%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN468-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:39:14 AM UTC 2025
% Result : Unsatisfiable 0.72s 0.92s
% Output : Proof 0.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN468-1 : TPTP v9.0.0. Released v2.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:36:42 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.72/0.92 % SZS status Unsatisfiable
% 0.72/0.92 % SZS output start Proof
% 0.72/0.92 tff(hskp7_type, type, (
% 0.72/0.92 hskp7: $o)).
% 0.72/0.92 tff(c3_1_type, type, (
% 0.72/0.92 c3_1: $i > $o)).
% 0.72/0.92 tff(a297_type, type, (
% 0.72/0.92 a297: $i)).
% 0.72/0.92 tff(c1_1_type, type, (
% 0.72/0.92 c1_1: $i > $o)).
% 0.72/0.92 tff(a301_type, type, (
% 0.72/0.92 a301: $i)).
% 0.72/0.92 tff(c2_1_type, type, (
% 0.72/0.92 c2_1: $i > $o)).
% 0.72/0.92 tff(a300_type, type, (
% 0.72/0.92 a300: $i)).
% 0.72/0.92 tff(c0_1_type, type, (
% 0.72/0.92 c0_1: $i > $o)).
% 0.72/0.92 tff(ndr1_0_type, type, (
% 0.72/0.92 ndr1_0: $o)).
% 0.72/0.92 tff(hskp5_type, type, (
% 0.72/0.92 hskp5: $o)).
% 0.72/0.92 tff(a315_type, type, (
% 0.72/0.92 a315: $i)).
% 0.72/0.92 tff(hskp16_type, type, (
% 0.72/0.92 hskp16: $o)).
% 0.72/0.92 tff(hskp24_type, type, (
% 0.72/0.92 hskp24: $o)).
% 0.72/0.92 tff(a294_type, type, (
% 0.72/0.92 a294: $i)).
% 0.72/0.92 tff(hskp3_type, type, (
% 0.72/0.92 hskp3: $o)).
% 0.72/0.92 tff(hskp29_type, type, (
% 0.72/0.92 hskp29: $o)).
% 0.72/0.92 tff(hskp4_type, type, (
% 0.72/0.92 hskp4: $o)).
% 0.72/0.92 tff(a306_type, type, (
% 0.72/0.92 a306: $i)).
% 0.72/0.92 tff(hskp11_type, type, (
% 0.72/0.92 hskp11: $o)).
% 0.72/0.92 tff(a299_type, type, (
% 0.72/0.92 a299: $i)).
% 0.72/0.92 tff(hskp22_type, type, (
% 0.72/0.92 hskp22: $o)).
% 0.72/0.92 tff(a331_type, type, (
% 0.72/0.92 a331: $i)).
% 0.72/0.92 tff(hskp31_type, type, (
% 0.72/0.92 hskp31: $o)).
% 0.72/0.92 tff(hskp27_type, type, (
% 0.72/0.92 hskp27: $o)).
% 0.72/0.92 tff(a368_type, type, (
% 0.72/0.92 a368: $i)).
% 0.72/0.92 tff(hskp26_type, type, (
% 0.72/0.92 hskp26: $o)).
% 0.72/0.92 tff(a367_type, type, (
% 0.72/0.92 a367: $i)).
% 0.72/0.92 tff(a359_type, type, (
% 0.72/0.92 a359: $i)).
% 0.72/0.92 tff(a308_type, type, (
% 0.72/0.92 a308: $i)).
% 0.72/0.92 tff(a341_type, type, (
% 0.72/0.92 a341: $i)).
% 0.72/0.92 tff(hskp8_type, type, (
% 0.72/0.92 hskp8: $o)).
% 0.72/0.92 tff(hskp13_type, type, (
% 0.72/0.92 hskp13: $o)).
% 0.72/0.92 tff(a311_type, type, (
% 0.72/0.92 a311: $i)).
% 0.72/0.92 tff(hskp15_type, type, (
% 0.72/0.92 hskp15: $o)).
% 0.72/0.92 tff(a337_type, type, (
% 0.72/0.92 a337: $i)).
% 0.72/0.92 tff(hskp23_type, type, (
% 0.72/0.92 hskp23: $o)).
% 0.72/0.92 tff(hskp12_type, type, (
% 0.72/0.92 hskp12: $o)).
% 0.72/0.92 tff(a291_type, type, (
% 0.72/0.92 a291: $i)).
% 0.72/0.92 tff(hskp0_type, type, (
% 0.72/0.92 hskp0: $o)).
% 0.72/0.92 tff(a307_type, type, (
% 0.72/0.92 a307: $i)).
% 0.72/0.92 tff(a295_type, type, (
% 0.72/0.92 a295: $i)).
% 0.72/0.92 tff(a304_type, type, (
% 0.72/0.92 a304: $i)).
% 0.72/0.92 tff(hskp9_type, type, (
% 0.72/0.92 hskp9: $o)).
% 0.72/0.92 tff(a296_type, type, (
% 0.72/0.92 a296: $i)).
% 0.72/0.92 tff(hskp2_type, type, (
% 0.72/0.92 hskp2: $o)).
% 0.72/0.92 tff(hskp28_type, type, (
% 0.72/0.92 hskp28: $o)).
% 0.72/0.92 tff(a293_type, type, (
% 0.72/0.92 a293: $i)).
% 0.72/0.92 tff(a330_type, type, (
% 0.72/0.92 a330: $i)).
% 0.72/0.92 tff(hskp21_type, type, (
% 0.72/0.92 hskp21: $o)).
% 0.72/0.92 tff(a329_type, type, (
% 0.72/0.92 a329: $i)).
% 0.72/0.92 tff(hskp20_type, type, (
% 0.72/0.92 hskp20: $o)).
% 0.72/0.92 tff(a325_type, type, (
% 0.72/0.92 a325: $i)).
% 0.72/0.92 tff(hskp18_type, type, (
% 0.72/0.92 hskp18: $o)).
% 0.72/0.92 tff(1,assumption,(~c3_1(a297)), introduced(assumption)).
% 0.72/0.92 tff(2,plain,
% 0.72/0.92 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 0.72/0.92 inference(bind,[status(th)],[])).
% 0.72/0.92 tff(3,plain,
% 0.72/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.72/0.92 inference(quant_intro,[status(thm)],[2])).
% 0.72/0.92 tff(4,plain,
% 0.72/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(5,plain,
% 0.72/0.92 (^[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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 0.72/0.92 inference(bind,[status(th)],[])).
% 0.72/0.92 tff(6,plain,
% 0.72/0.92 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.72/0.92 inference(quant_intro,[status(thm)],[5])).
% 0.72/0.92 tff(7,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause195')).
% 0.72/0.92 tff(8,plain,
% 0.72/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.72/0.92 tff(9,plain,
% 0.72/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.72/0.92 tff(10,plain,(
% 0.72/0.92 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.72/0.92 inference(skolemize,[status(sab)],[9])).
% 0.72/0.92 tff(11,plain,
% 0.72/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.72/0.92 tff(12,plain,
% 0.72/0.92 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))),
% 0.72/0.92 inference(bind,[status(th)],[])).
% 0.72/0.92 tff(13,plain,
% 0.72/0.92 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.72/0.92 inference(quant_intro,[status(thm)],[12])).
% 0.72/0.92 tff(14,plain,
% 0.72/0.92 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(15,plain,
% 0.72/0.92 (^[V: $i, U: $i] : 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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))))),
% 0.72/0.92 inference(bind,[status(th)],[])).
% 0.72/0.92 tff(16,plain,
% 0.72/0.92 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.72/0.92 inference(quant_intro,[status(thm)],[15])).
% 0.72/0.92 tff(17,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 0.72/0.92 tff(18,plain,
% 0.72/0.92 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.72/0.92 tff(19,plain,
% 0.72/0.92 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.72/0.92 tff(20,plain,(
% 0.72/0.92 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.72/0.92 inference(skolemize,[status(sab)],[19])).
% 0.72/0.92 tff(21,plain,
% 0.72/0.92 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.72/0.92 tff(22,plain,
% 0.72/0.92 (^[U: $i] : refl((hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.72/0.92 inference(bind,[status(th)],[])).
% 0.72/0.92 tff(23,plain,
% 0.72/0.92 (![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.72/0.92 inference(quant_intro,[status(thm)],[22])).
% 0.72/0.92 tff(24,plain,
% 0.72/0.92 (![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(25,plain,
% 0.72/0.92 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp24))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp24) <=> (hskp24 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) <=> (hskp24 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp16) <=> ((hskp24 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp16))), rewrite(((hskp24 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp16) <=> (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp16) <=> (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.72/0.92 inference(bind,[status(th)],[])).
% 0.72/0.92 tff(26,plain,
% 0.72/0.92 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp16) <=> ![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.72/0.92 inference(quant_intro,[status(thm)],[25])).
% 0.72/0.92 tff(27,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 0.72/0.92 tff(28,plain,
% 0.72/0.92 (![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.72/0.92 tff(29,plain,
% 0.72/0.92 (![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.72/0.92 tff(30,plain,(
% 0.72/0.92 ![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.72/0.92 inference(skolemize,[status(sab)],[29])).
% 0.72/0.92 tff(31,plain,
% 0.72/0.92 (![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.72/0.92 tff(32,assumption,(~hskp16), introduced(assumption)).
% 0.72/0.92 tff(33,plain,
% 0.72/0.92 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 0.72/0.92 inference(bind,[status(th)],[])).
% 0.72/0.92 tff(34,plain,
% 0.72/0.92 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.72/0.92 inference(quant_intro,[status(thm)],[33])).
% 0.72/0.92 tff(35,plain,
% 0.72/0.92 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(36,plain,
% 0.72/0.92 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V)))), ((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V))), ((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)))), (((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp4) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp4))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 0.72/0.92 inference(bind,[status(th)],[])).
% 0.72/0.92 tff(37,plain,
% 0.72/0.92 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.72/0.92 inference(quant_intro,[status(thm)],[36])).
% 0.72/0.92 tff(38,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 0.72/0.92 tff(39,plain,
% 0.72/0.92 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.72/0.92 tff(40,plain,
% 0.72/0.92 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.72/0.92 tff(41,plain,(
% 0.72/0.92 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.72/0.92 inference(skolemize,[status(sab)],[40])).
% 0.72/0.92 tff(42,plain,
% 0.72/0.92 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.72/0.92 tff(43,plain,
% 0.72/0.92 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 0.72/0.92 inference(bind,[status(th)],[])).
% 0.72/0.92 tff(44,plain,
% 0.72/0.92 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.72/0.92 inference(quant_intro,[status(thm)],[43])).
% 0.72/0.92 tff(45,plain,
% 0.72/0.92 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(46,plain,
% 0.72/0.92 (^[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) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp7))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.72/0.93 inference(bind,[status(th)],[])).
% 0.72/0.93 tff(47,plain,
% 0.72/0.93 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.72/0.93 inference(quant_intro,[status(thm)],[46])).
% 0.72/0.93 tff(48,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 0.72/0.93 tff(49,plain,
% 0.72/0.93 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.72/0.93 tff(50,plain,
% 0.72/0.93 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.72/0.93 tff(51,plain,(
% 0.72/0.93 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.72/0.93 inference(skolemize,[status(sab)],[50])).
% 0.72/0.93 tff(52,plain,
% 0.72/0.93 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.72/0.93 tff(53,assumption,(~hskp29), introduced(assumption)).
% 0.72/0.93 tff(54,plain,
% 0.72/0.93 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.72/0.93 inference(bind,[status(th)],[])).
% 0.72/0.93 tff(55,plain,
% 0.72/0.93 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.72/0.93 inference(quant_intro,[status(thm)],[54])).
% 0.72/0.93 tff(56,plain,
% 0.72/0.93 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(57,plain,
% 0.72/0.93 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp29))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.72/0.93 inference(bind,[status(th)],[])).
% 0.72/0.93 tff(58,plain,
% 0.72/0.93 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.72/0.93 inference(quant_intro,[status(thm)],[57])).
% 0.72/0.93 tff(59,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 0.72/0.93 tff(60,plain,
% 0.72/0.93 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.72/0.93 tff(61,plain,
% 0.72/0.93 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.72/0.93 tff(62,plain,(
% 0.72/0.93 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.72/0.93 inference(skolemize,[status(sab)],[61])).
% 0.72/0.93 tff(63,plain,
% 0.72/0.93 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.72/0.93 tff(64,assumption,(~hskp3), introduced(assumption)).
% 0.72/0.93 tff(65,assumption,(hskp22), introduced(assumption)).
% 0.72/0.93 tff(66,plain,
% 0.72/0.93 (((~hskp22) | (~c2_1(a331))) <=> ((~hskp22) | (~c2_1(a331)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(67,plain,
% 0.72/0.93 (((~c2_1(a331)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a331)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(68,axiom,((~c2_1(a331)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 0.72/0.93 tff(69,plain,
% 0.72/0.93 ((~hskp22) | (~c2_1(a331))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.72/0.93 tff(70,plain,
% 0.72/0.93 ((~hskp22) | (~c2_1(a331))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[69, 66])).
% 0.72/0.93 tff(71,plain,
% 0.72/0.93 (~c2_1(a331)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[70, 65])).
% 0.72/0.93 tff(72,plain,
% 0.72/0.93 (((~hskp22) | (~c1_1(a331))) <=> ((~hskp22) | (~c1_1(a331)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(73,plain,
% 0.72/0.93 (((~c1_1(a331)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a331)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(74,axiom,((~c1_1(a331)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 0.72/0.93 tff(75,plain,
% 0.72/0.93 ((~hskp22) | (~c1_1(a331))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.72/0.93 tff(76,plain,
% 0.72/0.93 ((~hskp22) | (~c1_1(a331))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[75, 72])).
% 0.72/0.93 tff(77,plain,
% 0.72/0.93 (~c1_1(a331)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[76, 65])).
% 0.72/0.93 tff(78,plain,
% 0.72/0.93 (((~hskp22) | (~c3_1(a331))) <=> ((~hskp22) | (~c3_1(a331)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(79,plain,
% 0.72/0.93 (((~c3_1(a331)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a331)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(80,axiom,((~c3_1(a331)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 0.72/0.93 tff(81,plain,
% 0.72/0.93 ((~hskp22) | (~c3_1(a331))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.72/0.93 tff(82,plain,
% 0.72/0.93 ((~hskp22) | (~c3_1(a331))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[81, 78])).
% 0.72/0.93 tff(83,plain,
% 0.72/0.93 (~c3_1(a331)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[82, 65])).
% 0.72/0.93 tff(84,plain,
% 0.72/0.93 (^[U: $i] : refl((hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 0.72/0.93 inference(bind,[status(th)],[])).
% 0.72/0.93 tff(85,plain,
% 0.72/0.93 (![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.72/0.93 inference(quant_intro,[status(thm)],[84])).
% 0.72/0.93 tff(86,plain,
% 0.72/0.93 (![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(87,plain,
% 0.72/0.93 (^[U: $i] : 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)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 0.72/0.93 inference(bind,[status(th)],[])).
% 0.72/0.93 tff(88,plain,
% 0.72/0.93 (![U: $i] : (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) <=> ![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.72/0.93 inference(quant_intro,[status(thm)],[87])).
% 0.72/0.93 tff(89,axiom,(![U: $i] : (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 0.72/0.93 tff(90,plain,
% 0.72/0.93 (![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.72/0.93 tff(91,plain,
% 0.72/0.93 (![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.72/0.93 tff(92,plain,(
% 0.72/0.93 ![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.72/0.93 inference(skolemize,[status(sab)],[91])).
% 0.72/0.93 tff(93,plain,
% 0.72/0.93 (![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.72/0.93 tff(94,assumption,(~c3_1(a331)), introduced(assumption)).
% 0.72/0.93 tff(95,assumption,(~c1_1(a331)), introduced(assumption)).
% 0.72/0.93 tff(96,assumption,(~ndr1_0), introduced(assumption)).
% 0.72/0.93 tff(97,plain,
% 0.72/0.93 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(98,plain,
% 0.72/0.93 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(99,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause8')).
% 0.72/0.93 tff(100,plain,
% 0.72/0.93 (ndr1_0 | (~hskp24)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.72/0.93 tff(101,plain,
% 0.72/0.93 (ndr1_0 | (~hskp24)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[100, 97])).
% 0.72/0.93 tff(102,plain,
% 0.72/0.93 (~hskp24),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[101, 96])).
% 0.72/0.93 tff(103,plain,
% 0.72/0.93 (((~hskp31) | ndr1_0) <=> ((~hskp31) | ndr1_0)),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(104,axiom,((~hskp31) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 0.72/0.93 tff(105,plain,
% 0.72/0.93 ((~hskp31) | ndr1_0),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.72/0.93 tff(106,plain,
% 0.72/0.93 ((~hskp31) | ndr1_0),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[105, 103])).
% 0.72/0.93 tff(107,plain,
% 0.72/0.93 ((~hskp31) | ndr1_0),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[106, 103])).
% 0.72/0.93 tff(108,plain,
% 0.72/0.93 ((~hskp31) | ndr1_0),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.72/0.93 tff(109,plain,
% 0.72/0.93 ((~hskp31) | ndr1_0),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[108, 103])).
% 0.72/0.93 tff(110,plain,
% 0.72/0.93 (~hskp31),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[109, 96])).
% 0.72/0.93 tff(111,plain,
% 0.72/0.93 ((ndr1_0 | (~hskp27)) <=> (ndr1_0 | (~hskp27))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(112,plain,
% 0.72/0.93 (((~hskp27) | ndr1_0) <=> (ndr1_0 | (~hskp27))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(113,axiom,((~hskp27) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause5')).
% 0.72/0.93 tff(114,plain,
% 0.72/0.93 (ndr1_0 | (~hskp27)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.72/0.93 tff(115,plain,
% 0.72/0.93 (ndr1_0 | (~hskp27)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[114, 111])).
% 0.72/0.93 tff(116,plain,
% 0.72/0.93 (~hskp27),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[115, 96])).
% 0.72/0.93 tff(117,plain,
% 0.72/0.93 ((hskp31 | hskp27 | hskp24) <=> (hskp31 | hskp27 | hskp24)),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(118,plain,
% 0.72/0.93 (((hskp31 | hskp27) | hskp24) <=> (hskp31 | hskp27 | hskp24)),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(119,plain,
% 0.72/0.93 ((hskp31 | hskp27) <=> (hskp31 | hskp27)),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(120,plain,
% 0.72/0.93 (((hskp31 | hskp27) | hskp24) <=> ((hskp31 | hskp27) | hskp24)),
% 0.72/0.93 inference(monotonicity,[status(thm)],[119])).
% 0.72/0.93 tff(121,plain,
% 0.72/0.93 (((hskp31 | hskp27) | hskp24) <=> (hskp31 | hskp27 | hskp24)),
% 0.72/0.93 inference(transitivity,[status(thm)],[120, 118])).
% 0.72/0.93 tff(122,axiom,((hskp31 | hskp27) | hskp24), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 0.72/0.93 tff(123,plain,
% 0.72/0.93 (hskp31 | hskp27 | hskp24),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.72/0.93 tff(124,plain,
% 0.72/0.93 (hskp31 | hskp27 | hskp24),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[123, 117])).
% 0.72/0.93 tff(125,plain,
% 0.72/0.93 (hskp31 | hskp27 | hskp24),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.72/0.93 tff(126,plain,
% 0.72/0.93 (hskp31 | hskp27 | hskp24),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[125, 117])).
% 0.72/0.93 tff(127,plain,
% 0.72/0.93 (hskp31 | hskp27 | hskp24),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[126, 117])).
% 0.72/0.93 tff(128,plain,
% 0.72/0.93 ($false),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[127, 116, 110, 102])).
% 0.72/0.93 tff(129,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.72/0.93 tff(130,plain,
% 0.72/0.93 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | c1_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c1_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(131,plain,
% 0.72/0.93 ((hskp3 | (~ndr1_0) | c3_1(a331) | c1_1(a331) | c0_1(a331)) <=> (hskp3 | c1_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(132,plain,
% 0.72/0.93 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a331) | c1_1(a331) | c0_1(a331))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | c1_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331)))),
% 0.72/0.93 inference(monotonicity,[status(thm)],[131])).
% 0.72/0.93 tff(133,plain,
% 0.72/0.93 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a331) | c1_1(a331) | c0_1(a331))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c1_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331))),
% 0.72/0.93 inference(transitivity,[status(thm)],[132, 130])).
% 0.72/0.93 tff(134,plain,
% 0.72/0.93 ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a331) | c1_1(a331) | c0_1(a331))),
% 0.72/0.93 inference(quant_inst,[status(thm)],[])).
% 0.72/0.93 tff(135,plain,
% 0.72/0.93 ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c1_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.72/0.93 tff(136,plain,
% 0.72/0.93 (hskp3 | c0_1(a331)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[135, 129, 95, 94, 93])).
% 0.72/0.93 tff(137,plain,
% 0.72/0.93 (c0_1(a331)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[136, 64])).
% 0.72/0.93 tff(138,plain,
% 0.72/0.93 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 0.72/0.93 inference(bind,[status(th)],[])).
% 0.72/0.93 tff(139,plain,
% 0.72/0.93 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.72/0.93 inference(quant_intro,[status(thm)],[138])).
% 0.72/0.93 tff(140,plain,
% 0.72/0.93 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(141,plain,
% 0.72/0.93 (^[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)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 0.72/0.93 inference(bind,[status(th)],[])).
% 0.72/0.93 tff(142,plain,
% 0.72/0.93 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.72/0.93 inference(quant_intro,[status(thm)],[141])).
% 0.72/0.93 tff(143,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 0.72/0.93 tff(144,plain,
% 0.72/0.93 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.72/0.93 tff(145,plain,
% 0.72/0.93 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.72/0.93 tff(146,plain,(
% 0.72/0.93 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.72/0.93 inference(skolemize,[status(sab)],[145])).
% 0.72/0.93 tff(147,plain,
% 0.72/0.93 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[146, 139])).
% 0.72/0.93 tff(148,assumption,(~c2_1(a331)), introduced(assumption)).
% 0.72/0.93 tff(149,plain,
% 0.72/0.93 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c1_1(a331) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | (~c0_1(a331)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c1_1(a331) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | (~c0_1(a331)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(150,plain,
% 0.72/0.93 ((hskp3 | (~ndr1_0) | c3_1(a331) | c1_1(a331) | (~c0_1(a331)) | c2_1(a331) | c1_1(a331) | c3_1(a331)) <=> (hskp3 | c1_1(a331) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | (~c0_1(a331)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(151,plain,
% 0.72/0.93 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a331) | c1_1(a331) | (~c0_1(a331)) | c2_1(a331) | c1_1(a331) | c3_1(a331))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c1_1(a331) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | (~c0_1(a331))))),
% 0.72/0.93 inference(monotonicity,[status(thm)],[150])).
% 0.72/0.93 tff(152,plain,
% 0.72/0.93 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a331) | c1_1(a331) | (~c0_1(a331)) | c2_1(a331) | c1_1(a331) | c3_1(a331))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c1_1(a331) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | (~c0_1(a331)))),
% 0.72/0.93 inference(transitivity,[status(thm)],[151, 149])).
% 0.72/0.93 tff(153,plain,
% 0.72/0.93 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a331) | c1_1(a331) | (~c0_1(a331)) | c2_1(a331) | c1_1(a331) | c3_1(a331))),
% 0.72/0.93 inference(quant_inst,[status(thm)],[])).
% 0.72/0.93 tff(154,plain,
% 0.72/0.93 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c1_1(a331) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | (~c0_1(a331))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.72/0.93 tff(155,plain,
% 0.72/0.93 (hskp3 | (~c0_1(a331))),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[154, 129, 95, 148, 94, 147])).
% 0.72/0.93 tff(156,plain,
% 0.72/0.93 ($false),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[155, 137, 64])).
% 0.72/0.93 tff(157,plain,(hskp3 | c1_1(a331) | c2_1(a331) | c3_1(a331)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.93 tff(158,plain,
% 0.72/0.93 ($false),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[157, 83, 77, 64, 71])).
% 0.72/0.93 tff(159,plain,((~hskp22) | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.72/0.93 tff(160,plain,
% 0.72/0.93 (~hskp22),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[159, 64])).
