.51 tff(353,plain,
% 1.34/1.51 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c0_1(a1646) | (~c3_1(a1646)) | (~c1_1(a1646)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.34/1.51 inference(transitivity,[status(thm)],[352, 350])).
% 1.34/1.51 tff(354,plain,
% 1.34/1.51 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c0_1(a1646) | (~c3_1(a1646)) | (~c1_1(a1646)))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(355,plain,
% 1.34/1.51 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[354, 353])).
% 1.34/1.51 tff(356,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[355, 119, 45, 283, 349, 348, 340, 334, 280, 270])).
% 1.34/1.51 tff(357,plain,(c0_1(a1646) | hskp11 | (~c1_1(a1646)) | (~c3_1(a1646)) | (~c2_1(a1737)) | (~c3_1(a1737)) | (~c1_1(a1643)) | c0_1(a1737) | c3_1(a1643) | (~c0_1(a1648)) | (~c2_1(a1646)) | (~c2_1(a1648)) | c3_1(a1648) | c2_1(a1643)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(358,plain,
% 1.34/1.51 (c0_1(a1646)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[357, 269, 45, 224, 216, 261, 253, 208, 245, 170, 239, 169, 168, 183])).
% 1.34/1.51 tff(359,plain,
% 1.34/1.51 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.34/1.51 inference(bind,[status(th)],[])).
% 1.34/1.51 tff(360,plain,
% 1.34/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.34/1.51 inference(quant_intro,[status(thm)],[359])).
% 1.34/1.51 tff(361,plain,
% 1.34/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(362,plain,
% 1.34/1.51 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.34/1.51 inference(bind,[status(th)],[])).
% 1.34/1.51 tff(363,plain,
% 1.34/1.51 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.34/1.51 inference(quant_intro,[status(thm)],[362])).
% 1.34/1.51 tff(364,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause196')).
% 1.34/1.51 tff(365,plain,
% 1.34/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[364, 363])).
% 1.34/1.51 tff(366,plain,
% 1.34/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[365, 361])).
% 1.34/1.51 tff(367,plain,(
% 1.34/1.51 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.34/1.51 inference(skolemize,[status(sab)],[366])).
% 1.34/1.51 tff(368,plain,
% 1.34/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[367, 360])).
% 1.34/1.51 tff(369,plain,
% 1.34/1.51 (^[U: $i] : refl((hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))),
% 1.34/1.51 inference(bind,[status(th)],[])).
% 1.34/1.51 tff(370,plain,
% 1.34/1.51 (![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.34/1.51 inference(quant_intro,[status(thm)],[369])).
% 1.34/1.51 tff(371,plain,
% 1.34/1.51 (![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(372,plain,
% 1.34/1.51 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp7) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp7))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp7) | hskp11) <=> ((hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp11))), rewrite(((hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp11) <=> (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp7) | hskp11) <=> (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.34/1.51 inference(bind,[status(th)],[])).
% 1.34/1.51 tff(373,plain,
% 1.34/1.51 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp7) | hskp11) <=> ![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.34/1.51 inference(quant_intro,[status(thm)],[372])).
% 1.34/1.51 tff(374,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp7) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause165')).
% 1.34/1.51 tff(375,plain,
% 1.34/1.51 (![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[374, 373])).
% 1.34/1.51 tff(376,plain,
% 1.34/1.51 (![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[375, 371])).
% 1.34/1.51 tff(377,plain,(
% 1.34/1.51 ![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.34/1.51 inference(skolemize,[status(sab)],[376])).
% 1.34/1.51 tff(378,plain,
% 1.34/1.51 (![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[377, 370])).
% 1.34/1.51 tff(379,assumption,(hskp28), introduced(assumption)).
% 1.34/1.51 tff(380,plain,
% 1.34/1.51 (c3_1(a1646)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[268, 379])).
% 1.34/1.51 tff(381,plain,
% 1.34/1.51 (c2_1(a1646)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[238, 379])).
% 1.34/1.51 tff(382,plain,
% 1.34/1.51 (c1_1(a1646)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[260, 379])).
% 1.34/1.51 tff(383,assumption,(~hskp7), introduced(assumption)).
% 1.34/1.51 tff(384,plain,
% 1.34/1.51 (((~![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))) <=> ((~![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp11 | hskp7 | (~ndr1_0) | (~c2_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(385,plain,
% 1.34/1.51 ((hskp11 | hskp7 | (~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c1_1(a1646))) <=> (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(386,plain,
% 1.34/1.52 (((~![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c1_1(a1646)))) <=> ((~![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[385])).
% 1.34/1.52 tff(387,plain,
% 1.34/1.52 (((~![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c1_1(a1646)))) <=> ((~![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp11 | hskp7 | (~ndr1_0) | (~c2_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[386, 384])).
% 1.34/1.52 tff(388,plain,
% 1.34/1.52 ((~![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c1_1(a1646)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(389,plain,
% 1.34/1.52 ((~![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp11 | hskp7 | (~ndr1_0) | (~c2_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[388, 387])).
% 1.34/1.52 tff(390,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[389, 296, 45, 383, 382, 381, 380, 378])).
% 1.34/1.52 tff(391,plain,((~hskp28) | (~ndr1_0) | hskp11 | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(392,plain,
% 1.34/1.52 ((~hskp28) | hskp11 | hskp7),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[391, 119])).
% 1.34/1.52 tff(393,plain,
% 1.34/1.52 (hskp7),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[392, 231, 45])).
% 1.34/1.52 tff(394,plain,
% 1.34/1.52 (((~hskp7) | (~c3_1(a1642))) <=> ((~hskp7) | (~c3_1(a1642)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(395,plain,
% 1.34/1.52 (((~c3_1(a1642)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a1642)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(396,axiom,((~c3_1(a1642)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 1.34/1.52 tff(397,plain,
% 1.34/1.52 ((~hskp7) | (~c3_1(a1642))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[396, 395])).
% 1.34/1.52 tff(398,plain,
% 1.34/1.52 ((~hskp7) | (~c3_1(a1642))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[397, 394])).
% 1.34/1.52 tff(399,plain,
% 1.34/1.52 (~c3_1(a1642)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[398, 393])).
% 1.34/1.52 tff(400,plain,
% 1.34/1.52 ((hskp17 | hskp11 | hskp1) <=> (hskp17 | hskp11 | hskp1)),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(401,plain,
% 1.34/1.52 (((hskp11 | hskp17) | hskp1) <=> (hskp17 | hskp11 | hskp1)),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(402,axiom,((hskp11 | hskp17) | hskp1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 1.34/1.52 tff(403,plain,
% 1.34/1.52 (hskp17 | hskp11 | hskp1),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[402, 401])).
% 1.34/1.52 tff(404,plain,
% 1.34/1.52 (hskp17 | hskp11 | hskp1),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[403, 400])).
% 1.34/1.52 tff(405,plain,
% 1.34/1.52 (hskp17 | hskp11 | hskp1),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[404, 400])).
% 1.34/1.52 tff(406,plain,
% 1.34/1.52 (hskp17 | hskp11 | hskp1),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[405, 400])).
% 1.34/1.52 tff(407,plain,
% 1.34/1.52 (hskp17 | hskp11 | hskp1),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[406, 400])).
% 1.34/1.52 tff(408,plain,
% 1.34/1.52 (hskp17),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[407, 45, 21])).
% 1.34/1.52 tff(409,plain,
% 1.34/1.52 (((~hskp17) | (~c1_1(a1675))) <=> ((~hskp17) | (~c1_1(a1675)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(410,plain,
% 1.34/1.52 (((~c1_1(a1675)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a1675)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(411,axiom,((~c1_1(a1675)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 1.34/1.52 tff(412,plain,
% 1.34/1.52 ((~hskp17) | (~c1_1(a1675))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[411, 410])).
% 1.34/1.52 tff(413,plain,
% 1.34/1.52 ((~hskp17) | (~c1_1(a1675))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[412, 409])).
% 1.34/1.52 tff(414,plain,
% 1.34/1.52 (~c1_1(a1675)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[413, 408])).
% 1.34/1.52 tff(415,plain,
% 1.34/1.52 (((~hskp17) | (~c0_1(a1675))) <=> ((~hskp17) | (~c0_1(a1675)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(416,plain,
% 1.34/1.52 (((~c0_1(a1675)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a1675)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(417,axiom,((~c0_1(a1675)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 1.34/1.52 tff(418,plain,
% 1.34/1.52 ((~hskp17) | (~c0_1(a1675))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[417, 416])).
% 1.34/1.52 tff(419,plain,
% 1.34/1.52 ((~hskp17) | (~c0_1(a1675))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[418, 415])).
% 1.34/1.52 tff(420,plain,
% 1.34/1.52 (~c0_1(a1675)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[419, 408])).
% 1.34/1.52 tff(421,plain,
% 1.34/1.52 (((~hskp7) | c0_1(a1642)) <=> ((~hskp7) | c0_1(a1642))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(422,axiom,((~hskp7) | c0_1(a1642)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 1.34/1.52 tff(423,plain,
% 1.34/1.52 ((~hskp7) | c0_1(a1642)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[422, 421])).
% 1.34/1.52 tff(424,plain,
% 1.34/1.52 ((~hskp7) | c0_1(a1642)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[423, 421])).
% 1.34/1.52 tff(425,plain,
% 1.34/1.52 ((~hskp7) | c0_1(a1642)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[424, 421])).
% 1.34/1.52 tff(426,plain,
% 1.34/1.52 ((~hskp7) | c0_1(a1642)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[425, 421])).
% 1.34/1.52 tff(427,plain,
% 1.34/1.52 ((~hskp7) | c0_1(a1642)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[426, 421])).
% 1.34/1.52 tff(428,plain,
% 1.34/1.52 (c0_1(a1642)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[427, 393])).
% 1.34/1.52 tff(429,plain,
% 1.34/1.52 (((~hskp17) | c2_1(a1675)) <=> ((~hskp17) | c2_1(a1675))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(430,axiom,((~hskp17) | c2_1(a1675)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 1.34/1.52 tff(431,plain,
% 1.34/1.52 ((~hskp17) | c2_1(a1675)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[430, 429])).
% 1.34/1.52 tff(432,plain,
% 1.34/1.52 ((~hskp17) | c2_1(a1675)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[431, 429])).
% 1.34/1.52 tff(433,plain,
% 1.34/1.52 ((~hskp17) | c2_1(a1675)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[432, 429])).
% 1.34/1.52 tff(434,plain,
% 1.34/1.52 ((~hskp17) | c2_1(a1675)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[433, 429])).
% 1.34/1.52 tff(435,plain,
% 1.34/1.52 ((~hskp17) | c2_1(a1675)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[434, 429])).
% 1.34/1.52 tff(436,plain,
% 1.34/1.52 (c2_1(a1675)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[435, 408])).
% 1.34/1.52 tff(437,plain,
% 1.34/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1675) | c1_1(a1675) | c3_1(a1642) | (~ndr1_0) | (~c1_1(a1642)) | (~c0_1(a1642)) | (~c2_1(a1675)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1675) | c1_1(a1675) | c3_1(a1642) | (~ndr1_0) | (~c1_1(a1642)) | (~c0_1(a1642)) | (~c2_1(a1675)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(438,plain,
% 1.34/1.52 (((~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c0_1(a1646)) | c3_1(a1642) | (~c1_1(a1642)) | (~c0_1(a1642)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675))) <=> (c0_1(a1675) | c1_1(a1675) | c3_1(a1642) | (~ndr1_0) | (~c1_1(a1642)) | (~c0_1(a1642)) | (~c2_1(a1675)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(439,plain,
% 1.34/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c0_1(a1646)) | c3_1(a1642) | (~c1_1(a1642)) | (~c0_1(a1642)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1675) | c1_1(a1675) | c3_1(a1642) | (~ndr1_0) | (~c1_1(a1642)) | (~c0_1(a1642)) | (~c2_1(a1675)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[438])).
% 1.34/1.52 tff(440,plain,
% 1.34/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c0_1(a1646)) | c3_1(a1642) | (~c1_1(a1642)) | (~c0_1(a1642)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1675) | c1_1(a1675) | c3_1(a1642) | (~ndr1_0) | (~c1_1(a1642)) | (~c0_1(a1642)) | (~c2_1(a1675)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[439, 437])).
% 1.34/1.52 tff(441,plain,
% 1.34/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c0_1(a1646)) | c3_1(a1642) | (~c1_1(a1642)) | (~c0_1(a1642)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(442,plain,
% 1.34/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1675) | c1_1(a1675) | c3_1(a1642) | (~ndr1_0) | (~c1_1(a1642)) | (~c0_1(a1642)) | (~c2_1(a1675)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[441, 440])).
% 1.34/1.52 tff(443,plain,
% 1.34/1.52 (~c1_1(a1642)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[442, 119, 239, 269, 436, 428, 420, 414, 399, 368, 358])).
% 1.34/1.52 tff(444,plain,
% 1.34/1.52 (((~hskp7) | (~c2_1(a1642))) <=> ((~hskp7) | (~c2_1(a1642)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(445,plain,
% 1.34/1.52 (((~c2_1(a1642)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a1642)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(446,axiom,((~c2_1(a1642)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 1.34/1.52 tff(447,plain,
% 1.34/1.52 ((~hskp7) | (~c2_1(a1642))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[446, 445])).
% 1.34/1.52 tff(448,plain,
% 1.34/1.52 ((~hskp7) | (~c2_1(a1642))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[447, 444])).
% 1.34/1.52 tff(449,plain,
% 1.34/1.52 (~c2_1(a1642)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[448, 393])).
% 1.34/1.52 tff(450,plain,
% 1.34/1.52 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | c0_1(a1737) | c2_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c0_1(a1642)) | (~c1_1(a1737)) | (~c3_1(a1737)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c0_1(a1737) | c2_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c0_1(a1642)) | (~c1_1(a1737)) | (~c3_1(a1737)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(451,plain,
% 1.34/1.52 ((hskp11 | (~ndr1_0) | c2_1(a1642) | c1_1(a1642) | (~c0_1(a1642)) | c0_1(a1737) | (~c3_1(a1737)) | (~c1_1(a1737))) <=> (hskp11 | c0_1(a1737) | c2_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c0_1(a1642)) | (~c1_1(a1737)) | (~c3_1(a1737)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(452,plain,
% 1.34/1.52 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1642) | c1_1(a1642) | (~c0_1(a1642)) | c0_1(a1737) | (~c3_1(a1737)) | (~c1_1(a1737)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | c0_1(a1737) | c2_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c0_1(a1642)) | (~c1_1(a1737)) | (~c3_1(a1737))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[451])).
% 1.34/1.52 tff(453,plain,
% 1.34/1.52 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1642) | c1_1(a1642) | (~c0_1(a1642)) | c0_1(a1737) | (~c3_1(a1737)) | (~c1_1(a1737)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c0_1(a1737) | c2_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c0_1(a1642)) | (~c1_1(a1737)) | (~c3_1(a1737)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[452, 450])).
% 1.34/1.52 tff(454,plain,
% 1.34/1.52 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1642) | c1_1(a1642) | (~c0_1(a1642)) | c0_1(a1737) | (~c3_1(a1737)) | (~c1_1(a1737)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(455,plain,
% 1.34/1.52 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c0_1(a1737) | c2_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c0_1(a1642)) | (~c1_1(a1737)) | (~c3_1(a1737))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[454, 453])).
% 1.34/1.52 tff(456,plain,
% 1.34/1.52 (~c1_1(a1737)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[455, 119, 45, 216, 428, 208, 449, 280, 443])).
% 1.34/1.52 tff(457,plain,
% 1.34/1.52 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.34/1.52 inference(bind,[status(th)],[])).
% 1.34/1.52 tff(458,plain,
% 1.34/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.34/1.52 inference(quant_intro,[status(thm)],[457])).
% 1.34/1.52 tff(459,plain,
% 1.34/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(460,plain,
% 1.34/1.52 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.34/1.52 inference(bind,[status(th)],[])).
% 1.34/1.52 tff(461,plain,
% 1.34/1.52 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.34/1.52 inference(quant_intro,[status(thm)],[460])).
% 1.34/1.52 tff(462,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause197')).
% 1.34/1.52 tff(463,plain,
% 1.34/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[462, 461])).
% 1.34/1.52 tff(464,plain,
% 1.34/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[463, 459])).
% 1.34/1.52 tff(465,plain,(
% 1.34/1.52 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.34/1.52 inference(skolemize,[status(sab)],[464])).
% 1.34/1.52 tff(466,plain,
% 1.34/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[465, 458])).
% 1.34/1.52 tff(467,plain,
% 1.34/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1737) | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646)) | c1_1(a1737) | (~c3_1(a1737)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1737) | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646)) | c1_1(a1737) | (~c3_1(a1737)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(468,plain,
% 1.34/1.52 (((~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c0_1(a1646)) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c1_1(a1737) | c0_1(a1737) | (~c3_1(a1737))) <=> (c0_1(a1737) | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646)) | c1_1(a1737) | (~c3_1(a1737)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(469,plain,
% 1.34/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c0_1(a1646)) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c1_1(a1737) | c0_1(a1737) | (~c3_1(a1737)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1737) | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646)) | c1_1(a1737) | (~c3_1(a1737))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[468])).
% 1.34/1.52 tff(470,plain,
% 1.34/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c0_1(a1646)) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c1_1(a1737) | c0_1(a1737) | (~c3_1(a1737)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1737) | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646)) | c1_1(a1737) | (~c3_1(a1737)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[469, 467])).
% 1.34/1.52 tff(471,plain,
% 1.34/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c0_1(a1646)) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c1_1(a1737) | c0_1(a1737) | (~c3_1(a1737)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(472,plain,
% 1.34/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1737) | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646)) | c1_1(a1737) | (~c3_1(a1737))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[471, 470])).
% 1.34/1.52 tff(473,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[472, 119, 239, 269, 216, 170, 169, 208, 168, 466, 358, 456])).
% 1.34/1.52 tff(474,plain,(hskp0 | (~c0_1(a1648)) | (~c2_1(a1648)) | c3_1(a1648) | hskp11 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(475,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[474, 167, 159, 33, 151, 45, 21])).
% 1.34/1.52 tff(476,plain,(hskp11 | hskp0 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(477,plain,
% 1.34/1.52 (hskp0),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[476, 45, 21])).
% 1.34/1.52 tff(478,plain,
% 1.34/1.52 (((~hskp0) | (~c1_1(a1634))) <=> ((~hskp0) | (~c1_1(a1634)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(479,plain,
% 1.34/1.52 (((~c1_1(a1634)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a1634)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(480,axiom,((~c1_1(a1634)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 1.34/1.52 tff(481,plain,
% 1.34/1.52 ((~hskp0) | (~c1_1(a1634))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[480, 479])).
% 1.34/1.52 tff(482,plain,
% 1.34/1.52 ((~hskp0) | (~c1_1(a1634))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[481, 478])).
% 1.34/1.52 tff(483,plain,
% 1.34/1.52 (~c1_1(a1634)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[482, 477])).
% 1.34/1.52 tff(484,plain,
% 1.34/1.52 (((~hskp0) | c3_1(a1634)) <=> ((~hskp0) | c3_1(a1634))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(485,axiom,((~hskp0) | c3_1(a1634)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 1.34/1.52 tff(486,plain,
% 1.34/1.52 ((~hskp0) | c3_1(a1634)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[485, 484])).
% 1.34/1.52 tff(487,plain,
% 1.34/1.52 ((~hskp0) | c3_1(a1634)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[486, 484])).
% 1.34/1.52 tff(488,plain,
% 1.34/1.52 ((~hskp0) | c3_1(a1634)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[487, 484])).
% 1.34/1.52 tff(489,plain,
% 1.34/1.52 ((~hskp0) | c3_1(a1634)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[488, 484])).
% 1.34/1.52 tff(490,plain,
% 1.34/1.52 ((~hskp0) | c3_1(a1634)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[489, 484])).
% 1.34/1.52 tff(491,plain,
% 1.34/1.52 (c3_1(a1634)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[490, 477])).
% 1.34/1.52 tff(492,plain,
% 1.34/1.52 (((~hskp0) | c0_1(a1634)) <=> ((~hskp0) | c0_1(a1634))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(493,axiom,((~hskp0) | c0_1(a1634)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 1.34/1.52 tff(494,plain,
% 1.34/1.52 ((~hskp0) | c0_1(a1634)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[493, 492])).
% 1.34/1.52 tff(495,plain,
% 1.34/1.52 ((~hskp0) | c0_1(a1634)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[494, 492])).
% 1.34/1.52 tff(496,plain,
% 1.34/1.52 ((~hskp0) | c0_1(a1634)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[495, 492])).
% 1.34/1.52 tff(497,plain,
% 1.34/1.52 ((~hskp0) | c0_1(a1634)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[496, 492])).
% 1.34/1.52 tff(498,plain,
% 1.34/1.52 ((~hskp0) | c0_1(a1634)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[497, 492])).
% 1.34/1.52 tff(499,plain,
% 1.34/1.52 (c0_1(a1634)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[498, 477])).
% 1.34/1.52 tff(500,assumption,(~hskp2), introduced(assumption)).
% 1.34/1.52 tff(501,assumption,(~hskp28), introduced(assumption)).
% 1.34/1.52 tff(502,assumption,(c3_1(a1634)), introduced(assumption)).
% 1.34/1.52 tff(503,assumption,(~c1_1(a1634)), introduced(assumption)).
% 1.34/1.52 tff(504,assumption,(c0_1(a1634)), introduced(assumption)).
% 1.34/1.52 tff(505,plain,
% 1.34/1.52 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 1.34/1.52 inference(bind,[status(th)],[])).
% 1.34/1.52 tff(506,plain,
% 1.34/1.52 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.34/1.52 inference(quant_intro,[status(thm)],[505])).
% 1.34/1.52 tff(507,plain,
% 1.34/1.52 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(508,plain,
% 1.34/1.52 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp28) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp28))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.34/1.52 inference(bind,[status(th)],[])).
% 1.34/1.52 tff(509,plain,
% 1.34/1.52 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.34/1.52 inference(quant_intro,[status(thm)],[508])).
% 1.34/1.52 tff(510,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause188')).
% 1.34/1.52 tff(511,plain,
% 1.34/1.52 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[510, 509])).
% 1.34/1.52 tff(512,plain,
% 1.34/1.52 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[511, 507])).
% 1.34/1.52 tff(513,plain,(
% 1.34/1.52 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.34/1.52 inference(skolemize,[status(sab)],[512])).
% 1.34/1.52 tff(514,plain,
% 1.34/1.52 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[513, 506])).
% 1.34/1.52 tff(515,plain,
% 1.34/1.52 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c1_1(a1648)) | (~c0_1(a1648)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c1_1(a1648)) | (~c0_1(a1648)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(516,plain,
% 1.34/1.52 ((hskp28 | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1648)) | c3_1(a1648) | (~c1_1(a1648)) | (~c0_1(a1648))) <=> (hskp28 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c1_1(a1648)) | (~c0_1(a1648)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(517,plain,
% 1.34/1.52 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1648)) | c3_1(a1648) | (~c1_1(a1648)) | (~c0_1(a1648)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c1_1(a1648)) | (~c0_1(a1648))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[516])).
% 1.34/1.52 tff(518,plain,
% 1.34/1.52 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1648)) | c3_1(a1648) | (~c1_1(a1648)) | (~c0_1(a1648)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c1_1(a1648)) | (~c0_1(a1648)))),
% 1.34/1.53 inference(transitivity,[status(thm)],[517, 515])).
% 1.34/1.53 tff(519,plain,
% 1.34/1.53 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1648)) | c3_1(a1648) | (~c1_1(a1648)) | (~c0_1(a1648)))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(520,plain,
% 1.34/1.53 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c1_1(a1648)) | (~c0_1(a1648))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[519, 518])).
% 1.34/1.53 tff(521,plain,
% 1.34/1.53 (hskp28 | (~c1_1(a1648))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[520, 119, 170, 169, 168, 514])).
% 1.34/1.53 tff(522,plain,
% 1.34/1.53 (~c1_1(a1648)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[521, 501])).
% 1.34/1.53 tff(523,plain,
% 1.34/1.53 (^[U: $i] : refl((hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))),
% 1.34/1.53 inference(bind,[status(th)],[])).
% 1.34/1.53 tff(524,plain,
% 1.34/1.53 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.34/1.53 inference(quant_intro,[status(thm)],[523])).
% 1.34/1.53 tff(525,plain,
% 1.34/1.53 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(526,plain,
% 1.34/1.53 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp9) <=> ((hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp9))), rewrite(((hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp9) <=> (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp9) <=> (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))))),
% 1.34/1.53 inference(bind,[status(th)],[])).
% 1.34/1.53 tff(527,plain,
% 1.34/1.53 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp9) <=> ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.34/1.53 inference(quant_intro,[status(thm)],[526])).
% 1.34/1.53 tff(528,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 1.34/1.53 tff(529,plain,
% 1.34/1.53 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[528, 527])).
% 1.34/1.53 tff(530,plain,
% 1.34/1.53 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[529, 525])).
% 1.34/1.53 tff(531,plain,(
% 1.34/1.53 ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.34/1.53 inference(skolemize,[status(sab)],[530])).
% 1.34/1.53 tff(532,plain,
% 1.34/1.53 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[531, 524])).
% 1.34/1.53 tff(533,plain,
% 1.34/1.53 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp9 | hskp2 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | c1_1(a1648))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp9 | hskp2 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | c1_1(a1648))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(534,plain,
% 1.34/1.53 ((hskp9 | hskp2 | (~ndr1_0) | c1_1(a1648) | c3_1(a1648) | (~c2_1(a1648))) <=> (hskp9 | hskp2 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | c1_1(a1648))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(535,plain,
% 1.34/1.53 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c1_1(a1648) | c3_1(a1648) | (~c2_1(a1648)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp9 | hskp2 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | c1_1(a1648)))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[534])).
% 1.34/1.53 tff(536,plain,
% 1.34/1.53 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c1_1(a1648) | c3_1(a1648) | (~c2_1(a1648)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp9 | hskp2 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | c1_1(a1648))),
% 1.34/1.53 inference(transitivity,[status(thm)],[535, 533])).
% 1.34/1.53 tff(537,plain,
% 1.34/1.53 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c1_1(a1648) | c3_1(a1648) | (~c2_1(a1648)))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(538,plain,
% 1.34/1.53 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp9 | hskp2 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | c1_1(a1648)),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[537, 536])).
% 1.34/1.53 tff(539,plain,
% 1.34/1.53 (hskp9 | hskp2 | c1_1(a1648)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[538, 119, 169, 168, 532])).
% 1.34/1.53 tff(540,plain,
% 1.34/1.53 (hskp9),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[539, 522, 500])).
% 1.34/1.53 tff(541,assumption,(hskp9), introduced(assumption)).
% 1.34/1.53 tff(542,plain,
% 1.34/1.53 (((~hskp9) | (~c3_1(a1644))) <=> ((~hskp9) | (~c3_1(a1644)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(543,plain,
% 1.34/1.53 (((~c3_1(a1644)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a1644)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(544,axiom,((~c3_1(a1644)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 1.34/1.53 tff(545,plain,
% 1.34/1.53 ((~hskp9) | (~c3_1(a1644))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[544, 543])).
% 1.34/1.53 tff(546,plain,
% 1.34/1.53 ((~hskp9) | (~c3_1(a1644))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[545, 542])).
% 1.34/1.53 tff(547,plain,
% 1.34/1.53 (~c3_1(a1644)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[546, 541])).
% 1.34/1.53 tff(548,assumption,(hskp19), introduced(assumption)).
% 1.34/1.53 tff(549,plain,
% 1.34/1.53 (((~hskp9) | (~c0_1(a1644))) <=> ((~hskp9) | (~c0_1(a1644)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(550,plain,
% 1.34/1.53 (((~c0_1(a1644)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a1644)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(551,axiom,((~c0_1(a1644)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 1.34/1.53 tff(552,plain,
% 1.34/1.53 ((~hskp9) | (~c0_1(a1644))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[551, 550])).
% 1.34/1.53 tff(553,plain,
% 1.34/1.53 ((~hskp9) | (~c0_1(a1644))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[552, 549])).
% 1.34/1.53 tff(554,plain,
% 1.34/1.53 (~c0_1(a1644)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[553, 541])).
% 1.34/1.53 tff(555,plain,
% 1.34/1.53 (((~hskp9) | (~c1_1(a1644))) <=> ((~hskp9) | (~c1_1(a1644)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(556,plain,
% 1.34/1.53 (((~c1_1(a1644)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a1644)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(557,axiom,((~c1_1(a1644)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 1.34/1.53 tff(558,plain,
% 1.34/1.53 ((~hskp9) | (~c1_1(a1644))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[557, 556])).
% 1.34/1.53 tff(559,plain,
% 1.34/1.53 ((~hskp9) | (~c1_1(a1644))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[558, 555])).
% 1.34/1.53 tff(560,plain,
% 1.34/1.53 (~c1_1(a1644)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[559, 541])).
% 1.36/1.53 tff(561,assumption,(~c3_1(a1644)), introduced(assumption)).
% 1.36/1.53 tff(562,assumption,(~c1_1(a1644)), introduced(assumption)).
% 1.36/1.53 tff(563,assumption,(~c0_1(a1644)), introduced(assumption)).
% 1.36/1.53 tff(564,plain,
% 1.36/1.53 (((~hskp19) | (~c3_1(a1682))) <=> ((~hskp19) | (~c3_1(a1682)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(565,plain,
% 1.36/1.53 (((~c3_1(a1682)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a1682)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(566,axiom,((~c3_1(a1682)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 1.36/1.53 tff(567,plain,
% 1.36/1.53 ((~hskp19) | (~c3_1(a1682))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[566, 565])).
% 1.36/1.53 tff(568,plain,
% 1.36/1.53 ((~hskp19) | (~c3_1(a1682))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[567, 564])).
% 1.36/1.53 tff(569,plain,
% 1.36/1.53 (~c3_1(a1682)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[568, 548])).
% 1.36/1.53 tff(570,plain,
% 1.36/1.53 (((~hskp19) | c1_1(a1682)) <=> ((~hskp19) | c1_1(a1682))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(571,axiom,((~hskp19) | c1_1(a1682)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 1.36/1.53 tff(572,plain,
% 1.36/1.53 ((~hskp19) | c1_1(a1682)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[571, 570])).
% 1.36/1.53 tff(573,plain,
% 1.36/1.53 ((~hskp19) | c1_1(a1682)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[572, 570])).
% 1.36/1.53 tff(574,plain,
% 1.36/1.53 ((~hskp19) | c1_1(a1682)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[573, 570])).
% 1.36/1.53 tff(575,plain,
% 1.36/1.53 ((~hskp19) | c1_1(a1682)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[574, 570])).
% 1.36/1.53 tff(576,plain,
% 1.36/1.53 ((~hskp19) | c1_1(a1682)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[575, 570])).
% 1.36/1.53 tff(577,plain,
% 1.36/1.53 (c1_1(a1682)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[576, 548])).
% 1.36/1.53 tff(578,plain,
% 1.36/1.53 (((~hskp19) | c2_1(a1682)) <=> ((~hskp19) | c2_1(a1682))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(579,axiom,((~hskp19) | c2_1(a1682)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 1.36/1.53 tff(580,plain,
% 1.36/1.53 ((~hskp19) | c2_1(a1682)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[579, 578])).
% 1.36/1.53 tff(581,plain,
% 1.36/1.53 ((~hskp19) | c2_1(a1682)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[580, 578])).
% 1.36/1.53 tff(582,plain,
% 1.36/1.53 ((~hskp19) | c2_1(a1682)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[581, 578])).
% 1.36/1.53 tff(583,plain,
% 1.36/1.53 ((~hskp19) | c2_1(a1682)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[582, 578])).
% 1.36/1.53 tff(584,plain,
% 1.36/1.53 ((~hskp19) | c2_1(a1682)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[583, 578])).
% 1.36/1.53 tff(585,plain,
% 1.36/1.53 (c2_1(a1682)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[584, 548])).
% 1.36/1.53 tff(586,plain,
% 1.36/1.53 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)))),
% 1.36/1.53 inference(bind,[status(th)],[])).
% 1.36/1.53 tff(587,plain,
% 1.36/1.53 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.36/1.53 inference(quant_intro,[status(thm)],[586])).
% 1.36/1.53 tff(588,plain,
% 1.36/1.53 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(589,plain,
% 1.36/1.53 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))))),
% 1.36/1.53 inference(bind,[status(th)],[])).
% 1.36/1.53 tff(590,plain,
% 1.36/1.53 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.36/1.53 inference(quant_intro,[status(thm)],[589])).
% 1.36/1.53 tff(591,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause192')).
% 1.36/1.53 tff(592,plain,
% 1.36/1.53 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[591, 590])).
% 1.36/1.53 tff(593,plain,
% 1.36/1.53 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[592, 588])).
% 1.36/1.53 tff(594,plain,(
% 1.36/1.53 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.36/1.53 inference(skolemize,[status(sab)],[593])).
% 1.36/1.53 tff(595,plain,
% 1.36/1.53 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[594, 587])).
% 1.36/1.53 tff(596,assumption,(~c3_1(a1682)), introduced(assumption)).
% 1.36/1.53 tff(597,plain,
% 1.36/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1682) | c0_1(a1644) | c1_1(a1644) | c3_1(a1644) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1682)) | (~c1_1(a1682)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1682) | c0_1(a1644) | c1_1(a1644) | c3_1(a1644) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1682)) | (~c1_1(a1682)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(598,plain,
% 1.36/1.53 (((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1644) | c0_1(a1644) | c3_1(a1644)) <=> (c3_1(a1682) | c0_1(a1644) | c1_1(a1644) | c3_1(a1644) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1682)) | (~c1_1(a1682)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(599,plain,
% 1.36/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1644) | c0_1(a1644) | c3_1(a1644))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1682) | c0_1(a1644) | c1_1(a1644) | c3_1(a1644) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1682)) | (~c1_1(a1682))))),
% 1.36/1.53 inference(monotonicity,[status(thm)],[598])).
% 1.36/1.53 tff(600,plain,
% 1.36/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1644) | c0_1(a1644) | c3_1(a1644))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1682) | c0_1(a1644) | c1_1(a1644) | c3_1(a1644) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1682)) | (~c1_1(a1682)))),
% 1.36/1.53 inference(transitivity,[status(thm)],[599, 597])).
% 1.36/1.53 tff(601,plain,
% 1.36/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1644) | c0_1(a1644) | c3_1(a1644))),
% 1.36/1.53 inference(quant_inst,[status(thm)],[])).
% 1.36/1.53 tff(602,plain,
% 1.36/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1682) | c0_1(a1644) | c1_1(a1644) | c3_1(a1644) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1682)) | (~c1_1(a1682))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[601, 600])).
% 1.36/1.53 tff(603,plain,
% 1.36/1.53 ((~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1682)) | (~c1_1(a1682))),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[602, 296, 596, 563, 562, 561, 503, 595])).
% 1.36/1.53 tff(604,plain,
% 1.36/1.53 ($false),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[603, 585, 577, 504, 502])).
% 1.36/1.53 tff(605,plain,((~hskp19) | (~c0_1(a1634)) | (~c3_1(a1634)) | (~ndr1_0) | c3_1(a1682) | c0_1(a1644) | c1_1(a1644) | c3_1(a1644) | c1_1(a1634)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.53 tff(606,plain,
% 1.36/1.53 ($false),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[605, 569, 548, 502, 296, 504, 563, 562, 561, 503])).
% 1.36/1.53 tff(607,plain,((~hskp19) | (~c3_1(a1634)) | (~ndr1_0) | (~c0_1(a1634)) | c0_1(a1644) | c1_1(a1644) | c3_1(a1644) | c1_1(a1634)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.53 tff(608,plain,
% 1.36/1.53 ($false),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[607, 560, 554, 296, 504, 502, 548, 547, 503])).
% 1.36/1.53 tff(609,plain,((~hskp9) | (~ndr1_0) | (~c0_1(a1634)) | (~c3_1(a1634)) | (~hskp19) | c1_1(a1634)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.53 tff(610,plain,
% 1.36/1.53 ((~hskp9) | (~c0_1(a1634)) | (~c3_1(a1634)) | (~hskp19) | c1_1(a1634)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[609, 119])).
% 1.36/1.53 tff(611,plain,
% 1.36/1.53 (~hskp19),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[610, 540, 504, 502, 503])).
% 1.36/1.53 tff(612,plain,
% 1.36/1.53 (^[U: $i] : refl((hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 1.36/1.53 inference(bind,[status(th)],[])).
% 1.36/1.53 tff(613,plain,
% 1.36/1.53 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.36/1.53 inference(quant_intro,[status(thm)],[612])).
% 1.36/1.53 tff(614,plain,
% 1.36/1.53 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(615,plain,
% 1.36/1.53 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp28))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp19) <=> ((hskp28 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp19))), rewrite(((hskp28 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp19) <=> (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp19) <=> (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 1.36/1.53 inference(bind,[status(th)],[])).
% 1.36/1.53 tff(616,plain,
% 1.36/1.53 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp19) <=> ![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.36/1.53 inference(quant_intro,[status(thm)],[615])).
% 1.36/1.53 tff(617,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause157')).
% 1.36/1.53 tff(618,plain,
% 1.36/1.53 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[617, 616])).
% 1.36/1.53 tff(619,plain,
% 1.36/1.53 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[618, 614])).
% 1.36/1.53 tff(620,plain,(
% 1.36/1.53 ![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.36/1.53 inference(skolemize,[status(sab)],[619])).
% 1.36/1.53 tff(621,plain,
% 1.36/1.53 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[620, 613])).
% 1.36/1.53 tff(622,plain,
% 1.36/1.53 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp28 | hskp19 | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp28 | hskp19 | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(623,plain,
% 1.36/1.53 ((hskp28 | hskp19 | (~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634))) <=> (hskp28 | hskp19 | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(624,plain,
% 1.36/1.53 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp28 | hskp19 | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634))))),
% 1.36/1.53 inference(monotonicity,[status(thm)],[623])).
% 1.36/1.53 tff(625,plain,
% 1.36/1.53 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp28 | hskp19 | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)))),
% 1.36/1.53 inference(transitivity,[status(thm)],[624, 622])).
% 1.36/1.53 tff(626,plain,
% 1.36/1.53 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634)))),
% 1.36/1.53 inference(quant_inst,[status(thm)],[])).
% 1.36/1.53 tff(627,plain,
% 1.36/1.53 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp28 | hskp19 | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[626, 625])).
% 1.36/1.53 tff(628,plain,
% 1.36/1.53 (hskp28 | hskp19 | (~c2_1(a1634)) | (~c3_1(a1634))),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[627, 119, 503, 621])).
% 1.36/1.53 tff(629,plain,
% 1.36/1.53 (~c2_1(a1634)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[628, 611, 502, 501])).
% 1.36/1.53 tff(630,plain,
% 1.36/1.53 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.36/1.53 inference(bind,[status(th)],[])).
% 1.36/1.53 tff(631,plain,
% 1.36/1.53 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.36/1.53 inference(quant_intro,[status(thm)],[630])).
% 1.36/1.53 tff(632,plain,
% 1.36/1.53 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(633,plain,
% 1.36/1.53 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.36/1.53 inference(bind,[status(th)],[])).
% 1.36/1.53 tff(634,plain,
% 1.36/1.53 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.36/1.53 inference(quant_intro,[status(thm)],[633])).
% 1.36/1.53 tff(635,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 1.36/1.53 tff(636,plain,
% 1.36/1.53 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[635, 634])).
% 1.36/1.53 tff(637,plain,
% 1.36/1.53 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[636, 632])).
% 1.36/1.53 tff(638,plain,(
% 1.36/1.53 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.36/1.53 inference(skolemize,[status(sab)],[637])).
% 1.36/1.53 tff(639,plain,
% 1.36/1.53 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[638, 631])).
% 1.36/1.53 tff(640,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp2 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(641,plain,
% 1.36/1.53 ((hskp2 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648))) <=> (hskp2 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(642,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648))))),
% 1.36/1.53 inference(monotonicity,[status(thm)],[641])).
% 1.36/1.53 tff(643,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp2 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648)))),
% 1.36/1.53 inference(transitivity,[status(thm)],[642, 640])).
% 1.36/1.53 tff(644,plain,
% 1.36/1.53 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)))),
% 1.36/1.53 inference(quant_inst,[status(thm)],[])).
% 1.36/1.53 tff(645,plain,
% 1.36/1.53 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp2 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[644, 643])).
% 1.36/1.53 tff(646,plain,
% 1.36/1.53 ($false),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[645, 119, 500, 170, 169, 504, 502, 639, 522, 629])).
% 1.36/1.53 tff(647,plain,(hskp28 | hskp2 | (~c0_1(a1648)) | (~c2_1(a1648)) | (~c0_1(a1634)) | (~c3_1(a1634)) | c1_1(a1634) | c3_1(a1648)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.53 tff(648,plain,
% 1.36/1.53 (hskp28),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[647, 500, 159, 167, 499, 491, 483, 151])).
% 1.36/1.53 tff(649,plain,
% 1.36/1.53 (c3_1(a1646)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[268, 648])).
% 1.36/1.53 tff(650,plain,
% 1.36/1.53 (c1_1(a1646)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[260, 648])).
% 1.36/1.53 tff(651,plain,
% 1.36/1.53 (c2_1(a1646)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[238, 648])).
% 1.36/1.53 tff(652,assumption,(~c3_1(a1638)), introduced(assumption)).
% 1.36/1.53 tff(653,plain,
% 1.36/1.53 (((~hskp3) | c3_1(a1638)) <=> ((~hskp3) | c3_1(a1638))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(654,axiom,((~hskp3) | c3_1(a1638)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 1.36/1.53 tff(655,plain,
% 1.36/1.53 ((~hskp3) | c3_1(a1638)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[654, 653])).
% 1.36/1.53 tff(656,plain,
% 1.36/1.53 ((~hskp3) | c3_1(a1638)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[655, 653])).
% 1.36/1.53 tff(657,plain,
% 1.36/1.53 ((~hskp3) | c3_1(a1638)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[656, 653])).
% 1.36/1.53 tff(658,plain,
% 1.36/1.53 ((~hskp3) | c3_1(a1638)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[657, 653])).
% 1.36/1.53 tff(659,plain,
% 1.36/1.53 ((~hskp3) | c3_1(a1638)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[658, 653])).
% 1.36/1.53 tff(660,plain,
% 1.36/1.53 (~hskp3),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[659, 652])).
% 1.36/1.53 tff(661,assumption,(~hskp3), introduced(assumption)).
% 1.36/1.53 tff(662,plain,
% 1.36/1.53 (hskp11),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[144, 56, 21])).
% 1.36/1.53 tff(663,plain,
% 1.36/1.53 (((~hskp11) | (~c3_1(a1650))) <=> ((~hskp11) | (~c3_1(a1650)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(664,plain,
% 1.36/1.53 (((~c3_1(a1650)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a1650)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(665,axiom,((~c3_1(a1650)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 1.36/1.53 tff(666,plain,
% 1.36/1.53 ((~hskp11) | (~c3_1(a1650))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[665, 664])).
% 1.36/1.53 tff(667,plain,
% 1.36/1.53 ((~hskp11) | (~c3_1(a1650))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[666, 663])).
% 1.36/1.53 tff(668,plain,
% 1.36/1.53 (~c3_1(a1650)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[667, 662])).
% 1.36/1.53 tff(669,plain,
% 1.36/1.53 (((~hskp11) | (~c0_1(a1650))) <=> ((~hskp11) | (~c0_1(a1650)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(670,plain,
% 1.36/1.54 (((~c0_1(a1650)) | (~hskp11)) <=> ((~hskp11) | (~c0_1(a1650)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(671,axiom,((~c0_1(a1650)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 1.36/1.54 tff(672,plain,
% 1.36/1.54 ((~hskp11) | (~c0_1(a1650))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[671, 670])).
% 1.36/1.54 tff(673,plain,
% 1.36/1.54 ((~hskp11) | (~c0_1(a1650))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[672, 669])).
% 1.36/1.54 tff(674,plain,
% 1.36/1.54 (~c0_1(a1650)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[673, 662])).
% 1.36/1.54 tff(675,plain,
% 1.36/1.54 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp1 | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | c2_1(a1650))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp1 | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | c2_1(a1650))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(676,plain,
% 1.36/1.54 ((hskp10 | hskp1 | (~ndr1_0) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650)) <=> (hskp10 | hskp1 | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | c2_1(a1650))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(677,plain,
% 1.36/1.54 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp1 | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | c2_1(a1650)))),
% 1.36/1.54 inference(monotonicity,[status(thm)],[676])).
% 1.36/1.54 tff(678,plain,
% 1.36/1.54 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp1 | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | c2_1(a1650))),
% 1.36/1.54 inference(transitivity,[status(thm)],[677, 675])).
% 1.36/1.54 tff(679,plain,
% 1.36/1.54 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650))),
% 1.36/1.54 inference(quant_inst,[status(thm)],[])).
% 1.36/1.54 tff(680,plain,
% 1.36/1.54 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp1 | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | c2_1(a1650)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[679, 678])).
% 1.36/1.54 tff(681,plain,
% 1.36/1.54 (c2_1(a1650)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[680, 119, 56, 21, 674, 668, 136])).
% 1.36/1.54 tff(682,plain,
% 1.36/1.54 (^[V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.36/1.54 inference(bind,[status(th)],[])).
% 1.36/1.54 tff(683,plain,
% 1.36/1.54 (![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.36/1.54 inference(quant_intro,[status(thm)],[682])).
% 1.36/1.54 tff(684,plain,
% 1.36/1.54 (![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(685,plain,
% 1.36/1.54 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.36/1.54 inference(bind,[status(th)],[])).
% 1.36/1.54 tff(686,plain,
% 1.36/1.54 (![V: $i, U: $i] : (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.36/1.54 inference(quant_intro,[status(thm)],[685])).
% 1.36/1.54 tff(687,axiom,(![V: $i, U: $i] : (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 1.36/1.54 tff(688,plain,
% 1.36/1.54 (![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[687, 686])).
% 1.36/1.54 tff(689,plain,
% 1.36/1.54 (![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[688, 684])).
% 1.36/1.54 tff(690,plain,(
% 1.36/1.54 ![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.36/1.54 inference(skolemize,[status(sab)],[689])).
% 1.36/1.54 tff(691,plain,
% 1.36/1.54 (![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[690, 683])).
% 1.36/1.54 tff(692,assumption,(hskp21), introduced(assumption)).
% 1.36/1.54 tff(693,plain,
% 1.36/1.54 (((~hskp21) | (~c1_1(a1691))) <=> ((~hskp21) | (~c1_1(a1691)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(694,plain,
% 1.36/1.54 (((~c1_1(a1691)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a1691)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(695,axiom,((~c1_1(a1691)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 1.36/1.54 tff(696,plain,
% 1.36/1.54 ((~hskp21) | (~c1_1(a1691))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[695, 694])).
% 1.36/1.54 tff(697,plain,
% 1.36/1.54 ((~hskp21) | (~c1_1(a1691))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[696, 693])).
% 1.36/1.54 tff(698,plain,
% 1.36/1.54 (~c1_1(a1691)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[697, 692])).
% 1.36/1.54 tff(699,plain,
% 1.36/1.54 (((~hskp11) | c1_1(a1650)) <=> ((~hskp11) | c1_1(a1650))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(700,axiom,((~hskp11) | c1_1(a1650)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 1.36/1.54 tff(701,plain,
% 1.36/1.54 ((~hskp11) | c1_1(a1650)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[700, 699])).
% 1.36/1.54 tff(702,plain,
% 1.36/1.54 ((~hskp11) | c1_1(a1650)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[701, 699])).
% 1.36/1.54 tff(703,plain,
% 1.36/1.54 ((~hskp11) | c1_1(a1650)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[702, 699])).
% 1.36/1.54 tff(704,plain,
% 1.36/1.54 ((~hskp11) | c1_1(a1650)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[703, 699])).
% 1.36/1.54 tff(705,plain,
% 1.36/1.54 ((~hskp11) | c1_1(a1650)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[704, 699])).
% 1.36/1.54 tff(706,plain,
% 1.36/1.54 (c1_1(a1650)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[705, 662])).
% 1.36/1.54 tff(707,plain,
% 1.36/1.54 (((~hskp21) | c3_1(a1691)) <=> ((~hskp21) | c3_1(a1691))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(708,axiom,((~hskp21) | c3_1(a1691)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 1.36/1.54 tff(709,plain,
% 1.36/1.54 ((~hskp21) | c3_1(a1691)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[708, 707])).
% 1.36/1.54 tff(710,plain,
% 1.36/1.54 ((~hskp21) | c3_1(a1691)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[709, 707])).
% 1.36/1.54 tff(711,plain,
% 1.36/1.54 ((~hskp21) | c3_1(a1691)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[710, 707])).
% 1.36/1.54 tff(712,plain,
% 1.36/1.54 ((~hskp21) | c3_1(a1691)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[711, 707])).
% 1.36/1.54 tff(713,plain,
% 1.36/1.54 ((~hskp21) | c3_1(a1691)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[712, 707])).
% 1.36/1.54 tff(714,plain,
% 1.36/1.54 (c3_1(a1691)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[713, 692])).
% 1.36/1.54 tff(715,plain,
% 1.36/1.54 (((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (c1_1(a1691) | c0_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1691)) | c0_1(a1691))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | c1_1(a1691) | c0_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1691)) | c0_1(a1691))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(716,plain,
% 1.36/1.54 (((~ndr1_0) | c0_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1691) | c0_1(a1691) | (~c3_1(a1691))) <=> (c1_1(a1691) | c0_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1691)) | c0_1(a1691))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(717,plain,
% 1.36/1.54 (((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | ((~ndr1_0) | c0_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1691) | c0_1(a1691) | (~c3_1(a1691)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (c1_1(a1691) | c0_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1691)) | c0_1(a1691)))),
% 1.36/1.54 inference(monotonicity,[status(thm)],[716])).
% 1.36/1.54 tff(718,plain,
% 1.36/1.54 (((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | ((~ndr1_0) | c0_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1691) | c0_1(a1691) | (~c3_1(a1691)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | c1_1(a1691) | c0_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1691)) | c0_1(a1691))),
% 1.36/1.54 inference(transitivity,[status(thm)],[717, 715])).
% 1.36/1.54 tff(719,plain,
% 1.36/1.54 ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | ((~ndr1_0) | c0_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1691) | c0_1(a1691) | (~c3_1(a1691)))),
% 1.36/1.54 inference(quant_inst,[status(thm)],[])).
% 1.36/1.54 tff(720,plain,
% 1.36/1.54 ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | c1_1(a1691) | c0_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1691)) | c0_1(a1691)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[719, 718])).
% 1.36/1.54 tff(721,plain,
% 1.36/1.54 (c0_1(a1691)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[720, 119, 714, 706, 698, 674, 691, 681])).
% 1.36/1.54 tff(722,plain,
% 1.36/1.54 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.36/1.54 inference(bind,[status(th)],[])).
% 1.36/1.54 tff(723,plain,
% 1.36/1.54 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.36/1.54 inference(quant_intro,[status(thm)],[722])).
% 1.36/1.54 tff(724,plain,
% 1.36/1.54 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(725,plain,
% 1.36/1.54 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp18) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp18))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.36/1.54 inference(bind,[status(th)],[])).
% 1.36/1.54 tff(726,plain,
% 1.36/1.54 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.36/1.54 inference(quant_intro,[status(thm)],[725])).
% 1.36/1.54 tff(727,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause186')).
% 1.36/1.54 tff(728,plain,
% 1.36/1.54 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[727, 726])).
% 1.36/1.54 tff(729,plain,
% 1.36/1.54 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[728, 724])).
% 1.36/1.54 tff(730,plain,(
% 1.36/1.54 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.36/1.54 inference(skolemize,[status(sab)],[729])).
% 1.36/1.54 tff(731,plain,
% 1.36/1.54 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[730, 723])).
% 1.36/1.54 tff(732,plain,
% 1.36/1.54 (((~hskp21) | c2_1(a1691)) <=> ((~hskp21) | c2_1(a1691))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(733,axiom,((~hskp21) | c2_1(a1691)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 1.36/1.54 tff(734,plain,
% 1.36/1.54 ((~hskp21) | c2_1(a1691)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[733, 732])).
% 1.36/1.54 tff(735,plain,
% 1.36/1.54 ((~hskp21) | c2_1(a1691)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[734, 732])).
% 1.36/1.54 tff(736,plain,
% 1.36/1.54 ((~hskp21) | c2_1(a1691)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[735, 732])).
% 1.36/1.54 tff(737,plain,
% 1.36/1.54 ((~hskp21) | c2_1(a1691)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[736, 732])).
% 1.36/1.54 tff(738,plain,
% 1.36/1.54 ((~hskp21) | c2_1(a1691)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[737, 732])).
% 1.36/1.54 tff(739,plain,
% 1.36/1.54 (c2_1(a1691)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[738, 692])).
% 1.36/1.54 tff(740,plain,
% 1.36/1.54 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp18 | c1_1(a1691) | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1691)) | (~c2_1(a1691)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp18 | c1_1(a1691) | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1691)) | (~c2_1(a1691)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(741,plain,
% 1.36/1.54 ((hskp18 | (~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1691) | (~c3_1(a1691)) | (~c2_1(a1691))) <=> (hskp18 | c1_1(a1691) | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1691)) | (~c2_1(a1691)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(742,plain,
% 1.36/1.54 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1691) | (~c3_1(a1691)) | (~c2_1(a1691)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp18 | c1_1(a1691) | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1691)) | (~c2_1(a1691))))),
% 1.36/1.54 inference(monotonicity,[status(thm)],[741])).
% 1.36/1.54 tff(743,plain,
% 1.36/1.54 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1691) | (~c3_1(a1691)) | (~c2_1(a1691)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp18 | c1_1(a1691) | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1691)) | (~c2_1(a1691)))),
% 1.36/1.54 inference(transitivity,[status(thm)],[742, 740])).
% 1.36/1.54 tff(744,plain,
% 1.36/1.54 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1691) | (~c3_1(a1691)) | (~c2_1(a1691)))),
% 1.36/1.54 inference(quant_inst,[status(thm)],[])).
% 1.36/1.54 tff(745,plain,
% 1.36/1.54 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp18 | c1_1(a1691) | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1691)) | (~c2_1(a1691))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[744, 743])).
% 1.36/1.54 tff(746,plain,
% 1.36/1.54 (hskp18),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[745, 119, 739, 714, 706, 698, 668, 731, 681])).
% 1.36/1.54 tff(747,plain,
% 1.36/1.54 (~c0_1(a1680)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[76, 746])).
% 1.36/1.54 tff(748,plain,
% 1.36/1.54 (c1_1(a1680)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[84, 746])).
% 1.36/1.54 tff(749,plain,
% 1.36/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c1_1(a1691) | c0_1(a1680) | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1680)) | (~c1_1(a1680)) | (~c3_1(a1691)) | (~c0_1(a1691)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c1_1(a1691) | c0_1(a1680) | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1680)) | (~c1_1(a1680)) | (~c3_1(a1691)) | (~c0_1(a1691)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(750,plain,
% 1.36/1.54 (((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1691) | (~c3_1(a1691)) | (~c0_1(a1691)) | c0_1(a1680) | (~c1_1(a1680)) | (~c3_1(a1680))) <=> (c1_1(a1691) | c0_1(a1680) | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1680)) | (~c1_1(a1680)) | (~c3_1(a1691)) | (~c0_1(a1691)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(751,plain,
% 1.36/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1691) | (~c3_1(a1691)) | (~c0_1(a1691)) | c0_1(a1680) | (~c1_1(a1680)) | (~c3_1(a1680)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c1_1(a1691) | c0_1(a1680) | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1680)) | (~c1_1(a1680)) | (~c3_1(a1691)) | (~c0_1(a1691))))),
% 1.36/1.54 inference(monotonicity,[status(thm)],[750])).
% 1.36/1.54 tff(752,plain,
% 1.36/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1691) | (~c3_1(a1691)) | (~c0_1(a1691)) | c0_1(a1680) | (~c1_1(a1680)) | (~c3_1(a1680)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c1_1(a1691) | c0_1(a1680) | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1680)) | (~c1_1(a1680)) | (~c3_1(a1691)) | (~c0_1(a1691)))),
% 1.36/1.54 inference(transitivity,[status(thm)],[751, 749])).
% 1.36/1.54 tff(753,plain,
% 1.36/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1691) | (~c3_1(a1691)) | (~c0_1(a1691)) | c0_1(a1680) | (~c1_1(a1680)) | (~c3_1(a1680)))),
% 1.36/1.54 inference(quant_inst,[status(thm)],[])).
% 1.36/1.54 tff(754,plain,
% 1.36/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c1_1(a1691) | c0_1(a1680) | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1680)) | (~c1_1(a1680)) | (~c3_1(a1691)) | (~c0_1(a1691))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[753, 752])).
% 1.36/1.54 tff(755,plain,
% 1.36/1.54 (~c3_1(a1680)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[754, 119, 714, 748, 706, 698, 747, 668, 20, 681, 721])).
% 1.36/1.54 tff(756,plain,
% 1.36/1.54 (~c2_1(a1680)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[70, 746])).
% 1.36/1.54 tff(757,plain,
% 1.36/1.54 ($false),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[142, 119, 56, 21, 747, 756, 136, 755])).
% 1.36/1.54 tff(758,plain,((~hskp21) | hskp10 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.36/1.54 tff(759,plain,
% 1.36/1.54 (~hskp21),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[758, 56, 21])).
% 1.36/1.54 tff(760,plain,
% 1.36/1.54 (^[U: $i] : refl((hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.36/1.54 inference(bind,[status(th)],[])).
% 1.36/1.54 tff(761,plain,
% 1.36/1.54 (![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.36/1.54 inference(quant_intro,[status(thm)],[760])).
% 1.36/1.54 tff(762,plain,
% 1.36/1.54 (![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(763,plain,
% 1.36/1.54 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp21) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp21))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp21) | hskp3) <=> ((hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp3))), rewrite(((hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp3) <=> (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp21) | hskp3) <=> (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.36/1.54 inference(bind,[status(th)],[])).
% 1.36/1.54 tff(764,plain,
% 1.36/1.54 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp21) | hskp3) <=> ![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.36/1.54 inference(quant_intro,[status(thm)],[763])).
% 1.36/1.54 tff(765,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp21) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause159')).
% 1.36/1.54 tff(766,plain,
% 1.36/1.54 (![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[765, 764])).
% 1.36/1.54 tff(767,plain,
% 1.36/1.54 (![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[766, 762])).
% 1.36/1.54 tff(768,plain,(
% 1.36/1.54 ![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.36/1.54 inference(skolemize,[status(sab)],[767])).
% 1.36/1.54 tff(769,plain,
% 1.36/1.54 (![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[768, 761])).
% 1.36/1.54 tff(770,assumption,(hskp18), introduced(assumption)).
% 1.36/1.54 tff(771,plain,
% 1.36/1.54 (~c2_1(a1680)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[70, 770])).
% 1.36/1.54 tff(772,plain,
% 1.36/1.54 (c1_1(a1680)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[84, 770])).
% 1.36/1.54 tff(773,plain,
% 1.36/1.54 (((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | c2_1(a1680) | (~ndr1_0) | (~c3_1(a1680)) | (~c1_1(a1680)))) <=> ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp3 | c2_1(a1680) | (~ndr1_0) | (~c3_1(a1680)) | (~c1_1(a1680)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(774,plain,
% 1.36/1.54 ((hskp21 | hskp3 | (~ndr1_0) | c2_1(a1680) | (~c3_1(a1680)) | (~c1_1(a1680))) <=> (hskp21 | hskp3 | c2_1(a1680) | (~ndr1_0) | (~c3_1(a1680)) | (~c1_1(a1680)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(775,plain,
% 1.36/1.54 (((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | (~ndr1_0) | c2_1(a1680) | (~c3_1(a1680)) | (~c1_1(a1680)))) <=> ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | c2_1(a1680) | (~ndr1_0) | (~c3_1(a1680)) | (~c1_1(a1680))))),
% 1.36/1.54 inference(monotonicity,[status(thm)],[774])).
% 1.36/1.54 tff(776,plain,
% 1.36/1.54 (((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | (~ndr1_0) | c2_1(a1680) | (~c3_1(a1680)) | (~c1_1(a1680)))) <=> ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp3 | c2_1(a1680) | (~ndr1_0) | (~c3_1(a1680)) | (~c1_1(a1680)))),
% 1.36/1.54 inference(transitivity,[status(thm)],[775, 773])).
% 1.36/1.54 tff(777,plain,
% 1.36/1.54 ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | (~ndr1_0) | c2_1(a1680) | (~c3_1(a1680)) | (~c1_1(a1680)))),
% 1.36/1.54 inference(quant_inst,[status(thm)],[])).
% 1.36/1.54 tff(778,plain,
% 1.36/1.54 ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp3 | c2_1(a1680) | (~ndr1_0) | (~c3_1(a1680)) | (~c1_1(a1680))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[777, 776])).
% 1.36/1.54 tff(779,plain,
% 1.36/1.54 (~c3_1(a1680)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[778, 119, 759, 661, 772, 771, 769])).
% 1.36/1.55 tff(780,plain,
% 1.36/1.55 (~c0_1(a1680)),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[76, 770])).
% 1.36/1.55 tff(781,plain,
% 1.36/1.55 ($false),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[142, 119, 56, 21, 780, 771, 136, 779])).
% 1.36/1.55 tff(782,plain,((~hskp18) | hskp10 | hskp1 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.36/1.55 tff(783,plain,
% 1.36/1.55 (~hskp18),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[782, 56, 21, 661])).
% 1.36/1.55 tff(784,assumption,(hskp8), introduced(assumption)).
% 1.36/1.55 tff(785,plain,
% 1.36/1.55 (~c2_1(a1643)),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[182, 784])).
% 1.36/1.55 tff(786,plain,
% 1.36/1.55 (~c3_1(a1643)),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[244, 784])).
% 1.36/1.55 tff(787,plain,
% 1.36/1.55 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp1 | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp1 | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643))),
% 1.36/1.55 inference(rewrite,[status(thm)],[])).
% 1.36/1.55 tff(788,plain,
% 1.36/1.55 ((hskp10 | hskp1 | (~ndr1_0) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643)) <=> (hskp10 | hskp1 | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643))),
% 1.36/1.55 inference(rewrite,[status(thm)],[])).
% 1.36/1.55 tff(789,plain,
% 1.36/1.55 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp1 | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643)))),
% 1.36/1.55 inference(monotonicity,[status(thm)],[788])).
% 1.36/1.55 tff(790,plain,
% 1.36/1.55 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp1 | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643))),
% 1.36/1.55 inference(transitivity,[status(thm)],[789, 787])).
% 1.36/1.55 tff(791,plain,
% 1.36/1.55 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643))),
% 1.36/1.55 inference(quant_inst,[status(thm)],[])).
% 1.36/1.55 tff(792,plain,
% 1.36/1.55 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp1 | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643)),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[791, 790])).
% 1.36/1.55 tff(793,plain,
% 1.36/1.55 (c3_1(a1643) | c0_1(a1643)),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[792, 119, 56, 21, 282, 136])).
% 1.36/1.55 tff(794,plain,
% 1.36/1.55 (c0_1(a1643)),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[793, 281])).
% 1.36/1.55 tff(795,plain,
% 1.36/1.55 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c1_1(a1643) | c0_1(a1650) | c3_1(a1650) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1650)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c1_1(a1643) | c0_1(a1650) | c3_1(a1650) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1650)))),
% 1.36/1.55 inference(rewrite,[status(thm)],[])).
% 1.36/1.55 tff(796,plain,
% 1.36/1.55 ((hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1643) | c1_1(a1643) | c3_1(a1643)) <=> (hskp3 | c1_1(a1643) | c0_1(a1650) | c3_1(a1650) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1650)))),
% 1.36/1.55 inference(rewrite,[status(thm)],[])).
% 1.36/1.55 tff(797,plain,
% 1.36/1.55 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1643) | c1_1(a1643) | c3_1(a1643))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c1_1(a1643) | c0_1(a1650) | c3_1(a1650) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1650))))),
% 1.36/1.55 inference(monotonicity,[status(thm)],[796])).
% 1.36/1.55 tff(798,plain,
% 1.36/1.55 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1643) | c1_1(a1643) | c3_1(a1643))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c1_1(a1643) | c0_1(a1650) | c3_1(a1650) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1650)))),
% 1.36/1.55 inference(transitivity,[status(thm)],[797, 795])).
% 1.36/1.55 tff(799,plain,
% 1.36/1.55 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1643) | c1_1(a1643) | c3_1(a1643))),
% 1.36/1.55 inference(quant_inst,[status(thm)],[])).
% 1.36/1.55 tff(800,plain,
% 1.36/1.55 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c1_1(a1643) | c0_1(a1650) | c3_1(a1650) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1650))),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[799, 798])).
% 1.36/1.55 tff(801,plain,
% 1.36/1.55 (c1_1(a1643) | c3_1(a1643)),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[800, 119, 661, 706, 674, 668, 282, 10])).
% 1.36/1.55 tff(802,plain,
% 1.36/1.55 (c1_1(a1643)),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[801, 281])).
% 1.36/1.55 tff(803,plain,
% 1.36/1.55 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.36/1.55 inference(bind,[status(th)],[])).
% 1.36/1.55 tff(804,plain,
% 1.36/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.36/1.55 inference(quant_intro,[status(thm)],[803])).
% 1.36/1.55 tff(805,plain,
% 1.36/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.36/1.55 inference(rewrite,[status(thm)],[])).
% 1.36/1.55 tff(806,plain,
% 1.36/1.55 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.36/1.55 inference(bind,[status(th)],[])).
% 1.36/1.55 tff(807,plain,
% 1.36/1.55 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.36/1.55 inference(quant_intro,[status(thm)],[806])).
% 1.36/1.55 tff(808,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 1.36/1.55 tff(809,plain,
% 1.36/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[808, 807])).
% 1.36/1.55 tff(810,plain,
% 1.36/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[809, 805])).
% 1.36/1.55 tff(811,plain,(
% 1.36/1.55 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.36/1.55 inference(skolemize,[status(sab)],[810])).
% 1.36/1.55 tff(812,plain,
% 1.36/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[811, 804])).
% 1.36/1.55 tff(813,assumption,(c0_1(a1643)), introduced(assumption)).
% 1.36/1.55 tff(814,plain,
% 1.36/1.55 (hskp15),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[326, 119, 224, 216, 318, 208, 281, 316, 813])).
% 1.36/1.55 tff(815,plain,
% 1.36/1.55 (~c2_1(a1664)),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[333, 814])).
% 1.36/1.55 tff(816,plain,
% 1.36/1.55 (~c1_1(a1664)),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[339, 814])).
% 1.36/1.55 tff(817,plain,
% 1.36/1.55 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))))),
% 1.36/1.55 inference(bind,[status(th)],[])).
% 1.36/1.55 tff(818,plain,
% 1.36/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.36/1.55 inference(quant_intro,[status(thm)],[817])).
% 1.36/1.55 tff(819,plain,
% 1.36/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.36/1.55 inference(rewrite,[status(thm)],[])).
% 1.36/1.55 tff(820,plain,
% 1.36/1.55 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))))),
% 1.36/1.55 inference(bind,[status(th)],[])).
% 1.36/1.55 tff(821,plain,
% 1.36/1.55 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.36/1.55 inference(quant_intro,[status(thm)],[820])).
% 1.36/1.55 tff(822,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause195')).
% 1.36/1.55 tff(823,plain,
% 1.36/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[822, 821])).
% 1.36/1.55 tff(824,plain,
% 1.36/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[823, 819])).
% 1.36/1.55 tff(825,plain,(
% 1.36/1.55 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.36/1.55 inference(skolemize,[status(sab)],[824])).
% 1.36/1.55 tff(826,plain,
% 1.36/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[825, 818])).
% 1.36/1.55 tff(827,plain,
% 1.36/1.55 ((hskp5 | hskp1 | hskp0) <=> (hskp5 | hskp1 | hskp0)),
% 1.36/1.55 inference(rewrite,[status(thm)],[])).
% 1.36/1.55 tff(828,plain,
% 1.36/1.55 (((hskp0 | hskp5) | hskp1) <=> (hskp5 | hskp1 | hskp0)),
% 1.36/1.55 inference(rewrite,[status(thm)],[])).
% 1.36/1.55 tff(829,axiom,((hskp0 | hskp5) | hskp1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 1.36/1.55 tff(830,plain,
% 1.36/1.55 (hskp5 | hskp1 | hskp0),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[829, 828])).
% 1.36/1.55 tff(831,plain,
% 1.36/1.55 (hskp5 | hskp1 | hskp0),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[830, 827])).
% 1.36/1.55 tff(832,plain,
% 1.36/1.55 (hskp5 | hskp1 | hskp0),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[831, 827])).
% 1.36/1.55 tff(833,plain,
% 1.36/1.55 (hskp5 | hskp1 | hskp0),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[832, 827])).
% 1.36/1.55 tff(834,plain,
% 1.36/1.55 (hskp5 | hskp1 | hskp0),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[833, 827])).
% 1.36/1.55 tff(835,plain,
% 1.36/1.55 (hskp5),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[834, 33, 21])).
% 1.36/1.55 tff(836,plain,
% 1.36/1.55 (((~hskp5) | (~c2_1(a1640))) <=> ((~hskp5) | (~c2_1(a1640)))),
% 1.36/1.55 inference(rewrite,[status(thm)],[])).
% 1.36/1.55 tff(837,plain,
% 1.36/1.55 (((~c2_1(a1640)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a1640)))),
% 1.36/1.55 inference(rewrite,[status(thm)],[])).
% 1.36/1.55 tff(838,axiom,((~c2_1(a1640)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 1.36/1.55 tff(839,plain,
% 1.36/1.55 ((~hskp5) | (~c2_1(a1640))),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[838, 837])).