% 0.72/0.93 tff(161,plain,
% 0.72/0.93 (^[U: $i] : refl((hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 0.72/0.93 inference(bind,[status(th)],[])).
% 0.72/0.93 tff(162,plain,
% 0.72/0.93 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.72/0.93 inference(quant_intro,[status(thm)],[161])).
% 0.72/0.93 tff(163,plain,
% 0.72/0.93 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(164,plain,
% 0.72/0.93 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp3))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) | hskp26) <=> ((hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp26))), rewrite(((hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp26) <=> (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) | hskp26) <=> (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.72/0.93 inference(bind,[status(th)],[])).
% 0.72/0.93 tff(165,plain,
% 0.72/0.93 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) | hskp26) <=> ![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.72/0.93 inference(quant_intro,[status(thm)],[164])).
% 0.72/0.93 tff(166,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) | hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause165')).
% 0.72/0.93 tff(167,plain,
% 0.72/0.93 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.72/0.93 tff(168,plain,
% 0.72/0.93 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.72/0.93 tff(169,plain,(
% 0.72/0.93 ![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.72/0.93 inference(skolemize,[status(sab)],[168])).
% 0.72/0.93 tff(170,plain,
% 0.72/0.93 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[169, 162])).
% 0.72/0.93 tff(171,assumption,(hskp31), introduced(assumption)).
% 0.72/0.93 tff(172,plain,
% 0.72/0.93 (((~hskp31) | c2_1(a367)) <=> ((~hskp31) | c2_1(a367))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(173,axiom,((~hskp31) | c2_1(a367)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 0.72/0.93 tff(174,plain,
% 0.72/0.93 ((~hskp31) | c2_1(a367)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.72/0.93 tff(175,plain,
% 0.72/0.93 ((~hskp31) | c2_1(a367)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[174, 172])).
% 0.72/0.93 tff(176,plain,
% 0.72/0.93 ((~hskp31) | c2_1(a367)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[175, 172])).
% 0.72/0.93 tff(177,plain,
% 0.72/0.93 ((~hskp31) | c2_1(a367)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[176, 172])).
% 0.72/0.93 tff(178,plain,
% 0.72/0.93 ((~hskp31) | c2_1(a367)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[177, 172])).
% 0.72/0.93 tff(179,plain,
% 0.72/0.93 (c2_1(a367)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[178, 171])).
% 0.72/0.93 tff(180,plain,
% 0.72/0.93 (((~hskp31) | c1_1(a367)) <=> ((~hskp31) | c1_1(a367))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(181,axiom,((~hskp31) | c1_1(a367)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 0.72/0.93 tff(182,plain,
% 0.72/0.93 ((~hskp31) | c1_1(a367)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.72/0.93 tff(183,plain,
% 0.72/0.93 ((~hskp31) | c1_1(a367)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[182, 180])).
% 0.72/0.93 tff(184,plain,
% 0.72/0.93 ((~hskp31) | c1_1(a367)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[183, 180])).
% 0.72/0.93 tff(185,plain,
% 0.72/0.93 ((~hskp31) | c1_1(a367)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[184, 180])).
% 0.72/0.93 tff(186,plain,
% 0.72/0.93 ((~hskp31) | c1_1(a367)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[185, 180])).
% 0.72/0.93 tff(187,plain,
% 0.72/0.93 (c1_1(a367)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[186, 171])).
% 0.72/0.93 tff(188,plain,
% 0.72/0.93 (((~hskp31) | c0_1(a367)) <=> ((~hskp31) | c0_1(a367))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(189,axiom,((~hskp31) | c0_1(a367)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 0.78/0.93 tff(190,plain,
% 0.78/0.93 ((~hskp31) | c0_1(a367)),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.78/0.93 tff(191,plain,
% 0.78/0.93 ((~hskp31) | c0_1(a367)),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[190, 188])).
% 0.78/0.93 tff(192,plain,
% 0.78/0.93 ((~hskp31) | c0_1(a367)),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[191, 188])).
% 0.78/0.93 tff(193,plain,
% 0.78/0.93 ((~hskp31) | c0_1(a367)),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[192, 188])).
% 0.78/0.93 tff(194,plain,
% 0.78/0.93 ((~hskp31) | c0_1(a367)),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[193, 188])).
% 0.78/0.93 tff(195,plain,
% 0.78/0.93 (c0_1(a367)),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[194, 171])).
% 0.78/0.93 tff(196,assumption,(hskp26), introduced(assumption)).
% 0.78/0.93 tff(197,plain,
% 0.78/0.93 (((~hskp26) | (~c3_1(a359))) <=> ((~hskp26) | (~c3_1(a359)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(198,plain,
% 0.78/0.93 (((~c3_1(a359)) | (~hskp26)) <=> ((~hskp26) | (~c3_1(a359)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(199,axiom,((~c3_1(a359)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 0.78/0.93 tff(200,plain,
% 0.78/0.93 ((~hskp26) | (~c3_1(a359))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.78/0.93 tff(201,plain,
% 0.78/0.93 ((~hskp26) | (~c3_1(a359))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[200, 197])).
% 0.78/0.93 tff(202,plain,
% 0.78/0.93 (~c3_1(a359)),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[201, 196])).
% 0.78/0.93 tff(203,plain,
% 0.78/0.93 (((~hskp26) | (~c1_1(a359))) <=> ((~hskp26) | (~c1_1(a359)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(204,plain,
% 0.78/0.93 (((~c1_1(a359)) | (~hskp26)) <=> ((~hskp26) | (~c1_1(a359)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(205,axiom,((~c1_1(a359)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 0.78/0.93 tff(206,plain,
% 0.78/0.93 ((~hskp26) | (~c1_1(a359))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.78/0.93 tff(207,plain,
% 0.78/0.93 ((~hskp26) | (~c1_1(a359))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[206, 203])).
% 0.78/0.93 tff(208,plain,
% 0.78/0.93 (~c1_1(a359)),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[207, 196])).
% 0.78/0.93 tff(209,plain,
% 0.78/0.93 (((~hskp26) | (~c0_1(a359))) <=> ((~hskp26) | (~c0_1(a359)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(210,plain,
% 0.78/0.93 (((~c0_1(a359)) | (~hskp26)) <=> ((~hskp26) | (~c0_1(a359)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(211,axiom,((~c0_1(a359)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 0.78/0.93 tff(212,plain,
% 0.78/0.93 ((~hskp26) | (~c0_1(a359))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.78/0.93 tff(213,plain,
% 0.78/0.93 ((~hskp26) | (~c0_1(a359))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[212, 209])).
% 0.78/0.93 tff(214,plain,
% 0.78/0.93 (~c0_1(a359)),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[213, 196])).
% 0.78/0.93 tff(215,plain,
% 0.78/0.93 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(216,plain,
% 0.78/0.93 ((hskp3 | (~ndr1_0) | c3_1(a359) | c1_1(a359) | c0_1(a359)) <=> (hskp3 | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(217,plain,
% 0.78/0.93 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a359) | c1_1(a359) | c0_1(a359))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0)))),
% 0.78/0.93 inference(monotonicity,[status(thm)],[216])).
% 0.78/0.93 tff(218,plain,
% 0.78/0.93 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a359) | c1_1(a359) | c0_1(a359))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0))),
% 0.78/0.93 inference(transitivity,[status(thm)],[217, 215])).
% 0.78/0.93 tff(219,plain,
% 0.78/0.93 ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a359) | c1_1(a359) | c0_1(a359))),
% 0.78/0.93 inference(quant_inst,[status(thm)],[])).
% 0.78/0.93 tff(220,plain,
% 0.78/0.93 ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0)),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.78/0.93 tff(221,plain,
% 0.78/0.93 ($false),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[220, 129, 64, 214, 208, 202, 93])).
% 0.78/0.93 tff(222,plain,((~hskp26) | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.78/0.93 tff(223,plain,
% 0.78/0.93 (~hskp26),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[222, 64])).
% 0.78/0.93 tff(224,plain,
% 0.78/0.93 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a367)) | (~c1_1(a367)) | (~c2_1(a367)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a367)) | (~c1_1(a367)) | (~c2_1(a367)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(225,plain,
% 0.78/0.93 ((hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a367)) | (~c1_1(a367)) | (~c0_1(a367))) <=> (hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a367)) | (~c1_1(a367)) | (~c2_1(a367)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(226,plain,
% 0.78/0.93 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a367)) | (~c1_1(a367)) | (~c0_1(a367)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a367)) | (~c1_1(a367)) | (~c2_1(a367))))),
% 0.78/0.93 inference(monotonicity,[status(thm)],[225])).
% 0.78/0.93 tff(227,plain,
% 0.78/0.93 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a367)) | (~c1_1(a367)) | (~c0_1(a367)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a367)) | (~c1_1(a367)) | (~c2_1(a367)))),
% 0.78/0.93 inference(transitivity,[status(thm)],[226, 224])).
% 0.78/0.93 tff(228,plain,
% 0.78/0.93 ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a367)) | (~c1_1(a367)) | (~c0_1(a367)))),
% 0.78/0.93 inference(quant_inst,[status(thm)],[])).
% 0.78/0.93 tff(229,plain,
% 0.78/0.93 ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a367)) | (~c1_1(a367)) | (~c2_1(a367))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.78/0.93 tff(230,plain,
% 0.78/0.93 ($false),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[229, 129, 223, 64, 195, 187, 179, 170])).
% 0.78/0.93 tff(231,plain,((~hskp31) | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.78/0.93 tff(232,plain,
% 0.78/0.93 (~hskp31),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[231, 64])).
% 0.78/0.93 tff(233,assumption,(hskp24), introduced(assumption)).
% 0.78/0.93 tff(234,plain,
% 0.78/0.93 (((~hskp24) | (~c3_1(a341))) <=> ((~hskp24) | (~c3_1(a341)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(235,plain,
% 0.78/0.93 (((~c3_1(a341)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a341)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(236,axiom,((~c3_1(a341)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 0.78/0.93 tff(237,plain,
% 0.78/0.93 ((~hskp24) | (~c3_1(a341))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.78/0.93 tff(238,plain,
% 0.78/0.93 ((~hskp24) | (~c3_1(a341))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[237, 234])).
% 0.78/0.93 tff(239,plain,
% 0.78/0.93 (~c3_1(a341)),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[238, 233])).
% 0.78/0.93 tff(240,plain,
% 0.78/0.93 (((~hskp24) | (~c0_1(a341))) <=> ((~hskp24) | (~c0_1(a341)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(241,plain,
% 0.78/0.93 (((~c0_1(a341)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a341)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(242,axiom,((~c0_1(a341)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 0.78/0.93 tff(243,plain,
% 0.78/0.93 ((~hskp24) | (~c0_1(a341))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.78/0.93 tff(244,plain,
% 0.78/0.93 ((~hskp24) | (~c0_1(a341))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[243, 240])).
% 0.78/0.93 tff(245,plain,
% 0.78/0.93 (~c0_1(a341)),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[244, 233])).
% 0.78/0.94 tff(246,plain,
% 0.78/0.94 (((~hskp24) | c1_1(a341)) <=> ((~hskp24) | c1_1(a341))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(247,axiom,((~hskp24) | c1_1(a341)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 0.78/0.94 tff(248,plain,
% 0.78/0.94 ((~hskp24) | c1_1(a341)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.78/0.94 tff(249,plain,
% 0.78/0.94 ((~hskp24) | c1_1(a341)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[248, 246])).
% 0.78/0.94 tff(250,plain,
% 0.78/0.94 ((~hskp24) | c1_1(a341)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[249, 246])).
% 0.78/0.94 tff(251,plain,
% 0.78/0.94 ((~hskp24) | c1_1(a341)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[250, 246])).
% 0.78/0.94 tff(252,plain,
% 0.78/0.94 ((~hskp24) | c1_1(a341)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[251, 246])).
% 0.78/0.94 tff(253,plain,
% 0.78/0.94 (c1_1(a341)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[252, 233])).
% 0.78/0.94 tff(254,plain,
% 0.78/0.94 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 0.78/0.94 inference(bind,[status(th)],[])).
% 0.78/0.94 tff(255,plain,
% 0.78/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.78/0.94 inference(quant_intro,[status(thm)],[254])).
% 0.78/0.94 tff(256,plain,
% 0.78/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(257,plain,
% 0.78/0.94 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(W)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(W))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 0.78/0.94 inference(bind,[status(th)],[])).
% 0.78/0.94 tff(258,plain,
% 0.78/0.94 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.78/0.94 inference(quant_intro,[status(thm)],[257])).
% 0.78/0.94 tff(259,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause192')).
% 0.78/0.94 tff(260,plain,
% 0.78/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.78/0.94 tff(261,plain,
% 0.78/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[260, 256])).
% 0.78/0.94 tff(262,plain,(
% 0.78/0.94 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.78/0.94 inference(skolemize,[status(sab)],[261])).
% 0.78/0.94 tff(263,plain,
% 0.78/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[262, 255])).
% 0.78/0.94 tff(264,plain,
% 0.78/0.94 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 0.78/0.94 inference(bind,[status(th)],[])).
% 0.78/0.94 tff(265,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.78/0.94 inference(quant_intro,[status(thm)],[264])).
% 0.78/0.94 tff(266,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(267,plain,
% 0.78/0.94 (^[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))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_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))) | c1_1(U)) <=> ((~ndr1_0) | c1_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))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_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))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_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))) | c1_1(U)) | c1_1(V)) | hskp16) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp16))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_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))) | c1_1(U)) | c1_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.78/0.94 inference(bind,[status(th)],[])).
% 0.78/0.94 tff(268,plain,
% 0.78/0.94 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.78/0.94 inference(quant_intro,[status(thm)],[267])).
% 0.78/0.94 tff(269,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 0.78/0.94 tff(270,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.78/0.94 tff(271,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[270, 266])).
% 0.78/0.94 tff(272,plain,(
% 0.78/0.94 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.78/0.94 inference(skolemize,[status(sab)],[271])).
% 0.78/0.94 tff(273,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[272, 265])).
% 0.78/0.94 tff(274,assumption,(~c3_1(a341)), introduced(assumption)).
% 0.78/0.94 tff(275,assumption,(~c0_1(a341)), introduced(assumption)).
% 0.78/0.94 tff(276,assumption,(c1_1(a341)), introduced(assumption)).
% 0.78/0.94 tff(277,plain,
% 0.78/0.94 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 0.78/0.94 inference(bind,[status(th)],[])).
% 0.78/0.94 tff(278,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.78/0.94 inference(quant_intro,[status(thm)],[277])).
% 0.78/0.94 tff(279,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(280,plain,
% 0.78/0.94 (^[V: $i, U: $i] : 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))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp13) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp13))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.78/0.94 inference(bind,[status(th)],[])).
% 0.78/0.94 tff(281,plain,
% 0.78/0.94 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.78/0.94 inference(quant_intro,[status(thm)],[280])).
% 0.78/0.94 tff(282,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause189')).
% 0.78/0.94 tff(283,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.78/0.94 tff(284,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[283, 279])).
% 0.78/0.94 tff(285,plain,(
% 0.78/0.94 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.78/0.94 inference(skolemize,[status(sab)],[284])).
% 0.78/0.94 tff(286,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[285, 278])).
% 0.78/0.94 tff(287,assumption,(~c2_1(a341)), introduced(assumption)).
% 0.78/0.94 tff(288,plain,
% 0.78/0.94 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 0.78/0.94 inference(bind,[status(th)],[])).
% 0.78/0.94 tff(289,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.78/0.94 inference(quant_intro,[status(thm)],[288])).
% 0.78/0.94 tff(290,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(291,plain,
% 0.78/0.94 (^[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) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | 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)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 0.78/0.94 inference(bind,[status(th)],[])).
% 0.78/0.94 tff(292,plain,
% 0.78/0.94 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.78/0.94 inference(quant_intro,[status(thm)],[291])).
% 0.78/0.94 tff(293,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 0.78/0.94 tff(294,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.78/0.94 tff(295,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[294, 290])).
% 0.78/0.94 tff(296,plain,(
% 0.78/0.94 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.78/0.94 inference(skolemize,[status(sab)],[295])).
% 0.78/0.94 tff(297,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[296, 289])).
% 0.78/0.94 tff(298,plain,
% 0.78/0.94 (^[U: $i] : refl((hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 0.78/0.94 inference(bind,[status(th)],[])).
% 0.78/0.94 tff(299,plain,
% 0.78/0.94 (![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.78/0.94 inference(quant_intro,[status(thm)],[298])).
% 0.78/0.94 tff(300,plain,
% 0.78/0.94 (![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(301,plain,
% 0.78/0.94 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp23))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.78/0.94 inference(bind,[status(th)],[])).
% 0.78/0.94 tff(302,plain,
% 0.78/0.94 (![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) <=> ![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.78/0.94 inference(quant_intro,[status(thm)],[301])).
% 0.78/0.94 tff(303,axiom,(![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 0.78/0.94 tff(304,plain,
% 0.78/0.94 (![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.78/0.94 tff(305,plain,
% 0.78/0.94 (![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[304, 300])).
% 0.78/0.94 tff(306,plain,(
% 0.78/0.94 ![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.78/0.94 inference(skolemize,[status(sab)],[305])).
% 0.78/0.94 tff(307,plain,
% 0.78/0.94 (![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[306, 299])).
% 0.78/0.94 tff(308,plain,
% 0.78/0.94 (^[U: $i] : refl((hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.78/0.94 inference(bind,[status(th)],[])).
% 0.78/0.94 tff(309,plain,
% 0.78/0.94 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.78/0.94 inference(quant_intro,[status(thm)],[308])).
% 0.78/0.94 tff(310,plain,
% 0.78/0.94 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(311,plain,
% 0.78/0.94 (^[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)) | hskp15) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp15))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp29) <=> ((hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp29))), rewrite(((hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp29) <=> (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp29) <=> (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.78/0.94 inference(bind,[status(th)],[])).
% 0.78/0.94 tff(312,plain,
% 0.78/0.94 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp29) <=> ![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.78/0.94 inference(quant_intro,[status(thm)],[311])).
% 0.78/0.94 tff(313,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 0.78/0.94 tff(314,plain,
% 0.78/0.94 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.78/0.94 tff(315,plain,
% 0.78/0.94 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[314, 310])).
% 0.78/0.94 tff(316,plain,(
% 0.78/0.94 ![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.78/0.94 inference(skolemize,[status(sab)],[315])).
% 0.78/0.94 tff(317,plain,
% 0.78/0.94 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[316, 309])).
% 0.78/0.94 tff(318,assumption,(~hskp23), introduced(assumption)).
% 0.78/0.94 tff(319,assumption,(hskp29), introduced(assumption)).
% 0.78/0.94 tff(320,plain,
% 0.78/0.94 (((~hskp29) | c2_1(a301)) <=> ((~hskp29) | c2_1(a301))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(321,axiom,((~hskp29) | c2_1(a301)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 0.78/0.94 tff(322,plain,
% 0.78/0.94 ((~hskp29) | c2_1(a301)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.78/0.94 tff(323,plain,
% 0.78/0.94 ((~hskp29) | c2_1(a301)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[322, 320])).
% 0.78/0.94 tff(324,plain,
% 0.78/0.94 ((~hskp29) | c2_1(a301)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[323, 320])).
% 0.78/0.94 tff(325,plain,
% 0.78/0.94 ((~hskp29) | c2_1(a301)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[324, 320])).
% 0.78/0.94 tff(326,plain,
% 0.78/0.94 ((~hskp29) | c2_1(a301)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[325, 320])).
% 0.78/0.94 tff(327,plain,
% 0.78/0.94 (c2_1(a301)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[326, 319])).
% 0.78/0.94 tff(328,plain,
% 0.78/0.94 (((~hskp29) | c0_1(a301)) <=> ((~hskp29) | c0_1(a301))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(329,axiom,((~hskp29) | c0_1(a301)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 0.78/0.94 tff(330,plain,
% 0.78/0.94 ((~hskp29) | c0_1(a301)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.78/0.94 tff(331,plain,
% 0.78/0.94 ((~hskp29) | c0_1(a301)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[330, 328])).
% 0.78/0.94 tff(332,plain,
% 0.78/0.94 ((~hskp29) | c0_1(a301)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[331, 328])).
% 0.78/0.94 tff(333,plain,
% 0.78/0.94 ((~hskp29) | c0_1(a301)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[332, 328])).
% 0.78/0.94 tff(334,plain,
% 0.78/0.94 ((~hskp29) | c0_1(a301)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[333, 328])).
% 0.78/0.94 tff(335,plain,
% 0.78/0.94 (c0_1(a301)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[334, 319])).
% 0.78/0.94 tff(336,plain,
% 0.78/0.94 (((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(337,plain,
% 0.78/0.94 ((hskp23 | (~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c0_1(a301))) <=> (hskp23 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(338,plain,
% 0.78/0.94 (((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c0_1(a301)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[337])).
% 0.78/0.94 tff(339,plain,
% 0.78/0.94 (((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c0_1(a301)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.78/0.94 inference(transitivity,[status(thm)],[338, 336])).
% 0.78/0.94 tff(340,plain,
% 0.78/0.94 ((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c0_1(a301)))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(341,plain,
% 0.78/0.94 ((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.78/0.94 tff(342,plain,
% 0.78/0.94 (~c1_1(a301)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[341, 129, 318, 335, 327, 307])).
% 0.78/0.94 tff(343,plain,
% 0.78/0.94 (((~hskp29) | c3_1(a301)) <=> ((~hskp29) | c3_1(a301))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(344,axiom,((~hskp29) | c3_1(a301)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 0.78/0.94 tff(345,plain,
% 0.78/0.94 ((~hskp29) | c3_1(a301)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.78/0.94 tff(346,plain,
% 0.78/0.94 ((~hskp29) | c3_1(a301)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[345, 343])).
% 0.78/0.94 tff(347,plain,
% 0.78/0.94 ((~hskp29) | c3_1(a301)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[346, 343])).
% 0.78/0.94 tff(348,plain,
% 0.78/0.94 ((~hskp29) | c3_1(a301)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[347, 343])).
% 0.78/0.94 tff(349,plain,
% 0.78/0.94 ((~hskp29) | c3_1(a301)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[348, 343])).
% 0.78/0.94 tff(350,plain,
% 0.78/0.94 (c3_1(a301)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[349, 319])).
% 0.78/0.94 tff(351,plain,
% 0.78/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a341) | c3_1(a341) | (~ndr1_0) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | (~ndr1_0) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(352,plain,
% 0.78/0.94 (((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341))) <=> (c0_1(a341) | c3_1(a341) | (~ndr1_0) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(353,plain,
% 0.78/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a341) | c3_1(a341) | (~ndr1_0) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)) | (~c1_1(a341))))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[352])).
% 0.78/0.94 tff(354,plain,
% 0.78/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | (~ndr1_0) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)))),
% 0.78/0.94 inference(transitivity,[status(thm)],[353, 351])).
% 0.78/0.94 tff(355,plain,
% 0.78/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(356,plain,
% 0.78/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | (~ndr1_0) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)) | (~c1_1(a341))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.78/0.94 tff(357,plain,
% 0.78/0.94 ($false),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[356, 129, 335, 327, 350, 276, 275, 274, 11, 342])).
% 0.78/0.94 tff(358,plain,((~hskp29) | (~c1_1(a341)) | c0_1(a341) | c3_1(a341) | hskp23), inference(lemma,lemma(discharge,[]))).
% 0.78/0.94 tff(359,plain,
% 0.78/0.94 (~hskp29),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[358, 318, 275, 274, 276])).
% 0.78/0.94 tff(360,assumption,(hskp5), introduced(assumption)).
% 0.78/0.94 tff(361,plain,
% 0.78/0.94 (((~hskp5) | (~c0_1(a297))) <=> ((~hskp5) | (~c0_1(a297)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(362,plain,
% 0.78/0.94 (((~c0_1(a297)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a297)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(363,axiom,((~c0_1(a297)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 0.78/0.94 tff(364,plain,
% 0.78/0.94 ((~hskp5) | (~c0_1(a297))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.78/0.94 tff(365,plain,
% 0.78/0.94 ((~hskp5) | (~c0_1(a297))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[364, 361])).
% 0.78/0.94 tff(366,plain,
% 0.78/0.94 (~c0_1(a297)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[365, 360])).
% 0.78/0.94 tff(367,plain,
% 0.78/0.94 (((~hskp5) | c1_1(a297)) <=> ((~hskp5) | c1_1(a297))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(368,axiom,((~hskp5) | c1_1(a297)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 0.78/0.94 tff(369,plain,
% 0.78/0.94 ((~hskp5) | c1_1(a297)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[368, 367])).
% 0.78/0.94 tff(370,plain,
% 0.78/0.94 ((~hskp5) | c1_1(a297)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[369, 367])).
% 0.78/0.94 tff(371,plain,
% 0.78/0.94 ((~hskp5) | c1_1(a297)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[370, 367])).
% 0.78/0.94 tff(372,plain,
% 0.78/0.94 ((~hskp5) | c1_1(a297)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[371, 367])).
% 0.78/0.94 tff(373,plain,
% 0.78/0.94 ((~hskp5) | c1_1(a297)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[372, 367])).
% 0.78/0.94 tff(374,plain,
% 0.78/0.94 (c1_1(a297)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[373, 360])).
% 0.78/0.95 tff(375,plain,
% 0.78/0.95 (((~hskp5) | c2_1(a297)) <=> ((~hskp5) | c2_1(a297))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(376,axiom,((~hskp5) | c2_1(a297)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 0.78/0.95 tff(377,plain,
% 0.78/0.95 ((~hskp5) | c2_1(a297)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[376, 375])).
% 0.78/0.95 tff(378,plain,
% 0.78/0.95 ((~hskp5) | c2_1(a297)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[377, 375])).
% 0.78/0.95 tff(379,plain,
% 0.78/0.95 ((~hskp5) | c2_1(a297)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[378, 375])).
% 0.78/0.95 tff(380,plain,
% 0.78/0.95 ((~hskp5) | c2_1(a297)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[379, 375])).
% 0.78/0.95 tff(381,plain,
% 0.78/0.95 ((~hskp5) | c2_1(a297)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[380, 375])).
% 0.78/0.95 tff(382,plain,
% 0.78/0.95 (c2_1(a297)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[381, 360])).
% 0.78/0.95 tff(383,assumption,(~c0_1(a297)), introduced(assumption)).
% 0.78/0.95 tff(384,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a341) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a341)) | c2_1(a341))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a341)) | c2_1(a341))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(385,plain,
% 0.78/0.95 ((hskp29 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a341) | c0_1(a341) | (~c1_1(a341))) <=> (hskp29 | c0_1(a341) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a341)) | c2_1(a341))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(386,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a341) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a341)) | c2_1(a341)))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[385])).
% 0.78/0.95 tff(387,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a341)) | c2_1(a341))),
% 0.78/0.95 inference(transitivity,[status(thm)],[386, 384])).
% 0.78/0.95 tff(388,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a341) | c0_1(a341) | (~c1_1(a341)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(389,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a341)) | c2_1(a341)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.78/0.95 tff(390,plain,
% 0.78/0.95 ((~c2_1(a297)) | (~c1_1(a297))),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[389, 129, 53, 276, 275, 383, 63, 287])).
% 0.78/0.95 tff(391,plain,
% 0.78/0.95 ($false),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[390, 382, 374])).
% 0.78/0.95 tff(392,plain,((~hskp5) | hskp29 | (~c1_1(a341)) | c0_1(a341) | c0_1(a297) | c2_1(a341)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.95 tff(393,plain,
% 0.78/0.95 ($false),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[392, 366, 360, 276, 275, 53, 287])).
% 0.78/0.95 tff(394,plain,((~hskp5) | (~c1_1(a341)) | c0_1(a341) | hskp29 | c2_1(a341)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.95 tff(395,plain,
% 0.78/0.95 (~hskp5),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[394, 287, 275, 53, 276])).
% 0.78/0.95 tff(396,plain,
% 0.78/0.95 ((hskp22 | hskp16 | hskp5) <=> (hskp22 | hskp16 | hskp5)),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(397,plain,
% 0.80/0.95 (((hskp16 | hskp5) | hskp22) <=> (hskp22 | hskp16 | hskp5)),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(398,plain,
% 0.80/0.95 ((hskp5 | hskp16) <=> (hskp16 | hskp5)),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(399,plain,
% 0.80/0.95 (((hskp5 | hskp16) | hskp22) <=> ((hskp16 | hskp5) | hskp22)),
% 0.80/0.95 inference(monotonicity,[status(thm)],[398])).
% 0.80/0.95 tff(400,plain,
% 0.80/0.95 (((hskp5 | hskp16) | hskp22) <=> (hskp22 | hskp16 | hskp5)),
% 0.80/0.95 inference(transitivity,[status(thm)],[399, 397])).
% 0.80/0.95 tff(401,axiom,((hskp5 | hskp16) | hskp22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 0.80/0.95 tff(402,plain,
% 0.80/0.95 (hskp22 | hskp16 | hskp5),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.80/0.95 tff(403,plain,
% 0.80/0.95 (hskp22 | hskp16 | hskp5),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[402, 396])).
% 0.80/0.95 tff(404,plain,
% 0.80/0.95 (hskp22 | hskp16 | hskp5),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[403, 396])).
% 0.80/0.95 tff(405,plain,
% 0.80/0.95 (hskp22 | hskp16 | hskp5),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[404, 396])).
% 0.80/0.95 tff(406,plain,
% 0.80/0.95 (hskp22 | hskp16 | hskp5),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[405, 396])).
% 0.80/0.95 tff(407,plain,
% 0.80/0.95 (hskp16),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[406, 395, 160])).
% 0.80/0.95 tff(408,plain,
% 0.80/0.95 (((~hskp16) | c2_1(a315)) <=> ((~hskp16) | c2_1(a315))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(409,axiom,((~hskp16) | c2_1(a315)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 0.80/0.95 tff(410,plain,
% 0.80/0.95 ((~hskp16) | c2_1(a315)),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.80/0.95 tff(411,plain,
% 0.80/0.95 ((~hskp16) | c2_1(a315)),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[410, 408])).
% 0.80/0.95 tff(412,plain,
% 0.80/0.95 ((~hskp16) | c2_1(a315)),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[411, 408])).
% 0.80/0.95 tff(413,plain,
% 0.80/0.95 ((~hskp16) | c2_1(a315)),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[412, 408])).
% 0.80/0.95 tff(414,plain,
% 0.80/0.95 ((~hskp16) | c2_1(a315)),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[413, 408])).
% 0.80/0.95 tff(415,plain,
% 0.80/0.95 (c2_1(a315)),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[414, 407])).
% 0.80/0.95 tff(416,plain,
% 0.80/0.95 (((~hskp16) | (~c0_1(a315))) <=> ((~hskp16) | (~c0_1(a315)))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(417,plain,
% 0.80/0.95 (((~c0_1(a315)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a315)))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(418,axiom,((~c0_1(a315)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 0.80/0.95 tff(419,plain,
% 0.80/0.95 ((~hskp16) | (~c0_1(a315))),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.80/0.95 tff(420,plain,
% 0.80/0.95 ((~hskp16) | (~c0_1(a315))),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[419, 416])).
% 0.80/0.95 tff(421,plain,
% 0.80/0.95 (~c0_1(a315)),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[420, 407])).
% 0.80/0.95 tff(422,assumption,(c1_1(a315)), introduced(assumption)).
% 0.80/0.95 tff(423,assumption,(~c0_1(a315)), introduced(assumption)).
% 0.80/0.95 tff(424,assumption,(c2_1(a315)), introduced(assumption)).
% 0.80/0.95 tff(425,plain,
% 0.80/0.95 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a341) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a341)) | c2_1(a341))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a341)) | c2_1(a341))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(426,plain,
% 0.80/0.95 ((hskp29 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a341) | c0_1(a341) | (~c1_1(a341))) <=> (hskp29 | c0_1(a341) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a341)) | c2_1(a341))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(427,plain,
% 0.80/0.95 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a341) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a341)) | c2_1(a341)))),
% 0.80/0.95 inference(monotonicity,[status(thm)],[426])).
% 0.80/0.95 tff(428,plain,
% 0.80/0.95 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a341)) | c2_1(a341))),
% 0.80/0.95 inference(transitivity,[status(thm)],[427, 425])).
% 0.80/0.95 tff(429,plain,
% 0.80/0.95 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a341) | c0_1(a341) | (~c1_1(a341)))),
% 0.80/0.95 inference(quant_inst,[status(thm)],[])).
% 0.80/0.95 tff(430,plain,
% 0.80/0.95 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a341)) | c2_1(a341)),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[429, 428])).
% 0.80/0.95 tff(431,plain,
% 0.80/0.95 ($false),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[430, 129, 53, 276, 424, 275, 423, 63, 287, 422])).
% 0.80/0.95 tff(432,plain,(c2_1(a341) | hskp29 | (~c1_1(a341)) | (~c2_1(a315)) | c0_1(a341) | c0_1(a315) | (~c1_1(a315))), inference(lemma,lemma(discharge,[]))).
% 0.80/0.95 tff(433,plain,
% 0.80/0.95 (~c1_1(a315)),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[432, 421, 276, 53, 275, 287, 415])).
% 0.80/0.95 tff(434,plain,
% 0.80/0.95 (((~hskp16) | (~c3_1(a315))) <=> ((~hskp16) | (~c3_1(a315)))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(435,plain,
% 0.80/0.95 (((~c3_1(a315)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a315)))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(436,axiom,((~c3_1(a315)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 0.80/0.95 tff(437,plain,
% 0.80/0.95 ((~hskp16) | (~c3_1(a315))),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.80/0.95 tff(438,plain,
% 0.80/0.95 ((~hskp16) | (~c3_1(a315))),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[437, 434])).
% 0.80/0.95 tff(439,plain,
% 0.80/0.95 (~c3_1(a315)),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[438, 407])).
% 0.80/0.95 tff(440,plain,
% 0.80/0.95 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(441,plain,
% 0.80/0.95 ((hskp3 | (~ndr1_0) | c3_1(a315) | c1_1(a315) | c0_1(a315)) <=> (hskp3 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(442,plain,
% 0.80/0.95 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a315) | c1_1(a315) | c0_1(a315))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315)))),
% 0.80/0.95 inference(monotonicity,[status(thm)],[441])).
% 0.80/0.95 tff(443,plain,
% 0.80/0.95 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a315) | c1_1(a315) | c0_1(a315))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315))),
% 0.80/0.95 inference(transitivity,[status(thm)],[442, 440])).
% 0.80/0.95 tff(444,plain,
% 0.80/0.95 ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a315) | c1_1(a315) | c0_1(a315))),
% 0.80/0.95 inference(quant_inst,[status(thm)],[])).
% 0.80/0.95 tff(445,plain,
% 0.80/0.95 ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315)),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.80/0.95 tff(446,plain,
% 0.80/0.95 ($false),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[445, 129, 64, 421, 439, 93, 433])).
% 0.80/0.95 tff(447,plain,(c2_1(a341) | hskp3 | (~c1_1(a341)) | hskp29 | c0_1(a341)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.95 tff(448,plain,
% 0.80/0.95 (c2_1(a341)),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[447, 64, 276, 359, 275])).
% 0.80/0.95 tff(449,plain,
% 0.80/0.95 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 0.80/0.95 inference(bind,[status(th)],[])).
% 0.80/0.95 tff(450,plain,
% 0.80/0.95 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.80/0.95 inference(quant_intro,[status(thm)],[449])).
% 0.80/0.95 tff(451,plain,
% 0.80/0.95 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(452,plain,
% 0.80/0.95 (^[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) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | hskp7) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp7))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 0.80/0.95 inference(bind,[status(th)],[])).
% 0.80/0.95 tff(453,plain,
% 0.80/0.95 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.80/0.95 inference(quant_intro,[status(thm)],[452])).
% 0.80/0.95 tff(454,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 0.80/0.95 tff(455,plain,
% 0.80/0.95 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[454, 453])).
% 0.80/0.95 tff(456,plain,
% 0.80/0.95 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[455, 451])).
% 0.80/0.95 tff(457,plain,(
% 0.80/0.95 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.80/0.95 inference(skolemize,[status(sab)],[456])).
% 0.80/0.95 tff(458,plain,
% 0.80/0.95 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[457, 450])).
% 0.80/0.95 tff(459,plain,
% 0.80/0.95 ((hskp23 | hskp3 | hskp0) <=> (hskp23 | hskp3 | hskp0)),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(460,plain,
% 0.80/0.95 (((hskp23 | hskp3) | hskp0) <=> (hskp23 | hskp3 | hskp0)),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(461,plain,
% 0.80/0.95 ((hskp3 | hskp23) <=> (hskp23 | hskp3)),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(462,plain,
% 0.80/0.95 (((hskp3 | hskp23) | hskp0) <=> ((hskp23 | hskp3) | hskp0)),
% 0.80/0.95 inference(monotonicity,[status(thm)],[461])).
% 0.80/0.95 tff(463,plain,
% 0.80/0.95 (((hskp3 | hskp23) | hskp0) <=> (hskp23 | hskp3 | hskp0)),
% 0.80/0.95 inference(transitivity,[status(thm)],[462, 460])).
% 0.80/0.95 tff(464,axiom,((hskp3 | hskp23) | hskp0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 0.80/0.95 tff(465,plain,
% 0.80/0.95 (hskp23 | hskp3 | hskp0),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[464, 463])).
% 0.80/0.95 tff(466,plain,
% 0.80/0.95 (hskp23 | hskp3 | hskp0),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[465, 459])).
% 0.80/0.95 tff(467,plain,
% 0.80/0.95 (hskp23 | hskp3 | hskp0),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[466, 459])).
% 0.80/0.95 tff(468,plain,
% 0.80/0.95 (hskp23 | hskp3 | hskp0),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[467, 459])).
% 0.80/0.95 tff(469,plain,
% 0.80/0.95 (hskp23 | hskp3 | hskp0),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[468, 459])).
% 0.80/0.95 tff(470,plain,
% 0.80/0.95 (hskp0),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[469, 64, 318])).
% 0.80/0.95 tff(471,plain,
% 0.80/0.95 (((~hskp0) | (~c2_1(a291))) <=> ((~hskp0) | (~c2_1(a291)))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(472,plain,
% 0.80/0.95 (((~c2_1(a291)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a291)))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(473,axiom,((~c2_1(a291)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 0.80/0.95 tff(474,plain,
% 0.80/0.95 ((~hskp0) | (~c2_1(a291))),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[473, 472])).
% 0.80/0.95 tff(475,plain,
% 0.80/0.95 ((~hskp0) | (~c2_1(a291))),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[474, 471])).
% 0.80/0.95 tff(476,plain,
% 0.80/0.95 (~c2_1(a291)),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[475, 470])).
% 0.80/0.95 tff(477,plain,
% 0.80/0.95 (((~hskp0) | c1_1(a291)) <=> ((~hskp0) | c1_1(a291))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(478,axiom,((~hskp0) | c1_1(a291)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 0.80/0.95 tff(479,plain,
% 0.80/0.95 ((~hskp0) | c1_1(a291)),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[478, 477])).
% 0.80/0.95 tff(480,plain,
% 0.80/0.95 ((~hskp0) | c1_1(a291)),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[479, 477])).
% 0.80/0.95 tff(481,plain,
% 0.80/0.95 ((~hskp0) | c1_1(a291)),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[480, 477])).
% 0.80/0.95 tff(482,plain,
% 0.80/0.95 ((~hskp0) | c1_1(a291)),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[481, 477])).
% 0.80/0.95 tff(483,plain,
% 0.80/0.95 ((~hskp0) | c1_1(a291)),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[482, 477])).
% 0.80/0.95 tff(484,plain,
% 0.80/0.95 (c1_1(a291)),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[483, 470])).
% 0.80/0.95 tff(485,plain,
% 0.80/0.95 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a341) | c2_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | (~c1_1(a341)) | (~c2_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c2_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(486,plain,
% 0.80/0.95 ((hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a291) | c0_1(a291) | (~c1_1(a291))) <=> (hskp29 | c0_1(a341) | c2_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(487,plain,
% 0.80/0.95 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a291) | c0_1(a291) | (~c1_1(a291)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a341) | c2_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | (~c1_1(a341)) | (~c2_1(a341))))),
% 0.80/0.95 inference(monotonicity,[status(thm)],[486])).
% 0.80/0.95 tff(488,plain,
% 0.80/0.95 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a291) | c0_1(a291) | (~c1_1(a291)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c2_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 0.80/0.95 inference(transitivity,[status(thm)],[487, 485])).
% 0.80/0.95 tff(489,plain,
% 0.80/0.95 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a291) | c0_1(a291) | (~c1_1(a291)))),
% 0.80/0.95 inference(quant_inst,[status(thm)],[])).
% 0.80/0.95 tff(490,plain,
% 0.80/0.95 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c2_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | (~c1_1(a341)) | (~c2_1(a341))),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[489, 488])).
% 0.80/0.95 tff(491,plain,
% 0.80/0.95 (c0_1(a291) | (~c2_1(a341))),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[490, 129, 359, 276, 484, 275, 476, 63])).
% 0.80/0.95 tff(492,plain,
% 0.80/0.95 (c0_1(a291)),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[491, 448])).
% 0.80/0.95 tff(493,plain,
% 0.80/0.95 (((~hskp0) | (~c3_1(a291))) <=> ((~hskp0) | (~c3_1(a291)))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(494,plain,
% 0.80/0.95 (((~c3_1(a291)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a291)))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(495,axiom,((~c3_1(a291)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 0.80/0.95 tff(496,plain,
% 0.80/0.95 ((~hskp0) | (~c3_1(a291))),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[495, 494])).
% 0.80/0.95 tff(497,plain,
% 0.80/0.95 ((~hskp0) | (~c3_1(a291))),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[496, 493])).
% 0.80/0.95 tff(498,plain,
% 0.80/0.95 (~c3_1(a291)),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[497, 470])).
% 0.80/0.95 tff(499,assumption,(hskp8), introduced(assumption)).
% 0.80/0.95 tff(500,plain,
% 0.80/0.95 (((~hskp8) | (~c1_1(a300))) <=> ((~hskp8) | (~c1_1(a300)))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(501,plain,
% 0.80/0.95 (((~c1_1(a300)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a300)))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(502,axiom,((~c1_1(a300)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 0.80/0.95 tff(503,plain,
% 0.80/0.95 ((~hskp8) | (~c1_1(a300))),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[502, 501])).
% 0.80/0.95 tff(504,plain,
% 0.80/0.95 ((~hskp8) | (~c1_1(a300))),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[503, 500])).
% 0.80/0.95 tff(505,plain,
% 0.80/0.95 (~c1_1(a300)),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[504, 499])).
% 0.80/0.95 tff(506,plain,
% 0.80/0.95 (((~hskp8) | c3_1(a300)) <=> ((~hskp8) | c3_1(a300))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(507,axiom,((~hskp8) | c3_1(a300)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 0.80/0.95 tff(508,plain,
% 0.80/0.95 ((~hskp8) | c3_1(a300)),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[507, 506])).
% 0.80/0.95 tff(509,plain,
% 0.80/0.95 ((~hskp8) | c3_1(a300)),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[508, 506])).
% 0.80/0.95 tff(510,plain,
% 0.80/0.95 ((~hskp8) | c3_1(a300)),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[509, 506])).
% 0.80/0.95 tff(511,plain,
% 0.80/0.95 ((~hskp8) | c3_1(a300)),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[510, 506])).
% 0.80/0.95 tff(512,plain,
% 0.80/0.95 ((~hskp8) | c3_1(a300)),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[511, 506])).
% 0.80/0.95 tff(513,plain,
% 0.80/0.95 (c3_1(a300)),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[512, 499])).
% 0.80/0.95 tff(514,plain,
% 0.80/0.95 (((~hskp8) | c0_1(a300)) <=> ((~hskp8) | c0_1(a300))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(515,axiom,((~hskp8) | c0_1(a300)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 0.80/0.95 tff(516,plain,
% 0.80/0.95 ((~hskp8) | c0_1(a300)),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[515, 514])).
% 0.80/0.95 tff(517,plain,
% 0.80/0.95 ((~hskp8) | c0_1(a300)),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[516, 514])).
% 0.80/0.95 tff(518,plain,
% 0.80/0.95 ((~hskp8) | c0_1(a300)),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[517, 514])).
% 0.80/0.95 tff(519,plain,
% 0.80/0.95 ((~hskp8) | c0_1(a300)),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[518, 514])).
% 0.80/0.95 tff(520,plain,
% 0.80/0.95 ((~hskp8) | c0_1(a300)),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[519, 514])).
% 0.80/0.95 tff(521,plain,
% 0.80/0.95 (c0_1(a300)),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[520, 499])).
% 0.80/0.95 tff(522,plain,
% 0.80/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a341) | c3_1(a341) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300)) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300)) | (~c1_1(a341)))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(523,plain,
% 0.80/0.95 (((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341))) <=> (c0_1(a341) | c3_1(a341) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300)) | (~c1_1(a341)))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(524,plain,
% 0.80/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a341) | c3_1(a341) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300)) | (~c1_1(a341))))),
% 0.80/0.95 inference(monotonicity,[status(thm)],[523])).
% 0.80/0.95 tff(525,plain,
% 0.80/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300)) | (~c1_1(a341)))),
% 0.80/0.95 inference(transitivity,[status(thm)],[524, 522])).
% 0.80/0.95 tff(526,plain,
% 0.80/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))),
% 0.80/0.95 inference(quant_inst,[status(thm)],[])).
% 0.80/0.95 tff(527,plain,
% 0.80/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300)) | (~c1_1(a341))),
% 0.80/0.95 inference(modus_ponens,[status(thm)],[526, 525])).
% 0.80/0.95 tff(528,plain,
% 0.80/0.95 (~c2_1(a300)),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[527, 129, 276, 521, 513, 275, 274, 505, 11])).
% 0.80/0.95 tff(529,assumption,(c0_1(a291)), introduced(assumption)).
% 0.80/0.95 tff(530,assumption,(c2_1(a341)), introduced(assumption)).
% 0.80/0.95 tff(531,plain,
% 0.80/0.95 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.80/0.95 inference(bind,[status(th)],[])).
% 0.80/0.95 tff(532,plain,
% 0.80/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_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)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.80/0.95 inference(quant_intro,[status(thm)],[531])).
% 0.80/0.95 tff(533,plain,
% 0.80/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_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)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.80/0.95 inference(rewrite,[status(thm)],[])).
% 0.80/0.95 tff(534,plain,
% 0.80/0.95 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.80/0.96 inference(bind,[status(th)],[])).
% 0.80/0.96 tff(535,plain,
% 0.80/0.96 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.80/0.96 inference(quant_intro,[status(thm)],[534])).
% 0.80/0.96 tff(536,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 0.80/0.96 tff(537,plain,
% 0.80/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.80/0.96 tff(538,plain,
% 0.80/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[537, 533])).
% 0.80/0.96 tff(539,plain,(
% 0.80/0.96 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.80/0.96 inference(skolemize,[status(sab)],[538])).
% 0.80/0.96 tff(540,plain,
% 0.80/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[539, 532])).
% 0.80/0.96 tff(541,assumption,(~c3_1(a291)), introduced(assumption)).
% 0.80/0.96 tff(542,assumption,(~c2_1(a291)), introduced(assumption)).
% 0.80/0.96 tff(543,plain,
% 0.80/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a341)))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(544,plain,
% 0.80/0.96 (((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341))) <=> (c0_1(a341) | c3_1(a341) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a341)))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(545,plain,
% 0.80/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a341))))),
% 0.80/0.96 inference(monotonicity,[status(thm)],[544])).
% 0.80/0.96 tff(546,plain,
% 0.80/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a341)))),
% 0.80/0.96 inference(transitivity,[status(thm)],[545, 543])).
% 0.80/0.96 tff(547,plain,
% 0.80/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))),
% 0.80/0.96 inference(quant_inst,[status(thm)],[])).
% 0.80/0.96 tff(548,plain,
% 0.80/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a341))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[547, 546])).
% 0.80/0.96 tff(549,plain,
% 0.80/0.96 ($false),
% 0.80/0.96 inference(unit_resolution,[status(thm)],[548, 129, 521, 513, 275, 274, 542, 541, 540, 530, 529, 528])).