% 1.36/1.55 tff(840,plain,
% 1.36/1.55 ((~hskp5) | (~c2_1(a1640))),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[839, 836])).
% 1.36/1.55 tff(841,plain,
% 1.36/1.55 (~c2_1(a1640)),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[840, 835])).
% 1.36/1.55 tff(842,assumption,(~c3_1(a1650)), introduced(assumption)).
% 1.36/1.55 tff(843,assumption,(~c0_1(a1650)), introduced(assumption)).
% 1.36/1.55 tff(844,plain,
% 1.36/1.55 (((~hskp5) | c0_1(a1640)) <=> ((~hskp5) | c0_1(a1640))),
% 1.36/1.55 inference(rewrite,[status(thm)],[])).
% 1.36/1.55 tff(845,axiom,((~hskp5) | c0_1(a1640)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 1.36/1.55 tff(846,plain,
% 1.36/1.55 ((~hskp5) | c0_1(a1640)),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[845, 844])).
% 1.36/1.55 tff(847,plain,
% 1.36/1.55 ((~hskp5) | c0_1(a1640)),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[846, 844])).
% 1.36/1.55 tff(848,plain,
% 1.36/1.55 ((~hskp5) | c0_1(a1640)),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[847, 844])).
% 1.36/1.55 tff(849,plain,
% 1.36/1.55 ((~hskp5) | c0_1(a1640)),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[848, 844])).
% 1.36/1.55 tff(850,plain,
% 1.36/1.55 ((~hskp5) | c0_1(a1640)),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[849, 844])).
% 1.36/1.55 tff(851,plain,
% 1.36/1.55 (c0_1(a1640)),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[850, 835])).
% 1.36/1.55 tff(852,assumption,(c1_1(a1650)), introduced(assumption)).
% 1.36/1.55 tff(853,plain,
% 1.36/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a1650) | c3_1(a1650) | c3_1(a1643) | c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c1_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a1650) | c3_1(a1650) | c3_1(a1643) | c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c1_1(a1650)))),
% 1.36/1.55 inference(rewrite,[status(thm)],[])).
% 1.36/1.55 tff(854,plain,
% 1.36/1.55 (((~ndr1_0) | c3_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c2_1(a1640) | c1_1(a1640) | (~c0_1(a1640)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650))) <=> (c0_1(a1650) | c3_1(a1650) | c3_1(a1643) | c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c1_1(a1650)))),
% 1.36/1.55 inference(rewrite,[status(thm)],[])).
% 1.36/1.55 tff(855,plain,
% 1.36/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c2_1(a1640) | c1_1(a1640) | (~c0_1(a1640)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a1650) | c3_1(a1650) | c3_1(a1643) | c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c1_1(a1650))))),
% 1.36/1.55 inference(monotonicity,[status(thm)],[854])).
% 1.36/1.55 tff(856,plain,
% 1.36/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c2_1(a1640) | c1_1(a1640) | (~c0_1(a1640)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a1650) | c3_1(a1650) | c3_1(a1643) | c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c1_1(a1650)))),
% 1.36/1.55 inference(transitivity,[status(thm)],[855, 853])).
% 1.36/1.55 tff(857,plain,
% 1.36/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c2_1(a1640) | c1_1(a1640) | (~c0_1(a1640)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)))),
% 1.36/1.55 inference(quant_inst,[status(thm)],[])).
% 1.36/1.55 tff(858,plain,
% 1.36/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a1650) | c3_1(a1650) | c3_1(a1643) | c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c1_1(a1650))),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[857, 856])).
% 1.36/1.55 tff(859,plain,
% 1.36/1.55 (c1_1(a1640)),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[858, 119, 852, 318, 851, 843, 842, 281, 841, 826, 813])).
% 1.36/1.55 tff(860,plain,
% 1.36/1.55 (((~hskp5) | c3_1(a1640)) <=> ((~hskp5) | c3_1(a1640))),
% 1.36/1.55 inference(rewrite,[status(thm)],[])).
% 1.36/1.55 tff(861,axiom,((~hskp5) | c3_1(a1640)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 1.36/1.55 tff(862,plain,
% 1.36/1.55 ((~hskp5) | c3_1(a1640)),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[861, 860])).
% 1.36/1.55 tff(863,plain,
% 1.36/1.55 ((~hskp5) | c3_1(a1640)),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[862, 860])).
% 1.36/1.55 tff(864,plain,
% 1.36/1.55 ((~hskp5) | c3_1(a1640)),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[863, 860])).
% 1.36/1.55 tff(865,plain,
% 1.36/1.55 ((~hskp5) | c3_1(a1640)),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[864, 860])).
% 1.36/1.55 tff(866,plain,
% 1.36/1.55 ((~hskp5) | c3_1(a1640)),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[865, 860])).
% 1.36/1.55 tff(867,plain,
% 1.36/1.55 (c3_1(a1640)),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[866, 835])).
% 1.36/1.55 tff(868,plain,
% 1.36/1.55 (((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | c2_1(a1640) | (~ndr1_0) | (~c3_1(a1640)) | (~c1_1(a1640)))) <=> ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp3 | c2_1(a1640) | (~ndr1_0) | (~c3_1(a1640)) | (~c1_1(a1640)))),
% 1.36/1.55 inference(rewrite,[status(thm)],[])).
% 1.36/1.55 tff(869,plain,
% 1.36/1.55 ((hskp21 | hskp3 | (~ndr1_0) | c2_1(a1640) | (~c3_1(a1640)) | (~c1_1(a1640))) <=> (hskp21 | hskp3 | c2_1(a1640) | (~ndr1_0) | (~c3_1(a1640)) | (~c1_1(a1640)))),
% 1.36/1.55 inference(rewrite,[status(thm)],[])).
% 1.36/1.55 tff(870,plain,
% 1.36/1.55 (((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | (~ndr1_0) | c2_1(a1640) | (~c3_1(a1640)) | (~c1_1(a1640)))) <=> ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | c2_1(a1640) | (~ndr1_0) | (~c3_1(a1640)) | (~c1_1(a1640))))),
% 1.36/1.55 inference(monotonicity,[status(thm)],[869])).
% 1.36/1.55 tff(871,plain,
% 1.36/1.55 (((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | (~ndr1_0) | c2_1(a1640) | (~c3_1(a1640)) | (~c1_1(a1640)))) <=> ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp3 | c2_1(a1640) | (~ndr1_0) | (~c3_1(a1640)) | (~c1_1(a1640)))),
% 1.36/1.55 inference(transitivity,[status(thm)],[870, 868])).
% 1.36/1.55 tff(872,plain,
% 1.36/1.55 ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | (~ndr1_0) | c2_1(a1640) | (~c3_1(a1640)) | (~c1_1(a1640)))),
% 1.36/1.55 inference(quant_inst,[status(thm)],[])).
% 1.36/1.55 tff(873,plain,
% 1.36/1.55 ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp3 | c2_1(a1640) | (~ndr1_0) | (~c3_1(a1640)) | (~c1_1(a1640))),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[872, 871])).
% 1.36/1.55 tff(874,plain,
% 1.36/1.55 (hskp21 | (~c1_1(a1640))),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[873, 119, 661, 867, 841, 769])).
% 1.36/1.55 tff(875,plain,
% 1.36/1.55 (hskp21),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[874, 859])).
% 1.36/1.55 tff(876,plain,
% 1.36/1.55 (~c1_1(a1691)),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[697, 875])).
% 1.36/1.55 tff(877,plain,
% 1.36/1.55 (c0_1(a1664)),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[347, 814])).
% 1.36/1.55 tff(878,plain,
% 1.36/1.55 (c3_1(a1691)),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[713, 875])).
% 1.36/1.55 tff(879,plain,
% 1.36/1.55 (c2_1(a1691)),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[738, 875])).
% 1.36/1.55 tff(880,plain,
% 1.36/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1691) | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664)) | (~c3_1(a1691)) | c0_1(a1691) | (~c2_1(a1691)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1691) | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664)) | (~c3_1(a1691)) | c0_1(a1691) | (~c2_1(a1691)))),
% 1.36/1.55 inference(rewrite,[status(thm)],[])).
% 1.36/1.55 tff(881,plain,
% 1.36/1.55 (((~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1691) | c0_1(a1691) | (~c2_1(a1691))) <=> (c1_1(a1691) | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664)) | (~c3_1(a1691)) | c0_1(a1691) | (~c2_1(a1691)))),
% 1.36/1.55 inference(rewrite,[status(thm)],[])).
% 1.36/1.55 tff(882,plain,
% 1.36/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1691) | c0_1(a1691) | (~c2_1(a1691)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1691) | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664)) | (~c3_1(a1691)) | c0_1(a1691) | (~c2_1(a1691))))),
% 1.36/1.55 inference(monotonicity,[status(thm)],[881])).
% 1.36/1.55 tff(883,plain,
% 1.36/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1691) | c0_1(a1691) | (~c2_1(a1691)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1691) | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664)) | (~c3_1(a1691)) | c0_1(a1691) | (~c2_1(a1691)))),
% 1.36/1.55 inference(transitivity,[status(thm)],[882, 880])).
% 1.36/1.55 tff(884,plain,
% 1.36/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1691) | c0_1(a1691) | (~c2_1(a1691)))),
% 1.36/1.55 inference(quant_inst,[status(thm)],[])).
% 1.36/1.55 tff(885,plain,
% 1.36/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1691) | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664)) | (~c3_1(a1691)) | c0_1(a1691) | (~c2_1(a1691))),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[884, 883])).
% 1.36/1.55 tff(886,plain,
% 1.36/1.55 (c0_1(a1691)),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[885, 119, 879, 878, 877, 876, 816, 815, 812])).
% 1.36/1.55 tff(887,plain,
% 1.36/1.55 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | c1_1(a1691) | c2_1(a1640) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c0_1(a1691)) | (~c2_1(a1691)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp2 | c1_1(a1691) | c2_1(a1640) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c0_1(a1691)) | (~c2_1(a1691)))),
% 1.36/1.55 inference(rewrite,[status(thm)],[])).
% 1.36/1.55 tff(888,plain,
% 1.36/1.55 ((hskp2 | (~ndr1_0) | c2_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c1_1(a1691) | (~c2_1(a1691)) | (~c0_1(a1691))) <=> (hskp2 | c1_1(a1691) | c2_1(a1640) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c0_1(a1691)) | (~c2_1(a1691)))),
% 1.36/1.55 inference(rewrite,[status(thm)],[])).
% 1.36/1.55 tff(889,plain,
% 1.36/1.55 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c1_1(a1691) | (~c2_1(a1691)) | (~c0_1(a1691)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | c1_1(a1691) | c2_1(a1640) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c0_1(a1691)) | (~c2_1(a1691))))),
% 1.36/1.55 inference(monotonicity,[status(thm)],[888])).
% 1.36/1.55 tff(890,plain,
% 1.36/1.55 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c1_1(a1691) | (~c2_1(a1691)) | (~c0_1(a1691)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp2 | c1_1(a1691) | c2_1(a1640) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c0_1(a1691)) | (~c2_1(a1691)))),
% 1.36/1.55 inference(transitivity,[status(thm)],[889, 887])).
% 1.36/1.55 tff(891,plain,
% 1.36/1.55 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c1_1(a1691) | (~c2_1(a1691)) | (~c0_1(a1691)))),
% 1.36/1.55 inference(quant_inst,[status(thm)],[])).
% 1.36/1.55 tff(892,plain,
% 1.36/1.55 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp2 | c1_1(a1691) | c2_1(a1640) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c0_1(a1691)) | (~c2_1(a1691))),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[891, 890])).
% 1.36/1.55 tff(893,plain,
% 1.36/1.55 ($false),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[892, 119, 500, 879, 851, 867, 876, 841, 639, 886])).
% 1.36/1.55 tff(894,plain,(hskp0 | hskp2 | hskp3 | (~c1_1(a1650)) | (~c1_1(a1643)) | c0_1(a1650) | c3_1(a1650) | c3_1(a1643) | (~c0_1(a1643)) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.36/1.55 tff(895,plain,
% 1.36/1.55 (hskp0),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[894, 802, 661, 706, 500, 674, 668, 281, 794, 21])).
% 1.36/1.55 tff(896,plain,
% 1.36/1.55 (c3_1(a1634)),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[490, 895])).
% 1.36/1.55 tff(897,assumption,(~c0_1(a1634)), introduced(assumption)).
% 1.36/1.55 tff(898,plain,
% 1.36/1.55 (((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (c0_1(a1634) | c0_1(a1650) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c2_1(a1650)) | (~c1_1(a1650)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | c0_1(a1634) | c0_1(a1650) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.36/1.55 inference(rewrite,[status(thm)],[])).
% 1.36/1.55 tff(899,plain,
% 1.36/1.55 (((~ndr1_0) | c0_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1634) | c0_1(a1634) | (~c3_1(a1634))) <=> (c0_1(a1634) | c0_1(a1650) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.36/1.55 inference(rewrite,[status(thm)],[])).
% 1.36/1.55 tff(900,plain,
% 1.36/1.55 (((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | ((~ndr1_0) | c0_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1634) | c0_1(a1634) | (~c3_1(a1634)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (c0_1(a1634) | c0_1(a1650) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c2_1(a1650)) | (~c1_1(a1650))))),
% 1.36/1.55 inference(monotonicity,[status(thm)],[899])).
% 1.36/1.55 tff(901,plain,
% 1.36/1.55 (((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | ((~ndr1_0) | c0_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1634) | c0_1(a1634) | (~c3_1(a1634)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | c0_1(a1634) | c0_1(a1650) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.36/1.55 inference(transitivity,[status(thm)],[900, 898])).
% 1.36/1.55 tff(902,plain,
% 1.36/1.55 ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | ((~ndr1_0) | c0_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1634) | c0_1(a1634) | (~c3_1(a1634)))),
% 1.36/1.55 inference(quant_inst,[status(thm)],[])).
% 1.36/1.55 tff(903,plain,
% 1.36/1.55 ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | c0_1(a1634) | c0_1(a1650) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c2_1(a1650)) | (~c1_1(a1650))),
% 1.36/1.55 inference(modus_ponens,[status(thm)],[902, 901])).
% 1.36/1.55 tff(904,plain,
% 1.36/1.55 (c0_1(a1634) | (~c3_1(a1634)) | (~c2_1(a1650))),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[903, 119, 852, 843, 503, 691])).
% 1.36/1.55 tff(905,plain,
% 1.36/1.55 (~c3_1(a1634)),
% 1.36/1.55 inference(unit_resolution,[status(thm)],[904, 897, 34])).
% 1.36/1.55 tff(906,plain,
% 1.36/1.55 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 1.36/1.56 inference(bind,[status(th)],[])).
% 1.36/1.56 tff(907,plain,
% 1.36/1.56 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.36/1.56 inference(quant_intro,[status(thm)],[906])).
% 1.36/1.56 tff(908,plain,
% 1.36/1.56 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.36/1.56 inference(rewrite,[status(thm)],[])).
% 1.36/1.56 tff(909,plain,
% 1.36/1.56 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp4) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp4))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 1.36/1.56 inference(bind,[status(th)],[])).
% 1.36/1.56 tff(910,plain,
% 1.36/1.56 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.36/1.56 inference(quant_intro,[status(thm)],[909])).
% 1.36/1.56 tff(911,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 1.36/1.56 tff(912,plain,
% 1.36/1.56 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[911, 910])).
% 1.36/1.56 tff(913,plain,
% 1.36/1.56 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[912, 908])).
% 1.36/1.56 tff(914,plain,(
% 1.36/1.56 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.36/1.56 inference(skolemize,[status(sab)],[913])).
% 1.36/1.56 tff(915,plain,
% 1.36/1.56 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[914, 907])).
% 1.36/1.56 tff(916,plain,
% 1.36/1.56 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | c0_1(a1634) | c3_1(a1634) | c2_1(a1643) | c1_1(a1634) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c0_1(a1634) | c3_1(a1634) | c2_1(a1643) | c1_1(a1634) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643)))),
% 1.36/1.56 inference(rewrite,[status(thm)],[])).
% 1.36/1.56 tff(917,plain,
% 1.36/1.56 ((hskp4 | (~ndr1_0) | c2_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c1_1(a1634) | c0_1(a1634) | c3_1(a1634)) <=> (hskp4 | c0_1(a1634) | c3_1(a1634) | c2_1(a1643) | c1_1(a1634) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643)))),
% 1.36/1.56 inference(rewrite,[status(thm)],[])).
% 1.36/1.56 tff(918,plain,
% 1.36/1.56 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c1_1(a1634) | c0_1(a1634) | c3_1(a1634))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | c0_1(a1634) | c3_1(a1634) | c2_1(a1643) | c1_1(a1634) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643))))),
% 1.36/1.56 inference(monotonicity,[status(thm)],[917])).
% 1.36/1.56 tff(919,plain,
% 1.36/1.56 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c1_1(a1634) | c0_1(a1634) | c3_1(a1634))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c0_1(a1634) | c3_1(a1634) | c2_1(a1643) | c1_1(a1634) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643)))),
% 1.36/1.56 inference(transitivity,[status(thm)],[918, 916])).
% 1.36/1.56 tff(920,plain,
% 1.36/1.56 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c1_1(a1634) | c0_1(a1634) | c3_1(a1634))),
% 1.36/1.56 inference(quant_inst,[status(thm)],[])).
% 1.36/1.56 tff(921,plain,
% 1.36/1.56 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c0_1(a1634) | c3_1(a1634) | c2_1(a1643) | c1_1(a1634) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643))),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[920, 919])).
% 1.36/1.56 tff(922,plain,
% 1.36/1.56 (hskp4 | c0_1(a1634) | c3_1(a1634) | (~c1_1(a1643)) | (~c0_1(a1643))),
% 1.36/1.56 inference(unit_resolution,[status(thm)],[921, 119, 282, 503, 915])).
% 1.36/1.56 tff(923,plain,
% 1.36/1.56 (hskp4),
% 1.36/1.56 inference(unit_resolution,[status(thm)],[922, 897, 318, 905, 813])).
% 1.36/1.56 tff(924,plain,
% 1.36/1.56 (((~hskp4) | (~c2_1(a1639))) <=> ((~hskp4) | (~c2_1(a1639)))),
% 1.36/1.56 inference(rewrite,[status(thm)],[])).
% 1.36/1.56 tff(925,plain,
% 1.36/1.56 (((~c2_1(a1639)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a1639)))),
% 1.36/1.56 inference(rewrite,[status(thm)],[])).
% 1.36/1.56 tff(926,axiom,((~c2_1(a1639)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 1.36/1.56 tff(927,plain,
% 1.36/1.56 ((~hskp4) | (~c2_1(a1639))),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[926, 925])).
% 1.36/1.56 tff(928,plain,
% 1.36/1.56 ((~hskp4) | (~c2_1(a1639))),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[927, 924])).
% 1.36/1.56 tff(929,plain,
% 1.36/1.56 (~c2_1(a1639)),
% 1.36/1.56 inference(unit_resolution,[status(thm)],[928, 923])).
% 1.36/1.56 tff(930,plain,
% 1.36/1.56 (((~hskp4) | (~c1_1(a1639))) <=> ((~hskp4) | (~c1_1(a1639)))),
% 1.36/1.56 inference(rewrite,[status(thm)],[])).
% 1.36/1.56 tff(931,plain,
% 1.36/1.56 (((~c1_1(a1639)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a1639)))),
% 1.36/1.56 inference(rewrite,[status(thm)],[])).
% 1.36/1.56 tff(932,axiom,((~c1_1(a1639)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 1.36/1.56 tff(933,plain,
% 1.36/1.56 ((~hskp4) | (~c1_1(a1639))),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[932, 931])).
% 1.36/1.56 tff(934,plain,
% 1.36/1.56 ((~hskp4) | (~c1_1(a1639))),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[933, 930])).
% 1.36/1.56 tff(935,plain,
% 1.36/1.56 (~c1_1(a1639)),
% 1.36/1.56 inference(unit_resolution,[status(thm)],[934, 923])).
% 1.36/1.56 tff(936,plain,
% 1.36/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a1650) | c3_1(a1650) | c3_1(a1643) | c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | (~c0_1(a1639)) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c1_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a1650) | c3_1(a1650) | c3_1(a1643) | c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | (~c0_1(a1639)) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c1_1(a1650)))),
% 1.36/1.56 inference(rewrite,[status(thm)],[])).
% 1.36/1.56 tff(937,plain,
% 1.36/1.56 (((~ndr1_0) | c3_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c2_1(a1639) | c1_1(a1639) | (~c0_1(a1639)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650))) <=> (c0_1(a1650) | c3_1(a1650) | c3_1(a1643) | c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | (~c0_1(a1639)) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c1_1(a1650)))),
% 1.36/1.56 inference(rewrite,[status(thm)],[])).
% 1.36/1.56 tff(938,plain,
% 1.36/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c2_1(a1639) | c1_1(a1639) | (~c0_1(a1639)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a1650) | c3_1(a1650) | c3_1(a1643) | c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | (~c0_1(a1639)) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c1_1(a1650))))),
% 1.36/1.56 inference(monotonicity,[status(thm)],[937])).
% 1.36/1.56 tff(939,plain,
% 1.36/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c2_1(a1639) | c1_1(a1639) | (~c0_1(a1639)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a1650) | c3_1(a1650) | c3_1(a1643) | c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | (~c0_1(a1639)) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c1_1(a1650)))),
% 1.36/1.56 inference(transitivity,[status(thm)],[938, 936])).
% 1.36/1.56 tff(940,plain,
% 1.36/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c2_1(a1639) | c1_1(a1639) | (~c0_1(a1639)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)))),
% 1.36/1.56 inference(quant_inst,[status(thm)],[])).
% 1.36/1.56 tff(941,plain,
% 1.36/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a1650) | c3_1(a1650) | c3_1(a1643) | c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | (~c0_1(a1639)) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c1_1(a1650))),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[940, 939])).
% 1.36/1.56 tff(942,plain,
% 1.36/1.56 (~c0_1(a1639)),
% 1.36/1.56 inference(unit_resolution,[status(thm)],[941, 119, 852, 318, 843, 842, 281, 935, 929, 826, 813])).
% 1.36/1.56 tff(943,plain,
% 1.36/1.56 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.36/1.56 inference(bind,[status(th)],[])).
% 1.36/1.56 tff(944,plain,
% 1.36/1.56 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.56 inference(quant_intro,[status(thm)],[943])).
% 1.36/1.56 tff(945,plain,
% 1.36/1.56 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.56 inference(rewrite,[status(thm)],[])).
% 1.36/1.56 tff(946,plain,
% 1.36/1.56 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.36/1.56 inference(bind,[status(th)],[])).
% 1.36/1.56 tff(947,plain,
% 1.36/1.56 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.56 inference(quant_intro,[status(thm)],[946])).
% 1.36/1.56 tff(948,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 1.36/1.56 tff(949,plain,
% 1.36/1.56 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[948, 947])).
% 1.36/1.56 tff(950,plain,
% 1.36/1.56 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[949, 945])).
% 1.36/1.56 tff(951,plain,(
% 1.36/1.56 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.56 inference(skolemize,[status(sab)],[950])).
% 1.36/1.56 tff(952,plain,
% 1.36/1.56 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[951, 944])).
% 1.36/1.56 tff(953,plain,
% 1.36/1.56 (~hskp0),
% 1.36/1.56 inference(unit_resolution,[status(thm)],[498, 897])).
% 1.36/1.56 tff(954,plain,
% 1.36/1.56 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c2_1(a1643) | c3_1(a1643) | c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | c0_1(a1639) | (~c0_1(a1643)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a1643) | c3_1(a1643) | c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | c0_1(a1639) | (~c0_1(a1643)))),
% 1.36/1.56 inference(rewrite,[status(thm)],[])).
% 1.36/1.56 tff(955,plain,
% 1.36/1.56 ((hskp0 | (~ndr1_0) | c2_1(a1643) | c3_1(a1643) | (~c0_1(a1643)) | c2_1(a1639) | c1_1(a1639) | c0_1(a1639)) <=> (hskp0 | c2_1(a1643) | c3_1(a1643) | c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | c0_1(a1639) | (~c0_1(a1643)))),
% 1.36/1.56 inference(rewrite,[status(thm)],[])).
% 1.36/1.56 tff(956,plain,
% 1.36/1.56 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1643) | c3_1(a1643) | (~c0_1(a1643)) | c2_1(a1639) | c1_1(a1639) | c0_1(a1639))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c2_1(a1643) | c3_1(a1643) | c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | c0_1(a1639) | (~c0_1(a1643))))),
% 1.36/1.56 inference(monotonicity,[status(thm)],[955])).
% 1.36/1.56 tff(957,plain,
% 1.36/1.56 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1643) | c3_1(a1643) | (~c0_1(a1643)) | c2_1(a1639) | c1_1(a1639) | c0_1(a1639))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a1643) | c3_1(a1643) | c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | c0_1(a1639) | (~c0_1(a1643)))),
% 1.36/1.56 inference(transitivity,[status(thm)],[956, 954])).
% 1.36/1.56 tff(958,plain,
% 1.36/1.56 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1643) | c3_1(a1643) | (~c0_1(a1643)) | c2_1(a1639) | c1_1(a1639) | c0_1(a1639))),
% 1.36/1.56 inference(quant_inst,[status(thm)],[])).
% 1.36/1.56 tff(959,plain,
% 1.36/1.56 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a1643) | c3_1(a1643) | c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | c0_1(a1639) | (~c0_1(a1643))),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[958, 957])).
% 1.36/1.56 tff(960,plain,
% 1.36/1.56 ($false),
% 1.36/1.56 inference(unit_resolution,[status(thm)],[959, 119, 953, 282, 281, 935, 929, 952, 813, 942])).
% 1.36/1.56 tff(961,plain,(c0_1(a1634) | c2_1(a1643) | c3_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1650)) | (~c1_1(a1643)) | c0_1(a1650) | c3_1(a1650) | c1_1(a1634) | (~c2_1(a1650))), inference(lemma,lemma(discharge,[]))).
% 1.36/1.56 tff(962,plain,
% 1.36/1.56 (c0_1(a1634)),
% 1.36/1.56 inference(unit_resolution,[status(thm)],[961, 281, 282, 794, 706, 802, 674, 668, 503, 681])).
% 1.36/1.56 tff(963,assumption,(~c2_1(a1634)), introduced(assumption)).
% 1.36/1.56 tff(964,plain,
% 1.36/1.56 (^[U: $i] : refl((hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 1.36/1.56 inference(bind,[status(th)],[])).
% 1.36/1.56 tff(965,plain,
% 1.36/1.56 (![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.36/1.56 inference(quant_intro,[status(thm)],[964])).
% 1.36/1.56 tff(966,plain,
% 1.36/1.56 (![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.36/1.56 inference(rewrite,[status(thm)],[])).
% 1.36/1.56 tff(967,plain,
% 1.36/1.56 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp16))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) | hskp10) <=> ((hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp10))), rewrite(((hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp10) <=> (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) | hskp10) <=> (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 1.36/1.56 inference(bind,[status(th)],[])).
% 1.36/1.56 tff(968,plain,
% 1.36/1.56 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) | hskp10) <=> ![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.36/1.56 inference(quant_intro,[status(thm)],[967])).
% 1.36/1.56 tff(969,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 1.36/1.56 tff(970,plain,
% 1.36/1.56 (![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[969, 968])).
% 1.36/1.56 tff(971,plain,
% 1.36/1.56 (![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[970, 966])).
% 1.36/1.56 tff(972,plain,(
% 1.36/1.56 ![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.36/1.56 inference(skolemize,[status(sab)],[971])).
% 1.36/1.56 tff(973,plain,
% 1.36/1.56 (![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[972, 965])).
% 1.36/1.56 tff(974,plain,
% 1.36/1.56 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp16 | hskp10 | c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp16 | hskp10 | c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)))),
% 1.36/1.56 inference(rewrite,[status(thm)],[])).
% 1.36/1.56 tff(975,plain,
% 1.36/1.56 ((hskp16 | hskp10 | (~ndr1_0) | c2_1(a1634) | c1_1(a1634) | (~c3_1(a1634))) <=> (hskp16 | hskp10 | c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)))),
% 1.36/1.56 inference(rewrite,[status(thm)],[])).
% 1.36/1.56 tff(976,plain,
% 1.36/1.56 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp16 | hskp10 | (~ndr1_0) | c2_1(a1634) | c1_1(a1634) | (~c3_1(a1634)))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp16 | hskp10 | c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634))))),
% 1.36/1.56 inference(monotonicity,[status(thm)],[975])).
% 1.36/1.56 tff(977,plain,
% 1.36/1.56 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp16 | hskp10 | (~ndr1_0) | c2_1(a1634) | c1_1(a1634) | (~c3_1(a1634)))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp16 | hskp10 | c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)))),
% 1.36/1.56 inference(transitivity,[status(thm)],[976, 974])).
% 1.36/1.56 tff(978,plain,
% 1.36/1.56 ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp16 | hskp10 | (~ndr1_0) | c2_1(a1634) | c1_1(a1634) | (~c3_1(a1634)))),
% 1.36/1.56 inference(quant_inst,[status(thm)],[])).
% 1.36/1.56 tff(979,plain,
% 1.36/1.56 ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp16 | hskp10 | c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634))),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[978, 977])).
% 1.36/1.56 tff(980,plain,
% 1.36/1.56 (hskp16 | hskp10 | c2_1(a1634) | (~c3_1(a1634))),
% 1.36/1.56 inference(unit_resolution,[status(thm)],[979, 119, 503, 973])).
% 1.36/1.56 tff(981,plain,
% 1.36/1.56 (hskp16),
% 1.36/1.56 inference(unit_resolution,[status(thm)],[980, 963, 56, 502])).
% 1.36/1.56 tff(982,plain,
% 1.36/1.56 (((~hskp16) | (~c1_1(a1667))) <=> ((~hskp16) | (~c1_1(a1667)))),
% 1.36/1.56 inference(rewrite,[status(thm)],[])).
% 1.36/1.56 tff(983,plain,
% 1.36/1.56 (((~c1_1(a1667)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a1667)))),
% 1.36/1.56 inference(rewrite,[status(thm)],[])).
% 1.36/1.56 tff(984,axiom,((~c1_1(a1667)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 1.36/1.56 tff(985,plain,
% 1.36/1.56 ((~hskp16) | (~c1_1(a1667))),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[984, 983])).
% 1.36/1.56 tff(986,plain,
% 1.36/1.56 ((~hskp16) | (~c1_1(a1667))),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[985, 982])).
% 1.36/1.56 tff(987,plain,
% 1.36/1.56 (~c1_1(a1667)),
% 1.36/1.56 inference(unit_resolution,[status(thm)],[986, 981])).
% 1.36/1.56 tff(988,plain,
% 1.36/1.56 (((~hskp16) | c2_1(a1667)) <=> ((~hskp16) | c2_1(a1667))),
% 1.36/1.56 inference(rewrite,[status(thm)],[])).
% 1.36/1.56 tff(989,axiom,((~hskp16) | c2_1(a1667)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 1.36/1.56 tff(990,plain,
% 1.36/1.56 ((~hskp16) | c2_1(a1667)),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[989, 988])).
% 1.36/1.56 tff(991,plain,
% 1.36/1.56 ((~hskp16) | c2_1(a1667)),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[990, 988])).
% 1.36/1.56 tff(992,plain,
% 1.36/1.56 ((~hskp16) | c2_1(a1667)),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[991, 988])).
% 1.36/1.56 tff(993,plain,
% 1.36/1.56 ((~hskp16) | c2_1(a1667)),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[992, 988])).
% 1.36/1.56 tff(994,plain,
% 1.36/1.56 ((~hskp16) | c2_1(a1667)),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[993, 988])).
% 1.36/1.56 tff(995,plain,
% 1.36/1.56 (c2_1(a1667)),
% 1.36/1.56 inference(unit_resolution,[status(thm)],[994, 981])).
% 1.36/1.56 tff(996,plain,
% 1.36/1.56 (((~hskp16) | c0_1(a1667)) <=> ((~hskp16) | c0_1(a1667))),
% 1.36/1.56 inference(rewrite,[status(thm)],[])).
% 1.36/1.56 tff(997,axiom,((~hskp16) | c0_1(a1667)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 1.36/1.56 tff(998,plain,
% 1.36/1.56 ((~hskp16) | c0_1(a1667)),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[997, 996])).
% 1.36/1.56 tff(999,plain,
% 1.36/1.56 ((~hskp16) | c0_1(a1667)),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[998, 996])).
% 1.36/1.56 tff(1000,plain,
% 1.36/1.56 ((~hskp16) | c0_1(a1667)),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[999, 996])).
% 1.36/1.56 tff(1001,plain,
% 1.36/1.56 ((~hskp16) | c0_1(a1667)),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[1000, 996])).
% 1.36/1.56 tff(1002,plain,
% 1.36/1.56 ((~hskp16) | c0_1(a1667)),
% 1.36/1.56 inference(modus_ponens,[status(thm)],[1001, 996])).
% 1.36/1.56 tff(1003,plain,
% 1.36/1.56 (c0_1(a1667)),
% 1.36/1.56 inference(unit_resolution,[status(thm)],[1002, 981])).
% 1.36/1.56 tff(1004,plain,
% 1.36/1.56 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | c1_1(a1667) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c0_1(a1667)) | (~c2_1(a1667)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp2 | c1_1(a1667) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c0_1(a1667)) | (~c2_1(a1667)))),
% 1.36/1.56 inference(rewrite,[status(thm)],[])).
% 1.36/1.56 tff(1005,plain,
% 1.36/1.56 ((hskp2 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1667) | (~c2_1(a1667)) | (~c0_1(a1667))) <=> (hskp2 | c1_1(a1667) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c0_1(a1667)) | (~c2_1(a1667)))),
% 1.36/1.56 inference(rewrite,[status(thm)],[])).
% 1.36/1.56 tff(1006,plain,
% 1.36/1.56 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1667) | (~c2_1(a1667)) | (~c0_1(a1667)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | c1_1(a1667) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c0_1(a1667)) | (~c2_1(a1667))))),
% 1.36/1.56 inference(monotonicity,[status(thm)],[1005])).
% 1.36/1.56 tff(1007,plain,
% 1.36/1.56 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1667) | (~c2_1(a1667)) | (~c0_1(a1667)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp2 | c1_1(a1667) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c0_1(a1667)) | (~c2_1(a1667)))),
% 1.36/1.57 inference(transitivity,[status(thm)],[1006, 1004])).
% 1.36/1.57 tff(1008,plain,
% 1.36/1.57 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1667) | (~c2_1(a1667)) | (~c0_1(a1667)))),
% 1.36/1.57 inference(quant_inst,[status(thm)],[])).
% 1.36/1.57 tff(1009,plain,
% 1.36/1.57 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp2 | c1_1(a1667) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c0_1(a1667)) | (~c2_1(a1667))),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1008, 1007])).
% 1.36/1.57 tff(1010,plain,
% 1.36/1.57 ($false),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[1009, 119, 500, 1003, 995, 504, 502, 987, 639, 963])).
% 1.36/1.57 tff(1011,plain,(c2_1(a1634) | hskp2 | (~c0_1(a1634)) | (~c3_1(a1634)) | hskp10 | c1_1(a1634)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.57 tff(1012,plain,
% 1.36/1.57 (c2_1(a1634)),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[1011, 962, 500, 896, 56, 503])).
% 1.36/1.57 tff(1013,plain,
% 1.36/1.57 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp18 | c3_1(a1650) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | (~c2_1(a1650)) | (~c1_1(a1650)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp18 | c3_1(a1650) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.36/1.57 inference(rewrite,[status(thm)],[])).
% 1.36/1.57 tff(1014,plain,
% 1.36/1.57 ((hskp18 | (~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1634) | (~c3_1(a1634)) | (~c2_1(a1634))) <=> (hskp18 | c3_1(a1650) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.36/1.57 inference(rewrite,[status(thm)],[])).
% 1.36/1.57 tff(1015,plain,
% 1.36/1.57 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1634) | (~c3_1(a1634)) | (~c2_1(a1634)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp18 | c3_1(a1650) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | (~c2_1(a1650)) | (~c1_1(a1650))))),
% 1.36/1.57 inference(monotonicity,[status(thm)],[1014])).
% 1.36/1.57 tff(1016,plain,
% 1.36/1.57 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1634) | (~c3_1(a1634)) | (~c2_1(a1634)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp18 | c3_1(a1650) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.36/1.57 inference(transitivity,[status(thm)],[1015, 1013])).
% 1.36/1.57 tff(1017,plain,
% 1.36/1.57 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1634) | (~c3_1(a1634)) | (~c2_1(a1634)))),
% 1.36/1.57 inference(quant_inst,[status(thm)],[])).
% 1.36/1.57 tff(1018,plain,
% 1.36/1.57 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp18 | c3_1(a1650) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | (~c2_1(a1650)) | (~c1_1(a1650))),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1017, 1016])).
% 1.36/1.57 tff(1019,plain,
% 1.36/1.57 (hskp18 | (~c2_1(a1634)) | (~c3_1(a1634))),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[1018, 119, 706, 668, 503, 731, 681])).
% 1.36/1.57 tff(1020,plain,
% 1.36/1.57 (hskp18),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[1019, 1012, 896])).
% 1.36/1.57 tff(1021,plain,
% 1.36/1.57 (~c2_1(a1680)),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[70, 1020])).
% 1.36/1.57 tff(1022,plain,
% 1.36/1.57 (~c0_1(a1680)),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[76, 1020])).
% 1.36/1.57 tff(1023,plain,
% 1.36/1.57 (c3_1(a1680)),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[142, 119, 56, 21, 1022, 1021, 136])).
% 1.36/1.57 tff(1024,plain,
% 1.36/1.57 (c1_1(a1680)),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[84, 1020])).
% 1.36/1.57 tff(1025,plain,
% 1.36/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1680) | c3_1(a1650) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1680)) | (~c1_1(a1680)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1680) | c3_1(a1650) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1680)) | (~c1_1(a1680)))),
% 1.36/1.57 inference(rewrite,[status(thm)],[])).
% 1.36/1.57 tff(1026,plain,
% 1.36/1.57 (((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1680) | (~c1_1(a1680)) | (~c3_1(a1680))) <=> (c0_1(a1680) | c3_1(a1650) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1680)) | (~c1_1(a1680)))),
% 1.36/1.57 inference(rewrite,[status(thm)],[])).
% 1.36/1.57 tff(1027,plain,
% 1.36/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1680) | (~c1_1(a1680)) | (~c3_1(a1680)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1680) | c3_1(a1650) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1680)) | (~c1_1(a1680))))),
% 1.36/1.57 inference(monotonicity,[status(thm)],[1026])).
% 1.36/1.57 tff(1028,plain,
% 1.36/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1680) | (~c1_1(a1680)) | (~c3_1(a1680)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1680) | c3_1(a1650) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1680)) | (~c1_1(a1680)))),
% 1.36/1.57 inference(transitivity,[status(thm)],[1027, 1025])).
% 1.36/1.57 tff(1029,plain,
% 1.36/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1680) | (~c1_1(a1680)) | (~c3_1(a1680)))),
% 1.36/1.57 inference(quant_inst,[status(thm)],[])).
% 1.36/1.57 tff(1030,plain,
% 1.36/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1680) | c3_1(a1650) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1680)) | (~c1_1(a1680))),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1029, 1028])).
% 1.36/1.57 tff(1031,plain,
% 1.36/1.57 ($false),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[1030, 119, 1024, 706, 962, 896, 1022, 668, 503, 20, 681, 1023])).
% 1.36/1.57 tff(1032,plain,(c3_1(a1643) | c1_1(a1634) | hskp10 | hskp1 | hskp2 | hskp3 | c2_1(a1643)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.57 tff(1033,plain,
% 1.36/1.57 ($false),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[1032, 786, 785, 56, 21, 500, 661, 503])).
% 1.36/1.57 tff(1034,plain,((~hskp8) | hskp10 | hskp1 | hskp2 | hskp3 | c1_1(a1634)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.57 tff(1035,plain,
% 1.36/1.57 (~hskp8),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[1034, 500, 21, 56, 661, 503])).
% 1.36/1.57 tff(1036,plain,
% 1.36/1.57 (^[U: $i] : refl((hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 1.36/1.57 inference(bind,[status(th)],[])).
% 1.36/1.57 tff(1037,plain,
% 1.36/1.57 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.36/1.57 inference(quant_intro,[status(thm)],[1036])).
% 1.36/1.57 tff(1038,plain,
% 1.36/1.57 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.36/1.57 inference(rewrite,[status(thm)],[])).
% 1.36/1.57 tff(1039,plain,
% 1.36/1.57 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp3) <=> ((hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp3))), rewrite(((hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp3) <=> (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp3) <=> (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 1.36/1.57 inference(bind,[status(th)],[])).
% 1.36/1.57 tff(1040,plain,
% 1.36/1.57 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp3) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.36/1.57 inference(quant_intro,[status(thm)],[1039])).
% 1.36/1.57 tff(1041,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause141')).
% 1.36/1.57 tff(1042,plain,
% 1.36/1.57 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1041, 1040])).
% 1.36/1.57 tff(1043,plain,
% 1.36/1.57 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1042, 1038])).
% 1.36/1.57 tff(1044,plain,(
% 1.36/1.57 ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.36/1.57 inference(skolemize,[status(sab)],[1043])).
% 1.36/1.57 tff(1045,plain,
% 1.36/1.57 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1044, 1037])).
% 1.36/1.57 tff(1046,plain,
% 1.36/1.57 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a1634) | c1_1(a1634) | (~ndr1_0) | c2_1(a1634))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a1634) | c1_1(a1634) | (~ndr1_0) | c2_1(a1634))),
% 1.36/1.57 inference(rewrite,[status(thm)],[])).
% 1.36/1.57 tff(1047,plain,
% 1.36/1.57 ((hskp3 | hskp2 | (~ndr1_0) | c2_1(a1634) | c1_1(a1634) | c0_1(a1634)) <=> (hskp3 | hskp2 | c0_1(a1634) | c1_1(a1634) | (~ndr1_0) | c2_1(a1634))),
% 1.36/1.57 inference(rewrite,[status(thm)],[])).
% 1.36/1.57 tff(1048,plain,
% 1.36/1.57 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a1634) | c1_1(a1634) | c0_1(a1634))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a1634) | c1_1(a1634) | (~ndr1_0) | c2_1(a1634)))),
% 1.36/1.57 inference(monotonicity,[status(thm)],[1047])).
% 1.36/1.57 tff(1049,plain,
% 1.36/1.57 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a1634) | c1_1(a1634) | c0_1(a1634))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a1634) | c1_1(a1634) | (~ndr1_0) | c2_1(a1634))),
% 1.36/1.57 inference(transitivity,[status(thm)],[1048, 1046])).
% 1.36/1.57 tff(1050,plain,
% 1.36/1.57 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a1634) | c1_1(a1634) | c0_1(a1634))),
% 1.36/1.57 inference(quant_inst,[status(thm)],[])).
% 1.36/1.57 tff(1051,plain,
% 1.36/1.57 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a1634) | c1_1(a1634) | (~ndr1_0) | c2_1(a1634)),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1050, 1049])).
% 1.36/1.57 tff(1052,plain,
% 1.36/1.57 (hskp2 | c0_1(a1634) | c2_1(a1634)),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[1051, 119, 661, 503, 1045])).
% 1.36/1.57 tff(1053,plain,
% 1.36/1.57 (c2_1(a1634)),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[1052, 897, 500])).
% 1.36/1.57 tff(1054,assumption,(~hskp8), introduced(assumption)).
% 1.36/1.57 tff(1055,plain,
% 1.36/1.57 (^[U: $i] : refl((hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 1.36/1.57 inference(bind,[status(th)],[])).
% 1.36/1.57 tff(1056,plain,
% 1.36/1.57 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.36/1.57 inference(quant_intro,[status(thm)],[1055])).
% 1.36/1.57 tff(1057,plain,
% 1.36/1.57 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.36/1.57 inference(rewrite,[status(thm)],[])).
% 1.36/1.57 tff(1058,plain,
% 1.36/1.57 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp7) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp7))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp7) | hskp8) <=> ((hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp8))), rewrite(((hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp8) <=> (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp7) | hskp8) <=> (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 1.36/1.57 inference(bind,[status(th)],[])).
% 1.36/1.57 tff(1059,plain,
% 1.36/1.57 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp7) | hskp8) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.36/1.57 inference(quant_intro,[status(thm)],[1058])).
% 1.36/1.57 tff(1060,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp7) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause144')).
% 1.36/1.57 tff(1061,plain,
% 1.36/1.57 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1060, 1059])).
% 1.36/1.57 tff(1062,plain,
% 1.36/1.57 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1061, 1057])).
% 1.36/1.57 tff(1063,plain,(
% 1.36/1.57 ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.36/1.57 inference(skolemize,[status(sab)],[1062])).
% 1.36/1.57 tff(1064,plain,
% 1.36/1.57 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1063, 1056])).
% 1.36/1.57 tff(1065,plain,
% 1.36/1.57 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp8 | hskp7 | c0_1(a1634) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp8 | hskp7 | c0_1(a1634) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)))),
% 1.36/1.57 inference(rewrite,[status(thm)],[])).
% 1.36/1.57 tff(1066,plain,
% 1.36/1.57 ((hskp8 | hskp7 | (~ndr1_0) | c1_1(a1634) | c0_1(a1634) | (~c2_1(a1634))) <=> (hskp8 | hskp7 | c0_1(a1634) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)))),
% 1.36/1.57 inference(rewrite,[status(thm)],[])).
% 1.36/1.57 tff(1067,plain,
% 1.36/1.57 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c1_1(a1634) | c0_1(a1634) | (~c2_1(a1634)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp8 | hskp7 | c0_1(a1634) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634))))),
% 1.36/1.57 inference(monotonicity,[status(thm)],[1066])).
% 1.36/1.57 tff(1068,plain,
% 1.36/1.57 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c1_1(a1634) | c0_1(a1634) | (~c2_1(a1634)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp8 | hskp7 | c0_1(a1634) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)))),
% 1.36/1.57 inference(transitivity,[status(thm)],[1067, 1065])).
% 1.36/1.57 tff(1069,plain,
% 1.36/1.57 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c1_1(a1634) | c0_1(a1634) | (~c2_1(a1634)))),
% 1.36/1.57 inference(quant_inst,[status(thm)],[])).
% 1.36/1.57 tff(1070,plain,
% 1.36/1.57 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp8 | hskp7 | c0_1(a1634) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634))),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1069, 1068])).
% 1.36/1.57 tff(1071,plain,
% 1.36/1.57 (hskp8 | hskp7 | c0_1(a1634) | (~c2_1(a1634))),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[1070, 119, 503, 1064])).
% 1.36/1.57 tff(1072,plain,
% 1.36/1.57 (hskp7),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[1071, 897, 1054, 1053])).
% 1.36/1.57 tff(1073,plain,
% 1.36/1.57 (~c3_1(a1642)),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[398, 1072])).
% 1.36/1.57 tff(1074,plain,
% 1.36/1.57 (~c2_1(a1642)),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[448, 1072])).
% 1.36/1.57 tff(1075,plain,
% 1.36/1.57 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c0_1(a1650) | c3_1(a1650) | c2_1(a1642) | c3_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c1_1(a1650)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c0_1(a1650) | c3_1(a1650) | c2_1(a1642) | c3_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c1_1(a1650)))),
% 1.36/1.57 inference(rewrite,[status(thm)],[])).
% 1.36/1.57 tff(1076,plain,
% 1.36/1.57 ((hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1642) | c1_1(a1642) | c3_1(a1642)) <=> (hskp3 | c0_1(a1650) | c3_1(a1650) | c2_1(a1642) | c3_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c1_1(a1650)))),
% 1.36/1.57 inference(rewrite,[status(thm)],[])).
% 1.36/1.57 tff(1077,plain,
% 1.36/1.57 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1642) | c1_1(a1642) | c3_1(a1642))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c0_1(a1650) | c3_1(a1650) | c2_1(a1642) | c3_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c1_1(a1650))))),
% 1.36/1.57 inference(monotonicity,[status(thm)],[1076])).
% 1.36/1.57 tff(1078,plain,
% 1.36/1.57 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1642) | c1_1(a1642) | c3_1(a1642))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c0_1(a1650) | c3_1(a1650) | c2_1(a1642) | c3_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c1_1(a1650)))),
% 1.36/1.57 inference(transitivity,[status(thm)],[1077, 1075])).
% 1.36/1.57 tff(1079,plain,
% 1.36/1.57 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1642) | c1_1(a1642) | c3_1(a1642))),
% 1.36/1.57 inference(quant_inst,[status(thm)],[])).
% 1.36/1.57 tff(1080,plain,
% 1.36/1.57 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c0_1(a1650) | c3_1(a1650) | c2_1(a1642) | c3_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c1_1(a1650))),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1079, 1078])).
% 1.36/1.57 tff(1081,plain,
% 1.36/1.57 (c1_1(a1642)),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[1080, 119, 661, 852, 843, 842, 1074, 1073, 10])).
% 1.36/1.57 tff(1082,plain,
% 1.36/1.57 (hskp5),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[834, 953, 21])).
% 1.36/1.57 tff(1083,plain,
% 1.36/1.57 (~c2_1(a1640)),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[840, 1082])).
% 1.36/1.57 tff(1084,plain,
% 1.36/1.57 (c0_1(a1640)),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[850, 1082])).
% 1.36/1.57 tff(1085,plain,
% 1.36/1.57 (c0_1(a1642)),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[427, 1072])).
% 1.36/1.57 tff(1086,plain,
% 1.36/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a1650) | c3_1(a1650) | c3_1(a1642) | c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c1_1(a1642)) | (~c0_1(a1642)) | (~c1_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a1650) | c3_1(a1650) | c3_1(a1642) | c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c1_1(a1642)) | (~c0_1(a1642)) | (~c1_1(a1650)))),
% 1.36/1.57 inference(rewrite,[status(thm)],[])).
% 1.36/1.57 tff(1087,plain,
% 1.36/1.57 (((~ndr1_0) | c3_1(a1642) | (~c0_1(a1642)) | (~c1_1(a1642)) | c2_1(a1640) | c1_1(a1640) | (~c0_1(a1640)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650))) <=> (c0_1(a1650) | c3_1(a1650) | c3_1(a1642) | c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c1_1(a1642)) | (~c0_1(a1642)) | (~c1_1(a1650)))),
% 1.36/1.57 inference(rewrite,[status(thm)],[])).
% 1.36/1.57 tff(1088,plain,
% 1.36/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1642) | (~c0_1(a1642)) | (~c1_1(a1642)) | c2_1(a1640) | c1_1(a1640) | (~c0_1(a1640)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a1650) | c3_1(a1650) | c3_1(a1642) | c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c1_1(a1642)) | (~c0_1(a1642)) | (~c1_1(a1650))))),
% 1.36/1.57 inference(monotonicity,[status(thm)],[1087])).
% 1.36/1.57 tff(1089,plain,
% 1.36/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1642) | (~c0_1(a1642)) | (~c1_1(a1642)) | c2_1(a1640) | c1_1(a1640) | (~c0_1(a1640)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a1650) | c3_1(a1650) | c3_1(a1642) | c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c1_1(a1642)) | (~c0_1(a1642)) | (~c1_1(a1650)))),
% 1.36/1.57 inference(transitivity,[status(thm)],[1088, 1086])).
% 1.36/1.57 tff(1090,plain,
% 1.36/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1642) | (~c0_1(a1642)) | (~c1_1(a1642)) | c2_1(a1640) | c1_1(a1640) | (~c0_1(a1640)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)))),
% 1.36/1.57 inference(quant_inst,[status(thm)],[])).
% 1.36/1.57 tff(1091,plain,
% 1.36/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a1650) | c3_1(a1650) | c3_1(a1642) | c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c1_1(a1642)) | (~c0_1(a1642)) | (~c1_1(a1650))),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1090, 1089])).
% 1.36/1.57 tff(1092,plain,
% 1.36/1.57 (c1_1(a1640)),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[1091, 119, 852, 1085, 1084, 843, 842, 1073, 1083, 826, 1081])).
% 1.36/1.57 tff(1093,plain,
% 1.36/1.57 (c3_1(a1640)),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[866, 1082])).
% 1.36/1.57 tff(1094,assumption,(~hskp21), introduced(assumption)).
% 1.36/1.57 tff(1095,plain,
% 1.36/1.57 ($false),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[873, 119, 1094, 661, 1093, 1083, 769, 1092])).
% 1.36/1.57 tff(1096,plain,(c0_1(a1634) | hskp21 | hskp3 | (~c1_1(a1650)) | c0_1(a1650) | c3_1(a1650) | hskp1 | hskp8 | c1_1(a1634) | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.36/1.57 tff(1097,plain,
% 1.36/1.57 (c0_1(a1634)),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[1096, 1035, 661, 706, 674, 668, 21, 759, 503, 500])).
% 1.36/1.57 tff(1098,assumption,(~c3_1(a1634)), introduced(assumption)).
% 1.36/1.57 tff(1099,plain,
% 1.36/1.57 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp8 | hskp1 | c3_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c0_1(a1634)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp8 | hskp1 | c3_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c0_1(a1634)))),
% 1.36/1.57 inference(rewrite,[status(thm)],[])).
% 1.36/1.57 tff(1100,plain,
% 1.36/1.57 ((hskp8 | hskp1 | (~ndr1_0) | c3_1(a1634) | (~c2_1(a1634)) | (~c0_1(a1634))) <=> (hskp8 | hskp1 | c3_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c0_1(a1634)))),
% 1.36/1.57 inference(rewrite,[status(thm)],[])).
% 1.36/1.57 tff(1101,plain,
% 1.36/1.57 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c3_1(a1634) | (~c2_1(a1634)) | (~c0_1(a1634)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp8 | hskp1 | c3_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c0_1(a1634))))),
% 1.36/1.57 inference(monotonicity,[status(thm)],[1100])).
% 1.36/1.57 tff(1102,plain,
% 1.36/1.57 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c3_1(a1634) | (~c2_1(a1634)) | (~c0_1(a1634)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp8 | hskp1 | c3_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c0_1(a1634)))),
% 1.36/1.57 inference(transitivity,[status(thm)],[1101, 1099])).
% 1.36/1.57 tff(1103,plain,
% 1.36/1.57 ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c3_1(a1634) | (~c2_1(a1634)) | (~c0_1(a1634)))),
% 1.36/1.57 inference(quant_inst,[status(thm)],[])).
% 1.36/1.57 tff(1104,plain,
% 1.36/1.57 ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp8 | hskp1 | c3_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c0_1(a1634))),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1103, 1102])).
% 1.36/1.57 tff(1105,plain,
% 1.36/1.57 (c3_1(a1634) | (~c2_1(a1634))),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[1104, 119, 1054, 21, 504, 32])).
% 1.36/1.57 tff(1106,plain,
% 1.36/1.57 (~c2_1(a1634)),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[1105, 1098])).
% 1.36/1.57 tff(1107,plain,
% 1.36/1.57 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c3_1(a1634) | c0_1(a1650) | c3_1(a1650) | c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c1_1(a1650)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c3_1(a1634) | c0_1(a1650) | c3_1(a1650) | c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c1_1(a1650)))),
% 1.36/1.57 inference(rewrite,[status(thm)],[])).
% 1.36/1.57 tff(1108,plain,
% 1.36/1.57 ((hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1634) | c1_1(a1634) | c3_1(a1634)) <=> (hskp3 | c3_1(a1634) | c0_1(a1650) | c3_1(a1650) | c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c1_1(a1650)))),
% 1.36/1.57 inference(rewrite,[status(thm)],[])).
% 1.36/1.57 tff(1109,plain,
% 1.36/1.57 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1634) | c1_1(a1634) | c3_1(a1634))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c3_1(a1634) | c0_1(a1650) | c3_1(a1650) | c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c1_1(a1650))))),
% 1.36/1.57 inference(monotonicity,[status(thm)],[1108])).
% 1.36/1.57 tff(1110,plain,
% 1.36/1.57 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1634) | c1_1(a1634) | c3_1(a1634))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c3_1(a1634) | c0_1(a1650) | c3_1(a1650) | c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c1_1(a1650)))),
% 1.36/1.57 inference(transitivity,[status(thm)],[1109, 1107])).
% 1.36/1.57 tff(1111,plain,
% 1.36/1.57 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1634) | c1_1(a1634) | c3_1(a1634))),
% 1.36/1.57 inference(quant_inst,[status(thm)],[])).
% 1.36/1.57 tff(1112,plain,
% 1.36/1.57 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c3_1(a1634) | c0_1(a1650) | c3_1(a1650) | c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c1_1(a1650))),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1111, 1110])).
% 1.36/1.57 tff(1113,plain,
% 1.36/1.57 ($false),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[1112, 119, 661, 852, 1098, 843, 842, 503, 10, 1106])).
% 1.36/1.57 tff(1114,plain,(c3_1(a1634) | hskp3 | (~c1_1(a1650)) | c0_1(a1650) | c3_1(a1650) | c1_1(a1634) | hskp8 | hskp1 | (~c0_1(a1634))), inference(lemma,lemma(discharge,[]))).
% 1.36/1.57 tff(1115,plain,
% 1.36/1.57 (c3_1(a1634)),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[1114, 1035, 706, 674, 668, 503, 661, 21, 1097])).
% 1.36/1.57 tff(1116,plain,
% 1.36/1.57 (c2_1(a1634)),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[1011, 1115, 500, 1097, 56, 503])).
% 1.36/1.57 tff(1117,plain,
% 1.36/1.57 ($false),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[1019, 1116, 1115, 783])).
% 1.36/1.57 tff(1118,plain,(hskp2 | c1_1(a1634) | hskp10 | hskp3 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.36/1.57 tff(1119,plain,
% 1.36/1.57 (hskp2),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[1118, 56, 503, 661, 21])).
% 1.36/1.57 tff(1120,plain,
% 1.36/1.57 (((~hskp2) | (~c0_1(a1637))) <=> ((~hskp2) | (~c0_1(a1637)))),
% 1.36/1.57 inference(rewrite,[status(thm)],[])).
% 1.36/1.57 tff(1121,plain,
% 1.36/1.57 (((~c0_1(a1637)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a1637)))),
% 1.36/1.57 inference(rewrite,[status(thm)],[])).
% 1.36/1.57 tff(1122,axiom,((~c0_1(a1637)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 1.36/1.57 tff(1123,plain,
% 1.36/1.57 ((~hskp2) | (~c0_1(a1637))),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 1.36/1.57 tff(1124,plain,
% 1.36/1.57 ((~hskp2) | (~c0_1(a1637))),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1123, 1120])).
% 1.36/1.57 tff(1125,plain,
% 1.36/1.57 (~c0_1(a1637)),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[1124, 1119])).
% 1.36/1.57 tff(1126,plain,
% 1.36/1.57 (((~hskp2) | c3_1(a1637)) <=> ((~hskp2) | c3_1(a1637))),
% 1.36/1.57 inference(rewrite,[status(thm)],[])).
% 1.36/1.57 tff(1127,axiom,((~hskp2) | c3_1(a1637)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 1.36/1.57 tff(1128,plain,
% 1.36/1.57 ((~hskp2) | c3_1(a1637)),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1127, 1126])).
% 1.36/1.57 tff(1129,plain,
% 1.36/1.57 ((~hskp2) | c3_1(a1637)),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1128, 1126])).
% 1.36/1.57 tff(1130,plain,
% 1.36/1.57 ((~hskp2) | c3_1(a1637)),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1129, 1126])).
% 1.36/1.57 tff(1131,plain,
% 1.36/1.57 ((~hskp2) | c3_1(a1637)),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1130, 1126])).
% 1.36/1.57 tff(1132,plain,
% 1.36/1.57 ((~hskp2) | c3_1(a1637)),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1131, 1126])).
% 1.36/1.57 tff(1133,plain,
% 1.36/1.57 (c3_1(a1637)),
% 1.36/1.57 inference(unit_resolution,[status(thm)],[1132, 1119])).
% 1.36/1.57 tff(1134,plain,
% 1.36/1.57 (((~hskp2) | c1_1(a1637)) <=> ((~hskp2) | c1_1(a1637))),
% 1.36/1.57 inference(rewrite,[status(thm)],[])).
% 1.36/1.57 tff(1135,axiom,((~hskp2) | c1_1(a1637)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 1.36/1.57 tff(1136,plain,
% 1.36/1.57 ((~hskp2) | c1_1(a1637)),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1135, 1134])).
% 1.36/1.57 tff(1137,plain,
% 1.36/1.57 ((~hskp2) | c1_1(a1637)),
% 1.36/1.57 inference(modus_ponens,[status(thm)],[1136, 1134])).
% 1.36/1.58 tff(1138,plain,
% 1.36/1.58 ((~hskp2) | c1_1(a1637)),
% 1.36/1.58 inference(modus_ponens,[status(thm)],[1137, 1134])).
% 1.36/1.58 tff(1139,plain,
% 1.36/1.58 ((~hskp2) | c1_1(a1637)),
% 1.36/1.58 inference(modus_ponens,[status(thm)],[1138, 1134])).
% 1.36/1.58 tff(1140,plain,
% 1.36/1.58 ((~hskp2) | c1_1(a1637)),
% 1.36/1.58 inference(modus_ponens,[status(thm)],[1139, 1134])).
% 1.36/1.58 tff(1141,plain,
% 1.36/1.58 (c1_1(a1637)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[1140, 1119])).
% 1.36/1.58 tff(1142,assumption,(hskp5), introduced(assumption)).
% 1.36/1.58 tff(1143,plain,
% 1.36/1.58 (~c2_1(a1640)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[840, 1142])).
% 1.36/1.58 tff(1144,plain,
% 1.36/1.58 (c3_1(a1640)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[866, 1142])).
% 1.36/1.58 tff(1145,plain,
% 1.36/1.58 (~c1_1(a1640)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[873, 119, 1094, 661, 1144, 1143, 769])).
% 1.36/1.58 tff(1146,assumption,(~c0_1(a1637)), introduced(assumption)).
% 1.36/1.58 tff(1147,assumption,(c3_1(a1637)), introduced(assumption)).
% 1.36/1.58 tff(1148,assumption,(c1_1(a1637)), introduced(assumption)).
% 1.36/1.58 tff(1149,plain,
% 1.36/1.58 (c0_1(a1640)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[850, 1142])).
% 1.36/1.58 tff(1150,plain,
% 1.36/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1650) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1640) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1650)) | (~c1_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1650) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1640) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.36/1.58 inference(rewrite,[status(thm)],[])).
% 1.36/1.58 tff(1151,plain,
% 1.36/1.58 (((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637))) <=> (c3_1(a1650) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1640) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.36/1.58 inference(rewrite,[status(thm)],[])).
% 1.36/1.58 tff(1152,plain,
% 1.36/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1650) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1640) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1650)) | (~c1_1(a1650))))),
% 1.36/1.58 inference(monotonicity,[status(thm)],[1151])).
% 1.36/1.58 tff(1153,plain,
% 1.36/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1650) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1640) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.36/1.58 inference(transitivity,[status(thm)],[1152, 1150])).
% 1.36/1.58 tff(1154,plain,
% 1.36/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637)))),
% 1.36/1.58 inference(quant_inst,[status(thm)],[])).
% 1.36/1.58 tff(1155,plain,
% 1.36/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1650) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1640) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1650)) | (~c1_1(a1650))),
% 1.36/1.58 inference(modus_ponens,[status(thm)],[1154, 1153])).
% 1.36/1.58 tff(1156,plain,
% 1.36/1.58 ($false),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[1155, 119, 852, 1149, 1144, 1148, 1147, 842, 1146, 20, 34, 1145])).
% 1.36/1.58 tff(1157,plain,((~hskp5) | (~c1_1(a1650)) | (~c1_1(a1637)) | (~c3_1(a1637)) | c3_1(a1650) | c0_1(a1637) | (~c2_1(a1650)) | hskp21 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.36/1.58 tff(1158,plain,
% 1.36/1.58 (~hskp5),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[1157, 706, 1141, 1133, 668, 1125, 681, 759, 661])).
% 1.36/1.58 tff(1159,plain,
% 1.36/1.58 (hskp0),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[834, 1158, 21])).
% 1.36/1.58 tff(1160,plain,
% 1.36/1.58 (c0_1(a1634)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[498, 1159])).
% 1.36/1.58 tff(1161,plain,
% 1.36/1.58 (c3_1(a1634)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[490, 1159])).
% 1.36/1.58 tff(1162,plain,
% 1.36/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1650) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c2_1(a1650)) | (~c1_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1650) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.36/1.58 inference(rewrite,[status(thm)],[])).
% 1.36/1.58 tff(1163,plain,
% 1.36/1.58 (((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637))) <=> (c3_1(a1650) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.36/1.58 inference(rewrite,[status(thm)],[])).
% 1.36/1.58 tff(1164,plain,
% 1.36/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1650) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c2_1(a1650)) | (~c1_1(a1650))))),
% 1.36/1.58 inference(monotonicity,[status(thm)],[1163])).
% 1.36/1.58 tff(1165,plain,
% 1.36/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1650) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.36/1.58 inference(transitivity,[status(thm)],[1164, 1162])).
% 1.36/1.58 tff(1166,plain,
% 1.36/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637)))),
% 1.36/1.58 inference(quant_inst,[status(thm)],[])).
% 1.36/1.58 tff(1167,plain,
% 1.36/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1650) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c2_1(a1650)) | (~c1_1(a1650))),
% 1.36/1.58 inference(modus_ponens,[status(thm)],[1166, 1165])).
% 1.36/1.58 tff(1168,plain,
% 1.36/1.58 ((~c3_1(a1634)) | (~c0_1(a1634))),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[1167, 119, 706, 1141, 1133, 668, 1125, 503, 20, 681])).
% 1.36/1.58 tff(1169,plain,
% 1.36/1.58 ($false),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[1168, 1161, 1160])).
% 1.36/1.58 tff(1170,plain,(hskp10 | c1_1(a1634) | hskp1 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.36/1.58 tff(1171,plain,
% 1.36/1.58 (hskp10),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[1170, 21, 503, 660])).
% 1.36/1.58 tff(1172,plain,
% 1.36/1.58 (~c3_1(a1648)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[150, 1171])).
% 1.36/1.58 tff(1173,plain,
% 1.36/1.58 (c2_1(a1648)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[166, 1171])).
% 1.36/1.58 tff(1174,plain,
% 1.36/1.58 (c0_1(a1648)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[158, 1171])).
% 1.36/1.58 tff(1175,assumption,(~c1_1(a1650)), introduced(assumption)).
% 1.36/1.58 tff(1176,plain,
% 1.36/1.58 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c1_1(a1650) | c0_1(a1650) | (~ndr1_0) | c2_1(a1650))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c1_1(a1650) | c0_1(a1650) | (~ndr1_0) | c2_1(a1650))),
% 1.36/1.58 inference(rewrite,[status(thm)],[])).
% 1.36/1.58 tff(1177,plain,
% 1.36/1.58 ((hskp3 | hskp2 | (~ndr1_0) | c2_1(a1650) | c1_1(a1650) | c0_1(a1650)) <=> (hskp3 | hskp2 | c1_1(a1650) | c0_1(a1650) | (~ndr1_0) | c2_1(a1650))),
% 1.36/1.58 inference(rewrite,[status(thm)],[])).
% 1.36/1.58 tff(1178,plain,
% 1.36/1.58 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a1650) | c1_1(a1650) | c0_1(a1650))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c1_1(a1650) | c0_1(a1650) | (~ndr1_0) | c2_1(a1650)))),
% 1.36/1.58 inference(monotonicity,[status(thm)],[1177])).
% 1.36/1.58 tff(1179,plain,
% 1.36/1.58 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a1650) | c1_1(a1650) | c0_1(a1650))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c1_1(a1650) | c0_1(a1650) | (~ndr1_0) | c2_1(a1650))),
% 1.36/1.58 inference(transitivity,[status(thm)],[1178, 1176])).
% 1.36/1.58 tff(1180,plain,
% 1.36/1.58 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a1650) | c1_1(a1650) | c0_1(a1650))),
% 1.36/1.58 inference(quant_inst,[status(thm)],[])).
% 1.36/1.58 tff(1181,plain,
% 1.36/1.58 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c1_1(a1650) | c0_1(a1650) | (~ndr1_0) | c2_1(a1650)),
% 1.36/1.58 inference(modus_ponens,[status(thm)],[1180, 1179])).
% 1.36/1.58 tff(1182,plain,
% 1.36/1.58 (hskp2 | c0_1(a1650) | c2_1(a1650)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[1181, 119, 660, 1175, 1045])).
% 1.36/1.58 tff(1183,plain,
% 1.36/1.58 (c2_1(a1650)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[1182, 843, 500])).
% 1.36/1.58 tff(1184,plain,
% 1.36/1.58 (~hskp11),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[705, 1175])).
% 1.36/1.58 tff(1185,plain,
% 1.36/1.58 (c0_1(a1646)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[357, 261, 1184, 269, 224, 216, 253, 208, 245, 170, 239, 169, 168, 183])).
% 1.36/1.58 tff(1186,plain,
% 1.36/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1650) | c0_1(a1650) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c2_1(a1650)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1650) | c0_1(a1650) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c2_1(a1650)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646)))),
% 1.36/1.58 inference(rewrite,[status(thm)],[])).
% 1.36/1.58 tff(1187,plain,
% 1.36/1.58 (((~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c0_1(a1646)) | c3_1(a1643) | (~c1_1(a1643)) | (~c0_1(a1643)) | c1_1(a1650) | c0_1(a1650) | (~c2_1(a1650))) <=> (c1_1(a1650) | c0_1(a1650) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c2_1(a1650)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646)))),
% 1.36/1.58 inference(rewrite,[status(thm)],[])).