% 0.80/0.96 tff(550,plain,((~hskp8) | c0_1(a341) | c3_1(a341) | c2_1(a291) | c3_1(a291) | (~c2_1(a341)) | (~c0_1(a291)) | (~c1_1(a341))), inference(lemma,lemma(discharge,[]))).
% 0.80/0.96 tff(551,plain,
% 0.80/0.96 (~hskp8),
% 0.80/0.96 inference(unit_resolution,[status(thm)],[550, 476, 274, 275, 498, 448, 492, 276])).
% 0.80/0.96 tff(552,plain,
% 0.80/0.96 (^[U: $i] : refl((hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))),
% 0.80/0.96 inference(bind,[status(th)],[])).
% 0.80/0.96 tff(553,plain,
% 0.80/0.96 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.80/0.96 inference(quant_intro,[status(thm)],[552])).
% 0.80/0.96 tff(554,plain,
% 0.80/0.96 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(555,plain,
% 0.80/0.96 (^[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) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp8))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp23) <=> ((hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp23))), rewrite(((hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp23) <=> (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp23) <=> (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))))),
% 0.80/0.96 inference(bind,[status(th)],[])).
% 0.80/0.96 tff(556,plain,
% 0.80/0.96 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp23) <=> ![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.80/0.96 inference(quant_intro,[status(thm)],[555])).
% 0.80/0.96 tff(557,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause152')).
% 0.80/0.96 tff(558,plain,
% 0.80/0.96 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[557, 556])).
% 0.80/0.96 tff(559,plain,
% 0.80/0.96 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[558, 554])).
% 0.80/0.96 tff(560,plain,(
% 0.80/0.96 ![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.80/0.96 inference(skolemize,[status(sab)],[559])).
% 0.80/0.96 tff(561,plain,
% 0.80/0.96 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[560, 553])).
% 0.80/0.96 tff(562,assumption,(hskp12), introduced(assumption)).
% 0.80/0.96 tff(563,plain,
% 0.80/0.96 (((~hskp12) | (~c3_1(a307))) <=> ((~hskp12) | (~c3_1(a307)))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(564,plain,
% 0.80/0.96 (((~c3_1(a307)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a307)))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(565,axiom,((~c3_1(a307)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 0.80/0.96 tff(566,plain,
% 0.80/0.96 ((~hskp12) | (~c3_1(a307))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[565, 564])).
% 0.80/0.96 tff(567,plain,
% 0.80/0.96 ((~hskp12) | (~c3_1(a307))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[566, 563])).
% 0.80/0.96 tff(568,plain,
% 0.80/0.96 (~c3_1(a307)),
% 0.80/0.96 inference(unit_resolution,[status(thm)],[567, 562])).
% 0.80/0.96 tff(569,plain,
% 0.80/0.96 (((~hskp12) | (~c1_1(a307))) <=> ((~hskp12) | (~c1_1(a307)))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(570,plain,
% 0.80/0.96 (((~c1_1(a307)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a307)))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(571,axiom,((~c1_1(a307)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 0.80/0.96 tff(572,plain,
% 0.80/0.96 ((~hskp12) | (~c1_1(a307))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[571, 570])).
% 0.80/0.96 tff(573,plain,
% 0.80/0.96 ((~hskp12) | (~c1_1(a307))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[572, 569])).
% 0.80/0.96 tff(574,plain,
% 0.80/0.96 (~c1_1(a307)),
% 0.80/0.96 inference(unit_resolution,[status(thm)],[573, 562])).
% 0.80/0.96 tff(575,plain,
% 0.80/0.96 (((~hskp12) | c2_1(a307)) <=> ((~hskp12) | c2_1(a307))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(576,axiom,((~hskp12) | c2_1(a307)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 0.80/0.96 tff(577,plain,
% 0.80/0.96 ((~hskp12) | c2_1(a307)),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[576, 575])).
% 0.80/0.96 tff(578,plain,
% 0.80/0.96 ((~hskp12) | c2_1(a307)),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[577, 575])).
% 0.80/0.96 tff(579,plain,
% 0.80/0.96 ((~hskp12) | c2_1(a307)),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[578, 575])).
% 0.80/0.96 tff(580,plain,
% 0.80/0.96 ((~hskp12) | c2_1(a307)),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[579, 575])).
% 0.80/0.96 tff(581,plain,
% 0.80/0.96 ((~hskp12) | c2_1(a307)),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[580, 575])).
% 0.80/0.96 tff(582,plain,
% 0.80/0.96 (c2_1(a307)),
% 0.80/0.96 inference(unit_resolution,[status(thm)],[581, 562])).
% 0.80/0.96 tff(583,assumption,(~hskp8), introduced(assumption)).
% 0.80/0.96 tff(584,plain,
% 0.80/0.96 (((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | c1_1(a307) | c3_1(a307) | (~ndr1_0) | (~c2_1(a307)))) <=> ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp23 | hskp8 | c1_1(a307) | c3_1(a307) | (~ndr1_0) | (~c2_1(a307)))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(585,plain,
% 0.80/0.96 ((hskp23 | hskp8 | (~ndr1_0) | c3_1(a307) | c1_1(a307) | (~c2_1(a307))) <=> (hskp23 | hskp8 | c1_1(a307) | c3_1(a307) | (~ndr1_0) | (~c2_1(a307)))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(586,plain,
% 0.80/0.96 (((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | (~ndr1_0) | c3_1(a307) | c1_1(a307) | (~c2_1(a307)))) <=> ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | c1_1(a307) | c3_1(a307) | (~ndr1_0) | (~c2_1(a307))))),
% 0.80/0.96 inference(monotonicity,[status(thm)],[585])).
% 0.80/0.96 tff(587,plain,
% 0.80/0.96 (((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | (~ndr1_0) | c3_1(a307) | c1_1(a307) | (~c2_1(a307)))) <=> ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp23 | hskp8 | c1_1(a307) | c3_1(a307) | (~ndr1_0) | (~c2_1(a307)))),
% 0.80/0.96 inference(transitivity,[status(thm)],[586, 584])).
% 0.80/0.96 tff(588,plain,
% 0.80/0.96 ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | (~ndr1_0) | c3_1(a307) | c1_1(a307) | (~c2_1(a307)))),
% 0.80/0.96 inference(quant_inst,[status(thm)],[])).
% 0.80/0.96 tff(589,plain,
% 0.80/0.96 ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp23 | hskp8 | c1_1(a307) | c3_1(a307) | (~ndr1_0) | (~c2_1(a307))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[588, 587])).
% 0.80/0.96 tff(590,plain,
% 0.80/0.96 ($false),
% 0.80/0.96 inference(unit_resolution,[status(thm)],[589, 129, 318, 583, 582, 574, 568, 561])).
% 0.80/0.96 tff(591,plain,((~hskp12) | hskp23 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.80/0.96 tff(592,plain,
% 0.80/0.96 (~hskp12),
% 0.80/0.96 inference(unit_resolution,[status(thm)],[591, 551, 318])).
% 0.80/0.96 tff(593,plain,
% 0.80/0.96 (^[U: $i] : refl((hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))),
% 0.80/0.96 inference(bind,[status(th)],[])).
% 0.80/0.96 tff(594,plain,
% 0.80/0.96 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.80/0.96 inference(quant_intro,[status(thm)],[593])).
% 0.80/0.96 tff(595,plain,
% 0.80/0.96 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(596,plain,
% 0.80/0.96 (^[U: $i] : 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)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp11) | hskp12) <=> ((hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp12))), rewrite(((hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp12) <=> (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp11) | hskp12) <=> (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))))),
% 0.80/0.96 inference(bind,[status(th)],[])).
% 0.80/0.96 tff(597,plain,
% 0.80/0.96 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp11) | hskp12) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.80/0.96 inference(quant_intro,[status(thm)],[596])).
% 0.80/0.96 tff(598,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp11) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 0.80/0.96 tff(599,plain,
% 0.80/0.96 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[598, 597])).
% 0.80/0.96 tff(600,plain,
% 0.80/0.96 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[599, 595])).
% 0.80/0.96 tff(601,plain,(
% 0.80/0.96 ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.80/0.96 inference(skolemize,[status(sab)],[600])).
% 0.80/0.96 tff(602,plain,
% 0.80/0.96 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[601, 594])).
% 0.80/0.96 tff(603,plain,
% 0.80/0.96 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp12 | hskp11 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c1_1(a341)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c1_1(a341)))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(604,plain,
% 0.80/0.96 ((hskp12 | hskp11 | (~ndr1_0) | c3_1(a341) | c0_1(a341) | (~c1_1(a341))) <=> (hskp12 | hskp11 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c1_1(a341)))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(605,plain,
% 0.80/0.96 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp12 | hskp11 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c1_1(a341))))),
% 0.80/0.96 inference(monotonicity,[status(thm)],[604])).
% 0.80/0.96 tff(606,plain,
% 0.80/0.96 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c1_1(a341)))),
% 0.80/0.96 inference(transitivity,[status(thm)],[605, 603])).
% 0.80/0.96 tff(607,plain,
% 0.80/0.96 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))),
% 0.80/0.96 inference(quant_inst,[status(thm)],[])).
% 0.80/0.96 tff(608,plain,
% 0.80/0.96 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c1_1(a341))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[607, 606])).
% 0.80/0.96 tff(609,plain,
% 0.80/0.96 (hskp12 | hskp11),
% 0.80/0.96 inference(unit_resolution,[status(thm)],[608, 129, 276, 275, 274, 602])).
% 0.80/0.96 tff(610,plain,
% 0.80/0.96 (hskp11),
% 0.80/0.96 inference(unit_resolution,[status(thm)],[609, 592])).
% 0.80/0.96 tff(611,plain,
% 0.80/0.96 (((~hskp11) | (~c0_1(a306))) <=> ((~hskp11) | (~c0_1(a306)))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(612,plain,
% 0.80/0.96 (((~c0_1(a306)) | (~hskp11)) <=> ((~hskp11) | (~c0_1(a306)))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(613,axiom,((~c0_1(a306)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 0.80/0.96 tff(614,plain,
% 0.80/0.96 ((~hskp11) | (~c0_1(a306))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[613, 612])).
% 0.80/0.96 tff(615,plain,
% 0.80/0.96 ((~hskp11) | (~c0_1(a306))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[614, 611])).
% 0.80/0.96 tff(616,plain,
% 0.80/0.96 (~c0_1(a306)),
% 0.80/0.96 inference(unit_resolution,[status(thm)],[615, 610])).
% 0.80/0.96 tff(617,plain,
% 0.80/0.96 (((~hskp11) | c3_1(a306)) <=> ((~hskp11) | c3_1(a306))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(618,axiom,((~hskp11) | c3_1(a306)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 0.80/0.96 tff(619,plain,
% 0.80/0.96 ((~hskp11) | c3_1(a306)),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[618, 617])).
% 0.80/0.96 tff(620,plain,
% 0.80/0.96 ((~hskp11) | c3_1(a306)),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[619, 617])).
% 0.80/0.96 tff(621,plain,
% 0.80/0.96 ((~hskp11) | c3_1(a306)),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[620, 617])).
% 0.80/0.96 tff(622,plain,
% 0.80/0.96 ((~hskp11) | c3_1(a306)),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[621, 617])).
% 0.80/0.96 tff(623,plain,
% 0.80/0.96 ((~hskp11) | c3_1(a306)),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[622, 617])).
% 0.80/0.96 tff(624,plain,
% 0.80/0.96 (c3_1(a306)),
% 0.80/0.96 inference(unit_resolution,[status(thm)],[623, 610])).
% 0.80/0.96 tff(625,plain,
% 0.80/0.96 (((~hskp11) | c1_1(a306)) <=> ((~hskp11) | c1_1(a306))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(626,axiom,((~hskp11) | c1_1(a306)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 0.80/0.96 tff(627,plain,
% 0.80/0.96 ((~hskp11) | c1_1(a306)),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[626, 625])).
% 0.80/0.96 tff(628,plain,
% 0.80/0.96 ((~hskp11) | c1_1(a306)),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[627, 625])).
% 0.80/0.96 tff(629,plain,
% 0.80/0.96 ((~hskp11) | c1_1(a306)),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[628, 625])).
% 0.80/0.96 tff(630,plain,
% 0.80/0.96 ((~hskp11) | c1_1(a306)),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[629, 625])).
% 0.80/0.96 tff(631,plain,
% 0.80/0.96 ((~hskp11) | c1_1(a306)),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[630, 625])).
% 0.80/0.96 tff(632,plain,
% 0.80/0.96 (c1_1(a306)),
% 0.80/0.96 inference(unit_resolution,[status(thm)],[631, 610])).
% 0.80/0.96 tff(633,plain,
% 0.80/0.96 (~hskp12),
% 0.80/0.96 inference(unit_resolution,[status(thm)],[591, 583, 318])).
% 0.80/0.96 tff(634,plain,
% 0.80/0.96 (hskp11),
% 0.80/0.96 inference(unit_resolution,[status(thm)],[609, 633])).
% 0.80/0.96 tff(635,plain,
% 0.80/0.96 (~c0_1(a306)),
% 0.80/0.96 inference(unit_resolution,[status(thm)],[615, 634])).
% 0.80/0.96 tff(636,plain,
% 0.80/0.96 (c1_1(a306)),
% 0.80/0.96 inference(unit_resolution,[status(thm)],[631, 634])).
% 0.80/0.96 tff(637,plain,
% 0.80/0.96 (c3_1(a306)),
% 0.80/0.96 inference(unit_resolution,[status(thm)],[623, 634])).
% 0.80/0.96 tff(638,assumption,(c3_1(a306)), introduced(assumption)).
% 0.80/0.96 tff(639,plain,
% 0.80/0.96 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)))),
% 0.80/0.96 inference(bind,[status(th)],[])).
% 0.80/0.96 tff(640,plain,
% 0.80/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.80/0.96 inference(quant_intro,[status(thm)],[639])).
% 0.80/0.96 tff(641,plain,
% 0.80/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(642,plain,
% 0.80/0.96 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | 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)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))))),
% 0.80/0.96 inference(bind,[status(th)],[])).
% 0.80/0.96 tff(643,plain,
% 0.80/0.96 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | 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) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.80/0.96 inference(quant_intro,[status(thm)],[642])).
% 0.80/0.96 tff(644,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause190')).
% 0.80/0.96 tff(645,plain,
% 0.80/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[644, 643])).
% 0.80/0.96 tff(646,plain,
% 0.80/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[645, 641])).
% 0.80/0.96 tff(647,plain,(
% 0.80/0.96 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.80/0.96 inference(skolemize,[status(sab)],[646])).
% 0.80/0.96 tff(648,plain,
% 0.80/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[647, 640])).
% 0.80/0.96 tff(649,assumption,(~c0_1(a306)), introduced(assumption)).
% 0.80/0.96 tff(650,plain,
% 0.80/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a341) | c3_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c2_1(a306)) | (~c1_1(a341)) | c2_1(a341))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a341) | c3_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c2_1(a306)) | (~c1_1(a341)) | c2_1(a341))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(651,plain,
% 0.80/0.96 (((~ndr1_0) | c3_1(a341) | c2_1(a341) | (~c1_1(a341)) | c0_1(a306) | (~c3_1(a306)) | (~c2_1(a306)) | c3_1(a341) | c2_1(a341) | c0_1(a341)) <=> (c0_1(a341) | c3_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c2_1(a306)) | (~c1_1(a341)) | c2_1(a341))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(652,plain,
% 0.80/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a341) | c2_1(a341) | (~c1_1(a341)) | c0_1(a306) | (~c3_1(a306)) | (~c2_1(a306)) | c3_1(a341) | c2_1(a341) | c0_1(a341))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a341) | c3_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c2_1(a306)) | (~c1_1(a341)) | c2_1(a341)))),
% 0.80/0.96 inference(monotonicity,[status(thm)],[651])).
% 0.80/0.96 tff(653,plain,
% 0.80/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a341) | c2_1(a341) | (~c1_1(a341)) | c0_1(a306) | (~c3_1(a306)) | (~c2_1(a306)) | c3_1(a341) | c2_1(a341) | c0_1(a341))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a341) | c3_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c2_1(a306)) | (~c1_1(a341)) | c2_1(a341))),
% 0.80/0.96 inference(transitivity,[status(thm)],[652, 650])).
% 0.80/0.96 tff(654,plain,
% 0.80/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a341) | c2_1(a341) | (~c1_1(a341)) | c0_1(a306) | (~c3_1(a306)) | (~c2_1(a306)) | c3_1(a341) | c2_1(a341) | c0_1(a341))),
% 0.80/0.96 inference(quant_inst,[status(thm)],[])).
% 0.80/0.96 tff(655,plain,
% 0.80/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a341) | c3_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c2_1(a306)) | (~c1_1(a341)) | c2_1(a341)),
% 0.80/0.96 inference(modus_ponens,[status(thm)],[654, 653])).
% 0.80/0.96 tff(656,plain,
% 0.80/0.96 ((~c3_1(a306)) | (~c2_1(a306)) | c2_1(a341)),
% 0.80/0.96 inference(unit_resolution,[status(thm)],[655, 129, 276, 275, 274, 649, 648])).
% 0.80/0.96 tff(657,plain,
% 0.80/0.96 (~c2_1(a306)),
% 0.80/0.96 inference(unit_resolution,[status(thm)],[656, 287, 638])).
% 0.80/0.96 tff(658,assumption,(c1_1(a306)), introduced(assumption)).
% 0.80/0.96 tff(659,plain,
% 0.80/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c3_1(a306)) | c2_1(a306) | (~c1_1(a306)) | c2_1(a341))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c3_1(a306)) | c2_1(a306) | (~c1_1(a306)) | c2_1(a341))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(660,plain,
% 0.80/0.96 ((hskp8 | (~ndr1_0) | c2_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c2_1(a341) | c0_1(a341) | c3_1(a341)) <=> (hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c3_1(a306)) | c2_1(a306) | (~c1_1(a306)) | c2_1(a341))),
% 0.80/0.96 inference(rewrite,[status(thm)],[])).
% 0.80/0.96 tff(661,plain,
% 0.80/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c2_1(a341) | c0_1(a341) | c3_1(a341))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c3_1(a306)) | c2_1(a306) | (~c1_1(a306)) | c2_1(a341)))),
% 0.80/0.97 inference(monotonicity,[status(thm)],[660])).
% 0.80/0.97 tff(662,plain,
% 0.80/0.97 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c2_1(a341) | c0_1(a341) | c3_1(a341))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c3_1(a306)) | c2_1(a306) | (~c1_1(a306)) | c2_1(a341))),
% 0.80/0.97 inference(transitivity,[status(thm)],[661, 659])).
% 0.80/0.97 tff(663,plain,
% 0.80/0.97 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c2_1(a341) | c0_1(a341) | c3_1(a341))),
% 0.80/0.97 inference(quant_inst,[status(thm)],[])).
% 0.80/0.97 tff(664,plain,
% 0.80/0.97 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c3_1(a306)) | c2_1(a306) | (~c1_1(a306)) | c2_1(a341)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[663, 662])).
% 0.80/0.97 tff(665,plain,
% 0.80/0.97 ($false),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[664, 129, 583, 658, 638, 275, 274, 297, 287, 657])).
% 0.80/0.97 tff(666,plain,(c2_1(a341) | hskp8 | (~c1_1(a306)) | (~c3_1(a306)) | c0_1(a341) | c3_1(a341) | (~c1_1(a341)) | c0_1(a306)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.97 tff(667,plain,
% 0.80/0.97 (c2_1(a341)),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[666, 637, 636, 583, 275, 274, 276, 635])).
% 0.80/0.97 tff(668,assumption,(c1_1(a291)), introduced(assumption)).
% 0.80/0.97 tff(669,plain,
% 0.80/0.97 (c0_1(a291) | (~c2_1(a341))),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[490, 129, 359, 276, 668, 275, 542, 63])).
% 0.80/0.97 tff(670,plain,
% 0.80/0.97 (c0_1(a291)),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[669, 667])).
% 0.80/0.97 tff(671,plain,
% 0.80/0.97 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | c0_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306)) | (~c1_1(a341)) | (~c2_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | c0_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(672,plain,
% 0.80/0.97 ((hskp7 | (~ndr1_0) | c0_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341))) <=> (hskp7 | c0_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(673,plain,
% 0.80/0.97 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | c0_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306)) | (~c1_1(a341)) | (~c2_1(a341))))),
% 0.80/0.97 inference(monotonicity,[status(thm)],[672])).
% 0.80/0.97 tff(674,plain,
% 0.80/0.97 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | c0_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 0.80/0.97 inference(transitivity,[status(thm)],[673, 671])).
% 0.80/0.97 tff(675,plain,
% 0.80/0.97 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)))),
% 0.80/0.97 inference(quant_inst,[status(thm)],[])).
% 0.80/0.97 tff(676,plain,
% 0.80/0.97 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | c0_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306)) | (~c1_1(a341)) | (~c2_1(a341))),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[675, 674])).
% 0.80/0.97 tff(677,plain,
% 0.80/0.97 (hskp7),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[676, 129, 276, 636, 637, 275, 635, 458, 667])).
% 0.80/0.97 tff(678,plain,
% 0.80/0.97 (((~hskp7) | c0_1(a299)) <=> ((~hskp7) | c0_1(a299))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(679,axiom,((~hskp7) | c0_1(a299)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 0.80/0.97 tff(680,plain,
% 0.80/0.97 ((~hskp7) | c0_1(a299)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[679, 678])).
% 0.80/0.97 tff(681,plain,
% 0.80/0.97 ((~hskp7) | c0_1(a299)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[680, 678])).
% 0.80/0.97 tff(682,plain,
% 0.80/0.97 ((~hskp7) | c0_1(a299)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[681, 678])).
% 0.80/0.97 tff(683,plain,
% 0.80/0.97 ((~hskp7) | c0_1(a299)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[682, 678])).
% 0.80/0.97 tff(684,plain,
% 0.80/0.97 ((~hskp7) | c0_1(a299)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[683, 678])).
% 0.80/0.97 tff(685,plain,
% 0.80/0.97 (c0_1(a299)),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[684, 677])).
% 0.80/0.97 tff(686,plain,
% 0.80/0.97 (((~hskp7) | c3_1(a299)) <=> ((~hskp7) | c3_1(a299))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(687,axiom,((~hskp7) | c3_1(a299)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 0.80/0.97 tff(688,plain,
% 0.80/0.97 ((~hskp7) | c3_1(a299)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[687, 686])).
% 0.80/0.97 tff(689,plain,
% 0.80/0.97 ((~hskp7) | c3_1(a299)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[688, 686])).
% 0.80/0.97 tff(690,plain,
% 0.80/0.97 ((~hskp7) | c3_1(a299)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[689, 686])).
% 0.80/0.97 tff(691,plain,
% 0.80/0.97 ((~hskp7) | c3_1(a299)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[690, 686])).
% 0.80/0.97 tff(692,plain,
% 0.80/0.97 ((~hskp7) | c3_1(a299)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[691, 686])).
% 0.80/0.97 tff(693,plain,
% 0.80/0.97 (c3_1(a299)),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[692, 677])).
% 0.80/0.97 tff(694,assumption,(~c2_1(a299)), introduced(assumption)).
% 0.80/0.97 tff(695,plain,
% 0.80/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a299) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a299) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a341)))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(696,plain,
% 0.80/0.97 (((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341))) <=> (c0_1(a341) | c3_1(a341) | c2_1(a299) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a341)))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(697,plain,
% 0.80/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a299) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a341))))),
% 0.80/0.97 inference(monotonicity,[status(thm)],[696])).
% 0.80/0.97 tff(698,plain,
% 0.80/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a299) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a341)))),
% 0.80/0.97 inference(transitivity,[status(thm)],[697, 695])).
% 0.80/0.97 tff(699,plain,
% 0.80/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))),
% 0.80/0.97 inference(quant_inst,[status(thm)],[])).
% 0.80/0.97 tff(700,plain,
% 0.80/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a299) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a341))),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[699, 698])).
% 0.80/0.97 tff(701,plain,
% 0.80/0.97 ((~c0_1(a291)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a341))),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[700, 129, 275, 274, 694, 542, 541, 540])).