% 1.36/1.58 tff(1188,plain,
% 1.36/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c0_1(a1646)) | c3_1(a1643) | (~c1_1(a1643)) | (~c0_1(a1643)) | c1_1(a1650) | c0_1(a1650) | (~c2_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1650) | c0_1(a1650) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c2_1(a1650)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646))))),
% 1.36/1.58 inference(monotonicity,[status(thm)],[1187])).
% 1.36/1.58 tff(1189,plain,
% 1.36/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c0_1(a1646)) | c3_1(a1643) | (~c1_1(a1643)) | (~c0_1(a1643)) | c1_1(a1650) | c0_1(a1650) | (~c2_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1650) | c0_1(a1650) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c2_1(a1650)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646)))),
% 1.36/1.58 inference(transitivity,[status(thm)],[1188, 1186])).
% 1.36/1.58 tff(1190,plain,
% 1.36/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c0_1(a1646)) | c3_1(a1643) | (~c1_1(a1643)) | (~c0_1(a1643)) | c1_1(a1650) | c0_1(a1650) | (~c2_1(a1650)))),
% 1.36/1.58 inference(quant_inst,[status(thm)],[])).
% 1.36/1.58 tff(1191,plain,
% 1.36/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1650) | c0_1(a1650) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c2_1(a1650)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646))),
% 1.36/1.58 inference(modus_ponens,[status(thm)],[1190, 1189])).
% 1.36/1.58 tff(1192,plain,
% 1.36/1.58 ((~c0_1(a1643)) | (~c0_1(a1646))),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[1191, 119, 239, 269, 1175, 253, 843, 245, 368, 34])).
% 1.36/1.58 tff(1193,plain,
% 1.36/1.58 (~c0_1(a1643)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[1192, 1185])).
% 1.36/1.58 tff(1194,plain,
% 1.36/1.58 (hskp7),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[392, 231, 1184])).
% 1.36/1.58 tff(1195,plain,
% 1.36/1.58 (~c3_1(a1642)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[398, 1194])).
% 1.36/1.58 tff(1196,plain,
% 1.36/1.58 (c0_1(a1642)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[427, 1194])).
% 1.36/1.58 tff(1197,plain,
% 1.36/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1650) | c0_1(a1650) | c3_1(a1642) | (~ndr1_0) | (~c1_1(a1642)) | (~c0_1(a1642)) | (~c2_1(a1650)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1650) | c0_1(a1650) | c3_1(a1642) | (~ndr1_0) | (~c1_1(a1642)) | (~c0_1(a1642)) | (~c2_1(a1650)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646)))),
% 1.36/1.58 inference(rewrite,[status(thm)],[])).
% 1.36/1.58 tff(1198,plain,
% 1.36/1.58 (((~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c0_1(a1646)) | c3_1(a1642) | (~c1_1(a1642)) | (~c0_1(a1642)) | c1_1(a1650) | c0_1(a1650) | (~c2_1(a1650))) <=> (c1_1(a1650) | c0_1(a1650) | c3_1(a1642) | (~ndr1_0) | (~c1_1(a1642)) | (~c0_1(a1642)) | (~c2_1(a1650)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646)))),
% 1.36/1.58 inference(rewrite,[status(thm)],[])).
% 1.36/1.58 tff(1199,plain,
% 1.36/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c0_1(a1646)) | c3_1(a1642) | (~c1_1(a1642)) | (~c0_1(a1642)) | c1_1(a1650) | c0_1(a1650) | (~c2_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1650) | c0_1(a1650) | c3_1(a1642) | (~ndr1_0) | (~c1_1(a1642)) | (~c0_1(a1642)) | (~c2_1(a1650)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646))))),
% 1.36/1.58 inference(monotonicity,[status(thm)],[1198])).
% 1.36/1.58 tff(1200,plain,
% 1.36/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c0_1(a1646)) | c3_1(a1642) | (~c1_1(a1642)) | (~c0_1(a1642)) | c1_1(a1650) | c0_1(a1650) | (~c2_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1650) | c0_1(a1650) | c3_1(a1642) | (~ndr1_0) | (~c1_1(a1642)) | (~c0_1(a1642)) | (~c2_1(a1650)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646)))),
% 1.36/1.58 inference(transitivity,[status(thm)],[1199, 1197])).
% 1.36/1.58 tff(1201,plain,
% 1.36/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c0_1(a1646)) | c3_1(a1642) | (~c1_1(a1642)) | (~c0_1(a1642)) | c1_1(a1650) | c0_1(a1650) | (~c2_1(a1650)))),
% 1.36/1.58 inference(quant_inst,[status(thm)],[])).
% 1.36/1.58 tff(1202,plain,
% 1.36/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1650) | c0_1(a1650) | c3_1(a1642) | (~ndr1_0) | (~c1_1(a1642)) | (~c0_1(a1642)) | (~c2_1(a1650)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646))),
% 1.36/1.58 inference(modus_ponens,[status(thm)],[1201, 1200])).
% 1.36/1.58 tff(1203,plain,
% 1.36/1.58 ((~c1_1(a1642)) | (~c0_1(a1646))),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[1202, 119, 239, 269, 1175, 1196, 843, 1195, 368, 34])).
% 1.36/1.58 tff(1204,plain,
% 1.36/1.58 (~c1_1(a1642)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[1203, 1185])).
% 1.36/1.58 tff(1205,plain,
% 1.36/1.58 (~c2_1(a1642)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[448, 1194])).
% 1.36/1.58 tff(1206,plain,
% 1.36/1.58 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c3_1(a1643) | c2_1(a1642) | c3_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c1_1(a1643)) | c0_1(a1643))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c3_1(a1643) | c2_1(a1642) | c3_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c1_1(a1643)) | c0_1(a1643))),
% 1.36/1.58 inference(rewrite,[status(thm)],[])).
% 1.36/1.58 tff(1207,plain,
% 1.36/1.58 ((hskp3 | (~ndr1_0) | c0_1(a1643) | c3_1(a1643) | (~c1_1(a1643)) | c2_1(a1642) | c1_1(a1642) | c3_1(a1642)) <=> (hskp3 | c3_1(a1643) | c2_1(a1642) | c3_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c1_1(a1643)) | c0_1(a1643))),
% 1.36/1.58 inference(rewrite,[status(thm)],[])).
% 1.36/1.58 tff(1208,plain,
% 1.36/1.58 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1643) | c3_1(a1643) | (~c1_1(a1643)) | c2_1(a1642) | c1_1(a1642) | c3_1(a1642))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c3_1(a1643) | c2_1(a1642) | c3_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c1_1(a1643)) | c0_1(a1643)))),
% 1.36/1.58 inference(monotonicity,[status(thm)],[1207])).
% 1.36/1.58 tff(1209,plain,
% 1.36/1.58 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1643) | c3_1(a1643) | (~c1_1(a1643)) | c2_1(a1642) | c1_1(a1642) | c3_1(a1642))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c3_1(a1643) | c2_1(a1642) | c3_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c1_1(a1643)) | c0_1(a1643))),
% 1.36/1.58 inference(transitivity,[status(thm)],[1208, 1206])).
% 1.36/1.58 tff(1210,plain,
% 1.36/1.58 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1643) | c3_1(a1643) | (~c1_1(a1643)) | c2_1(a1642) | c1_1(a1642) | c3_1(a1642))),
% 1.36/1.58 inference(quant_inst,[status(thm)],[])).
% 1.36/1.58 tff(1211,plain,
% 1.36/1.58 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c3_1(a1643) | c2_1(a1642) | c3_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c1_1(a1643)) | c0_1(a1643)),
% 1.36/1.58 inference(modus_ponens,[status(thm)],[1210, 1209])).
% 1.36/1.58 tff(1212,plain,
% 1.36/1.58 ($false),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[1211, 119, 661, 253, 245, 1205, 1195, 10, 1204, 1193])).
% 1.36/1.58 tff(1213,plain,(hskp0 | hskp3 | c1_1(a1650) | c0_1(a1650) | (~c2_1(a1650)) | (~c0_1(a1648)) | (~c2_1(a1648)) | c3_1(a1648) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.36/1.58 tff(1214,plain,
% 1.36/1.58 (hskp0),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[1213, 843, 1175, 660, 1183, 1174, 1173, 1172, 21])).
% 1.36/1.58 tff(1215,plain,
% 1.36/1.58 (c0_1(a1634)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[498, 1214])).
% 1.36/1.58 tff(1216,plain,
% 1.36/1.58 (c3_1(a1634)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[490, 1214])).
% 1.36/1.58 tff(1217,assumption,(~c2_1(a1638)), introduced(assumption)).
% 1.36/1.58 tff(1218,plain,
% 1.36/1.58 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp1 | c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp1 | c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0))),
% 1.36/1.58 inference(rewrite,[status(thm)],[])).
% 1.36/1.58 tff(1219,plain,
% 1.36/1.58 ((hskp10 | hskp1 | (~ndr1_0) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638)) <=> (hskp10 | hskp1 | c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0))),
% 1.36/1.58 inference(rewrite,[status(thm)],[])).
% 1.36/1.58 tff(1220,plain,
% 1.36/1.58 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp1 | c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0)))),
% 1.36/1.58 inference(monotonicity,[status(thm)],[1219])).
% 1.36/1.58 tff(1221,plain,
% 1.36/1.58 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp1 | c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0))),
% 1.36/1.58 inference(transitivity,[status(thm)],[1220, 1218])).
% 1.36/1.58 tff(1222,plain,
% 1.36/1.58 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638))),
% 1.36/1.58 inference(quant_inst,[status(thm)],[])).
% 1.36/1.58 tff(1223,plain,
% 1.36/1.58 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp1 | c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0)),
% 1.36/1.58 inference(modus_ponens,[status(thm)],[1222, 1221])).
% 1.36/1.58 tff(1224,plain,
% 1.36/1.58 (hskp10 | hskp1 | c3_1(a1638) | c2_1(a1638)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[1223, 119, 22, 136])).
% 1.36/1.58 tff(1225,plain,
% 1.36/1.58 (hskp10),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[1224, 21, 652, 1217])).
% 1.36/1.58 tff(1226,plain,
% 1.36/1.58 (~c3_1(a1648)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[150, 1225])).
% 1.36/1.58 tff(1227,plain,
% 1.36/1.58 (c2_1(a1648)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[166, 1225])).
% 1.36/1.58 tff(1228,plain,
% 1.36/1.58 (c0_1(a1648)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[158, 1225])).
% 1.36/1.58 tff(1229,plain,
% 1.36/1.58 (hskp8),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[176, 119, 21, 1228, 1227, 1226, 32])).
% 1.36/1.58 tff(1230,plain,
% 1.36/1.58 (c1_1(a1643)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[252, 1229])).
% 1.36/1.58 tff(1231,plain,
% 1.36/1.58 (~c3_1(a1643)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[244, 1229])).
% 1.36/1.58 tff(1232,plain,
% 1.36/1.58 (~c2_1(a1643)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[182, 1229])).
% 1.36/1.58 tff(1233,assumption,(~c1_1(a1638)), introduced(assumption)).
% 1.36/1.58 tff(1234,plain,
% 1.36/1.58 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c2_1(a1643) | c3_1(a1643) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c0_1(a1643)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a1643) | c3_1(a1643) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c0_1(a1643)))),
% 1.36/1.58 inference(rewrite,[status(thm)],[])).
% 1.36/1.58 tff(1235,plain,
% 1.36/1.58 ((hskp0 | (~ndr1_0) | c2_1(a1643) | c3_1(a1643) | (~c0_1(a1643)) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638)) <=> (hskp0 | c2_1(a1643) | c3_1(a1643) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c0_1(a1643)))),
% 1.36/1.58 inference(rewrite,[status(thm)],[])).
% 1.36/1.58 tff(1236,plain,
% 1.36/1.58 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1643) | c3_1(a1643) | (~c0_1(a1643)) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c2_1(a1643) | c3_1(a1643) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c0_1(a1643))))),
% 1.36/1.58 inference(monotonicity,[status(thm)],[1235])).
% 1.36/1.58 tff(1237,plain,
% 1.36/1.58 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1643) | c3_1(a1643) | (~c0_1(a1643)) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a1643) | c3_1(a1643) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c0_1(a1643)))),
% 1.36/1.58 inference(transitivity,[status(thm)],[1236, 1234])).
% 1.36/1.58 tff(1238,plain,
% 1.36/1.58 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1643) | c3_1(a1643) | (~c0_1(a1643)) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))),
% 1.36/1.58 inference(quant_inst,[status(thm)],[])).
% 1.36/1.58 tff(1239,plain,
% 1.36/1.58 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a1643) | c3_1(a1643) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c0_1(a1643))),
% 1.36/1.58 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 1.36/1.58 tff(1240,plain,
% 1.36/1.58 (hskp0 | c1_1(a1638) | (~c0_1(a1643))),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[1239, 296, 282, 281, 22, 1217, 952])).
% 1.36/1.58 tff(1241,plain,
% 1.36/1.58 (~c0_1(a1643)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[1240, 33, 1233])).
% 1.36/1.58 tff(1242,assumption,(~c3_1(a1642)), introduced(assumption)).
% 1.36/1.58 tff(1243,assumption,(~c2_1(a1642)), introduced(assumption)).
% 1.36/1.58 tff(1244,plain,
% 1.36/1.58 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c2_1(a1642) | c3_1(a1642) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c0_1(a1642)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a1642) | c3_1(a1642) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c0_1(a1642)))),
% 1.36/1.58 inference(rewrite,[status(thm)],[])).
% 1.36/1.58 tff(1245,plain,
% 1.36/1.58 ((hskp0 | (~ndr1_0) | c2_1(a1642) | c3_1(a1642) | (~c0_1(a1642)) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638)) <=> (hskp0 | c2_1(a1642) | c3_1(a1642) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c0_1(a1642)))),
% 1.36/1.58 inference(rewrite,[status(thm)],[])).
% 1.36/1.58 tff(1246,plain,
% 1.36/1.58 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1642) | c3_1(a1642) | (~c0_1(a1642)) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c2_1(a1642) | c3_1(a1642) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c0_1(a1642))))),
% 1.36/1.58 inference(monotonicity,[status(thm)],[1245])).
% 1.36/1.58 tff(1247,plain,
% 1.36/1.58 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1642) | c3_1(a1642) | (~c0_1(a1642)) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a1642) | c3_1(a1642) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c0_1(a1642)))),
% 1.36/1.58 inference(transitivity,[status(thm)],[1246, 1244])).
% 1.36/1.58 tff(1248,plain,
% 1.36/1.58 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1642) | c3_1(a1642) | (~c0_1(a1642)) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))),
% 1.36/1.58 inference(quant_inst,[status(thm)],[])).
% 1.36/1.58 tff(1249,plain,
% 1.36/1.58 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a1642) | c3_1(a1642) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c0_1(a1642))),
% 1.36/1.58 inference(modus_ponens,[status(thm)],[1248, 1247])).
% 1.36/1.58 tff(1250,plain,
% 1.36/1.58 (hskp0 | c1_1(a1638) | (~c0_1(a1642))),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[1249, 296, 1243, 1242, 22, 1217, 952])).
% 1.36/1.58 tff(1251,plain,
% 1.36/1.58 (~c0_1(a1642)),
% 1.36/1.58 inference(unit_resolution,[status(thm)],[1250, 33, 1233])).
% 1.36/1.58 tff(1252,plain,
% 1.36/1.58 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.36/1.58 inference(bind,[status(th)],[])).
% 1.36/1.58 tff(1253,plain,
% 1.36/1.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.36/1.58 inference(quant_intro,[status(thm)],[1252])).
% 1.36/1.58 tff(1254,plain,
% 1.36/1.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.36/1.58 inference(rewrite,[status(thm)],[])).
% 1.36/1.58 tff(1255,plain,
% 1.36/1.58 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W))), (((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.36/1.59 inference(bind,[status(th)],[])).
% 1.36/1.59 tff(1256,plain,
% 1.36/1.59 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.36/1.59 inference(quant_intro,[status(thm)],[1255])).
% 1.36/1.59 tff(1257,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 1.36/1.59 tff(1258,plain,
% 1.36/1.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.36/1.59 inference(modus_ponens,[status(thm)],[1257, 1256])).
% 1.36/1.59 tff(1259,plain,
% 1.36/1.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.36/1.59 inference(modus_ponens,[status(thm)],[1258, 1254])).
% 1.36/1.59 tff(1260,plain,(
% 1.36/1.59 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.36/1.59 inference(skolemize,[status(sab)],[1259])).
% 1.36/1.59 tff(1261,plain,
% 1.36/1.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.36/1.59 inference(modus_ponens,[status(thm)],[1260, 1253])).
% 1.36/1.59 tff(1262,plain,
% 1.36/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1642) | c2_1(a1642) | c3_1(a1642) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c1_1(a1642)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1642) | c2_1(a1642) | c3_1(a1642) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c1_1(a1642)))),
% 1.36/1.59 inference(rewrite,[status(thm)],[])).
% 1.36/1.59 tff(1263,plain,
% 1.36/1.59 (((~ndr1_0) | c2_1(a1642) | c0_1(a1642) | (~c1_1(a1642)) | c2_1(a1642) | c0_1(a1642) | c3_1(a1642) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638)) <=> (c0_1(a1642) | c2_1(a1642) | c3_1(a1642) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c1_1(a1642)))),
% 1.36/1.59 inference(rewrite,[status(thm)],[])).
% 1.36/1.59 tff(1264,plain,
% 1.36/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1642) | c0_1(a1642) | (~c1_1(a1642)) | c2_1(a1642) | c0_1(a1642) | c3_1(a1642) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1642) | c2_1(a1642) | c3_1(a1642) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c1_1(a1642))))),
% 1.36/1.59 inference(monotonicity,[status(thm)],[1263])).
% 1.36/1.59 tff(1265,plain,
% 1.36/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1642) | c0_1(a1642) | (~c1_1(a1642)) | c2_1(a1642) | c0_1(a1642) | c3_1(a1642) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1642) | c2_1(a1642) | c3_1(a1642) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c1_1(a1642)))),
% 1.36/1.59 inference(transitivity,[status(thm)],[1264, 1262])).
% 1.36/1.59 tff(1266,plain,
% 1.36/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1642) | c0_1(a1642) | (~c1_1(a1642)) | c2_1(a1642) | c0_1(a1642) | c3_1(a1642) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))),
% 1.36/1.59 inference(quant_inst,[status(thm)],[])).
% 1.36/1.59 tff(1267,plain,
% 1.36/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1642) | c2_1(a1642) | c3_1(a1642) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c1_1(a1642))),
% 1.36/1.59 inference(modus_ponens,[status(thm)],[1266, 1265])).
% 1.36/1.59 tff(1268,plain,
% 1.36/1.59 (c0_1(a1642) | c1_1(a1638) | (~c1_1(a1642))),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[1267, 296, 1243, 1242, 22, 1217, 1261])).
% 1.36/1.59 tff(1269,plain,
% 1.36/1.59 (~c1_1(a1642)),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[1268, 1251, 1233])).
% 1.36/1.59 tff(1270,plain,
% 1.36/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1642) | c2_1(a1643) | c3_1(a1643) | c2_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c1_1(a1643)) | c0_1(a1643))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1642) | c2_1(a1643) | c3_1(a1643) | c2_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c1_1(a1643)) | c0_1(a1643))),
% 1.36/1.59 inference(rewrite,[status(thm)],[])).
% 1.36/1.59 tff(1271,plain,
% 1.36/1.59 (((~ndr1_0) | c2_1(a1643) | c0_1(a1643) | (~c1_1(a1643)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643) | c2_1(a1642) | c1_1(a1642) | c0_1(a1642)) <=> (c0_1(a1642) | c2_1(a1643) | c3_1(a1643) | c2_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c1_1(a1643)) | c0_1(a1643))),
% 1.36/1.59 inference(rewrite,[status(thm)],[])).
% 1.36/1.59 tff(1272,plain,
% 1.36/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1643) | c0_1(a1643) | (~c1_1(a1643)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643) | c2_1(a1642) | c1_1(a1642) | c0_1(a1642))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1642) | c2_1(a1643) | c3_1(a1643) | c2_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c1_1(a1643)) | c0_1(a1643)))),
% 1.36/1.59 inference(monotonicity,[status(thm)],[1271])).
% 1.36/1.59 tff(1273,plain,
% 1.36/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1643) | c0_1(a1643) | (~c1_1(a1643)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643) | c2_1(a1642) | c1_1(a1642) | c0_1(a1642))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1642) | c2_1(a1643) | c3_1(a1643) | c2_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c1_1(a1643)) | c0_1(a1643))),
% 1.36/1.59 inference(transitivity,[status(thm)],[1272, 1270])).
% 1.36/1.59 tff(1274,plain,
% 1.36/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1643) | c0_1(a1643) | (~c1_1(a1643)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643) | c2_1(a1642) | c1_1(a1642) | c0_1(a1642))),
% 1.36/1.59 inference(quant_inst,[status(thm)],[])).
% 1.36/1.59 tff(1275,plain,
% 1.36/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1642) | c2_1(a1643) | c3_1(a1643) | c2_1(a1642) | (~ndr1_0) | c1_1(a1642) | (~c1_1(a1643)) | c0_1(a1643)),
% 1.36/1.59 inference(modus_ponens,[status(thm)],[1274, 1273])).
% 1.36/1.59 tff(1276,plain,
% 1.36/1.59 (c0_1(a1642) | c1_1(a1642) | (~c1_1(a1643)) | c0_1(a1643)),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[1275, 296, 282, 281, 1243, 1261])).
% 1.36/1.59 tff(1277,plain,
% 1.36/1.59 (~c1_1(a1643)),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[1276, 1251, 1269, 1241])).
% 1.36/1.59 tff(1278,plain,
% 1.36/1.59 (~hskp7),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[427, 1251])).
% 1.36/1.59 tff(1279,plain,
% 1.36/1.59 ((hskp8 | hskp7 | hskp0) <=> (hskp8 | hskp7 | hskp0)),
% 1.36/1.59 inference(rewrite,[status(thm)],[])).
% 1.36/1.59 tff(1280,plain,
% 1.36/1.59 (((hskp0 | hskp7) | hskp8) <=> (hskp8 | hskp7 | hskp0)),
% 1.36/1.59 inference(rewrite,[status(thm)],[])).
% 1.36/1.59 tff(1281,axiom,((hskp0 | hskp7) | hskp8), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 1.36/1.59 tff(1282,plain,
% 1.36/1.59 (hskp8 | hskp7 | hskp0),
% 1.36/1.59 inference(modus_ponens,[status(thm)],[1281, 1280])).
% 1.36/1.59 tff(1283,plain,
% 1.36/1.59 (hskp8 | hskp7 | hskp0),
% 1.36/1.59 inference(modus_ponens,[status(thm)],[1282, 1279])).
% 1.36/1.59 tff(1284,plain,
% 1.36/1.59 (hskp8 | hskp7 | hskp0),
% 1.36/1.59 inference(modus_ponens,[status(thm)],[1283, 1279])).
% 1.36/1.59 tff(1285,plain,
% 1.36/1.59 (hskp8 | hskp7 | hskp0),
% 1.36/1.59 inference(modus_ponens,[status(thm)],[1284, 1279])).
% 1.36/1.59 tff(1286,plain,
% 1.36/1.59 (hskp8 | hskp7 | hskp0),
% 1.36/1.59 inference(modus_ponens,[status(thm)],[1285, 1279])).
% 1.36/1.59 tff(1287,plain,
% 1.36/1.59 (hskp8),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[1286, 1278, 33])).
% 1.36/1.59 tff(1288,plain,
% 1.36/1.59 ($false),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[252, 1287, 1277])).
% 1.36/1.59 tff(1289,plain,(hskp0 | (~ndr1_0) | c2_1(a1643) | c3_1(a1643) | c2_1(a1642) | c1_1(a1638) | c3_1(a1642) | c0_1(a1638) | c2_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.59 tff(1290,plain,
% 1.36/1.59 (hskp0 | c2_1(a1643) | c3_1(a1643) | c2_1(a1642) | c1_1(a1638) | c3_1(a1642) | c0_1(a1638) | c2_1(a1638)),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[1289, 119])).
% 1.36/1.59 tff(1291,plain,
% 1.36/1.59 (c1_1(a1638)),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[1290, 449, 1217, 1231, 1232, 33, 399, 22])).
% 1.36/1.59 tff(1292,plain,
% 1.36/1.59 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.36/1.59 inference(bind,[status(th)],[])).
% 1.36/1.59 tff(1293,plain,
% 1.36/1.59 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.36/1.59 inference(quant_intro,[status(thm)],[1292])).
% 1.36/1.59 tff(1294,plain,
% 1.36/1.59 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.36/1.59 inference(rewrite,[status(thm)],[])).
% 1.36/1.59 tff(1295,plain,
% 1.36/1.59 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.36/1.59 inference(bind,[status(th)],[])).
% 1.36/1.59 tff(1296,plain,
% 1.36/1.59 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.36/1.59 inference(quant_intro,[status(thm)],[1295])).
% 1.36/1.59 tff(1297,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 1.36/1.59 tff(1298,plain,
% 1.36/1.59 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.36/1.59 inference(modus_ponens,[status(thm)],[1297, 1296])).
% 1.36/1.59 tff(1299,plain,
% 1.36/1.59 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.36/1.59 inference(modus_ponens,[status(thm)],[1298, 1294])).
% 1.36/1.59 tff(1300,plain,(
% 1.36/1.59 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.36/1.59 inference(skolemize,[status(sab)],[1299])).
% 1.36/1.59 tff(1301,plain,
% 1.36/1.59 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.36/1.59 inference(modus_ponens,[status(thm)],[1300, 1293])).
% 1.36/1.59 tff(1302,plain,
% 1.36/1.59 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c3_1(a1643) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c1_1(a1638)) | (~c1_1(a1643)) | (~c0_1(a1643)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c3_1(a1643) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c1_1(a1638)) | (~c1_1(a1643)) | (~c0_1(a1643)))),
% 1.36/1.59 inference(rewrite,[status(thm)],[])).
% 1.36/1.59 tff(1303,plain,
% 1.36/1.59 ((hskp11 | (~ndr1_0) | c3_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c2_1(a1638) | c0_1(a1638) | (~c1_1(a1638))) <=> (hskp11 | c3_1(a1643) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c1_1(a1638)) | (~c1_1(a1643)) | (~c0_1(a1643)))),
% 1.36/1.59 inference(rewrite,[status(thm)],[])).
% 1.36/1.59 tff(1304,plain,
% 1.36/1.59 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c2_1(a1638) | c0_1(a1638) | (~c1_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c3_1(a1643) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c1_1(a1638)) | (~c1_1(a1643)) | (~c0_1(a1643))))),
% 1.36/1.59 inference(monotonicity,[status(thm)],[1303])).
% 1.36/1.59 tff(1305,plain,
% 1.36/1.59 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c2_1(a1638) | c0_1(a1638) | (~c1_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c3_1(a1643) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c1_1(a1638)) | (~c1_1(a1643)) | (~c0_1(a1643)))),
% 1.36/1.59 inference(transitivity,[status(thm)],[1304, 1302])).
% 1.36/1.59 tff(1306,plain,
% 1.36/1.59 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c2_1(a1638) | c0_1(a1638) | (~c1_1(a1638)))),
% 1.36/1.59 inference(quant_inst,[status(thm)],[])).
% 1.36/1.59 tff(1307,plain,
% 1.36/1.59 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c3_1(a1643) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c1_1(a1638)) | (~c1_1(a1643)) | (~c0_1(a1643))),
% 1.36/1.59 inference(modus_ponens,[status(thm)],[1306, 1305])).
% 1.36/1.59 tff(1308,plain,
% 1.36/1.59 (hskp11 | (~c1_1(a1638)) | (~c0_1(a1643))),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[1307, 119, 1230, 1231, 22, 1217, 1301])).
% 1.36/1.59 tff(1309,plain,
% 1.36/1.59 (~c0_1(a1643)),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[1308, 1291, 45])).
% 1.36/1.59 tff(1310,plain,
% 1.36/1.59 (c0_1(a1646)),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[304, 382, 285, 381, 170, 169, 168, 282, 281, 296])).
% 1.36/1.59 tff(1311,plain,
% 1.36/1.59 (hskp7),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[391, 379, 296, 45])).
% 1.36/1.59 tff(1312,plain,
% 1.36/1.59 (~c3_1(a1642)),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[398, 1311])).
% 1.36/1.59 tff(1313,assumption,(~c1_1(a1675)), introduced(assumption)).
% 1.36/1.59 tff(1314,assumption,(~c0_1(a1675)), introduced(assumption)).
% 1.36/1.59 tff(1315,plain,
% 1.36/1.59 (c0_1(a1642)),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[427, 1311])).
% 1.36/1.59 tff(1316,assumption,(c2_1(a1675)), introduced(assumption)).
% 1.36/1.59 tff(1317,plain,
% 1.36/1.59 (~c1_1(a1642)),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[442, 296, 381, 380, 1316, 1315, 1314, 1313, 1312, 368, 1310])).
% 1.36/1.59 tff(1318,assumption,(c1_1(a1638)), introduced(assumption)).
% 1.36/1.59 tff(1319,plain,
% 1.36/1.59 (~c2_1(a1642)),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[448, 1311])).
% 1.36/1.59 tff(1320,plain,
% 1.36/1.59 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c3_1(a1638) | c2_1(a1642) | c3_1(a1642) | c0_1(a1638) | (~ndr1_0) | (~c1_1(a1638)) | c1_1(a1642))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c3_1(a1638) | c2_1(a1642) | c3_1(a1642) | c0_1(a1638) | (~ndr1_0) | (~c1_1(a1638)) | c1_1(a1642))),
% 1.36/1.59 inference(rewrite,[status(thm)],[])).
% 1.36/1.59 tff(1321,plain,
% 1.36/1.59 ((hskp3 | (~ndr1_0) | c0_1(a1638) | c3_1(a1638) | (~c1_1(a1638)) | c2_1(a1642) | c1_1(a1642) | c3_1(a1642)) <=> (hskp3 | c3_1(a1638) | c2_1(a1642) | c3_1(a1642) | c0_1(a1638) | (~ndr1_0) | (~c1_1(a1638)) | c1_1(a1642))),
% 1.36/1.59 inference(rewrite,[status(thm)],[])).
% 1.36/1.59 tff(1322,plain,
% 1.36/1.59 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1638) | c3_1(a1638) | (~c1_1(a1638)) | c2_1(a1642) | c1_1(a1642) | c3_1(a1642))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c3_1(a1638) | c2_1(a1642) | c3_1(a1642) | c0_1(a1638) | (~ndr1_0) | (~c1_1(a1638)) | c1_1(a1642)))),
% 1.36/1.59 inference(monotonicity,[status(thm)],[1321])).
% 1.36/1.59 tff(1323,plain,
% 1.36/1.59 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1638) | c3_1(a1638) | (~c1_1(a1638)) | c2_1(a1642) | c1_1(a1642) | c3_1(a1642))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c3_1(a1638) | c2_1(a1642) | c3_1(a1642) | c0_1(a1638) | (~ndr1_0) | (~c1_1(a1638)) | c1_1(a1642))),
% 1.36/1.59 inference(transitivity,[status(thm)],[1322, 1320])).
% 1.36/1.59 tff(1324,plain,
% 1.36/1.59 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1638) | c3_1(a1638) | (~c1_1(a1638)) | c2_1(a1642) | c1_1(a1642) | c3_1(a1642))),
% 1.36/1.59 inference(quant_inst,[status(thm)],[])).
% 1.36/1.59 tff(1325,plain,
% 1.36/1.59 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c3_1(a1638) | c2_1(a1642) | c3_1(a1642) | c0_1(a1638) | (~ndr1_0) | (~c1_1(a1638)) | c1_1(a1642)),
% 1.36/1.59 inference(modus_ponens,[status(thm)],[1324, 1323])).
% 1.36/1.59 tff(1326,plain,
% 1.36/1.59 ($false),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[1325, 296, 660, 652, 1319, 1312, 22, 10, 1318, 1317])).
% 1.36/1.59 tff(1327,plain,((~hskp28) | (~ndr1_0) | c3_1(a1638) | c0_1(a1638) | (~c1_1(a1638)) | (~c2_1(a1675)) | c0_1(a1675) | c1_1(a1675) | c0_1(a1643) | (~c0_1(a1648)) | (~c2_1(a1648)) | c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.36/1.59 tff(1328,plain,
% 1.36/1.59 ((~hskp28) | c3_1(a1638) | c0_1(a1638) | (~c1_1(a1638)) | (~c2_1(a1675)) | c0_1(a1675) | c1_1(a1675) | c0_1(a1643) | (~c0_1(a1648)) | (~c2_1(a1648)) | c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | hskp11),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[1327, 119])).
% 1.36/1.59 tff(1329,plain,
% 1.36/1.59 ($false),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[1328, 1309, 1291, 652, 22, 45, 436, 420, 414, 231, 1228, 1227, 1226, 1232, 1231])).
% 1.36/1.59 tff(1330,plain,(hskp0 | c3_1(a1638) | c0_1(a1638) | hskp11 | c2_1(a1638) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.36/1.59 tff(1331,plain,
% 1.36/1.59 (hskp0),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[1330, 45, 22, 652, 1217, 21])).
% 1.36/1.59 tff(1332,plain,
% 1.36/1.59 (c3_1(a1634)),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[490, 1331])).
% 1.36/1.59 tff(1333,plain,
% 1.36/1.59 (c0_1(a1634)),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[498, 1331])).
% 1.36/1.59 tff(1334,plain,
% 1.36/1.59 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638))),
% 1.36/1.59 inference(rewrite,[status(thm)],[])).
% 1.36/1.59 tff(1335,plain,
% 1.36/1.59 ((hskp3 | hskp2 | (~ndr1_0) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638)) <=> (hskp3 | hskp2 | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638))),
% 1.36/1.59 inference(rewrite,[status(thm)],[])).
% 1.36/1.59 tff(1336,plain,
% 1.36/1.59 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638)))),
% 1.36/1.59 inference(monotonicity,[status(thm)],[1335])).
% 1.36/1.59 tff(1337,plain,
% 1.36/1.59 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638))),
% 1.36/1.59 inference(transitivity,[status(thm)],[1336, 1334])).
% 1.36/1.59 tff(1338,plain,
% 1.36/1.59 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))),
% 1.36/1.59 inference(quant_inst,[status(thm)],[])).
% 1.36/1.59 tff(1339,plain,
% 1.36/1.59 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638)),
% 1.36/1.59 inference(modus_ponens,[status(thm)],[1338, 1337])).
% 1.36/1.59 tff(1340,plain,
% 1.36/1.59 (hskp3 | hskp2 | c2_1(a1638) | c1_1(a1638)),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[1339, 119, 22, 1045])).
% 1.36/1.59 tff(1341,plain,
% 1.36/1.59 (c1_1(a1638)),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[1340, 500, 660, 1217])).
% 1.36/1.59 tff(1342,plain,
% 1.36/1.59 (hskp11 | (~c1_1(a1638)) | (~c0_1(a1643))),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[1307, 119, 318, 281, 22, 1217, 1301])).
% 1.36/1.59 tff(1343,plain,
% 1.36/1.59 (~c0_1(a1643)),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[1342, 1318, 45])).
% 1.36/1.59 tff(1344,plain,
% 1.36/1.59 ($false),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[1328, 1343, 1318, 652, 22, 45, 1316, 1314, 1313, 379, 170, 169, 168, 282, 281])).
% 1.36/1.59 tff(1345,plain,((~c1_1(a1638)) | c3_1(a1638) | c0_1(a1638) | hskp11 | (~c2_1(a1675)) | c0_1(a1675) | c1_1(a1675) | (~hskp28) | (~c0_1(a1648)) | (~c2_1(a1648)) | c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | (~c1_1(a1643)) | c2_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.59 tff(1346,plain,
% 1.36/1.59 (~hskp28),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[1345, 1341, 22, 45, 1316, 1314, 1313, 652, 170, 169, 168, 282, 281, 318, 1217])).
% 1.36/1.59 tff(1347,plain,
% 1.36/1.59 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c3_1(a1648) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c1_1(a1638)) | (~c1_1(a1648)) | (~c0_1(a1648)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c3_1(a1648) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c1_1(a1638)) | (~c1_1(a1648)) | (~c0_1(a1648)))),
% 1.36/1.59 inference(rewrite,[status(thm)],[])).
% 1.36/1.59 tff(1348,plain,
% 1.36/1.59 ((hskp11 | (~ndr1_0) | c3_1(a1648) | (~c0_1(a1648)) | (~c1_1(a1648)) | c2_1(a1638) | c0_1(a1638) | (~c1_1(a1638))) <=> (hskp11 | c3_1(a1648) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c1_1(a1638)) | (~c1_1(a1648)) | (~c0_1(a1648)))),
% 1.36/1.59 inference(rewrite,[status(thm)],[])).
% 1.36/1.59 tff(1349,plain,
% 1.36/1.59 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1648) | (~c0_1(a1648)) | (~c1_1(a1648)) | c2_1(a1638) | c0_1(a1638) | (~c1_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c3_1(a1648) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c1_1(a1638)) | (~c1_1(a1648)) | (~c0_1(a1648))))),
% 1.36/1.59 inference(monotonicity,[status(thm)],[1348])).
% 1.36/1.59 tff(1350,plain,
% 1.36/1.59 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1648) | (~c0_1(a1648)) | (~c1_1(a1648)) | c2_1(a1638) | c0_1(a1638) | (~c1_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c3_1(a1648) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c1_1(a1638)) | (~c1_1(a1648)) | (~c0_1(a1648)))),
% 1.36/1.59 inference(transitivity,[status(thm)],[1349, 1347])).
% 1.36/1.59 tff(1351,plain,
% 1.36/1.59 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1648) | (~c0_1(a1648)) | (~c1_1(a1648)) | c2_1(a1638) | c0_1(a1638) | (~c1_1(a1638)))),
% 1.36/1.59 inference(quant_inst,[status(thm)],[])).
% 1.36/1.59 tff(1352,plain,
% 1.36/1.59 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c3_1(a1648) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c1_1(a1638)) | (~c1_1(a1648)) | (~c0_1(a1648))),
% 1.36/1.59 inference(modus_ponens,[status(thm)],[1351, 1350])).
% 1.36/1.59 tff(1353,plain,
% 1.36/1.59 (hskp11 | (~c1_1(a1638)) | (~c1_1(a1648))),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[1352, 119, 170, 168, 22, 1217, 1301])).
% 1.36/1.59 tff(1354,plain,
% 1.36/1.59 (~c1_1(a1648)),
% 1.36/1.59 inference(unit_resolution,[status(thm)],[1353, 1341, 45])).
% 1.36/1.60 tff(1355,plain,
% 1.36/1.60 (hskp9),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[539, 1354, 500])).
% 1.36/1.60 tff(1356,plain,
% 1.36/1.60 (~hskp19),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[610, 1355, 504, 502, 503])).
% 1.36/1.60 tff(1357,plain,
% 1.36/1.60 (~c2_1(a1634)),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[628, 1356, 502, 1346])).
% 1.36/1.60 tff(1358,plain,
% 1.36/1.60 ($false),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[645, 119, 500, 170, 169, 504, 502, 639, 1354, 1357])).
% 1.36/1.60 tff(1359,plain,(hskp2 | (~c0_1(a1648)) | (~c2_1(a1648)) | (~c0_1(a1634)) | (~c3_1(a1634)) | c1_1(a1634) | c3_1(a1648) | c0_1(a1638) | hskp11 | (~c2_1(a1675)) | c0_1(a1675) | c1_1(a1675) | c3_1(a1638) | c2_1(a1643) | c3_1(a1643) | (~c1_1(a1643)) | c2_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.60 tff(1360,plain,
% 1.36/1.60 (hskp2),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[1359, 1333, 1227, 1228, 1332, 503, 1226, 22, 45, 436, 420, 414, 652, 1232, 1231, 1230, 1217])).
% 1.36/1.60 tff(1361,plain,
% 1.36/1.60 (~c0_1(a1637)),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[1124, 1360])).
% 1.36/1.60 tff(1362,plain,
% 1.36/1.60 (c1_1(a1637)),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[1140, 1360])).
% 1.36/1.60 tff(1363,plain,
% 1.36/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1638) | c3_1(a1648) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c2_1(a1637)) | (~c2_1(a1648)) | (~c0_1(a1648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1638) | c3_1(a1648) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c2_1(a1637)) | (~c2_1(a1648)) | (~c0_1(a1648)))),
% 1.36/1.60 inference(rewrite,[status(thm)],[])).
% 1.36/1.60 tff(1364,plain,
% 1.36/1.60 (((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1637) | (~c1_1(a1637)) | (~c2_1(a1637)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638)) <=> (c3_1(a1638) | c3_1(a1648) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c2_1(a1637)) | (~c2_1(a1648)) | (~c0_1(a1648)))),
% 1.36/1.60 inference(rewrite,[status(thm)],[])).
% 1.36/1.60 tff(1365,plain,
% 1.36/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1637) | (~c1_1(a1637)) | (~c2_1(a1637)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1638) | c3_1(a1648) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c2_1(a1637)) | (~c2_1(a1648)) | (~c0_1(a1648))))),
% 1.36/1.60 inference(monotonicity,[status(thm)],[1364])).
% 1.36/1.60 tff(1366,plain,
% 1.36/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1637) | (~c1_1(a1637)) | (~c2_1(a1637)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1638) | c3_1(a1648) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c2_1(a1637)) | (~c2_1(a1648)) | (~c0_1(a1648)))),
% 1.36/1.60 inference(transitivity,[status(thm)],[1365, 1363])).
% 1.36/1.60 tff(1367,plain,
% 1.36/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1637) | (~c1_1(a1637)) | (~c2_1(a1637)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638))),
% 1.36/1.60 inference(quant_inst,[status(thm)],[])).
% 1.36/1.60 tff(1368,plain,
% 1.36/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1638) | c3_1(a1648) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c2_1(a1637)) | (~c2_1(a1648)) | (~c0_1(a1648))),
% 1.36/1.60 inference(modus_ponens,[status(thm)],[1367, 1366])).
% 1.36/1.60 tff(1369,plain,
% 1.36/1.60 (~c2_1(a1637)),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[1368, 119, 1228, 1227, 652, 1362, 1226, 22, 1217, 1361, 295])).
% 1.36/1.60 tff(1370,plain,
% 1.36/1.60 (c3_1(a1637)),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[1132, 1360])).
% 1.36/1.60 tff(1371,plain,
% 1.36/1.60 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | (~c3_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | (~c3_1(a1637)))),
% 1.36/1.60 inference(rewrite,[status(thm)],[])).
% 1.36/1.60 tff(1372,plain,
% 1.36/1.60 ((hskp11 | (~ndr1_0) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)) | c2_1(a1637) | c0_1(a1637) | (~c3_1(a1637))) <=> (hskp11 | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | (~c3_1(a1637)))),
% 1.36/1.60 inference(rewrite,[status(thm)],[])).
% 1.36/1.60 tff(1373,plain,
% 1.36/1.60 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)) | c2_1(a1637) | c0_1(a1637) | (~c3_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | (~c3_1(a1637))))),
% 1.36/1.60 inference(monotonicity,[status(thm)],[1372])).
% 1.36/1.60 tff(1374,plain,
% 1.36/1.60 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)) | c2_1(a1637) | c0_1(a1637) | (~c3_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | (~c3_1(a1637)))),
% 1.36/1.60 inference(transitivity,[status(thm)],[1373, 1371])).
% 1.36/1.60 tff(1375,plain,
% 1.36/1.60 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)) | c2_1(a1637) | c0_1(a1637) | (~c3_1(a1637)))),
% 1.36/1.60 inference(quant_inst,[status(thm)],[])).
% 1.36/1.60 tff(1376,plain,
% 1.36/1.60 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | (~c3_1(a1637))),
% 1.36/1.60 inference(modus_ponens,[status(thm)],[1375, 1374])).
% 1.36/1.60 tff(1377,plain,
% 1.36/1.60 ($false),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[1376, 119, 45, 1362, 1370, 1361, 55, 1369])).
% 1.36/1.60 tff(1378,plain,(hskp11 | c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | c1_1(a1634) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.36/1.60 tff(1379,plain,
% 1.36/1.60 (hskp11),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[1378, 21, 22, 1217, 503, 652])).
% 1.36/1.60 tff(1380,plain,
% 1.36/1.60 (~c3_1(a1650)),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[667, 1379])).
% 1.36/1.60 tff(1381,plain,
% 1.36/1.60 (~c0_1(a1650)),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[673, 1379])).
% 1.36/1.60 tff(1382,plain,
% 1.36/1.60 (c1_1(a1650)),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[705, 1379])).
% 1.36/1.60 tff(1383,plain,
% 1.36/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1638) | c0_1(a1737) | c3_1(a1648) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1737)) | (~c2_1(a1737)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1638) | c0_1(a1737) | c3_1(a1648) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1737)) | (~c2_1(a1737)))),
% 1.36/1.60 inference(rewrite,[status(thm)],[])).
% 1.36/1.60 tff(1384,plain,
% 1.36/1.60 (((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1737) | (~c1_1(a1737)) | (~c2_1(a1737)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638)) <=> (c3_1(a1638) | c0_1(a1737) | c3_1(a1648) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1737)) | (~c2_1(a1737)))),
% 1.36/1.60 inference(rewrite,[status(thm)],[])).
% 1.36/1.60 tff(1385,plain,
% 1.36/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1737) | (~c1_1(a1737)) | (~c2_1(a1737)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1638) | c0_1(a1737) | c3_1(a1648) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1737)) | (~c2_1(a1737))))),
% 1.36/1.60 inference(monotonicity,[status(thm)],[1384])).
% 1.36/1.60 tff(1386,plain,
% 1.36/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1737) | (~c1_1(a1737)) | (~c2_1(a1737)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1638) | c0_1(a1737) | c3_1(a1648) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1737)) | (~c2_1(a1737)))),
% 1.36/1.60 inference(transitivity,[status(thm)],[1385, 1383])).
% 1.36/1.60 tff(1387,plain,
% 1.36/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1737) | (~c1_1(a1737)) | (~c2_1(a1737)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638))),
% 1.36/1.60 inference(quant_inst,[status(thm)],[])).
% 1.36/1.60 tff(1388,plain,
% 1.36/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1638) | c0_1(a1737) | c3_1(a1648) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1737)) | (~c2_1(a1737))),
% 1.36/1.60 inference(modus_ponens,[status(thm)],[1387, 1386])).
% 1.36/1.60 tff(1389,plain,
% 1.36/1.60 (~c1_1(a1737)),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[1388, 119, 224, 1228, 1227, 652, 208, 1226, 22, 1217, 295])).
% 1.36/1.60 tff(1390,assumption,(hskp15), introduced(assumption)).
% 1.36/1.60 tff(1391,plain,
% 1.36/1.60 (~c2_1(a1664)),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[333, 1390])).
% 1.36/1.60 tff(1392,plain,
% 1.36/1.60 (~c1_1(a1664)),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[339, 1390])).
% 1.36/1.60 tff(1393,plain,
% 1.36/1.60 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | c3_1(a1664))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | c3_1(a1664))),
% 1.36/1.60 inference(rewrite,[status(thm)],[])).
% 1.36/1.60 tff(1394,plain,
% 1.36/1.60 ((hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1664) | c1_1(a1664) | c3_1(a1664)) <=> (hskp3 | c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | c3_1(a1664))),
% 1.36/1.60 inference(rewrite,[status(thm)],[])).
% 1.36/1.60 tff(1395,plain,
% 1.36/1.60 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1664) | c1_1(a1664) | c3_1(a1664))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | c3_1(a1664)))),
% 1.36/1.60 inference(monotonicity,[status(thm)],[1394])).
% 1.36/1.60 tff(1396,plain,
% 1.36/1.60 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1664) | c1_1(a1664) | c3_1(a1664))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | c3_1(a1664))),
% 1.36/1.60 inference(transitivity,[status(thm)],[1395, 1393])).
% 1.36/1.60 tff(1397,plain,
% 1.36/1.60 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1664) | c1_1(a1664) | c3_1(a1664))),
% 1.36/1.60 inference(quant_inst,[status(thm)],[])).
% 1.36/1.60 tff(1398,plain,
% 1.36/1.60 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | c3_1(a1664)),
% 1.36/1.60 inference(modus_ponens,[status(thm)],[1397, 1396])).
% 1.36/1.60 tff(1399,plain,
% 1.36/1.60 (c3_1(a1664)),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[1398, 296, 661, 852, 1392, 1391, 843, 842, 10])).
% 1.36/1.60 tff(1400,plain,
% 1.36/1.60 (c0_1(a1664)),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[347, 1390])).
% 1.36/1.60 tff(1401,plain,
% 1.36/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c1_1(a1650)) | (~c0_1(a1664)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c1_1(a1650)) | (~c0_1(a1664)))),
% 1.36/1.60 inference(rewrite,[status(thm)],[])).
% 1.36/1.60 tff(1402,plain,
% 1.36/1.60 (((~ndr1_0) | c3_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650))) <=> (c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c1_1(a1650)) | (~c0_1(a1664)))),
% 1.36/1.60 inference(rewrite,[status(thm)],[])).
% 1.36/1.60 tff(1403,plain,
% 1.36/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c1_1(a1650)) | (~c0_1(a1664))))),
% 1.36/1.60 inference(monotonicity,[status(thm)],[1402])).
% 1.36/1.60 tff(1404,plain,
% 1.36/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c1_1(a1650)) | (~c0_1(a1664)))),
% 1.36/1.60 inference(transitivity,[status(thm)],[1403, 1401])).
% 1.36/1.60 tff(1405,plain,
% 1.36/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1643) | (~c0_1(a1643)) | (~c1_1(a1643)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)))),
% 1.36/1.60 inference(quant_inst,[status(thm)],[])).
% 1.36/1.60 tff(1406,plain,
% 1.36/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | (~c0_1(a1643)) | (~c1_1(a1650)) | (~c0_1(a1664))),
% 1.36/1.60 inference(modus_ponens,[status(thm)],[1405, 1404])).
% 1.36/1.60 tff(1407,plain,
% 1.36/1.60 (~c0_1(a1643)),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[1406, 296, 1400, 852, 318, 1392, 1391, 843, 842, 281, 826])).
% 1.36/1.60 tff(1408,plain,
% 1.36/1.60 (c0_1(a1646)),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[304, 1407, 283, 284, 170, 169, 168, 282, 281, 296])).
% 1.36/1.60 tff(1409,plain,
% 1.36/1.60 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))))),
% 1.36/1.60 inference(bind,[status(th)],[])).
% 1.36/1.60 tff(1410,plain,
% 1.36/1.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.36/1.60 inference(quant_intro,[status(thm)],[1409])).
% 1.36/1.60 tff(1411,plain,
% 1.36/1.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.36/1.60 inference(rewrite,[status(thm)],[])).
% 1.36/1.60 tff(1412,plain,
% 1.36/1.60 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))))),
% 1.36/1.60 inference(bind,[status(th)],[])).
% 1.36/1.60 tff(1413,plain,
% 1.36/1.60 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.36/1.60 inference(quant_intro,[status(thm)],[1412])).
% 1.36/1.60 tff(1414,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause200')).
% 1.36/1.60 tff(1415,plain,
% 1.36/1.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.36/1.60 inference(modus_ponens,[status(thm)],[1414, 1413])).
% 1.36/1.60 tff(1416,plain,
% 1.36/1.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.36/1.60 inference(modus_ponens,[status(thm)],[1415, 1411])).
% 1.36/1.60 tff(1417,plain,(
% 1.36/1.60 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.36/1.60 inference(skolemize,[status(sab)],[1416])).
% 1.36/1.60 tff(1418,plain,
% 1.36/1.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.36/1.60 inference(modus_ponens,[status(thm)],[1417, 1410])).
% 1.36/1.60 tff(1419,plain,
% 1.36/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c3_1(a1664)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c3_1(a1664)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.36/1.60 inference(rewrite,[status(thm)],[])).
% 1.36/1.60 tff(1420,plain,
% 1.36/1.60 (((~ndr1_0) | (~c3_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c1_1(a1646)) | (~c2_1(a1646)) | (~c0_1(a1646)) | c2_1(a1664) | c1_1(a1664) | (~c3_1(a1664))) <=> (c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c3_1(a1664)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.36/1.60 inference(rewrite,[status(thm)],[])).
% 1.36/1.60 tff(1421,plain,
% 1.36/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c1_1(a1646)) | (~c2_1(a1646)) | (~c0_1(a1646)) | c2_1(a1664) | c1_1(a1664) | (~c3_1(a1664)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c3_1(a1664)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646))))),
% 1.36/1.60 inference(monotonicity,[status(thm)],[1420])).
% 1.36/1.60 tff(1422,plain,
% 1.36/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c1_1(a1646)) | (~c2_1(a1646)) | (~c0_1(a1646)) | c2_1(a1664) | c1_1(a1664) | (~c3_1(a1664)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c3_1(a1664)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.36/1.60 inference(transitivity,[status(thm)],[1421, 1419])).
% 1.36/1.60 tff(1423,plain,
% 1.36/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c1_1(a1646)) | (~c2_1(a1646)) | (~c0_1(a1646)) | c2_1(a1664) | c1_1(a1664) | (~c3_1(a1664)))),
% 1.36/1.60 inference(quant_inst,[status(thm)],[])).
% 1.36/1.60 tff(1424,plain,
% 1.36/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c3_1(a1664)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646))),
% 1.36/1.60 inference(modus_ponens,[status(thm)],[1423, 1422])).
% 1.36/1.60 tff(1425,plain,
% 1.36/1.60 ((~c3_1(a1664)) | (~c0_1(a1646))),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[1424, 296, 283, 284, 349, 1392, 1391, 1418])).
% 1.36/1.60 tff(1426,plain,
% 1.36/1.60 ($false),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[1425, 1408, 1399])).
% 1.36/1.60 tff(1427,plain,((~hskp15) | (~ndr1_0) | (~c1_1(a1646)) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c0_1(a1648)) | (~c2_1(a1648)) | c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | hskp3 | (~c1_1(a1650)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1643))), inference(lemma,lemma(discharge,[]))).
% 1.36/1.60 tff(1428,plain,
% 1.36/1.60 ((~hskp15) | (~c1_1(a1646)) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c0_1(a1648)) | (~c2_1(a1648)) | c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | hskp3 | (~c1_1(a1650)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1643))),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[1427, 119])).
% 1.36/1.60 tff(1429,plain,
% 1.36/1.60 (~hskp15),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[1428, 269, 660, 852, 261, 1227, 1226, 1228, 1231, 1232, 239, 843, 842, 1230])).
% 1.36/1.60 tff(1430,plain,
% 1.36/1.60 (hskp15 | (~c0_1(a1643))),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[326, 119, 224, 216, 1230, 208, 1231, 316])).
% 1.36/1.60 tff(1431,plain,
% 1.36/1.60 (~c0_1(a1643)),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[1430, 1429])).
% 1.36/1.60 tff(1432,plain,
% 1.36/1.60 (c0_1(a1646)),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[305, 1431, 261, 239, 1228, 1227, 1226, 1232, 1231])).
% 1.36/1.60 tff(1433,plain,
% 1.36/1.60 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.36/1.60 inference(bind,[status(th)],[])).
% 1.36/1.60 tff(1434,plain,
% 1.36/1.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.36/1.60 inference(quant_intro,[status(thm)],[1433])).
% 1.36/1.60 tff(1435,plain,
% 1.36/1.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.36/1.60 inference(rewrite,[status(thm)],[])).
% 1.36/1.60 tff(1436,plain,
% 1.36/1.60 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.36/1.60 inference(bind,[status(th)],[])).
% 1.36/1.60 tff(1437,plain,
% 1.36/1.60 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.36/1.60 inference(quant_intro,[status(thm)],[1436])).
% 1.36/1.60 tff(1438,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause198')).
% 1.36/1.60 tff(1439,plain,
% 1.36/1.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.36/1.60 inference(modus_ponens,[status(thm)],[1438, 1437])).
% 1.36/1.60 tff(1440,plain,
% 1.36/1.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.36/1.60 inference(modus_ponens,[status(thm)],[1439, 1435])).
% 1.36/1.60 tff(1441,plain,(
% 1.36/1.60 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.36/1.60 inference(skolemize,[status(sab)],[1440])).
% 1.36/1.60 tff(1442,plain,
% 1.36/1.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.36/1.60 inference(modus_ponens,[status(thm)],[1441, 1434])).
% 1.36/1.60 tff(1443,plain,
% 1.36/1.60 ((hskp19 | hskp15 | hskp1) <=> (hskp19 | hskp15 | hskp1)),
% 1.36/1.60 inference(rewrite,[status(thm)],[])).
% 1.36/1.60 tff(1444,plain,
% 1.36/1.60 (((hskp15 | hskp19) | hskp1) <=> (hskp19 | hskp15 | hskp1)),
% 1.36/1.60 inference(rewrite,[status(thm)],[])).
% 1.36/1.60 tff(1445,axiom,((hskp15 | hskp19) | hskp1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 1.36/1.60 tff(1446,plain,
% 1.36/1.60 (hskp19 | hskp15 | hskp1),
% 1.36/1.60 inference(modus_ponens,[status(thm)],[1445, 1444])).
% 1.36/1.60 tff(1447,plain,
% 1.36/1.60 (hskp19 | hskp15 | hskp1),
% 1.36/1.60 inference(modus_ponens,[status(thm)],[1446, 1443])).
% 1.36/1.60 tff(1448,plain,
% 1.36/1.60 (hskp19 | hskp15 | hskp1),
% 1.36/1.60 inference(modus_ponens,[status(thm)],[1447, 1443])).
% 1.36/1.60 tff(1449,plain,
% 1.36/1.60 (hskp19 | hskp15 | hskp1),
% 1.36/1.60 inference(modus_ponens,[status(thm)],[1448, 1443])).
% 1.36/1.60 tff(1450,plain,
% 1.36/1.60 (hskp19 | hskp15 | hskp1),
% 1.36/1.60 inference(modus_ponens,[status(thm)],[1449, 1443])).
% 1.36/1.60 tff(1451,plain,
% 1.36/1.60 (hskp19),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[1450, 1429, 21])).
% 1.36/1.60 tff(1452,plain,
% 1.36/1.60 (~c3_1(a1682)),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[568, 1451])).
% 1.36/1.60 tff(1453,plain,
% 1.36/1.60 (c2_1(a1682)),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[584, 1451])).
% 1.36/1.60 tff(1454,plain,
% 1.36/1.60 (c1_1(a1682)),
% 1.36/1.60 inference(unit_resolution,[status(thm)],[576, 1451])).
% 1.36/1.60 tff(1455,plain,
% 1.36/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1737) | c3_1(a1682) | (~ndr1_0) | (~c2_1(a1682)) | (~c1_1(a1682)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | c1_1(a1737) | (~c3_1(a1737)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1737) | c3_1(a1682) | (~ndr1_0) | (~c2_1(a1682)) | (~c1_1(a1682)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | c1_1(a1737) | (~c3_1(a1737)))),
% 1.36/1.61 inference(rewrite,[status(thm)],[])).
% 1.36/1.61 tff(1456,plain,
% 1.36/1.61 (((~ndr1_0) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | c3_1(a1682) | (~c1_1(a1682)) | (~c2_1(a1682)) | c1_1(a1737) | c0_1(a1737) | (~c3_1(a1737))) <=> (c0_1(a1737) | c3_1(a1682) | (~ndr1_0) | (~c2_1(a1682)) | (~c1_1(a1682)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | c1_1(a1737) | (~c3_1(a1737)))),
% 1.36/1.61 inference(rewrite,[status(thm)],[])).
% 1.36/1.61 tff(1457,plain,
% 1.36/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | c3_1(a1682) | (~c1_1(a1682)) | (~c2_1(a1682)) | c1_1(a1737) | c0_1(a1737) | (~c3_1(a1737)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1737) | c3_1(a1682) | (~ndr1_0) | (~c2_1(a1682)) | (~c1_1(a1682)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | c1_1(a1737) | (~c3_1(a1737))))),
% 1.36/1.61 inference(monotonicity,[status(thm)],[1456])).
% 1.36/1.61 tff(1458,plain,
% 1.36/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | c3_1(a1682) | (~c1_1(a1682)) | (~c2_1(a1682)) | c1_1(a1737) | c0_1(a1737) | (~c3_1(a1737)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1737) | c3_1(a1682) | (~ndr1_0) | (~c2_1(a1682)) | (~c1_1(a1682)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | c1_1(a1737) | (~c3_1(a1737)))),
% 1.36/1.61 inference(transitivity,[status(thm)],[1457, 1455])).
% 1.36/1.61 tff(1459,plain,
% 1.36/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | c3_1(a1682) | (~c1_1(a1682)) | (~c2_1(a1682)) | c1_1(a1737) | c0_1(a1737) | (~c3_1(a1737)))),
% 1.36/1.61 inference(quant_inst,[status(thm)],[])).
% 1.36/1.61 tff(1460,plain,
% 1.36/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1737) | c3_1(a1682) | (~ndr1_0) | (~c2_1(a1682)) | (~c1_1(a1682)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | c1_1(a1737) | (~c3_1(a1737))),
% 1.36/1.61 inference(modus_ponens,[status(thm)],[1459, 1458])).
% 1.36/1.61 tff(1461,plain,
% 1.36/1.61 ($false),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1460, 119, 261, 239, 216, 1454, 1453, 208, 1452, 1442, 1432, 1389])).
% 1.36/1.61 tff(1462,plain,(hskp0 | hskp1 | (~c1_1(a1650)) | c0_1(a1650) | c3_1(a1650) | c3_1(a1638) | c0_1(a1638) | c2_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.61 tff(1463,plain,
% 1.36/1.61 (hskp0),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1462, 21, 1382, 1381, 1380, 652, 22, 1217])).
% 1.36/1.61 tff(1464,plain,
% 1.36/1.61 (c3_1(a1634)),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[490, 1463])).
% 1.36/1.61 tff(1465,plain,
% 1.36/1.61 (c0_1(a1634)),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[498, 1463])).
% 1.36/1.61 tff(1466,plain,
% 1.36/1.61 (hskp28),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[647, 500, 170, 169, 504, 502, 503, 168])).
% 1.36/1.61 tff(1467,plain,
% 1.36/1.61 (c2_1(a1646)),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[238, 1466])).
% 1.36/1.61 tff(1468,plain,
% 1.36/1.61 (c1_1(a1646)),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[260, 1466])).
% 1.36/1.61 tff(1469,plain,
% 1.36/1.61 (c3_1(a1646)),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[268, 1466])).
% 1.36/1.61 tff(1470,plain,
% 1.36/1.61 (~hskp15),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1428, 1469, 661, 852, 1468, 169, 168, 170, 245, 183, 1467, 843, 842, 253])).
% 1.36/1.61 tff(1471,plain,
% 1.36/1.61 (hskp19),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1450, 1470, 21])).
% 1.36/1.61 tff(1472,plain,
% 1.36/1.61 (~hskp9),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[610, 1471, 504, 502, 503])).
% 1.36/1.61 tff(1473,plain,
% 1.36/1.61 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.36/1.61 inference(bind,[status(th)],[])).
% 1.36/1.61 tff(1474,plain,
% 1.36/1.61 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.36/1.61 inference(quant_intro,[status(thm)],[1473])).
% 1.36/1.61 tff(1475,plain,
% 1.36/1.61 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.36/1.61 inference(rewrite,[status(thm)],[])).
% 1.36/1.61 tff(1476,plain,
% 1.36/1.61 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp9))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.36/1.61 inference(bind,[status(th)],[])).
% 1.36/1.61 tff(1477,plain,
% 1.36/1.61 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.36/1.61 inference(quant_intro,[status(thm)],[1476])).
% 1.36/1.61 tff(1478,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause189')).
% 1.36/1.61 tff(1479,plain,
% 1.36/1.61 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.36/1.61 inference(modus_ponens,[status(thm)],[1478, 1477])).
% 1.36/1.61 tff(1480,plain,
% 1.36/1.61 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.36/1.61 inference(modus_ponens,[status(thm)],[1479, 1475])).
% 1.36/1.61 tff(1481,plain,(
% 1.36/1.61 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.36/1.61 inference(skolemize,[status(sab)],[1480])).
% 1.36/1.61 tff(1482,plain,
% 1.36/1.61 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.36/1.61 inference(modus_ponens,[status(thm)],[1481, 1474])).
% 1.36/1.61 tff(1483,plain,
% 1.36/1.61 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp9 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c1_1(a1648)) | (~c0_1(a1648)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp9 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c1_1(a1648)) | (~c0_1(a1648)))),
% 1.36/1.61 inference(rewrite,[status(thm)],[])).
% 1.36/1.61 tff(1484,plain,
% 1.36/1.61 ((hskp9 | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1648)) | c3_1(a1648) | (~c1_1(a1648)) | (~c2_1(a1648))) <=> (hskp9 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c1_1(a1648)) | (~c0_1(a1648)))),
% 1.36/1.61 inference(rewrite,[status(thm)],[])).
% 1.36/1.61 tff(1485,plain,
% 1.36/1.61 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1648)) | c3_1(a1648) | (~c1_1(a1648)) | (~c2_1(a1648)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp9 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c1_1(a1648)) | (~c0_1(a1648))))),
% 1.36/1.61 inference(monotonicity,[status(thm)],[1484])).
% 1.36/1.61 tff(1486,plain,
% 1.36/1.61 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1648)) | c3_1(a1648) | (~c1_1(a1648)) | (~c2_1(a1648)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp9 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c1_1(a1648)) | (~c0_1(a1648)))),
% 1.36/1.61 inference(transitivity,[status(thm)],[1485, 1483])).
% 1.36/1.61 tff(1487,plain,
% 1.36/1.61 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1648)) | c3_1(a1648) | (~c1_1(a1648)) | (~c2_1(a1648)))),
% 1.36/1.61 inference(quant_inst,[status(thm)],[])).
% 1.36/1.61 tff(1488,plain,
% 1.36/1.61 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp9 | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c1_1(a1648)) | (~c0_1(a1648))),
% 1.36/1.61 inference(modus_ponens,[status(thm)],[1487, 1486])).
% 1.36/1.61 tff(1489,plain,
% 1.36/1.61 (hskp9 | (~c1_1(a1648))),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1488, 119, 170, 169, 168, 1482])).
% 1.36/1.61 tff(1490,plain,
% 1.36/1.61 (~c1_1(a1648)),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1489, 1472])).
% 1.36/1.61 tff(1491,plain,
% 1.36/1.61 ($false),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[539, 1490, 1472, 500])).
% 1.36/1.61 tff(1492,plain,(hskp2 | (~c2_1(a1648)) | c3_1(a1648) | (~c0_1(a1648)) | (~c0_1(a1634)) | (~c3_1(a1634)) | c1_1(a1634) | hskp1 | hskp3 | (~c1_1(a1650)) | c0_1(a1650) | c3_1(a1650)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.61 tff(1493,plain,
% 1.36/1.61 (hskp2),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1492, 1227, 1226, 1228, 1465, 1464, 503, 21, 660, 1382, 1381, 1380])).
% 1.36/1.61 tff(1494,plain,
% 1.36/1.61 (~c0_1(a1637)),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1124, 1493])).
% 1.36/1.61 tff(1495,plain,
% 1.36/1.61 (c3_1(a1637)),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1132, 1493])).
% 1.36/1.61 tff(1496,plain,
% 1.36/1.61 (c1_1(a1637)),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1140, 1493])).
% 1.36/1.61 tff(1497,plain,
% 1.36/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1682) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c2_1(a1682)) | (~c1_1(a1682)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1682) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c2_1(a1682)) | (~c1_1(a1682)))),
% 1.36/1.61 inference(rewrite,[status(thm)],[])).
% 1.36/1.61 tff(1498,plain,
% 1.36/1.61 (((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637))) <=> (c3_1(a1682) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c2_1(a1682)) | (~c1_1(a1682)))),
% 1.36/1.61 inference(rewrite,[status(thm)],[])).
% 1.36/1.61 tff(1499,plain,
% 1.36/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1682) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c2_1(a1682)) | (~c1_1(a1682))))),
% 1.36/1.61 inference(monotonicity,[status(thm)],[1498])).
% 1.36/1.61 tff(1500,plain,
% 1.36/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1682) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c2_1(a1682)) | (~c1_1(a1682)))),
% 1.36/1.61 inference(transitivity,[status(thm)],[1499, 1497])).
% 1.36/1.61 tff(1501,plain,
% 1.36/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637)))),
% 1.36/1.61 inference(quant_inst,[status(thm)],[])).
% 1.36/1.61 tff(1502,plain,
% 1.36/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1682) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c2_1(a1682)) | (~c1_1(a1682))),
% 1.36/1.61 inference(modus_ponens,[status(thm)],[1501, 1500])).
% 1.36/1.61 tff(1503,plain,
% 1.36/1.61 ($false),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1502, 119, 577, 585, 1148, 1147, 504, 502, 569, 1146, 503, 20])).
% 1.36/1.61 tff(1504,plain,((~hskp19) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c0_1(a1634)) | (~c3_1(a1634)) | c0_1(a1637) | c1_1(a1634)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.61 tff(1505,plain,
% 1.36/1.61 (~hskp19),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1504, 1496, 1495, 1465, 1464, 1494, 503])).
% 1.36/1.61 tff(1506,plain,
% 1.36/1.61 (~c2_1(a1637)),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1368, 119, 1228, 1227, 652, 1496, 1226, 22, 1217, 1494, 295])).
% 1.36/1.61 tff(1507,plain,
% 1.36/1.61 (((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | (~c3_1(a1637)))) <=> ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp3 | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | (~c3_1(a1637)))),
% 1.36/1.61 inference(rewrite,[status(thm)],[])).
% 1.36/1.61 tff(1508,plain,
% 1.36/1.61 ((hskp21 | hskp3 | (~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637))) <=> (hskp21 | hskp3 | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | (~c3_1(a1637)))),
% 1.36/1.61 inference(rewrite,[status(thm)],[])).
% 1.36/1.61 tff(1509,plain,
% 1.36/1.61 (((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | (~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))) <=> ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | (~c3_1(a1637))))),
% 1.36/1.61 inference(monotonicity,[status(thm)],[1508])).
% 1.36/1.61 tff(1510,plain,
% 1.36/1.61 (((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | (~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))) <=> ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp3 | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | (~c3_1(a1637)))),
% 1.36/1.61 inference(transitivity,[status(thm)],[1509, 1507])).
% 1.36/1.61 tff(1511,plain,
% 1.36/1.61 ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | (~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))),
% 1.36/1.61 inference(quant_inst,[status(thm)],[])).
% 1.36/1.61 tff(1512,plain,
% 1.36/1.61 ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp3 | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | (~c3_1(a1637))),
% 1.36/1.61 inference(modus_ponens,[status(thm)],[1511, 1510])).
% 1.36/1.61 tff(1513,plain,
% 1.36/1.61 (hskp21 | c2_1(a1637)),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1512, 119, 660, 1496, 1495, 769])).
% 1.36/1.61 tff(1514,plain,
% 1.36/1.61 (hskp21),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1513, 1506])).
% 1.36/1.61 tff(1515,plain,
% 1.36/1.61 (~c1_1(a1691)),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[697, 1514])).
% 1.36/1.61 tff(1516,plain,
% 1.36/1.61 (c3_1(a1691)),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[713, 1514])).
% 1.36/1.61 tff(1517,plain,
% 1.36/1.61 (c2_1(a1691)),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[738, 1514])).
% 1.36/1.61 tff(1518,plain,
% 1.36/1.61 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp28 | hskp19 | c1_1(a1691) | (~ndr1_0) | (~c3_1(a1691)) | (~c2_1(a1691)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp28 | hskp19 | c1_1(a1691) | (~ndr1_0) | (~c3_1(a1691)) | (~c2_1(a1691)))),
% 1.36/1.61 inference(rewrite,[status(thm)],[])).
% 1.36/1.61 tff(1519,plain,
% 1.36/1.61 ((hskp28 | hskp19 | (~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691))) <=> (hskp28 | hskp19 | c1_1(a1691) | (~ndr1_0) | (~c3_1(a1691)) | (~c2_1(a1691)))),
% 1.36/1.61 inference(rewrite,[status(thm)],[])).
% 1.36/1.61 tff(1520,plain,
% 1.36/1.61 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp28 | hskp19 | c1_1(a1691) | (~ndr1_0) | (~c3_1(a1691)) | (~c2_1(a1691))))),
% 1.36/1.61 inference(monotonicity,[status(thm)],[1519])).
% 1.36/1.61 tff(1521,plain,
% 1.36/1.61 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp28 | hskp19 | c1_1(a1691) | (~ndr1_0) | (~c3_1(a1691)) | (~c2_1(a1691)))),
% 1.36/1.61 inference(transitivity,[status(thm)],[1520, 1518])).
% 1.36/1.61 tff(1522,plain,
% 1.36/1.61 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691)))),
% 1.36/1.61 inference(quant_inst,[status(thm)],[])).
% 1.36/1.61 tff(1523,plain,
% 1.36/1.61 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp28 | hskp19 | c1_1(a1691) | (~ndr1_0) | (~c3_1(a1691)) | (~c2_1(a1691))),
% 1.36/1.61 inference(modus_ponens,[status(thm)],[1522, 1521])).
% 1.36/1.61 tff(1524,plain,
% 1.36/1.61 (hskp28 | hskp19),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1523, 119, 1517, 1516, 1515, 621])).
% 1.36/1.61 tff(1525,plain,
% 1.36/1.61 (hskp28),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1524, 1505])).
% 1.36/1.61 tff(1526,plain,
% 1.36/1.61 (c2_1(a1646)),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[238, 1525])).
% 1.36/1.61 tff(1527,plain,
% 1.36/1.61 (hskp15),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1450, 1505, 21])).
% 1.36/1.61 tff(1528,plain,
% 1.36/1.61 (c1_1(a1646)),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[260, 1525])).
% 1.36/1.61 tff(1529,plain,
% 1.36/1.61 (c3_1(a1646)),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[268, 1525])).
% 1.36/1.61 tff(1530,plain,
% 1.36/1.61 ($false),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1428, 1529, 1528, 660, 1382, 1527, 1227, 1226, 1228, 1231, 1232, 1526, 1381, 1380, 1230])).
% 1.36/1.61 tff(1531,plain,(hskp1 | c1_1(a1634) | c3_1(a1638) | c0_1(a1638) | c2_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.61 tff(1532,plain,
% 1.36/1.61 (hskp1),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1531, 1217, 652, 22, 503])).
% 1.36/1.61 tff(1533,plain,
% 1.36/1.61 (((~hskp1) | (~c1_1(a1636))) <=> ((~hskp1) | (~c1_1(a1636)))),
% 1.36/1.61 inference(rewrite,[status(thm)],[])).
% 1.36/1.61 tff(1534,plain,
% 1.36/1.61 (((~c1_1(a1636)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a1636)))),
% 1.36/1.61 inference(rewrite,[status(thm)],[])).
% 1.36/1.61 tff(1535,axiom,((~c1_1(a1636)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 1.36/1.61 tff(1536,plain,
% 1.36/1.61 ((~hskp1) | (~c1_1(a1636))),
% 1.36/1.61 inference(modus_ponens,[status(thm)],[1535, 1534])).
% 1.36/1.61 tff(1537,plain,
% 1.36/1.61 ((~hskp1) | (~c1_1(a1636))),
% 1.36/1.61 inference(modus_ponens,[status(thm)],[1536, 1533])).
% 1.36/1.61 tff(1538,plain,
% 1.36/1.61 (~c1_1(a1636)),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1537, 1532])).
% 1.36/1.61 tff(1539,plain,
% 1.36/1.61 (((~hskp1) | (~c0_1(a1636))) <=> ((~hskp1) | (~c0_1(a1636)))),
% 1.36/1.61 inference(rewrite,[status(thm)],[])).
% 1.36/1.61 tff(1540,plain,
% 1.36/1.61 (((~c0_1(a1636)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a1636)))),
% 1.36/1.61 inference(rewrite,[status(thm)],[])).
% 1.36/1.61 tff(1541,axiom,((~c0_1(a1636)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 1.36/1.61 tff(1542,plain,
% 1.36/1.61 ((~hskp1) | (~c0_1(a1636))),
% 1.36/1.61 inference(modus_ponens,[status(thm)],[1541, 1540])).
% 1.36/1.61 tff(1543,plain,
% 1.36/1.61 ((~hskp1) | (~c0_1(a1636))),
% 1.36/1.61 inference(modus_ponens,[status(thm)],[1542, 1539])).
% 1.36/1.61 tff(1544,plain,
% 1.36/1.61 (~c0_1(a1636)),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1543, 1532])).
% 1.36/1.61 tff(1545,plain,
% 1.36/1.61 (((~hskp1) | (~c2_1(a1636))) <=> ((~hskp1) | (~c2_1(a1636)))),
% 1.36/1.61 inference(rewrite,[status(thm)],[])).
% 1.36/1.61 tff(1546,plain,
% 1.36/1.61 (((~c2_1(a1636)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a1636)))),
% 1.36/1.61 inference(rewrite,[status(thm)],[])).
% 1.36/1.61 tff(1547,axiom,((~c2_1(a1636)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 1.36/1.61 tff(1548,plain,
% 1.36/1.61 ((~hskp1) | (~c2_1(a1636))),
% 1.36/1.61 inference(modus_ponens,[status(thm)],[1547, 1546])).
% 1.36/1.61 tff(1549,plain,
% 1.36/1.61 ((~hskp1) | (~c2_1(a1636))),
% 1.36/1.61 inference(modus_ponens,[status(thm)],[1548, 1545])).
% 1.36/1.61 tff(1550,plain,
% 1.36/1.61 (~c2_1(a1636)),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1549, 1532])).
% 1.36/1.61 tff(1551,assumption,(~c2_1(a1636)), introduced(assumption)).
% 1.36/1.61 tff(1552,assumption,(~c1_1(a1636)), introduced(assumption)).
% 1.36/1.61 tff(1553,assumption,(~c0_1(a1636)), introduced(assumption)).
% 1.36/1.61 tff(1554,plain,
% 1.36/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1638)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1638)))),
% 1.36/1.61 inference(rewrite,[status(thm)],[])).
% 1.36/1.61 tff(1555,plain,
% 1.36/1.61 (((~ndr1_0) | c2_1(a1638) | c0_1(a1638) | (~c1_1(a1638)) | c2_1(a1636) | c0_1(a1636) | c3_1(a1636) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636)) <=> (c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1638)))),
% 1.36/1.61 inference(rewrite,[status(thm)],[])).
% 1.36/1.61 tff(1556,plain,
% 1.36/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1638) | c0_1(a1638) | (~c1_1(a1638)) | c2_1(a1636) | c0_1(a1636) | c3_1(a1636) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1638))))),
% 1.36/1.61 inference(monotonicity,[status(thm)],[1555])).
% 1.36/1.61 tff(1557,plain,
% 1.36/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1638) | c0_1(a1638) | (~c1_1(a1638)) | c2_1(a1636) | c0_1(a1636) | c3_1(a1636) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1638)))),
% 1.36/1.61 inference(transitivity,[status(thm)],[1556, 1554])).
% 1.36/1.61 tff(1558,plain,
% 1.36/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1638) | c0_1(a1638) | (~c1_1(a1638)) | c2_1(a1636) | c0_1(a1636) | c3_1(a1636) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636))),
% 1.36/1.61 inference(quant_inst,[status(thm)],[])).
% 1.36/1.61 tff(1559,plain,
% 1.36/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1638))),
% 1.36/1.61 inference(modus_ponens,[status(thm)],[1558, 1557])).
% 1.36/1.61 tff(1560,plain,
% 1.36/1.61 (c0_1(a1638) | c3_1(a1636) | (~c1_1(a1638))),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1559, 296, 1217, 1553, 1552, 1551, 1261])).
% 1.36/1.61 tff(1561,plain,
% 1.36/1.61 (c3_1(a1636)),
% 1.36/1.61 inference(unit_resolution,[status(thm)],[1560, 1318, 22])).
% 1.36/1.61 tff(1562,plain,
% 1.36/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c1_1(a1638)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c1_1(a1638)))),
% 1.36/1.61 inference(rewrite,[status(thm)],[])).
% 1.36/1.61 tff(1563,plain,
% 1.36/1.61 (((~ndr1_0) | c2_1(a1638) | c0_1(a1638) | (~c1_1(a1638)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636)) <=> (c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c1_1(a1638)))),
% 1.36/1.61 inference(rewrite,[status(thm)],[])).
% 1.36/1.61 tff(1564,plain,
% 1.36/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1638) | c0_1(a1638) | (~c1_1(a1638)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c1_1(a1638))))),
% 1.36/1.61 inference(monotonicity,[status(thm)],[1563])).
% 1.36/1.61 tff(1565,plain,
% 1.36/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1638) | c0_1(a1638) | (~c1_1(a1638)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c1_1(a1638)))),
% 1.36/1.62 inference(transitivity,[status(thm)],[1564, 1562])).
% 1.36/1.62 tff(1566,plain,
% 1.36/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1638) | c0_1(a1638) | (~c1_1(a1638)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636))),
% 1.36/1.62 inference(quant_inst,[status(thm)],[])).
% 1.36/1.62 tff(1567,plain,
% 1.36/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c1_1(a1638))),
% 1.36/1.62 inference(modus_ponens,[status(thm)],[1566, 1565])).
% 1.36/1.62 tff(1568,plain,
% 1.36/1.62 (c3_1(a1638) | c0_1(a1638) | (~c1_1(a1638))),
% 1.36/1.62 inference(unit_resolution,[status(thm)],[1567, 296, 1217, 1553, 1552, 1551, 1261])).
% 1.45/1.62 tff(1569,plain,
% 1.45/1.62 (c3_1(a1638)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1568, 1318, 22])).
% 1.45/1.62 tff(1570,plain,
% 1.45/1.62 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | (~c1_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | (~c1_1(a1638)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1571,plain,
% 1.45/1.62 ((hskp11 | (~ndr1_0) | c0_1(a1638) | (~c3_1(a1638)) | (~c1_1(a1638)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638))) <=> (hskp11 | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | (~c1_1(a1638)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1572,plain,
% 1.45/1.62 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a1638) | (~c3_1(a1638)) | (~c1_1(a1638)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | (~c1_1(a1638))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[1571])).
% 1.45/1.62 tff(1573,plain,
% 1.45/1.62 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a1638) | (~c3_1(a1638)) | (~c1_1(a1638)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | (~c1_1(a1638)))),
% 1.45/1.62 inference(transitivity,[status(thm)],[1572, 1570])).
% 1.45/1.62 tff(1574,plain,
% 1.45/1.62 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a1638) | (~c3_1(a1638)) | (~c1_1(a1638)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638)))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(1575,plain,
% 1.45/1.62 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | (~c1_1(a1638))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1574, 1573])).
% 1.45/1.62 tff(1576,plain,
% 1.45/1.62 (hskp11 | (~c3_1(a1638)) | (~c1_1(a1638))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1575, 296, 22, 1217, 55])).
% 1.45/1.62 tff(1577,plain,
% 1.45/1.62 (hskp11),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1576, 1318, 1569])).
% 1.45/1.62 tff(1578,plain,
% 1.45/1.62 (~c0_1(a1650)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[673, 1577])).
% 1.45/1.62 tff(1579,plain,
% 1.45/1.62 (c1_1(a1650)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[705, 1577])).
% 1.45/1.62 tff(1580,plain,
% 1.45/1.62 (((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (c0_1(a1650) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c2_1(a1650)) | (~c1_1(a1650)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | c0_1(a1650) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1581,plain,
% 1.45/1.62 (((~ndr1_0) | c0_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1636) | c0_1(a1636) | (~c3_1(a1636))) <=> (c0_1(a1650) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1582,plain,
% 1.45/1.62 (((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | ((~ndr1_0) | c0_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1636) | c0_1(a1636) | (~c3_1(a1636)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (c0_1(a1650) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c2_1(a1650)) | (~c1_1(a1650))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[1581])).
% 1.45/1.62 tff(1583,plain,
% 1.45/1.62 (((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | ((~ndr1_0) | c0_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1636) | c0_1(a1636) | (~c3_1(a1636)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | c0_1(a1650) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.45/1.62 inference(transitivity,[status(thm)],[1582, 1580])).
% 1.45/1.62 tff(1584,plain,
% 1.45/1.62 ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | ((~ndr1_0) | c0_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1636) | c0_1(a1636) | (~c3_1(a1636)))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(1585,plain,
% 1.45/1.62 ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | c0_1(a1650) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c2_1(a1650)) | (~c1_1(a1650))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1584, 1583])).
% 1.45/1.62 tff(1586,plain,
% 1.45/1.62 (~c2_1(a1650)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1585, 296, 1579, 1578, 1553, 1552, 691, 1561])).
% 1.45/1.62 tff(1587,plain,
% 1.45/1.62 (~c3_1(a1650)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[667, 1577])).
% 1.45/1.62 tff(1588,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c1_1(a1638)) | c2_1(a1650))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c1_1(a1638)) | c2_1(a1650))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1589,plain,
% 1.45/1.62 (((~ndr1_0) | c2_1(a1638) | c0_1(a1638) | (~c1_1(a1638)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636)) <=> (c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c1_1(a1638)) | c2_1(a1650))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1590,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1638) | c0_1(a1638) | (~c1_1(a1638)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c1_1(a1638)) | c2_1(a1650)))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[1589])).
% 1.45/1.62 tff(1591,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1638) | c0_1(a1638) | (~c1_1(a1638)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c1_1(a1638)) | c2_1(a1650))),
% 1.45/1.62 inference(transitivity,[status(thm)],[1590, 1588])).
% 1.45/1.62 tff(1592,plain,
% 1.45/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1638) | c0_1(a1638) | (~c1_1(a1638)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(1593,plain,
% 1.45/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c1_1(a1638)) | c2_1(a1650)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1592, 1591])).
% 1.45/1.62 tff(1594,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1593, 296, 1578, 1587, 22, 1217, 1553, 1552, 1551, 1261, 1318, 1586])).
% 1.45/1.62 tff(1595,plain,((~c1_1(a1638)) | (~ndr1_0) | c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(1596,plain,
% 1.45/1.62 ((~c1_1(a1638)) | c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1595, 119])).
% 1.45/1.62 tff(1597,plain,
% 1.45/1.62 (~c1_1(a1638)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1596, 1550, 22, 1217, 1544, 1538])).
% 1.45/1.62 tff(1598,plain,
% 1.45/1.62 (hskp2),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1340, 1597, 660, 1217])).
% 1.45/1.62 tff(1599,plain,
% 1.45/1.62 (~c0_1(a1637)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1124, 1598])).
% 1.45/1.62 tff(1600,plain,
% 1.45/1.62 (c1_1(a1637)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1140, 1598])).
% 1.45/1.62 tff(1601,assumption,(~c2_1(a1637)), introduced(assumption)).
% 1.45/1.62 tff(1602,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | c1_1(a1638))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | c1_1(a1638))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1603,plain,
% 1.45/1.62 (((~ndr1_0) | c2_1(a1637) | c0_1(a1637) | (~c1_1(a1637)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638)) <=> (c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | c1_1(a1638))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1604,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1637) | c0_1(a1637) | (~c1_1(a1637)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | c1_1(a1638)))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[1603])).
% 1.45/1.62 tff(1605,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1637) | c0_1(a1637) | (~c1_1(a1637)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | c1_1(a1638))),
% 1.45/1.62 inference(transitivity,[status(thm)],[1604, 1602])).
% 1.45/1.62 tff(1606,plain,
% 1.45/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1637) | c0_1(a1637) | (~c1_1(a1637)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(1607,plain,
% 1.45/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | c1_1(a1638)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1606, 1605])).
% 1.45/1.62 tff(1608,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1607, 296, 652, 1148, 22, 1217, 1146, 1261, 1601, 1233])).
% 1.45/1.62 tff(1609,plain,(c2_1(a1637) | (~ndr1_0) | c3_1(a1638) | (~c1_1(a1637)) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | c1_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(1610,plain,
% 1.45/1.62 (c2_1(a1637) | c3_1(a1638) | (~c1_1(a1637)) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | c1_1(a1638)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1609, 119])).
% 1.45/1.62 tff(1611,plain,
% 1.45/1.62 (c2_1(a1637)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1610, 1600, 652, 1597, 22, 1217, 1599])).
% 1.45/1.62 tff(1612,plain,
% 1.45/1.62 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 1.45/1.62 inference(bind,[status(th)],[])).
% 1.45/1.62 tff(1613,plain,
% 1.45/1.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.45/1.62 inference(quant_intro,[status(thm)],[1612])).
% 1.45/1.62 tff(1614,plain,
% 1.45/1.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1615,plain,
% 1.45/1.62 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 1.45/1.62 inference(bind,[status(th)],[])).
% 1.45/1.62 tff(1616,plain,
% 1.45/1.62 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.45/1.62 inference(quant_intro,[status(thm)],[1615])).
% 1.45/1.62 tff(1617,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause191')).
% 1.45/1.62 tff(1618,plain,
% 1.45/1.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1617, 1616])).
% 1.45/1.62 tff(1619,plain,
% 1.45/1.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1618, 1614])).
% 1.45/1.62 tff(1620,plain,(
% 1.45/1.62 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.45/1.62 inference(skolemize,[status(sab)],[1619])).
% 1.45/1.62 tff(1621,plain,
% 1.45/1.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1620, 1613])).
% 1.45/1.62 tff(1622,plain,
% 1.45/1.62 (c3_1(a1637)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1132, 1598])).
% 1.45/1.62 tff(1623,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c2_1(a1637)) | (~c3_1(a1637)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c2_1(a1637)) | (~c3_1(a1637)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1624,plain,
% 1.45/1.62 (((~ndr1_0) | c0_1(a1637) | (~c2_1(a1637)) | (~c3_1(a1637)) | c2_1(a1636) | c0_1(a1636) | (~c3_1(a1636)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638)) <=> (c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c2_1(a1637)) | (~c3_1(a1637)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1625,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1637) | (~c2_1(a1637)) | (~c3_1(a1637)) | c2_1(a1636) | c0_1(a1636) | (~c3_1(a1636)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c2_1(a1637)) | (~c3_1(a1637))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[1624])).
% 1.45/1.62 tff(1626,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1637) | (~c2_1(a1637)) | (~c3_1(a1637)) | c2_1(a1636) | c0_1(a1636) | (~c3_1(a1636)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c2_1(a1637)) | (~c3_1(a1637)))),
% 1.45/1.62 inference(transitivity,[status(thm)],[1625, 1623])).
% 1.45/1.62 tff(1627,plain,
% 1.45/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1637) | (~c2_1(a1637)) | (~c3_1(a1637)) | c2_1(a1636) | c0_1(a1636) | (~c3_1(a1636)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(1628,plain,
% 1.45/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1638) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c2_1(a1637)) | (~c3_1(a1637))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1627, 1626])).
% 1.45/1.62 tff(1629,plain,
% 1.45/1.62 (~c3_1(a1636)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1628, 119, 652, 1622, 22, 1217, 1599, 1544, 1550, 1621, 1611])).
% 1.45/1.62 tff(1630,assumption,(~hskp20), introduced(assumption)).
% 1.45/1.62 tff(1631,plain,
% 1.45/1.62 ((hskp20 | hskp14) <=> (hskp20 | hskp14)),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1632,axiom,(hskp20 | hskp14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 1.45/1.62 tff(1633,plain,
% 1.45/1.62 (hskp20 | hskp14),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1632, 1631])).
% 1.45/1.62 tff(1634,plain,
% 1.45/1.62 (hskp20 | hskp14),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1633, 1631])).
% 1.45/1.62 tff(1635,plain,
% 1.45/1.62 (hskp20 | hskp14),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1634, 1631])).
% 1.45/1.62 tff(1636,plain,
% 1.45/1.62 (hskp20 | hskp14),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1635, 1631])).
% 1.45/1.62 tff(1637,plain,
% 1.45/1.62 (hskp20 | hskp14),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1636, 1631])).
% 1.45/1.62 tff(1638,plain,
% 1.45/1.62 (hskp14),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1637, 1630])).
% 1.45/1.62 tff(1639,plain,
% 1.45/1.62 ((ndr1_0 | (~hskp14)) <=> (ndr1_0 | (~hskp14))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1640,plain,
% 1.45/1.62 (((~hskp14) | ndr1_0) <=> (ndr1_0 | (~hskp14))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1641,axiom,((~hskp14) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause18')).
% 1.45/1.62 tff(1642,plain,
% 1.45/1.62 (ndr1_0 | (~hskp14)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1641, 1640])).
% 1.45/1.62 tff(1643,plain,
% 1.45/1.62 (ndr1_0 | (~hskp14)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1642, 1639])).
% 1.45/1.62 tff(1644,plain,
% 1.45/1.62 (ndr1_0),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1643, 1638])).
% 1.45/1.62 tff(1645,plain,
% 1.45/1.62 (((~hskp14) | (~c3_1(a1661))) <=> ((~hskp14) | (~c3_1(a1661)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1646,plain,
% 1.45/1.62 (((~c3_1(a1661)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a1661)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1647,axiom,((~c3_1(a1661)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 1.45/1.62 tff(1648,plain,
% 1.45/1.62 ((~hskp14) | (~c3_1(a1661))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1647, 1646])).
% 1.45/1.62 tff(1649,plain,
% 1.45/1.62 ((~hskp14) | (~c3_1(a1661))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1648, 1645])).
% 1.45/1.62 tff(1650,plain,
% 1.45/1.62 (~c3_1(a1661)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1649, 1638])).
% 1.45/1.62 tff(1651,plain,
% 1.45/1.62 (((~hskp14) | (~c1_1(a1661))) <=> ((~hskp14) | (~c1_1(a1661)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1652,plain,
% 1.45/1.62 (((~c1_1(a1661)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a1661)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1653,axiom,((~c1_1(a1661)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 1.45/1.62 tff(1654,plain,
% 1.45/1.62 ((~hskp14) | (~c1_1(a1661))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1653, 1652])).
% 1.45/1.62 tff(1655,plain,
% 1.45/1.62 ((~hskp14) | (~c1_1(a1661))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1654, 1651])).
% 1.45/1.62 tff(1656,plain,
% 1.45/1.62 (~c1_1(a1661)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1655, 1638])).
% 1.45/1.62 tff(1657,plain,
% 1.45/1.62 (~c1_1(a1638)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1595, 22, 1644, 1217, 1553, 1552, 1551])).
% 1.45/1.62 tff(1658,plain,
% 1.45/1.62 (((~hskp14) | c0_1(a1661)) <=> ((~hskp14) | c0_1(a1661))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1659,axiom,((~hskp14) | c0_1(a1661)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 1.45/1.62 tff(1660,plain,
% 1.45/1.62 ((~hskp14) | c0_1(a1661)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1659, 1658])).
% 1.45/1.62 tff(1661,plain,
% 1.45/1.62 ((~hskp14) | c0_1(a1661)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1660, 1658])).
% 1.45/1.62 tff(1662,plain,
% 1.45/1.62 ((~hskp14) | c0_1(a1661)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1661, 1658])).
% 1.45/1.62 tff(1663,plain,
% 1.45/1.62 ((~hskp14) | c0_1(a1661)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1662, 1658])).
% 1.45/1.62 tff(1664,plain,
% 1.45/1.62 ((~hskp14) | c0_1(a1661)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1663, 1658])).
% 1.45/1.62 tff(1665,plain,
% 1.45/1.62 (c0_1(a1661)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1664, 1638])).
% 1.45/1.62 tff(1666,plain,
% 1.45/1.62 (~c1_1(a1638)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1595, 22, 296, 1217, 1553, 1552, 1551])).
% 1.45/1.62 tff(1667,plain,
% 1.45/1.62 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1668,plain,
% 1.45/1.62 ((hskp3 | hskp2 | (~ndr1_0) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636)) <=> (hskp3 | hskp2 | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1669,plain,
% 1.45/1.62 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0)))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[1668])).
% 1.45/1.62 tff(1670,plain,
% 1.45/1.62 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0))),
% 1.45/1.62 inference(transitivity,[status(thm)],[1669, 1667])).
% 1.45/1.62 tff(1671,plain,
% 1.45/1.62 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(1672,plain,
% 1.45/1.62 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1671, 1670])).
% 1.45/1.62 tff(1673,plain,
% 1.45/1.62 (hskp3 | hskp2 | c0_1(a1636) | c1_1(a1636)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1672, 296, 1551, 1045])).
% 1.45/1.62 tff(1674,plain,
% 1.45/1.62 (hskp2),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1673, 660, 1553, 1552])).
% 1.45/1.62 tff(1675,plain,
% 1.45/1.62 (c1_1(a1637)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1140, 1674])).
% 1.45/1.62 tff(1676,plain,
% 1.45/1.62 (c2_1(a1637)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1609, 652, 296, 1675, 22, 1217, 1146, 1666])).
% 1.45/1.62 tff(1677,assumption,(~c3_1(a1661)), introduced(assumption)).
% 1.45/1.62 tff(1678,assumption,(c0_1(a1661)), introduced(assumption)).
% 1.45/1.62 tff(1679,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1638) | c3_1(a1661) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c2_1(a1661)) | (~c0_1(a1661)) | (~c1_1(a1637)) | (~c2_1(a1637)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1638) | c3_1(a1661) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c2_1(a1661)) | (~c0_1(a1661)) | (~c1_1(a1637)) | (~c2_1(a1637)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1680,plain,
% 1.45/1.62 (((~ndr1_0) | c3_1(a1661) | (~c2_1(a1661)) | (~c0_1(a1661)) | c0_1(a1637) | (~c1_1(a1637)) | (~c2_1(a1637)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638)) <=> (c3_1(a1638) | c3_1(a1661) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c2_1(a1661)) | (~c0_1(a1661)) | (~c1_1(a1637)) | (~c2_1(a1637)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1681,plain,
% 1.45/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1661) | (~c2_1(a1661)) | (~c0_1(a1661)) | c0_1(a1637) | (~c1_1(a1637)) | (~c2_1(a1637)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1638) | c3_1(a1661) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c2_1(a1661)) | (~c0_1(a1661)) | (~c1_1(a1637)) | (~c2_1(a1637))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[1680])).
% 1.45/1.63 tff(1682,plain,
% 1.45/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1661) | (~c2_1(a1661)) | (~c0_1(a1661)) | c0_1(a1637) | (~c1_1(a1637)) | (~c2_1(a1637)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1638) | c3_1(a1661) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c2_1(a1661)) | (~c0_1(a1661)) | (~c1_1(a1637)) | (~c2_1(a1637)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[1681, 1679])).
% 1.45/1.63 tff(1683,plain,
% 1.45/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1661) | (~c2_1(a1661)) | (~c0_1(a1661)) | c0_1(a1637) | (~c1_1(a1637)) | (~c2_1(a1637)) | c2_1(a1638) | c0_1(a1638) | c3_1(a1638))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(1684,plain,
% 1.45/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1638) | c3_1(a1661) | c0_1(a1638) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c2_1(a1661)) | (~c0_1(a1661)) | (~c1_1(a1637)) | (~c2_1(a1637))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1683, 1682])).
% 1.45/1.63 tff(1685,plain,
% 1.45/1.63 (c3_1(a1638) | c0_1(a1638) | (~c2_1(a1661)) | (~c1_1(a1637)) | (~c2_1(a1637))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1684, 296, 1678, 1677, 1217, 1146, 295])).
% 1.45/1.63 tff(1686,plain,
% 1.45/1.63 (~c2_1(a1661)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1685, 1676, 22, 1675, 652])).
% 1.45/1.63 tff(1687,assumption,(~c1_1(a1661)), introduced(assumption)).
% 1.45/1.63 tff(1688,plain,
% 1.45/1.63 (c3_1(a1637)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1132, 1674])).
% 1.45/1.63 tff(1689,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | c1_1(a1661) | c0_1(a1637) | (~ndr1_0) | c2_1(a1661) | (~c0_1(a1661)) | (~c1_1(a1637)) | (~c3_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c1_1(a1661) | c0_1(a1637) | (~ndr1_0) | c2_1(a1661) | (~c0_1(a1661)) | (~c1_1(a1637)) | (~c3_1(a1637)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1690,plain,
% 1.45/1.63 ((hskp11 | (~ndr1_0) | c2_1(a1661) | c1_1(a1661) | (~c0_1(a1661)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637))) <=> (hskp11 | c1_1(a1661) | c0_1(a1637) | (~ndr1_0) | c2_1(a1661) | (~c0_1(a1661)) | (~c1_1(a1637)) | (~c3_1(a1637)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1691,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1661) | c1_1(a1661) | (~c0_1(a1661)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | c1_1(a1661) | c0_1(a1637) | (~ndr1_0) | c2_1(a1661) | (~c0_1(a1661)) | (~c1_1(a1637)) | (~c3_1(a1637))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[1690])).
% 1.45/1.63 tff(1692,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1661) | c1_1(a1661) | (~c0_1(a1661)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c1_1(a1661) | c0_1(a1637) | (~ndr1_0) | c2_1(a1661) | (~c0_1(a1661)) | (~c1_1(a1637)) | (~c3_1(a1637)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[1691, 1689])).
% 1.45/1.63 tff(1693,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1661) | c1_1(a1661) | (~c0_1(a1661)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(1694,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c1_1(a1661) | c0_1(a1637) | (~ndr1_0) | c2_1(a1661) | (~c0_1(a1661)) | (~c1_1(a1637)) | (~c3_1(a1637))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1693, 1692])).
% 1.45/1.63 tff(1695,plain,
% 1.45/1.63 (hskp11),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1694, 296, 1678, 1675, 1688, 1687, 1146, 280, 1686])).
% 1.45/1.63 tff(1696,plain,
% 1.45/1.63 (~c3_1(a1650)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[667, 1695])).
% 1.45/1.63 tff(1697,plain,
% 1.45/1.63 (~c0_1(a1650)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[673, 1695])).
% 1.45/1.63 tff(1698,plain,
% 1.45/1.63 (c1_1(a1650)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[705, 1695])).
% 1.45/1.63 tff(1699,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c3_1(a1638) | c0_1(a1650) | c3_1(a1650) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c1_1(a1650)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c3_1(a1638) | c0_1(a1650) | c3_1(a1650) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c1_1(a1650)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1700,plain,
% 1.45/1.63 ((hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1638) | c1_1(a1638) | c3_1(a1638)) <=> (hskp3 | c3_1(a1638) | c0_1(a1650) | c3_1(a1650) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c1_1(a1650)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1701,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1638) | c1_1(a1638) | c3_1(a1638))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c3_1(a1638) | c0_1(a1650) | c3_1(a1650) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c1_1(a1650))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[1700])).
% 1.45/1.63 tff(1702,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1638) | c1_1(a1638) | c3_1(a1638))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c3_1(a1638) | c0_1(a1650) | c3_1(a1650) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c1_1(a1650)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[1701, 1699])).
% 1.45/1.63 tff(1703,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1638) | c1_1(a1638) | c3_1(a1638))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(1704,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c3_1(a1638) | c0_1(a1650) | c3_1(a1650) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c1_1(a1650))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1703, 1702])).
% 1.45/1.63 tff(1705,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1704, 296, 660, 1698, 652, 1697, 1696, 1217, 10, 1666])).
% 1.45/1.63 tff(1706,plain,(c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | (~c0_1(a1661)) | c1_1(a1661) | c0_1(a1637) | c0_1(a1638) | c3_1(a1661) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(1707,plain,
% 1.45/1.63 (c3_1(a1638)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1706, 22, 1217, 1665, 1656, 1146, 1644, 1650, 1553, 1552, 1551])).
% 1.45/1.63 tff(1708,assumption,(c3_1(a1638)), introduced(assumption)).
% 1.45/1.63 tff(1709,plain,
% 1.45/1.63 (^[U: $i] : refl((hskp28 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp28 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.45/1.63 inference(bind,[status(th)],[])).
% 1.45/1.63 tff(1710,plain,
% 1.45/1.63 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.45/1.63 inference(quant_intro,[status(thm)],[1709])).
% 1.45/1.63 tff(1711,plain,
% 1.45/1.63 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1712,plain,
% 1.45/1.63 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp0) | hskp28) <=> ((hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp28))), rewrite(((hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp28) <=> (hskp28 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp0) | hskp28) <=> (hskp28 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.45/1.63 inference(bind,[status(th)],[])).
% 1.45/1.63 tff(1713,plain,
% 1.45/1.63 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp0) | hskp28) <=> ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.45/1.63 inference(quant_intro,[status(thm)],[1712])).
% 1.45/1.63 tff(1714,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp0) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 1.45/1.63 tff(1715,plain,
% 1.45/1.63 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1714, 1713])).
% 1.45/1.63 tff(1716,plain,
% 1.45/1.63 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1715, 1711])).
% 1.45/1.63 tff(1717,plain,(
% 1.45/1.63 ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.45/1.63 inference(skolemize,[status(sab)],[1716])).
% 1.45/1.63 tff(1718,plain,
% 1.45/1.63 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1717, 1710])).
% 1.45/1.63 tff(1719,plain,
% 1.45/1.63 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp28 | hskp0 | c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp28 | hskp0 | c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1720,plain,
% 1.45/1.63 ((hskp28 | hskp0 | (~ndr1_0) | c1_1(a1638) | c0_1(a1638) | (~c3_1(a1638))) <=> (hskp28 | hskp0 | c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1721,plain,
% 1.45/1.63 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c1_1(a1638) | c0_1(a1638) | (~c3_1(a1638)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp28 | hskp0 | c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[1720])).
% 1.45/1.63 tff(1722,plain,
% 1.45/1.63 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c1_1(a1638) | c0_1(a1638) | (~c3_1(a1638)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp28 | hskp0 | c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[1721, 1719])).
% 1.45/1.63 tff(1723,plain,
% 1.45/1.63 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c1_1(a1638) | c0_1(a1638) | (~c3_1(a1638)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(1724,plain,
% 1.45/1.63 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp28 | hskp0 | c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1723, 1722])).
% 1.45/1.63 tff(1725,plain,
% 1.45/1.63 (hskp28 | hskp0 | c1_1(a1638) | (~c3_1(a1638))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1724, 1644, 22, 1718])).
% 1.45/1.63 tff(1726,plain,
% 1.45/1.63 (hskp0),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1725, 501, 1708, 1233])).
% 1.45/1.63 tff(1727,plain,
% 1.45/1.63 (c0_1(a1634)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[498, 1726])).
% 1.45/1.63 tff(1728,plain,
% 1.45/1.63 (c3_1(a1634)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[490, 1726])).
% 1.45/1.63 tff(1729,plain,
% 1.45/1.63 (^[U: $i] : refl((hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.45/1.63 inference(bind,[status(th)],[])).
% 1.45/1.63 tff(1730,plain,
% 1.45/1.63 (![U: $i] : (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.45/1.63 inference(quant_intro,[status(thm)],[1729])).
% 1.45/1.63 tff(1731,plain,
% 1.45/1.63 (![U: $i] : (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1732,plain,
% 1.45/1.63 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp28) <=> ((hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28))), rewrite(((hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28) <=> (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp28) <=> (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.45/1.63 inference(bind,[status(th)],[])).
% 1.45/1.63 tff(1733,plain,
% 1.45/1.63 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp28) <=> ![U: $i] : (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.45/1.63 inference(quant_intro,[status(thm)],[1732])).
% 1.45/1.63 tff(1734,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 1.45/1.63 tff(1735,plain,
% 1.45/1.63 (![U: $i] : (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1734, 1733])).
% 1.45/1.63 tff(1736,plain,
% 1.45/1.63 (![U: $i] : (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1735, 1731])).
% 1.45/1.63 tff(1737,plain,(
% 1.45/1.63 ![U: $i] : (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.45/1.63 inference(skolemize,[status(sab)],[1736])).
% 1.45/1.63 tff(1738,plain,
% 1.45/1.63 (![U: $i] : (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1737, 1730])).
% 1.45/1.63 tff(1739,plain,
% 1.45/1.63 (((~![U: $i] : (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp28 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)))) <=> ((~![U: $i] : (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp28 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1740,plain,
% 1.45/1.63 ((~![U: $i] : (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp28 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(1741,plain,
% 1.45/1.63 ((~![U: $i] : (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp28 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1740, 1739])).
% 1.45/1.63 tff(1742,plain,
% 1.45/1.63 (hskp28 | c2_1(a1634)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1741, 1630, 1644, 504, 502, 1738])).
% 1.45/1.63 tff(1743,plain,
% 1.45/1.63 (c2_1(a1634)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1742, 501])).
% 1.45/1.63 tff(1744,plain,
% 1.45/1.63 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.45/1.63 inference(bind,[status(th)],[])).
% 1.45/1.63 tff(1745,plain,
% 1.45/1.63 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.45/1.63 inference(quant_intro,[status(thm)],[1744])).
% 1.45/1.63 tff(1746,plain,
% 1.45/1.63 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1747,plain,
% 1.45/1.63 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp29))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.45/1.63 inference(bind,[status(th)],[])).
% 1.45/1.63 tff(1748,plain,
% 1.45/1.63 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.45/1.63 inference(quant_intro,[status(thm)],[1747])).
% 1.45/1.63 tff(1749,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 1.45/1.63 tff(1750,plain,
% 1.45/1.63 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1749, 1748])).
% 1.45/1.63 tff(1751,plain,
% 1.45/1.63 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1750, 1746])).
% 1.45/1.63 tff(1752,plain,(
% 1.45/1.63 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.45/1.63 inference(skolemize,[status(sab)],[1751])).
% 1.45/1.63 tff(1753,plain,
% 1.45/1.63 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1752, 1745])).
% 1.45/1.63 tff(1754,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1638) | c2_1(a1638) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1638) | c2_1(a1638) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1638)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1755,plain,
% 1.45/1.63 ((hskp29 | (~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c0_1(a1634)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638))) <=> (hskp29 | c0_1(a1638) | c2_1(a1638) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1638)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1756,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c0_1(a1634)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1638) | c2_1(a1638) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1638))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[1755])).
% 1.45/1.63 tff(1757,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c0_1(a1634)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1638) | c2_1(a1638) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1638)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[1756, 1754])).
% 1.45/1.63 tff(1758,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c0_1(a1634)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(1759,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1638) | c2_1(a1638) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1638))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1758, 1757])).
% 1.45/1.63 tff(1760,plain,
% 1.45/1.63 (hskp29 | c0_1(a1638) | (~c2_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1638))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1759, 1644, 1217, 503, 1753])).
% 1.45/1.63 tff(1761,plain,
% 1.45/1.63 (hskp29),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1760, 1743, 504, 22, 1708])).
% 1.45/1.63 tff(1762,plain,
% 1.45/1.63 (((~hskp29) | c3_1(a1647)) <=> ((~hskp29) | c3_1(a1647))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1763,axiom,((~hskp29) | c3_1(a1647)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 1.45/1.63 tff(1764,plain,
% 1.45/1.63 ((~hskp29) | c3_1(a1647)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1763, 1762])).
% 1.45/1.63 tff(1765,plain,
% 1.45/1.63 ((~hskp29) | c3_1(a1647)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1764, 1762])).
% 1.45/1.63 tff(1766,plain,
% 1.45/1.63 ((~hskp29) | c3_1(a1647)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1765, 1762])).
% 1.45/1.63 tff(1767,plain,
% 1.45/1.63 ((~hskp29) | c3_1(a1647)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1766, 1762])).
% 1.45/1.63 tff(1768,plain,
% 1.45/1.63 ((~hskp29) | c3_1(a1647)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1767, 1762])).
% 1.45/1.63 tff(1769,plain,
% 1.45/1.63 (c3_1(a1647)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1768, 1761])).
% 1.45/1.63 tff(1770,plain,
% 1.45/1.63 (((~hskp29) | c1_1(a1647)) <=> ((~hskp29) | c1_1(a1647))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1771,axiom,((~hskp29) | c1_1(a1647)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 1.45/1.63 tff(1772,plain,
% 1.45/1.63 ((~hskp29) | c1_1(a1647)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1771, 1770])).
% 1.45/1.63 tff(1773,plain,
% 1.45/1.63 ((~hskp29) | c1_1(a1647)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1772, 1770])).
% 1.45/1.63 tff(1774,plain,
% 1.45/1.63 ((~hskp29) | c1_1(a1647)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1773, 1770])).
% 1.45/1.63 tff(1775,plain,
% 1.45/1.63 ((~hskp29) | c1_1(a1647)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1774, 1770])).
% 1.45/1.63 tff(1776,plain,
% 1.45/1.63 ((~hskp29) | c1_1(a1647)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1775, 1770])).
% 1.45/1.63 tff(1777,plain,
% 1.45/1.63 (c1_1(a1647)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1776, 1761])).
% 1.45/1.63 tff(1778,plain,
% 1.45/1.63 (((~hskp29) | c0_1(a1647)) <=> ((~hskp29) | c0_1(a1647))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1779,axiom,((~hskp29) | c0_1(a1647)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 1.45/1.63 tff(1780,plain,
% 1.45/1.63 ((~hskp29) | c0_1(a1647)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1779, 1778])).
% 1.45/1.63 tff(1781,plain,
% 1.45/1.63 ((~hskp29) | c0_1(a1647)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1780, 1778])).
% 1.45/1.63 tff(1782,plain,
% 1.45/1.63 ((~hskp29) | c0_1(a1647)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1781, 1778])).
% 1.45/1.63 tff(1783,plain,
% 1.45/1.63 ((~hskp29) | c0_1(a1647)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1782, 1778])).
% 1.45/1.63 tff(1784,plain,
% 1.45/1.63 ((~hskp29) | c0_1(a1647)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1783, 1778])).
% 1.45/1.63 tff(1785,plain,
% 1.45/1.63 (c0_1(a1647)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1784, 1761])).
% 1.45/1.63 tff(1786,plain,
% 1.45/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c3_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c3_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1787,plain,
% 1.45/1.63 (((~ndr1_0) | (~c3_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)) | (~c1_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | c2_1(a1638) | c1_1(a1638) | (~c3_1(a1638))) <=> (c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c3_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1788,plain,
% 1.45/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)) | (~c1_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | c2_1(a1638) | c1_1(a1638) | (~c3_1(a1638)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c3_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[1787])).
% 1.45/1.63 tff(1789,plain,
% 1.45/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)) | (~c1_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | c2_1(a1638) | c1_1(a1638) | (~c3_1(a1638)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c3_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[1788, 1786])).
% 1.45/1.63 tff(1790,plain,
% 1.45/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)) | (~c1_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | c2_1(a1638) | c1_1(a1638) | (~c3_1(a1638)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(1791,plain,
% 1.45/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c3_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1790, 1789])).
% 1.45/1.64 tff(1792,plain,
% 1.45/1.64 (~c2_1(a1647)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1791, 1644, 1785, 1777, 1769, 1708, 1217, 1418, 1233])).
% 1.45/1.64 tff(1793,plain,
% 1.45/1.64 (((~![U: $i] : (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp28 | (~ndr1_0) | (~c3_1(a1647)) | c2_1(a1647) | (~c0_1(a1647)))) <=> ((~![U: $i] : (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp28 | (~ndr1_0) | (~c3_1(a1647)) | c2_1(a1647) | (~c0_1(a1647)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1794,plain,
% 1.45/1.64 ((hskp20 | hskp28 | (~ndr1_0) | c2_1(a1647) | (~c3_1(a1647)) | (~c0_1(a1647))) <=> (hskp20 | hskp28 | (~ndr1_0) | (~c3_1(a1647)) | c2_1(a1647) | (~c0_1(a1647)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1795,plain,
% 1.45/1.64 (((~![U: $i] : (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp28 | (~ndr1_0) | c2_1(a1647) | (~c3_1(a1647)) | (~c0_1(a1647)))) <=> ((~![U: $i] : (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp28 | (~ndr1_0) | (~c3_1(a1647)) | c2_1(a1647) | (~c0_1(a1647))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[1794])).
% 1.45/1.64 tff(1796,plain,
% 1.45/1.64 (((~![U: $i] : (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp28 | (~ndr1_0) | c2_1(a1647) | (~c3_1(a1647)) | (~c0_1(a1647)))) <=> ((~![U: $i] : (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp28 | (~ndr1_0) | (~c3_1(a1647)) | c2_1(a1647) | (~c0_1(a1647)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[1795, 1793])).
% 1.45/1.64 tff(1797,plain,
% 1.45/1.64 ((~![U: $i] : (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp28 | (~ndr1_0) | c2_1(a1647) | (~c3_1(a1647)) | (~c0_1(a1647)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(1798,plain,
% 1.45/1.64 ((~![U: $i] : (hskp20 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp28 | (~ndr1_0) | (~c3_1(a1647)) | c2_1(a1647) | (~c0_1(a1647))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1797, 1796])).
% 1.45/1.64 tff(1799,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1798, 1630, 1644, 501, 1785, 1769, 1738, 1792])).
% 1.45/1.64 tff(1800,plain,(hskp28 | hskp20 | (~c3_1(a1638)) | c2_1(a1638) | c1_1(a1638) | (~c0_1(a1634)) | c0_1(a1638) | c1_1(a1634) | (~c3_1(a1634))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(1801,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1800, 1728, 1727, 1708, 1217, 1233, 1630, 22, 503, 501])).
% 1.45/1.64 tff(1802,plain,(hskp28 | (~c3_1(a1638)) | c2_1(a1638) | c1_1(a1638) | hskp20 | c0_1(a1638) | c1_1(a1634)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(1803,plain,
% 1.45/1.64 (hskp28),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1802, 1707, 1217, 1657, 1630, 22, 503])).
% 1.45/1.64 tff(1804,plain,
% 1.45/1.64 (c3_1(a1646)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[268, 1803])).
% 1.45/1.64 tff(1805,plain,
% 1.45/1.64 (c2_1(a1646)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[238, 1803])).
% 1.45/1.64 tff(1806,plain,
% 1.45/1.64 (c1_1(a1646)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[260, 1803])).
% 1.45/1.64 tff(1807,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1808,plain,
% 1.45/1.64 (((~ndr1_0) | (~c3_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c1_1(a1646)) | (~c2_1(a1646)) | (~c0_1(a1646)) | c2_1(a1638) | c1_1(a1638) | (~c3_1(a1638))) <=> (c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1809,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c1_1(a1646)) | (~c2_1(a1646)) | (~c0_1(a1646)) | c2_1(a1638) | c1_1(a1638) | (~c3_1(a1638)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[1808])).
% 1.45/1.64 tff(1810,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c1_1(a1646)) | (~c2_1(a1646)) | (~c0_1(a1646)) | c2_1(a1638) | c1_1(a1638) | (~c3_1(a1638)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[1809, 1807])).
% 1.45/1.64 tff(1811,plain,
% 1.45/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c1_1(a1646)) | (~c2_1(a1646)) | (~c0_1(a1646)) | c2_1(a1638) | c1_1(a1638) | (~c3_1(a1638)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(1812,plain,
% 1.45/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1811, 1810])).
% 1.45/1.64 tff(1813,plain,
% 1.45/1.64 (~c0_1(a1646)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1812, 1644, 1806, 1805, 1804, 1707, 1217, 1418, 1657])).
% 1.45/1.64 tff(1814,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c3_1(a1638)) | (~c2_1(a1646)) | c0_1(a1646) | (~c3_1(a1646)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c3_1(a1638)) | (~c2_1(a1646)) | c0_1(a1646) | (~c3_1(a1646)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1815,plain,
% 1.45/1.64 (((~ndr1_0) | c0_1(a1646) | (~c2_1(a1646)) | (~c3_1(a1646)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638)) | c2_1(a1636) | c0_1(a1636) | c3_1(a1636)) <=> (c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c3_1(a1638)) | (~c2_1(a1646)) | c0_1(a1646) | (~c3_1(a1646)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1816,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1646) | (~c2_1(a1646)) | (~c3_1(a1646)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638)) | c2_1(a1636) | c0_1(a1636) | c3_1(a1636))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c3_1(a1638)) | (~c2_1(a1646)) | c0_1(a1646) | (~c3_1(a1646))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[1815])).
% 1.45/1.64 tff(1817,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1646) | (~c2_1(a1646)) | (~c3_1(a1646)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638)) | c2_1(a1636) | c0_1(a1636) | c3_1(a1636))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c3_1(a1638)) | (~c2_1(a1646)) | c0_1(a1646) | (~c3_1(a1646)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[1816, 1814])).
% 1.45/1.64 tff(1818,plain,
% 1.45/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1646) | (~c2_1(a1646)) | (~c3_1(a1646)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638)) | c2_1(a1636) | c0_1(a1636) | c3_1(a1636))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(1819,plain,
% 1.45/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1638) | c2_1(a1638) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c3_1(a1638)) | (~c2_1(a1646)) | c0_1(a1646) | (~c3_1(a1646))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1818, 1817])).
% 1.45/1.64 tff(1820,plain,
% 1.45/1.64 (c3_1(a1636)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1819, 1644, 1805, 1804, 1707, 22, 1217, 1553, 1551, 1621, 1813])).
% 1.45/1.64 tff(1821,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1822,plain,
% 1.45/1.64 (((~ndr1_0) | c0_1(a1646) | (~c2_1(a1646)) | (~c1_1(a1646)) | c1_1(a1636) | c0_1(a1636) | (~c3_1(a1636))) <=> (c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1823,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | ((~ndr1_0) | c0_1(a1646) | (~c2_1(a1646)) | (~c1_1(a1646)) | c1_1(a1636) | c0_1(a1636) | (~c3_1(a1636)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[1822])).
% 1.45/1.64 tff(1824,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | ((~ndr1_0) | c0_1(a1646) | (~c2_1(a1646)) | (~c1_1(a1646)) | c1_1(a1636) | c0_1(a1636) | (~c3_1(a1636)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[1823, 1821])).
% 1.45/1.64 tff(1825,plain,
% 1.45/1.64 ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | ((~ndr1_0) | c0_1(a1646) | (~c2_1(a1646)) | (~c1_1(a1646)) | c1_1(a1636) | c0_1(a1636) | (~c3_1(a1636)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(1826,plain,
% 1.45/1.64 ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1825, 1824])).
% 1.45/1.64 tff(1827,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1826, 1644, 1806, 1805, 1553, 1552, 691, 1820, 1813])).
% 1.45/1.64 tff(1828,plain,(c0_1(a1638) | c0_1(a1636) | c1_1(a1636) | c2_1(a1638) | c2_1(a1636) | hskp20 | c1_1(a1634) | c0_1(a1637)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(1829,plain,
% 1.45/1.64 (c0_1(a1638)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1828, 1217, 1552, 1553, 1551, 1630, 503, 1146])).
% 1.45/1.64 tff(1830,assumption,(c0_1(a1638)), introduced(assumption)).
% 1.45/1.64 tff(1831,plain,
% 1.45/1.64 (((~hskp3) | (~c0_1(a1638))) <=> ((~hskp3) | (~c0_1(a1638)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1832,plain,
% 1.45/1.64 (((~c0_1(a1638)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a1638)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1833,axiom,((~c0_1(a1638)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 1.45/1.64 tff(1834,plain,
% 1.45/1.64 ((~hskp3) | (~c0_1(a1638))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1833, 1832])).
% 1.45/1.64 tff(1835,plain,
% 1.45/1.64 ((~hskp3) | (~c0_1(a1638))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1834, 1831])).
% 1.45/1.64 tff(1836,plain,
% 1.45/1.64 (~hskp3),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1835, 1830])).
% 1.45/1.64 tff(1837,plain,
% 1.45/1.64 (hskp2),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1673, 1836, 1553, 1552])).
% 1.45/1.64 tff(1838,plain,
% 1.45/1.64 (c3_1(a1637)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1132, 1837])).
% 1.45/1.64 tff(1839,plain,
% 1.45/1.64 (c1_1(a1637)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1140, 1837])).
% 1.45/1.64 tff(1840,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~c0_1(a1638)) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1638))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | (~c0_1(a1638)) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1638))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1841,plain,
% 1.45/1.64 ((hskp11 | (~ndr1_0) | c2_1(a1638) | c1_1(a1638) | (~c0_1(a1638)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637))) <=> (hskp11 | (~c0_1(a1638)) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1638))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1842,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1638) | c1_1(a1638) | (~c0_1(a1638)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~c0_1(a1638)) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1638)))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[1841])).
% 1.45/1.64 tff(1843,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1638) | c1_1(a1638) | (~c0_1(a1638)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | (~c0_1(a1638)) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1638))),
% 1.45/1.64 inference(transitivity,[status(thm)],[1842, 1840])).
% 1.45/1.64 tff(1844,plain,
% 1.45/1.64 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1638) | c1_1(a1638) | (~c0_1(a1638)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(1845,plain,
% 1.45/1.64 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | (~c0_1(a1638)) | c2_1(a1638) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1638)),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1844, 1843])).
% 1.45/1.64 tff(1846,plain,
% 1.45/1.64 (hskp11 | (~c0_1(a1638)) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1638)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1845, 296, 1217, 1146, 280])).
% 1.45/1.64 tff(1847,plain,
% 1.45/1.64 (hskp11),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1846, 1233, 1830, 1839, 1838])).
% 1.45/1.64 tff(1848,plain,
% 1.45/1.64 (~c3_1(a1650)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[667, 1847])).
% 1.45/1.64 tff(1849,plain,
% 1.45/1.64 (~c0_1(a1650)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[673, 1847])).
% 1.45/1.64 tff(1850,plain,
% 1.45/1.64 (c1_1(a1650)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[705, 1847])).
% 1.45/1.64 tff(1851,plain,
% 1.45/1.64 (c3_1(a1638)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1704, 296, 1836, 1850, 1849, 1848, 1217, 10, 1233])).
% 1.45/1.64 tff(1852,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1650) | (~c0_1(a1638)) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1650) | (~c0_1(a1638)) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1853,plain,
% 1.45/1.64 (((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1638) | (~c3_1(a1638)) | (~c0_1(a1638)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637))) <=> (c3_1(a1650) | (~c0_1(a1638)) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1854,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1638) | (~c3_1(a1638)) | (~c0_1(a1638)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1650) | (~c0_1(a1638)) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[1853])).
% 1.45/1.64 tff(1855,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1638) | (~c3_1(a1638)) | (~c0_1(a1638)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1650) | (~c0_1(a1638)) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[1854, 1852])).
% 1.45/1.64 tff(1856,plain,
% 1.45/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1638) | (~c3_1(a1638)) | (~c0_1(a1638)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(1857,plain,
% 1.45/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1650) | (~c0_1(a1638)) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1856, 1855])).
% 1.45/1.64 tff(1858,plain,
% 1.45/1.64 ((~c3_1(a1638)) | (~c2_1(a1650))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1857, 296, 1850, 1839, 1838, 1848, 1830, 1146, 20, 1233])).
% 1.45/1.64 tff(1859,plain,
% 1.45/1.64 (~c2_1(a1650)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1858, 1851])).
% 1.45/1.64 tff(1860,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c0_1(a1650) | c3_1(a1650) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1650)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c0_1(a1650) | c3_1(a1650) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1650)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1861,plain,
% 1.45/1.64 ((hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1636) | c1_1(a1636) | c3_1(a1636)) <=> (hskp3 | c0_1(a1650) | c3_1(a1650) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1650)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1862,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1636) | c1_1(a1636) | c3_1(a1636))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c0_1(a1650) | c3_1(a1650) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1650))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[1861])).
% 1.45/1.64 tff(1863,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1636) | c1_1(a1636) | c3_1(a1636))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c0_1(a1650) | c3_1(a1650) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1650)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[1862, 1860])).
% 1.45/1.64 tff(1864,plain,
% 1.45/1.64 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)) | c2_1(a1636) | c1_1(a1636) | c3_1(a1636))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(1865,plain,
% 1.45/1.64 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c0_1(a1650) | c3_1(a1650) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1650))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1864, 1863])).
% 1.45/1.64 tff(1866,plain,
% 1.45/1.64 (c3_1(a1636)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1865, 296, 1836, 1850, 1849, 1848, 1552, 1551, 10])).
% 1.45/1.64 tff(1867,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (c0_1(a1637) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c1_1(a1637)) | (~c2_1(a1637)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | c0_1(a1637) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c1_1(a1637)) | (~c2_1(a1637)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1868,plain,
% 1.45/1.64 (((~ndr1_0) | c0_1(a1637) | (~c2_1(a1637)) | (~c1_1(a1637)) | c1_1(a1636) | c0_1(a1636) | (~c3_1(a1636))) <=> (c0_1(a1637) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c1_1(a1637)) | (~c2_1(a1637)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1869,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | ((~ndr1_0) | c0_1(a1637) | (~c2_1(a1637)) | (~c1_1(a1637)) | c1_1(a1636) | c0_1(a1636) | (~c3_1(a1636)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (c0_1(a1637) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c1_1(a1637)) | (~c2_1(a1637))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[1868])).
% 1.45/1.64 tff(1870,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | ((~ndr1_0) | c0_1(a1637) | (~c2_1(a1637)) | (~c1_1(a1637)) | c1_1(a1636) | c0_1(a1636) | (~c3_1(a1636)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | c0_1(a1637) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c1_1(a1637)) | (~c2_1(a1637)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[1869, 1867])).
% 1.45/1.64 tff(1871,plain,
% 1.45/1.64 ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | ((~ndr1_0) | c0_1(a1637) | (~c2_1(a1637)) | (~c1_1(a1637)) | c1_1(a1636) | c0_1(a1636) | (~c3_1(a1636)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(1872,plain,
% 1.45/1.64 ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | c0_1(a1637) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c1_1(a1637)) | (~c2_1(a1637))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1871, 1870])).
% 1.45/1.64 tff(1873,plain,
% 1.45/1.64 ((~c3_1(a1636)) | (~c1_1(a1637)) | (~c2_1(a1637))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1872, 296, 1146, 1553, 1552, 691])).
% 1.45/1.64 tff(1874,plain,
% 1.45/1.64 (~c2_1(a1637)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1873, 1866, 1839])).
% 1.45/1.64 tff(1875,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1650) | c3_1(a1650) | c0_1(a1637) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | c2_1(a1650))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1650) | c3_1(a1650) | c0_1(a1637) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | c2_1(a1650))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1876,plain,
% 1.45/1.64 (((~ndr1_0) | c2_1(a1637) | c0_1(a1637) | (~c1_1(a1637)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636)) <=> (c0_1(a1650) | c3_1(a1650) | c0_1(a1637) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | c2_1(a1650))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1877,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1637) | c0_1(a1637) | (~c1_1(a1637)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1650) | c3_1(a1650) | c0_1(a1637) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | c2_1(a1650)))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[1876])).
% 1.45/1.64 tff(1878,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1637) | c0_1(a1637) | (~c1_1(a1637)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1650) | c3_1(a1650) | c0_1(a1637) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | c2_1(a1650))),
% 1.45/1.64 inference(transitivity,[status(thm)],[1877, 1875])).
% 1.45/1.64 tff(1879,plain,
% 1.45/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1637) | c0_1(a1637) | (~c1_1(a1637)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(1880,plain,
% 1.45/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1650) | c3_1(a1650) | c0_1(a1637) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | c2_1(a1650)),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1879, 1878])).
% 1.45/1.64 tff(1881,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1880, 296, 1839, 1849, 1848, 1146, 1553, 1552, 1551, 1261, 1874, 1859])).
% 1.45/1.64 tff(1882,plain,(c1_1(a1638) | (~ndr1_0) | c0_1(a1637) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~c0_1(a1638)) | c2_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(1883,plain,
% 1.45/1.65 (c1_1(a1638)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1882, 1830, 1146, 1553, 1552, 1551, 296, 1217])).
% 1.45/1.65 tff(1884,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a1637) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c1_1(a1637)) | (~c3_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a1637) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c1_1(a1637)) | (~c3_1(a1637)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1885,plain,
% 1.45/1.65 ((hskp11 | (~ndr1_0) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)) | c2_1(a1636) | c0_1(a1636) | (~c3_1(a1636))) <=> (hskp11 | c0_1(a1637) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c1_1(a1637)) | (~c3_1(a1637)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1886,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)) | c2_1(a1636) | c0_1(a1636) | (~c3_1(a1636)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a1637) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c1_1(a1637)) | (~c3_1(a1637))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[1885])).
% 1.45/1.65 tff(1887,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)) | c2_1(a1636) | c0_1(a1636) | (~c3_1(a1636)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a1637) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c1_1(a1637)) | (~c3_1(a1637)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[1886, 1884])).
% 1.45/1.65 tff(1888,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)) | c2_1(a1636) | c0_1(a1636) | (~c3_1(a1636)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(1889,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a1637) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c1_1(a1637)) | (~c3_1(a1637))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1888, 1887])).
% 1.45/1.65 tff(1890,plain,
% 1.45/1.65 (hskp11 | (~c3_1(a1636)) | (~c1_1(a1637)) | (~c3_1(a1637))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1889, 296, 1146, 1553, 1551, 55])).
% 1.45/1.65 tff(1891,plain,
% 1.45/1.65 (~c3_1(a1636)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1890, 45, 1839, 1838])).
% 1.45/1.65 tff(1892,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~c0_1(a1638)) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1638)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | (~c0_1(a1638)) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1638)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1893,plain,
% 1.45/1.65 ((hskp4 | (~ndr1_0) | c2_1(a1638) | (~c0_1(a1638)) | (~c1_1(a1638)) | c1_1(a1636) | c0_1(a1636) | c3_1(a1636)) <=> (hskp4 | (~c0_1(a1638)) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1638)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1894,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1638) | (~c0_1(a1638)) | (~c1_1(a1638)) | c1_1(a1636) | c0_1(a1636) | c3_1(a1636))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~c0_1(a1638)) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1638))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[1893])).
% 1.45/1.65 tff(1895,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1638) | (~c0_1(a1638)) | (~c1_1(a1638)) | c1_1(a1636) | c0_1(a1636) | c3_1(a1636))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | (~c0_1(a1638)) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1638)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[1894, 1892])).
% 1.45/1.65 tff(1896,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1638) | (~c0_1(a1638)) | (~c1_1(a1638)) | c1_1(a1636) | c0_1(a1636) | c3_1(a1636))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(1897,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | (~c0_1(a1638)) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1638))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1896, 1895])).
% 1.45/1.65 tff(1898,plain,
% 1.45/1.65 (hskp4 | (~c0_1(a1638)) | c3_1(a1636) | (~c1_1(a1638))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1897, 296, 1217, 1553, 1552, 915])).
% 1.45/1.65 tff(1899,plain,
% 1.45/1.65 (hskp4),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1898, 1891, 1830, 1883])).
% 1.45/1.65 tff(1900,plain,
% 1.45/1.65 (~c2_1(a1639)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[928, 1899])).
% 1.45/1.65 tff(1901,plain,
% 1.45/1.65 (~c1_1(a1639)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[934, 1899])).
% 1.45/1.65 tff(1902,assumption,(~c1_1(a1639)), introduced(assumption)).
% 1.45/1.65 tff(1903,assumption,(~c2_1(a1639)), introduced(assumption)).
% 1.45/1.65 tff(1904,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | c1_1(a1639) | c2_1(a1639) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c0_1(a1639)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c1_1(a1639) | c2_1(a1639) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c0_1(a1639)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1905,plain,
% 1.45/1.65 ((hskp11 | (~ndr1_0) | c2_1(a1639) | c1_1(a1639) | (~c0_1(a1639)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637))) <=> (hskp11 | c1_1(a1639) | c2_1(a1639) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c0_1(a1639)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1906,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1639) | c1_1(a1639) | (~c0_1(a1639)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | c1_1(a1639) | c2_1(a1639) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c0_1(a1639))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[1905])).
% 1.45/1.65 tff(1907,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1639) | c1_1(a1639) | (~c0_1(a1639)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c1_1(a1639) | c2_1(a1639) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c0_1(a1639)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[1906, 1904])).
% 1.45/1.65 tff(1908,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1639) | c1_1(a1639) | (~c0_1(a1639)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(1909,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c1_1(a1639) | c2_1(a1639) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c0_1(a1639))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1908, 1907])).
% 1.45/1.65 tff(1910,plain,
% 1.45/1.65 (hskp11 | c1_1(a1639) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c0_1(a1639))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1909, 296, 1903, 1146, 280])).
% 1.45/1.65 tff(1911,plain,
% 1.45/1.65 (~c0_1(a1639)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1910, 45, 1147, 1902, 1148])).
% 1.45/1.65 tff(1912,plain,
% 1.45/1.65 (((~![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp11 | hskp7 | (~ndr1_0) | (~c1_1(a1637)) | (~c2_1(a1637)) | (~c3_1(a1637)))) <=> ((~![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp11 | hskp7 | (~ndr1_0) | (~c1_1(a1637)) | (~c2_1(a1637)) | (~c3_1(a1637)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1913,plain,
% 1.45/1.65 ((hskp11 | hskp7 | (~ndr1_0) | (~c2_1(a1637)) | (~c3_1(a1637)) | (~c1_1(a1637))) <=> (hskp11 | hskp7 | (~ndr1_0) | (~c1_1(a1637)) | (~c2_1(a1637)) | (~c3_1(a1637)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1914,plain,
% 1.45/1.65 (((~![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(a1637)) | (~c3_1(a1637)) | (~c1_1(a1637)))) <=> ((~![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp11 | hskp7 | (~ndr1_0) | (~c1_1(a1637)) | (~c2_1(a1637)) | (~c3_1(a1637))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[1913])).
% 1.45/1.65 tff(1915,plain,
% 1.45/1.65 (((~![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(a1637)) | (~c3_1(a1637)) | (~c1_1(a1637)))) <=> ((~![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp11 | hskp7 | (~ndr1_0) | (~c1_1(a1637)) | (~c2_1(a1637)) | (~c3_1(a1637)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[1914, 1912])).
% 1.45/1.65 tff(1916,plain,
% 1.45/1.65 ((~![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(a1637)) | (~c3_1(a1637)) | (~c1_1(a1637)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(1917,plain,
% 1.45/1.65 ((~![U: $i] : (hskp11 | hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp11 | hskp7 | (~ndr1_0) | (~c1_1(a1637)) | (~c2_1(a1637)) | (~c3_1(a1637))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1916, 1915])).
% 1.45/1.65 tff(1918,plain,
% 1.45/1.65 (hskp11 | (~c2_1(a1637))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1917, 296, 383, 1148, 1147, 378])).
% 1.45/1.65 tff(1919,plain,
% 1.45/1.65 (~c2_1(a1637)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1918, 45])).
% 1.45/1.65 tff(1920,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a1639) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c0_1(a1639) | (~c3_1(a1639)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a1639) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c0_1(a1639) | (~c3_1(a1639)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1921,plain,
% 1.45/1.65 ((hskp11 | (~ndr1_0) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)) | c2_1(a1639) | c0_1(a1639) | (~c3_1(a1639))) <=> (hskp11 | c2_1(a1639) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c0_1(a1639) | (~c3_1(a1639)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1922,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)) | c2_1(a1639) | c0_1(a1639) | (~c3_1(a1639)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a1639) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c0_1(a1639) | (~c3_1(a1639))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[1921])).
% 1.45/1.65 tff(1923,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)) | c2_1(a1639) | c0_1(a1639) | (~c3_1(a1639)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a1639) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c0_1(a1639) | (~c3_1(a1639)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[1922, 1920])).
% 1.45/1.65 tff(1924,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)) | c2_1(a1639) | c0_1(a1639) | (~c3_1(a1639)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(1925,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a1639) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c0_1(a1639) | (~c3_1(a1639))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1924, 1923])).
% 1.45/1.65 tff(1926,plain,
% 1.45/1.65 (hskp11 | (~c1_1(a1637)) | (~c3_1(a1637)) | c0_1(a1639) | (~c3_1(a1639))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1925, 296, 1903, 1146, 55])).