% 0.80/0.97 tff(702,plain,
% 0.80/0.97 ($false),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[701, 693, 685, 667, 670])).
% 0.80/0.97 tff(703,plain,(hskp8 | c0_1(a341) | c3_1(a341) | c2_1(a299) | c2_1(a291) | c3_1(a291) | (~c1_1(a341)) | (~c1_1(a291)) | hskp23), inference(lemma,lemma(discharge,[]))).
% 0.80/0.97 tff(704,plain,
% 0.80/0.97 (c2_1(a299)),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[703, 551, 274, 275, 476, 498, 276, 484, 318])).
% 0.80/0.97 tff(705,plain,
% 0.80/0.97 (((~hskp7) | (~c2_1(a299))) <=> ((~hskp7) | (~c2_1(a299)))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(706,plain,
% 0.80/0.97 (((~c2_1(a299)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a299)))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(707,axiom,((~c2_1(a299)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 0.80/0.97 tff(708,plain,
% 0.80/0.97 ((~hskp7) | (~c2_1(a299))),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[707, 706])).
% 0.80/0.97 tff(709,plain,
% 0.80/0.97 ((~hskp7) | (~c2_1(a299))),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[708, 705])).
% 0.80/0.97 tff(710,plain,
% 0.80/0.97 (~hskp7),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[709, 704])).
% 0.80/0.97 tff(711,plain,
% 0.80/0.97 ($false),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[676, 129, 710, 276, 632, 624, 275, 616, 458, 448])).
% 0.80/0.97 tff(712,plain,(hskp3 | (~c1_1(a341)) | c0_1(a341) | c3_1(a341) | hskp23), inference(lemma,lemma(discharge,[]))).
% 0.80/0.97 tff(713,plain,
% 0.80/0.97 (hskp3),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[712, 318, 275, 274, 276])).
% 0.80/0.97 tff(714,plain,
% 0.80/0.97 (((~hskp3) | (~c1_1(a294))) <=> ((~hskp3) | (~c1_1(a294)))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(715,plain,
% 0.80/0.97 (((~c1_1(a294)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a294)))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(716,axiom,((~c1_1(a294)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 0.80/0.97 tff(717,plain,
% 0.80/0.97 ((~hskp3) | (~c1_1(a294))),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[716, 715])).
% 0.80/0.97 tff(718,plain,
% 0.80/0.97 ((~hskp3) | (~c1_1(a294))),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[717, 714])).
% 0.80/0.97 tff(719,plain,
% 0.80/0.97 (~c1_1(a294)),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[718, 713])).
% 0.80/0.97 tff(720,plain,
% 0.80/0.97 (((~hskp3) | c2_1(a294)) <=> ((~hskp3) | c2_1(a294))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(721,axiom,((~hskp3) | c2_1(a294)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 0.80/0.97 tff(722,plain,
% 0.80/0.97 ((~hskp3) | c2_1(a294)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[721, 720])).
% 0.80/0.97 tff(723,plain,
% 0.80/0.97 ((~hskp3) | c2_1(a294)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[722, 720])).
% 0.80/0.97 tff(724,plain,
% 0.80/0.97 ((~hskp3) | c2_1(a294)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[723, 720])).
% 0.80/0.97 tff(725,plain,
% 0.80/0.97 ((~hskp3) | c2_1(a294)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[724, 720])).
% 0.80/0.97 tff(726,plain,
% 0.80/0.97 ((~hskp3) | c2_1(a294)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[725, 720])).
% 0.80/0.97 tff(727,plain,
% 0.80/0.97 (c2_1(a294)),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[726, 713])).
% 0.80/0.97 tff(728,plain,
% 0.80/0.97 (((~hskp3) | c0_1(a294)) <=> ((~hskp3) | c0_1(a294))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(729,axiom,((~hskp3) | c0_1(a294)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 0.80/0.97 tff(730,plain,
% 0.80/0.97 ((~hskp3) | c0_1(a294)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[729, 728])).
% 0.80/0.97 tff(731,plain,
% 0.80/0.97 ((~hskp3) | c0_1(a294)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[730, 728])).
% 0.80/0.97 tff(732,plain,
% 0.80/0.97 ((~hskp3) | c0_1(a294)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[731, 728])).
% 0.80/0.97 tff(733,plain,
% 0.80/0.97 ((~hskp3) | c0_1(a294)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[732, 728])).
% 0.80/0.97 tff(734,plain,
% 0.80/0.97 ((~hskp3) | c0_1(a294)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[733, 728])).
% 0.80/0.97 tff(735,plain,
% 0.80/0.97 (c0_1(a294)),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[734, 713])).
% 0.80/0.97 tff(736,plain,
% 0.80/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a341)))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(737,plain,
% 0.80/0.97 (((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a294) | (~c3_1(a294)) | (~c0_1(a294)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341))) <=> (c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a341)))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(738,plain,
% 0.80/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a294) | (~c3_1(a294)) | (~c0_1(a294)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a341))))),
% 0.80/0.97 inference(monotonicity,[status(thm)],[737])).
% 0.80/0.97 tff(739,plain,
% 0.80/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a294) | (~c3_1(a294)) | (~c0_1(a294)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a341)))),
% 0.80/0.97 inference(transitivity,[status(thm)],[738, 736])).
% 0.80/0.97 tff(740,plain,
% 0.80/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a294) | (~c3_1(a294)) | (~c0_1(a294)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))),
% 0.80/0.97 inference(quant_inst,[status(thm)],[])).
% 0.80/0.97 tff(741,plain,
% 0.80/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a341))),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[740, 739])).
% 0.80/0.97 tff(742,plain,
% 0.80/0.97 (~c3_1(a294)),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[741, 129, 276, 735, 727, 275, 274, 719, 11])).
% 0.80/0.97 tff(743,plain,
% 0.80/0.97 (((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294))) <=> ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp23 | hskp8 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(744,plain,
% 0.80/0.97 ((hskp23 | hskp8 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c2_1(a294))) <=> (hskp23 | hskp8 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(745,plain,
% 0.80/0.97 (((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c2_1(a294)))) <=> ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294)))),
% 0.80/0.97 inference(monotonicity,[status(thm)],[744])).
% 0.80/0.97 tff(746,plain,
% 0.80/0.97 (((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c2_1(a294)))) <=> ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp23 | hskp8 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294))),
% 0.80/0.97 inference(transitivity,[status(thm)],[745, 743])).
% 0.80/0.97 tff(747,plain,
% 0.80/0.97 ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c2_1(a294)))),
% 0.80/0.97 inference(quant_inst,[status(thm)],[])).
% 0.80/0.97 tff(748,plain,
% 0.80/0.97 ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp23 | hskp8 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[747, 746])).
% 0.80/0.97 tff(749,plain,
% 0.80/0.97 (hskp8 | c3_1(a294)),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[748, 129, 318, 727, 719, 561])).
% 0.80/0.97 tff(750,plain,
% 0.80/0.97 (hskp8),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[749, 742])).
% 0.80/0.97 tff(751,plain,
% 0.80/0.97 (~c1_1(a300)),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[504, 750])).
% 0.80/0.97 tff(752,plain,
% 0.80/0.97 (c3_1(a300)),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[512, 750])).
% 0.80/0.97 tff(753,plain,
% 0.80/0.97 (c0_1(a300)),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[520, 750])).
% 0.80/0.97 tff(754,plain,
% 0.80/0.97 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp29 | hskp15 | c1_1(a300) | (~ndr1_0) | (~c3_1(a300)) | (~c0_1(a300)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp29 | hskp15 | c1_1(a300) | (~ndr1_0) | (~c3_1(a300)) | (~c0_1(a300)))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(755,plain,
% 0.80/0.97 ((hskp29 | hskp15 | (~ndr1_0) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300))) <=> (hskp29 | hskp15 | c1_1(a300) | (~ndr1_0) | (~c3_1(a300)) | (~c0_1(a300)))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(756,plain,
% 0.80/0.97 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp29 | hskp15 | c1_1(a300) | (~ndr1_0) | (~c3_1(a300)) | (~c0_1(a300))))),
% 0.80/0.97 inference(monotonicity,[status(thm)],[755])).
% 0.80/0.97 tff(757,plain,
% 0.80/0.97 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp29 | hskp15 | c1_1(a300) | (~ndr1_0) | (~c3_1(a300)) | (~c0_1(a300)))),
% 0.80/0.97 inference(transitivity,[status(thm)],[756, 754])).
% 0.80/0.97 tff(758,plain,
% 0.80/0.97 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)))),
% 0.80/0.97 inference(quant_inst,[status(thm)],[])).
% 0.80/0.97 tff(759,plain,
% 0.80/0.97 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp29 | hskp15 | c1_1(a300) | (~ndr1_0) | (~c3_1(a300)) | (~c0_1(a300))),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[758, 757])).
% 0.80/0.97 tff(760,plain,
% 0.80/0.97 (hskp15),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[759, 129, 359, 753, 752, 751, 317])).
% 0.80/0.97 tff(761,plain,
% 0.80/0.97 (((~hskp15) | c1_1(a311)) <=> ((~hskp15) | c1_1(a311))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(762,axiom,((~hskp15) | c1_1(a311)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 0.80/0.97 tff(763,plain,
% 0.80/0.97 ((~hskp15) | c1_1(a311)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[762, 761])).
% 0.80/0.97 tff(764,plain,
% 0.80/0.97 ((~hskp15) | c1_1(a311)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[763, 761])).
% 0.80/0.97 tff(765,plain,
% 0.80/0.97 ((~hskp15) | c1_1(a311)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[764, 761])).
% 0.80/0.97 tff(766,plain,
% 0.80/0.97 ((~hskp15) | c1_1(a311)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[765, 761])).
% 0.80/0.97 tff(767,plain,
% 0.80/0.97 ((~hskp15) | c1_1(a311)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[766, 761])).
% 0.80/0.97 tff(768,plain,
% 0.80/0.97 (c1_1(a311)),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[767, 760])).
% 0.80/0.97 tff(769,plain,
% 0.80/0.97 (((~hskp15) | c0_1(a311)) <=> ((~hskp15) | c0_1(a311))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(770,axiom,((~hskp15) | c0_1(a311)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 0.80/0.97 tff(771,plain,
% 0.80/0.97 ((~hskp15) | c0_1(a311)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[770, 769])).
% 0.80/0.97 tff(772,plain,
% 0.80/0.97 ((~hskp15) | c0_1(a311)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[771, 769])).
% 0.80/0.97 tff(773,plain,
% 0.80/0.97 ((~hskp15) | c0_1(a311)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[772, 769])).
% 0.80/0.97 tff(774,plain,
% 0.80/0.97 ((~hskp15) | c0_1(a311)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[773, 769])).
% 0.80/0.97 tff(775,plain,
% 0.80/0.97 ((~hskp15) | c0_1(a311)),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[774, 769])).
% 0.80/0.97 tff(776,plain,
% 0.80/0.97 (c0_1(a311)),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[775, 760])).
% 0.80/0.97 tff(777,plain,
% 0.80/0.97 (((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | (~c0_1(a311)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(778,plain,
% 0.80/0.97 ((hskp23 | (~ndr1_0) | (~c2_1(a311)) | (~c1_1(a311)) | (~c0_1(a311))) <=> (hskp23 | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(779,plain,
% 0.80/0.97 (((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | (~c2_1(a311)) | (~c1_1(a311)) | (~c0_1(a311)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | (~c0_1(a311))))),
% 0.80/0.97 inference(monotonicity,[status(thm)],[778])).
% 0.80/0.97 tff(780,plain,
% 0.80/0.97 (((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | (~c2_1(a311)) | (~c1_1(a311)) | (~c0_1(a311)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 0.80/0.97 inference(transitivity,[status(thm)],[779, 777])).
% 0.80/0.97 tff(781,plain,
% 0.80/0.97 ((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | (~c2_1(a311)) | (~c1_1(a311)) | (~c0_1(a311)))),
% 0.80/0.97 inference(quant_inst,[status(thm)],[])).
% 0.80/0.97 tff(782,plain,
% 0.80/0.97 ((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | (~c0_1(a311))),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[781, 780])).
% 0.80/0.97 tff(783,plain,
% 0.80/0.97 (~c2_1(a311)),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[782, 129, 318, 776, 768, 307])).
% 0.80/0.97 tff(784,plain,
% 0.80/0.97 (((~hskp15) | (~c3_1(a311))) <=> ((~hskp15) | (~c3_1(a311)))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(785,plain,
% 0.80/0.97 (((~c3_1(a311)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a311)))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(786,axiom,((~c3_1(a311)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 0.80/0.97 tff(787,plain,
% 0.80/0.97 ((~hskp15) | (~c3_1(a311))),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[786, 785])).
% 0.80/0.97 tff(788,plain,
% 0.80/0.97 ((~hskp15) | (~c3_1(a311))),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[787, 784])).
% 0.80/0.97 tff(789,plain,
% 0.80/0.97 (~c3_1(a311)),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[788, 760])).
% 0.80/0.97 tff(790,plain,
% 0.80/0.97 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c3_1(a311) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a311) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311)))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(791,plain,
% 0.80/0.97 ((hskp7 | (~ndr1_0) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294))) <=> (hskp7 | c3_1(a311) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311)))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(792,plain,
% 0.80/0.97 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c3_1(a311) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311))))),
% 0.80/0.97 inference(monotonicity,[status(thm)],[791])).
% 0.80/0.97 tff(793,plain,
% 0.80/0.97 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a311) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311)))),
% 0.80/0.97 inference(transitivity,[status(thm)],[792, 790])).
% 0.80/0.97 tff(794,plain,
% 0.80/0.97 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))),
% 0.80/0.97 inference(quant_inst,[status(thm)],[])).
% 0.80/0.97 tff(795,plain,
% 0.80/0.97 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a311) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311))),
% 0.80/0.97 inference(modus_ponens,[status(thm)],[794, 793])).
% 0.80/0.97 tff(796,plain,
% 0.80/0.97 (hskp7),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[795, 129, 776, 768, 735, 727, 789, 719, 52])).
% 0.80/0.97 tff(797,plain,
% 0.80/0.97 (~c2_1(a299)),
% 0.80/0.97 inference(unit_resolution,[status(thm)],[709, 796])).
% 0.80/0.97 tff(798,plain,
% 0.80/0.97 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | c1_1(a300) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c3_1(a300)) | (~c0_1(a300)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a300) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c3_1(a300)) | (~c0_1(a300)))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(799,plain,
% 0.80/0.97 ((hskp16 | (~ndr1_0) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294))) <=> (hskp16 | c1_1(a300) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c3_1(a300)) | (~c0_1(a300)))),
% 0.80/0.97 inference(rewrite,[status(thm)],[])).
% 0.80/0.97 tff(800,plain,
% 0.80/0.97 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | c1_1(a300) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c3_1(a300)) | (~c0_1(a300))))),
% 0.80/0.97 inference(monotonicity,[status(thm)],[799])).
% 0.80/0.97 tff(801,plain,
% 0.80/0.97 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a300) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c3_1(a300)) | (~c0_1(a300)))),
% 0.80/0.98 inference(transitivity,[status(thm)],[800, 798])).
% 0.80/0.98 tff(802,plain,
% 0.80/0.98 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))),
% 0.80/0.98 inference(quant_inst,[status(thm)],[])).
% 0.80/0.98 tff(803,plain,
% 0.80/0.98 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a300) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c3_1(a300)) | (~c0_1(a300))),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[802, 801])).
% 0.80/0.98 tff(804,plain,
% 0.80/0.98 (hskp16),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[803, 129, 753, 752, 735, 727, 751, 719, 273])).
% 0.80/0.98 tff(805,plain,
% 0.80/0.98 (~c3_1(a315)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[438, 804])).
% 0.80/0.98 tff(806,plain,
% 0.80/0.98 (~c0_1(a315)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[420, 804])).
% 0.80/0.98 tff(807,plain,
% 0.80/0.98 (c3_1(a299)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[692, 796])).
% 0.80/0.98 tff(808,plain,
% 0.80/0.98 (c0_1(a299)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[684, 796])).
% 0.80/0.98 tff(809,plain,
% 0.80/0.98 (c2_1(a315)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[414, 804])).
% 0.80/0.98 tff(810,plain,
% 0.80/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315)))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(811,plain,
% 0.80/0.98 (((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315))) <=> (c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315)))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(812,plain,
% 0.80/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315))))),
% 0.80/0.98 inference(monotonicity,[status(thm)],[811])).
% 0.80/0.98 tff(813,plain,
% 0.80/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315)))),
% 0.80/0.98 inference(transitivity,[status(thm)],[812, 810])).
% 0.80/0.98 tff(814,plain,
% 0.80/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))),
% 0.80/0.98 inference(quant_inst,[status(thm)],[])).
% 0.80/0.98 tff(815,plain,
% 0.80/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315))),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[814, 813])).
% 0.80/0.98 tff(816,plain,
% 0.80/0.98 ($false),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[815, 129, 809, 776, 808, 807, 806, 805, 789, 797, 540, 783])).
% 0.80/0.98 tff(817,plain,(hskp23 | (~c1_1(a341)) | c0_1(a341) | c3_1(a341)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.98 tff(818,plain,
% 0.80/0.98 (hskp23),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[817, 276, 275, 274])).
% 0.80/0.98 tff(819,plain,
% 0.80/0.98 (((~hskp23) | (~c2_1(a337))) <=> ((~hskp23) | (~c2_1(a337)))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(820,plain,
% 0.80/0.98 (((~c2_1(a337)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a337)))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(821,axiom,((~c2_1(a337)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 0.80/0.98 tff(822,plain,
% 0.80/0.98 ((~hskp23) | (~c2_1(a337))),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[821, 820])).
% 0.80/0.98 tff(823,plain,
% 0.80/0.98 ((~hskp23) | (~c2_1(a337))),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[822, 819])).
% 0.80/0.98 tff(824,plain,
% 0.80/0.98 (~c2_1(a337)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[823, 818])).
% 0.80/0.98 tff(825,plain,
% 0.80/0.98 (((~hskp23) | c3_1(a337)) <=> ((~hskp23) | c3_1(a337))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(826,axiom,((~hskp23) | c3_1(a337)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 0.80/0.98 tff(827,plain,
% 0.80/0.98 ((~hskp23) | c3_1(a337)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[826, 825])).
% 0.80/0.98 tff(828,plain,
% 0.80/0.98 ((~hskp23) | c3_1(a337)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[827, 825])).
% 0.80/0.98 tff(829,plain,
% 0.80/0.98 ((~hskp23) | c3_1(a337)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[828, 825])).
% 0.80/0.98 tff(830,plain,
% 0.80/0.98 ((~hskp23) | c3_1(a337)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[829, 825])).
% 0.80/0.98 tff(831,plain,
% 0.80/0.98 ((~hskp23) | c3_1(a337)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[830, 825])).
% 0.80/0.98 tff(832,plain,
% 0.80/0.98 (c3_1(a337)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[831, 818])).
% 0.80/0.98 tff(833,plain,
% 0.80/0.98 (((~hskp23) | c1_1(a337)) <=> ((~hskp23) | c1_1(a337))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(834,axiom,((~hskp23) | c1_1(a337)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 0.80/0.98 tff(835,plain,
% 0.80/0.98 ((~hskp23) | c1_1(a337)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[834, 833])).
% 0.80/0.98 tff(836,plain,
% 0.80/0.98 ((~hskp23) | c1_1(a337)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[835, 833])).
% 0.80/0.98 tff(837,plain,
% 0.80/0.98 ((~hskp23) | c1_1(a337)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[836, 833])).
% 0.80/0.98 tff(838,plain,
% 0.80/0.98 ((~hskp23) | c1_1(a337)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[837, 833])).
% 0.80/0.98 tff(839,plain,
% 0.80/0.98 ((~hskp23) | c1_1(a337)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[838, 833])).
% 0.80/0.98 tff(840,plain,
% 0.80/0.98 (c1_1(a337)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[839, 818])).
% 0.80/0.98 tff(841,plain,
% 0.80/0.98 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a341) | c3_1(a341) | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a341))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a341) | c3_1(a341) | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a341))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(842,plain,
% 0.80/0.98 ((hskp8 | (~ndr1_0) | c2_1(a337) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a341) | c0_1(a341) | c3_1(a341)) <=> (hskp8 | c0_1(a341) | c3_1(a341) | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a341))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(843,plain,
% 0.80/0.98 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a337) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a341) | c0_1(a341) | c3_1(a341))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a341) | c3_1(a341) | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a341)))),
% 0.80/0.98 inference(monotonicity,[status(thm)],[842])).
% 0.80/0.98 tff(844,plain,
% 0.80/0.98 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a337) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a341) | c0_1(a341) | c3_1(a341))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a341) | c3_1(a341) | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a341))),
% 0.80/0.98 inference(transitivity,[status(thm)],[843, 841])).
% 0.80/0.98 tff(845,plain,
% 0.80/0.98 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a337) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a341) | c0_1(a341) | c3_1(a341))),
% 0.80/0.98 inference(quant_inst,[status(thm)],[])).
% 0.80/0.98 tff(846,plain,
% 0.80/0.98 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a341) | c3_1(a341) | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a341)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[845, 844])).
% 0.80/0.98 tff(847,plain,
% 0.80/0.98 (hskp8),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[846, 129, 840, 832, 275, 274, 824, 297, 287])).
% 0.80/0.98 tff(848,plain,
% 0.80/0.98 (~c1_1(a300)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[504, 847])).
% 0.80/0.98 tff(849,plain,
% 0.80/0.98 (c3_1(a300)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[512, 847])).
% 0.80/0.98 tff(850,plain,
% 0.80/0.98 (c0_1(a300)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[520, 847])).
% 0.80/0.98 tff(851,plain,
% 0.80/0.98 (~c2_1(a300)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[527, 129, 276, 850, 849, 275, 274, 848, 11])).
% 0.80/0.98 tff(852,plain,
% 0.80/0.98 (hskp29),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[447, 287, 276, 64, 275])).
% 0.80/0.98 tff(853,plain,
% 0.80/0.98 (c3_1(a301)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[349, 852])).
% 0.80/0.98 tff(854,plain,
% 0.80/0.98 (c2_1(a301)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[326, 852])).
% 0.80/0.98 tff(855,plain,
% 0.80/0.98 (c0_1(a301)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[334, 852])).
% 0.80/0.98 tff(856,assumption,(~hskp22), introduced(assumption)).
% 0.80/0.98 tff(857,plain,
% 0.80/0.98 (hskp5),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[406, 32, 856])).
% 0.80/0.98 tff(858,plain,
% 0.80/0.98 (~c0_1(a297)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[365, 857])).
% 0.80/0.98 tff(859,plain,
% 0.80/0.98 (c2_1(a297)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[381, 857])).
% 0.80/0.98 tff(860,plain,
% 0.80/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a341) | c3_1(a341) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a341)) | c2_1(a341))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a341) | c3_1(a341) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a341)) | c2_1(a341))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(861,plain,
% 0.80/0.98 (((~ndr1_0) | c3_1(a341) | c2_1(a341) | (~c1_1(a341)) | c0_1(a297) | (~c3_1(a297)) | (~c2_1(a297)) | c3_1(a341) | c2_1(a341) | c0_1(a341)) <=> (c0_1(a341) | c3_1(a341) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a341)) | c2_1(a341))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(862,plain,
% 0.80/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a341) | c2_1(a341) | (~c1_1(a341)) | c0_1(a297) | (~c3_1(a297)) | (~c2_1(a297)) | c3_1(a341) | c2_1(a341) | c0_1(a341))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a341) | c3_1(a341) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a341)) | c2_1(a341)))),
% 0.80/0.98 inference(monotonicity,[status(thm)],[861])).
% 0.80/0.98 tff(863,plain,
% 0.80/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a341) | c2_1(a341) | (~c1_1(a341)) | c0_1(a297) | (~c3_1(a297)) | (~c2_1(a297)) | c3_1(a341) | c2_1(a341) | c0_1(a341))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a341) | c3_1(a341) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a341)) | c2_1(a341))),
% 0.80/0.98 inference(transitivity,[status(thm)],[862, 860])).
% 0.80/0.98 tff(864,plain,
% 0.80/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a341) | c2_1(a341) | (~c1_1(a341)) | c0_1(a297) | (~c3_1(a297)) | (~c2_1(a297)) | c3_1(a341) | c2_1(a341) | c0_1(a341))),
% 0.80/0.98 inference(quant_inst,[status(thm)],[])).
% 0.80/0.98 tff(865,plain,
% 0.80/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a341) | c3_1(a341) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a341)) | c2_1(a341)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[864, 863])).
% 0.80/0.98 tff(866,plain,
% 0.80/0.98 (~c3_1(a297)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[865, 129, 276, 859, 275, 274, 858, 648, 287])).
% 0.80/0.98 tff(867,plain,
% 0.80/0.98 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 0.80/0.98 inference(bind,[status(th)],[])).
% 0.80/0.98 tff(868,plain,
% 0.80/0.98 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.80/0.98 inference(quant_intro,[status(thm)],[867])).
% 0.80/0.98 tff(869,plain,
% 0.80/0.98 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(870,plain,
% 0.80/0.98 (^[V: $i, U: $i] : 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(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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp4) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp4))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~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(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.80/0.98 inference(bind,[status(th)],[])).
% 0.80/0.98 tff(871,plain,
% 0.80/0.98 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.80/0.98 inference(quant_intro,[status(thm)],[870])).
% 0.80/0.98 tff(872,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 0.80/0.98 tff(873,plain,
% 0.80/0.98 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[872, 871])).
% 0.80/0.98 tff(874,plain,
% 0.80/0.98 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[873, 869])).
% 0.80/0.98 tff(875,plain,(
% 0.80/0.98 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.80/0.98 inference(skolemize,[status(sab)],[874])).
% 0.80/0.98 tff(876,plain,
% 0.80/0.98 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[875, 868])).
% 0.80/0.98 tff(877,plain,
% 0.80/0.98 ((hskp22 | hskp16 | hskp9) <=> (hskp22 | hskp16 | hskp9)),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(878,plain,
% 0.80/0.98 (((hskp16 | hskp9) | hskp22) <=> (hskp22 | hskp16 | hskp9)),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(879,plain,
% 0.80/0.98 ((hskp9 | hskp16) <=> (hskp16 | hskp9)),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(880,plain,
% 0.80/0.98 (((hskp9 | hskp16) | hskp22) <=> ((hskp16 | hskp9) | hskp22)),
% 0.80/0.98 inference(monotonicity,[status(thm)],[879])).
% 0.80/0.98 tff(881,plain,
% 0.80/0.98 (((hskp9 | hskp16) | hskp22) <=> (hskp22 | hskp16 | hskp9)),
% 0.80/0.98 inference(transitivity,[status(thm)],[880, 878])).
% 0.80/0.98 tff(882,axiom,((hskp9 | hskp16) | hskp22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 0.80/0.98 tff(883,plain,
% 0.80/0.98 (hskp22 | hskp16 | hskp9),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[882, 881])).
% 0.80/0.98 tff(884,plain,
% 0.80/0.98 (hskp22 | hskp16 | hskp9),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[883, 877])).
% 0.80/0.98 tff(885,plain,
% 0.80/0.98 (hskp22 | hskp16 | hskp9),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[884, 877])).
% 0.80/0.98 tff(886,plain,
% 0.80/0.98 (hskp22 | hskp16 | hskp9),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[885, 877])).
% 0.80/0.98 tff(887,plain,
% 0.80/0.98 (hskp22 | hskp16 | hskp9),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[886, 877])).
% 0.80/0.98 tff(888,plain,
% 0.80/0.98 (hskp9),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[887, 32, 856])).
% 0.80/0.98 tff(889,plain,
% 0.80/0.98 (((~hskp9) | (~c2_1(a304))) <=> ((~hskp9) | (~c2_1(a304)))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(890,plain,
% 0.80/0.98 (((~c2_1(a304)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a304)))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(891,axiom,((~c2_1(a304)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 0.80/0.98 tff(892,plain,
% 0.80/0.98 ((~hskp9) | (~c2_1(a304))),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[891, 890])).
% 0.80/0.98 tff(893,plain,
% 0.80/0.98 ((~hskp9) | (~c2_1(a304))),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[892, 889])).
% 0.80/0.98 tff(894,plain,
% 0.80/0.98 (~c2_1(a304)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[893, 888])).
% 0.80/0.98 tff(895,plain,
% 0.80/0.98 (((~hskp9) | c1_1(a304)) <=> ((~hskp9) | c1_1(a304))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(896,axiom,((~hskp9) | c1_1(a304)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 0.80/0.98 tff(897,plain,
% 0.80/0.98 ((~hskp9) | c1_1(a304)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[896, 895])).
% 0.80/0.98 tff(898,plain,
% 0.80/0.98 ((~hskp9) | c1_1(a304)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[897, 895])).
% 0.80/0.98 tff(899,plain,
% 0.80/0.98 ((~hskp9) | c1_1(a304)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[898, 895])).
% 0.80/0.98 tff(900,plain,
% 0.80/0.98 ((~hskp9) | c1_1(a304)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[899, 895])).
% 0.80/0.98 tff(901,plain,
% 0.80/0.98 ((~hskp9) | c1_1(a304)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[900, 895])).
% 0.80/0.98 tff(902,plain,
% 0.80/0.98 (c1_1(a304)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[901, 888])).
% 0.80/0.98 tff(903,plain,
% 0.80/0.98 (((~hskp9) | c0_1(a304)) <=> ((~hskp9) | c0_1(a304))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(904,axiom,((~hskp9) | c0_1(a304)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 0.80/0.98 tff(905,plain,
% 0.80/0.98 ((~hskp9) | c0_1(a304)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[904, 903])).
% 0.80/0.98 tff(906,plain,
% 0.80/0.98 ((~hskp9) | c0_1(a304)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[905, 903])).
% 0.80/0.98 tff(907,plain,
% 0.80/0.98 ((~hskp9) | c0_1(a304)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[906, 903])).
% 0.80/0.98 tff(908,plain,
% 0.80/0.98 ((~hskp9) | c0_1(a304)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[907, 903])).
% 0.80/0.98 tff(909,plain,
% 0.80/0.98 ((~hskp9) | c0_1(a304)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[908, 903])).
% 0.80/0.98 tff(910,plain,
% 0.80/0.98 (c0_1(a304)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[909, 888])).
% 0.80/0.98 tff(911,assumption,(c3_1(a301)), introduced(assumption)).
% 0.80/0.98 tff(912,assumption,(c2_1(a301)), introduced(assumption)).
% 0.80/0.98 tff(913,assumption,(c0_1(a301)), introduced(assumption)).
% 0.80/0.98 tff(914,plain,
% 0.80/0.98 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp4 | c2_1(a304) | (~ndr1_0) | (~c1_1(a304)) | (~c0_1(a304)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp4 | c2_1(a304) | (~ndr1_0) | (~c1_1(a304)) | (~c0_1(a304)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(915,plain,
% 0.80/0.98 ((hskp4 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c2_1(a304) | (~c1_1(a304)) | (~c0_1(a304))) <=> (hskp4 | c2_1(a304) | (~ndr1_0) | (~c1_1(a304)) | (~c0_1(a304)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(916,plain,
% 0.80/0.98 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c2_1(a304) | (~c1_1(a304)) | (~c0_1(a304)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp4 | c2_1(a304) | (~ndr1_0) | (~c1_1(a304)) | (~c0_1(a304)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))))),
% 0.80/0.98 inference(monotonicity,[status(thm)],[915])).
% 0.80/0.98 tff(917,plain,
% 0.80/0.98 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c2_1(a304) | (~c1_1(a304)) | (~c0_1(a304)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp4 | c2_1(a304) | (~ndr1_0) | (~c1_1(a304)) | (~c0_1(a304)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.80/0.98 inference(transitivity,[status(thm)],[916, 914])).
% 0.80/0.98 tff(918,plain,
% 0.80/0.98 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c2_1(a304) | (~c1_1(a304)) | (~c0_1(a304)))),
% 0.80/0.98 inference(quant_inst,[status(thm)],[])).
% 0.80/0.98 tff(919,plain,
% 0.80/0.98 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp4 | c2_1(a304) | (~ndr1_0) | (~c1_1(a304)) | (~c0_1(a304)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[918, 917])).
% 0.80/0.98 tff(920,plain,
% 0.80/0.98 (hskp4),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[919, 129, 913, 912, 911, 910, 902, 894, 876])).
% 0.80/0.98 tff(921,plain,
% 0.80/0.98 (((~hskp4) | (~c3_1(a295))) <=> ((~hskp4) | (~c3_1(a295)))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(922,plain,
% 0.80/0.98 (((~c3_1(a295)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a295)))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(923,axiom,((~c3_1(a295)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 0.80/0.98 tff(924,plain,
% 0.80/0.98 ((~hskp4) | (~c3_1(a295))),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[923, 922])).
% 0.80/0.98 tff(925,plain,
% 0.80/0.98 ((~hskp4) | (~c3_1(a295))),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[924, 921])).
% 0.80/0.98 tff(926,plain,
% 0.80/0.98 (~c3_1(a295)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[925, 920])).
% 0.80/0.98 tff(927,plain,
% 0.80/0.98 (((~hskp4) | (~c2_1(a295))) <=> ((~hskp4) | (~c2_1(a295)))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(928,plain,
% 0.80/0.98 (((~c2_1(a295)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a295)))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(929,axiom,((~c2_1(a295)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 0.80/0.98 tff(930,plain,
% 0.80/0.98 ((~hskp4) | (~c2_1(a295))),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[929, 928])).
% 0.80/0.98 tff(931,plain,
% 0.80/0.98 ((~hskp4) | (~c2_1(a295))),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[930, 927])).
% 0.80/0.98 tff(932,plain,
% 0.80/0.98 (~c2_1(a295)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[931, 920])).
% 0.80/0.98 tff(933,plain,
% 0.80/0.98 (^[U: $i] : refl((hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 0.80/0.98 inference(bind,[status(th)],[])).
% 0.80/0.98 tff(934,plain,
% 0.80/0.98 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.80/0.98 inference(quant_intro,[status(thm)],[933])).
% 0.80/0.98 tff(935,plain,
% 0.80/0.98 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(936,plain,
% 0.80/0.98 (^[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) | hskp16) <=> ((hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp16))), rewrite(((hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp16) <=> (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) | hskp16) <=> (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 0.80/0.98 inference(bind,[status(th)],[])).
% 0.80/0.98 tff(937,plain,
% 0.80/0.98 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) | hskp16) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.80/0.98 inference(quant_intro,[status(thm)],[936])).
% 0.80/0.98 tff(938,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 0.80/0.98 tff(939,plain,
% 0.80/0.98 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[938, 937])).
% 0.80/0.98 tff(940,plain,
% 0.80/0.98 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[939, 935])).
% 0.80/0.98 tff(941,plain,(
% 0.80/0.98 ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.80/0.98 inference(skolemize,[status(sab)],[940])).
% 0.80/0.98 tff(942,plain,
% 0.80/0.98 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[941, 934])).
% 0.80/0.98 tff(943,plain,
% 0.80/0.98 (c1_1(a297)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[373, 857])).
% 0.80/0.98 tff(944,plain,
% 0.80/0.98 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp13 | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp16 | hskp13 | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(945,plain,
% 0.80/0.98 ((hskp16 | hskp13 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297))) <=> (hskp16 | hskp13 | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(946,plain,
% 0.80/0.98 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp13 | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297))))),
% 0.80/0.98 inference(monotonicity,[status(thm)],[945])).
% 0.80/0.98 tff(947,plain,
% 0.80/0.98 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp16 | hskp13 | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)))),
% 0.80/0.98 inference(transitivity,[status(thm)],[946, 944])).
% 0.80/0.98 tff(948,plain,
% 0.80/0.98 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)))),
% 0.80/0.98 inference(quant_inst,[status(thm)],[])).
% 0.80/0.98 tff(949,plain,
% 0.80/0.98 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp16 | hskp13 | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297))),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[948, 947])).
% 0.80/0.98 tff(950,plain,
% 0.80/0.98 (hskp13),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[949, 129, 32, 943, 859, 858, 942])).
% 0.80/0.98 tff(951,plain,
% 0.80/0.98 (((~hskp13) | (~c2_1(a308))) <=> ((~hskp13) | (~c2_1(a308)))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(952,plain,
% 0.80/0.98 (((~c2_1(a308)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a308)))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(953,axiom,((~c2_1(a308)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 0.80/0.98 tff(954,plain,
% 0.80/0.98 ((~hskp13) | (~c2_1(a308))),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[953, 952])).
% 0.80/0.98 tff(955,plain,
% 0.80/0.98 ((~hskp13) | (~c2_1(a308))),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[954, 951])).
% 0.80/0.98 tff(956,plain,
% 0.80/0.98 (~c2_1(a308)),
% 0.80/0.98 inference(unit_resolution,[status(thm)],[955, 950])).
% 0.80/0.98 tff(957,plain,
% 0.80/0.98 (((~hskp4) | c0_1(a295)) <=> ((~hskp4) | c0_1(a295))),
% 0.80/0.98 inference(rewrite,[status(thm)],[])).
% 0.80/0.98 tff(958,axiom,((~hskp4) | c0_1(a295)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 0.80/0.98 tff(959,plain,
% 0.80/0.98 ((~hskp4) | c0_1(a295)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[958, 957])).
% 0.80/0.98 tff(960,plain,
% 0.80/0.98 ((~hskp4) | c0_1(a295)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[959, 957])).
% 0.80/0.98 tff(961,plain,
% 0.80/0.98 ((~hskp4) | c0_1(a295)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[960, 957])).
% 0.80/0.98 tff(962,plain,
% 0.80/0.98 ((~hskp4) | c0_1(a295)),
% 0.80/0.98 inference(modus_ponens,[status(thm)],[961, 957])).
% 0.80/0.98 tff(963,plain,
% 0.80/0.98 ((~hskp4) | c0_1(a295)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[962, 957])).
% 0.80/0.99 tff(964,plain,
% 0.80/0.99 (c0_1(a295)),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[963, 920])).
% 0.80/0.99 tff(965,plain,
% 0.80/0.99 (((~hskp13) | c0_1(a308)) <=> ((~hskp13) | c0_1(a308))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(966,axiom,((~hskp13) | c0_1(a308)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 0.80/0.99 tff(967,plain,
% 0.80/0.99 ((~hskp13) | c0_1(a308)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[966, 965])).
% 0.80/0.99 tff(968,plain,
% 0.80/0.99 ((~hskp13) | c0_1(a308)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[967, 965])).
% 0.80/0.99 tff(969,plain,
% 0.80/0.99 ((~hskp13) | c0_1(a308)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[968, 965])).
% 0.80/0.99 tff(970,plain,
% 0.80/0.99 ((~hskp13) | c0_1(a308)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[969, 965])).
% 0.80/0.99 tff(971,plain,
% 0.80/0.99 ((~hskp13) | c0_1(a308)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[970, 965])).
% 0.80/0.99 tff(972,plain,
% 0.80/0.99 (c0_1(a308)),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[971, 950])).
% 0.80/0.99 tff(973,plain,
% 0.80/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a308) | c0_1(a297) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | c3_1(a297) | (~c2_1(a297)) | (~c3_1(a308)) | (~c0_1(a308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a308) | c0_1(a297) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | c3_1(a297) | (~c2_1(a297)) | (~c3_1(a308)) | (~c0_1(a308)))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(974,plain,
% 0.80/0.99 (((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a297) | c0_1(a297) | (~c2_1(a297))) <=> (c2_1(a308) | c0_1(a297) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | c3_1(a297) | (~c2_1(a297)) | (~c3_1(a308)) | (~c0_1(a308)))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(975,plain,
% 0.80/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a297) | c0_1(a297) | (~c2_1(a297)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a308) | c0_1(a297) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | c3_1(a297) | (~c2_1(a297)) | (~c3_1(a308)) | (~c0_1(a308))))),
% 0.80/0.99 inference(monotonicity,[status(thm)],[974])).
% 0.80/0.99 tff(976,plain,
% 0.80/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a297) | c0_1(a297) | (~c2_1(a297)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a308) | c0_1(a297) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | c3_1(a297) | (~c2_1(a297)) | (~c3_1(a308)) | (~c0_1(a308)))),
% 0.80/0.99 inference(transitivity,[status(thm)],[975, 973])).
% 0.80/0.99 tff(977,plain,
% 0.80/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a297) | c0_1(a297) | (~c2_1(a297)))),
% 0.80/0.99 inference(quant_inst,[status(thm)],[])).
% 0.80/0.99 tff(978,plain,
% 0.80/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a308) | c0_1(a297) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | c3_1(a297) | (~c2_1(a297)) | (~c3_1(a308)) | (~c0_1(a308))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[977, 976])).
% 0.80/0.99 tff(979,plain,
% 0.80/0.99 (~c3_1(a308)),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[978, 129, 972, 859, 964, 956, 858, 932, 926, 540, 866])).
% 0.80/0.99 tff(980,plain,
% 0.80/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a308) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a308) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308)))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(981,plain,
% 0.80/0.99 (((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a297) | c0_1(a297) | (~c2_1(a297))) <=> (c2_1(a308) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308)))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(982,plain,
% 0.80/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a297) | c0_1(a297) | (~c2_1(a297)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a308) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308))))),
% 0.80/0.99 inference(monotonicity,[status(thm)],[981])).
% 0.80/0.99 tff(983,plain,
% 0.80/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a297) | c0_1(a297) | (~c2_1(a297)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a308) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308)))),
% 0.80/0.99 inference(transitivity,[status(thm)],[982, 980])).
% 0.80/0.99 tff(984,plain,
% 0.80/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a297) | c0_1(a297) | (~c2_1(a297)))),
% 0.80/0.99 inference(quant_inst,[status(thm)],[])).
% 0.80/0.99 tff(985,plain,
% 0.80/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a308) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[984, 983])).
% 0.80/0.99 tff(986,plain,
% 0.80/0.99 ($false),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[985, 129, 972, 850, 849, 859, 956, 858, 540, 851, 866, 979])).
% 0.80/0.99 tff(987,plain,(hskp16 | (~c1_1(a341)) | c0_1(a341) | c3_1(a341) | c2_1(a341) | (~c0_1(a301)) | (~c2_1(a301)) | (~c3_1(a301)) | hskp22), inference(lemma,lemma(discharge,[]))).
% 0.80/0.99 tff(988,plain,
% 0.80/0.99 (hskp16),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[987, 287, 275, 274, 276, 855, 854, 853, 160])).
% 0.80/0.99 tff(989,plain,
% 0.80/0.99 (~c3_1(a315)),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[438, 988])).
% 0.80/0.99 tff(990,plain,
% 0.80/0.99 (~c0_1(a315)),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[420, 988])).
% 0.80/0.99 tff(991,plain,
% 0.80/0.99 (c1_1(a315)),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[445, 129, 64, 990, 989, 93])).
% 0.80/0.99 tff(992,plain,
% 0.80/0.99 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W)))),
% 0.80/0.99 inference(bind,[status(th)],[])).
% 0.80/0.99 tff(993,plain,
% 0.80/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 0.80/0.99 inference(quant_intro,[status(thm)],[992])).
% 0.80/0.99 tff(994,plain,
% 0.80/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(995,plain,
% 0.80/0.99 (^[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))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | c1_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))))),
% 0.80/0.99 inference(bind,[status(th)],[])).
% 0.80/0.99 tff(996,plain,
% 0.80/0.99 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 0.80/0.99 inference(quant_intro,[status(thm)],[995])).
% 0.80/0.99 tff(997,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause196')).
% 0.80/0.99 tff(998,plain,
% 0.80/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[997, 996])).
% 0.80/0.99 tff(999,plain,
% 0.80/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[998, 994])).
% 0.80/0.99 tff(1000,plain,(
% 0.80/0.99 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 0.80/0.99 inference(skolemize,[status(sab)],[999])).
% 0.80/0.99 tff(1001,plain,
% 0.80/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1000, 993])).
% 0.80/0.99 tff(1002,plain,
% 0.80/0.99 (c2_1(a315)),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[414, 988])).
% 0.80/0.99 tff(1003,plain,
% 0.80/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c3_1(a315) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c1_1(a315)) | (~c2_1(a315)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a315) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c1_1(a315)) | (~c2_1(a315)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(1004,plain,
% 0.80/0.99 (((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300)) <=> (c3_1(a315) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c1_1(a315)) | (~c2_1(a315)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(1005,plain,
% 0.80/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c3_1(a315) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c1_1(a315)) | (~c2_1(a315)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301))))),
% 0.80/0.99 inference(monotonicity,[status(thm)],[1004])).
% 0.80/0.99 tff(1006,plain,
% 0.80/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a315) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c1_1(a315)) | (~c2_1(a315)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))),
% 0.80/0.99 inference(transitivity,[status(thm)],[1005, 1003])).
% 0.80/0.99 tff(1007,plain,
% 0.80/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300))),
% 0.80/0.99 inference(quant_inst,[status(thm)],[])).
% 0.80/0.99 tff(1008,plain,
% 0.80/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a315) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c1_1(a315)) | (~c2_1(a315)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 0.80/0.99 tff(1009,plain,
% 0.80/0.99 (~c1_1(a301)),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[1008, 129, 854, 853, 1002, 849, 989, 848, 1001, 991, 851])).
% 0.80/0.99 tff(1010,plain,
% 0.80/0.99 ($false),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[356, 129, 855, 854, 853, 276, 275, 274, 11, 1009])).
% 0.80/0.99 tff(1011,plain,(c2_1(a341) | (~c1_1(a341)) | c0_1(a341) | c3_1(a341) | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.80/0.99 tff(1012,plain,
% 0.80/0.99 (c2_1(a341)),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[1011, 64, 275, 274, 276])).
% 0.80/0.99 tff(1013,plain,
% 0.80/0.99 (^[U: $i] : refl((hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.80/0.99 inference(bind,[status(th)],[])).
% 0.80/0.99 tff(1014,plain,
% 0.80/0.99 (![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.80/0.99 inference(quant_intro,[status(thm)],[1013])).
% 0.80/0.99 tff(1015,plain,
% 0.80/0.99 (![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(1016,plain,
% 0.80/0.99 (^[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)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp15))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp8) <=> ((hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp8))), rewrite(((hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp8) <=> (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp8) <=> (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.80/0.99 inference(bind,[status(th)],[])).
% 0.80/0.99 tff(1017,plain,
% 0.80/0.99 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp8) <=> ![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.80/0.99 inference(quant_intro,[status(thm)],[1016])).
% 0.80/0.99 tff(1018,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 0.80/0.99 tff(1019,plain,
% 0.80/0.99 (![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1018, 1017])).
% 0.80/0.99 tff(1020,plain,
% 0.80/0.99 (![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1019, 1015])).
% 0.80/0.99 tff(1021,plain,(
% 0.80/0.99 ![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.80/0.99 inference(skolemize,[status(sab)],[1020])).
% 0.80/0.99 tff(1022,plain,
% 0.80/0.99 (![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1021, 1014])).
% 0.80/0.99 tff(1023,plain,
% 0.80/0.99 (((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp15 | hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c2_1(a341)))) <=> ((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp15 | hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c2_1(a341)))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(1024,plain,
% 0.80/0.99 ((hskp15 | hskp8 | (~ndr1_0) | c3_1(a341) | c0_1(a341) | (~c2_1(a341))) <=> (hskp15 | hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c2_1(a341)))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(1025,plain,
% 0.80/0.99 (((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp15 | hskp8 | (~ndr1_0) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp15 | hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c2_1(a341))))),
% 0.80/0.99 inference(monotonicity,[status(thm)],[1024])).
% 0.80/0.99 tff(1026,plain,
% 0.80/0.99 (((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp15 | hskp8 | (~ndr1_0) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp15 | hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c2_1(a341)))),
% 0.80/0.99 inference(transitivity,[status(thm)],[1025, 1023])).
% 0.80/0.99 tff(1027,plain,
% 0.80/0.99 ((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp15 | hskp8 | (~ndr1_0) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))),
% 0.80/0.99 inference(quant_inst,[status(thm)],[])).
% 0.80/0.99 tff(1028,plain,
% 0.80/0.99 ((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp15 | hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c2_1(a341))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1027, 1026])).