% 1.45/1.65 tff(1927,plain,
% 1.45/1.65 (~c3_1(a1639)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1926, 1911, 1148, 1147, 45])).
% 1.45/1.65 tff(1928,plain,
% 1.45/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a1639) | c1_1(a1639) | c2_1(a1639) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | c0_1(a1639))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1639) | c1_1(a1639) | c2_1(a1639) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | c0_1(a1639))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1929,plain,
% 1.45/1.65 (((~ndr1_0) | c2_1(a1637) | c0_1(a1637) | (~c1_1(a1637)) | c2_1(a1639) | c0_1(a1639) | c3_1(a1639) | c2_1(a1639) | c1_1(a1639) | c0_1(a1639)) <=> (c3_1(a1639) | c1_1(a1639) | c2_1(a1639) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | c0_1(a1639))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1930,plain,
% 1.45/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1637) | c0_1(a1637) | (~c1_1(a1637)) | c2_1(a1639) | c0_1(a1639) | c3_1(a1639) | c2_1(a1639) | c1_1(a1639) | c0_1(a1639))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a1639) | c1_1(a1639) | c2_1(a1639) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | c0_1(a1639)))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[1929])).
% 1.45/1.65 tff(1931,plain,
% 1.45/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1637) | c0_1(a1637) | (~c1_1(a1637)) | c2_1(a1639) | c0_1(a1639) | c3_1(a1639) | c2_1(a1639) | c1_1(a1639) | c0_1(a1639))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1639) | c1_1(a1639) | c2_1(a1639) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | c0_1(a1639))),
% 1.45/1.65 inference(transitivity,[status(thm)],[1930, 1928])).
% 1.45/1.65 tff(1932,plain,
% 1.45/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1637) | c0_1(a1637) | (~c1_1(a1637)) | c2_1(a1639) | c0_1(a1639) | c3_1(a1639) | c2_1(a1639) | c1_1(a1639) | c0_1(a1639))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(1933,plain,
% 1.45/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1639) | c1_1(a1639) | c2_1(a1639) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | c2_1(a1637) | c0_1(a1639)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1932, 1931])).
% 1.45/1.65 tff(1934,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1933, 296, 1927, 1148, 1902, 1903, 1146, 1261, 1919, 1911])).
% 1.45/1.65 tff(1935,plain,(hskp11 | (~ndr1_0) | (~c1_1(a1637)) | c1_1(a1639) | c2_1(a1639) | c0_1(a1637) | (~c3_1(a1637)) | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(1936,plain,
% 1.45/1.65 (hskp7),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1935, 1900, 296, 1839, 1838, 1146, 45, 1901])).
% 1.45/1.65 tff(1937,plain,
% 1.45/1.65 (c0_1(a1642)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[427, 1936])).
% 1.45/1.65 tff(1938,plain,
% 1.45/1.65 (~c2_1(a1642)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[448, 1936])).
% 1.45/1.65 tff(1939,assumption,(hskp2), introduced(assumption)).
% 1.45/1.65 tff(1940,plain,
% 1.45/1.65 (c1_1(a1637)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1140, 1939])).
% 1.45/1.65 tff(1941,plain,
% 1.45/1.65 (c3_1(a1637)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1132, 1939])).
% 1.45/1.65 tff(1942,plain,
% 1.45/1.65 (~c0_1(a1639)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1910, 1941, 45, 1902, 1940])).
% 1.45/1.65 tff(1943,plain,
% 1.45/1.65 (~c3_1(a1639)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1926, 1941, 1940, 45, 1942])).
% 1.45/1.65 tff(1944,plain,
% 1.45/1.65 (((~hskp4) | c3_1(a1639)) <=> ((~hskp4) | c3_1(a1639))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1945,axiom,((~hskp4) | c3_1(a1639)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 1.45/1.65 tff(1946,plain,
% 1.45/1.65 ((~hskp4) | c3_1(a1639)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1945, 1944])).
% 1.45/1.65 tff(1947,plain,
% 1.45/1.65 ((~hskp4) | c3_1(a1639)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1946, 1944])).
% 1.45/1.65 tff(1948,plain,
% 1.45/1.65 ((~hskp4) | c3_1(a1639)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1947, 1944])).
% 1.45/1.65 tff(1949,plain,
% 1.45/1.65 ((~hskp4) | c3_1(a1639)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1948, 1944])).
% 1.45/1.65 tff(1950,plain,
% 1.45/1.65 ((~hskp4) | c3_1(a1639)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1949, 1944])).
% 1.45/1.65 tff(1951,plain,
% 1.45/1.65 (~hskp4),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1950, 1943])).
% 1.45/1.65 tff(1952,assumption,(c0_1(a1642)), introduced(assumption)).
% 1.45/1.65 tff(1953,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | c2_1(a1642) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1642) | (~c0_1(a1642)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c2_1(a1642) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1642) | (~c0_1(a1642)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1954,plain,
% 1.45/1.65 ((hskp11 | (~ndr1_0) | c2_1(a1642) | c1_1(a1642) | (~c0_1(a1642)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637))) <=> (hskp11 | c2_1(a1642) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1642) | (~c0_1(a1642)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1955,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1642) | c1_1(a1642) | (~c0_1(a1642)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | c2_1(a1642) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1642) | (~c0_1(a1642))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[1954])).
% 1.45/1.65 tff(1956,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1642) | c1_1(a1642) | (~c0_1(a1642)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c2_1(a1642) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1642) | (~c0_1(a1642)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[1955, 1953])).
% 1.45/1.65 tff(1957,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1642) | c1_1(a1642) | (~c0_1(a1642)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(1958,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c2_1(a1642) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1642) | (~c0_1(a1642))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1957, 1956])).
% 1.45/1.65 tff(1959,plain,
% 1.45/1.65 (hskp11 | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1642) | (~c0_1(a1642))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1958, 296, 1243, 1146, 280])).
% 1.45/1.65 tff(1960,plain,
% 1.45/1.65 (c1_1(a1642)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1959, 1941, 1952, 45, 1940])).
% 1.45/1.65 tff(1961,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | c3_1(a1639) | c2_1(a1642) | c1_1(a1639) | (~ndr1_0) | c0_1(a1639) | (~c1_1(a1642)) | (~c0_1(a1642)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c3_1(a1639) | c2_1(a1642) | c1_1(a1639) | (~ndr1_0) | c0_1(a1639) | (~c1_1(a1642)) | (~c0_1(a1642)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1962,plain,
% 1.45/1.65 ((hskp4 | (~ndr1_0) | c2_1(a1642) | (~c0_1(a1642)) | (~c1_1(a1642)) | c1_1(a1639) | c0_1(a1639) | c3_1(a1639)) <=> (hskp4 | c3_1(a1639) | c2_1(a1642) | c1_1(a1639) | (~ndr1_0) | c0_1(a1639) | (~c1_1(a1642)) | (~c0_1(a1642)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1963,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1642) | (~c0_1(a1642)) | (~c1_1(a1642)) | c1_1(a1639) | c0_1(a1639) | c3_1(a1639))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | c3_1(a1639) | c2_1(a1642) | c1_1(a1639) | (~ndr1_0) | c0_1(a1639) | (~c1_1(a1642)) | (~c0_1(a1642))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[1962])).
% 1.45/1.65 tff(1964,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1642) | (~c0_1(a1642)) | (~c1_1(a1642)) | c1_1(a1639) | c0_1(a1639) | c3_1(a1639))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c3_1(a1639) | c2_1(a1642) | c1_1(a1639) | (~ndr1_0) | c0_1(a1639) | (~c1_1(a1642)) | (~c0_1(a1642)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[1963, 1961])).
% 1.45/1.65 tff(1965,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1642) | (~c0_1(a1642)) | (~c1_1(a1642)) | c1_1(a1639) | c0_1(a1639) | c3_1(a1639))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(1966,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c3_1(a1639) | c2_1(a1642) | c1_1(a1639) | (~ndr1_0) | c0_1(a1639) | (~c1_1(a1642)) | (~c0_1(a1642))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1965, 1964])).
% 1.45/1.65 tff(1967,plain,
% 1.45/1.65 (hskp4 | c3_1(a1639) | c0_1(a1639) | (~c1_1(a1642)) | (~c0_1(a1642))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1966, 296, 1243, 1902, 915])).
% 1.45/1.65 tff(1968,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1967, 1960, 1943, 1952, 1942, 1951])).
% 1.45/1.65 tff(1969,plain,((~hskp2) | (~c0_1(a1642)) | (~ndr1_0) | c2_1(a1642) | c1_1(a1639) | hskp11 | c0_1(a1637) | c2_1(a1639)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(1970,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1969, 1938, 1937, 296, 1837, 1901, 45, 1146, 1900])).
% 1.45/1.65 tff(1971,plain,(hskp11 | (~ndr1_0) | c0_1(a1637) | (~c0_1(a1638)) | c2_1(a1638) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(1972,plain,
% 1.45/1.65 (hskp11),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1971, 1829, 1146, 1644, 1217, 1553, 1552, 1551])).
% 1.45/1.65 tff(1973,plain,
% 1.45/1.65 (~c3_1(a1650)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[667, 1972])).
% 1.45/1.65 tff(1974,plain,
% 1.45/1.65 (~c0_1(a1650)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[673, 1972])).
% 1.45/1.65 tff(1975,plain,
% 1.45/1.65 (c1_1(a1650)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[705, 1972])).
% 1.45/1.65 tff(1976,plain,
% 1.45/1.65 (~hskp3),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1835, 1829])).
% 1.45/1.65 tff(1977,plain,
% 1.45/1.65 (c3_1(a1636)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1865, 1644, 1976, 1975, 1974, 1973, 1552, 1551, 10])).
% 1.45/1.65 tff(1978,plain,
% 1.45/1.65 ((~c3_1(a1636)) | (~c2_1(a1650))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1585, 1644, 1975, 1974, 1553, 1552, 691])).
% 1.45/1.65 tff(1979,plain,
% 1.45/1.65 (~c2_1(a1650)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1978, 1977])).
% 1.45/1.65 tff(1980,plain,
% 1.45/1.65 (hskp3 | hskp2 | c0_1(a1636) | c1_1(a1636)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1672, 1644, 1551, 1045])).
% 1.45/1.65 tff(1981,plain,
% 1.45/1.65 (hskp2),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1980, 1976, 1553, 1552])).
% 1.45/1.65 tff(1982,plain,
% 1.45/1.65 (c1_1(a1637)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1140, 1981])).
% 1.45/1.65 tff(1983,plain,
% 1.45/1.65 ((~c3_1(a1636)) | (~c1_1(a1637)) | (~c2_1(a1637))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1872, 1644, 1146, 1553, 1552, 691])).
% 1.45/1.65 tff(1984,plain,
% 1.45/1.65 (~c2_1(a1637)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1983, 1977, 1982])).
% 1.45/1.65 tff(1985,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1880, 1644, 1982, 1974, 1973, 1146, 1553, 1552, 1551, 1261, 1984, 1979])).
% 1.45/1.65 tff(1986,plain,(c2_1(a1638) | c0_1(a1637) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | hskp20 | c1_1(a1634)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(1987,plain,
% 1.45/1.65 (c2_1(a1638)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1986, 1146, 1553, 1552, 1551, 1630, 503])).
% 1.45/1.65 tff(1988,plain,
% 1.45/1.65 (((~hskp3) | (~c2_1(a1638))) <=> ((~hskp3) | (~c2_1(a1638)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1989,plain,
% 1.45/1.65 (((~c2_1(a1638)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a1638)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1990,axiom,((~c2_1(a1638)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 1.45/1.65 tff(1991,plain,
% 1.45/1.65 ((~hskp3) | (~c2_1(a1638))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1990, 1989])).
% 1.45/1.65 tff(1992,plain,
% 1.45/1.65 ((~hskp3) | (~c2_1(a1638))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1991, 1988])).
% 1.45/1.65 tff(1993,plain,
% 1.45/1.65 (~hskp3),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1992, 1987])).
% 1.45/1.65 tff(1994,plain,
% 1.45/1.65 (hskp2),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1980, 1993, 1553, 1552])).
% 1.45/1.65 tff(1995,plain,
% 1.45/1.65 (c3_1(a1637)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1132, 1994])).
% 1.45/1.65 tff(1996,plain,
% 1.45/1.65 (c1_1(a1637)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1140, 1994])).
% 1.45/1.65 tff(1997,plain,
% 1.45/1.65 (~c3_1(a1636)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1890, 45, 1148, 1147])).
% 1.45/1.65 tff(1998,assumption,(~c3_1(a1636)), introduced(assumption)).
% 1.45/1.65 tff(1999,plain,
% 1.45/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1637) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1637)) | c2_1(a1637))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1637) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1637)) | c2_1(a1637))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(2000,plain,
% 1.45/1.65 (((~ndr1_0) | c2_1(a1637) | c0_1(a1637) | (~c1_1(a1637)) | c2_1(a1636) | c0_1(a1636) | c3_1(a1636) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636)) <=> (c0_1(a1637) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1637)) | c2_1(a1637))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(2001,plain,
% 1.45/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1637) | c0_1(a1637) | (~c1_1(a1637)) | c2_1(a1636) | c0_1(a1636) | c3_1(a1636) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1637) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1637)) | c2_1(a1637)))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[2000])).
% 1.45/1.65 tff(2002,plain,
% 1.45/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1637) | c0_1(a1637) | (~c1_1(a1637)) | c2_1(a1636) | c0_1(a1636) | c3_1(a1636) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1637) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1637)) | c2_1(a1637))),
% 1.45/1.65 inference(transitivity,[status(thm)],[2001, 1999])).
% 1.45/1.65 tff(2003,plain,
% 1.45/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1637) | c0_1(a1637) | (~c1_1(a1637)) | c2_1(a1636) | c0_1(a1636) | c3_1(a1636) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(2004,plain,
% 1.45/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1637) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1637)) | c2_1(a1637)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[2003, 2002])).
% 1.45/1.65 tff(2005,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[2004, 296, 1148, 1146, 1553, 1552, 1551, 1261, 1998, 1601])).
% 1.45/1.65 tff(2006,plain,(c2_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | c0_1(a1637) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | c3_1(a1636)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(2007,plain,
% 1.45/1.65 (c2_1(a1637)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[2006, 1997, 1148, 1146, 1553, 1552, 1551, 296])).
% 1.45/1.65 tff(2008,plain,
% 1.45/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1661) | c0_1(a1637) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c2_1(a1661)) | (~c0_1(a1661)) | c3_1(a1636) | (~c1_1(a1637)) | (~c2_1(a1637)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1661) | c0_1(a1637) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c2_1(a1661)) | (~c0_1(a1661)) | c3_1(a1636) | (~c1_1(a1637)) | (~c2_1(a1637)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(2009,plain,
% 1.45/1.65 (((~ndr1_0) | c3_1(a1661) | (~c2_1(a1661)) | (~c0_1(a1661)) | c0_1(a1637) | (~c1_1(a1637)) | (~c2_1(a1637)) | c2_1(a1636) | c0_1(a1636) | c3_1(a1636)) <=> (c3_1(a1661) | c0_1(a1637) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c2_1(a1661)) | (~c0_1(a1661)) | c3_1(a1636) | (~c1_1(a1637)) | (~c2_1(a1637)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(2010,plain,
% 1.45/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1661) | (~c2_1(a1661)) | (~c0_1(a1661)) | c0_1(a1637) | (~c1_1(a1637)) | (~c2_1(a1637)) | c2_1(a1636) | c0_1(a1636) | c3_1(a1636))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1661) | c0_1(a1637) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c2_1(a1661)) | (~c0_1(a1661)) | c3_1(a1636) | (~c1_1(a1637)) | (~c2_1(a1637))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[2009])).
% 1.45/1.65 tff(2011,plain,
% 1.45/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1661) | (~c2_1(a1661)) | (~c0_1(a1661)) | c0_1(a1637) | (~c1_1(a1637)) | (~c2_1(a1637)) | c2_1(a1636) | c0_1(a1636) | c3_1(a1636))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1661) | c0_1(a1637) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c2_1(a1661)) | (~c0_1(a1661)) | c3_1(a1636) | (~c1_1(a1637)) | (~c2_1(a1637)))),
% 1.45/1.66 inference(transitivity,[status(thm)],[2010, 2008])).
% 1.45/1.66 tff(2012,plain,
% 1.45/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1661) | (~c2_1(a1661)) | (~c0_1(a1661)) | c0_1(a1637) | (~c1_1(a1637)) | (~c2_1(a1637)) | c2_1(a1636) | c0_1(a1636) | c3_1(a1636))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(2013,plain,
% 1.45/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1661) | c0_1(a1637) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c2_1(a1661)) | (~c0_1(a1661)) | c3_1(a1636) | (~c1_1(a1637)) | (~c2_1(a1637))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[2012, 2011])).
% 1.45/1.66 tff(2014,plain,
% 1.45/1.66 ((~c2_1(a1661)) | c3_1(a1636) | (~c1_1(a1637)) | (~c2_1(a1637))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2013, 296, 1678, 1677, 1146, 1553, 1551, 295])).
% 1.45/1.66 tff(2015,plain,
% 1.45/1.66 (~c2_1(a1661)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2014, 2007, 1997, 1148])).
% 1.45/1.66 tff(2016,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1694, 296, 45, 1678, 1148, 1147, 1687, 1146, 280, 2015])).
% 1.45/1.66 tff(2017,plain,(hskp11 | (~ndr1_0) | (~c0_1(a1661)) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1661) | c0_1(a1637) | c3_1(a1661) | c0_1(a1636) | c2_1(a1636) | c1_1(a1636)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(2018,plain,
% 1.45/1.66 (hskp11),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2017, 1996, 1665, 1644, 1995, 1656, 1146, 1650, 1553, 1551, 1552])).
% 1.45/1.66 tff(2019,plain,
% 1.45/1.66 (~c3_1(a1650)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[667, 2018])).
% 1.45/1.66 tff(2020,plain,
% 1.45/1.66 (~c0_1(a1650)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[673, 2018])).
% 1.45/1.66 tff(2021,plain,
% 1.45/1.66 (c1_1(a1650)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[705, 2018])).
% 1.45/1.66 tff(2022,plain,
% 1.45/1.66 (c3_1(a1636)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1865, 1644, 1993, 2021, 2020, 2019, 1552, 1551, 10])).
% 1.45/1.66 tff(2023,plain,
% 1.45/1.66 ((~c3_1(a1636)) | (~c2_1(a1650))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1585, 1644, 2021, 2020, 1553, 1552, 691])).
% 1.45/1.66 tff(2024,plain,
% 1.45/1.66 (~c2_1(a1650)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2023, 2022])).
% 1.45/1.66 tff(2025,plain,
% 1.45/1.66 (~c2_1(a1637)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1983, 2022, 1996])).
% 1.45/1.66 tff(2026,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1880, 1644, 1996, 2020, 2019, 1146, 1553, 1552, 1551, 1261, 2025, 2024])).
% 1.45/1.66 tff(2027,plain,(c0_1(a1637) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | hskp20 | c1_1(a1634)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(2028,plain,
% 1.45/1.66 (c0_1(a1637)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2027, 1553, 1552, 1551, 1630, 503])).
% 1.45/1.66 tff(2029,plain,
% 1.45/1.66 (~hskp2),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1124, 2028])).
% 1.45/1.66 tff(2030,plain,
% 1.45/1.66 (hskp3),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1980, 2029, 1553, 1552])).
% 1.45/1.66 tff(2031,plain,
% 1.45/1.66 (~c0_1(a1638)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1835, 2030])).
% 1.45/1.66 tff(2032,plain,
% 1.45/1.66 (~c2_1(a1638)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1992, 2030])).
% 1.45/1.66 tff(2033,plain,
% 1.45/1.66 (~c1_1(a1638)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1595, 2032, 2031, 1644, 1553, 1552, 1551])).
% 1.45/1.66 tff(2034,plain,
% 1.45/1.66 (c3_1(a1638)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[659, 2030])).
% 1.45/1.66 tff(2035,plain,
% 1.45/1.66 (hskp28),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1802, 2033, 2032, 2031, 1630, 2034, 503])).
% 1.45/1.66 tff(2036,plain,
% 1.45/1.66 (c3_1(a1646)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[268, 2035])).
% 1.45/1.66 tff(2037,plain,
% 1.45/1.66 (c2_1(a1646)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[238, 2035])).
% 1.45/1.66 tff(2038,plain,
% 1.45/1.66 (c1_1(a1646)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[260, 2035])).
% 1.45/1.66 tff(2039,plain,
% 1.45/1.66 (~c0_1(a1646)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1812, 1644, 2038, 2037, 2036, 2034, 2032, 1418, 2033])).
% 1.45/1.66 tff(2040,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(2041,plain,
% 1.45/1.66 (((~ndr1_0) | c0_1(a1646) | (~c2_1(a1646)) | (~c1_1(a1646)) | c1_1(a1638) | c0_1(a1638) | (~c3_1(a1638))) <=> (c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(2042,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | ((~ndr1_0) | c0_1(a1646) | (~c2_1(a1646)) | (~c1_1(a1646)) | c1_1(a1638) | c0_1(a1638) | (~c3_1(a1638)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[2041])).
% 1.45/1.66 tff(2043,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | ((~ndr1_0) | c0_1(a1646) | (~c2_1(a1646)) | (~c1_1(a1646)) | c1_1(a1638) | c0_1(a1638) | (~c3_1(a1638)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646)))),
% 1.45/1.66 inference(transitivity,[status(thm)],[2042, 2040])).
% 1.45/1.66 tff(2044,plain,
% 1.45/1.66 ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | ((~ndr1_0) | c0_1(a1646) | (~c2_1(a1646)) | (~c1_1(a1646)) | c1_1(a1638) | c0_1(a1638) | (~c3_1(a1638)))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(2045,plain,
% 1.45/1.66 ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[2044, 2043])).
% 1.45/1.66 tff(2046,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2045, 1644, 2038, 2037, 2034, 2031, 691, 2033, 2039])).
% 1.45/1.66 tff(2047,plain,(c0_1(a1636) | hskp20 | c1_1(a1634) | c1_1(a1636) | c2_1(a1636)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(2048,plain,
% 1.45/1.66 (hskp20),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2047, 1538, 503, 1544, 1550])).
% 1.45/1.66 tff(2049,plain,
% 1.45/1.66 (((~hskp20) | (~c2_1(a1689))) <=> ((~hskp20) | (~c2_1(a1689)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(2050,plain,
% 1.45/1.66 (((~c2_1(a1689)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a1689)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(2051,axiom,((~c2_1(a1689)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 1.45/1.66 tff(2052,plain,
% 1.45/1.66 ((~hskp20) | (~c2_1(a1689))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[2051, 2050])).
% 1.45/1.66 tff(2053,plain,
% 1.45/1.66 ((~hskp20) | (~c2_1(a1689))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[2052, 2049])).
% 1.45/1.66 tff(2054,plain,
% 1.45/1.66 (~c2_1(a1689)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2053, 2048])).
% 1.45/1.66 tff(2055,plain,
% 1.45/1.66 (((~hskp20) | c1_1(a1689)) <=> ((~hskp20) | c1_1(a1689))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(2056,axiom,((~hskp20) | c1_1(a1689)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 1.45/1.66 tff(2057,plain,
% 1.45/1.66 ((~hskp20) | c1_1(a1689)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[2056, 2055])).
% 1.45/1.66 tff(2058,plain,
% 1.45/1.66 ((~hskp20) | c1_1(a1689)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[2057, 2055])).
% 1.45/1.66 tff(2059,plain,
% 1.45/1.66 ((~hskp20) | c1_1(a1689)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[2058, 2055])).
% 1.45/1.66 tff(2060,plain,
% 1.45/1.66 ((~hskp20) | c1_1(a1689)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[2059, 2055])).
% 1.45/1.66 tff(2061,plain,
% 1.45/1.66 ((~hskp20) | c1_1(a1689)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[2060, 2055])).
% 1.45/1.66 tff(2062,plain,
% 1.45/1.66 (c1_1(a1689)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2061, 2048])).
% 1.45/1.66 tff(2063,plain,
% 1.45/1.66 (((~hskp20) | c0_1(a1689)) <=> ((~hskp20) | c0_1(a1689))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(2064,axiom,((~hskp20) | c0_1(a1689)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 1.45/1.66 tff(2065,plain,
% 1.45/1.66 ((~hskp20) | c0_1(a1689)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[2064, 2063])).
% 1.45/1.66 tff(2066,plain,
% 1.45/1.66 ((~hskp20) | c0_1(a1689)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[2065, 2063])).
% 1.45/1.66 tff(2067,plain,
% 1.45/1.66 ((~hskp20) | c0_1(a1689)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[2066, 2063])).
% 1.45/1.66 tff(2068,plain,
% 1.45/1.66 ((~hskp20) | c0_1(a1689)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[2067, 2063])).
% 1.45/1.66 tff(2069,plain,
% 1.45/1.66 ((~hskp20) | c0_1(a1689)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[2068, 2063])).
% 1.45/1.66 tff(2070,plain,
% 1.45/1.66 (c0_1(a1689)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2069, 2048])).
% 1.45/1.66 tff(2071,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | c2_1(a1689) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c0_1(a1689)) | (~c1_1(a1689)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c2_1(a1689) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c0_1(a1689)) | (~c1_1(a1689)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(2072,plain,
% 1.45/1.66 ((hskp4 | (~ndr1_0) | c2_1(a1689) | (~c0_1(a1689)) | (~c1_1(a1689)) | c1_1(a1636) | c0_1(a1636) | c3_1(a1636)) <=> (hskp4 | c2_1(a1689) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c0_1(a1689)) | (~c1_1(a1689)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(2073,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1689) | (~c0_1(a1689)) | (~c1_1(a1689)) | c1_1(a1636) | c0_1(a1636) | c3_1(a1636))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | c2_1(a1689) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c0_1(a1689)) | (~c1_1(a1689))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[2072])).
% 1.45/1.66 tff(2074,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1689) | (~c0_1(a1689)) | (~c1_1(a1689)) | c1_1(a1636) | c0_1(a1636) | c3_1(a1636))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c2_1(a1689) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c0_1(a1689)) | (~c1_1(a1689)))),
% 1.45/1.66 inference(transitivity,[status(thm)],[2073, 2071])).
% 1.45/1.66 tff(2075,plain,
% 1.45/1.66 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1689) | (~c0_1(a1689)) | (~c1_1(a1689)) | c1_1(a1636) | c0_1(a1636) | c3_1(a1636))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(2076,plain,
% 1.45/1.66 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c2_1(a1689) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c0_1(a1689)) | (~c1_1(a1689))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[2075, 2074])).
% 1.45/1.66 tff(2077,plain,
% 1.45/1.66 (hskp4),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2076, 119, 2070, 2062, 2054, 1544, 1538, 915, 1629])).
% 1.45/1.66 tff(2078,plain,
% 1.45/1.66 (~c1_1(a1639)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[934, 2077])).
% 1.45/1.66 tff(2079,plain,
% 1.45/1.66 (~c2_1(a1639)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[928, 2077])).
% 1.45/1.66 tff(2080,plain,
% 1.45/1.66 (hskp11),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1935, 1675, 296, 1902, 1903, 1146, 1688, 383])).
% 1.45/1.66 tff(2081,plain,
% 1.45/1.66 (~c3_1(a1650)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[667, 2080])).
% 1.45/1.66 tff(2082,plain,
% 1.45/1.66 (~c0_1(a1650)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[673, 2080])).
% 1.45/1.66 tff(2083,plain,
% 1.45/1.66 (c1_1(a1650)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[705, 2080])).
% 1.45/1.66 tff(2084,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1704, 296, 660, 2083, 652, 2082, 2081, 1217, 10, 1233])).
% 1.45/1.66 tff(2085,plain,(c3_1(a1638) | (~ndr1_0) | c2_1(a1638) | c1_1(a1638) | c1_1(a1639) | c2_1(a1639) | c0_1(a1637) | hskp7 | c0_1(a1636) | c1_1(a1636) | c2_1(a1636)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(2086,plain,
% 1.45/1.66 (c3_1(a1638) | c2_1(a1638) | c1_1(a1638) | c1_1(a1639) | c2_1(a1639) | c0_1(a1637) | hskp7 | c0_1(a1636) | c1_1(a1636) | c2_1(a1636)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2085, 119])).
% 1.45/1.66 tff(2087,plain,
% 1.45/1.66 (hskp7),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2086, 2079, 652, 1217, 1550, 1597, 1599, 2078, 1544, 1538])).
% 1.45/1.66 tff(2088,plain,
% 1.45/1.66 (c0_1(a1642)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[427, 2087])).
% 1.45/1.66 tff(2089,plain,
% 1.45/1.66 (hskp7),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1935, 1902, 296, 1940, 1941, 1146, 45, 1903])).
% 1.45/1.66 tff(2090,plain,
% 1.45/1.66 (c0_1(a1642)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[427, 2089])).
% 1.45/1.66 tff(2091,plain,
% 1.45/1.66 (~c2_1(a1642)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[448, 2089])).
% 1.45/1.66 tff(2092,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1969, 2091, 2090, 296, 1939, 1902, 45, 1146, 1903])).
% 1.45/1.66 tff(2093,plain,(c1_1(a1639) | (~ndr1_0) | (~hskp2) | hskp11 | c0_1(a1637) | c2_1(a1639)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(2094,plain,
% 1.45/1.66 (c1_1(a1639) | (~hskp2) | hskp11 | c0_1(a1637) | c2_1(a1639)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2093, 119])).
% 1.45/1.66 tff(2095,plain,
% 1.45/1.66 (hskp11),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2094, 2079, 2078, 1598, 1599])).
% 1.45/1.66 tff(2096,plain,
% 1.45/1.66 (~c3_1(a1650)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[667, 2095])).
% 1.45/1.66 tff(2097,plain,
% 1.45/1.66 (~c0_1(a1650)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[673, 2095])).
% 1.45/1.66 tff(2098,plain,
% 1.45/1.66 (~c2_1(a1642)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[448, 2087])).
% 1.45/1.66 tff(2099,plain,
% 1.45/1.66 (hskp3 | c3_1(a1638) | c1_1(a1638) | (~c1_1(a1650))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1704, 296, 843, 842, 1217, 10])).
% 1.45/1.66 tff(2100,plain,
% 1.45/1.66 (~c1_1(a1650)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2099, 660, 652, 1233])).
% 1.45/1.66 tff(2101,plain,
% 1.45/1.66 (~hskp11),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[705, 2100])).
% 1.45/1.66 tff(2102,plain,
% 1.45/1.66 (~c0_1(a1639)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1910, 2101, 1688, 1902, 1675])).
% 1.45/1.66 tff(2103,plain,
% 1.45/1.66 (~c3_1(a1639)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1926, 2101, 1675, 1688, 2102])).
% 1.45/1.66 tff(2104,plain,
% 1.45/1.66 (c1_1(a1642)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1959, 2101, 1952, 1688, 1675])).
% 1.45/1.66 tff(2105,plain,
% 1.45/1.66 (~c3_1(a1636)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1890, 2101, 1688, 1675])).
% 1.45/1.66 tff(2106,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | c2_1(a1642) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1642)) | (~c0_1(a1642)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c2_1(a1642) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1642)) | (~c0_1(a1642)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(2107,plain,
% 1.45/1.66 ((hskp4 | (~ndr1_0) | c2_1(a1642) | (~c0_1(a1642)) | (~c1_1(a1642)) | c1_1(a1636) | c0_1(a1636) | c3_1(a1636)) <=> (hskp4 | c2_1(a1642) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1642)) | (~c0_1(a1642)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(2108,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1642) | (~c0_1(a1642)) | (~c1_1(a1642)) | c1_1(a1636) | c0_1(a1636) | c3_1(a1636))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | c2_1(a1642) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1642)) | (~c0_1(a1642))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[2107])).
% 1.45/1.66 tff(2109,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1642) | (~c0_1(a1642)) | (~c1_1(a1642)) | c1_1(a1636) | c0_1(a1636) | c3_1(a1636))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c2_1(a1642) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1642)) | (~c0_1(a1642)))),
% 1.45/1.66 inference(transitivity,[status(thm)],[2108, 2106])).
% 1.45/1.66 tff(2110,plain,
% 1.45/1.66 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1642) | (~c0_1(a1642)) | (~c1_1(a1642)) | c1_1(a1636) | c0_1(a1636) | c3_1(a1636))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(2111,plain,
% 1.45/1.66 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c2_1(a1642) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c1_1(a1642)) | (~c0_1(a1642))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[2110, 2109])).
% 1.45/1.66 tff(2112,plain,
% 1.45/1.66 (hskp4 | c3_1(a1636) | (~c1_1(a1642)) | (~c0_1(a1642))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2111, 296, 1243, 1553, 1552, 915])).
% 1.45/1.66 tff(2113,plain,
% 1.45/1.66 (hskp4),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2112, 2105, 1952, 2104])).
% 1.45/1.66 tff(2114,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1950, 2113, 2103])).
% 1.45/1.66 tff(2115,plain,(c3_1(a1638) | (~c0_1(a1642)) | (~ndr1_0) | c2_1(a1642) | c0_1(a1636) | c1_1(a1636) | c0_1(a1637) | c2_1(a1639) | c1_1(a1639) | c2_1(a1636) | c1_1(a1638) | c0_1(a1650) | c3_1(a1650) | c2_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(2116,plain,
% 1.45/1.66 (c3_1(a1638) | (~c0_1(a1642)) | c2_1(a1642) | c0_1(a1636) | c1_1(a1636) | c0_1(a1637) | c2_1(a1639) | c1_1(a1639) | c2_1(a1636) | c1_1(a1638) | c0_1(a1650) | c3_1(a1650) | c2_1(a1638)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2115, 119])).
% 1.45/1.66 tff(2117,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2116, 2098, 2097, 652, 1217, 1544, 1538, 1599, 2078, 1550, 1597, 2079, 2096, 2088])).
% 1.45/1.66 tff(2118,plain,(c2_1(a1638) | c3_1(a1638) | c0_1(a1638) | c1_1(a1634)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(2119,plain,
% 1.45/1.66 (c2_1(a1638)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2118, 503, 22, 652])).
% 1.45/1.66 tff(2120,plain,
% 1.45/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a1650) | c3_1(a1638) | c0_1(a1650) | c3_1(a1650) | (~c2_1(a1638)) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1638)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1650) | c3_1(a1638) | c0_1(a1650) | c3_1(a1650) | (~c2_1(a1638)) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1638)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(2121,plain,
% 1.45/1.66 (((~ndr1_0) | c3_1(a1638) | (~c2_1(a1638)) | (~c1_1(a1638)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1650) | c0_1(a1650) | c3_1(a1650)) <=> (c1_1(a1650) | c3_1(a1638) | c0_1(a1650) | c3_1(a1650) | (~c2_1(a1638)) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1638)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(2122,plain,
% 1.45/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1638) | (~c2_1(a1638)) | (~c1_1(a1638)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1650) | c0_1(a1650) | c3_1(a1650))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a1650) | c3_1(a1638) | c0_1(a1650) | c3_1(a1650) | (~c2_1(a1638)) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1638))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[2121])).
% 1.45/1.66 tff(2123,plain,
% 1.45/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1638) | (~c2_1(a1638)) | (~c1_1(a1638)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1650) | c0_1(a1650) | c3_1(a1650))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1650) | c3_1(a1638) | c0_1(a1650) | c3_1(a1650) | (~c2_1(a1638)) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1638)))),
% 1.45/1.66 inference(transitivity,[status(thm)],[2122, 2120])).
% 1.45/1.66 tff(2124,plain,
% 1.45/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1638) | (~c2_1(a1638)) | (~c1_1(a1638)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1650) | c0_1(a1650) | c3_1(a1650))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(2125,plain,
% 1.45/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1650) | c3_1(a1638) | c0_1(a1650) | c3_1(a1650) | (~c2_1(a1638)) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1638))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[2124, 2123])).
% 1.45/1.66 tff(2126,plain,
% 1.45/1.66 (c0_1(a1650) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1638))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2125, 119, 1175, 652, 842, 2119, 503, 595])).
% 1.45/1.66 tff(2127,plain,
% 1.45/1.66 (~c1_1(a1638)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2126, 1216, 843, 1215])).
% 1.45/1.66 tff(2128,plain,
% 1.45/1.66 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp9 | hskp2 | c1_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp9 | hskp2 | c1_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(2129,plain,
% 1.45/1.66 ((hskp9 | hskp2 | (~ndr1_0) | c1_1(a1650) | c3_1(a1650) | (~c2_1(a1650))) <=> (hskp9 | hskp2 | c1_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(2130,plain,
% 1.45/1.66 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c1_1(a1650) | c3_1(a1650) | (~c2_1(a1650)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp9 | hskp2 | c1_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[2129])).
% 1.45/1.66 tff(2131,plain,
% 1.45/1.66 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c1_1(a1650) | c3_1(a1650) | (~c2_1(a1650)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp9 | hskp2 | c1_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650)))),
% 1.45/1.66 inference(transitivity,[status(thm)],[2130, 2128])).
% 1.45/1.66 tff(2132,plain,
% 1.45/1.66 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c1_1(a1650) | c3_1(a1650) | (~c2_1(a1650)))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(2133,plain,
% 1.45/1.66 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp9 | hskp2 | c1_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[2132, 2131])).
% 1.45/1.66 tff(2134,plain,
% 1.45/1.66 (hskp9 | hskp2 | c1_1(a1650) | (~c2_1(a1650))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2133, 119, 842, 532])).
% 1.45/1.66 tff(2135,plain,
% 1.45/1.66 (hskp9),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2134, 1183, 1175, 500])).
% 1.45/1.66 tff(2136,plain,
% 1.45/1.66 (~hskp19),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[610, 1215, 2135, 1216, 503])).
% 1.45/1.66 tff(2137,plain,
% 1.45/1.66 (hskp15),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1450, 2136, 21])).
% 1.45/1.66 tff(2138,plain,
% 1.45/1.66 (~c2_1(a1664)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[333, 2137])).
% 1.45/1.66 tff(2139,plain,
% 1.45/1.66 (~c1_1(a1664)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[339, 2137])).
% 1.45/1.66 tff(2140,plain,
% 1.45/1.66 (c0_1(a1664)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[347, 2137])).
% 1.45/1.66 tff(2141,plain,
% 1.45/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1664) | c2_1(a1664) | c0_1(a1638) | (~c2_1(a1638)) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | c1_1(a1638) | (~c0_1(a1664)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1664) | c2_1(a1664) | c0_1(a1638) | (~c2_1(a1638)) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | c1_1(a1638) | (~c0_1(a1664)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(2142,plain,
% 1.45/1.66 (((~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1638) | c0_1(a1638) | (~c2_1(a1638))) <=> (c1_1(a1664) | c2_1(a1664) | c0_1(a1638) | (~c2_1(a1638)) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | c1_1(a1638) | (~c0_1(a1664)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(2143,plain,
% 1.45/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1638) | c0_1(a1638) | (~c2_1(a1638)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1664) | c2_1(a1664) | c0_1(a1638) | (~c2_1(a1638)) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | c1_1(a1638) | (~c0_1(a1664))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[2142])).
% 1.45/1.66 tff(2144,plain,
% 1.45/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1638) | c0_1(a1638) | (~c2_1(a1638)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1664) | c2_1(a1664) | c0_1(a1638) | (~c2_1(a1638)) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | c1_1(a1638) | (~c0_1(a1664)))),
% 1.45/1.66 inference(transitivity,[status(thm)],[2143, 2141])).
% 1.45/1.66 tff(2145,plain,
% 1.45/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1638) | c0_1(a1638) | (~c2_1(a1638)))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(2146,plain,
% 1.45/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1664) | c2_1(a1664) | c0_1(a1638) | (~c2_1(a1638)) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | c1_1(a1638) | (~c0_1(a1664))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[2145, 2144])).
% 1.45/1.66 tff(2147,plain,
% 1.45/1.66 (~c2_1(a1634)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2146, 119, 2140, 1216, 2139, 2138, 22, 2119, 503, 812, 2127])).
% 1.45/1.66 tff(2148,plain,
% 1.45/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a1650) | c0_1(a1650) | c3_1(a1650) | c3_1(a1648) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | (~c1_1(a1648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1650) | c0_1(a1650) | c3_1(a1650) | c3_1(a1648) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | (~c1_1(a1648)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(2149,plain,
% 1.45/1.66 (((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c1_1(a1648)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1650) | c0_1(a1650) | c3_1(a1650)) <=> (c1_1(a1650) | c0_1(a1650) | c3_1(a1650) | c3_1(a1648) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | (~c1_1(a1648)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(2150,plain,
% 1.45/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c1_1(a1648)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1650) | c0_1(a1650) | c3_1(a1650))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a1650) | c0_1(a1650) | c3_1(a1650) | c3_1(a1648) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | (~c1_1(a1648))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[2149])).
% 1.45/1.66 tff(2151,plain,
% 1.45/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c1_1(a1648)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1650) | c0_1(a1650) | c3_1(a1650))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1650) | c0_1(a1650) | c3_1(a1650) | c3_1(a1648) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | (~c1_1(a1648)))),
% 1.45/1.66 inference(transitivity,[status(thm)],[2150, 2148])).
% 1.45/1.66 tff(2152,plain,
% 1.45/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c1_1(a1648)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1650) | c0_1(a1650) | c3_1(a1650))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(2153,plain,
% 1.45/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1650) | c0_1(a1650) | c3_1(a1650) | c3_1(a1648) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | (~c1_1(a1648))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[2152, 2151])).
% 1.45/1.66 tff(2154,plain,
% 1.45/1.66 (c0_1(a1650) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1648))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2153, 119, 1175, 1173, 842, 1172, 503, 595])).
% 1.45/1.66 tff(2155,plain,
% 1.45/1.66 (~c1_1(a1648)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2154, 1216, 843, 1215])).
% 1.45/1.66 tff(2156,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[645, 119, 500, 1174, 1173, 1215, 1216, 639, 2155, 2147])).
% 1.45/1.66 tff(2157,plain,(c0_1(a1650) | hskp2 | c0_1(a1638) | c1_1(a1634) | hskp1 | c1_1(a1650) | c3_1(a1650) | c3_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(2158,plain,
% 1.45/1.66 (c0_1(a1650)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2157, 500, 22, 503, 21, 1175, 842, 652])).
% 1.45/1.66 tff(2159,assumption,(c0_1(a1650)), introduced(assumption)).
% 1.45/1.66 tff(2160,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | c1_1(a1650) | (~c0_1(a1650)) | c2_1(a1640) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1650)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp2 | c1_1(a1650) | (~c0_1(a1650)) | c2_1(a1640) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1650)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(2161,plain,
% 1.45/1.66 ((hskp2 | (~ndr1_0) | c2_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c1_1(a1650) | (~c2_1(a1650)) | (~c0_1(a1650))) <=> (hskp2 | c1_1(a1650) | (~c0_1(a1650)) | c2_1(a1640) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1650)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(2162,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c1_1(a1650) | (~c2_1(a1650)) | (~c0_1(a1650)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | c1_1(a1650) | (~c0_1(a1650)) | c2_1(a1640) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1650))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[2161])).
% 1.45/1.67 tff(2163,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c1_1(a1650) | (~c2_1(a1650)) | (~c0_1(a1650)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp2 | c1_1(a1650) | (~c0_1(a1650)) | c2_1(a1640) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1650)))),
% 1.45/1.67 inference(transitivity,[status(thm)],[2162, 2160])).
% 1.45/1.67 tff(2164,plain,
% 1.45/1.67 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c1_1(a1650) | (~c2_1(a1650)) | (~c0_1(a1650)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(2165,plain,
% 1.45/1.67 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp2 | c1_1(a1650) | (~c0_1(a1650)) | c2_1(a1640) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1650))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[2164, 2163])).
% 1.45/1.67 tff(2166,plain,
% 1.45/1.67 (~c2_1(a1650)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2165, 119, 500, 1175, 851, 867, 2159, 841, 639])).
% 1.45/1.67 tff(2167,plain,
% 1.45/1.67 (^[U: $i] : refl((hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.45/1.67 inference(bind,[status(th)],[])).
% 1.45/1.67 tff(2168,plain,
% 1.45/1.67 (![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.45/1.67 inference(quant_intro,[status(thm)],[2167])).
% 1.45/1.67 tff(2169,plain,
% 1.45/1.67 (![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(2170,plain,
% 1.45/1.67 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp16))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) | hskp0) <=> ((hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp0))), rewrite(((hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp0) <=> (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) | hskp0) <=> (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.45/1.67 inference(bind,[status(th)],[])).
% 1.45/1.67 tff(2171,plain,
% 1.45/1.67 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) | hskp0) <=> ![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.45/1.67 inference(quant_intro,[status(thm)],[2170])).
% 1.45/1.67 tff(2172,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 1.45/1.67 tff(2173,plain,
% 1.45/1.67 (![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[2172, 2171])).
% 1.45/1.67 tff(2174,plain,
% 1.45/1.67 (![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[2173, 2169])).
% 1.45/1.67 tff(2175,plain,(
% 1.45/1.67 ![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.45/1.67 inference(skolemize,[status(sab)],[2174])).
% 1.45/1.67 tff(2176,plain,
% 1.45/1.67 (![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[2175, 2168])).
% 1.45/1.67 tff(2177,plain,
% 1.45/1.67 (((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | hskp0 | c1_1(a1650) | (~c0_1(a1650)) | (~ndr1_0) | c2_1(a1650))) <=> ((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | hskp0 | c1_1(a1650) | (~c0_1(a1650)) | (~ndr1_0) | c2_1(a1650))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(2178,plain,
% 1.45/1.67 ((hskp16 | hskp0 | (~ndr1_0) | c2_1(a1650) | c1_1(a1650) | (~c0_1(a1650))) <=> (hskp16 | hskp0 | c1_1(a1650) | (~c0_1(a1650)) | (~ndr1_0) | c2_1(a1650))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(2179,plain,
% 1.45/1.67 (((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | hskp0 | (~ndr1_0) | c2_1(a1650) | c1_1(a1650) | (~c0_1(a1650)))) <=> ((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | hskp0 | c1_1(a1650) | (~c0_1(a1650)) | (~ndr1_0) | c2_1(a1650)))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[2178])).
% 1.45/1.67 tff(2180,plain,
% 1.45/1.67 (((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | hskp0 | (~ndr1_0) | c2_1(a1650) | c1_1(a1650) | (~c0_1(a1650)))) <=> ((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | hskp0 | c1_1(a1650) | (~c0_1(a1650)) | (~ndr1_0) | c2_1(a1650))),
% 1.45/1.67 inference(transitivity,[status(thm)],[2179, 2177])).
% 1.45/1.67 tff(2181,plain,
% 1.45/1.67 ((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | hskp0 | (~ndr1_0) | c2_1(a1650) | c1_1(a1650) | (~c0_1(a1650)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(2182,plain,
% 1.45/1.67 ((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | hskp0 | c1_1(a1650) | (~c0_1(a1650)) | (~ndr1_0) | c2_1(a1650)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[2181, 2180])).
% 1.45/1.67 tff(2183,plain,
% 1.45/1.67 (hskp16 | hskp0 | (~c0_1(a1650)) | c2_1(a1650)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2182, 119, 1175, 2176])).
% 1.45/1.67 tff(2184,plain,
% 1.45/1.67 (hskp16),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2183, 2166, 2159, 33])).
% 1.45/1.67 tff(2185,plain,
% 1.45/1.67 (~c1_1(a1667)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[986, 2184])).
% 1.45/1.67 tff(2186,plain,
% 1.45/1.67 (c2_1(a1667)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[994, 2184])).
% 1.45/1.67 tff(2187,plain,
% 1.45/1.67 (c0_1(a1667)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1002, 2184])).
% 1.45/1.67 tff(2188,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | c1_1(a1667) | c2_1(a1640) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c0_1(a1667)) | (~c2_1(a1667)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp2 | c1_1(a1667) | c2_1(a1640) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c0_1(a1667)) | (~c2_1(a1667)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(2189,plain,
% 1.45/1.67 ((hskp2 | (~ndr1_0) | c2_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c1_1(a1667) | (~c2_1(a1667)) | (~c0_1(a1667))) <=> (hskp2 | c1_1(a1667) | c2_1(a1640) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c0_1(a1667)) | (~c2_1(a1667)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(2190,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c1_1(a1667) | (~c2_1(a1667)) | (~c0_1(a1667)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | c1_1(a1667) | c2_1(a1640) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c0_1(a1667)) | (~c2_1(a1667))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[2189])).
% 1.45/1.67 tff(2191,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c1_1(a1667) | (~c2_1(a1667)) | (~c0_1(a1667)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp2 | c1_1(a1667) | c2_1(a1640) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c0_1(a1667)) | (~c2_1(a1667)))),
% 1.45/1.67 inference(transitivity,[status(thm)],[2190, 2188])).
% 1.45/1.67 tff(2192,plain,
% 1.45/1.67 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c1_1(a1667) | (~c2_1(a1667)) | (~c0_1(a1667)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(2193,plain,
% 1.45/1.67 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp2 | c1_1(a1667) | c2_1(a1640) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c0_1(a1667)) | (~c2_1(a1667))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[2192, 2191])).
% 1.45/1.67 tff(2194,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2193, 119, 500, 2187, 2186, 851, 867, 2185, 841, 639])).
% 1.45/1.67 tff(2195,plain,(hskp0 | hskp2 | (~c0_1(a1650)) | c1_1(a1650) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(2196,plain,
% 1.45/1.67 (hskp0),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2195, 500, 2158, 1175, 21])).
% 1.45/1.67 tff(2197,plain,
% 1.45/1.67 (c3_1(a1634)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[490, 2196])).
% 1.45/1.67 tff(2198,plain,
% 1.45/1.67 (c0_1(a1634)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[498, 2196])).
% 1.45/1.67 tff(2199,plain,
% 1.45/1.67 (hskp17),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[407, 1184, 21])).
% 1.45/1.67 tff(2200,plain,
% 1.45/1.67 (c2_1(a1675)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[435, 2199])).
% 1.45/1.67 tff(2201,plain,
% 1.45/1.67 (~c1_1(a1675)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[413, 2199])).
% 1.45/1.67 tff(2202,plain,
% 1.45/1.67 (~c0_1(a1675)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[419, 2199])).
% 1.45/1.67 tff(2203,assumption,(~c2_1(a1650)), introduced(assumption)).
% 1.45/1.67 tff(2204,plain,
% 1.45/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1650) | c0_1(a1675) | c1_1(a1675) | (~c0_1(a1650)) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1650) | (~c2_1(a1675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1650) | c0_1(a1675) | c1_1(a1675) | (~c0_1(a1650)) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1650) | (~c2_1(a1675)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(2205,plain,
% 1.45/1.67 (((~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1650) | c1_1(a1650) | (~c0_1(a1650)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675))) <=> (c1_1(a1650) | c0_1(a1675) | c1_1(a1675) | (~c0_1(a1650)) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1650) | (~c2_1(a1675)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(2206,plain,
% 1.45/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1650) | c1_1(a1650) | (~c0_1(a1650)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1650) | c0_1(a1675) | c1_1(a1675) | (~c0_1(a1650)) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1650) | (~c2_1(a1675))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[2205])).
% 1.45/1.67 tff(2207,plain,
% 1.45/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1650) | c1_1(a1650) | (~c0_1(a1650)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1650) | c0_1(a1675) | c1_1(a1675) | (~c0_1(a1650)) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1650) | (~c2_1(a1675)))),
% 1.45/1.67 inference(transitivity,[status(thm)],[2206, 2204])).
% 1.45/1.67 tff(2208,plain,
% 1.45/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1650) | c1_1(a1650) | (~c0_1(a1650)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(2209,plain,
% 1.45/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1650) | c0_1(a1675) | c1_1(a1675) | (~c0_1(a1650)) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1650) | (~c2_1(a1675))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[2208, 2207])).
% 1.45/1.67 tff(2210,plain,
% 1.45/1.67 (~c2_1(a1634)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2209, 119, 1316, 1175, 502, 1314, 1313, 2159, 503, 812, 2203])).
% 1.45/1.67 tff(2211,plain,
% 1.45/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1650) | c0_1(a1675) | c1_1(a1675) | (~c0_1(a1650)) | (~ndr1_0) | c2_1(a1650) | (~c3_1(a1675)) | (~c2_1(a1675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1650) | c0_1(a1675) | c1_1(a1675) | (~c0_1(a1650)) | (~ndr1_0) | c2_1(a1650) | (~c3_1(a1675)) | (~c2_1(a1675)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(2212,plain,
% 1.45/1.67 (((~ndr1_0) | c1_1(a1675) | (~c2_1(a1675)) | (~c3_1(a1675)) | c2_1(a1650) | c1_1(a1650) | (~c0_1(a1650)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675))) <=> (c1_1(a1650) | c0_1(a1675) | c1_1(a1675) | (~c0_1(a1650)) | (~ndr1_0) | c2_1(a1650) | (~c3_1(a1675)) | (~c2_1(a1675)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(2213,plain,
% 1.45/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1675) | (~c2_1(a1675)) | (~c3_1(a1675)) | c2_1(a1650) | c1_1(a1650) | (~c0_1(a1650)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1650) | c0_1(a1675) | c1_1(a1675) | (~c0_1(a1650)) | (~ndr1_0) | c2_1(a1650) | (~c3_1(a1675)) | (~c2_1(a1675))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[2212])).
% 1.45/1.67 tff(2214,plain,
% 1.45/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1675) | (~c2_1(a1675)) | (~c3_1(a1675)) | c2_1(a1650) | c1_1(a1650) | (~c0_1(a1650)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1650) | c0_1(a1675) | c1_1(a1675) | (~c0_1(a1650)) | (~ndr1_0) | c2_1(a1650) | (~c3_1(a1675)) | (~c2_1(a1675)))),
% 1.45/1.67 inference(transitivity,[status(thm)],[2213, 2211])).
% 1.45/1.67 tff(2215,plain,
% 1.45/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1675) | (~c2_1(a1675)) | (~c3_1(a1675)) | c2_1(a1650) | c1_1(a1650) | (~c0_1(a1650)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(2216,plain,
% 1.45/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1650) | c0_1(a1675) | c1_1(a1675) | (~c0_1(a1650)) | (~ndr1_0) | c2_1(a1650) | (~c3_1(a1675)) | (~c2_1(a1675))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[2215, 2214])).
% 1.45/1.67 tff(2217,plain,
% 1.45/1.67 (~c3_1(a1675)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2216, 119, 1316, 1175, 1314, 1313, 2159, 812, 2203])).
% 1.45/1.67 tff(2218,plain,
% 1.45/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1675) | c1_1(a1675) | c3_1(a1648) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | (~c1_1(a1648)) | c3_1(a1675))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1675) | c1_1(a1675) | c3_1(a1648) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | (~c1_1(a1648)) | c3_1(a1675))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(2219,plain,
% 1.45/1.67 (((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c1_1(a1648)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1675) | c0_1(a1675) | c3_1(a1675)) <=> (c0_1(a1675) | c1_1(a1675) | c3_1(a1648) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | (~c1_1(a1648)) | c3_1(a1675))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(2220,plain,
% 1.45/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c1_1(a1648)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1675) | c0_1(a1675) | c3_1(a1675))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1675) | c1_1(a1675) | c3_1(a1648) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | (~c1_1(a1648)) | c3_1(a1675)))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[2219])).
% 1.45/1.67 tff(2221,plain,
% 1.45/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c1_1(a1648)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1675) | c0_1(a1675) | c3_1(a1675))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1675) | c1_1(a1675) | c3_1(a1648) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | (~c1_1(a1648)) | c3_1(a1675))),
% 1.45/1.67 inference(transitivity,[status(thm)],[2220, 2218])).
% 1.45/1.67 tff(2222,plain,
% 1.45/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c1_1(a1648)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1675) | c0_1(a1675) | c3_1(a1675))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(2223,plain,
% 1.45/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1675) | c1_1(a1675) | c3_1(a1648) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | (~c1_1(a1648)) | c3_1(a1675)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[2222, 2221])).
% 1.45/1.67 tff(2224,plain,
% 1.45/1.67 ((~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1648)) | c3_1(a1675)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2223, 119, 169, 1314, 1313, 168, 503, 595])).
% 1.45/1.67 tff(2225,plain,
% 1.45/1.67 (~c1_1(a1648)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2224, 2217, 504, 502])).
% 1.45/1.67 tff(2226,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[645, 119, 500, 170, 169, 504, 502, 639, 2225, 2210])).
% 1.45/1.67 tff(2227,plain,(c2_1(a1650) | hskp2 | (~c0_1(a1648)) | (~c2_1(a1648)) | (~c0_1(a1634)) | (~c3_1(a1634)) | c0_1(a1675) | c1_1(a1675) | c3_1(a1648) | c1_1(a1634) | (~c2_1(a1675)) | c1_1(a1650) | (~c0_1(a1650))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(2228,plain,
% 1.45/1.67 (c2_1(a1650)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2227, 500, 1174, 1173, 2198, 2197, 2202, 2201, 1172, 503, 2200, 1175, 2158])).
% 1.45/1.67 tff(2229,plain,
% 1.45/1.67 (hskp9),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2134, 2228, 1175, 500])).
% 1.45/1.67 tff(2230,plain,
% 1.45/1.67 (~hskp19),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[610, 2229, 2198, 2197, 503])).
% 1.45/1.67 tff(2231,plain,
% 1.45/1.67 (hskp15),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1450, 2230, 21])).
% 1.45/1.67 tff(2232,plain,
% 1.45/1.67 (~c2_1(a1664)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[333, 2231])).
% 1.45/1.67 tff(2233,plain,
% 1.45/1.67 (~c1_1(a1664)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[339, 2231])).
% 1.45/1.67 tff(2234,plain,
% 1.45/1.67 (c0_1(a1664)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[347, 2231])).
% 1.45/1.67 tff(2235,plain,
% 1.45/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1675) | c1_1(a1675) | c1_1(a1664) | c2_1(a1664) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | (~c0_1(a1664)) | (~c2_1(a1675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1675) | c1_1(a1675) | c1_1(a1664) | c2_1(a1664) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | (~c0_1(a1664)) | (~c2_1(a1675)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(2236,plain,
% 1.45/1.67 (((~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675))) <=> (c0_1(a1675) | c1_1(a1675) | c1_1(a1664) | c2_1(a1664) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | (~c0_1(a1664)) | (~c2_1(a1675)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(2237,plain,
% 1.45/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1675) | c1_1(a1675) | c1_1(a1664) | c2_1(a1664) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | (~c0_1(a1664)) | (~c2_1(a1675))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[2236])).
% 1.45/1.67 tff(2238,plain,
% 1.45/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1675) | c1_1(a1675) | c1_1(a1664) | c2_1(a1664) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | (~c0_1(a1664)) | (~c2_1(a1675)))),
% 1.45/1.67 inference(transitivity,[status(thm)],[2237, 2235])).
% 1.45/1.67 tff(2239,plain,
% 1.45/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(2240,plain,
% 1.45/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1675) | c1_1(a1675) | c1_1(a1664) | c2_1(a1664) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | (~c0_1(a1664)) | (~c2_1(a1675))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[2239, 2238])).
% 1.45/1.67 tff(2241,plain,
% 1.45/1.67 (~c2_1(a1634)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2240, 119, 2200, 2234, 2197, 2202, 2201, 2233, 2232, 503, 812])).
% 1.45/1.67 tff(2242,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | c1_1(a1650) | (~c0_1(a1650)) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1650)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp2 | c1_1(a1650) | (~c0_1(a1650)) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1650)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(2243,plain,
% 1.45/1.67 ((hskp2 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1650) | (~c2_1(a1650)) | (~c0_1(a1650))) <=> (hskp2 | c1_1(a1650) | (~c0_1(a1650)) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1650)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(2244,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1650) | (~c2_1(a1650)) | (~c0_1(a1650)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | c1_1(a1650) | (~c0_1(a1650)) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1650))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[2243])).
% 1.45/1.67 tff(2245,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1650) | (~c2_1(a1650)) | (~c0_1(a1650)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp2 | c1_1(a1650) | (~c0_1(a1650)) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1650)))),
% 1.45/1.67 inference(transitivity,[status(thm)],[2244, 2242])).
% 1.45/1.67 tff(2246,plain,
% 1.45/1.67 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1650) | (~c2_1(a1650)) | (~c0_1(a1650)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(2247,plain,
% 1.45/1.67 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp2 | c1_1(a1650) | (~c0_1(a1650)) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1650))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[2246, 2245])).
% 1.45/1.67 tff(2248,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2247, 119, 500, 1175, 2198, 2197, 2158, 639, 2228, 2241])).
% 1.45/1.67 tff(2249,plain,(hskp2 | c1_1(a1650) | c1_1(a1634) | hskp1 | c3_1(a1650) | c0_1(a1638) | c3_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(2250,plain,
% 1.45/1.67 (hskp2),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2249, 1175, 503, 21, 842, 22, 652])).
% 1.45/1.67 tff(2251,plain,
% 1.45/1.67 (~c0_1(a1637)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1124, 2250])).
% 1.45/1.67 tff(2252,plain,
% 1.45/1.67 (c3_1(a1637)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1132, 2250])).
% 1.45/1.67 tff(2253,plain,
% 1.45/1.67 (c1_1(a1637)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1140, 2250])).
% 1.45/1.67 tff(2254,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | c1_1(a1664) | c2_1(a1664) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c0_1(a1664)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c1_1(a1664) | c2_1(a1664) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c0_1(a1664)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(2255,plain,
% 1.45/1.67 ((hskp11 | (~ndr1_0) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637))) <=> (hskp11 | c1_1(a1664) | c2_1(a1664) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c0_1(a1664)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(2256,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | c1_1(a1664) | c2_1(a1664) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c0_1(a1664))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[2255])).
% 1.45/1.67 tff(2257,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c1_1(a1664) | c2_1(a1664) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c0_1(a1664)))),
% 1.45/1.67 inference(transitivity,[status(thm)],[2256, 2254])).
% 1.45/1.67 tff(2258,plain,
% 1.45/1.67 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(2259,plain,
% 1.45/1.67 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c1_1(a1664) | c2_1(a1664) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c0_1(a1664))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[2258, 2257])).
% 1.45/1.67 tff(2260,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2259, 119, 45, 1400, 1148, 1147, 1392, 1391, 1146, 280])).
% 1.45/1.67 tff(2261,plain,((~hskp15) | hskp11 | (~c1_1(a1637)) | (~c3_1(a1637)) | c0_1(a1637)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(2262,plain,
% 1.45/1.67 (~hskp15),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2261, 1184, 2253, 2252, 2251])).
% 1.45/1.67 tff(2263,plain,
% 1.45/1.67 (hskp19),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1450, 2262, 21])).
% 1.45/1.67 tff(2264,plain,
% 1.45/1.67 (~c3_1(a1682)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[568, 2263])).
% 1.45/1.67 tff(2265,assumption,(hskp0), introduced(assumption)).
% 1.45/1.67 tff(2266,plain,
% 1.45/1.67 (c0_1(a1634)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[498, 2265])).
% 1.45/1.67 tff(2267,plain,
% 1.45/1.67 (c3_1(a1634)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[490, 2265])).
% 1.45/1.67 tff(2268,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1504, 2267, 2266, 1147, 1148, 548, 1146, 503])).
% 1.45/1.67 tff(2269,plain,((~hskp0) | (~c3_1(a1637)) | (~c1_1(a1637)) | (~hskp19) | c0_1(a1637) | c1_1(a1634)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(2270,plain,
% 1.45/1.67 (~hskp0),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2269, 2252, 2253, 2263, 2251, 503])).
% 1.45/1.67 tff(2271,plain,
% 1.45/1.67 (hskp26),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[201, 2270, 21])).
% 1.45/1.67 tff(2272,plain,
% 1.45/1.67 (~c0_1(a1737)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[207, 2271])).
% 1.45/1.67 tff(2273,plain,
% 1.45/1.67 (c1_1(a1682)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[576, 2263])).
% 1.45/1.67 tff(2274,plain,
% 1.45/1.67 (c3_1(a1737)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[215, 2271])).
% 1.45/1.67 tff(2275,plain,
% 1.45/1.67 (c2_1(a1737)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[223, 2271])).
% 1.45/1.67 tff(2276,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c0_1(a1737) | c3_1(a1682) | (~ndr1_0) | (~c1_1(a1682)) | (~c0_1(a1682)) | (~c3_1(a1737)) | (~c2_1(a1737)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c0_1(a1737) | c3_1(a1682) | (~ndr1_0) | (~c1_1(a1682)) | (~c0_1(a1682)) | (~c3_1(a1737)) | (~c2_1(a1737)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(2277,plain,
% 1.45/1.67 ((hskp15 | (~ndr1_0) | c3_1(a1682) | (~c0_1(a1682)) | (~c1_1(a1682)) | c0_1(a1737) | (~c3_1(a1737)) | (~c2_1(a1737))) <=> (hskp15 | c0_1(a1737) | c3_1(a1682) | (~ndr1_0) | (~c1_1(a1682)) | (~c0_1(a1682)) | (~c3_1(a1737)) | (~c2_1(a1737)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2278,plain,
% 1.45/1.68 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a1682) | (~c0_1(a1682)) | (~c1_1(a1682)) | c0_1(a1737) | (~c3_1(a1737)) | (~c2_1(a1737)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c0_1(a1737) | c3_1(a1682) | (~ndr1_0) | (~c1_1(a1682)) | (~c0_1(a1682)) | (~c3_1(a1737)) | (~c2_1(a1737))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[2277])).
% 1.45/1.68 tff(2279,plain,
% 1.45/1.68 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a1682) | (~c0_1(a1682)) | (~c1_1(a1682)) | c0_1(a1737) | (~c3_1(a1737)) | (~c2_1(a1737)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c0_1(a1737) | c3_1(a1682) | (~ndr1_0) | (~c1_1(a1682)) | (~c0_1(a1682)) | (~c3_1(a1737)) | (~c2_1(a1737)))),
% 1.45/1.68 inference(transitivity,[status(thm)],[2278, 2276])).
% 1.45/1.68 tff(2280,plain,
% 1.45/1.68 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a1682) | (~c0_1(a1682)) | (~c1_1(a1682)) | c0_1(a1737) | (~c3_1(a1737)) | (~c2_1(a1737)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(2281,plain,
% 1.45/1.68 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c0_1(a1737) | c3_1(a1682) | (~ndr1_0) | (~c1_1(a1682)) | (~c0_1(a1682)) | (~c3_1(a1737)) | (~c2_1(a1737))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[2280, 2279])).
% 1.45/1.68 tff(2282,plain,
% 1.45/1.68 (~c0_1(a1682)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2281, 119, 2262, 2275, 2274, 2273, 2272, 2264, 316])).
% 1.45/1.68 tff(2283,plain,
% 1.45/1.68 (hskp5),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[834, 2270, 21])).
% 1.45/1.68 tff(2284,plain,
% 1.45/1.68 (~c2_1(a1640)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[840, 2283])).
% 1.45/1.68 tff(2285,plain,
% 1.45/1.68 (c0_1(a1640)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[850, 2283])).
% 1.45/1.68 tff(2286,plain,
% 1.45/1.68 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | c2_1(a1640) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1640) | (~c0_1(a1640)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c2_1(a1640) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1640) | (~c0_1(a1640)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2287,plain,
% 1.45/1.68 ((hskp11 | (~ndr1_0) | c2_1(a1640) | c1_1(a1640) | (~c0_1(a1640)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637))) <=> (hskp11 | c2_1(a1640) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1640) | (~c0_1(a1640)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2288,plain,
% 1.45/1.68 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1640) | c1_1(a1640) | (~c0_1(a1640)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | c2_1(a1640) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1640) | (~c0_1(a1640))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[2287])).
% 1.45/1.68 tff(2289,plain,
% 1.45/1.68 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1640) | c1_1(a1640) | (~c0_1(a1640)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c2_1(a1640) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1640) | (~c0_1(a1640)))),
% 1.45/1.68 inference(transitivity,[status(thm)],[2288, 2286])).
% 1.45/1.68 tff(2290,plain,
% 1.45/1.68 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a1640) | c1_1(a1640) | (~c0_1(a1640)) | c0_1(a1637) | (~c3_1(a1637)) | (~c1_1(a1637)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(2291,plain,
% 1.45/1.68 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c2_1(a1640) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c3_1(a1637)) | c1_1(a1640) | (~c0_1(a1640))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[2290, 2289])).
% 1.45/1.68 tff(2292,plain,
% 1.45/1.68 (c1_1(a1640)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2291, 119, 1184, 2285, 2253, 2252, 2284, 2251, 280])).
% 1.45/1.68 tff(2293,plain,
% 1.45/1.68 (c3_1(a1640)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[866, 2283])).
% 1.45/1.68 tff(2294,plain,
% 1.45/1.68 (c2_1(a1682)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[584, 2263])).
% 1.45/1.68 tff(2295,plain,
% 1.45/1.68 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp22 | c3_1(a1682) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c1_1(a1640)) | (~c2_1(a1682)) | (~c1_1(a1682)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp22 | c3_1(a1682) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c1_1(a1640)) | (~c2_1(a1682)) | (~c1_1(a1682)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2296,plain,
% 1.45/1.68 ((hskp22 | (~ndr1_0) | (~c3_1(a1640)) | (~c0_1(a1640)) | (~c1_1(a1640)) | c3_1(a1682) | (~c1_1(a1682)) | (~c2_1(a1682))) <=> (hskp22 | c3_1(a1682) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c1_1(a1640)) | (~c2_1(a1682)) | (~c1_1(a1682)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2297,plain,
% 1.45/1.68 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | (~c3_1(a1640)) | (~c0_1(a1640)) | (~c1_1(a1640)) | c3_1(a1682) | (~c1_1(a1682)) | (~c2_1(a1682)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp22 | c3_1(a1682) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c1_1(a1640)) | (~c2_1(a1682)) | (~c1_1(a1682))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[2296])).