% 0.80/0.99 tff(1029,plain,
% 0.80/0.99 (hskp15 | hskp8 | (~c2_1(a341))),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[1028, 129, 275, 274, 1022])).
% 0.80/0.99 tff(1030,plain,
% 0.80/0.99 (hskp15),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[1029, 583, 1012])).
% 0.80/0.99 tff(1031,plain,
% 0.80/0.99 (~c3_1(a311)),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[788, 1030])).
% 0.80/0.99 tff(1032,plain,
% 0.80/0.99 (c1_1(a311)),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[767, 1030])).
% 0.80/0.99 tff(1033,plain,
% 0.80/0.99 (c0_1(a311)),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[775, 1030])).
% 0.80/0.99 tff(1034,plain,
% 0.80/0.99 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a341) | c2_1(a337) | (~ndr1_0) | c0_1(a337) | (~c1_1(a337)) | (~c1_1(a341)) | (~c2_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c2_1(a337) | (~ndr1_0) | c0_1(a337) | (~c1_1(a337)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(1035,plain,
% 0.80/0.99 ((hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a337) | c0_1(a337) | (~c1_1(a337))) <=> (hskp29 | c0_1(a341) | c2_1(a337) | (~ndr1_0) | c0_1(a337) | (~c1_1(a337)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(1036,plain,
% 0.80/0.99 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a337) | c0_1(a337) | (~c1_1(a337)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a341) | c2_1(a337) | (~ndr1_0) | c0_1(a337) | (~c1_1(a337)) | (~c1_1(a341)) | (~c2_1(a341))))),
% 0.80/0.99 inference(monotonicity,[status(thm)],[1035])).
% 0.80/0.99 tff(1037,plain,
% 0.80/0.99 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a337) | c0_1(a337) | (~c1_1(a337)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c2_1(a337) | (~ndr1_0) | c0_1(a337) | (~c1_1(a337)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 0.80/0.99 inference(transitivity,[status(thm)],[1036, 1034])).
% 0.80/0.99 tff(1038,plain,
% 0.80/0.99 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a337) | c0_1(a337) | (~c1_1(a337)))),
% 0.80/0.99 inference(quant_inst,[status(thm)],[])).
% 0.80/0.99 tff(1039,plain,
% 0.80/0.99 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c2_1(a337) | (~ndr1_0) | c0_1(a337) | (~c1_1(a337)) | (~c1_1(a341)) | (~c2_1(a341))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 0.80/0.99 tff(1040,plain,
% 0.80/0.99 (hskp29 | c0_1(a337) | (~c2_1(a341))),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[1039, 129, 276, 840, 275, 824, 63])).
% 0.80/0.99 tff(1041,plain,
% 0.80/0.99 (c0_1(a337)),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[1040, 53, 1012])).
% 0.80/0.99 tff(1042,plain,
% 0.80/0.99 (^[U: $i] : refl((hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))),
% 0.80/0.99 inference(bind,[status(th)],[])).
% 0.80/0.99 tff(1043,plain,
% 0.80/0.99 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.80/0.99 inference(quant_intro,[status(thm)],[1042])).
% 0.80/0.99 tff(1044,plain,
% 0.80/0.99 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(1045,plain,
% 0.80/0.99 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp8) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp8))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp8) | hskp28) <=> ((hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp28))), rewrite(((hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp28) <=> (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp8) | hskp28) <=> (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.80/0.99 inference(bind,[status(th)],[])).
% 0.80/0.99 tff(1046,plain,
% 0.80/0.99 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp8) | hskp28) <=> ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.80/0.99 inference(quant_intro,[status(thm)],[1045])).
% 0.80/0.99 tff(1047,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp8) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 0.80/0.99 tff(1048,plain,
% 0.80/0.99 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1047, 1046])).
% 0.80/0.99 tff(1049,plain,
% 0.80/0.99 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1048, 1044])).
% 0.80/0.99 tff(1050,plain,(
% 0.80/0.99 ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.80/0.99 inference(skolemize,[status(sab)],[1049])).
% 0.80/0.99 tff(1051,plain,
% 0.80/0.99 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1050, 1043])).
% 0.80/0.99 tff(1052,plain,
% 0.80/0.99 (((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | (~c0_1(a337)))) <=> ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp8 | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | (~c0_1(a337)))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(1053,plain,
% 0.80/0.99 ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | (~c0_1(a337)))),
% 0.80/0.99 inference(quant_inst,[status(thm)],[])).
% 0.80/0.99 tff(1054,plain,
% 0.80/0.99 ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp8 | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | (~c0_1(a337))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 0.80/0.99 tff(1055,plain,
% 0.80/0.99 (hskp28 | hskp8 | (~c0_1(a337))),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[1054, 129, 840, 832, 1051])).
% 0.80/0.99 tff(1056,plain,
% 0.80/0.99 (hskp28),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[1055, 1041, 583])).
% 0.80/0.99 tff(1057,plain,
% 0.80/0.99 (((~hskp28) | c3_1(a296)) <=> ((~hskp28) | c3_1(a296))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(1058,axiom,((~hskp28) | c3_1(a296)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 0.80/0.99 tff(1059,plain,
% 0.80/0.99 ((~hskp28) | c3_1(a296)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1058, 1057])).
% 0.80/0.99 tff(1060,plain,
% 0.80/0.99 ((~hskp28) | c3_1(a296)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1059, 1057])).
% 0.80/0.99 tff(1061,plain,
% 0.80/0.99 ((~hskp28) | c3_1(a296)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1060, 1057])).
% 0.80/0.99 tff(1062,plain,
% 0.80/0.99 ((~hskp28) | c3_1(a296)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1061, 1057])).
% 0.80/0.99 tff(1063,plain,
% 0.80/0.99 ((~hskp28) | c3_1(a296)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1062, 1057])).
% 0.80/0.99 tff(1064,plain,
% 0.80/0.99 (c3_1(a296)),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[1063, 1056])).
% 0.80/0.99 tff(1065,plain,
% 0.80/0.99 (((~hskp28) | c2_1(a296)) <=> ((~hskp28) | c2_1(a296))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(1066,axiom,((~hskp28) | c2_1(a296)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 0.80/0.99 tff(1067,plain,
% 0.80/0.99 ((~hskp28) | c2_1(a296)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 0.80/0.99 tff(1068,plain,
% 0.80/0.99 ((~hskp28) | c2_1(a296)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1067, 1065])).
% 0.80/0.99 tff(1069,plain,
% 0.80/0.99 ((~hskp28) | c2_1(a296)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1068, 1065])).
% 0.80/0.99 tff(1070,plain,
% 0.80/0.99 ((~hskp28) | c2_1(a296)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1069, 1065])).
% 0.80/0.99 tff(1071,plain,
% 0.80/0.99 ((~hskp28) | c2_1(a296)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1070, 1065])).
% 0.80/0.99 tff(1072,plain,
% 0.80/0.99 (c2_1(a296)),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[1071, 1056])).
% 0.80/0.99 tff(1073,plain,
% 0.80/0.99 (((~hskp28) | c1_1(a296)) <=> ((~hskp28) | c1_1(a296))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(1074,axiom,((~hskp28) | c1_1(a296)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 0.80/0.99 tff(1075,plain,
% 0.80/0.99 ((~hskp28) | c1_1(a296)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1074, 1073])).
% 0.80/0.99 tff(1076,plain,
% 0.80/0.99 ((~hskp28) | c1_1(a296)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1075, 1073])).
% 0.80/0.99 tff(1077,plain,
% 0.80/0.99 ((~hskp28) | c1_1(a296)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1076, 1073])).
% 0.80/0.99 tff(1078,plain,
% 0.80/0.99 ((~hskp28) | c1_1(a296)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1077, 1073])).
% 0.80/0.99 tff(1079,plain,
% 0.80/0.99 ((~hskp28) | c1_1(a296)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1078, 1073])).
% 0.80/0.99 tff(1080,plain,
% 0.80/0.99 (c1_1(a296)),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[1079, 1056])).
% 0.80/0.99 tff(1081,assumption,(hskp2), introduced(assumption)).
% 0.80/0.99 tff(1082,plain,
% 0.80/0.99 (((~hskp2) | (~c2_1(a293))) <=> ((~hskp2) | (~c2_1(a293)))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(1083,plain,
% 0.80/0.99 (((~c2_1(a293)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a293)))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(1084,axiom,((~c2_1(a293)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 0.80/0.99 tff(1085,plain,
% 0.80/0.99 ((~hskp2) | (~c2_1(a293))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1084, 1083])).
% 0.80/0.99 tff(1086,plain,
% 0.80/0.99 ((~hskp2) | (~c2_1(a293))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1085, 1082])).
% 0.80/0.99 tff(1087,plain,
% 0.80/0.99 (~c2_1(a293)),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[1086, 1081])).
% 0.80/0.99 tff(1088,plain,
% 0.80/0.99 (((~hskp2) | (~c1_1(a293))) <=> ((~hskp2) | (~c1_1(a293)))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(1089,plain,
% 0.80/0.99 (((~c1_1(a293)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a293)))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(1090,axiom,((~c1_1(a293)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 0.80/0.99 tff(1091,plain,
% 0.80/0.99 ((~hskp2) | (~c1_1(a293))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1090, 1089])).
% 0.80/0.99 tff(1092,plain,
% 0.80/0.99 ((~hskp2) | (~c1_1(a293))),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1091, 1088])).
% 0.80/0.99 tff(1093,plain,
% 0.80/0.99 (~c1_1(a293)),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[1092, 1081])).
% 0.80/0.99 tff(1094,plain,
% 0.80/0.99 (((~hskp2) | c3_1(a293)) <=> ((~hskp2) | c3_1(a293))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(1095,axiom,((~hskp2) | c3_1(a293)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 0.80/0.99 tff(1096,plain,
% 0.80/0.99 ((~hskp2) | c3_1(a293)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1095, 1094])).
% 0.80/0.99 tff(1097,plain,
% 0.80/0.99 ((~hskp2) | c3_1(a293)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1096, 1094])).
% 0.80/0.99 tff(1098,plain,
% 0.80/0.99 ((~hskp2) | c3_1(a293)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1097, 1094])).
% 0.80/0.99 tff(1099,plain,
% 0.80/0.99 ((~hskp2) | c3_1(a293)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1098, 1094])).
% 0.80/0.99 tff(1100,plain,
% 0.80/0.99 ((~hskp2) | c3_1(a293)),
% 0.80/0.99 inference(modus_ponens,[status(thm)],[1099, 1094])).
% 0.80/0.99 tff(1101,plain,
% 0.80/0.99 (c3_1(a293)),
% 0.80/0.99 inference(unit_resolution,[status(thm)],[1100, 1081])).
% 0.80/0.99 tff(1102,assumption,(c3_1(a296)), introduced(assumption)).
% 0.80/0.99 tff(1103,assumption,(c2_1(a296)), introduced(assumption)).
% 0.80/0.99 tff(1104,assumption,(c1_1(a296)), introduced(assumption)).
% 0.80/0.99 tff(1105,plain,
% 0.80/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c3_1(a341) | c1_1(a293) | c2_1(a293) | (~ndr1_0) | (~c3_1(a293)) | (~c1_1(a341)) | (~c2_1(a341)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a341) | c1_1(a293) | c2_1(a293) | (~ndr1_0) | (~c3_1(a293)) | (~c1_1(a341)) | (~c2_1(a341)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296)))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(1106,plain,
% 0.80/0.99 (((~ndr1_0) | (~c2_1(a296)) | (~c1_1(a296)) | (~c3_1(a296)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a293) | (~c3_1(a293)) | c1_1(a293)) <=> (c3_1(a341) | c1_1(a293) | c2_1(a293) | (~ndr1_0) | (~c3_1(a293)) | (~c1_1(a341)) | (~c2_1(a341)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296)))),
% 0.80/0.99 inference(rewrite,[status(thm)],[])).
% 0.80/0.99 tff(1107,plain,
% 0.80/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a296)) | (~c1_1(a296)) | (~c3_1(a296)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a293) | (~c3_1(a293)) | c1_1(a293))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c3_1(a341) | c1_1(a293) | c2_1(a293) | (~ndr1_0) | (~c3_1(a293)) | (~c1_1(a341)) | (~c2_1(a341)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296))))),
% 0.80/1.00 inference(monotonicity,[status(thm)],[1106])).
% 0.80/1.00 tff(1108,plain,
% 0.80/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a296)) | (~c1_1(a296)) | (~c3_1(a296)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a293) | (~c3_1(a293)) | c1_1(a293))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a341) | c1_1(a293) | c2_1(a293) | (~ndr1_0) | (~c3_1(a293)) | (~c1_1(a341)) | (~c2_1(a341)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296)))),
% 0.80/1.00 inference(transitivity,[status(thm)],[1107, 1105])).
% 0.80/1.00 tff(1109,plain,
% 0.80/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a296)) | (~c1_1(a296)) | (~c3_1(a296)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a293) | (~c3_1(a293)) | c1_1(a293))),
% 0.80/1.00 inference(quant_inst,[status(thm)],[])).
% 0.80/1.00 tff(1110,plain,
% 0.80/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a341) | c1_1(a293) | c2_1(a293) | (~ndr1_0) | (~c3_1(a293)) | (~c1_1(a341)) | (~c2_1(a341)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[1109, 1108])).
% 0.80/1.00 tff(1111,plain,
% 0.80/1.00 ($false),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[1110, 129, 1104, 1103, 1102, 276, 1101, 274, 1093, 1087, 1001, 530])).
% 0.80/1.00 tff(1112,plain,((~hskp2) | (~c1_1(a296)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a341)) | c3_1(a341) | (~c2_1(a341))), inference(lemma,lemma(discharge,[]))).
% 0.80/1.00 tff(1113,plain,
% 0.80/1.00 (~hskp2),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[1112, 1080, 1072, 1064, 276, 274, 1012])).
% 0.80/1.00 tff(1114,plain,
% 0.80/1.00 (^[U: $i] : refl((hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 0.80/1.00 inference(bind,[status(th)],[])).
% 0.80/1.00 tff(1115,plain,
% 0.80/1.00 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.80/1.00 inference(quant_intro,[status(thm)],[1114])).
% 0.80/1.00 tff(1116,plain,
% 0.80/1.00 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(1117,plain,
% 0.80/1.00 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp3))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp2) <=> ((hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp2))), rewrite(((hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp2) <=> (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp2) <=> (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 0.80/1.00 inference(bind,[status(th)],[])).
% 0.80/1.00 tff(1118,plain,
% 0.80/1.00 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp2) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.80/1.00 inference(quant_intro,[status(thm)],[1117])).
% 0.80/1.00 tff(1119,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause156')).
% 0.80/1.00 tff(1120,plain,
% 0.80/1.00 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[1119, 1118])).
% 0.80/1.00 tff(1121,plain,
% 0.80/1.00 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[1120, 1116])).
% 0.80/1.00 tff(1122,plain,(
% 0.80/1.00 ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.80/1.00 inference(skolemize,[status(sab)],[1121])).
% 0.80/1.00 tff(1123,plain,
% 0.80/1.00 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[1122, 1115])).
% 0.80/1.00 tff(1124,plain,
% 0.80/1.00 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp3 | hskp2 | (~ndr1_0) | c0_1(a296) | (~c3_1(a296)) | (~c1_1(a296)))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp3 | hskp2 | (~ndr1_0) | c0_1(a296) | (~c3_1(a296)) | (~c1_1(a296)))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(1125,plain,
% 0.80/1.00 ((hskp3 | hskp2 | (~ndr1_0) | c0_1(a296) | (~c1_1(a296)) | (~c3_1(a296))) <=> (hskp3 | hskp2 | (~ndr1_0) | c0_1(a296) | (~c3_1(a296)) | (~c1_1(a296)))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(1126,plain,
% 0.80/1.00 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp3 | hskp2 | (~ndr1_0) | c0_1(a296) | (~c1_1(a296)) | (~c3_1(a296)))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp3 | hskp2 | (~ndr1_0) | c0_1(a296) | (~c3_1(a296)) | (~c1_1(a296))))),
% 0.80/1.00 inference(monotonicity,[status(thm)],[1125])).
% 0.80/1.00 tff(1127,plain,
% 0.80/1.00 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp3 | hskp2 | (~ndr1_0) | c0_1(a296) | (~c1_1(a296)) | (~c3_1(a296)))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp3 | hskp2 | (~ndr1_0) | c0_1(a296) | (~c3_1(a296)) | (~c1_1(a296)))),
% 0.80/1.00 inference(transitivity,[status(thm)],[1126, 1124])).
% 0.80/1.00 tff(1128,plain,
% 0.80/1.00 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp3 | hskp2 | (~ndr1_0) | c0_1(a296) | (~c1_1(a296)) | (~c3_1(a296)))),
% 0.80/1.00 inference(quant_inst,[status(thm)],[])).
% 0.80/1.00 tff(1129,plain,
% 0.80/1.00 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp3 | hskp2 | (~ndr1_0) | c0_1(a296) | (~c3_1(a296)) | (~c1_1(a296))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[1128, 1127])).
% 0.80/1.00 tff(1130,plain,
% 0.80/1.00 (hskp2 | c0_1(a296)),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[1129, 129, 64, 1080, 1064, 1123])).
% 0.80/1.00 tff(1131,plain,
% 0.80/1.00 (c0_1(a296)),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[1130, 1113])).
% 0.80/1.00 tff(1132,plain,
% 0.80/1.00 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp4 | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a337)) | (~c0_1(a296)) | (~c2_1(a296)) | (~c3_1(a296)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp4 | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a337)) | (~c0_1(a296)) | (~c2_1(a296)) | (~c3_1(a296)))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(1133,plain,
% 0.80/1.00 ((hskp4 | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c2_1(a337) | (~c1_1(a337)) | (~c0_1(a337))) <=> (hskp4 | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a337)) | (~c0_1(a296)) | (~c2_1(a296)) | (~c3_1(a296)))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(1134,plain,
% 0.80/1.00 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c2_1(a337) | (~c1_1(a337)) | (~c0_1(a337)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp4 | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a337)) | (~c0_1(a296)) | (~c2_1(a296)) | (~c3_1(a296))))),
% 0.80/1.00 inference(monotonicity,[status(thm)],[1133])).
% 0.80/1.00 tff(1135,plain,
% 0.80/1.00 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c2_1(a337) | (~c1_1(a337)) | (~c0_1(a337)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp4 | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a337)) | (~c0_1(a296)) | (~c2_1(a296)) | (~c3_1(a296)))),
% 0.80/1.00 inference(transitivity,[status(thm)],[1134, 1132])).
% 0.80/1.00 tff(1136,plain,
% 0.80/1.00 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c2_1(a337) | (~c1_1(a337)) | (~c0_1(a337)))),
% 0.80/1.00 inference(quant_inst,[status(thm)],[])).
% 0.80/1.00 tff(1137,plain,
% 0.80/1.00 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp4 | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a337)) | (~c0_1(a296)) | (~c2_1(a296)) | (~c3_1(a296))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[1136, 1135])).
% 0.80/1.00 tff(1138,plain,
% 0.80/1.00 (hskp4 | (~c0_1(a296))),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[1137, 129, 1072, 1064, 840, 824, 876, 1041])).
% 0.80/1.00 tff(1139,plain,
% 0.80/1.00 (hskp4),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[1138, 1131])).
% 0.80/1.00 tff(1140,plain,
% 0.80/1.00 (~c2_1(a295)),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[931, 1139])).
% 0.80/1.00 tff(1141,plain,
% 0.80/1.00 (~c3_1(a295)),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[925, 1139])).
% 0.80/1.00 tff(1142,assumption,(~c3_1(a295)), introduced(assumption)).
% 0.80/1.00 tff(1143,assumption,(~c2_1(a295)), introduced(assumption)).
% 0.80/1.00 tff(1144,assumption,(~c0_1(a295)), introduced(assumption)).
% 0.80/1.00 tff(1145,plain,
% 0.80/1.00 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a295) | c0_1(a341) | c2_1(a295) | (~ndr1_0) | (~c1_1(a295)) | (~c1_1(a341)) | (~c2_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a295) | c0_1(a341) | c2_1(a295) | (~ndr1_0) | (~c1_1(a295)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(1146,plain,
% 0.80/1.00 ((hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a295) | c0_1(a295) | (~c1_1(a295))) <=> (hskp29 | c0_1(a295) | c0_1(a341) | c2_1(a295) | (~ndr1_0) | (~c1_1(a295)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(1147,plain,
% 0.80/1.00 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a295) | c0_1(a295) | (~c1_1(a295)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a295) | c0_1(a341) | c2_1(a295) | (~ndr1_0) | (~c1_1(a295)) | (~c1_1(a341)) | (~c2_1(a341))))),
% 0.80/1.00 inference(monotonicity,[status(thm)],[1146])).
% 0.80/1.00 tff(1148,plain,
% 0.80/1.00 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a295) | c0_1(a295) | (~c1_1(a295)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a295) | c0_1(a341) | c2_1(a295) | (~ndr1_0) | (~c1_1(a295)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 0.80/1.00 inference(transitivity,[status(thm)],[1147, 1145])).
% 0.80/1.00 tff(1149,plain,
% 0.80/1.00 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a295) | c0_1(a295) | (~c1_1(a295)))),
% 0.80/1.00 inference(quant_inst,[status(thm)],[])).
% 0.80/1.00 tff(1150,plain,
% 0.80/1.00 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a295) | c0_1(a341) | c2_1(a295) | (~ndr1_0) | (~c1_1(a295)) | (~c1_1(a341)) | (~c2_1(a341))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[1149, 1148])).
% 0.80/1.00 tff(1151,plain,
% 0.80/1.00 (c0_1(a295) | (~c1_1(a295)) | (~c2_1(a341))),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[1150, 129, 53, 276, 275, 1143, 63])).
% 0.80/1.00 tff(1152,plain,
% 0.80/1.00 (~c1_1(a295)),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[1151, 1144, 530])).
% 0.80/1.00 tff(1153,plain,
% 0.80/1.00 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | c0_1(a295) | c3_1(a295) | (~ndr1_0) | c1_1(a295))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c0_1(a295) | c3_1(a295) | (~ndr1_0) | c1_1(a295))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(1154,plain,
% 0.80/1.00 ((hskp3 | (~ndr1_0) | c3_1(a295) | c1_1(a295) | c0_1(a295)) <=> (hskp3 | c0_1(a295) | c3_1(a295) | (~ndr1_0) | c1_1(a295))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(1155,plain,
% 0.80/1.00 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a295) | c1_1(a295) | c0_1(a295))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | c0_1(a295) | c3_1(a295) | (~ndr1_0) | c1_1(a295)))),
% 0.80/1.00 inference(monotonicity,[status(thm)],[1154])).
% 0.80/1.00 tff(1156,plain,
% 0.80/1.00 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a295) | c1_1(a295) | c0_1(a295))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c0_1(a295) | c3_1(a295) | (~ndr1_0) | c1_1(a295))),
% 0.80/1.00 inference(transitivity,[status(thm)],[1155, 1153])).
% 0.80/1.00 tff(1157,plain,
% 0.80/1.00 ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a295) | c1_1(a295) | c0_1(a295))),
% 0.80/1.00 inference(quant_inst,[status(thm)],[])).
% 0.80/1.00 tff(1158,plain,
% 0.80/1.00 ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c0_1(a295) | c3_1(a295) | (~ndr1_0) | c1_1(a295)),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[1157, 1156])).
% 0.80/1.00 tff(1159,plain,
% 0.80/1.00 (c0_1(a295) | c1_1(a295)),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[1158, 129, 64, 1142, 93])).
% 0.80/1.00 tff(1160,plain,
% 0.80/1.00 ($false),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[1159, 1152, 1144])).
% 0.80/1.00 tff(1161,plain,(c0_1(a295) | hskp3 | c3_1(a295) | (~c2_1(a341)) | hskp29 | (~c1_1(a341)) | c0_1(a341) | c2_1(a295)), inference(lemma,lemma(discharge,[]))).
% 0.80/1.00 tff(1162,plain,
% 0.80/1.00 (c0_1(a295)),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[1161, 1143, 1012, 64, 53, 276, 275, 1142])).
% 0.80/1.00 tff(1163,plain,
% 0.80/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(1164,plain,
% 0.80/1.00 (((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341))) <=> (c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(1165,plain,
% 0.80/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341))))),
% 0.80/1.00 inference(monotonicity,[status(thm)],[1164])).