% 1.45/1.68 tff(2298,plain,
% 1.45/1.68 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | (~c3_1(a1640)) | (~c0_1(a1640)) | (~c1_1(a1640)) | c3_1(a1682) | (~c1_1(a1682)) | (~c2_1(a1682)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp22 | c3_1(a1682) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c1_1(a1640)) | (~c2_1(a1682)) | (~c1_1(a1682)))),
% 1.45/1.68 inference(transitivity,[status(thm)],[2297, 2295])).
% 1.45/1.68 tff(2299,plain,
% 1.45/1.68 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | (~c3_1(a1640)) | (~c0_1(a1640)) | (~c1_1(a1640)) | c3_1(a1682) | (~c1_1(a1682)) | (~c2_1(a1682)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(2300,plain,
% 1.45/1.68 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp22 | c3_1(a1682) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c1_1(a1640)) | (~c2_1(a1682)) | (~c1_1(a1682))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[2299, 2298])).
% 1.45/1.68 tff(2301,plain,
% 1.45/1.68 (hskp22 | (~c1_1(a1640))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2300, 119, 2273, 2294, 2285, 2293, 2264, 44])).
% 1.45/1.68 tff(2302,plain,
% 1.45/1.68 (hskp22),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2301, 2292])).
% 1.45/1.68 tff(2303,plain,
% 1.45/1.68 (((~hskp22) | (~c3_1(a1697))) <=> ((~hskp22) | (~c3_1(a1697)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2304,plain,
% 1.45/1.68 (((~c3_1(a1697)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a1697)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2305,axiom,((~c3_1(a1697)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 1.45/1.68 tff(2306,plain,
% 1.45/1.68 ((~hskp22) | (~c3_1(a1697))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[2305, 2304])).
% 1.45/1.68 tff(2307,plain,
% 1.45/1.68 ((~hskp22) | (~c3_1(a1697))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[2306, 2303])).
% 1.45/1.68 tff(2308,plain,
% 1.45/1.68 (~c3_1(a1697)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2307, 2302])).
% 1.45/1.68 tff(2309,plain,
% 1.45/1.68 (((~hskp22) | (~c2_1(a1697))) <=> ((~hskp22) | (~c2_1(a1697)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2310,plain,
% 1.45/1.68 (((~c2_1(a1697)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a1697)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2311,axiom,((~c2_1(a1697)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 1.45/1.68 tff(2312,plain,
% 1.45/1.68 ((~hskp22) | (~c2_1(a1697))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[2311, 2310])).
% 1.45/1.68 tff(2313,plain,
% 1.45/1.68 ((~hskp22) | (~c2_1(a1697))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[2312, 2309])).
% 1.45/1.68 tff(2314,plain,
% 1.45/1.68 (~c2_1(a1697)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2313, 2302])).
% 1.45/1.68 tff(2315,plain,
% 1.45/1.68 (((~hskp22) | (~c0_1(a1697))) <=> ((~hskp22) | (~c0_1(a1697)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2316,plain,
% 1.45/1.68 (((~c0_1(a1697)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a1697)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2317,axiom,((~c0_1(a1697)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 1.45/1.68 tff(2318,plain,
% 1.45/1.68 ((~hskp22) | (~c0_1(a1697))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[2317, 2316])).
% 1.45/1.68 tff(2319,plain,
% 1.45/1.68 ((~hskp22) | (~c0_1(a1697))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[2318, 2315])).
% 1.45/1.68 tff(2320,plain,
% 1.45/1.68 (~c0_1(a1697)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2319, 2302])).
% 1.45/1.68 tff(2321,plain,
% 1.45/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1697) | c2_1(a1697) | c3_1(a1697) | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c2_1(a1682)) | (~c1_1(a1682)) | c0_1(a1682))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1697) | c2_1(a1697) | c3_1(a1697) | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c2_1(a1682)) | (~c1_1(a1682)) | c0_1(a1682))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2322,plain,
% 1.45/1.68 (((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1682) | (~c1_1(a1682)) | (~c2_1(a1682)) | c2_1(a1697) | c0_1(a1697) | c3_1(a1697)) <=> (c0_1(a1697) | c2_1(a1697) | c3_1(a1697) | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c2_1(a1682)) | (~c1_1(a1682)) | c0_1(a1682))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2323,plain,
% 1.45/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1682) | (~c1_1(a1682)) | (~c2_1(a1682)) | c2_1(a1697) | c0_1(a1697) | c3_1(a1697))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1697) | c2_1(a1697) | c3_1(a1697) | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c2_1(a1682)) | (~c1_1(a1682)) | c0_1(a1682)))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[2322])).
% 1.45/1.68 tff(2324,plain,
% 1.45/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1682) | (~c1_1(a1682)) | (~c2_1(a1682)) | c2_1(a1697) | c0_1(a1697) | c3_1(a1697))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1697) | c2_1(a1697) | c3_1(a1697) | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c2_1(a1682)) | (~c1_1(a1682)) | c0_1(a1682))),
% 1.45/1.68 inference(transitivity,[status(thm)],[2323, 2321])).
% 1.45/1.68 tff(2325,plain,
% 1.45/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1682) | (~c1_1(a1682)) | (~c2_1(a1682)) | c2_1(a1697) | c0_1(a1697) | c3_1(a1697))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(2326,plain,
% 1.45/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1697) | c2_1(a1697) | c3_1(a1697) | c3_1(a1648) | (~ndr1_0) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c2_1(a1682)) | (~c1_1(a1682)) | c0_1(a1682)),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[2325, 2324])).
% 1.45/1.68 tff(2327,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2326, 119, 2273, 2294, 1174, 1173, 2320, 2314, 2308, 1172, 295, 2282])).
% 1.45/1.68 tff(2328,plain,(c1_1(a1650) | hskp1 | c1_1(a1634) | c3_1(a1650) | c0_1(a1638) | c3_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(2329,plain,
% 1.45/1.68 (c1_1(a1650)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2328, 842, 503, 21, 22, 652])).
% 1.45/1.68 tff(2330,plain,
% 1.45/1.68 (~hskp15),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1428, 269, 661, 169, 852, 261, 168, 170, 245, 183, 239, 843, 842, 253])).
% 1.45/1.68 tff(2331,plain,
% 1.45/1.68 (hskp15 | (~c0_1(a1643))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[326, 119, 224, 216, 253, 208, 245, 316])).
% 1.45/1.68 tff(2332,plain,
% 1.45/1.68 (~c0_1(a1643)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2331, 2330])).
% 1.45/1.68 tff(2333,plain,
% 1.45/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1737) | c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1737)) | (~c2_1(a1737)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1737) | c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1737)) | (~c2_1(a1737)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2334,plain,
% 1.45/1.68 (((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1737) | (~c1_1(a1737)) | (~c2_1(a1737)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643)) <=> (c0_1(a1737) | c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1737)) | (~c2_1(a1737)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2335,plain,
% 1.45/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1737) | (~c1_1(a1737)) | (~c2_1(a1737)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1737) | c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1737)) | (~c2_1(a1737))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[2334])).
% 1.45/1.68 tff(2336,plain,
% 1.45/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1737) | (~c1_1(a1737)) | (~c2_1(a1737)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1737) | c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1737)) | (~c2_1(a1737)))),
% 1.45/1.68 inference(transitivity,[status(thm)],[2335, 2333])).
% 1.45/1.68 tff(2337,plain,
% 1.45/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1737) | (~c1_1(a1737)) | (~c2_1(a1737)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(2338,plain,
% 1.45/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1737) | c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1737)) | (~c2_1(a1737))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[2337, 2336])).
% 1.45/1.68 tff(2339,plain,
% 1.45/1.68 (c0_1(a1643) | (~c1_1(a1737))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2338, 119, 224, 170, 169, 208, 168, 183, 245, 295])).
% 1.45/1.68 tff(2340,plain,
% 1.45/1.68 (~c1_1(a1737)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2339, 2332])).
% 1.45/1.68 tff(2341,plain,
% 1.45/1.68 (c0_1(a1646)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[305, 2332, 170, 239, 261, 169, 168, 183, 245])).
% 1.45/1.68 tff(2342,plain,
% 1.45/1.68 (hskp19),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1450, 2330, 21])).
% 1.45/1.68 tff(2343,plain,
% 1.45/1.68 (~c3_1(a1682)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[568, 2342])).
% 1.45/1.68 tff(2344,plain,
% 1.45/1.68 (c2_1(a1682)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[584, 2342])).
% 1.45/1.68 tff(2345,plain,
% 1.45/1.68 (c1_1(a1682)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[576, 2342])).
% 1.45/1.68 tff(2346,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1460, 119, 261, 239, 216, 2345, 2344, 208, 2343, 1442, 2341, 2340])).
% 1.45/1.68 tff(2347,plain,(hskp0 | (~c0_1(a1648)) | (~c2_1(a1648)) | c3_1(a1648) | hskp1 | hskp3 | (~c1_1(a1650)) | c0_1(a1650) | c3_1(a1650)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(2348,plain,
% 1.45/1.68 (hskp0),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2347, 843, 1173, 1172, 21, 660, 2329, 1174, 842])).
% 1.45/1.68 tff(2349,plain,
% 1.45/1.68 (c0_1(a1634)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[498, 2348])).
% 1.45/1.68 tff(2350,plain,
% 1.45/1.68 (c3_1(a1634)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[490, 2348])).
% 1.45/1.68 tff(2351,plain,
% 1.45/1.68 (hskp10),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1170, 21, 503, 661])).
% 1.45/1.68 tff(2352,plain,
% 1.45/1.68 (c2_1(a1648)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[166, 2351])).
% 1.45/1.68 tff(2353,plain,
% 1.45/1.68 (c0_1(a1648)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[158, 2351])).
% 1.45/1.68 tff(2354,plain,
% 1.45/1.68 (~c3_1(a1648)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[150, 2351])).
% 1.45/1.68 tff(2355,plain,
% 1.45/1.68 (~c0_1(a1643)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[894, 33, 661, 245, 852, 843, 842, 500, 253, 21])).
% 1.45/1.68 tff(2356,plain,
% 1.45/1.68 (~c1_1(a1737)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2338, 119, 224, 170, 169, 208, 168, 183, 245, 295, 2355])).
% 1.45/1.68 tff(2357,plain,
% 1.45/1.68 (c0_1(a1646)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[305, 239, 170, 2355, 261, 169, 168, 183, 245])).
% 1.45/1.68 tff(2358,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1460, 119, 261, 239, 216, 2345, 2344, 208, 2343, 1442, 2357, 2356])).
% 1.45/1.68 tff(2359,plain,(hskp0 | hskp1 | hskp3 | (~c2_1(a1648)) | (~c1_1(a1650)) | c3_1(a1648) | (~c0_1(a1648)) | c0_1(a1650) | c3_1(a1650) | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(2360,plain,
% 1.45/1.68 (hskp0),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2359, 500, 661, 2352, 852, 2354, 2353, 843, 842, 21])).
% 1.45/1.68 tff(2361,plain,
% 1.45/1.68 (c0_1(a1634)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[498, 2360])).
% 1.45/1.68 tff(2362,plain,
% 1.45/1.68 (c3_1(a1634)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[490, 2360])).
% 1.45/1.68 tff(2363,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1492, 2362, 2361, 2354, 2353, 2352, 852, 503, 21, 661, 500, 843, 842])).
% 1.45/1.68 tff(2364,plain,(hskp2 | (~c1_1(a1650)) | c1_1(a1634) | hskp1 | hskp3 | c0_1(a1650) | c3_1(a1650)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(2365,plain,
% 1.45/1.68 (hskp2),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2364, 843, 503, 21, 660, 2329, 842])).
% 1.45/1.68 tff(2366,plain,
% 1.45/1.68 (~c0_1(a1637)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1124, 2365])).
% 1.45/1.68 tff(2367,plain,
% 1.45/1.68 (c3_1(a1637)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1132, 2365])).
% 1.45/1.68 tff(2368,plain,
% 1.45/1.68 (c1_1(a1637)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1140, 2365])).
% 1.45/1.68 tff(2369,plain,
% 1.45/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1638) | (~c2_1(a1638)) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c1_1(a1638)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1638) | (~c2_1(a1638)) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c1_1(a1638)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2370,plain,
% 1.45/1.68 (((~ndr1_0) | c3_1(a1638) | (~c2_1(a1638)) | (~c1_1(a1638)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637))) <=> (c3_1(a1638) | (~c2_1(a1638)) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c1_1(a1638)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2371,plain,
% 1.45/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1638) | (~c2_1(a1638)) | (~c1_1(a1638)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1638) | (~c2_1(a1638)) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c1_1(a1638))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[2370])).
% 1.45/1.68 tff(2372,plain,
% 1.45/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1638) | (~c2_1(a1638)) | (~c1_1(a1638)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1638) | (~c2_1(a1638)) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c1_1(a1638)))),
% 1.45/1.68 inference(transitivity,[status(thm)],[2371, 2369])).
% 1.45/1.68 tff(2373,plain,
% 1.45/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1638) | (~c2_1(a1638)) | (~c1_1(a1638)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(2374,plain,
% 1.45/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1638) | (~c2_1(a1638)) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c1_1(a1638))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[2373, 2372])).
% 1.45/1.68 tff(2375,plain,
% 1.45/1.68 ((~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1638))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2374, 119, 652, 2368, 2367, 2119, 2366, 503, 20])).
% 1.45/1.68 tff(2376,plain,
% 1.45/1.68 (~c1_1(a1638)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2375, 2350, 2349])).
% 1.45/1.68 tff(2377,plain,
% 1.45/1.68 (~hskp19),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2269, 2348, 2368, 2367, 2366, 503])).
% 1.45/1.68 tff(2378,plain,
% 1.45/1.68 (hskp15),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1450, 2377, 21])).
% 1.45/1.68 tff(2379,plain,
% 1.45/1.68 (~c2_1(a1664)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[333, 2378])).
% 1.45/1.68 tff(2380,plain,
% 1.45/1.68 (~c1_1(a1664)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[339, 2378])).
% 1.45/1.68 tff(2381,plain,
% 1.45/1.68 (c0_1(a1664)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[347, 2378])).
% 1.45/1.68 tff(2382,plain,
% 1.45/1.68 (~c2_1(a1634)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2146, 119, 2381, 2350, 2380, 2379, 22, 2119, 503, 812, 2376])).
% 1.45/1.68 tff(2383,plain,
% 1.45/1.68 (c3_1(a1664)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1398, 119, 660, 2329, 2380, 2379, 843, 842, 10])).
% 1.45/1.68 tff(2384,plain,
% 1.45/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1648) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c2_1(a1648)) | (~c1_1(a1648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1648) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c2_1(a1648)) | (~c1_1(a1648)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2385,plain,
% 1.45/1.68 (((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c1_1(a1648)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637))) <=> (c3_1(a1648) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c2_1(a1648)) | (~c1_1(a1648)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2386,plain,
% 1.45/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c1_1(a1648)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1648) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c2_1(a1648)) | (~c1_1(a1648))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[2385])).
% 1.45/1.68 tff(2387,plain,
% 1.45/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c1_1(a1648)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1648) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c2_1(a1648)) | (~c1_1(a1648)))),
% 1.45/1.68 inference(transitivity,[status(thm)],[2386, 2384])).
% 1.45/1.68 tff(2388,plain,
% 1.45/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c1_1(a1648)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1637) | (~c1_1(a1637)) | (~c3_1(a1637)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(2389,plain,
% 1.45/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1648) | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1637)) | (~c3_1(a1637)) | (~c2_1(a1648)) | (~c1_1(a1648))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[2388, 2387])).
% 1.45/1.68 tff(2390,plain,
% 1.45/1.68 ((~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1648))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2389, 119, 1173, 2368, 2367, 1172, 2366, 503, 20])).
% 1.45/1.68 tff(2391,plain,
% 1.45/1.68 (~c1_1(a1648)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2390, 2350, 2349])).
% 1.45/1.68 tff(2392,plain,
% 1.45/1.68 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.45/1.68 inference(bind,[status(th)],[])).
% 1.45/1.68 tff(2393,plain,
% 1.45/1.68 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.45/1.68 inference(quant_intro,[status(thm)],[2392])).
% 1.45/1.68 tff(2394,plain,
% 1.45/1.68 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2395,plain,
% 1.45/1.68 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.45/1.68 inference(bind,[status(th)],[])).
% 1.45/1.68 tff(2396,plain,
% 1.45/1.68 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.45/1.68 inference(quant_intro,[status(thm)],[2395])).
% 1.45/1.68 tff(2397,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause185')).
% 1.45/1.68 tff(2398,plain,
% 1.45/1.68 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[2397, 2396])).
% 1.45/1.68 tff(2399,plain,
% 1.45/1.68 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[2398, 2394])).
% 1.45/1.68 tff(2400,plain,(
% 1.45/1.68 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.45/1.68 inference(skolemize,[status(sab)],[2399])).
% 1.45/1.69 tff(2401,plain,
% 1.45/1.69 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2400, 2393])).
% 1.45/1.69 tff(2402,plain,
% 1.45/1.69 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | c2_1(a1664) | (~ndr1_0) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648)) | (~c0_1(a1664)) | (~c3_1(a1664)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | c2_1(a1664) | (~ndr1_0) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648)) | (~c0_1(a1664)) | (~c3_1(a1664)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2403,plain,
% 1.45/1.69 ((hskp17 | (~ndr1_0) | c2_1(a1664) | (~c3_1(a1664)) | (~c0_1(a1664)) | c1_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648))) <=> (hskp17 | c2_1(a1664) | (~ndr1_0) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648)) | (~c0_1(a1664)) | (~c3_1(a1664)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2404,plain,
% 1.45/1.69 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1664) | (~c3_1(a1664)) | (~c0_1(a1664)) | c1_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | c2_1(a1664) | (~ndr1_0) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648)) | (~c0_1(a1664)) | (~c3_1(a1664))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[2403])).
% 1.45/1.69 tff(2405,plain,
% 1.45/1.69 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1664) | (~c3_1(a1664)) | (~c0_1(a1664)) | c1_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | c2_1(a1664) | (~ndr1_0) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648)) | (~c0_1(a1664)) | (~c3_1(a1664)))),
% 1.45/1.69 inference(transitivity,[status(thm)],[2404, 2402])).
% 1.45/1.69 tff(2406,plain,
% 1.45/1.69 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1664) | (~c3_1(a1664)) | (~c0_1(a1664)) | c1_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(2407,plain,
% 1.45/1.69 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | c2_1(a1664) | (~ndr1_0) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648)) | (~c0_1(a1664)) | (~c3_1(a1664))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2406, 2405])).
% 1.45/1.69 tff(2408,plain,
% 1.45/1.69 (hskp17 | (~c3_1(a1664))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2407, 119, 2381, 1174, 1173, 2379, 2401, 2391])).
% 1.45/1.69 tff(2409,plain,
% 1.45/1.69 (hskp17),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2408, 2383])).
% 1.45/1.69 tff(2410,plain,
% 1.45/1.69 (~c1_1(a1675)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[413, 2409])).
% 1.45/1.69 tff(2411,plain,
% 1.45/1.69 (~c0_1(a1675)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[419, 2409])).
% 1.45/1.69 tff(2412,plain,
% 1.45/1.69 ((~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1650))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1167, 119, 2329, 2368, 2367, 842, 2366, 503, 20])).
% 1.45/1.69 tff(2413,plain,
% 1.45/1.69 (~c2_1(a1650)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2412, 2350, 2349])).
% 1.45/1.69 tff(2414,plain,
% 1.45/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1650) | c3_1(a1650) | c3_1(a1648) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c2_1(a1637)) | (~c2_1(a1648)) | (~c0_1(a1648)) | c2_1(a1650))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1650) | c3_1(a1650) | c3_1(a1648) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c2_1(a1637)) | (~c2_1(a1648)) | (~c0_1(a1648)) | c2_1(a1650))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2415,plain,
% 1.45/1.69 (((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1637) | (~c1_1(a1637)) | (~c2_1(a1637)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650)) <=> (c0_1(a1650) | c3_1(a1650) | c3_1(a1648) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c2_1(a1637)) | (~c2_1(a1648)) | (~c0_1(a1648)) | c2_1(a1650))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2416,plain,
% 1.45/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1637) | (~c1_1(a1637)) | (~c2_1(a1637)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1650) | c3_1(a1650) | c3_1(a1648) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c2_1(a1637)) | (~c2_1(a1648)) | (~c0_1(a1648)) | c2_1(a1650)))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[2415])).
% 1.45/1.69 tff(2417,plain,
% 1.45/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1637) | (~c1_1(a1637)) | (~c2_1(a1637)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1650) | c3_1(a1650) | c3_1(a1648) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c2_1(a1637)) | (~c2_1(a1648)) | (~c0_1(a1648)) | c2_1(a1650))),
% 1.45/1.69 inference(transitivity,[status(thm)],[2416, 2414])).
% 1.45/1.69 tff(2418,plain,
% 1.45/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1637) | (~c1_1(a1637)) | (~c2_1(a1637)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(2419,plain,
% 1.45/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1650) | c3_1(a1650) | c3_1(a1648) | c0_1(a1637) | (~ndr1_0) | (~c1_1(a1637)) | (~c2_1(a1637)) | (~c2_1(a1648)) | (~c0_1(a1648)) | c2_1(a1650)),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2418, 2417])).
% 1.45/1.69 tff(2420,plain,
% 1.45/1.69 (~c2_1(a1637)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2419, 119, 1174, 1173, 2368, 843, 842, 1172, 2366, 295, 2413])).
% 1.45/1.69 tff(2421,plain,
% 1.45/1.69 (hskp21 | c2_1(a1637)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1512, 119, 660, 2368, 2367, 769])).
% 1.45/1.69 tff(2422,plain,
% 1.45/1.69 (hskp21),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2421, 2420])).
% 1.45/1.69 tff(2423,plain,
% 1.45/1.69 (~c1_1(a1691)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[697, 2422])).
% 1.45/1.69 tff(2424,plain,
% 1.45/1.69 (c2_1(a1675)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[435, 2409])).
% 1.45/1.69 tff(2425,plain,
% 1.45/1.69 (c3_1(a1691)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[713, 2422])).
% 1.45/1.69 tff(2426,plain,
% 1.45/1.69 (c2_1(a1691)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[738, 2422])).
% 1.45/1.69 tff(2427,plain,
% 1.45/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1691) | c0_1(a1675) | c1_1(a1675) | c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c0_1(a1634)) | (~c2_1(a1675)) | (~c3_1(a1691)) | (~c2_1(a1691)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1691) | c0_1(a1675) | c1_1(a1675) | c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c0_1(a1634)) | (~c2_1(a1675)) | (~c3_1(a1691)) | (~c2_1(a1691)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2428,plain,
% 1.45/1.69 (((~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691)) | c2_1(a1634) | c1_1(a1634) | (~c0_1(a1634)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675))) <=> (c1_1(a1691) | c0_1(a1675) | c1_1(a1675) | c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c0_1(a1634)) | (~c2_1(a1675)) | (~c3_1(a1691)) | (~c2_1(a1691)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2429,plain,
% 1.45/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691)) | c2_1(a1634) | c1_1(a1634) | (~c0_1(a1634)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1691) | c0_1(a1675) | c1_1(a1675) | c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c0_1(a1634)) | (~c2_1(a1675)) | (~c3_1(a1691)) | (~c2_1(a1691))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[2428])).
% 1.45/1.69 tff(2430,plain,
% 1.45/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691)) | c2_1(a1634) | c1_1(a1634) | (~c0_1(a1634)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1691) | c0_1(a1675) | c1_1(a1675) | c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c0_1(a1634)) | (~c2_1(a1675)) | (~c3_1(a1691)) | (~c2_1(a1691)))),
% 1.45/1.69 inference(transitivity,[status(thm)],[2429, 2427])).
% 1.45/1.69 tff(2431,plain,
% 1.45/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691)) | c2_1(a1634) | c1_1(a1634) | (~c0_1(a1634)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675)))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(2432,plain,
% 1.45/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1691) | c0_1(a1675) | c1_1(a1675) | c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c0_1(a1634)) | (~c2_1(a1675)) | (~c3_1(a1691)) | (~c2_1(a1691))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2431, 2430])).
% 1.45/1.69 tff(2433,plain,
% 1.45/1.69 ($false),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2432, 119, 2426, 2425, 2424, 2349, 2423, 2411, 2410, 503, 812, 2382])).
% 1.45/1.69 tff(2434,plain,(c0_1(a1650) | c1_1(a1634) | c3_1(a1650) | c0_1(a1638) | hskp1 | c3_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.69 tff(2435,plain,
% 1.45/1.69 (c0_1(a1650)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2434, 842, 503, 22, 21, 652])).
% 1.45/1.69 tff(2436,plain,
% 1.45/1.69 (~hskp11),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[673, 2159])).
% 1.45/1.69 tff(2437,plain,
% 1.45/1.69 (c0_1(a1646)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[357, 269, 2436, 224, 261, 216, 253, 208, 245, 170, 239, 169, 168, 183])).
% 1.45/1.69 tff(2438,plain,
% 1.45/1.69 (hskp17),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[407, 2436, 21])).
% 1.45/1.69 tff(2439,plain,
% 1.45/1.69 (~c1_1(a1675)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[413, 2438])).
% 1.45/1.69 tff(2440,plain,
% 1.45/1.69 (~c0_1(a1675)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[419, 2438])).
% 1.45/1.69 tff(2441,plain,
% 1.45/1.69 (c2_1(a1675)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[435, 2438])).
% 1.45/1.69 tff(2442,plain,
% 1.45/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1675) | c1_1(a1675) | (~c0_1(a1650)) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | (~c2_1(a1675)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1675) | c1_1(a1675) | (~c0_1(a1650)) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | (~c2_1(a1675)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2443,plain,
% 1.45/1.69 (((~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c0_1(a1646)) | c3_1(a1650) | (~c1_1(a1650)) | (~c0_1(a1650)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675))) <=> (c0_1(a1675) | c1_1(a1675) | (~c0_1(a1650)) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | (~c2_1(a1675)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2444,plain,
% 1.45/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c0_1(a1646)) | c3_1(a1650) | (~c1_1(a1650)) | (~c0_1(a1650)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1675) | c1_1(a1675) | (~c0_1(a1650)) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | (~c2_1(a1675)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[2443])).
% 1.45/1.69 tff(2445,plain,
% 1.45/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c0_1(a1646)) | c3_1(a1650) | (~c1_1(a1650)) | (~c0_1(a1650)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1675) | c1_1(a1675) | (~c0_1(a1650)) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | (~c2_1(a1675)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646)))),
% 1.45/1.69 inference(transitivity,[status(thm)],[2444, 2442])).
% 1.45/1.69 tff(2446,plain,
% 1.45/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1646)) | (~c3_1(a1646)) | (~c0_1(a1646)) | c3_1(a1650) | (~c1_1(a1650)) | (~c0_1(a1650)) | c1_1(a1675) | c0_1(a1675) | (~c2_1(a1675)))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(2447,plain,
% 1.45/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1675) | c1_1(a1675) | (~c0_1(a1650)) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | (~c2_1(a1675)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c3_1(a1646))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2446, 2445])).
% 1.45/1.69 tff(2448,plain,
% 1.45/1.69 ($false),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2447, 119, 239, 269, 2441, 852, 2440, 2439, 2159, 842, 368, 2437])).
% 1.45/1.69 tff(2449,plain,(hskp0 | (~c1_1(a1650)) | (~c0_1(a1650)) | c3_1(a1650) | (~c0_1(a1648)) | (~c2_1(a1648)) | c3_1(a1648) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.45/1.69 tff(2450,plain,
% 1.45/1.69 (hskp0),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2449, 2329, 2435, 842, 1174, 1173, 1172, 21])).
% 1.45/1.69 tff(2451,plain,
% 1.45/1.69 (c3_1(a1634)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[490, 2450])).
% 1.45/1.69 tff(2452,plain,
% 1.45/1.69 (c0_1(a1634)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[498, 2450])).
% 1.45/1.69 tff(2453,plain,
% 1.45/1.69 (~hskp11),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[673, 2435])).
% 1.45/1.69 tff(2454,plain,
% 1.45/1.69 (hskp17),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[407, 2453, 21])).
% 1.45/1.69 tff(2455,plain,
% 1.45/1.69 (~c1_1(a1675)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[413, 2454])).
% 1.45/1.69 tff(2456,plain,
% 1.45/1.69 (~c0_1(a1675)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[419, 2454])).
% 1.45/1.69 tff(2457,plain,
% 1.45/1.69 (c2_1(a1675)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[435, 2454])).
% 1.45/1.69 tff(2458,plain,
% 1.45/1.69 (~c0_1(a1646)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2447, 119, 381, 380, 1316, 852, 1314, 1313, 2159, 842, 368])).
% 1.45/1.69 tff(2459,plain,
% 1.45/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1638) | (~c2_1(a1638)) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1638)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1638) | (~c2_1(a1638)) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1638)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2460,plain,
% 1.45/1.69 (((~ndr1_0) | c3_1(a1638) | (~c2_1(a1638)) | (~c1_1(a1638)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646))) <=> (c3_1(a1638) | (~c2_1(a1638)) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1638)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2461,plain,
% 1.45/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1638) | (~c2_1(a1638)) | (~c1_1(a1638)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1638) | (~c2_1(a1638)) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1638)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[2460])).
% 1.45/1.69 tff(2462,plain,
% 1.45/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1638) | (~c2_1(a1638)) | (~c1_1(a1638)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1638) | (~c2_1(a1638)) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1638)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.45/1.69 inference(transitivity,[status(thm)],[2461, 2459])).
% 1.45/1.69 tff(2463,plain,
% 1.45/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1638) | (~c2_1(a1638)) | (~c1_1(a1638)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(2464,plain,
% 1.45/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1638) | (~c2_1(a1638)) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c1_1(a1638)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2463, 2462])).
% 1.45/1.69 tff(2465,plain,
% 1.45/1.69 (~c1_1(a1638)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2464, 119, 382, 380, 652, 504, 502, 2119, 503, 20, 2458])).
% 1.45/1.69 tff(2466,plain,
% 1.45/1.69 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~c0_1(a1650)) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | (~c2_1(a1646)) | c0_1(a1646) | (~c3_1(a1646)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | (~c0_1(a1650)) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | (~c2_1(a1646)) | c0_1(a1646) | (~c3_1(a1646)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2467,plain,
% 1.45/1.69 ((hskp15 | (~ndr1_0) | c3_1(a1650) | (~c0_1(a1650)) | (~c1_1(a1650)) | c0_1(a1646) | (~c3_1(a1646)) | (~c2_1(a1646))) <=> (hskp15 | (~c0_1(a1650)) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | (~c2_1(a1646)) | c0_1(a1646) | (~c3_1(a1646)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2468,plain,
% 1.45/1.69 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a1650) | (~c0_1(a1650)) | (~c1_1(a1650)) | c0_1(a1646) | (~c3_1(a1646)) | (~c2_1(a1646)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~c0_1(a1650)) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | (~c2_1(a1646)) | c0_1(a1646) | (~c3_1(a1646))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[2467])).
% 1.45/1.69 tff(2469,plain,
% 1.45/1.69 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a1650) | (~c0_1(a1650)) | (~c1_1(a1650)) | c0_1(a1646) | (~c3_1(a1646)) | (~c2_1(a1646)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | (~c0_1(a1650)) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | (~c2_1(a1646)) | c0_1(a1646) | (~c3_1(a1646)))),
% 1.45/1.69 inference(transitivity,[status(thm)],[2468, 2466])).
% 1.45/1.69 tff(2470,plain,
% 1.45/1.69 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a1650) | (~c0_1(a1650)) | (~c1_1(a1650)) | c0_1(a1646) | (~c3_1(a1646)) | (~c2_1(a1646)))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(2471,plain,
% 1.45/1.69 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | (~c0_1(a1650)) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | (~c2_1(a1646)) | c0_1(a1646) | (~c3_1(a1646))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2470, 2469])).
% 1.45/1.69 tff(2472,plain,
% 1.45/1.69 (hskp15),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2471, 119, 381, 380, 852, 2159, 842, 316, 2458])).
% 1.45/1.69 tff(2473,plain,
% 1.45/1.69 (~c2_1(a1664)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[333, 2472])).
% 1.45/1.69 tff(2474,plain,
% 1.45/1.69 (~c1_1(a1664)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[339, 2472])).
% 1.45/1.69 tff(2475,plain,
% 1.45/1.69 (^[U: $i] : refl((hskp13 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp13 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.45/1.69 inference(bind,[status(th)],[])).
% 1.45/1.69 tff(2476,plain,
% 1.45/1.69 (![U: $i] : (hskp13 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp13 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.45/1.69 inference(quant_intro,[status(thm)],[2475])).
% 1.45/1.69 tff(2477,plain,
% 1.45/1.69 (![U: $i] : (hskp13 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp13 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2478,plain,
% 1.45/1.69 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp13))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) | hskp11) <=> ((hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp11))), rewrite(((hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp11) <=> (hskp13 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) | hskp11) <=> (hskp13 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.45/1.69 inference(bind,[status(th)],[])).
% 1.45/1.69 tff(2479,plain,
% 1.45/1.69 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) | hskp11) <=> ![U: $i] : (hskp13 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.45/1.69 inference(quant_intro,[status(thm)],[2478])).
% 1.45/1.69 tff(2480,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 1.45/1.69 tff(2481,plain,
% 1.45/1.69 (![U: $i] : (hskp13 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2480, 2479])).
% 1.45/1.69 tff(2482,plain,
% 1.45/1.69 (![U: $i] : (hskp13 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2481, 2477])).
% 1.45/1.69 tff(2483,plain,(
% 1.45/1.69 ![U: $i] : (hskp13 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.45/1.69 inference(skolemize,[status(sab)],[2482])).
% 1.45/1.69 tff(2484,plain,
% 1.45/1.69 (![U: $i] : (hskp13 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2483, 2476])).
% 1.45/1.69 tff(2485,plain,
% 1.45/1.69 (((~![U: $i] : (hskp13 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | hskp11 | (~ndr1_0) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646)))) <=> ((~![U: $i] : (hskp13 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | hskp11 | (~ndr1_0) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2486,plain,
% 1.45/1.69 ((hskp13 | hskp11 | (~ndr1_0) | c0_1(a1646) | (~c2_1(a1646)) | (~c1_1(a1646))) <=> (hskp13 | hskp11 | (~ndr1_0) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2487,plain,
% 1.45/1.69 (((~![U: $i] : (hskp13 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | hskp11 | (~ndr1_0) | c0_1(a1646) | (~c2_1(a1646)) | (~c1_1(a1646)))) <=> ((~![U: $i] : (hskp13 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | hskp11 | (~ndr1_0) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[2486])).
% 1.45/1.69 tff(2488,plain,
% 1.45/1.69 (((~![U: $i] : (hskp13 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | hskp11 | (~ndr1_0) | c0_1(a1646) | (~c2_1(a1646)) | (~c1_1(a1646)))) <=> ((~![U: $i] : (hskp13 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | hskp11 | (~ndr1_0) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646)))),
% 1.45/1.69 inference(transitivity,[status(thm)],[2487, 2485])).
% 1.45/1.69 tff(2489,plain,
% 1.45/1.69 ((~![U: $i] : (hskp13 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | hskp11 | (~ndr1_0) | c0_1(a1646) | (~c2_1(a1646)) | (~c1_1(a1646)))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(2490,plain,
% 1.45/1.69 ((~![U: $i] : (hskp13 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | hskp11 | (~ndr1_0) | (~c2_1(a1646)) | c0_1(a1646) | (~c1_1(a1646))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2489, 2488])).
% 1.45/1.69 tff(2491,plain,
% 1.45/1.69 (hskp13 | c0_1(a1646)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2490, 119, 2436, 382, 381, 2484])).
% 1.45/1.69 tff(2492,plain,
% 1.45/1.69 (hskp13),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2491, 2458])).
% 1.45/1.69 tff(2493,plain,
% 1.45/1.69 (((~hskp13) | (~c2_1(a1658))) <=> ((~hskp13) | (~c2_1(a1658)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2494,plain,
% 1.45/1.69 (((~c2_1(a1658)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a1658)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2495,axiom,((~c2_1(a1658)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 1.45/1.69 tff(2496,plain,
% 1.45/1.69 ((~hskp13) | (~c2_1(a1658))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2495, 2494])).
% 1.45/1.69 tff(2497,plain,
% 1.45/1.69 ((~hskp13) | (~c2_1(a1658))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2496, 2493])).
% 1.45/1.69 tff(2498,plain,
% 1.45/1.69 (~c2_1(a1658)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2497, 2492])).
% 1.45/1.69 tff(2499,plain,
% 1.45/1.69 (((~hskp13) | c3_1(a1658)) <=> ((~hskp13) | c3_1(a1658))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2500,axiom,((~hskp13) | c3_1(a1658)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 1.45/1.69 tff(2501,plain,
% 1.45/1.69 ((~hskp13) | c3_1(a1658)),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2500, 2499])).
% 1.45/1.69 tff(2502,plain,
% 1.45/1.69 ((~hskp13) | c3_1(a1658)),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2501, 2499])).
% 1.45/1.69 tff(2503,plain,
% 1.45/1.69 ((~hskp13) | c3_1(a1658)),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2502, 2499])).
% 1.45/1.69 tff(2504,plain,
% 1.45/1.69 ((~hskp13) | c3_1(a1658)),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2503, 2499])).
% 1.45/1.69 tff(2505,plain,
% 1.45/1.69 ((~hskp13) | c3_1(a1658)),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2504, 2499])).
% 1.45/1.69 tff(2506,plain,
% 1.45/1.69 (c3_1(a1658)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2505, 2492])).
% 1.45/1.69 tff(2507,plain,
% 1.45/1.69 (((~hskp13) | c1_1(a1658)) <=> ((~hskp13) | c1_1(a1658))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2508,axiom,((~hskp13) | c1_1(a1658)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 1.45/1.69 tff(2509,plain,
% 1.45/1.69 ((~hskp13) | c1_1(a1658)),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2508, 2507])).
% 1.45/1.69 tff(2510,plain,
% 1.45/1.69 ((~hskp13) | c1_1(a1658)),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2509, 2507])).
% 1.45/1.69 tff(2511,plain,
% 1.45/1.69 ((~hskp13) | c1_1(a1658)),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2510, 2507])).
% 1.45/1.69 tff(2512,plain,
% 1.45/1.69 ((~hskp13) | c1_1(a1658)),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2511, 2507])).
% 1.45/1.69 tff(2513,plain,
% 1.45/1.69 ((~hskp13) | c1_1(a1658)),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2512, 2507])).
% 1.45/1.69 tff(2514,plain,
% 1.45/1.69 (c1_1(a1658)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2513, 2492])).
% 1.45/1.69 tff(2515,plain,
% 1.45/1.69 (((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | c2_1(a1658) | (~ndr1_0) | (~c3_1(a1658)) | (~c1_1(a1658)))) <=> ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp3 | c2_1(a1658) | (~ndr1_0) | (~c3_1(a1658)) | (~c1_1(a1658)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2516,plain,
% 1.45/1.69 ((hskp21 | hskp3 | (~ndr1_0) | c2_1(a1658) | (~c3_1(a1658)) | (~c1_1(a1658))) <=> (hskp21 | hskp3 | c2_1(a1658) | (~ndr1_0) | (~c3_1(a1658)) | (~c1_1(a1658)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2517,plain,
% 1.45/1.69 (((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | (~ndr1_0) | c2_1(a1658) | (~c3_1(a1658)) | (~c1_1(a1658)))) <=> ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | c2_1(a1658) | (~ndr1_0) | (~c3_1(a1658)) | (~c1_1(a1658))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[2516])).
% 1.45/1.69 tff(2518,plain,
% 1.45/1.69 (((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | (~ndr1_0) | c2_1(a1658) | (~c3_1(a1658)) | (~c1_1(a1658)))) <=> ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp3 | c2_1(a1658) | (~ndr1_0) | (~c3_1(a1658)) | (~c1_1(a1658)))),
% 1.45/1.69 inference(transitivity,[status(thm)],[2517, 2515])).
% 1.45/1.69 tff(2519,plain,
% 1.45/1.69 ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | (~ndr1_0) | c2_1(a1658) | (~c3_1(a1658)) | (~c1_1(a1658)))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(2520,plain,
% 1.45/1.69 ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp3 | c2_1(a1658) | (~ndr1_0) | (~c3_1(a1658)) | (~c1_1(a1658))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2519, 2518])).
% 1.45/1.69 tff(2521,plain,
% 1.45/1.69 (hskp21),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2520, 119, 660, 2514, 2506, 2498, 769])).
% 1.45/1.69 tff(2522,plain,
% 1.45/1.69 (~c1_1(a1691)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[697, 2521])).
% 1.45/1.69 tff(2523,plain,
% 1.45/1.69 (c0_1(a1664)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[347, 2472])).
% 1.45/1.69 tff(2524,plain,
% 1.45/1.69 (c3_1(a1691)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[713, 2521])).
% 1.45/1.69 tff(2525,plain,
% 1.45/1.69 (c2_1(a1691)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[738, 2521])).
% 1.45/1.69 tff(2526,plain,
% 1.45/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1691) | c1_1(a1664) | c2_1(a1664) | c0_1(a1638) | (~c2_1(a1638)) | (~ndr1_0) | c1_1(a1638) | (~c0_1(a1664)) | (~c3_1(a1691)) | (~c2_1(a1691)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1691) | c1_1(a1664) | c2_1(a1664) | c0_1(a1638) | (~c2_1(a1638)) | (~ndr1_0) | c1_1(a1638) | (~c0_1(a1664)) | (~c3_1(a1691)) | (~c2_1(a1691)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2527,plain,
% 1.45/1.69 (((~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1638) | c0_1(a1638) | (~c2_1(a1638))) <=> (c1_1(a1691) | c1_1(a1664) | c2_1(a1664) | c0_1(a1638) | (~c2_1(a1638)) | (~ndr1_0) | c1_1(a1638) | (~c0_1(a1664)) | (~c3_1(a1691)) | (~c2_1(a1691)))),
% 1.45/1.70 inference(rewrite,[status(thm)],[])).
% 1.45/1.70 tff(2528,plain,
% 1.45/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1638) | c0_1(a1638) | (~c2_1(a1638)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1691) | c1_1(a1664) | c2_1(a1664) | c0_1(a1638) | (~c2_1(a1638)) | (~ndr1_0) | c1_1(a1638) | (~c0_1(a1664)) | (~c3_1(a1691)) | (~c2_1(a1691))))),
% 1.45/1.70 inference(monotonicity,[status(thm)],[2527])).
% 1.45/1.70 tff(2529,plain,
% 1.45/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1638) | c0_1(a1638) | (~c2_1(a1638)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1691) | c1_1(a1664) | c2_1(a1664) | c0_1(a1638) | (~c2_1(a1638)) | (~ndr1_0) | c1_1(a1638) | (~c0_1(a1664)) | (~c3_1(a1691)) | (~c2_1(a1691)))),
% 1.45/1.70 inference(transitivity,[status(thm)],[2528, 2526])).
% 1.45/1.70 tff(2530,plain,
% 1.45/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1638) | c0_1(a1638) | (~c2_1(a1638)))),
% 1.45/1.70 inference(quant_inst,[status(thm)],[])).
% 1.45/1.70 tff(2531,plain,
% 1.45/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1691) | c1_1(a1664) | c2_1(a1664) | c0_1(a1638) | (~c2_1(a1638)) | (~ndr1_0) | c1_1(a1638) | (~c0_1(a1664)) | (~c3_1(a1691)) | (~c2_1(a1691))),
% 1.45/1.70 inference(modus_ponens,[status(thm)],[2530, 2529])).
% 1.45/1.70 tff(2532,plain,
% 1.45/1.70 ($false),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[2531, 119, 2525, 2524, 2523, 2522, 2474, 2473, 22, 2119, 812, 2465])).
% 1.45/1.70 tff(2533,plain,((~hskp28) | c0_1(a1638) | (~c1_1(a1650)) | (~c0_1(a1650)) | c3_1(a1650) | c3_1(a1638) | (~c0_1(a1634)) | (~c3_1(a1634)) | c1_1(a1634) | (~c2_1(a1675)) | c0_1(a1675) | c1_1(a1675)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.70 tff(2534,plain,
% 1.45/1.70 (~hskp28),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[2533, 2329, 22, 2435, 842, 652, 2452, 2451, 503, 2457, 2456, 2455])).
% 1.45/1.70 tff(2535,plain,
% 1.45/1.70 (hskp2),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[647, 2534, 1174, 1173, 2452, 2451, 503, 1172])).
% 1.45/1.70 tff(2536,plain,
% 1.45/1.70 (~c0_1(a1637)),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[1124, 2535])).
% 1.45/1.70 tff(2537,plain,
% 1.45/1.70 (c3_1(a1637)),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[1132, 2535])).
% 1.45/1.70 tff(2538,plain,
% 1.45/1.70 (c1_1(a1637)),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[1140, 2535])).
% 1.45/1.70 tff(2539,plain,
% 1.45/1.70 (~hskp19),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[2269, 2538, 2450, 2537, 2536, 503])).
% 1.45/1.70 tff(2540,plain,
% 1.45/1.70 (~hskp15),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[2261, 2537, 2453, 2538, 2536])).
% 1.45/1.70 tff(2541,plain,
% 1.45/1.70 ($false),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[1450, 2540, 2539, 21])).
% 1.45/1.70 tff(2542,plain,(c3_1(a1650) | hskp1 | c1_1(a1634) | c0_1(a1638) | c3_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.70 tff(2543,plain,
% 1.45/1.70 (c3_1(a1650)),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[2542, 21, 503, 22, 652])).
% 1.45/1.70 tff(2544,plain,
% 1.45/1.70 (~hskp11),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[667, 2543])).
% 1.45/1.70 tff(2545,plain,
% 1.45/1.70 (hskp0),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[474, 1174, 1173, 1172, 2544, 21])).
% 1.45/1.70 tff(2546,plain,
% 1.45/1.70 (c3_1(a1634)),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[490, 2545])).
% 1.45/1.70 tff(2547,plain,
% 1.45/1.70 (c0_1(a1634)),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[498, 2545])).
% 1.45/1.70 tff(2548,assumption,(~hskp9), introduced(assumption)).
% 1.45/1.70 tff(2549,plain,
% 1.45/1.70 (~c1_1(a1648)),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[1489, 2548])).
% 1.45/1.70 tff(2550,plain,
% 1.45/1.70 ($false),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[539, 2549, 2548, 500])).
% 1.45/1.70 tff(2551,plain,(hskp9 | hskp2 | (~c2_1(a1648)) | c3_1(a1648) | (~c0_1(a1648))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.70 tff(2552,plain,
% 1.45/1.70 (hskp9),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[2551, 500, 2352, 2354, 2353])).
% 1.45/1.70 tff(2553,plain,
% 1.45/1.70 (~c1_1(a1644)),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[559, 2552])).
% 1.45/1.70 tff(2554,plain,
% 1.45/1.70 (~c0_1(a1644)),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[553, 2552])).
% 1.45/1.70 tff(2555,plain,
% 1.45/1.70 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a1644) | c1_1(a1644) | (~ndr1_0) | c2_1(a1644))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a1644) | c1_1(a1644) | (~ndr1_0) | c2_1(a1644))),
% 1.45/1.70 inference(rewrite,[status(thm)],[])).
% 1.45/1.70 tff(2556,plain,
% 1.45/1.70 ((hskp3 | hskp2 | (~ndr1_0) | c2_1(a1644) | c1_1(a1644) | c0_1(a1644)) <=> (hskp3 | hskp2 | c0_1(a1644) | c1_1(a1644) | (~ndr1_0) | c2_1(a1644))),
% 1.45/1.70 inference(rewrite,[status(thm)],[])).
% 1.45/1.70 tff(2557,plain,
% 1.45/1.70 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a1644) | c1_1(a1644) | c0_1(a1644))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a1644) | c1_1(a1644) | (~ndr1_0) | c2_1(a1644)))),
% 1.45/1.70 inference(monotonicity,[status(thm)],[2556])).
% 1.45/1.70 tff(2558,plain,
% 1.45/1.70 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a1644) | c1_1(a1644) | c0_1(a1644))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a1644) | c1_1(a1644) | (~ndr1_0) | c2_1(a1644))),
% 1.45/1.70 inference(transitivity,[status(thm)],[2557, 2555])).
% 1.45/1.70 tff(2559,plain,
% 1.45/1.70 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a1644) | c1_1(a1644) | c0_1(a1644))),
% 1.45/1.70 inference(quant_inst,[status(thm)],[])).
% 1.45/1.70 tff(2560,plain,
% 1.45/1.70 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a1644) | c1_1(a1644) | (~ndr1_0) | c2_1(a1644)),
% 1.45/1.70 inference(modus_ponens,[status(thm)],[2559, 2558])).
% 1.45/1.70 tff(2561,plain,
% 1.45/1.70 (c2_1(a1644)),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[2560, 119, 661, 500, 2554, 2553, 1045])).
% 1.45/1.70 tff(2562,plain,
% 1.45/1.70 (~hskp19),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[610, 2552, 504, 502, 503])).
% 1.45/1.70 tff(2563,plain,
% 1.45/1.70 (hskp15),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[1450, 2562, 21])).
% 1.45/1.70 tff(2564,plain,
% 1.45/1.70 (~c2_1(a1664)),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[333, 2563])).
% 1.45/1.70 tff(2565,plain,
% 1.45/1.70 (~c1_1(a1664)),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[339, 2563])).
% 1.45/1.70 tff(2566,plain,
% 1.45/1.70 (c0_1(a1664)),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[347, 2563])).
% 1.45/1.70 tff(2567,plain,
% 1.45/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1664) | c2_1(a1664) | c0_1(a1644) | c1_1(a1644) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | (~c2_1(a1644)) | (~c0_1(a1664)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1664) | c2_1(a1664) | c0_1(a1644) | c1_1(a1644) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | (~c2_1(a1644)) | (~c0_1(a1664)))),
% 1.45/1.70 inference(rewrite,[status(thm)],[])).
% 1.45/1.70 tff(2568,plain,
% 1.45/1.70 (((~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1644) | c0_1(a1644) | (~c2_1(a1644))) <=> (c1_1(a1664) | c2_1(a1664) | c0_1(a1644) | c1_1(a1644) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | (~c2_1(a1644)) | (~c0_1(a1664)))),
% 1.45/1.70 inference(rewrite,[status(thm)],[])).
% 1.45/1.70 tff(2569,plain,
% 1.45/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1644) | c0_1(a1644) | (~c2_1(a1644)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1664) | c2_1(a1664) | c0_1(a1644) | c1_1(a1644) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | (~c2_1(a1644)) | (~c0_1(a1664))))),
% 1.45/1.70 inference(monotonicity,[status(thm)],[2568])).
% 1.45/1.70 tff(2570,plain,
% 1.45/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1644) | c0_1(a1644) | (~c2_1(a1644)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1664) | c2_1(a1664) | c0_1(a1644) | c1_1(a1644) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | (~c2_1(a1644)) | (~c0_1(a1664)))),
% 1.45/1.70 inference(transitivity,[status(thm)],[2569, 2567])).
% 1.45/1.70 tff(2571,plain,
% 1.45/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1644) | c0_1(a1644) | (~c2_1(a1644)))),
% 1.45/1.70 inference(quant_inst,[status(thm)],[])).
% 1.45/1.70 tff(2572,plain,
% 1.45/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1664) | c2_1(a1664) | c0_1(a1644) | c1_1(a1644) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | (~c2_1(a1644)) | (~c0_1(a1664))),
% 1.45/1.70 inference(modus_ponens,[status(thm)],[2571, 2570])).
% 1.45/1.70 tff(2573,plain,
% 1.45/1.70 (~c2_1(a1634)),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[2572, 119, 2566, 502, 2565, 2564, 2554, 2553, 503, 812, 2561])).
% 1.45/1.70 tff(2574,plain,
% 1.45/1.70 (~c3_1(a1644)),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[546, 2552])).
% 1.45/1.70 tff(2575,plain,
% 1.45/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1648) | c0_1(a1644) | c1_1(a1644) | c3_1(a1644) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | (~c1_1(a1648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1648) | c0_1(a1644) | c1_1(a1644) | c3_1(a1644) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | (~c1_1(a1648)))),
% 1.45/1.70 inference(rewrite,[status(thm)],[])).
% 1.45/1.70 tff(2576,plain,
% 1.45/1.70 (((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c1_1(a1648)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1644) | c0_1(a1644) | c3_1(a1644)) <=> (c3_1(a1648) | c0_1(a1644) | c1_1(a1644) | c3_1(a1644) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | (~c1_1(a1648)))),
% 1.45/1.70 inference(rewrite,[status(thm)],[])).
% 1.45/1.70 tff(2577,plain,
% 1.45/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c1_1(a1648)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1644) | c0_1(a1644) | c3_1(a1644))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1648) | c0_1(a1644) | c1_1(a1644) | c3_1(a1644) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | (~c1_1(a1648))))),
% 1.45/1.70 inference(monotonicity,[status(thm)],[2576])).
% 1.53/1.70 tff(2578,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c1_1(a1648)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1644) | c0_1(a1644) | c3_1(a1644))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1648) | c0_1(a1644) | c1_1(a1644) | c3_1(a1644) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | (~c1_1(a1648)))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2577, 2575])).
% 1.53/1.70 tff(2579,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c1_1(a1648)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1644) | c0_1(a1644) | c3_1(a1644))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2580,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1648) | c0_1(a1644) | c1_1(a1644) | c3_1(a1644) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | (~c1_1(a1648))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2579, 2578])).
% 1.53/1.70 tff(2581,plain,
% 1.53/1.70 (~c1_1(a1648)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2580, 119, 2352, 504, 502, 2354, 2554, 2553, 2574, 503, 595])).
% 1.53/1.70 tff(2582,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[645, 119, 500, 2353, 2352, 504, 502, 639, 2581, 2573])).
% 1.53/1.70 tff(2583,plain,(hskp2 | (~c0_1(a1634)) | (~c3_1(a1634)) | c1_1(a1634) | hskp3 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(2584,plain,
% 1.53/1.70 (hskp2),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2583, 2547, 2546, 503, 660, 21])).
% 1.53/1.70 tff(2585,plain,
% 1.53/1.70 (~c0_1(a1637)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1124, 2584])).
% 1.53/1.70 tff(2586,plain,
% 1.53/1.70 (c1_1(a1637)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1140, 2584])).
% 1.53/1.70 tff(2587,plain,
% 1.53/1.70 (c3_1(a1637)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1132, 2584])).
% 1.53/1.70 tff(2588,plain,
% 1.53/1.70 (~hskp15),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2261, 2587, 2544, 2586, 2585])).
% 1.53/1.70 tff(2589,plain,
% 1.53/1.70 (~hskp19),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2269, 2587, 2545, 2586, 2585, 503])).
% 1.53/1.70 tff(2590,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1450, 2589, 2588, 21])).
% 1.53/1.70 tff(2591,plain,(hskp1 | c1_1(a1634) | c0_1(a1638) | c3_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(2592,plain,
% 1.53/1.70 (hskp1),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2591, 503, 22, 652])).
% 1.53/1.70 tff(2593,plain,
% 1.53/1.70 (~c2_1(a1636)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1549, 2592])).
% 1.53/1.70 tff(2594,plain,
% 1.53/1.70 (~c1_1(a1636)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1537, 2592])).
% 1.53/1.70 tff(2595,plain,
% 1.53/1.70 (~c0_1(a1636)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1543, 2592])).
% 1.53/1.70 tff(2596,plain,
% 1.53/1.70 (hskp2),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1672, 119, 660, 2595, 2594, 2593, 1045])).
% 1.53/1.70 tff(2597,plain,
% 1.53/1.70 (hskp20),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2047, 2594, 503, 2595, 2593])).
% 1.53/1.70 tff(2598,plain,
% 1.53/1.70 (~c2_1(a1689)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2053, 2597])).
% 1.53/1.70 tff(2599,plain,
% 1.53/1.70 (c1_1(a1689)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2061, 2597])).
% 1.53/1.70 tff(2600,plain,
% 1.53/1.70 (c0_1(a1689)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2069, 2597])).
% 1.53/1.70 tff(2601,plain,
% 1.53/1.70 (~c0_1(a1637)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1124, 1939])).
% 1.53/1.70 tff(2602,plain,
% 1.53/1.70 (hskp11 | (~c3_1(a1636))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1889, 119, 1940, 1941, 2601, 1553, 1551, 55])).
% 1.53/1.70 tff(2603,plain,
% 1.53/1.70 (~c3_1(a1636)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2602, 45])).
% 1.53/1.70 tff(2604,plain,
% 1.53/1.70 (c1_1(a1639)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2093, 1903, 1939, 45, 1146, 296])).
% 1.53/1.70 tff(2605,plain,
% 1.53/1.70 (~c3_1(a1636)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1890, 45, 1940, 1941])).
% 1.53/1.70 tff(2606,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~c1_1(a1639)) | c2_1(a1639) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | c0_1(a1639))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (~c1_1(a1639)) | c2_1(a1639) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | c0_1(a1639))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2607,plain,
% 1.53/1.70 (((~ndr1_0) | c2_1(a1639) | c0_1(a1639) | (~c1_1(a1639)) | c2_1(a1636) | c0_1(a1636) | c3_1(a1636) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636)) <=> ((~c1_1(a1639)) | c2_1(a1639) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | c0_1(a1639))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2608,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1639) | c0_1(a1639) | (~c1_1(a1639)) | c2_1(a1636) | c0_1(a1636) | c3_1(a1636) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~c1_1(a1639)) | c2_1(a1639) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | c0_1(a1639)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2607])).
% 1.53/1.70 tff(2609,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1639) | c0_1(a1639) | (~c1_1(a1639)) | c2_1(a1636) | c0_1(a1636) | c3_1(a1636) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (~c1_1(a1639)) | c2_1(a1639) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | c0_1(a1639))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2608, 2606])).
% 1.53/1.70 tff(2610,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1639) | c0_1(a1639) | (~c1_1(a1639)) | c2_1(a1636) | c0_1(a1636) | c3_1(a1636) | c2_1(a1636) | c1_1(a1636) | c0_1(a1636))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2611,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (~c1_1(a1639)) | c2_1(a1639) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | c0_1(a1639)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2610, 2609])).
% 1.53/1.70 tff(2612,plain,
% 1.53/1.70 ((~c1_1(a1639)) | c0_1(a1639)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2611, 296, 1903, 1553, 1552, 1551, 1261, 2605])).
% 1.53/1.70 tff(2613,plain,
% 1.53/1.70 (c0_1(a1639)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2612, 2604])).
% 1.53/1.70 tff(2614,plain,
% 1.53/1.70 (~hskp4),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[934, 2604])).
% 1.53/1.70 tff(2615,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~c1_1(a1639)) | c2_1(a1639) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c0_1(a1639)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | (~c1_1(a1639)) | c2_1(a1639) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c0_1(a1639)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2616,plain,
% 1.53/1.70 ((hskp4 | (~ndr1_0) | c2_1(a1639) | (~c0_1(a1639)) | (~c1_1(a1639)) | c1_1(a1636) | c0_1(a1636) | c3_1(a1636)) <=> (hskp4 | (~c1_1(a1639)) | c2_1(a1639) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c0_1(a1639)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2617,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1639) | (~c0_1(a1639)) | (~c1_1(a1639)) | c1_1(a1636) | c0_1(a1636) | c3_1(a1636))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~c1_1(a1639)) | c2_1(a1639) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c0_1(a1639))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2616])).
% 1.53/1.70 tff(2618,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1639) | (~c0_1(a1639)) | (~c1_1(a1639)) | c1_1(a1636) | c0_1(a1636) | c3_1(a1636))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | (~c1_1(a1639)) | c2_1(a1639) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c0_1(a1639)))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2617, 2615])).
% 1.53/1.70 tff(2619,plain,
% 1.53/1.70 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1639) | (~c0_1(a1639)) | (~c1_1(a1639)) | c1_1(a1636) | c0_1(a1636) | c3_1(a1636))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2620,plain,
% 1.53/1.70 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | (~c1_1(a1639)) | c2_1(a1639) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c0_1(a1639))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2619, 2618])).
% 1.53/1.70 tff(2621,plain,
% 1.53/1.70 (hskp4 | (~c1_1(a1639)) | (~c0_1(a1639))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2620, 296, 1903, 1553, 1552, 915, 2605])).
% 1.53/1.70 tff(2622,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2621, 2614, 2604, 2613])).
% 1.53/1.70 tff(2623,plain,(c2_1(a1639) | (~ndr1_0) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~hskp2) | hskp11 | c0_1(a1637)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(2624,plain,
% 1.53/1.70 (c2_1(a1639) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~hskp2) | hskp11 | c0_1(a1637)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2623, 119])).
% 1.53/1.70 tff(2625,plain,
% 1.53/1.70 (c2_1(a1639)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2624, 45, 1553, 1552, 1551, 1939, 2601])).
% 1.53/1.70 tff(2626,plain,
% 1.53/1.70 (~hskp4),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[928, 2625])).
% 1.53/1.70 tff(2627,assumption,(~c2_1(a1689)), introduced(assumption)).
% 1.53/1.70 tff(2628,assumption,(c1_1(a1689)), introduced(assumption)).
% 1.53/1.70 tff(2629,assumption,(c0_1(a1689)), introduced(assumption)).
% 1.53/1.70 tff(2630,plain,
% 1.53/1.70 (hskp4 | c3_1(a1636)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2076, 119, 2629, 2628, 2627, 1553, 1552, 915])).
% 1.53/1.70 tff(2631,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2630, 2626, 2603])).
% 1.53/1.70 tff(2632,plain,(hskp11 | (~c0_1(a1689)) | (~c1_1(a1689)) | c2_1(a1689) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~hskp2)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(2633,plain,
% 1.53/1.70 (hskp11),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2632, 2600, 2599, 2598, 2595, 2594, 2593, 2596])).
% 1.53/1.70 tff(2634,plain,
% 1.53/1.70 (~c3_1(a1650)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[667, 2633])).
% 1.53/1.70 tff(2635,plain,
% 1.53/1.70 (~c0_1(a1650)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[673, 2633])).
% 1.53/1.70 tff(2636,plain,
% 1.53/1.70 (c1_1(a1650)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[705, 2633])).
% 1.53/1.70 tff(2637,plain,
% 1.53/1.70 (c3_1(a1636)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1865, 119, 660, 2636, 2635, 2634, 2594, 2593, 10])).
% 1.53/1.70 tff(2638,plain,
% 1.53/1.70 ((~c3_1(a1636)) | (~c2_1(a1650))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1585, 119, 2636, 2635, 2595, 2594, 691])).
% 1.53/1.70 tff(2639,plain,
% 1.53/1.70 (~c2_1(a1650)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2638, 2637])).
% 1.53/1.70 tff(2640,plain,
% 1.53/1.70 (~c0_1(a1637)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1124, 2596])).
% 1.53/1.70 tff(2641,plain,
% 1.53/1.70 (c1_1(a1637)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1140, 2596])).
% 1.53/1.70 tff(2642,plain,
% 1.53/1.70 ((~c3_1(a1636)) | (~c2_1(a1637))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1872, 119, 2641, 2640, 2595, 2594, 691])).
% 1.53/1.70 tff(2643,plain,
% 1.53/1.70 (~c2_1(a1637)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2642, 2637])).
% 1.53/1.70 tff(2644,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1880, 119, 2641, 2635, 2634, 2640, 2595, 2594, 2593, 1261, 2643, 2639])).
% 1.53/1.70 tff(2645,plain,(c1_1(a1634) | c0_1(a1638) | c3_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(2646,plain,
% 1.53/1.70 (c1_1(a1634)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2645, 652, 22])).
% 1.53/1.70 tff(2647,plain,
% 1.53/1.70 (~hskp0),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[482, 2646])).
% 1.53/1.70 tff(2648,plain,
% 1.53/1.70 (hskp11),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[476, 21, 33])).
% 1.53/1.70 tff(2649,plain,
% 1.53/1.70 (~c0_1(a1650)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[673, 2648])).
% 1.53/1.70 tff(2650,plain,
% 1.53/1.70 (hskp5),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[834, 21, 33])).
% 1.53/1.70 tff(2651,plain,
% 1.53/1.70 (~c2_1(a1640)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[840, 2650])).
% 1.53/1.70 tff(2652,plain,
% 1.53/1.70 (hskp26),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[201, 21, 33])).
% 1.53/1.70 tff(2653,plain,
% 1.53/1.70 (~c0_1(a1737)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[207, 2652])).
% 1.53/1.70 tff(2654,plain,
% 1.53/1.70 (c3_1(a1737)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[215, 2652])).
% 1.53/1.70 tff(2655,plain,
% 1.53/1.70 (c2_1(a1737)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[223, 2652])).
% 1.53/1.70 tff(2656,plain,
% 1.53/1.70 (hskp28),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[230, 119, 33, 2655, 2654, 2653, 193])).
% 1.53/1.70 tff(2657,plain,
% 1.53/1.70 (c2_1(a1646)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[238, 2656])).
% 1.53/1.70 tff(2658,plain,
% 1.53/1.70 (~c3_1(a1650)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[667, 2648])).
% 1.53/1.70 tff(2659,plain,
% 1.53/1.70 (c3_1(a1640)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[866, 2650])).
% 1.53/1.70 tff(2660,plain,
% 1.53/1.70 (c0_1(a1640)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[850, 2650])).
% 1.53/1.70 tff(2661,plain,
% 1.53/1.70 (c1_1(a1650)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[705, 2648])).
% 1.53/1.70 tff(2662,plain,
% 1.53/1.70 (c3_1(a1646)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[268, 2656])).
% 1.53/1.70 tff(2663,plain,
% 1.53/1.70 (c1_1(a1646)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[260, 2656])).
% 1.53/1.70 tff(2664,assumption,(~c2_1(a1640)), introduced(assumption)).
% 1.53/1.70 tff(2665,assumption,(c3_1(a1640)), introduced(assumption)).
% 1.53/1.70 tff(2666,plain,
% 1.53/1.70 (hskp21 | (~c1_1(a1640))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[873, 119, 661, 2665, 2664, 769])).
% 1.53/1.70 tff(2667,plain,
% 1.53/1.70 (~c1_1(a1640)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2666, 759])).
% 1.53/1.70 tff(2668,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c3_1(a1640)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c3_1(a1640)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2669,plain,
% 1.53/1.70 (((~ndr1_0) | (~c3_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c1_1(a1646)) | (~c2_1(a1646)) | (~c0_1(a1646)) | c2_1(a1640) | c1_1(a1640) | (~c3_1(a1640))) <=> (c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c3_1(a1640)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2670,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c1_1(a1646)) | (~c2_1(a1646)) | (~c0_1(a1646)) | c2_1(a1640) | c1_1(a1640) | (~c3_1(a1640)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c3_1(a1640)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2669])).
% 1.53/1.70 tff(2671,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c1_1(a1646)) | (~c2_1(a1646)) | (~c0_1(a1646)) | c2_1(a1640) | c1_1(a1640) | (~c3_1(a1640)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c3_1(a1640)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2670, 2668])).
% 1.53/1.70 tff(2672,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c1_1(a1646)) | (~c2_1(a1646)) | (~c0_1(a1646)) | c2_1(a1640) | c1_1(a1640) | (~c3_1(a1640)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2673,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c3_1(a1640)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2672, 2671])).
% 1.53/1.70 tff(2674,plain,
% 1.53/1.70 (c1_1(a1640) | (~c0_1(a1646))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2673, 119, 283, 284, 349, 2665, 2664, 1418])).
% 1.53/1.70 tff(2675,plain,
% 1.53/1.70 (~c0_1(a1646)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2674, 2667])).
% 1.53/1.70 tff(2676,plain,
% 1.53/1.70 (hskp10 | c2_1(a1650)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[680, 119, 21, 843, 842, 136])).
% 1.53/1.70 tff(2677,plain,
% 1.53/1.70 (c2_1(a1650)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2676, 56])).
% 1.53/1.70 tff(2678,assumption,(c0_1(a1640)), introduced(assumption)).
% 1.53/1.70 tff(2679,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1650) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1650)) | (~c1_1(a1650)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1650) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1650)) | (~c1_1(a1650)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2680,plain,
% 1.53/1.70 (((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646))) <=> (c3_1(a1650) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1650)) | (~c1_1(a1650)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2681,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1650) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1650)) | (~c1_1(a1650)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2680])).
% 1.53/1.70 tff(2682,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1650) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1650)) | (~c1_1(a1650)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2681, 2679])).
% 1.53/1.71 tff(2683,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2684,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1650) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1650)) | (~c1_1(a1650)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2683, 2682])).
% 1.53/1.71 tff(2685,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2684, 119, 283, 349, 852, 2678, 2665, 842, 20, 2677, 2675, 2667])).
% 1.53/1.71 tff(2686,plain,(hskp10 | (~c1_1(a1646)) | (~c3_1(a1646)) | (~c1_1(a1650)) | (~c0_1(a1640)) | (~c3_1(a1640)) | c3_1(a1650) | (~c2_1(a1646)) | c2_1(a1640) | hskp3 | hskp1 | c0_1(a1650)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(2687,plain,
% 1.53/1.71 (hskp10),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2686, 2663, 2662, 2661, 2660, 2659, 2658, 2657, 2651, 661, 21, 2649])).
% 1.53/1.71 tff(2688,plain,
% 1.53/1.71 (c0_1(a1648)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[158, 2687])).
% 1.53/1.71 tff(2689,plain,
% 1.53/1.71 (c2_1(a1648)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[166, 2687])).
% 1.53/1.71 tff(2690,plain,
% 1.53/1.71 (~c3_1(a1648)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[150, 2687])).
% 1.53/1.71 tff(2691,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2347, 2690, 2689, 33, 2658, 21, 661, 2661, 2688, 2649])).
% 1.53/1.71 tff(2692,plain,(hskp1 | hskp0 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(2693,plain,
% 1.53/1.71 (hskp1),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2692, 2647, 660])).
% 1.53/1.71 tff(2694,plain,
% 1.53/1.71 (~c2_1(a1636)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1549, 2693])).
% 1.53/1.71 tff(2695,plain,
% 1.53/1.71 (~c1_1(a1636)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1537, 2693])).
% 1.53/1.71 tff(2696,plain,
% 1.53/1.71 (~c0_1(a1636)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1543, 2693])).
% 1.53/1.71 tff(2697,plain,
% 1.53/1.71 (hskp2),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1672, 119, 660, 2696, 2695, 2694, 1045])).
% 1.53/1.71 tff(2698,plain,
% 1.53/1.71 (c2_1(a1637) | (~c1_1(a1637)) | c0_1(a1637) | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | c3_1(a1636)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2006, 119])).
% 1.53/1.71 tff(2699,plain,
% 1.53/1.71 (c2_1(a1637)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2698, 2603, 1553, 2601, 1940, 1552, 1551])).
% 1.53/1.71 tff(2700,plain,
% 1.53/1.71 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 1.53/1.71 inference(bind,[status(th)],[])).
% 1.53/1.71 tff(2701,plain,
% 1.53/1.71 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.53/1.71 inference(quant_intro,[status(thm)],[2700])).
% 1.53/1.71 tff(2702,plain,
% 1.53/1.71 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2703,plain,
% 1.53/1.71 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V)))), ((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V))), ((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)))), (((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp5) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp5))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 1.53/1.71 inference(bind,[status(th)],[])).
% 1.53/1.71 tff(2704,plain,
% 1.53/1.71 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.53/1.71 inference(quant_intro,[status(thm)],[2703])).
% 1.53/1.71 tff(2705,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 1.53/1.71 tff(2706,plain,
% 1.53/1.71 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2705, 2704])).
% 1.53/1.71 tff(2707,plain,
% 1.53/1.71 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2706, 2702])).
% 1.53/1.71 tff(2708,plain,(
% 1.53/1.71 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.53/1.71 inference(skolemize,[status(sab)],[2707])).
% 1.53/1.71 tff(2709,plain,
% 1.53/1.71 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2708, 2701])).
% 1.53/1.71 tff(2710,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp5 | c0_1(a1637) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c2_1(a1637)) | (~c3_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp5 | c0_1(a1637) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c2_1(a1637)) | (~c3_1(a1637)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2711,plain,
% 1.53/1.71 ((hskp5 | (~ndr1_0) | c0_1(a1637) | (~c2_1(a1637)) | (~c3_1(a1637)) | c2_1(a1636) | c1_1(a1636) | c3_1(a1636)) <=> (hskp5 | c0_1(a1637) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c2_1(a1637)) | (~c3_1(a1637)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2712,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c0_1(a1637) | (~c2_1(a1637)) | (~c3_1(a1637)) | c2_1(a1636) | c1_1(a1636) | c3_1(a1636))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp5 | c0_1(a1637) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c2_1(a1637)) | (~c3_1(a1637))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2711])).
% 1.53/1.71 tff(2713,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c0_1(a1637) | (~c2_1(a1637)) | (~c3_1(a1637)) | c2_1(a1636) | c1_1(a1636) | c3_1(a1636))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp5 | c0_1(a1637) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c2_1(a1637)) | (~c3_1(a1637)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2712, 2710])).
% 1.53/1.71 tff(2714,plain,
% 1.53/1.71 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c0_1(a1637) | (~c2_1(a1637)) | (~c3_1(a1637)) | c2_1(a1636) | c1_1(a1636) | c3_1(a1636))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2715,plain,
% 1.53/1.71 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp5 | c0_1(a1637) | c1_1(a1636) | c2_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c2_1(a1637)) | (~c3_1(a1637))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2714, 2713])).
% 1.53/1.71 tff(2716,plain,
% 1.53/1.71 (hskp5 | c3_1(a1636) | (~c2_1(a1637))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2715, 119, 1941, 2601, 1552, 1551, 2709])).
% 1.53/1.71 tff(2717,plain,
% 1.53/1.71 (hskp5),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2716, 2603, 2699])).
% 1.53/1.71 tff(2718,plain,
% 1.53/1.71 (~c2_1(a1640)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[840, 2717])).
% 1.53/1.71 tff(2719,plain,
% 1.53/1.71 (c0_1(a1640)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[850, 2717])).
% 1.53/1.71 tff(2720,plain,
% 1.53/1.71 (c1_1(a1640)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2291, 119, 45, 2719, 1940, 1941, 2718, 2601, 280])).
% 1.53/1.71 tff(2721,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | c2_1(a1640) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c0_1(a1640)) | (~c1_1(a1640)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c2_1(a1640) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c0_1(a1640)) | (~c1_1(a1640)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2722,plain,
% 1.53/1.71 ((hskp4 | (~ndr1_0) | c2_1(a1640) | (~c0_1(a1640)) | (~c1_1(a1640)) | c1_1(a1636) | c0_1(a1636) | c3_1(a1636)) <=> (hskp4 | c2_1(a1640) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c0_1(a1640)) | (~c1_1(a1640)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2723,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1640) | (~c0_1(a1640)) | (~c1_1(a1640)) | c1_1(a1636) | c0_1(a1636) | c3_1(a1636))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | c2_1(a1640) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c0_1(a1640)) | (~c1_1(a1640))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2722])).
% 1.53/1.71 tff(2724,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1640) | (~c0_1(a1640)) | (~c1_1(a1640)) | c1_1(a1636) | c0_1(a1636) | c3_1(a1636))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c2_1(a1640) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c0_1(a1640)) | (~c1_1(a1640)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2723, 2721])).
% 1.53/1.71 tff(2725,plain,
% 1.53/1.71 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1640) | (~c0_1(a1640)) | (~c1_1(a1640)) | c1_1(a1636) | c0_1(a1636) | c3_1(a1636))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2726,plain,
% 1.53/1.71 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c2_1(a1640) | c0_1(a1636) | c1_1(a1636) | (~ndr1_0) | c3_1(a1636) | (~c0_1(a1640)) | (~c1_1(a1640))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2725, 2724])).
% 1.53/1.71 tff(2727,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2726, 119, 2626, 2719, 2718, 1553, 1552, 915, 2603, 2720])).
% 1.53/1.71 tff(2728,plain,(hskp11 | c0_1(a1636) | c1_1(a1636) | c2_1(a1636) | (~hskp2)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(2729,plain,
% 1.53/1.71 (hskp11),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2728, 2696, 2695, 2694, 2697])).
% 1.53/1.71 tff(2730,plain,
% 1.53/1.71 (~c3_1(a1650)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[667, 2729])).
% 1.53/1.71 tff(2731,plain,
% 1.53/1.71 (~c0_1(a1650)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[673, 2729])).
% 1.53/1.71 tff(2732,plain,
% 1.53/1.71 (c1_1(a1650)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[705, 2729])).
% 1.53/1.71 tff(2733,plain,
% 1.53/1.71 (c3_1(a1636)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1865, 119, 660, 2732, 2731, 2730, 2695, 2694, 10])).
% 1.53/1.71 tff(2734,plain,
% 1.53/1.71 ((~c3_1(a1636)) | (~c2_1(a1650))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1585, 119, 2732, 2731, 2696, 2695, 691])).
% 1.53/1.71 tff(2735,plain,
% 1.53/1.71 (~c2_1(a1650)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2734, 2733])).
% 1.53/1.71 tff(2736,plain,
% 1.53/1.71 (~c0_1(a1637)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1124, 2697])).
% 1.53/1.71 tff(2737,plain,
% 1.53/1.71 (c1_1(a1637)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1140, 2697])).
% 1.53/1.71 tff(2738,plain,
% 1.53/1.71 ((~c3_1(a1636)) | (~c2_1(a1637))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1872, 119, 2737, 2736, 2696, 2695, 691])).
% 1.53/1.71 tff(2739,plain,
% 1.53/1.71 (~c2_1(a1637)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2738, 2733])).
% 1.53/1.71 tff(2740,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1880, 119, 2737, 2731, 2730, 2736, 2696, 2695, 2694, 1261, 2739, 2735])).
% 1.53/1.71 tff(2741,plain,(c3_1(a1638) | c0_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(2742,plain,
% 1.53/1.71 (c3_1(a1638)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2741, 22])).
% 1.53/1.71 tff(2743,plain,
% 1.53/1.71 (hskp3),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2583, 500, 499, 483, 491, 21])).
% 1.53/1.71 tff(2744,plain,
% 1.53/1.71 (~c2_1(a1638)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1992, 2743])).
% 1.53/1.71 tff(2745,plain,
% 1.53/1.71 (c1_1(a1638) | (~c0_1(a1646))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1812, 296, 283, 284, 349, 1708, 1217, 1418])).
% 1.53/1.71 tff(2746,plain,
% 1.53/1.71 (~c0_1(a1646)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2745, 1233])).
% 1.53/1.71 tff(2747,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2045, 296, 283, 284, 1708, 22, 691, 1233, 2746])).
% 1.53/1.71 tff(2748,plain,(c1_1(a1638) | (~ndr1_0) | (~c1_1(a1646)) | (~c2_1(a1646)) | (~c3_1(a1638)) | c0_1(a1638) | (~c3_1(a1646)) | c2_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(2749,plain,
% 1.53/1.71 (c1_1(a1638) | (~c1_1(a1646)) | (~c2_1(a1646)) | (~c3_1(a1638)) | c0_1(a1638) | (~c3_1(a1646)) | c2_1(a1638)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2748, 119])).
% 1.53/1.71 tff(2750,plain,
% 1.53/1.71 (c1_1(a1638)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2749, 2744, 2742, 651, 650, 22, 649])).
% 1.53/1.71 tff(2751,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1575, 119, 45, 2742, 22, 2744, 55, 2750])).
% 1.53/1.71 tff(2752,plain,(hskp2 | hskp11 | c0_1(a1638) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(2753,plain,
% 1.53/1.71 (hskp2),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2752, 45, 22, 21])).
% 1.53/1.71 tff(2754,plain,
% 1.53/1.71 (~c0_1(a1637)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1124, 2753])).
% 1.53/1.71 tff(2755,plain,
% 1.53/1.71 (c1_1(a1637)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1140, 2753])).
% 1.53/1.71 tff(2756,plain,
% 1.53/1.71 (c3_1(a1637)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1132, 2753])).
% 1.53/1.71 tff(2757,plain,
% 1.53/1.71 (~hskp15),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2261, 2756, 45, 2755, 2754])).
% 1.53/1.71 tff(2758,plain,
% 1.53/1.71 (~hskp19),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2269, 2756, 477, 2755, 2754, 483])).
% 1.53/1.71 tff(2759,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1450, 2758, 2757, 21])).
% 1.53/1.71 tff(2760,plain,(hskp11 | hskp1 | c0_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(2761,plain,
% 1.53/1.71 (hskp11),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2760, 21, 22])).
% 1.53/1.71 tff(2762,plain,
% 1.53/1.71 (~c3_1(a1650)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[667, 2761])).
% 1.53/1.71 tff(2763,plain,
% 1.53/1.71 (c1_1(a1650)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[705, 2761])).
% 1.53/1.71 tff(2764,plain,
% 1.53/1.71 (hskp3),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2692, 33, 21])).
% 1.53/1.71 tff(2765,plain,
% 1.53/1.71 (~c2_1(a1638)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1992, 2764])).
% 1.53/1.71 tff(2766,assumption,(hskp22), introduced(assumption)).
% 1.53/1.71 tff(2767,plain,
% 1.53/1.71 (~c3_1(a1697)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2307, 2766])).
% 1.53/1.71 tff(2768,plain,
% 1.53/1.71 (~c2_1(a1697)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2313, 2766])).
% 1.53/1.71 tff(2769,plain,
% 1.53/1.71 (~c0_1(a1697)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2319, 2766])).
% 1.53/1.71 tff(2770,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1737) | c0_1(a1697) | c2_1(a1697) | c3_1(a1697) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | (~c3_1(a1737)) | (~c2_1(a1737)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1737) | c0_1(a1697) | c2_1(a1697) | c3_1(a1697) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | (~c3_1(a1737)) | (~c2_1(a1737)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2771,plain,
% 1.53/1.71 (((~ndr1_0) | c0_1(a1737) | (~c2_1(a1737)) | (~c3_1(a1737)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638)) | c2_1(a1697) | c0_1(a1697) | c3_1(a1697)) <=> (c0_1(a1737) | c0_1(a1697) | c2_1(a1697) | c3_1(a1697) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | (~c3_1(a1737)) | (~c2_1(a1737)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2772,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1737) | (~c2_1(a1737)) | (~c3_1(a1737)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638)) | c2_1(a1697) | c0_1(a1697) | c3_1(a1697))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1737) | c0_1(a1697) | c2_1(a1697) | c3_1(a1697) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | (~c3_1(a1737)) | (~c2_1(a1737))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2771])).
% 1.53/1.71 tff(2773,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1737) | (~c2_1(a1737)) | (~c3_1(a1737)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638)) | c2_1(a1697) | c0_1(a1697) | c3_1(a1697))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1737) | c0_1(a1697) | c2_1(a1697) | c3_1(a1697) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | (~c3_1(a1737)) | (~c2_1(a1737)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2772, 2770])).
% 1.53/1.71 tff(2774,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1737) | (~c2_1(a1737)) | (~c3_1(a1737)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638)) | c2_1(a1697) | c0_1(a1697) | c3_1(a1697))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2775,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1737) | c0_1(a1697) | c2_1(a1697) | c3_1(a1697) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | (~c3_1(a1737)) | (~c2_1(a1737))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2774, 2773])).
% 1.53/1.71 tff(2776,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2775, 119, 320, 319, 2742, 317, 2769, 2768, 2767, 22, 1217, 1621])).
% 1.53/1.71 tff(2777,plain,((~hskp22) | (~c2_1(a1737)) | (~c3_1(a1737)) | c0_1(a1737) | c0_1(a1638) | c2_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(2778,plain,
% 1.53/1.71 (~hskp22),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2777, 224, 216, 208, 22, 2765])).
% 1.53/1.71 tff(2779,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp22 | c3_1(a1650) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c1_1(a1640)) | (~c2_1(a1650)) | (~c1_1(a1650)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp22 | c3_1(a1650) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c1_1(a1640)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2780,plain,
% 1.53/1.71 ((hskp22 | (~ndr1_0) | (~c3_1(a1640)) | (~c0_1(a1640)) | (~c1_1(a1640)) | c3_1(a1650) | (~c1_1(a1650)) | (~c2_1(a1650))) <=> (hskp22 | c3_1(a1650) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c1_1(a1640)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2781,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | (~c3_1(a1640)) | (~c0_1(a1640)) | (~c1_1(a1640)) | c3_1(a1650) | (~c1_1(a1650)) | (~c2_1(a1650)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp22 | c3_1(a1650) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c1_1(a1640)) | (~c2_1(a1650)) | (~c1_1(a1650))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2780])).
% 1.53/1.71 tff(2782,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | (~c3_1(a1640)) | (~c0_1(a1640)) | (~c1_1(a1640)) | c3_1(a1650) | (~c1_1(a1650)) | (~c2_1(a1650)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp22 | c3_1(a1650) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c1_1(a1640)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2781, 2779])).
% 1.53/1.71 tff(2783,plain,
% 1.53/1.71 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | (~c3_1(a1640)) | (~c0_1(a1640)) | (~c1_1(a1640)) | c3_1(a1650) | (~c1_1(a1650)) | (~c2_1(a1650)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2784,plain,
% 1.53/1.71 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp22 | c3_1(a1650) | (~ndr1_0) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c1_1(a1640)) | (~c2_1(a1650)) | (~c1_1(a1650))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2783, 2782])).
% 1.53/1.71 tff(2785,plain,
% 1.53/1.71 ((~c1_1(a1640)) | (~c2_1(a1650))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2784, 119, 2778, 2763, 851, 867, 2762, 44])).
% 1.53/1.71 tff(2786,plain,
% 1.53/1.71 (~c1_1(a1640)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2785, 34])).
% 1.53/1.71 tff(2787,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp22 | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp22 | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2788,plain,
% 1.53/1.71 ((hskp22 | (~ndr1_0) | (~c3_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | c3_1(a1650) | (~c1_1(a1650)) | (~c2_1(a1650))) <=> (hskp22 | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2789,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | (~c3_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | c3_1(a1650) | (~c1_1(a1650)) | (~c2_1(a1650)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp22 | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2788])).
% 1.53/1.71 tff(2790,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | (~c3_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | c3_1(a1650) | (~c1_1(a1650)) | (~c2_1(a1650)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp22 | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2789, 2787])).
% 1.53/1.71 tff(2791,plain,
% 1.53/1.71 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | (~c3_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | c3_1(a1650) | (~c1_1(a1650)) | (~c2_1(a1650)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2792,plain,
% 1.53/1.71 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp22 | c3_1(a1650) | (~ndr1_0) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2791, 2790])).
% 1.53/1.71 tff(2793,plain,
% 1.53/1.71 ((~c2_1(a1650)) | (~c0_1(a1646))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2792, 119, 2778, 261, 269, 2763, 2762, 44])).
% 1.53/1.71 tff(2794,plain,
% 1.53/1.71 (~c0_1(a1646)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2793, 34])).
% 1.53/1.71 tff(2795,plain,
% 1.53/1.71 (c1_1(a1638)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2749, 239, 2742, 2765, 261, 22, 269])).
% 1.53/1.71 tff(2796,plain,
% 1.53/1.71 (~c0_1(a1650)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[673, 2761])).
% 1.53/1.71 tff(2797,plain,
% 1.53/1.71 (((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | hskp0 | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664)))) <=> ((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | hskp0 | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2798,plain,
% 1.53/1.71 ((hskp16 | hskp0 | (~ndr1_0) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664))) <=> (hskp16 | hskp0 | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2799,plain,
% 1.53/1.71 (((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | hskp0 | (~ndr1_0) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)))) <=> ((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | hskp0 | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2798])).
% 1.53/1.71 tff(2800,plain,
% 1.53/1.71 (((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | hskp0 | (~ndr1_0) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)))) <=> ((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | hskp0 | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2799, 2797])).
% 1.53/1.71 tff(2801,plain,
% 1.53/1.71 ((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | hskp0 | (~ndr1_0) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2802,plain,
% 1.53/1.71 ((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | hskp0 | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c0_1(a1664))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2801, 2800])).
% 1.53/1.71 tff(2803,plain,
% 1.53/1.71 (hskp16),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2802, 296, 33, 1400, 1392, 1391, 2176])).
% 1.53/1.71 tff(2804,plain,
% 1.53/1.71 (~c1_1(a1667)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[986, 2803])).
% 1.53/1.71 tff(2805,plain,
% 1.53/1.71 (c0_1(a1667)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1002, 2803])).
% 1.53/1.71 tff(2806,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c1_1(a1667) | c3_1(a1650) | c0_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | (~c1_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1667)) | (~c0_1(a1667)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c1_1(a1667) | c3_1(a1650) | c0_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | (~c1_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1667)) | (~c0_1(a1667)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2807,plain,
% 1.53/1.71 (((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1638) | (~c1_1(a1638)) | (~c3_1(a1638))) <=> (c1_1(a1667) | c3_1(a1650) | c0_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | (~c1_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1667)) | (~c0_1(a1667)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2808,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1638) | (~c1_1(a1638)) | (~c3_1(a1638)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c1_1(a1667) | c3_1(a1650) | c0_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | (~c1_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1667)) | (~c0_1(a1667))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2807])).
% 1.53/1.71 tff(2809,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1638) | (~c1_1(a1638)) | (~c3_1(a1638)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c1_1(a1667) | c3_1(a1650) | c0_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | (~c1_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1667)) | (~c0_1(a1667)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2808, 2806])).
% 1.53/1.71 tff(2810,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c0_1(a1638) | (~c1_1(a1638)) | (~c3_1(a1638)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2811,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c1_1(a1667) | c3_1(a1650) | c0_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | (~c1_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650)) | (~c3_1(a1667)) | (~c0_1(a1667))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2810, 2809])).
% 1.53/1.71 tff(2812,plain,
% 1.53/1.71 (~c3_1(a1667)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2811, 296, 2805, 852, 1708, 2804, 842, 22, 20, 1318, 34])).
% 1.53/1.71 tff(2813,plain,
% 1.53/1.71 (c2_1(a1667)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[994, 2803])).
% 1.53/1.71 tff(2814,plain,
% 1.53/1.71 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c3_1(a1667) | (~c0_1(a1667)) | (~c2_1(a1667)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp8 | hskp1 | (~ndr1_0) | c3_1(a1667) | (~c0_1(a1667)) | (~c2_1(a1667)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2815,plain,
% 1.53/1.71 ((hskp8 | hskp1 | (~ndr1_0) | c3_1(a1667) | (~c2_1(a1667)) | (~c0_1(a1667))) <=> (hskp8 | hskp1 | (~ndr1_0) | c3_1(a1667) | (~c0_1(a1667)) | (~c2_1(a1667)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2816,plain,
% 1.53/1.72 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c3_1(a1667) | (~c2_1(a1667)) | (~c0_1(a1667)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c3_1(a1667) | (~c0_1(a1667)) | (~c2_1(a1667))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2815])).
% 1.53/1.72 tff(2817,plain,
% 1.53/1.72 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c3_1(a1667) | (~c2_1(a1667)) | (~c0_1(a1667)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp8 | hskp1 | (~ndr1_0) | c3_1(a1667) | (~c0_1(a1667)) | (~c2_1(a1667)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2816, 2814])).
% 1.53/1.72 tff(2818,plain,
% 1.53/1.72 ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c3_1(a1667) | (~c2_1(a1667)) | (~c0_1(a1667)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2819,plain,
% 1.53/1.72 ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp8 | hskp1 | (~ndr1_0) | c3_1(a1667) | (~c0_1(a1667)) | (~c2_1(a1667))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2818, 2817])).
% 1.53/1.72 tff(2820,plain,
% 1.53/1.72 (hskp8),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2819, 296, 21, 2805, 2813, 32, 2812])).
% 1.53/1.72 tff(2821,plain,
% 1.53/1.72 (~c3_1(a1643)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[244, 2820])).
% 1.53/1.72 tff(2822,plain,
% 1.53/1.72 (~c2_1(a1643)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[182, 2820])).
% 1.53/1.72 tff(2823,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1650) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1650)) | (~c1_1(a1650)) | c3_1(a1667) | (~c0_1(a1667)) | (~c2_1(a1667)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1650) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1650)) | (~c1_1(a1650)) | c3_1(a1667) | (~c0_1(a1667)) | (~c2_1(a1667)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2824,plain,
% 1.53/1.72 (((~ndr1_0) | c3_1(a1667) | (~c2_1(a1667)) | (~c0_1(a1667)) | c0_1(a1650) | (~c1_1(a1650)) | (~c2_1(a1650)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643)) <=> (c0_1(a1650) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1650)) | (~c1_1(a1650)) | c3_1(a1667) | (~c0_1(a1667)) | (~c2_1(a1667)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2825,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1667) | (~c2_1(a1667)) | (~c0_1(a1667)) | c0_1(a1650) | (~c1_1(a1650)) | (~c2_1(a1650)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1650) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1650)) | (~c1_1(a1650)) | c3_1(a1667) | (~c0_1(a1667)) | (~c2_1(a1667))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2824])).
% 1.53/1.72 tff(2826,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1667) | (~c2_1(a1667)) | (~c0_1(a1667)) | c0_1(a1650) | (~c1_1(a1650)) | (~c2_1(a1650)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1650) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1650)) | (~c1_1(a1650)) | c3_1(a1667) | (~c0_1(a1667)) | (~c2_1(a1667)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2825, 2823])).
% 1.53/1.72 tff(2827,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1667) | (~c2_1(a1667)) | (~c0_1(a1667)) | c0_1(a1650) | (~c1_1(a1650)) | (~c2_1(a1650)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2828,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1650) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1650)) | (~c1_1(a1650)) | c3_1(a1667) | (~c0_1(a1667)) | (~c2_1(a1667))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2827, 2826])).
% 1.53/1.72 tff(2829,plain,
% 1.53/1.72 (c0_1(a1643)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2828, 296, 2805, 2813, 852, 843, 2822, 2821, 295, 34, 2812])).
% 1.53/1.72 tff(2830,plain,
% 1.53/1.72 (c1_1(a1643)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[252, 2820])).
% 1.53/1.72 tff(2831,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1406, 296, 1400, 852, 2830, 1392, 1391, 843, 842, 2821, 826, 2829])).
% 1.53/1.72 tff(2832,plain,((~hskp15) | (~ndr1_0) | (~c1_1(a1650)) | c0_1(a1650) | c3_1(a1650) | (~c2_1(a1650)) | hskp1 | (~c3_1(a1638)) | c0_1(a1638) | (~c1_1(a1638)) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2833,plain,
% 1.53/1.72 ((~hskp15) | (~c1_1(a1650)) | c0_1(a1650) | c3_1(a1650) | (~c2_1(a1650)) | hskp1 | (~c3_1(a1638)) | c0_1(a1638) | (~c1_1(a1638)) | hskp0),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2832, 119])).
% 1.53/1.72 tff(2834,plain,
% 1.53/1.72 (~hskp15),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2833, 34, 2742, 2796, 2762, 2763, 21, 33, 22, 2795])).
% 1.53/1.72 tff(2835,plain,
% 1.53/1.72 (hskp19),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1450, 2834, 21])).
% 1.53/1.72 tff(2836,plain,
% 1.53/1.72 (~c3_1(a1682)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[568, 2835])).
% 1.53/1.72 tff(2837,plain,
% 1.53/1.72 (c2_1(a1682)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[584, 2835])).
% 1.53/1.72 tff(2838,plain,
% 1.53/1.72 (c1_1(a1682)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[576, 2835])).
% 1.53/1.72 tff(2839,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1682) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1682)) | (~c1_1(a1682)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1682) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1682)) | (~c1_1(a1682)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2840,plain,
% 1.53/1.72 (((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646))) <=> (c3_1(a1682) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1682)) | (~c1_1(a1682)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2841,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1682) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1682)) | (~c1_1(a1682)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2840])).
% 1.53/1.72 tff(2842,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1682) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1682)) | (~c1_1(a1682)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2841, 2839])).
% 1.53/1.72 tff(2843,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1640) | (~c3_1(a1640)) | (~c0_1(a1640)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2844,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1682) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)) | (~c3_1(a1640)) | (~c2_1(a1682)) | (~c1_1(a1682)) | c0_1(a1646) | (~c1_1(a1646)) | (~c3_1(a1646))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2843, 2842])).
% 1.53/1.72 tff(2845,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2844, 119, 261, 269, 2838, 2837, 851, 867, 2836, 20, 2794, 2786])).
% 1.53/1.72 tff(2846,plain,((~c2_1(a1650)) | hskp1 | hskp0 | c0_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2847,plain,
% 1.53/1.72 (~c2_1(a1650)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2846, 33, 21, 22])).
% 1.53/1.72 tff(2848,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1737) | c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | c2_1(a1650) | (~c3_1(a1737)) | (~c2_1(a1737)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1737) | c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | c2_1(a1650) | (~c3_1(a1737)) | (~c2_1(a1737)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2849,plain,
% 1.53/1.72 (((~ndr1_0) | c0_1(a1737) | (~c2_1(a1737)) | (~c3_1(a1737)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650)) <=> (c0_1(a1737) | c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | c2_1(a1650) | (~c3_1(a1737)) | (~c2_1(a1737)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2850,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1737) | (~c2_1(a1737)) | (~c3_1(a1737)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1737) | c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | c2_1(a1650) | (~c3_1(a1737)) | (~c2_1(a1737))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2849])).
% 1.53/1.72 tff(2851,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1737) | (~c2_1(a1737)) | (~c3_1(a1737)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1737) | c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | c2_1(a1650) | (~c3_1(a1737)) | (~c2_1(a1737)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2850, 2848])).
% 1.53/1.72 tff(2852,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1737) | (~c2_1(a1737)) | (~c3_1(a1737)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2853,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1737) | c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | c2_1(a1650) | (~c3_1(a1737)) | (~c2_1(a1737))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2852, 2851])).
% 1.53/1.72 tff(2854,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2853, 119, 224, 216, 2742, 208, 2796, 2762, 22, 2765, 1621, 2847])).
% 1.53/1.72 tff(2855,plain,(hskp0 | c0_1(a1638) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2856,plain,
% 1.53/1.72 (hskp0),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2855, 21, 22])).
% 1.53/1.72 tff(2857,plain,
% 1.53/1.72 (~c1_1(a1634)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[482, 2856])).
% 1.53/1.72 tff(2858,assumption,(hskp16), introduced(assumption)).
% 1.53/1.72 tff(2859,plain,
% 1.53/1.72 (~c1_1(a1667)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[986, 2858])).
% 1.53/1.72 tff(2860,plain,
% 1.53/1.72 (c2_1(a1667)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[994, 2858])).
% 1.53/1.72 tff(2861,plain,
% 1.53/1.72 (c0_1(a1667)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1002, 2858])).
% 1.53/1.72 tff(2862,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2193, 119, 500, 2861, 2860, 2678, 2665, 2859, 2664, 639])).
% 1.53/1.72 tff(2863,plain,((~hskp16) | hskp2 | (~c0_1(a1640)) | (~c3_1(a1640)) | c2_1(a1640)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2864,plain,
% 1.53/1.72 (~hskp16),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2863, 851, 500, 867, 841])).
% 1.53/1.72 tff(2865,plain,
% 1.53/1.72 (((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | hskp0 | c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)))) <=> ((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | hskp0 | c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2866,plain,
% 1.53/1.72 ((hskp16 | hskp0 | (~ndr1_0) | c2_1(a1640) | c1_1(a1640) | (~c0_1(a1640))) <=> (hskp16 | hskp0 | c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2867,plain,
% 1.53/1.72 (((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | hskp0 | (~ndr1_0) | c2_1(a1640) | c1_1(a1640) | (~c0_1(a1640)))) <=> ((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | hskp0 | c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2866])).
% 1.53/1.72 tff(2868,plain,
% 1.53/1.72 (((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | hskp0 | (~ndr1_0) | c2_1(a1640) | c1_1(a1640) | (~c0_1(a1640)))) <=> ((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | hskp0 | c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2867, 2865])).
% 1.53/1.72 tff(2869,plain,
% 1.53/1.72 ((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | hskp0 | (~ndr1_0) | c2_1(a1640) | c1_1(a1640) | (~c0_1(a1640)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2870,plain,
% 1.53/1.72 ((~![U: $i] : (hskp16 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | hskp0 | c2_1(a1640) | (~ndr1_0) | c1_1(a1640) | (~c0_1(a1640))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2869, 2868])).
% 1.53/1.72 tff(2871,plain,
% 1.53/1.72 (hskp16 | c1_1(a1640)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2870, 119, 33, 851, 841, 2176])).
% 1.53/1.72 tff(2872,plain,
% 1.53/1.72 (c1_1(a1640)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2871, 2864])).
% 1.53/1.72 tff(2873,plain,
% 1.53/1.72 (hskp0),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2692, 661, 21])).
% 1.53/1.72 tff(2874,plain,
% 1.53/1.72 (c1_1(a1634)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2364, 661, 500, 21, 842, 852, 843])).
% 1.53/1.72 tff(2875,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[482, 2874, 2873])).
% 1.53/1.72 tff(2876,plain,(hskp3 | hskp2 | hskp1 | c3_1(a1650) | (~c1_1(a1650)) | c0_1(a1650)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2877,plain,
% 1.53/1.72 (hskp3),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2876, 500, 21, 2762, 2763, 2796])).
% 1.53/1.72 tff(2878,plain,
% 1.53/1.72 (~c2_1(a1638)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1992, 2877])).
% 1.53/1.72 tff(2879,plain,
% 1.53/1.72 (~hskp22),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2777, 224, 216, 208, 22, 2878])).
% 1.53/1.72 tff(2880,plain,
% 1.53/1.72 (hskp22 | (~c1_1(a1640)) | (~c2_1(a1650))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2784, 119, 2763, 851, 867, 2762, 44])).
% 1.53/1.72 tff(2881,plain,
% 1.53/1.72 (~c2_1(a1650)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2880, 2879, 2872])).
% 1.53/1.72 tff(2882,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2853, 119, 224, 216, 2742, 208, 2796, 2762, 22, 2878, 1621, 2881])).
% 1.53/1.72 tff(2883,plain,(hskp0 | c0_1(a1638) | hskp2 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2884,plain,
% 1.53/1.72 (hskp0),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2883, 500, 22, 21])).
% 1.53/1.72 tff(2885,plain,
% 1.53/1.72 (~c1_1(a1634)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[482, 2884])).
% 1.53/1.72 tff(2886,plain,
% 1.53/1.72 (c3_1(a1634)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[490, 2884])).
% 1.53/1.72 tff(2887,plain,
% 1.53/1.72 (c0_1(a1634)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[498, 2884])).
% 1.53/1.72 tff(2888,plain,
% 1.53/1.72 (c2_1(a1634)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1011, 56, 2887, 2886, 2885, 500])).
% 1.53/1.72 tff(2889,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1682) | c0_1(a1638) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1638)) | (~c1_1(a1638)) | (~c2_1(a1682)) | (~c1_1(a1682)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1682) | c0_1(a1638) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1638)) | (~c1_1(a1638)) | (~c2_1(a1682)) | (~c1_1(a1682)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2890,plain,
% 1.53/1.72 (((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1638) | (~c1_1(a1638)) | (~c3_1(a1638))) <=> (c3_1(a1682) | c0_1(a1638) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1638)) | (~c1_1(a1638)) | (~c2_1(a1682)) | (~c1_1(a1682)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2891,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1638) | (~c1_1(a1638)) | (~c3_1(a1638)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1682) | c0_1(a1638) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1638)) | (~c1_1(a1638)) | (~c2_1(a1682)) | (~c1_1(a1682))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2890])).
% 1.53/1.72 tff(2892,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1638) | (~c1_1(a1638)) | (~c3_1(a1638)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1682) | c0_1(a1638) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1638)) | (~c1_1(a1638)) | (~c2_1(a1682)) | (~c1_1(a1682)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2891, 2889])).
% 1.53/1.72 tff(2893,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1638) | (~c1_1(a1638)) | (~c3_1(a1638)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2894,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1682) | c0_1(a1638) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1638)) | (~c1_1(a1638)) | (~c2_1(a1682)) | (~c1_1(a1682))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2893, 2892])).
% 1.53/1.72 tff(2895,plain,
% 1.53/1.72 (~c1_1(a1638)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2894, 296, 577, 585, 1708, 504, 502, 569, 22, 503, 20])).
% 1.53/1.72 tff(2896,plain,
% 1.53/1.72 (^[U: $i] : refl((hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 1.53/1.72 inference(bind,[status(th)],[])).
% 1.53/1.72 tff(2897,plain,
% 1.53/1.72 (![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.53/1.72 inference(quant_intro,[status(thm)],[2896])).
% 1.53/1.72 tff(2898,plain,
% 1.53/1.72 (![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2899,plain,
% 1.53/1.72 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp27) | hskp1) <=> ((hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite(((hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp27) | hskp1) <=> (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 1.53/1.72 inference(bind,[status(th)],[])).
% 1.53/1.72 tff(2900,plain,
% 1.53/1.72 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp27) | hskp1) <=> ![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.53/1.72 inference(quant_intro,[status(thm)],[2899])).
% 1.53/1.72 tff(2901,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp27) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 1.53/1.72 tff(2902,plain,
% 1.53/1.72 (![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2901, 2900])).
% 1.53/1.72 tff(2903,plain,
% 1.53/1.72 (![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2902, 2898])).
% 1.53/1.72 tff(2904,plain,(
% 1.53/1.72 ![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.53/1.72 inference(skolemize,[status(sab)],[2903])).
% 1.53/1.72 tff(2905,plain,
% 1.53/1.72 (![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2904, 2897])).
% 1.53/1.72 tff(2906,plain,
% 1.53/1.72 (((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638))) <=> ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp1 | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2907,plain,
% 1.53/1.72 ((hskp27 | hskp1 | (~ndr1_0) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638)) <=> (hskp27 | hskp1 | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2908,plain,
% 1.53/1.72 (((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | (~ndr1_0) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))) <=> ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638)))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2907])).
% 1.53/1.72 tff(2909,plain,
% 1.53/1.72 (((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | (~ndr1_0) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))) <=> ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp1 | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2908, 2906])).
% 1.53/1.72 tff(2910,plain,
% 1.53/1.72 ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | (~ndr1_0) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2911,plain,
% 1.53/1.72 ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp1 | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2910, 2909])).
% 1.53/1.72 tff(2912,plain,
% 1.53/1.72 (hskp27 | c0_1(a1638) | c1_1(a1638)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2911, 296, 21, 1217, 2905])).
% 1.53/1.72 tff(2913,plain,
% 1.53/1.72 (hskp27),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2912, 2895, 22])).
% 1.53/1.72 tff(2914,plain,
% 1.53/1.72 (((~hskp27) | c2_1(a1635)) <=> ((~hskp27) | c2_1(a1635))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2915,axiom,((~hskp27) | c2_1(a1635)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 1.53/1.72 tff(2916,plain,
% 1.53/1.72 ((~hskp27) | c2_1(a1635)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2915, 2914])).
% 1.53/1.72 tff(2917,plain,
% 1.53/1.72 ((~hskp27) | c2_1(a1635)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2916, 2914])).
% 1.53/1.72 tff(2918,plain,
% 1.53/1.72 ((~hskp27) | c2_1(a1635)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2917, 2914])).
% 1.53/1.72 tff(2919,plain,
% 1.53/1.72 ((~hskp27) | c2_1(a1635)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2918, 2914])).
% 1.53/1.72 tff(2920,plain,
% 1.53/1.72 ((~hskp27) | c2_1(a1635)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2919, 2914])).
% 1.53/1.72 tff(2921,plain,
% 1.53/1.72 (c2_1(a1635)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2920, 2913])).
% 1.53/1.72 tff(2922,plain,
% 1.53/1.72 (((~hskp27) | c1_1(a1635)) <=> ((~hskp27) | c1_1(a1635))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2923,axiom,((~hskp27) | c1_1(a1635)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 1.53/1.72 tff(2924,plain,
% 1.53/1.72 ((~hskp27) | c1_1(a1635)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2923, 2922])).
% 1.53/1.72 tff(2925,plain,
% 1.53/1.72 ((~hskp27) | c1_1(a1635)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2924, 2922])).
% 1.53/1.72 tff(2926,plain,
% 1.53/1.72 ((~hskp27) | c1_1(a1635)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2925, 2922])).
% 1.53/1.72 tff(2927,plain,
% 1.53/1.72 ((~hskp27) | c1_1(a1635)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2926, 2922])).
% 1.53/1.72 tff(2928,plain,
% 1.53/1.72 ((~hskp27) | c1_1(a1635)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2927, 2922])).
% 1.53/1.72 tff(2929,plain,
% 1.53/1.72 (c1_1(a1635)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2928, 2913])).
% 1.53/1.72 tff(2930,plain,
% 1.53/1.72 (((~hskp27) | c0_1(a1635)) <=> ((~hskp27) | c0_1(a1635))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2931,axiom,((~hskp27) | c0_1(a1635)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 1.53/1.72 tff(2932,plain,
% 1.53/1.72 ((~hskp27) | c0_1(a1635)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2931, 2930])).
% 1.53/1.72 tff(2933,plain,
% 1.53/1.72 ((~hskp27) | c0_1(a1635)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2932, 2930])).
% 1.53/1.72 tff(2934,plain,
% 1.53/1.72 ((~hskp27) | c0_1(a1635)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2933, 2930])).
% 1.53/1.72 tff(2935,plain,
% 1.53/1.72 ((~hskp27) | c0_1(a1635)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2934, 2930])).
% 1.53/1.72 tff(2936,plain,
% 1.53/1.72 ((~hskp27) | c0_1(a1635)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2935, 2930])).
% 1.53/1.72 tff(2937,plain,
% 1.53/1.72 (c0_1(a1635)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2936, 2913])).
% 1.53/1.72 tff(2938,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a1682) | c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c0_1(a1635)) | (~c2_1(a1635)) | (~c1_1(a1635)) | (~c2_1(a1682)) | (~c1_1(a1682)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a1682) | c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c0_1(a1635)) | (~c2_1(a1635)) | (~c1_1(a1635)) | (~c2_1(a1682)) | (~c1_1(a1682)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2939,plain,
% 1.53/1.72 (((~ndr1_0) | (~c2_1(a1635)) | (~c0_1(a1635)) | (~c1_1(a1635)) | c3_1(a1682) | (~c1_1(a1682)) | (~c2_1(a1682)) | c1_1(a1638) | c0_1(a1638) | (~c3_1(a1638))) <=> (c3_1(a1682) | c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c0_1(a1635)) | (~c2_1(a1635)) | (~c1_1(a1635)) | (~c2_1(a1682)) | (~c1_1(a1682)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2940,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1635)) | (~c0_1(a1635)) | (~c1_1(a1635)) | c3_1(a1682) | (~c1_1(a1682)) | (~c2_1(a1682)) | c1_1(a1638) | c0_1(a1638) | (~c3_1(a1638)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a1682) | c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c0_1(a1635)) | (~c2_1(a1635)) | (~c1_1(a1635)) | (~c2_1(a1682)) | (~c1_1(a1682))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2939])).
% 1.53/1.72 tff(2941,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1635)) | (~c0_1(a1635)) | (~c1_1(a1635)) | c3_1(a1682) | (~c1_1(a1682)) | (~c2_1(a1682)) | c1_1(a1638) | c0_1(a1638) | (~c3_1(a1638)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a1682) | c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c0_1(a1635)) | (~c2_1(a1635)) | (~c1_1(a1635)) | (~c2_1(a1682)) | (~c1_1(a1682)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2940, 2938])).
% 1.53/1.72 tff(2942,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1635)) | (~c0_1(a1635)) | (~c1_1(a1635)) | c3_1(a1682) | (~c1_1(a1682)) | (~c2_1(a1682)) | c1_1(a1638) | c0_1(a1638) | (~c3_1(a1638)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2943,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a1682) | c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c0_1(a1635)) | (~c2_1(a1635)) | (~c1_1(a1635)) | (~c2_1(a1682)) | (~c1_1(a1682))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2942, 2941])).
% 1.53/1.72 tff(2944,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2943, 296, 2937, 2929, 2921, 577, 585, 1708, 569, 22, 1442, 2895])).
% 1.53/1.72 tff(2945,plain,((~hskp19) | (~ndr1_0) | (~c3_1(a1638)) | c0_1(a1638) | hskp1 | c2_1(a1638) | (~c0_1(a1634)) | (~c3_1(a1634)) | c1_1(a1634)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2946,plain,
% 1.53/1.72 ((~hskp19) | (~c3_1(a1638)) | c0_1(a1638) | hskp1 | c2_1(a1638) | (~c0_1(a1634)) | (~c3_1(a1634)) | c1_1(a1634)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2945, 119])).
% 1.53/1.72 tff(2947,plain,
% 1.53/1.72 (~hskp19),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2946, 2886, 2742, 22, 21, 2878, 2887, 2885])).
% 1.53/1.72 tff(2948,plain,
% 1.53/1.72 (hskp28 | (~c2_1(a1634))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[627, 119, 2947, 2886, 2885, 621])).
% 1.53/1.72 tff(2949,plain,
% 1.53/1.72 (hskp28),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2948, 2888])).
% 1.53/1.72 tff(2950,plain,
% 1.53/1.72 (c3_1(a1646)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[268, 2949])).
% 1.53/1.72 tff(2951,plain,
% 1.53/1.72 (hskp10 | c2_1(a1650)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[680, 119, 21, 2796, 2762, 136])).
% 1.53/1.73 tff(2952,plain,
% 1.53/1.73 (c2_1(a1650)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2951, 56])).
% 1.53/1.73 tff(2953,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1650) | c0_1(a1638) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1638)) | (~c1_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1650) | c0_1(a1638) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1638)) | (~c1_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2954,plain,
% 1.53/1.73 (((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1638) | (~c1_1(a1638)) | (~c3_1(a1638))) <=> (c3_1(a1650) | c0_1(a1638) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1638)) | (~c1_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2955,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1638) | (~c1_1(a1638)) | (~c3_1(a1638)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1650) | c0_1(a1638) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1638)) | (~c1_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2954])).
% 1.53/1.73 tff(2956,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1638) | (~c1_1(a1638)) | (~c3_1(a1638)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1650) | c0_1(a1638) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1638)) | (~c1_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2955, 2953])).
% 1.53/1.73 tff(2957,plain,
% 1.53/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1638) | (~c1_1(a1638)) | (~c3_1(a1638)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(2958,plain,
% 1.53/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1650) | c0_1(a1638) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1638)) | (~c1_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2957, 2956])).
% 1.53/1.73 tff(2959,plain,
% 1.53/1.73 ((~c3_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1638)) | (~c1_1(a1638)) | (~c2_1(a1650))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2958, 296, 852, 842, 22, 503, 20])).
% 1.53/1.73 tff(2960,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2959, 2267, 2266, 1708, 1318, 34])).
% 1.53/1.73 tff(2961,plain,((~hskp0) | (~c3_1(a1638)) | (~c1_1(a1638)) | (~c2_1(a1650)) | (~ndr1_0) | (~c1_1(a1650)) | c3_1(a1650) | c0_1(a1638) | c1_1(a1634)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(2962,plain,
% 1.53/1.73 ((~hskp0) | (~c3_1(a1638)) | (~c1_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650)) | c3_1(a1650) | c0_1(a1638) | c1_1(a1634)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2961, 119])).
% 1.53/1.73 tff(2963,plain,
% 1.53/1.73 (~c1_1(a1638)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2962, 2952, 2742, 2763, 2884, 2762, 22, 2885])).
% 1.53/1.73 tff(2964,plain,
% 1.53/1.73 (c1_1(a1646)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[260, 2949])).
% 1.53/1.73 tff(2965,plain,
% 1.53/1.73 (c2_1(a1646)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[238, 2949])).
% 1.53/1.73 tff(2966,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2749, 2965, 2964, 2742, 2878, 2963, 22, 2950])).
% 1.53/1.73 tff(2967,plain,(hskp10 | c0_1(a1638) | hskp2 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(2968,plain,
% 1.53/1.73 (hskp10),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2967, 500, 22, 21])).
% 1.53/1.73 tff(2969,plain,
% 1.53/1.73 (c0_1(a1648)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[158, 2968])).
% 1.53/1.73 tff(2970,plain,
% 1.53/1.73 (~c3_1(a1648)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[150, 2968])).
% 1.53/1.73 tff(2971,plain,
% 1.53/1.73 (c2_1(a1648)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[166, 2968])).
% 1.53/1.73 tff(2972,plain,
% 1.53/1.73 (hskp9),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2551, 2971, 500, 2970, 2969])).
% 1.53/1.73 tff(2973,plain,
% 1.53/1.73 (~c1_1(a1644)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[559, 2972])).
% 1.53/1.73 tff(2974,plain,
% 1.53/1.73 (~c0_1(a1644)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[553, 2972])).
% 1.53/1.73 tff(2975,plain,
% 1.53/1.73 (hskp15),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1450, 2947, 21])).
% 1.53/1.73 tff(2976,plain,
% 1.53/1.73 (~c2_1(a1664)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[333, 2975])).
% 1.53/1.73 tff(2977,plain,
% 1.53/1.73 (~c1_1(a1664)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[339, 2975])).
% 1.53/1.73 tff(2978,plain,
% 1.53/1.73 (hskp8),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[176, 119, 21, 2969, 2971, 2970, 32])).
% 1.53/1.73 tff(2979,plain,
% 1.53/1.73 (~c3_1(a1643)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[244, 2978])).
% 1.53/1.73 tff(2980,plain,
% 1.53/1.73 (~c2_1(a1643)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[182, 2978])).
% 1.53/1.73 tff(2981,plain,
% 1.53/1.73 (hskp28),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[647, 2969, 500, 2971, 2887, 2886, 2885, 2970])).
% 1.53/1.73 tff(2982,plain,
% 1.53/1.73 (c1_1(a1646)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[260, 2981])).
% 1.53/1.73 tff(2983,plain,
% 1.53/1.73 (c2_1(a1646)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[238, 2981])).
% 1.53/1.73 tff(2984,plain,
% 1.53/1.73 (c1_1(a1643)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[252, 2978])).
% 1.53/1.73 tff(2985,plain,
% 1.53/1.73 (c0_1(a1664)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[347, 2975])).
% 1.53/1.73 tff(2986,plain,
% 1.53/1.73 (~c0_1(a1643)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1406, 119, 2985, 2763, 2984, 2977, 2976, 2796, 2762, 2979, 826])).
% 1.53/1.73 tff(2987,plain,
% 1.53/1.73 (c0_1(a1646)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[305, 2986, 2969, 2983, 2982, 2971, 2970, 2980, 2979])).
% 1.53/1.73 tff(2988,plain,
% 1.53/1.73 (~c3_1(a1644)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[546, 2972])).
% 1.53/1.73 tff(2989,plain,
% 1.53/1.73 (~c1_1(a1648)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2580, 119, 2971, 2887, 2886, 2970, 2974, 2973, 2988, 2885, 595])).
% 1.53/1.73 tff(2990,assumption,(~c1_1(a1648)), introduced(assumption)).
% 1.53/1.73 tff(2991,assumption,(hskp20), introduced(assumption)).
% 1.53/1.73 tff(2992,plain,
% 1.53/1.73 (~c2_1(a1689)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2053, 2991])).
% 1.53/1.73 tff(2993,plain,
% 1.53/1.73 (c0_1(a1689)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2069, 2991])).
% 1.53/1.73 tff(2994,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | c2_1(a1689) | (~ndr1_0) | (~c0_1(a1689)) | (~c3_1(a1689)) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a1689) | (~ndr1_0) | (~c0_1(a1689)) | (~c3_1(a1689)) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2995,plain,
% 1.53/1.73 ((hskp2 | (~ndr1_0) | c2_1(a1689) | (~c3_1(a1689)) | (~c0_1(a1689)) | c1_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648))) <=> (hskp2 | c2_1(a1689) | (~ndr1_0) | (~c0_1(a1689)) | (~c3_1(a1689)) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2996,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a1689) | (~c3_1(a1689)) | (~c0_1(a1689)) | c1_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | c2_1(a1689) | (~ndr1_0) | (~c0_1(a1689)) | (~c3_1(a1689)) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2995])).
% 1.53/1.73 tff(2997,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a1689) | (~c3_1(a1689)) | (~c0_1(a1689)) | c1_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a1689) | (~ndr1_0) | (~c0_1(a1689)) | (~c3_1(a1689)) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2996, 2994])).
% 1.53/1.73 tff(2998,plain,
% 1.53/1.73 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a1689) | (~c3_1(a1689)) | (~c0_1(a1689)) | c1_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(2999,plain,
% 1.53/1.73 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a1689) | (~ndr1_0) | (~c0_1(a1689)) | (~c3_1(a1689)) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2998, 2997])).
% 1.53/1.73 tff(3000,plain,
% 1.53/1.73 (~c3_1(a1689)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2999, 119, 500, 2993, 170, 169, 2992, 639, 2990])).
% 1.53/1.73 tff(3001,assumption,(~c2_1(a1664)), introduced(assumption)).
% 1.53/1.73 tff(3002,assumption,(~c1_1(a1664)), introduced(assumption)).
% 1.53/1.73 tff(3003,assumption,(c0_1(a1664)), introduced(assumption)).
% 1.53/1.73 tff(3004,plain,
% 1.53/1.73 (c1_1(a1689)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2061, 2991])).
% 1.53/1.73 tff(3005,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c0_1(a1689)) | c3_1(a1689) | (~c1_1(a1689)) | (~c1_1(a1650)) | (~c0_1(a1664)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c0_1(a1689)) | c3_1(a1689) | (~c1_1(a1689)) | (~c1_1(a1650)) | (~c0_1(a1664)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(3006,plain,
% 1.53/1.73 (((~ndr1_0) | c3_1(a1689) | (~c0_1(a1689)) | (~c1_1(a1689)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650))) <=> (c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c0_1(a1689)) | c3_1(a1689) | (~c1_1(a1689)) | (~c1_1(a1650)) | (~c0_1(a1664)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(3007,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1689) | (~c0_1(a1689)) | (~c1_1(a1689)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c0_1(a1689)) | c3_1(a1689) | (~c1_1(a1689)) | (~c1_1(a1650)) | (~c0_1(a1664))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[3006])).
% 1.53/1.73 tff(3008,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1689) | (~c0_1(a1689)) | (~c1_1(a1689)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c0_1(a1689)) | c3_1(a1689) | (~c1_1(a1689)) | (~c1_1(a1650)) | (~c0_1(a1664)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[3007, 3005])).
% 1.53/1.73 tff(3009,plain,
% 1.53/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1689) | (~c0_1(a1689)) | (~c1_1(a1689)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(3010,plain,
% 1.53/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c0_1(a1689)) | c3_1(a1689) | (~c1_1(a1689)) | (~c1_1(a1650)) | (~c0_1(a1664))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[3009, 3008])).
% 1.53/1.73 tff(3011,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[3010, 119, 2993, 3004, 3003, 852, 3002, 3001, 843, 842, 826, 3000])).
% 1.53/1.73 tff(3012,plain,((~hskp20) | (~c0_1(a1664)) | (~c1_1(a1650)) | c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | hskp2 | (~c0_1(a1648)) | (~c2_1(a1648)) | c1_1(a1648)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(3013,plain,
% 1.53/1.73 (~hskp20),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[3012, 2985, 2763, 2977, 2976, 2796, 2762, 500, 2969, 2971, 2989])).
% 1.53/1.73 tff(3014,plain,
% 1.53/1.73 (^[U: $i] : refl((hskp20 | hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp20 | hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))),
% 1.53/1.73 inference(bind,[status(th)],[])).
% 1.53/1.73 tff(3015,plain,
% 1.53/1.73 (![U: $i] : (hskp20 | hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp20 | hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.73 inference(quant_intro,[status(thm)],[3014])).
% 1.53/1.73 tff(3016,plain,
% 1.53/1.73 (![U: $i] : (hskp20 | hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp20 | hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(3017,plain,
% 1.53/1.73 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp20) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp20))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp20) | hskp21) <=> ((hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp21))), rewrite(((hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp21) <=> (hskp20 | hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp20) | hskp21) <=> (hskp20 | hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))))),
% 1.53/1.73 inference(bind,[status(th)],[])).
% 1.53/1.73 tff(3018,plain,
% 1.53/1.73 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp20) | hskp21) <=> ![U: $i] : (hskp20 | hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.73 inference(quant_intro,[status(thm)],[3017])).
% 1.53/1.73 tff(3019,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp20) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 1.53/1.73 tff(3020,plain,
% 1.53/1.73 (![U: $i] : (hskp20 | hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[3019, 3018])).
% 1.53/1.73 tff(3021,plain,
% 1.53/1.73 (![U: $i] : (hskp20 | hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[3020, 3016])).
% 1.53/1.73 tff(3022,plain,(
% 1.53/1.73 ![U: $i] : (hskp20 | hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.73 inference(skolemize,[status(sab)],[3021])).
% 1.53/1.73 tff(3023,plain,
% 1.53/1.73 (![U: $i] : (hskp20 | hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[3022, 3015])).
% 1.53/1.73 tff(3024,plain,
% 1.53/1.73 (((~![U: $i] : (hskp20 | hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp20 | hskp21 | (~ndr1_0) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)))) <=> ((~![U: $i] : (hskp20 | hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp20 | hskp21 | (~ndr1_0) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(3025,plain,
% 1.53/1.73 ((~![U: $i] : (hskp20 | hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp20 | hskp21 | (~ndr1_0) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(3026,plain,
% 1.53/1.73 ((~![U: $i] : (hskp20 | hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp20 | hskp21 | (~ndr1_0) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[3025, 3024])).
% 1.53/1.73 tff(3027,plain,
% 1.53/1.73 (hskp20 | hskp21 | (~c0_1(a1646))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[3026, 119, 2982, 2983, 3023])).
% 1.53/1.73 tff(3028,plain,
% 1.53/1.73 (hskp21),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[3027, 3013, 2987])).
% 1.53/1.73 tff(3029,plain,
% 1.53/1.73 (~c1_1(a1691)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[697, 3028])).
% 1.53/1.73 tff(3030,plain,
% 1.53/1.73 (c3_1(a1691)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[713, 3028])).
% 1.53/1.73 tff(3031,plain,
% 1.53/1.73 (c2_1(a1691)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[738, 3028])).
% 1.53/1.73 tff(3032,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1691) | c1_1(a1664) | c2_1(a1664) | c0_1(a1644) | c1_1(a1644) | (~ndr1_0) | (~c2_1(a1644)) | (~c0_1(a1664)) | (~c3_1(a1691)) | (~c2_1(a1691)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1691) | c1_1(a1664) | c2_1(a1664) | c0_1(a1644) | c1_1(a1644) | (~ndr1_0) | (~c2_1(a1644)) | (~c0_1(a1664)) | (~c3_1(a1691)) | (~c2_1(a1691)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(3033,plain,
% 1.53/1.73 (((~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1644) | c0_1(a1644) | (~c2_1(a1644))) <=> (c1_1(a1691) | c1_1(a1664) | c2_1(a1664) | c0_1(a1644) | c1_1(a1644) | (~ndr1_0) | (~c2_1(a1644)) | (~c0_1(a1664)) | (~c3_1(a1691)) | (~c2_1(a1691)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(3034,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1644) | c0_1(a1644) | (~c2_1(a1644)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1691) | c1_1(a1664) | c2_1(a1664) | c0_1(a1644) | c1_1(a1644) | (~ndr1_0) | (~c2_1(a1644)) | (~c0_1(a1664)) | (~c3_1(a1691)) | (~c2_1(a1691))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[3033])).
% 1.53/1.73 tff(3035,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1644) | c0_1(a1644) | (~c2_1(a1644)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1691) | c1_1(a1664) | c2_1(a1664) | c0_1(a1644) | c1_1(a1644) | (~ndr1_0) | (~c2_1(a1644)) | (~c0_1(a1664)) | (~c3_1(a1691)) | (~c2_1(a1691)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[3034, 3032])).
% 1.53/1.73 tff(3036,plain,
% 1.53/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c1_1(a1644) | c0_1(a1644) | (~c2_1(a1644)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(3037,plain,
% 1.53/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1691) | c1_1(a1664) | c2_1(a1664) | c0_1(a1644) | c1_1(a1644) | (~ndr1_0) | (~c2_1(a1644)) | (~c0_1(a1664)) | (~c3_1(a1691)) | (~c2_1(a1691))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[3036, 3035])).
% 1.53/1.73 tff(3038,plain,
% 1.53/1.73 (~c2_1(a1644)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[3037, 119, 3031, 3030, 2985, 3029, 2977, 2976, 2974, 2973, 812])).
% 1.53/1.73 tff(3039,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1644) | c1_1(a1644) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | c0_1(a1643) | c2_1(a1644))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1644) | c1_1(a1644) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | c0_1(a1643) | c2_1(a1644))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(3040,plain,
% 1.53/1.73 (((~ndr1_0) | c2_1(a1643) | c0_1(a1643) | (~c1_1(a1643)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643) | c2_1(a1644) | c1_1(a1644) | c0_1(a1644)) <=> (c0_1(a1644) | c1_1(a1644) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | c0_1(a1643) | c2_1(a1644))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(3041,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1643) | c0_1(a1643) | (~c1_1(a1643)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643) | c2_1(a1644) | c1_1(a1644) | c0_1(a1644))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1644) | c1_1(a1644) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | c0_1(a1643) | c2_1(a1644)))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[3040])).
% 1.53/1.73 tff(3042,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1643) | c0_1(a1643) | (~c1_1(a1643)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643) | c2_1(a1644) | c1_1(a1644) | c0_1(a1644))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1644) | c1_1(a1644) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | c0_1(a1643) | c2_1(a1644))),
% 1.53/1.73 inference(transitivity,[status(thm)],[3041, 3039])).
% 1.53/1.73 tff(3043,plain,
% 1.53/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1643) | c0_1(a1643) | (~c1_1(a1643)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643) | c2_1(a1644) | c1_1(a1644) | c0_1(a1644))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(3044,plain,
% 1.53/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1644) | c1_1(a1644) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | (~c1_1(a1643)) | c0_1(a1643) | c2_1(a1644)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[3043, 3042])).
% 1.53/1.73 tff(3045,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[3044, 119, 2984, 2974, 2973, 2980, 2979, 1261, 2986, 3038])).
% 1.53/1.73 tff(3046,plain,(hskp2 | hskp1 | c0_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(3047,plain,
% 1.53/1.73 (hskp2),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[3046, 21, 22])).
% 1.53/1.73 tff(3048,plain,
% 1.53/1.73 (~c0_1(a1637)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1124, 3047])).
% 1.53/1.73 tff(3049,plain,
% 1.53/1.73 (c3_1(a1634)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[490, 2856])).
% 1.53/1.73 tff(3050,plain,
% 1.53/1.73 (c0_1(a1634)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[498, 2856])).
% 1.53/1.73 tff(3051,plain,
% 1.53/1.73 (c3_1(a1637)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1132, 3047])).
% 1.53/1.73 tff(3052,plain,
% 1.53/1.73 (c1_1(a1637)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1140, 3047])).
% 1.53/1.73 tff(3053,plain,
% 1.53/1.73 (~c2_1(a1650)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1167, 119, 2763, 3052, 3051, 3050, 3049, 2762, 3048, 2857, 20])).
% 1.53/1.73 tff(3054,plain,
% 1.53/1.73 (hskp10),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2951, 3053])).
% 1.53/1.73 tff(3055,plain,
% 1.53/1.73 (~c3_1(a1648)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[150, 3054])).
% 1.53/1.73 tff(3056,plain,
% 1.53/1.73 (c2_1(a1648)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[166, 3054])).
% 1.53/1.73 tff(3057,plain,
% 1.53/1.73 (c0_1(a1648)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[158, 3054])).
% 1.53/1.73 tff(3058,plain,
% 1.53/1.73 (hskp8),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[176, 119, 21, 3057, 3056, 3055, 32])).
% 1.53/1.73 tff(3059,plain,
% 1.53/1.73 (~c3_1(a1643)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[244, 3058])).
% 1.53/1.73 tff(3060,plain,
% 1.53/1.73 (~c2_1(a1643)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[182, 3058])).
% 1.53/1.73 tff(3061,plain,
% 1.53/1.73 (~hskp19),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2269, 2856, 3051, 3052, 3048, 2857])).
% 1.53/1.73 tff(3062,plain,
% 1.53/1.73 (hskp15),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1450, 3061, 21])).
% 1.53/1.73 tff(3063,plain,
% 1.53/1.73 (~c2_1(a1664)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[333, 3062])).
% 1.53/1.73 tff(3064,plain,
% 1.53/1.73 (~c1_1(a1664)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[339, 3062])).
% 1.53/1.73 tff(3065,plain,
% 1.53/1.73 (c1_1(a1643)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[252, 3058])).
% 1.53/1.73 tff(3066,plain,
% 1.53/1.73 (c0_1(a1664)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[347, 3062])).
% 1.53/1.73 tff(3067,plain,
% 1.53/1.73 (~c0_1(a1643)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1406, 119, 3066, 2763, 3065, 3064, 3063, 2796, 2762, 3059, 826])).
% 1.53/1.73 tff(3068,plain,
% 1.53/1.73 (~c2_1(a1637)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2419, 119, 3057, 3056, 3052, 2796, 2762, 3055, 3048, 295, 3053])).
% 1.53/1.73 tff(3069,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | (~c2_1(a1638)) | c0_1(a1637) | (~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c3_1(a1638)) | c2_1(a1650))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | (~c2_1(a1638)) | c0_1(a1637) | (~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c3_1(a1638)) | c2_1(a1650))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(3070,plain,
% 1.53/1.73 (((~ndr1_0) | c0_1(a1638) | (~c2_1(a1638)) | (~c3_1(a1638)) | c2_1(a1637) | c0_1(a1637) | (~c3_1(a1637)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650)) <=> (c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | (~c2_1(a1638)) | c0_1(a1637) | (~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c3_1(a1638)) | c2_1(a1650))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(3071,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1638) | (~c2_1(a1638)) | (~c3_1(a1638)) | c2_1(a1637) | c0_1(a1637) | (~c3_1(a1637)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | (~c2_1(a1638)) | c0_1(a1637) | (~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c3_1(a1638)) | c2_1(a1650)))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[3070])).
% 1.53/1.73 tff(3072,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1638) | (~c2_1(a1638)) | (~c3_1(a1638)) | c2_1(a1637) | c0_1(a1637) | (~c3_1(a1637)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | (~c2_1(a1638)) | c0_1(a1637) | (~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c3_1(a1638)) | c2_1(a1650))),
% 1.53/1.73 inference(transitivity,[status(thm)],[3071, 3069])).
% 1.53/1.73 tff(3073,plain,
% 1.53/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1638) | (~c2_1(a1638)) | (~c3_1(a1638)) | c2_1(a1637) | c0_1(a1637) | (~c3_1(a1637)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(3074,plain,
% 1.53/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | (~c2_1(a1638)) | c0_1(a1637) | (~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c3_1(a1638)) | c2_1(a1650)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[3073, 3072])).
% 1.53/1.73 tff(3075,plain,
% 1.53/1.73 (~c2_1(a1638)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[3074, 119, 2742, 3051, 2796, 2762, 22, 3048, 1621, 3068, 3053])).
% 1.53/1.73 tff(3076,assumption,(hskp12), introduced(assumption)).
% 1.53/1.73 tff(3077,plain,
% 1.53/1.73 (((~hskp12) | (~c3_1(a1653))) <=> ((~hskp12) | (~c3_1(a1653)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(3078,plain,
% 1.53/1.73 (((~c3_1(a1653)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a1653)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(3079,axiom,((~c3_1(a1653)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 1.53/1.73 tff(3080,plain,
% 1.53/1.73 ((~hskp12) | (~c3_1(a1653))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[3079, 3078])).
% 1.53/1.73 tff(3081,plain,
% 1.53/1.73 ((~hskp12) | (~c3_1(a1653))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[3080, 3077])).
% 1.53/1.73 tff(3082,plain,
% 1.53/1.73 (~c3_1(a1653)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[3081, 3076])).
% 1.53/1.73 tff(3083,plain,
% 1.53/1.73 (((~hskp12) | c1_1(a1653)) <=> ((~hskp12) | c1_1(a1653))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(3084,axiom,((~hskp12) | c1_1(a1653)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 1.53/1.73 tff(3085,plain,
% 1.53/1.73 ((~hskp12) | c1_1(a1653)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[3084, 3083])).
% 1.53/1.73 tff(3086,plain,
% 1.53/1.73 ((~hskp12) | c1_1(a1653)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[3085, 3083])).
% 1.53/1.73 tff(3087,plain,
% 1.53/1.73 ((~hskp12) | c1_1(a1653)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[3086, 3083])).
% 1.53/1.73 tff(3088,plain,
% 1.53/1.73 ((~hskp12) | c1_1(a1653)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[3087, 3083])).
% 1.53/1.73 tff(3089,plain,
% 1.53/1.73 ((~hskp12) | c1_1(a1653)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[3088, 3083])).
% 1.53/1.73 tff(3090,plain,
% 1.53/1.73 (c1_1(a1653)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[3089, 3076])).
% 1.53/1.73 tff(3091,plain,
% 1.53/1.73 (((~hskp12) | c0_1(a1653)) <=> ((~hskp12) | c0_1(a1653))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(3092,axiom,((~hskp12) | c0_1(a1653)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 1.53/1.73 tff(3093,plain,
% 1.53/1.73 ((~hskp12) | c0_1(a1653)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[3092, 3091])).
% 1.53/1.73 tff(3094,plain,
% 1.53/1.73 ((~hskp12) | c0_1(a1653)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[3093, 3091])).
% 1.53/1.73 tff(3095,plain,
% 1.53/1.73 ((~hskp12) | c0_1(a1653)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[3094, 3091])).
% 1.53/1.73 tff(3096,plain,
% 1.53/1.73 ((~hskp12) | c0_1(a1653)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[3095, 3091])).
% 1.53/1.73 tff(3097,plain,
% 1.53/1.73 ((~hskp12) | c0_1(a1653)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[3096, 3091])).
% 1.53/1.73 tff(3098,plain,
% 1.53/1.73 (c0_1(a1653)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[3097, 3076])).
% 1.53/1.73 tff(3099,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a1664) | c2_1(a1664) | c3_1(a1653) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | (~c1_1(a1653)) | (~c0_1(a1653)) | (~c0_1(a1664)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1664) | c2_1(a1664) | c3_1(a1653) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | (~c1_1(a1653)) | (~c0_1(a1653)) | (~c0_1(a1664)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(3100,plain,
% 1.53/1.73 (((~ndr1_0) | c3_1(a1653) | (~c0_1(a1653)) | (~c1_1(a1653)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650))) <=> (c1_1(a1664) | c2_1(a1664) | c3_1(a1653) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | (~c1_1(a1653)) | (~c0_1(a1653)) | (~c0_1(a1664)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(3101,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1653) | (~c0_1(a1653)) | (~c1_1(a1653)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a1664) | c2_1(a1664) | c3_1(a1653) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | (~c1_1(a1653)) | (~c0_1(a1653)) | (~c0_1(a1664))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[3100])).
% 1.53/1.73 tff(3102,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1653) | (~c0_1(a1653)) | (~c1_1(a1653)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1664) | c2_1(a1664) | c3_1(a1653) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | (~c1_1(a1653)) | (~c0_1(a1653)) | (~c0_1(a1664)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[3101, 3099])).
% 1.53/1.73 tff(3103,plain,
% 1.53/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1653) | (~c0_1(a1653)) | (~c1_1(a1653)) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c0_1(a1650) | c3_1(a1650) | (~c1_1(a1650)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(3104,plain,
% 1.53/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1664) | c2_1(a1664) | c3_1(a1653) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c1_1(a1650)) | (~c1_1(a1653)) | (~c0_1(a1653)) | (~c0_1(a1664))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[3103, 3102])).
% 1.53/1.73 tff(3105,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[3104, 119, 3003, 3098, 3090, 852, 3002, 3001, 3082, 843, 842, 826])).
% 1.53/1.73 tff(3106,plain,((~hskp12) | (~c0_1(a1664)) | (~c1_1(a1650)) | c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(3107,plain,
% 1.53/1.73 (~hskp12),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[3106, 3066, 2763, 3064, 3063, 2796, 2762])).
% 1.53/1.73 tff(3108,plain,
% 1.53/1.73 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.53/1.73 inference(bind,[status(th)],[])).
% 1.53/1.73 tff(3109,plain,
% 1.53/1.73 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.53/1.73 inference(quant_intro,[status(thm)],[3108])).
% 1.53/1.73 tff(3110,plain,
% 1.53/1.73 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(3111,plain,
% 1.53/1.73 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp12))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.53/1.74 inference(bind,[status(th)],[])).
% 1.53/1.74 tff(3112,plain,
% 1.53/1.74 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.53/1.74 inference(quant_intro,[status(thm)],[3111])).
% 1.53/1.74 tff(3113,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 1.53/1.74 tff(3114,plain,
% 1.53/1.74 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[3113, 3112])).
% 1.53/1.74 tff(3115,plain,
% 1.53/1.74 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[3114, 3110])).
% 1.53/1.74 tff(3116,plain,(
% 1.53/1.74 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.53/1.74 inference(skolemize,[status(sab)],[3115])).
% 1.53/1.74 tff(3117,plain,
% 1.53/1.74 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[3116, 3109])).
% 1.53/1.74 tff(3118,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1637) | (~c3_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1637) | (~c3_1(a1637)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(3119,plain,
% 1.53/1.74 ((hskp12 | (~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1637) | c0_1(a1637) | (~c3_1(a1637))) <=> (hskp12 | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1637) | (~c3_1(a1637)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(3120,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1637) | c0_1(a1637) | (~c3_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1637) | (~c3_1(a1637))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[3119])).
% 1.53/1.74 tff(3121,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1637) | c0_1(a1637) | (~c3_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1637) | (~c3_1(a1637)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[3120, 3118])).
% 1.53/1.74 tff(3122,plain,
% 1.53/1.74 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c1_1(a1634) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1637) | c0_1(a1637) | (~c3_1(a1637)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(3123,plain,
% 1.53/1.74 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a1637) | c1_1(a1634) | (~ndr1_0) | (~c2_1(a1634)) | (~c3_1(a1634)) | c2_1(a1637) | (~c3_1(a1637))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[3122, 3121])).
% 1.53/1.74 tff(3124,plain,
% 1.53/1.74 (hskp12 | (~c2_1(a1634))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[3123, 119, 3051, 3049, 3048, 2857, 3117, 3068])).
% 1.53/1.74 tff(3125,plain,
% 1.53/1.74 (~c2_1(a1634)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[3124, 3107])).
% 1.53/1.74 tff(3126,plain,
% 1.53/1.74 (~c1_1(a1648)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2389, 119, 3056, 3052, 3051, 3050, 3049, 3055, 3048, 2857, 20])).
% 1.53/1.74 tff(3127,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(3128,plain,
% 1.53/1.74 ((hskp17 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648))) <=> (hskp17 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(3129,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[3128])).
% 1.53/1.74 tff(3130,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[3129, 3127])).
% 1.53/1.74 tff(3131,plain,
% 1.53/1.74 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c1_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(3132,plain,
% 1.53/1.74 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c2_1(a1648)) | c1_1(a1648) | (~c0_1(a1648))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[3131, 3130])).
% 1.53/1.74 tff(3133,plain,
% 1.53/1.74 (hskp17),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[3132, 119, 3057, 3056, 3050, 3049, 2401, 3126, 3125])).
% 1.53/1.74 tff(3134,plain,
% 1.53/1.74 (~c0_1(a1675)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[419, 3133])).
% 1.53/1.74 tff(3135,plain,
% 1.53/1.74 (c2_1(a1675)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[435, 3133])).
% 1.53/1.74 tff(3136,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1675) | c2_1(a1643) | c3_1(a1643) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | c0_1(a1643) | (~c3_1(a1675)) | (~c2_1(a1675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1675) | c2_1(a1643) | c3_1(a1643) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | c0_1(a1643) | (~c3_1(a1675)) | (~c2_1(a1675)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(3137,plain,
% 1.53/1.74 (((~ndr1_0) | c0_1(a1675) | (~c2_1(a1675)) | (~c3_1(a1675)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643)) <=> (c0_1(a1675) | c2_1(a1643) | c3_1(a1643) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | c0_1(a1643) | (~c3_1(a1675)) | (~c2_1(a1675)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(3138,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1675) | (~c2_1(a1675)) | (~c3_1(a1675)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1675) | c2_1(a1643) | c3_1(a1643) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | c0_1(a1643) | (~c3_1(a1675)) | (~c2_1(a1675))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[3137])).
% 1.53/1.74 tff(3139,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1675) | (~c2_1(a1675)) | (~c3_1(a1675)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1675) | c2_1(a1643) | c3_1(a1643) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | c0_1(a1643) | (~c3_1(a1675)) | (~c2_1(a1675)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[3138, 3136])).
% 1.53/1.74 tff(3140,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1675) | (~c2_1(a1675)) | (~c3_1(a1675)) | c2_1(a1638) | c0_1(a1638) | (~c3_1(a1638)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(3141,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1675) | c2_1(a1643) | c3_1(a1643) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | (~c3_1(a1638)) | c0_1(a1643) | (~c3_1(a1675)) | (~c2_1(a1675))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[3140, 3139])).
% 1.53/1.74 tff(3142,plain,
% 1.53/1.74 (~c3_1(a1675)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[3141, 119, 3135, 2742, 3134, 3060, 3059, 22, 3075, 1621, 3067])).
% 1.53/1.74 tff(3143,plain,
% 1.53/1.74 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 1.53/1.74 inference(bind,[status(th)],[])).
% 1.53/1.74 tff(3144,plain,
% 1.53/1.74 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.53/1.74 inference(quant_intro,[status(thm)],[3143])).
% 1.53/1.74 tff(3145,plain,
% 1.53/1.74 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(3146,plain,
% 1.53/1.74 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp29) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp29))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 1.53/1.74 inference(bind,[status(th)],[])).
% 1.53/1.74 tff(3147,plain,
% 1.53/1.74 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.53/1.74 inference(quant_intro,[status(thm)],[3146])).
% 1.53/1.74 tff(3148,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 1.53/1.74 tff(3149,plain,
% 1.53/1.74 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[3148, 3147])).
% 1.53/1.74 tff(3150,plain,
% 1.53/1.74 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[3149, 3145])).
% 1.53/1.74 tff(3151,plain,(
% 1.53/1.74 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.53/1.74 inference(skolemize,[status(sab)],[3150])).
% 1.53/1.74 tff(3152,plain,
% 1.53/1.74 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[3151, 3144])).
% 1.53/1.74 tff(3153,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp29 | c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | c2_1(a1650) | (~c0_1(a1664)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp29 | c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | c2_1(a1650) | (~c0_1(a1664)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(3154,plain,
% 1.53/1.74 ((hskp29 | (~ndr1_0) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650)) <=> (hskp29 | c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | c2_1(a1650) | (~c0_1(a1664)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(3155,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp29 | (~ndr1_0) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp29 | c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | c2_1(a1650) | (~c0_1(a1664))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[3154])).
% 1.53/1.74 tff(3156,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp29 | (~ndr1_0) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp29 | c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | c2_1(a1650) | (~c0_1(a1664)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[3155, 3153])).
% 1.53/1.74 tff(3157,plain,
% 1.53/1.74 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp29 | (~ndr1_0) | c2_1(a1664) | c1_1(a1664) | (~c0_1(a1664)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(3158,plain,
% 1.53/1.74 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp29 | c1_1(a1664) | c2_1(a1664) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | c2_1(a1650) | (~c0_1(a1664))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[3157, 3156])).
% 1.53/1.74 tff(3159,plain,
% 1.53/1.74 (hskp29),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[3158, 119, 3066, 3064, 3063, 2796, 2762, 3152, 3053])).
% 1.53/1.74 tff(3160,plain,
% 1.53/1.74 (c3_1(a1647)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1768, 3159])).
% 1.53/1.74 tff(3161,plain,
% 1.53/1.74 (c1_1(a1647)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1776, 3159])).
% 1.53/1.74 tff(3162,plain,
% 1.53/1.74 (c0_1(a1647)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1784, 3159])).
% 1.53/1.74 tff(3163,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c3_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c3_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(3164,plain,
% 1.53/1.74 (((~ndr1_0) | (~c3_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)) | (~c1_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | c2_1(a1634) | c1_1(a1634) | (~c3_1(a1634))) <=> (c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c3_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(3165,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)) | (~c1_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | c2_1(a1634) | c1_1(a1634) | (~c3_1(a1634)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c3_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[3164])).
% 1.53/1.74 tff(3166,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)) | (~c1_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | c2_1(a1634) | c1_1(a1634) | (~c3_1(a1634)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c3_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[3165, 3163])).
% 1.53/1.74 tff(3167,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)) | (~c1_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | c2_1(a1634) | c1_1(a1634) | (~c3_1(a1634)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(3168,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1634) | (~ndr1_0) | c2_1(a1634) | (~c3_1(a1634)) | (~c3_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[3167, 3166])).
% 1.53/1.74 tff(3169,plain,
% 1.53/1.74 (~c2_1(a1647)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[3168, 119, 3162, 3161, 3160, 3049, 2857, 1418, 3125])).
% 1.53/1.74 tff(3170,plain,
% 1.53/1.74 (~c1_1(a1675)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[413, 3133])).
% 1.53/1.74 tff(3171,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | c0_1(a1675) | c1_1(a1675) | (~ndr1_0) | c3_1(a1675) | c2_1(a1647) | (~c0_1(a1647)) | (~c1_1(a1647)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c0_1(a1675) | c1_1(a1675) | (~ndr1_0) | c3_1(a1675) | c2_1(a1647) | (~c0_1(a1647)) | (~c1_1(a1647)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(3172,plain,
% 1.53/1.74 ((hskp4 | (~ndr1_0) | c2_1(a1647) | (~c0_1(a1647)) | (~c1_1(a1647)) | c1_1(a1675) | c0_1(a1675) | c3_1(a1675)) <=> (hskp4 | c0_1(a1675) | c1_1(a1675) | (~ndr1_0) | c3_1(a1675) | c2_1(a1647) | (~c0_1(a1647)) | (~c1_1(a1647)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(3173,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1647) | (~c0_1(a1647)) | (~c1_1(a1647)) | c1_1(a1675) | c0_1(a1675) | c3_1(a1675))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | c0_1(a1675) | c1_1(a1675) | (~ndr1_0) | c3_1(a1675) | c2_1(a1647) | (~c0_1(a1647)) | (~c1_1(a1647))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[3172])).
% 1.53/1.74 tff(3174,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1647) | (~c0_1(a1647)) | (~c1_1(a1647)) | c1_1(a1675) | c0_1(a1675) | c3_1(a1675))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c0_1(a1675) | c1_1(a1675) | (~ndr1_0) | c3_1(a1675) | c2_1(a1647) | (~c0_1(a1647)) | (~c1_1(a1647)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[3173, 3171])).
% 1.53/1.74 tff(3175,plain,
% 1.53/1.74 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a1647) | (~c0_1(a1647)) | (~c1_1(a1647)) | c1_1(a1675) | c0_1(a1675) | c3_1(a1675))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(3176,plain,
% 1.53/1.74 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c0_1(a1675) | c1_1(a1675) | (~ndr1_0) | c3_1(a1675) | c2_1(a1647) | (~c0_1(a1647)) | (~c1_1(a1647))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[3175, 3174])).
% 1.53/1.74 tff(3177,plain,
% 1.53/1.74 (hskp4 | c3_1(a1675)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[3176, 119, 3162, 3161, 3134, 3170, 915, 3169])).
% 1.53/1.74 tff(3178,plain,
% 1.53/1.74 (hskp4),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[3177, 3142])).
% 1.53/1.74 tff(3179,plain,
% 1.53/1.74 (~c2_1(a1639)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[928, 3178])).
% 1.53/1.74 tff(3180,plain,
% 1.53/1.74 (~c1_1(a1639)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[934, 3178])).
% 1.53/1.74 tff(3181,plain,
% 1.53/1.74 (c3_1(a1639)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1950, 3178])).
% 1.53/1.74 tff(3182,assumption,(c3_1(a1639)), introduced(assumption)).
% 1.53/1.74 tff(3183,assumption,(hskp27), introduced(assumption)).
% 1.53/1.74 tff(3184,plain,
% 1.53/1.74 (c2_1(a1635)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2920, 3183])).
% 1.53/1.74 tff(3185,plain,
% 1.53/1.74 (c1_1(a1635)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2928, 3183])).
% 1.53/1.74 tff(3186,plain,
% 1.53/1.74 (c0_1(a1635)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2936, 3183])).
% 1.53/1.74 tff(3187,assumption,(c3_1(a1647)), introduced(assumption)).
% 1.53/1.74 tff(3188,assumption,(c1_1(a1647)), introduced(assumption)).
% 1.53/1.74 tff(3189,assumption,(c0_1(a1647)), introduced(assumption)).
% 1.53/1.74 tff(3190,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | (~c3_1(a1639)) | (~c0_1(a1635)) | (~c2_1(a1635)) | (~c1_1(a1635)) | (~c3_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | (~c3_1(a1639)) | (~c0_1(a1635)) | (~c2_1(a1635)) | (~c1_1(a1635)) | (~c3_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(3191,plain,
% 1.53/1.74 (((~ndr1_0) | (~c3_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)) | (~c1_1(a1635)) | (~c2_1(a1635)) | (~c0_1(a1635)) | c2_1(a1639) | c1_1(a1639) | (~c3_1(a1639))) <=> (c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | (~c3_1(a1639)) | (~c0_1(a1635)) | (~c2_1(a1635)) | (~c1_1(a1635)) | (~c3_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(3192,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)) | (~c1_1(a1635)) | (~c2_1(a1635)) | (~c0_1(a1635)) | c2_1(a1639) | c1_1(a1639) | (~c3_1(a1639)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | (~c3_1(a1639)) | (~c0_1(a1635)) | (~c2_1(a1635)) | (~c1_1(a1635)) | (~c3_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[3191])).
% 1.53/1.74 tff(3193,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)) | (~c1_1(a1635)) | (~c2_1(a1635)) | (~c0_1(a1635)) | c2_1(a1639) | c1_1(a1639) | (~c3_1(a1639)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | (~c3_1(a1639)) | (~c0_1(a1635)) | (~c2_1(a1635)) | (~c1_1(a1635)) | (~c3_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[3192, 3190])).
% 1.53/1.74 tff(3194,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)) | (~c1_1(a1635)) | (~c2_1(a1635)) | (~c0_1(a1635)) | c2_1(a1639) | c1_1(a1639) | (~c3_1(a1639)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(3195,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | (~c3_1(a1639)) | (~c0_1(a1635)) | (~c2_1(a1635)) | (~c1_1(a1635)) | (~c3_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[3194, 3193])).
% 1.53/1.74 tff(3196,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[3195, 119, 3189, 3188, 3187, 3186, 3185, 3184, 3182, 1902, 1903, 1418])).
% 1.53/1.74 tff(3197,plain,((~hskp27) | (~c0_1(a1647)) | (~c1_1(a1647)) | (~c3_1(a1647)) | (~c3_1(a1639)) | c1_1(a1639) | c2_1(a1639)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(3198,plain,
% 1.53/1.74 (~hskp27),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[3197, 3162, 3161, 3160, 3181, 3180, 3179])).
% 1.53/1.74 tff(3199,assumption,(hskp25), introduced(assumption)).
% 1.53/1.74 tff(3200,plain,
% 1.53/1.74 (((~hskp25) | (~c0_1(a1709))) <=> ((~hskp25) | (~c0_1(a1709)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(3201,plain,
% 1.53/1.74 (((~c0_1(a1709)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a1709)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(3202,axiom,((~c0_1(a1709)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 1.53/1.74 tff(3203,plain,
% 1.53/1.74 ((~hskp25) | (~c0_1(a1709))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[3202, 3201])).
% 1.53/1.74 tff(3204,plain,
% 1.53/1.74 ((~hskp25) | (~c0_1(a1709))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[3203, 3200])).
% 1.53/1.74 tff(3205,plain,
% 1.53/1.74 (~c0_1(a1709)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[3204, 3199])).
% 1.53/1.74 tff(3206,plain,
% 1.53/1.74 (((~hskp25) | c2_1(a1709)) <=> ((~hskp25) | c2_1(a1709))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(3207,axiom,((~hskp25) | c2_1(a1709)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 1.53/1.74 tff(3208,plain,
% 1.53/1.74 ((~hskp25) | c2_1(a1709)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[3207, 3206])).
% 1.53/1.74 tff(3209,plain,
% 1.53/1.74 ((~hskp25) | c2_1(a1709)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[3208, 3206])).
% 1.53/1.74 tff(3210,plain,
% 1.53/1.74 ((~hskp25) | c2_1(a1709)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[3209, 3206])).
% 1.53/1.74 tff(3211,plain,
% 1.53/1.74 ((~hskp25) | c2_1(a1709)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[3210, 3206])).
% 1.53/1.74 tff(3212,plain,
% 1.53/1.74 ((~hskp25) | c2_1(a1709)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[3211, 3206])).
% 1.53/1.74 tff(3213,plain,
% 1.53/1.74 (c2_1(a1709)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[3212, 3199])).
% 1.53/1.74 tff(3214,plain,
% 1.53/1.74 (((~hskp25) | c1_1(a1709)) <=> ((~hskp25) | c1_1(a1709))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(3215,axiom,((~hskp25) | c1_1(a1709)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 1.53/1.74 tff(3216,plain,
% 1.53/1.74 ((~hskp25) | c1_1(a1709)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[3215, 3214])).
% 1.53/1.75 tff(3217,plain,
% 1.53/1.75 ((~hskp25) | c1_1(a1709)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3216, 3214])).
% 1.53/1.75 tff(3218,plain,
% 1.53/1.75 ((~hskp25) | c1_1(a1709)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3217, 3214])).
% 1.53/1.75 tff(3219,plain,
% 1.53/1.75 ((~hskp25) | c1_1(a1709)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3218, 3214])).
% 1.53/1.75 tff(3220,plain,
% 1.53/1.75 ((~hskp25) | c1_1(a1709)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3219, 3214])).
% 1.53/1.75 tff(3221,plain,
% 1.53/1.75 (c1_1(a1709)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3220, 3199])).
% 1.53/1.75 tff(3222,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1709) | c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1709)) | (~c2_1(a1709)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1709) | c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1709)) | (~c2_1(a1709)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3223,plain,
% 1.53/1.75 (((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1709) | (~c1_1(a1709)) | (~c2_1(a1709)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643)) <=> (c0_1(a1709) | c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1709)) | (~c2_1(a1709)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3224,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1709) | (~c1_1(a1709)) | (~c2_1(a1709)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1709) | c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1709)) | (~c2_1(a1709))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[3223])).
% 1.53/1.75 tff(3225,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1709) | (~c1_1(a1709)) | (~c2_1(a1709)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1709) | c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1709)) | (~c2_1(a1709)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[3224, 3222])).
% 1.53/1.75 tff(3226,plain,
% 1.53/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1648) | (~c2_1(a1648)) | (~c0_1(a1648)) | c0_1(a1709) | (~c1_1(a1709)) | (~c2_1(a1709)) | c2_1(a1643) | c0_1(a1643) | c3_1(a1643))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(3227,plain,
% 1.53/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1709) | c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | (~ndr1_0) | c0_1(a1643) | (~c2_1(a1648)) | (~c0_1(a1648)) | (~c1_1(a1709)) | (~c2_1(a1709))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3226, 3225])).
% 1.53/1.75 tff(3228,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3227, 119, 3221, 3213, 170, 169, 3205, 168, 282, 281, 295, 285])).
% 1.53/1.75 tff(3229,plain,((~hskp25) | (~c0_1(a1648)) | (~c2_1(a1648)) | c3_1(a1648) | c2_1(a1643) | c3_1(a1643) | c0_1(a1643)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(3230,plain,
% 1.53/1.75 (~hskp25),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3229, 3057, 3056, 3055, 3060, 3059, 3067])).
% 1.53/1.75 tff(3231,plain,
% 1.53/1.75 ((hskp25 | hskp24 | hskp12) <=> (hskp25 | hskp24 | hskp12)),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3232,plain,
% 1.53/1.75 (((hskp12 | hskp25) | hskp24) <=> (hskp25 | hskp24 | hskp12)),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3233,axiom,((hskp12 | hskp25) | hskp24), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 1.53/1.75 tff(3234,plain,
% 1.53/1.75 (hskp25 | hskp24 | hskp12),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3233, 3232])).
% 1.53/1.75 tff(3235,plain,
% 1.53/1.75 (hskp25 | hskp24 | hskp12),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3234, 3231])).
% 1.53/1.75 tff(3236,plain,
% 1.53/1.75 (hskp25 | hskp24 | hskp12),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3235, 3231])).
% 1.53/1.75 tff(3237,plain,
% 1.53/1.75 (hskp25 | hskp24 | hskp12),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3236, 3231])).
% 1.53/1.75 tff(3238,plain,
% 1.53/1.75 (hskp25 | hskp24 | hskp12),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3237, 3231])).
% 1.53/1.75 tff(3239,plain,
% 1.53/1.75 (hskp24),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3238, 3230, 3107])).
% 1.53/1.75 tff(3240,assumption,(hskp24), introduced(assumption)).
% 1.53/1.75 tff(3241,plain,
% 1.53/1.75 (((~hskp24) | (~c1_1(a1701))) <=> ((~hskp24) | (~c1_1(a1701)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3242,plain,
% 1.53/1.75 (((~c1_1(a1701)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a1701)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3243,axiom,((~c1_1(a1701)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 1.53/1.75 tff(3244,plain,
% 1.53/1.75 ((~hskp24) | (~c1_1(a1701))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3243, 3242])).
% 1.53/1.75 tff(3245,plain,
% 1.53/1.75 ((~hskp24) | (~c1_1(a1701))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3244, 3241])).
% 1.53/1.75 tff(3246,plain,
% 1.53/1.75 (~c1_1(a1701)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3245, 3240])).
% 1.53/1.75 tff(3247,plain,
% 1.53/1.75 (((~hskp24) | c3_1(a1701)) <=> ((~hskp24) | c3_1(a1701))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3248,axiom,((~hskp24) | c3_1(a1701)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 1.53/1.75 tff(3249,plain,
% 1.53/1.75 ((~hskp24) | c3_1(a1701)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3248, 3247])).
% 1.53/1.75 tff(3250,plain,
% 1.53/1.75 ((~hskp24) | c3_1(a1701)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3249, 3247])).
% 1.53/1.75 tff(3251,plain,
% 1.53/1.75 ((~hskp24) | c3_1(a1701)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3250, 3247])).
% 1.53/1.75 tff(3252,plain,
% 1.53/1.75 ((~hskp24) | c3_1(a1701)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3251, 3247])).
% 1.53/1.75 tff(3253,plain,
% 1.53/1.75 ((~hskp24) | c3_1(a1701)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3252, 3247])).
% 1.53/1.75 tff(3254,plain,
% 1.53/1.75 (c3_1(a1701)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3253, 3240])).
% 1.53/1.75 tff(3255,assumption,(~hskp19), introduced(assumption)).
% 1.53/1.75 tff(3256,plain,
% 1.53/1.75 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp28 | hskp19 | c1_1(a1701) | (~ndr1_0) | (~c3_1(a1701)) | (~c2_1(a1701)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp28 | hskp19 | c1_1(a1701) | (~ndr1_0) | (~c3_1(a1701)) | (~c2_1(a1701)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3257,plain,
% 1.53/1.75 ((hskp28 | hskp19 | (~ndr1_0) | c1_1(a1701) | (~c2_1(a1701)) | (~c3_1(a1701))) <=> (hskp28 | hskp19 | c1_1(a1701) | (~ndr1_0) | (~c3_1(a1701)) | (~c2_1(a1701)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3258,plain,
% 1.53/1.75 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c1_1(a1701) | (~c2_1(a1701)) | (~c3_1(a1701)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp28 | hskp19 | c1_1(a1701) | (~ndr1_0) | (~c3_1(a1701)) | (~c2_1(a1701))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[3257])).
% 1.53/1.75 tff(3259,plain,
% 1.53/1.75 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c1_1(a1701) | (~c2_1(a1701)) | (~c3_1(a1701)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp28 | hskp19 | c1_1(a1701) | (~ndr1_0) | (~c3_1(a1701)) | (~c2_1(a1701)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[3258, 3256])).
% 1.53/1.75 tff(3260,plain,
% 1.53/1.75 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c1_1(a1701) | (~c2_1(a1701)) | (~c3_1(a1701)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(3261,plain,
% 1.53/1.75 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp28 | hskp19 | c1_1(a1701) | (~ndr1_0) | (~c3_1(a1701)) | (~c2_1(a1701))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3260, 3259])).
% 1.53/1.75 tff(3262,plain,
% 1.53/1.75 (~c2_1(a1701)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3261, 119, 501, 3255, 3254, 3246, 621])).
% 1.53/1.75 tff(3263,plain,
% 1.53/1.75 (((~hskp24) | (~c0_1(a1701))) <=> ((~hskp24) | (~c0_1(a1701)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3264,plain,
% 1.53/1.75 (((~c0_1(a1701)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a1701)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3265,axiom,((~c0_1(a1701)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 1.53/1.75 tff(3266,plain,
% 1.53/1.75 ((~hskp24) | (~c0_1(a1701))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3265, 3264])).
% 1.53/1.75 tff(3267,plain,
% 1.53/1.75 ((~hskp24) | (~c0_1(a1701))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3266, 3263])).
% 1.53/1.75 tff(3268,plain,
% 1.53/1.75 (~c0_1(a1701)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3267, 3240])).
% 1.53/1.75 tff(3269,assumption,(~hskp27), introduced(assumption)).
% 1.53/1.75 tff(3270,plain,
% 1.53/1.75 (((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | c0_1(a1701) | c1_1(a1701) | (~ndr1_0) | c2_1(a1701))) <=> ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp1 | c0_1(a1701) | c1_1(a1701) | (~ndr1_0) | c2_1(a1701))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3271,plain,
% 1.53/1.75 ((hskp27 | hskp1 | (~ndr1_0) | c2_1(a1701) | c1_1(a1701) | c0_1(a1701)) <=> (hskp27 | hskp1 | c0_1(a1701) | c1_1(a1701) | (~ndr1_0) | c2_1(a1701))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3272,plain,
% 1.53/1.75 (((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | (~ndr1_0) | c2_1(a1701) | c1_1(a1701) | c0_1(a1701))) <=> ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | c0_1(a1701) | c1_1(a1701) | (~ndr1_0) | c2_1(a1701)))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[3271])).
% 1.53/1.75 tff(3273,plain,
% 1.53/1.75 (((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | (~ndr1_0) | c2_1(a1701) | c1_1(a1701) | c0_1(a1701))) <=> ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp1 | c0_1(a1701) | c1_1(a1701) | (~ndr1_0) | c2_1(a1701))),
% 1.53/1.75 inference(transitivity,[status(thm)],[3272, 3270])).
% 1.53/1.75 tff(3274,plain,
% 1.53/1.75 ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp1 | (~ndr1_0) | c2_1(a1701) | c1_1(a1701) | c0_1(a1701))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(3275,plain,
% 1.53/1.75 ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp1 | c0_1(a1701) | c1_1(a1701) | (~ndr1_0) | c2_1(a1701)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3274, 3273])).
% 1.53/1.75 tff(3276,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3275, 119, 3269, 21, 3268, 3246, 2905, 3262])).
% 1.53/1.75 tff(3277,plain,((~hskp24) | hskp27 | hskp1 | hskp28 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(3278,plain,
% 1.53/1.75 (hskp28),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3277, 3239, 21, 3198, 3061])).
% 1.53/1.75 tff(3279,plain,
% 1.53/1.75 (c1_1(a1646)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[260, 3278])).
% 1.53/1.75 tff(3280,plain,
% 1.53/1.75 (c2_1(a1646)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[238, 3278])).
% 1.53/1.75 tff(3281,plain,
% 1.53/1.75 (c0_1(a1646)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[305, 3280, 3057, 3067, 3279, 3056, 3055, 3060, 3059])).
% 1.53/1.75 tff(3282,plain,
% 1.53/1.75 (c3_1(a1646)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[268, 3278])).
% 1.53/1.75 tff(3283,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | (~c3_1(a1639)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | (~c3_1(a1639)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3284,plain,
% 1.53/1.75 (((~ndr1_0) | (~c3_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c1_1(a1646)) | (~c2_1(a1646)) | (~c0_1(a1646)) | c2_1(a1639) | c1_1(a1639) | (~c3_1(a1639))) <=> (c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | (~c3_1(a1639)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3285,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c1_1(a1646)) | (~c2_1(a1646)) | (~c0_1(a1646)) | c2_1(a1639) | c1_1(a1639) | (~c3_1(a1639)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | (~c3_1(a1639)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[3284])).
% 1.53/1.75 tff(3286,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c1_1(a1646)) | (~c2_1(a1646)) | (~c0_1(a1646)) | c2_1(a1639) | c1_1(a1639) | (~c3_1(a1639)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | (~c3_1(a1639)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[3285, 3283])).
% 1.53/1.75 tff(3287,plain,
% 1.53/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c1_1(a1646)) | (~c2_1(a1646)) | (~c0_1(a1646)) | c2_1(a1639) | c1_1(a1639) | (~c3_1(a1639)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(3288,plain,
% 1.53/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1639) | c2_1(a1639) | (~ndr1_0) | (~c3_1(a1639)) | (~c2_1(a1646)) | (~c0_1(a1646)) | (~c1_1(a1646)) | (~c3_1(a1646))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3287, 3286])).
% 1.53/1.75 tff(3289,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3288, 119, 3279, 3280, 3282, 3181, 3180, 3179, 1418, 3281])).
% 1.53/1.75 tff(3290,plain,(hskp1 | c0_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(3291,plain,
% 1.53/1.75 (hskp1),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3290, 22])).
% 1.53/1.75 tff(3292,plain,
% 1.53/1.75 (~c0_1(a1636)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1543, 3291])).
% 1.53/1.75 tff(3293,plain,
% 1.53/1.75 (~c2_1(a1636)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1549, 3291])).
% 1.53/1.75 tff(3294,plain,
% 1.53/1.75 (~c1_1(a1636)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1537, 3291])).
% 1.53/1.75 tff(3295,plain,
% 1.53/1.75 (~hskp2),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2728, 45, 3292, 3293, 3294])).
% 1.53/1.75 tff(3296,plain,
% 1.53/1.75 (hskp3 | hskp2),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1672, 119, 3292, 3294, 3293, 1045])).
% 1.53/1.75 tff(3297,plain,
% 1.53/1.75 (hskp3),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3296, 3295])).
% 1.53/1.75 tff(3298,plain,
% 1.53/1.75 (~c2_1(a1638)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1992, 3297])).
% 1.53/1.75 tff(3299,plain,
% 1.53/1.75 (~c1_1(a1638)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1596, 3298, 22, 3294, 3293, 3292])).
% 1.53/1.75 tff(3300,plain,
% 1.53/1.75 (~c1_1(a1638)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1596, 1217, 22, 3294, 3293, 3292])).
% 1.53/1.75 tff(3301,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2749, 381, 382, 2742, 1217, 3300, 22, 380])).
% 1.53/1.75 tff(3302,plain,((~hskp28) | c2_1(a1638) | c0_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(3303,plain,
% 1.53/1.75 (~hskp28),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3302, 3298, 22])).
% 1.53/1.75 tff(3304,plain,
% 1.53/1.75 (hskp28 | hskp0 | c1_1(a1638) | (~c3_1(a1638))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1724, 119, 22, 1718])).
% 1.53/1.75 tff(3305,plain,
% 1.53/1.75 (hskp0),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3304, 3303, 2742, 3299])).
% 1.53/1.75 tff(3306,plain,
% 1.53/1.75 (~c1_1(a1634)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[482, 3305])).
% 1.53/1.75 tff(3307,plain,
% 1.53/1.75 (c3_1(a1634)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[490, 3305])).
% 1.53/1.75 tff(3308,plain,
% 1.53/1.75 (c0_1(a1634)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[498, 3305])).
% 1.53/1.75 tff(3309,assumption,(hskp10), introduced(assumption)).
% 1.53/1.75 tff(3310,plain,
% 1.53/1.75 (~c3_1(a1648)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[150, 3309])).
% 1.53/1.75 tff(3311,plain,
% 1.53/1.75 (c0_1(a1648)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[158, 3309])).
% 1.53/1.75 tff(3312,plain,
% 1.53/1.75 (c2_1(a1648)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[166, 3309])).
% 1.53/1.75 tff(3313,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[647, 3312, 3311, 500, 501, 504, 502, 503, 3310])).
% 1.53/1.75 tff(3314,plain,((~hskp10) | hskp2 | hskp28 | (~c0_1(a1634)) | (~c3_1(a1634)) | c1_1(a1634)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(3315,plain,
% 1.53/1.75 (~hskp10),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3314, 3295, 3303, 3308, 3307, 3306])).
% 1.53/1.75 tff(3316,plain,
% 1.53/1.75 (hskp18),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[64, 3315, 45])).
% 1.53/1.75 tff(3317,plain,
% 1.53/1.75 (~c0_1(a1680)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[76, 3316])).
% 1.53/1.75 tff(3318,plain,
% 1.53/1.75 (c2_1(a1634)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1011, 3315, 3308, 3307, 3306, 3295])).
% 1.53/1.75 tff(3319,plain,
% 1.53/1.75 (hskp19 | (~c2_1(a1634))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[627, 119, 3303, 3307, 3306, 621])).
% 1.53/1.75 tff(3320,plain,
% 1.53/1.75 (hskp19),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3319, 3318])).
% 1.53/1.75 tff(3321,plain,
% 1.53/1.75 (~c3_1(a1682)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[568, 3320])).
% 1.53/1.75 tff(3322,plain,
% 1.53/1.75 (c1_1(a1680)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[84, 3316])).
% 1.53/1.75 tff(3323,plain,
% 1.53/1.75 (c2_1(a1682)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[584, 3320])).
% 1.53/1.75 tff(3324,plain,
% 1.53/1.75 (c1_1(a1682)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[576, 3320])).
% 1.53/1.75 tff(3325,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1682) | c0_1(a1680) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1680)) | (~c1_1(a1680)) | (~c2_1(a1682)) | (~c1_1(a1682)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1682) | c0_1(a1680) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1680)) | (~c1_1(a1680)) | (~c2_1(a1682)) | (~c1_1(a1682)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3326,plain,
% 1.53/1.75 (((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1680) | (~c1_1(a1680)) | (~c3_1(a1680))) <=> (c3_1(a1682) | c0_1(a1680) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1680)) | (~c1_1(a1680)) | (~c2_1(a1682)) | (~c1_1(a1682)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3327,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1680) | (~c1_1(a1680)) | (~c3_1(a1680)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1682) | c0_1(a1680) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1680)) | (~c1_1(a1680)) | (~c2_1(a1682)) | (~c1_1(a1682))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[3326])).
% 1.53/1.75 tff(3328,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1680) | (~c1_1(a1680)) | (~c3_1(a1680)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1682) | c0_1(a1680) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1680)) | (~c1_1(a1680)) | (~c2_1(a1682)) | (~c1_1(a1682)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[3327, 3325])).
% 1.53/1.75 tff(3329,plain,
% 1.53/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)) | c0_1(a1680) | (~c1_1(a1680)) | (~c3_1(a1680)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(3330,plain,
% 1.53/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1682) | c0_1(a1680) | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)) | (~c3_1(a1680)) | (~c1_1(a1680)) | (~c2_1(a1682)) | (~c1_1(a1682))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3329, 3328])).
% 1.53/1.75 tff(3331,plain,
% 1.53/1.75 (~c3_1(a1680)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3330, 119, 3324, 3323, 3322, 3308, 3307, 3321, 3317, 3306, 20])).
% 1.53/1.75 tff(3332,plain,
% 1.53/1.75 (~c2_1(a1680)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[70, 3316])).
% 1.53/1.75 tff(3333,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1680) | c2_1(a1680) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | c3_1(a1680) | (~c1_1(a1680)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1680) | c2_1(a1680) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | c3_1(a1680) | (~c1_1(a1680)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3334,plain,
% 1.53/1.75 (((~ndr1_0) | c2_1(a1680) | c0_1(a1680) | (~c1_1(a1680)) | c2_1(a1680) | c0_1(a1680) | c3_1(a1680) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638)) <=> (c0_1(a1680) | c2_1(a1680) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | c3_1(a1680) | (~c1_1(a1680)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3335,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1680) | c0_1(a1680) | (~c1_1(a1680)) | c2_1(a1680) | c0_1(a1680) | c3_1(a1680) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1680) | c2_1(a1680) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | c3_1(a1680) | (~c1_1(a1680))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[3334])).
% 1.53/1.75 tff(3336,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1680) | c0_1(a1680) | (~c1_1(a1680)) | c2_1(a1680) | c0_1(a1680) | c3_1(a1680) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1680) | c2_1(a1680) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | c3_1(a1680) | (~c1_1(a1680)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[3335, 3333])).
% 1.53/1.75 tff(3337,plain,
% 1.53/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1680) | c0_1(a1680) | (~c1_1(a1680)) | c2_1(a1680) | c0_1(a1680) | c3_1(a1680) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(3338,plain,
% 1.53/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1680) | c2_1(a1680) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | c3_1(a1680) | (~c1_1(a1680))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3337, 3336])).
% 1.53/1.75 tff(3339,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3338, 119, 3322, 3317, 3332, 22, 3298, 1261, 3299, 3331])).
% 1.53/1.75 tff(3340,plain,(hskp11 | c0_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(3341,plain,
% 1.53/1.75 (hskp11),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3340, 22])).
% 1.53/1.75 tff(3342,plain,
% 1.53/1.75 (~c0_1(a1650)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[673, 3341])).
% 1.53/1.75 tff(3343,plain,
% 1.53/1.75 (~c3_1(a1650)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[667, 3341])).
% 1.53/1.75 tff(3344,plain,
% 1.53/1.75 (~hskp2),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2728, 1184, 3292, 3293, 3294])).
% 1.53/1.75 tff(3345,plain,
% 1.53/1.75 (hskp3),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3296, 3344])).
% 1.53/1.75 tff(3346,plain,
% 1.53/1.75 (~c2_1(a1638)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1992, 3345])).
% 1.53/1.75 tff(3347,plain,
% 1.53/1.75 (~c1_1(a1638)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1596, 3346, 22, 3294, 3293, 3292])).
% 1.53/1.75 tff(3348,plain,
% 1.53/1.75 (~hskp28),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3302, 3346, 22])).
% 1.53/1.75 tff(3349,plain,
% 1.53/1.75 (hskp0),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3304, 3348, 2742, 3347])).
% 1.53/1.75 tff(3350,plain,
% 1.53/1.75 (~c1_1(a1634)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[482, 3349])).
% 1.53/1.75 tff(3351,plain,
% 1.53/1.75 (c3_1(a1634)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[490, 3349])).
% 1.53/1.75 tff(3352,plain,
% 1.53/1.75 (c0_1(a1634)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[498, 3349])).
% 1.53/1.75 tff(3353,plain,
% 1.53/1.75 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp16 | hskp10 | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp16 | hskp10 | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3354,plain,
% 1.53/1.75 ((hskp16 | hskp10 | (~ndr1_0) | c2_1(a1638) | c1_1(a1638) | (~c3_1(a1638))) <=> (hskp16 | hskp10 | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3355,plain,
% 1.53/1.75 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp16 | hskp10 | (~ndr1_0) | c2_1(a1638) | c1_1(a1638) | (~c3_1(a1638)))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp16 | hskp10 | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[3354])).
% 1.53/1.75 tff(3356,plain,
% 1.53/1.75 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp16 | hskp10 | (~ndr1_0) | c2_1(a1638) | c1_1(a1638) | (~c3_1(a1638)))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp16 | hskp10 | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[3355, 3353])).
% 1.53/1.75 tff(3357,plain,
% 1.53/1.75 ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp16 | hskp10 | (~ndr1_0) | c2_1(a1638) | c1_1(a1638) | (~c3_1(a1638)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(3358,plain,
% 1.53/1.75 ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp16 | hskp10 | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3357, 3356])).
% 1.53/1.75 tff(3359,plain,
% 1.53/1.75 (hskp16 | hskp10 | c2_1(a1638) | c1_1(a1638)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3358, 119, 1708, 973])).
% 1.53/1.75 tff(3360,plain,
% 1.53/1.75 (hskp16),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3359, 56, 1217, 1233])).
% 1.53/1.75 tff(3361,plain,
% 1.53/1.75 (~c1_1(a1667)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[986, 3360])).
% 1.53/1.75 tff(3362,plain,
% 1.53/1.75 (c2_1(a1634)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1011, 56, 504, 502, 503, 500])).
% 1.53/1.75 tff(3363,plain,
% 1.53/1.75 (hskp19 | (~c2_1(a1634))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[627, 119, 501, 502, 503, 621])).
% 1.53/1.75 tff(3364,plain,
% 1.53/1.75 (hskp19),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3363, 3362])).
% 1.53/1.75 tff(3365,plain,
% 1.53/1.75 (~c3_1(a1682)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[568, 3364])).
% 1.53/1.75 tff(3366,plain,
% 1.53/1.75 (c0_1(a1667)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1002, 3360])).
% 1.53/1.75 tff(3367,plain,
% 1.53/1.75 (c2_1(a1682)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[584, 3364])).
% 1.53/1.75 tff(3368,plain,
% 1.53/1.75 (c1_1(a1682)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[576, 3364])).
% 1.53/1.75 tff(3369,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a1650) | c3_1(a1682) | c1_1(a1667) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1682)) | (~c1_1(a1682)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1650) | c3_1(a1682) | c1_1(a1667) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1682)) | (~c1_1(a1682)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3370,plain,
% 1.53/1.75 (((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c1_1(a1650) | c0_1(a1650) | c3_1(a1650)) <=> (c1_1(a1650) | c3_1(a1682) | c1_1(a1667) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1682)) | (~c1_1(a1682)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3371,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c1_1(a1650) | c0_1(a1650) | c3_1(a1650))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a1650) | c3_1(a1682) | c1_1(a1667) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1682)) | (~c1_1(a1682))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[3370])).
% 1.53/1.75 tff(3372,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c1_1(a1650) | c0_1(a1650) | c3_1(a1650))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1650) | c3_1(a1682) | c1_1(a1667) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1682)) | (~c1_1(a1682)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[3371, 3369])).
% 1.53/1.75 tff(3373,plain,
% 1.53/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1682) | (~c2_1(a1682)) | (~c1_1(a1682)) | c1_1(a1667) | (~c3_1(a1667)) | (~c0_1(a1667)) | c1_1(a1650) | c0_1(a1650) | c3_1(a1650))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(3374,plain,
% 1.53/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1650) | c3_1(a1682) | c1_1(a1667) | c0_1(a1650) | c3_1(a1650) | (~ndr1_0) | (~c3_1(a1667)) | (~c0_1(a1667)) | (~c2_1(a1682)) | (~c1_1(a1682))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3373, 3372])).
% 1.53/1.75 tff(3375,plain,
% 1.53/1.75 (~c3_1(a1667)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3374, 119, 3368, 3367, 3366, 1175, 3365, 3361, 843, 842, 595])).
% 1.53/1.75 tff(3376,plain,
% 1.53/1.75 (c2_1(a1667)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[994, 3360])).
% 1.53/1.75 tff(3377,plain,
% 1.53/1.75 (~hskp9),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[610, 3364, 504, 502, 503])).
% 1.53/1.75 tff(3378,plain,
% 1.53/1.75 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp9 | hskp2 | c1_1(a1667) | (~ndr1_0) | c3_1(a1667) | (~c2_1(a1667)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp9 | hskp2 | c1_1(a1667) | (~ndr1_0) | c3_1(a1667) | (~c2_1(a1667)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3379,plain,
% 1.53/1.75 ((hskp9 | hskp2 | (~ndr1_0) | c1_1(a1667) | c3_1(a1667) | (~c2_1(a1667))) <=> (hskp9 | hskp2 | c1_1(a1667) | (~ndr1_0) | c3_1(a1667) | (~c2_1(a1667)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3380,plain,
% 1.53/1.75 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c1_1(a1667) | c3_1(a1667) | (~c2_1(a1667)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp9 | hskp2 | c1_1(a1667) | (~ndr1_0) | c3_1(a1667) | (~c2_1(a1667))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[3379])).
% 1.53/1.75 tff(3381,plain,
% 1.53/1.75 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c1_1(a1667) | c3_1(a1667) | (~c2_1(a1667)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp9 | hskp2 | c1_1(a1667) | (~ndr1_0) | c3_1(a1667) | (~c2_1(a1667)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[3380, 3378])).
% 1.53/1.75 tff(3382,plain,
% 1.53/1.75 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c1_1(a1667) | c3_1(a1667) | (~c2_1(a1667)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(3383,plain,
% 1.53/1.75 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp9 | hskp2 | c1_1(a1667) | (~ndr1_0) | c3_1(a1667) | (~c2_1(a1667))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3382, 3381])).
% 1.53/1.75 tff(3384,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3383, 119, 3377, 500, 3376, 3361, 532, 3375])).
% 1.53/1.75 tff(3385,plain,(hskp10 | hskp2 | c1_1(a1650) | c0_1(a1650) | c3_1(a1650) | (~c0_1(a1634)) | (~c3_1(a1634)) | c1_1(a1634) | hskp28 | c2_1(a1638) | c1_1(a1638) | (~c3_1(a1638))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(3386,plain,
% 1.53/1.75 (hskp10),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3385, 3344, 1175, 843, 842, 3352, 3351, 3350, 3348, 3346, 3347, 2742])).
% 1.53/1.75 tff(3387,plain,
% 1.53/1.75 (~c3_1(a1648)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[150, 3386])).
% 1.53/1.75 tff(3388,plain,
% 1.53/1.75 (c0_1(a1648)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[158, 3386])).
% 1.53/1.75 tff(3389,plain,
% 1.53/1.75 (c2_1(a1648)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[166, 3386])).
% 1.53/1.75 tff(3390,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[647, 3389, 3388, 3344, 3348, 3352, 3351, 3350, 3387])).
% 1.53/1.75 tff(3391,plain,(c1_1(a1650) | c0_1(a1650) | c3_1(a1650) | c0_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(3392,plain,
% 1.53/1.75 (c1_1(a1650)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3391, 843, 842, 22])).
% 1.53/1.75 tff(3393,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (c0_1(a1650) | c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | c0_1(a1650) | c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3394,plain,
% 1.53/1.75 (((~ndr1_0) | c0_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1638) | c0_1(a1638) | (~c3_1(a1638))) <=> (c0_1(a1650) | c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(3395,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | ((~ndr1_0) | c0_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1638) | c0_1(a1638) | (~c3_1(a1638)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (c0_1(a1650) | c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[3394])).
% 1.53/1.75 tff(3396,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | ((~ndr1_0) | c0_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1638) | c0_1(a1638) | (~c3_1(a1638)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | c0_1(a1650) | c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[3395, 3393])).
% 1.53/1.76 tff(3397,plain,
% 1.53/1.76 ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | ((~ndr1_0) | c0_1(a1650) | (~c2_1(a1650)) | (~c1_1(a1650)) | c1_1(a1638) | c0_1(a1638) | (~c3_1(a1638)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(3398,plain,
% 1.53/1.76 ((~![V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | c0_1(a1650) | c0_1(a1638) | (~ndr1_0) | c1_1(a1638) | (~c3_1(a1638)) | (~c2_1(a1650)) | (~c1_1(a1650))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[3397, 3396])).
% 1.53/1.76 tff(3399,plain,
% 1.53/1.76 (~c2_1(a1650)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3398, 119, 3392, 2742, 843, 22, 691, 3300])).
% 1.53/1.76 tff(3400,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | c2_1(a1650) | (~c1_1(a1650)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | c2_1(a1650) | (~c1_1(a1650)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(3401,plain,
% 1.53/1.76 (((~ndr1_0) | c2_1(a1650) | c0_1(a1650) | (~c1_1(a1650)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638)) <=> (c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | c2_1(a1650) | (~c1_1(a1650)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(3402,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1650) | c0_1(a1650) | (~c1_1(a1650)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | c2_1(a1650) | (~c1_1(a1650))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[3401])).
% 1.53/1.76 tff(3403,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1650) | c0_1(a1650) | (~c1_1(a1650)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | c2_1(a1650) | (~c1_1(a1650)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[3402, 3400])).
% 1.53/1.76 tff(3404,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1650) | c0_1(a1650) | (~c1_1(a1650)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650) | c2_1(a1638) | c1_1(a1638) | c0_1(a1638))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(3405,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | c2_1(a1638) | (~ndr1_0) | c1_1(a1638) | c2_1(a1650) | (~c1_1(a1650))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[3404, 3403])).
% 1.53/1.76 tff(3406,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3405, 119, 3392, 843, 842, 22, 1217, 1261, 3300, 3399])).
% 1.53/1.76 tff(3407,plain,(c2_1(a1638) | c0_1(a1650) | c3_1(a1650) | c0_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(3408,plain,
% 1.53/1.76 (c2_1(a1638)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3407, 843, 842, 22])).
% 1.53/1.76 tff(3409,plain,
% 1.53/1.76 (~hskp3),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1992, 3408])).
% 1.53/1.76 tff(3410,plain,
% 1.53/1.76 (hskp3 | c3_1(a1636) | (~c1_1(a1650))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1865, 119, 843, 842, 3294, 3293, 10])).
% 1.53/1.76 tff(3411,plain,
% 1.53/1.76 (c3_1(a1636)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3410, 3409, 3392])).
% 1.53/1.76 tff(3412,plain,
% 1.53/1.76 ((~c3_1(a1636)) | (~c2_1(a1650)) | (~c1_1(a1650))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1585, 119, 843, 3292, 3294, 691])).
% 1.53/1.76 tff(3413,plain,
% 1.53/1.76 (~c2_1(a1650)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3412, 3411, 3392])).
% 1.53/1.76 tff(3414,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | (~c2_1(a1638)) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c3_1(a1638)) | c2_1(a1650))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | (~c2_1(a1638)) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c3_1(a1638)) | c2_1(a1650))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(3415,plain,
% 1.53/1.76 (((~ndr1_0) | c0_1(a1638) | (~c2_1(a1638)) | (~c3_1(a1638)) | c2_1(a1636) | c0_1(a1636) | (~c3_1(a1636)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650)) <=> (c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | (~c2_1(a1638)) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c3_1(a1638)) | c2_1(a1650))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(3416,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1638) | (~c2_1(a1638)) | (~c3_1(a1638)) | c2_1(a1636) | c0_1(a1636) | (~c3_1(a1636)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | (~c2_1(a1638)) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c3_1(a1638)) | c2_1(a1650)))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[3415])).
% 1.53/1.76 tff(3417,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1638) | (~c2_1(a1638)) | (~c3_1(a1638)) | c2_1(a1636) | c0_1(a1636) | (~c3_1(a1636)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | (~c2_1(a1638)) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c3_1(a1638)) | c2_1(a1650))),
% 1.53/1.76 inference(transitivity,[status(thm)],[3416, 3414])).
% 1.53/1.76 tff(3418,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1638) | (~c2_1(a1638)) | (~c3_1(a1638)) | c2_1(a1636) | c0_1(a1636) | (~c3_1(a1636)) | c2_1(a1650) | c0_1(a1650) | c3_1(a1650))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(3419,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1650) | c3_1(a1650) | c0_1(a1638) | (~c2_1(a1638)) | c0_1(a1636) | c2_1(a1636) | (~ndr1_0) | (~c3_1(a1636)) | (~c3_1(a1638)) | c2_1(a1650)),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[3418, 3417])).
% 1.53/1.76 tff(3420,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3419, 119, 2742, 843, 842, 22, 3408, 3292, 3293, 1621, 3411, 3413])).
% 1.53/1.76 tff(3421,plain,(c0_1(a1650) | c3_1(a1650) | c0_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(3422,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3421, 3343, 3342, 22])).
% 1.53/1.76 tff(3423,plain,(c0_1(a1638)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(3424,plain,
% 1.53/1.76 (~hskp3),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1835, 3423])).
% 1.53/1.76 tff(3425,plain,
% 1.53/1.76 (hskp1 | hskp0),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2692, 3424])).
% 1.53/1.76 tff(3426,plain,
% 1.53/1.76 (hskp0),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3425, 21])).
% 1.53/1.76 tff(3427,plain,
% 1.53/1.76 (~c1_1(a1634)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[482, 3426])).
% 1.53/1.76 tff(3428,assumption,(hskp1), introduced(assumption)).
% 1.53/1.76 tff(3429,plain,
% 1.53/1.76 (~c1_1(a1636)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1537, 3428])).
% 1.53/1.76 tff(3430,plain,
% 1.53/1.76 (~c2_1(a1636)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1549, 3428])).
% 1.53/1.76 tff(3431,plain,
% 1.53/1.76 (~c0_1(a1636)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1543, 3428])).
% 1.53/1.76 tff(3432,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1672, 119, 3424, 500, 3431, 3429, 3430, 1045])).
% 1.53/1.76 tff(3433,plain,((~hskp1) | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(3434,plain,
% 1.53/1.76 (~hskp1),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3433, 500])).
% 1.53/1.76 tff(3435,plain,
% 1.53/1.76 (hskp0),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[476, 3434, 45])).
% 1.53/1.76 tff(3436,plain,
% 1.53/1.76 (~c1_1(a1634)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[482, 3435])).
% 1.53/1.76 tff(3437,plain,
% 1.53/1.76 (c0_1(a1634)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[498, 3435])).
% 1.53/1.76 tff(3438,plain,
% 1.53/1.76 (c3_1(a1634)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[490, 3435])).
% 1.53/1.76 tff(3439,plain,
% 1.53/1.76 (hskp2 | (~c0_1(a1634)) | (~c3_1(a1634)) | c1_1(a1634) | hskp1),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2583, 3424])).
% 1.53/1.76 tff(3440,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3439, 3438, 3437, 500, 3436, 3434])).
% 1.53/1.76 tff(3441,plain,(hskp2 | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(3442,plain,
% 1.53/1.76 (hskp2),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3441, 45])).
% 1.53/1.76 tff(3443,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2728, 3430, 3431, 45, 3442, 3429])).
% 1.53/1.76 tff(3444,plain,((~hskp1) | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(3445,plain,
% 1.53/1.76 (~hskp1),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3444, 45])).
% 1.53/1.76 tff(3446,plain,
% 1.53/1.76 (hskp0),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[476, 3445, 45])).
% 1.53/1.76 tff(3447,plain,
% 1.53/1.76 (~c0_1(a1637)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1124, 3442])).
% 1.53/1.76 tff(3448,plain,
% 1.53/1.76 (c3_1(a1637)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1132, 3442])).
% 1.53/1.76 tff(3449,plain,
% 1.53/1.76 (c1_1(a1637)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1140, 3442])).
% 1.53/1.76 tff(3450,plain,
% 1.53/1.76 (hskp0),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[476, 21, 45])).
% 1.53/1.76 tff(3451,plain,
% 1.53/1.76 (~hskp15),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2261, 3448, 45, 3449, 3447])).
% 1.53/1.76 tff(3452,plain,
% 1.53/1.76 (hskp19),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1450, 21, 3451])).
% 1.53/1.76 tff(3453,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2269, 3452, 3450, 3449, 3448, 3447, 503])).
% 1.53/1.76 tff(3454,plain,(hskp1 | c1_1(a1634) | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(3455,plain,
% 1.53/1.76 (c1_1(a1634)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3454, 3445, 45])).
% 1.53/1.76 tff(3456,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[482, 3455, 3446])).
% 1.53/1.76 tff(3457,plain,(hskp11), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(3458,plain,
% 1.53/1.76 (~c0_1(a1650)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[673, 3457])).
% 1.53/1.76 tff(3459,plain,
% 1.53/1.76 (c1_1(a1650)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[705, 3457])).
% 1.53/1.76 tff(3460,plain,
% 1.53/1.76 (~c3_1(a1650)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[667, 3457])).
% 1.53/1.76 tff(3461,plain,
% 1.53/1.76 (hskp2 | hskp1 | c3_1(a1650) | (~c1_1(a1650)) | c0_1(a1650)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2876, 3424])).
% 1.53/1.76 tff(3462,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3461, 3434, 500, 3460, 3459, 3458])).
% 1.53/1.76 tff(3463,plain,(hskp2), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(3464,plain,
% 1.53/1.76 (~c0_1(a1637)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1124, 3463])).
% 1.53/1.76 tff(3465,plain,
% 1.53/1.76 (c3_1(a1634)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[490, 3426])).
% 1.53/1.76 tff(3466,plain,
% 1.53/1.76 (c0_1(a1634)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[498, 3426])).
% 1.53/1.76 tff(3467,plain,
% 1.53/1.76 (c3_1(a1637)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1132, 3463])).
% 1.53/1.76 tff(3468,plain,
% 1.53/1.76 (c1_1(a1637)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1140, 3463])).
% 1.53/1.76 tff(3469,plain,
% 1.53/1.76 (~c2_1(a1650)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1167, 119, 3459, 3468, 3467, 3466, 3465, 3460, 3464, 3427, 20])).
% 1.53/1.76 tff(3470,plain,
% 1.53/1.76 (hskp10 | c1_1(a1634) | hskp1),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1170, 3424])).
% 1.53/1.76 tff(3471,plain,
% 1.53/1.76 (hskp10),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3470, 3427, 21])).
% 1.53/1.76 tff(3472,plain,
% 1.53/1.76 (~c3_1(a1648)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[150, 3471])).
% 1.53/1.76 tff(3473,plain,
% 1.53/1.76 (c2_1(a1648)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[166, 3471])).
% 1.53/1.76 tff(3474,plain,
% 1.53/1.76 (c0_1(a1648)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[158, 3471])).
% 1.53/1.76 tff(3475,plain,
% 1.53/1.76 (~c2_1(a1637)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2419, 119, 3474, 3473, 3468, 3458, 3460, 3472, 3464, 295, 3469])).
% 1.53/1.76 tff(3476,plain,
% 1.53/1.76 (~hskp19),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2269, 3426, 3468, 3467, 3464, 3427])).
% 1.53/1.76 tff(3477,plain,
% 1.53/1.76 (hskp15),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1450, 3476, 21])).
% 1.53/1.76 tff(3478,plain,
% 1.53/1.76 (~c2_1(a1664)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[333, 3477])).
% 1.53/1.76 tff(3479,plain,
% 1.53/1.76 (~c1_1(a1664)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[339, 3477])).
% 1.53/1.76 tff(3480,plain,
% 1.53/1.76 (c3_1(a1664)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1398, 119, 3424, 3459, 3479, 3478, 3458, 3460, 10])).
% 1.53/1.76 tff(3481,plain,
% 1.53/1.76 (^[U: $i] : refl((hskp29 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp29 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.53/1.76 inference(bind,[status(th)],[])).
% 1.53/1.76 tff(3482,plain,
% 1.53/1.76 (![U: $i] : (hskp29 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.53/1.76 inference(quant_intro,[status(thm)],[3481])).
% 1.53/1.76 tff(3483,plain,
% 1.53/1.76 (![U: $i] : (hskp29 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(3484,plain,
% 1.53/1.76 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp29) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp29))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp29) | hskp12) <=> ((hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp12))), rewrite(((hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp12) <=> (hskp29 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp29) | hskp12) <=> (hskp29 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.53/1.76 inference(bind,[status(th)],[])).
% 1.53/1.76 tff(3485,plain,
% 1.53/1.76 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp29) | hskp12) <=> ![U: $i] : (hskp29 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.53/1.76 inference(quant_intro,[status(thm)],[3484])).
% 1.53/1.76 tff(3486,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp29) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 1.53/1.76 tff(3487,plain,
% 1.53/1.76 (![U: $i] : (hskp29 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[3486, 3485])).
% 1.53/1.76 tff(3488,plain,
% 1.53/1.76 (![U: $i] : (hskp29 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[3487, 3483])).
% 1.53/1.76 tff(3489,plain,(
% 1.53/1.76 ![U: $i] : (hskp29 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.53/1.76 inference(skolemize,[status(sab)],[3488])).
% 1.53/1.76 tff(3490,plain,
% 1.53/1.76 (![U: $i] : (hskp29 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[3489, 3482])).
% 1.53/1.76 tff(3491,plain,
% 1.53/1.76 (c0_1(a1664)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[347, 3477])).
% 1.53/1.76 tff(3492,plain,
% 1.53/1.76 (~hskp12),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3106, 3479, 3491, 3459, 3478, 3458, 3460])).
% 1.53/1.76 tff(3493,plain,
% 1.53/1.76 (((~![U: $i] : (hskp29 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp29 | hskp12 | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)))) <=> ((~![U: $i] : (hskp29 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp29 | hskp12 | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(3494,plain,
% 1.53/1.76 ((hskp29 | hskp12 | (~ndr1_0) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634))) <=> (hskp29 | hskp12 | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(3495,plain,
% 1.53/1.76 (((~![U: $i] : (hskp29 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp29 | hskp12 | (~ndr1_0) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)))) <=> ((~![U: $i] : (hskp29 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp29 | hskp12 | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[3494])).
% 1.53/1.76 tff(3496,plain,
% 1.53/1.76 (((~![U: $i] : (hskp29 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp29 | hskp12 | (~ndr1_0) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)))) <=> ((~![U: $i] : (hskp29 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp29 | hskp12 | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[3495, 3493])).
% 1.53/1.76 tff(3497,plain,
% 1.53/1.76 ((~![U: $i] : (hskp29 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp29 | hskp12 | (~ndr1_0) | c1_1(a1634) | (~c3_1(a1634)) | (~c0_1(a1634)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(3498,plain,
% 1.53/1.76 ((~![U: $i] : (hskp29 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp29 | hskp12 | c1_1(a1634) | (~ndr1_0) | (~c3_1(a1634)) | (~c0_1(a1634))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[3497, 3496])).
% 1.53/1.76 tff(3499,plain,
% 1.53/1.76 (hskp29),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3498, 119, 3492, 3466, 3465, 3427, 3490])).
% 1.53/1.76 tff(3500,plain,
% 1.53/1.76 (c3_1(a1647)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1768, 3499])).
% 1.53/1.76 tff(3501,plain,
% 1.53/1.76 (c1_1(a1647)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1776, 3499])).
% 1.53/1.76 tff(3502,plain,
% 1.53/1.76 (c0_1(a1647)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1784, 3499])).
% 1.53/1.76 tff(3503,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c3_1(a1664)) | (~c3_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c3_1(a1664)) | (~c3_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(3504,plain,
% 1.53/1.76 (((~ndr1_0) | (~c3_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)) | (~c1_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | c2_1(a1664) | c1_1(a1664) | (~c3_1(a1664))) <=> (c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c3_1(a1664)) | (~c3_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(3505,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)) | (~c1_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | c2_1(a1664) | c1_1(a1664) | (~c3_1(a1664)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c3_1(a1664)) | (~c3_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[3504])).
% 1.53/1.76 tff(3506,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)) | (~c1_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | c2_1(a1664) | c1_1(a1664) | (~c3_1(a1664)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c3_1(a1664)) | (~c3_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[3505, 3503])).
% 1.53/1.76 tff(3507,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647)) | (~c1_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | c2_1(a1664) | c1_1(a1664) | (~c3_1(a1664)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(3508,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1664) | c2_1(a1664) | (~ndr1_0) | (~c3_1(a1664)) | (~c3_1(a1647)) | (~c2_1(a1647)) | (~c0_1(a1647)) | (~c1_1(a1647))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[3507, 3506])).
% 1.53/1.76 tff(3509,plain,
% 1.53/1.76 (~c2_1(a1647)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3508, 119, 3502, 3501, 3500, 3479, 3478, 1418, 3480])).
% 1.53/1.76 tff(3510,plain,
% 1.53/1.76 (((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | (~ndr1_0) | (~c3_1(a1647)) | c2_1(a1647) | (~c1_1(a1647)))) <=> ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp3 | (~ndr1_0) | (~c3_1(a1647)) | c2_1(a1647) | (~c1_1(a1647)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(3511,plain,
% 1.53/1.76 ((hskp21 | hskp3 | (~ndr1_0) | c2_1(a1647) | (~c3_1(a1647)) | (~c1_1(a1647))) <=> (hskp21 | hskp3 | (~ndr1_0) | (~c3_1(a1647)) | c2_1(a1647) | (~c1_1(a1647)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(3512,plain,
% 1.53/1.76 (((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | (~ndr1_0) | c2_1(a1647) | (~c3_1(a1647)) | (~c1_1(a1647)))) <=> ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | (~ndr1_0) | (~c3_1(a1647)) | c2_1(a1647) | (~c1_1(a1647))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[3511])).
% 1.53/1.76 tff(3513,plain,
% 1.53/1.76 (((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | (~ndr1_0) | c2_1(a1647) | (~c3_1(a1647)) | (~c1_1(a1647)))) <=> ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp3 | (~ndr1_0) | (~c3_1(a1647)) | c2_1(a1647) | (~c1_1(a1647)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[3512, 3510])).
% 1.53/1.76 tff(3514,plain,
% 1.53/1.76 ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp3 | (~ndr1_0) | c2_1(a1647) | (~c3_1(a1647)) | (~c1_1(a1647)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(3515,plain,
% 1.53/1.76 ((~![U: $i] : (hskp21 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp3 | (~ndr1_0) | (~c3_1(a1647)) | c2_1(a1647) | (~c1_1(a1647))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[3514, 3513])).
% 1.53/1.76 tff(3516,plain,
% 1.53/1.76 (hskp21),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3515, 119, 3424, 3501, 3500, 769, 3509])).
% 1.53/1.76 tff(3517,plain,
% 1.53/1.76 (~c1_1(a1691)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[697, 3516])).
% 1.53/1.76 tff(3518,plain,
% 1.53/1.76 (c3_1(a1691)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[713, 3516])).
% 1.53/1.76 tff(3519,plain,
% 1.53/1.76 (c2_1(a1691)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[738, 3516])).
% 1.53/1.76 tff(3520,plain,
% 1.53/1.76 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c1_1(a1691) | c0_1(a1637) | (~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c3_1(a1691)) | (~c2_1(a1691)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c1_1(a1691) | c0_1(a1637) | (~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c3_1(a1691)) | (~c2_1(a1691)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(3521,plain,
% 1.53/1.76 ((hskp12 | (~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691)) | c2_1(a1637) | c0_1(a1637) | (~c3_1(a1637))) <=> (hskp12 | c1_1(a1691) | c0_1(a1637) | (~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c3_1(a1691)) | (~c2_1(a1691)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(3522,plain,
% 1.53/1.76 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691)) | c2_1(a1637) | c0_1(a1637) | (~c3_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c1_1(a1691) | c0_1(a1637) | (~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c3_1(a1691)) | (~c2_1(a1691))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[3521])).
% 1.53/1.76 tff(3523,plain,
% 1.53/1.76 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691)) | c2_1(a1637) | c0_1(a1637) | (~c3_1(a1637)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c1_1(a1691) | c0_1(a1637) | (~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c3_1(a1691)) | (~c2_1(a1691)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[3522, 3520])).
% 1.53/1.76 tff(3524,plain,
% 1.53/1.76 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c1_1(a1691) | (~c2_1(a1691)) | (~c3_1(a1691)) | c2_1(a1637) | c0_1(a1637) | (~c3_1(a1637)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(3525,plain,
% 1.53/1.76 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c1_1(a1691) | c0_1(a1637) | (~ndr1_0) | c2_1(a1637) | (~c3_1(a1637)) | (~c3_1(a1691)) | (~c2_1(a1691))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[3524, 3523])).
% 1.53/1.76 tff(3526,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3525, 119, 3492, 3519, 3518, 3467, 3517, 3464, 3117, 3475])).
% 1.53/1.76 tff(3527,plain,(hskp1), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(3528,plain,
% 1.53/1.76 (~c2_1(a1636)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1549, 3527])).
% 1.53/1.76 tff(3529,plain,
% 1.53/1.76 (~c1_1(a1636)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1537, 3527])).
% 1.53/1.76 tff(3530,plain,
% 1.53/1.76 (c3_1(a1636)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1865, 119, 3424, 3459, 3458, 3460, 3529, 3528, 10])).
% 1.53/1.76 tff(3531,plain,
% 1.53/1.76 (~c0_1(a1636)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1543, 3527])).
% 1.53/1.76 tff(3532,plain,
% 1.53/1.76 ((~c3_1(a1636)) | (~c2_1(a1650))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1585, 119, 3459, 3458, 3531, 3529, 691])).
% 1.53/1.76 tff(3533,plain,
% 1.53/1.76 (~c2_1(a1650)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3532, 3530])).
% 1.53/1.76 tff(3534,plain,
% 1.53/1.76 ((~c3_1(a1636)) | (~c2_1(a1637))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1872, 119, 3468, 3464, 3531, 3529, 691])).
% 1.53/1.76 tff(3535,plain,
% 1.53/1.76 (~c2_1(a1637)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3534, 3530])).
% 1.53/1.76 tff(3536,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1880, 119, 3468, 3458, 3460, 3464, 3531, 3529, 3528, 1261, 3535, 3533])).
% 1.53/1.77 % SZS output end Proof
% 1.53/1.77 % E exiting
%------------------------------------------------------------------------------