% 0.80/1.00 tff(1166,plain,
% 0.80/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))),
% 0.80/1.00 inference(transitivity,[status(thm)],[1165, 1163])).
% 0.80/1.00 tff(1167,plain,
% 0.80/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))),
% 0.80/1.00 inference(quant_inst,[status(thm)],[])).
% 0.80/1.00 tff(1168,plain,
% 0.80/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[1167, 1166])).
% 0.80/1.00 tff(1169,plain,
% 0.80/1.00 ($false),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[1168, 129, 832, 1162, 275, 274, 824, 1143, 1142, 540, 1012, 1041])).
% 0.80/1.00 tff(1170,plain,(c2_1(a295) | c0_1(a341) | c3_1(a341) | c3_1(a295) | hskp3 | hskp29 | (~c1_1(a341))), inference(lemma,lemma(discharge,[]))).
% 0.80/1.00 tff(1171,plain,
% 0.80/1.00 ($false),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[1170, 1141, 1140, 274, 275, 64, 53, 276])).
% 0.80/1.00 tff(1172,plain,(hskp29 | c3_1(a341) | c0_1(a341) | hskp3 | (~c1_1(a341)) | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.80/1.00 tff(1173,plain,
% 0.80/1.00 (hskp29),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[1172, 583, 275, 64, 276, 274])).
% 0.80/1.00 tff(1174,plain,
% 0.80/1.00 (c3_1(a301)),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[349, 1173])).
% 0.80/1.00 tff(1175,plain,
% 0.80/1.00 (c2_1(a301)),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[326, 1173])).
% 0.80/1.00 tff(1176,plain,
% 0.80/1.00 (c0_1(a301)),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[334, 1173])).
% 0.80/1.00 tff(1177,plain,
% 0.80/1.00 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c0_1(a311)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c0_1(a311)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(1178,plain,
% 0.80/1.00 ((hskp13 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311))) <=> (hskp13 | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c0_1(a311)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(1179,plain,
% 0.80/1.00 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c0_1(a311)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))))),
% 0.80/1.00 inference(monotonicity,[status(thm)],[1178])).
% 0.80/1.00 tff(1180,plain,
% 0.80/1.00 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c0_1(a311)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.80/1.00 inference(transitivity,[status(thm)],[1179, 1177])).
% 0.80/1.00 tff(1181,plain,
% 0.80/1.00 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311)))),
% 0.80/1.00 inference(quant_inst,[status(thm)],[])).
% 0.80/1.00 tff(1182,plain,
% 0.80/1.00 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c0_1(a311)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[1181, 1180])).
% 0.80/1.00 tff(1183,plain,
% 0.80/1.00 (hskp13),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[1182, 129, 1176, 1175, 1174, 1033, 1032, 1031, 286])).
% 0.80/1.00 tff(1184,plain,
% 0.80/1.00 (~c2_1(a308)),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[955, 1183])).
% 0.80/1.00 tff(1185,plain,
% 0.80/1.00 (((~hskp13) | (~c1_1(a308))) <=> ((~hskp13) | (~c1_1(a308)))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(1186,plain,
% 0.80/1.00 (((~c1_1(a308)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a308)))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(1187,axiom,((~c1_1(a308)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 0.80/1.00 tff(1188,plain,
% 0.80/1.00 ((~hskp13) | (~c1_1(a308))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[1187, 1186])).
% 0.80/1.00 tff(1189,plain,
% 0.80/1.00 ((~hskp13) | (~c1_1(a308))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[1188, 1185])).
% 0.80/1.00 tff(1190,plain,
% 0.80/1.00 (~c1_1(a308)),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[1189, 1183])).
% 0.80/1.00 tff(1191,plain,
% 0.80/1.00 (c0_1(a308)),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[971, 1183])).
% 0.80/1.00 tff(1192,assumption,(~c3_1(a308)), introduced(assumption)).
% 0.80/1.00 tff(1193,assumption,(~c2_1(a308)), introduced(assumption)).
% 0.80/1.00 tff(1194,assumption,(~c1_1(a308)), introduced(assumption)).
% 0.80/1.00 tff(1195,assumption,(c0_1(a308)), introduced(assumption)).
% 0.80/1.00 tff(1196,plain,
% 0.80/1.00 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a308) | (~c0_1(a308)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a308) | (~c0_1(a308)))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(1197,plain,
% 0.80/1.00 ((hskp3 | (~ndr1_0) | c3_1(a308) | c1_1(a308) | (~c0_1(a308)) | c2_1(a308) | c1_1(a308) | c3_1(a308)) <=> (hskp3 | c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a308) | (~c0_1(a308)))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(1198,plain,
% 0.80/1.00 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a308) | c1_1(a308) | (~c0_1(a308)) | c2_1(a308) | c1_1(a308) | c3_1(a308))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a308) | (~c0_1(a308))))),
% 0.80/1.00 inference(monotonicity,[status(thm)],[1197])).
% 0.80/1.00 tff(1199,plain,
% 0.80/1.00 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a308) | c1_1(a308) | (~c0_1(a308)) | c2_1(a308) | c1_1(a308) | c3_1(a308))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a308) | (~c0_1(a308)))),
% 0.80/1.00 inference(transitivity,[status(thm)],[1198, 1196])).
% 0.80/1.00 tff(1200,plain,
% 0.80/1.00 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a308) | c1_1(a308) | (~c0_1(a308)) | c2_1(a308) | c1_1(a308) | c3_1(a308))),
% 0.80/1.00 inference(quant_inst,[status(thm)],[])).
% 0.80/1.00 tff(1201,plain,
% 0.80/1.00 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a308) | (~c0_1(a308))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[1200, 1199])).
% 0.80/1.00 tff(1202,plain,
% 0.80/1.00 ($false),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[1201, 129, 64, 1195, 1194, 1193, 147, 1192])).
% 0.80/1.00 tff(1203,plain,(c3_1(a308) | hskp3 | (~c0_1(a308)) | c1_1(a308) | c2_1(a308)), inference(lemma,lemma(discharge,[]))).
% 0.80/1.00 tff(1204,plain,
% 0.80/1.00 (c3_1(a308)),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[1203, 1191, 64, 1190, 1184])).
% 0.80/1.00 tff(1205,plain,
% 0.80/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c3_1(a341) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a341) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(1206,plain,
% 0.80/1.00 (((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a308) | (~c3_1(a308)) | c1_1(a308)) <=> (c3_1(a341) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 0.80/1.00 inference(rewrite,[status(thm)],[])).
% 0.80/1.00 tff(1207,plain,
% 0.80/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a308) | (~c3_1(a308)) | c1_1(a308))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c3_1(a341) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341))))),
% 0.80/1.00 inference(monotonicity,[status(thm)],[1206])).
% 0.80/1.00 tff(1208,plain,
% 0.80/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a308) | (~c3_1(a308)) | c1_1(a308))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a341) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 0.80/1.00 inference(transitivity,[status(thm)],[1207, 1205])).
% 0.80/1.00 tff(1209,plain,
% 0.80/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a308) | (~c3_1(a308)) | c1_1(a308))),
% 0.80/1.00 inference(quant_inst,[status(thm)],[])).
% 0.80/1.00 tff(1210,plain,
% 0.80/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a341) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341))),
% 0.80/1.00 inference(modus_ponens,[status(thm)],[1209, 1208])).
% 0.80/1.00 tff(1211,plain,
% 0.80/1.00 ((~c3_1(a308)) | (~c1_1(a301))),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[1210, 129, 1175, 1174, 276, 274, 1190, 1184, 1001, 1012])).
% 0.80/1.00 tff(1212,plain,
% 0.80/1.00 (~c1_1(a301)),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[1211, 1204])).
% 0.80/1.00 tff(1213,plain,
% 0.80/1.00 ($false),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[356, 129, 1176, 1175, 1174, 276, 275, 274, 11, 1212])).
% 0.80/1.00 tff(1214,plain,(hskp8 | (~c1_1(a341)) | c0_1(a341) | c3_1(a341) | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.80/1.00 tff(1215,plain,
% 0.80/1.00 (hskp8),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[1214, 64, 275, 274, 276])).
% 0.80/1.00 tff(1216,plain,
% 0.80/1.00 (~c1_1(a300)),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[504, 1215])).
% 0.80/1.00 tff(1217,plain,
% 0.80/1.00 (c3_1(a300)),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[512, 1215])).
% 0.80/1.00 tff(1218,plain,
% 0.80/1.00 (c0_1(a300)),
% 0.80/1.00 inference(unit_resolution,[status(thm)],[520, 1215])).
% 0.80/1.00 tff(1219,plain,
% 0.80/1.01 (~c2_1(a300)),
% 0.80/1.01 inference(unit_resolution,[status(thm)],[527, 129, 276, 1218, 1217, 275, 274, 1216, 11])).
% 0.80/1.01 tff(1220,assumption,(~c1_1(a300)), introduced(assumption)).
% 0.80/1.01 tff(1221,assumption,(c3_1(a300)), introduced(assumption)).
% 0.80/1.01 tff(1222,assumption,(c0_1(a300)), introduced(assumption)).
% 0.80/1.01 tff(1223,plain,
% 0.80/1.01 (~c2_1(a300)),
% 0.80/1.01 inference(unit_resolution,[status(thm)],[527, 129, 276, 1222, 1221, 275, 274, 1220, 11])).
% 0.80/1.01 tff(1224,plain,
% 0.80/1.01 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.80/1.01 inference(bind,[status(th)],[])).
% 0.80/1.01 tff(1225,plain,
% 0.80/1.01 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.80/1.01 inference(quant_intro,[status(thm)],[1224])).
% 0.80/1.01 tff(1226,plain,
% 0.80/1.01 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.80/1.01 inference(rewrite,[status(thm)],[])).
% 0.80/1.01 tff(1227,plain,
% 0.80/1.01 (^[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))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp22) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp22))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.80/1.01 inference(bind,[status(th)],[])).
% 0.80/1.01 tff(1228,plain,
% 0.80/1.01 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.80/1.01 inference(quant_intro,[status(thm)],[1227])).
% 0.80/1.01 tff(1229,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 0.80/1.01 tff(1230,plain,
% 0.80/1.01 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.80/1.01 inference(modus_ponens,[status(thm)],[1229, 1228])).
% 0.80/1.01 tff(1231,plain,
% 0.80/1.01 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.80/1.01 inference(modus_ponens,[status(thm)],[1230, 1226])).
% 0.80/1.01 tff(1232,plain,(
% 0.80/1.01 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.80/1.01 inference(skolemize,[status(sab)],[1231])).
% 0.80/1.01 tff(1233,plain,
% 0.80/1.01 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.80/1.01 inference(modus_ponens,[status(thm)],[1232, 1225])).
% 0.80/1.01 tff(1234,plain,
% 0.80/1.01 (hskp29 | hskp15),
% 0.80/1.01 inference(unit_resolution,[status(thm)],[759, 129, 1222, 1221, 1220, 317])).
% 0.80/1.01 tff(1235,plain,
% 0.80/1.01 (hskp15),
% 0.80/1.01 inference(unit_resolution,[status(thm)],[1234, 53])).
% 0.80/1.01 tff(1236,plain,
% 0.80/1.01 (~c3_1(a311)),
% 0.80/1.01 inference(unit_resolution,[status(thm)],[788, 1235])).
% 0.80/1.01 tff(1237,plain,
% 0.80/1.01 (c0_1(a311)),
% 0.80/1.01 inference(unit_resolution,[status(thm)],[775, 1235])).
% 0.80/1.01 tff(1238,plain,
% 0.80/1.01 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c3_1(a311) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c2_1(a311)) | (~c0_1(a311)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c3_1(a311) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 0.80/1.01 inference(rewrite,[status(thm)],[])).
% 0.80/1.01 tff(1239,plain,
% 0.80/1.01 ((hskp22 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300))) <=> (hskp22 | c3_1(a311) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 0.80/1.01 inference(rewrite,[status(thm)],[])).
% 0.80/1.01 tff(1240,plain,
% 0.80/1.01 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c3_1(a311) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c2_1(a311)) | (~c0_1(a311))))),
% 0.80/1.01 inference(monotonicity,[status(thm)],[1239])).
% 0.80/1.01 tff(1241,plain,
% 0.80/1.01 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c3_1(a311) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 0.80/1.01 inference(transitivity,[status(thm)],[1240, 1238])).
% 0.80/1.01 tff(1242,plain,
% 0.80/1.01 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300)))),
% 0.80/1.01 inference(quant_inst,[status(thm)],[])).
% 0.80/1.01 tff(1243,plain,
% 0.80/1.01 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c3_1(a311) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c2_1(a311)) | (~c0_1(a311))),
% 0.80/1.01 inference(modus_ponens,[status(thm)],[1242, 1241])).
% 0.80/1.01 tff(1244,plain,
% 0.80/1.01 (~c2_1(a311)),
% 0.80/1.01 inference(unit_resolution,[status(thm)],[1243, 129, 856, 1237, 1221, 1236, 1220, 1233, 1223])).
% 0.80/1.01 tff(1245,plain,
% 0.80/1.01 (c0_1(a337)),
% 0.80/1.01 inference(unit_resolution,[status(thm)],[1040, 53, 530])).
% 0.80/1.01 tff(1246,plain,
% 0.80/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a337) | c3_1(a311) | (~ndr1_0) | c2_1(a311) | (~c0_1(a311)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a337) | c3_1(a311) | (~ndr1_0) | c2_1(a311) | (~c0_1(a311)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))),
% 0.80/1.01 inference(rewrite,[status(thm)],[])).
% 0.80/1.01 tff(1247,plain,
% 0.80/1.01 (((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341))) <=> (c0_1(a341) | c3_1(a341) | c2_1(a337) | c3_1(a311) | (~ndr1_0) | c2_1(a311) | (~c0_1(a311)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))),
% 0.80/1.01 inference(rewrite,[status(thm)],[])).
% 0.80/1.01 tff(1248,plain,
% 0.80/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a337) | c3_1(a311) | (~ndr1_0) | c2_1(a311) | (~c0_1(a311)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341))))),
% 0.80/1.01 inference(monotonicity,[status(thm)],[1247])).
% 0.80/1.01 tff(1249,plain,
% 0.80/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a337) | c3_1(a311) | (~ndr1_0) | c2_1(a311) | (~c0_1(a311)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))),
% 0.80/1.01 inference(transitivity,[status(thm)],[1248, 1246])).
% 0.80/1.01 tff(1250,plain,
% 0.80/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))),
% 0.80/1.01 inference(quant_inst,[status(thm)],[])).
% 0.80/1.01 tff(1251,plain,
% 0.80/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a337) | c3_1(a311) | (~ndr1_0) | c2_1(a311) | (~c0_1(a311)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341))),
% 0.80/1.01 inference(modus_ponens,[status(thm)],[1250, 1249])).
% 0.80/1.01 tff(1252,plain,
% 0.80/1.01 ($false),
% 0.80/1.01 inference(unit_resolution,[status(thm)],[1251, 129, 832, 1237, 275, 274, 824, 1236, 540, 530, 1245, 1244])).
% 0.80/1.01 tff(1253,plain,(hskp29 | c0_1(a341) | c3_1(a341) | (~c2_1(a341)) | hskp22 | (~c3_1(a300)) | c1_1(a300) | (~c0_1(a300)) | (~c1_1(a341))), inference(lemma,lemma(discharge,[]))).
% 0.80/1.01 tff(1254,plain,
% 0.80/1.01 (hskp29),
% 0.80/1.01 inference(unit_resolution,[status(thm)],[1253, 1012, 274, 275, 160, 1217, 1216, 1218, 276])).
% 0.80/1.01 tff(1255,plain,
% 0.80/1.01 (c3_1(a301)),
% 0.80/1.01 inference(unit_resolution,[status(thm)],[349, 1254])).
% 0.80/1.01 tff(1256,plain,
% 0.80/1.01 (c2_1(a301)),
% 0.80/1.01 inference(unit_resolution,[status(thm)],[326, 1254])).
% 0.80/1.01 tff(1257,plain,
% 0.80/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c3_1(a341) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a341) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 0.80/1.01 inference(rewrite,[status(thm)],[])).
% 0.80/1.01 tff(1258,plain,
% 0.80/1.01 (((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300)) <=> (c3_1(a341) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 0.80/1.01 inference(rewrite,[status(thm)],[])).
% 0.80/1.01 tff(1259,plain,
% 0.80/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c3_1(a341) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341))))),
% 0.80/1.01 inference(monotonicity,[status(thm)],[1258])).
% 0.80/1.01 tff(1260,plain,
% 0.80/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a341) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 0.80/1.01 inference(transitivity,[status(thm)],[1259, 1257])).
% 0.80/1.01 tff(1261,plain,
% 0.80/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300))),
% 0.80/1.01 inference(quant_inst,[status(thm)],[])).
% 0.80/1.01 tff(1262,plain,
% 0.80/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a341) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341))),
% 0.80/1.01 inference(modus_ponens,[status(thm)],[1261, 1260])).
% 0.80/1.01 tff(1263,plain,
% 0.80/1.01 (~c1_1(a301)),
% 0.80/1.01 inference(unit_resolution,[status(thm)],[1262, 129, 1256, 1255, 276, 1217, 274, 1216, 1001, 1012, 1219])).
% 0.80/1.01 tff(1264,plain,
% 0.80/1.01 (c0_1(a301)),
% 0.80/1.01 inference(unit_resolution,[status(thm)],[334, 1254])).
% 0.80/1.01 tff(1265,plain,
% 0.80/1.01 ($false),
% 0.80/1.01 inference(unit_resolution,[status(thm)],[356, 129, 1264, 1256, 1255, 276, 275, 274, 11, 1263])).
% 0.86/1.01 tff(1266,plain,(hskp3 | (~c1_1(a341)) | c0_1(a341) | c3_1(a341)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.01 tff(1267,plain,
% 0.86/1.01 (hskp3),
% 0.86/1.01 inference(unit_resolution,[status(thm)],[1266, 276, 275, 274])).
% 0.86/1.01 tff(1268,plain,
% 0.86/1.01 (~c1_1(a294)),
% 0.86/1.01 inference(unit_resolution,[status(thm)],[718, 1267])).
% 0.86/1.01 tff(1269,plain,
% 0.86/1.01 (c2_1(a294)),
% 0.86/1.01 inference(unit_resolution,[status(thm)],[726, 1267])).
% 0.86/1.01 tff(1270,plain,
% 0.86/1.01 (c0_1(a294)),
% 0.86/1.01 inference(unit_resolution,[status(thm)],[734, 1267])).
% 0.86/1.01 tff(1271,plain,
% 0.86/1.01 (hskp16),
% 0.86/1.01 inference(unit_resolution,[status(thm)],[803, 129, 850, 849, 1270, 1269, 848, 1268, 273])).
% 0.86/1.01 tff(1272,plain,
% 0.86/1.01 (~c3_1(a315)),
% 0.86/1.01 inference(unit_resolution,[status(thm)],[438, 1271])).
% 0.86/1.01 tff(1273,plain,
% 0.86/1.01 (~c0_1(a315)),
% 0.86/1.01 inference(unit_resolution,[status(thm)],[420, 1271])).
% 0.86/1.01 tff(1274,plain,
% 0.86/1.01 (c2_1(a315)),
% 0.86/1.01 inference(unit_resolution,[status(thm)],[414, 1271])).
% 0.86/1.01 tff(1275,plain,
% 0.86/1.01 (~c3_1(a294)),
% 0.86/1.01 inference(unit_resolution,[status(thm)],[741, 129, 276, 1270, 1269, 275, 274, 1268, 11])).
% 0.86/1.01 tff(1276,plain,
% 0.86/1.01 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))),
% 0.86/1.01 inference(bind,[status(th)],[])).
% 0.86/1.01 tff(1277,plain,
% 0.86/1.01 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.86/1.01 inference(quant_intro,[status(thm)],[1276])).
% 0.86/1.01 tff(1278,plain,
% 0.86/1.01 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.86/1.01 inference(rewrite,[status(thm)],[])).
% 0.86/1.01 tff(1279,plain,
% 0.86/1.01 (^[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(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp13) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp13))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))))),
% 0.86/1.01 inference(bind,[status(th)],[])).
% 0.86/1.01 tff(1280,plain,
% 0.86/1.01 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.86/1.01 inference(quant_intro,[status(thm)],[1279])).
% 0.86/1.01 tff(1281,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 0.86/1.01 tff(1282,plain,
% 0.86/1.01 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.86/1.01 inference(modus_ponens,[status(thm)],[1281, 1280])).
% 0.86/1.01 tff(1283,plain,
% 0.86/1.01 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.86/1.01 inference(modus_ponens,[status(thm)],[1282, 1278])).
% 0.86/1.01 tff(1284,plain,(
% 0.86/1.01 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.86/1.01 inference(skolemize,[status(sab)],[1283])).
% 0.86/1.01 tff(1285,plain,
% 0.86/1.01 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.86/1.01 inference(modus_ponens,[status(thm)],[1284, 1277])).
% 0.86/1.01 tff(1286,plain,
% 0.86/1.01 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | c0_1(a315) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a315)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp13 | c0_1(a315) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a315)))),
% 0.86/1.01 inference(rewrite,[status(thm)],[])).
% 0.86/1.01 tff(1287,plain,
% 0.86/1.01 ((hskp13 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315))) <=> (hskp13 | c0_1(a315) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a315)))),
% 0.86/1.01 inference(rewrite,[status(thm)],[])).
% 0.86/1.01 tff(1288,plain,
% 0.86/1.01 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | c0_1(a315) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a315))))),
% 0.86/1.01 inference(monotonicity,[status(thm)],[1287])).
% 0.86/1.01 tff(1289,plain,
% 0.86/1.01 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp13 | c0_1(a315) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a315)))),
% 0.86/1.01 inference(transitivity,[status(thm)],[1288, 1286])).
% 0.86/1.01 tff(1290,plain,
% 0.86/1.01 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)))),
% 0.86/1.01 inference(quant_inst,[status(thm)],[])).
% 0.86/1.01 tff(1291,plain,
% 0.86/1.01 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp13 | c0_1(a315) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a315))),
% 0.86/1.01 inference(modus_ponens,[status(thm)],[1290, 1289])).
% 0.86/1.01 tff(1292,plain,
% 0.86/1.01 (hskp13),
% 0.86/1.01 inference(unit_resolution,[status(thm)],[1291, 129, 1274, 1270, 1273, 1272, 1268, 1285, 1275])).
% 0.86/1.01 tff(1293,plain,
% 0.86/1.01 (~c2_1(a308)),
% 0.86/1.01 inference(unit_resolution,[status(thm)],[955, 1292])).
% 0.86/1.01 tff(1294,plain,
% 0.86/1.01 (c0_1(a308)),
% 0.86/1.01 inference(unit_resolution,[status(thm)],[971, 1292])).
% 0.86/1.01 tff(1295,plain,
% 0.86/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c2_1(a308) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a308) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315)))),
% 0.86/1.01 inference(rewrite,[status(thm)],[])).
% 0.86/1.01 tff(1296,plain,
% 0.86/1.01 (((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315))) <=> (c0_1(a315) | c3_1(a315) | c2_1(a308) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315)))),
% 0.86/1.01 inference(rewrite,[status(thm)],[])).
% 0.86/1.01 tff(1297,plain,
% 0.86/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c2_1(a308) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315))))),
% 0.86/1.01 inference(monotonicity,[status(thm)],[1296])).
% 0.86/1.01 tff(1298,plain,
% 0.86/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a308) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315)))),
% 0.86/1.01 inference(transitivity,[status(thm)],[1297, 1295])).
% 0.86/1.01 tff(1299,plain,
% 0.86/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))),
% 0.86/1.01 inference(quant_inst,[status(thm)],[])).
% 0.86/1.01 tff(1300,plain,
% 0.86/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a308) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315))),
% 0.86/1.01 inference(modus_ponens,[status(thm)],[1299, 1298])).
% 0.86/1.01 tff(1301,plain,
% 0.86/1.01 (c3_1(a308)),
% 0.86/1.01 inference(unit_resolution,[status(thm)],[1300, 129, 1274, 1294, 850, 849, 1273, 1272, 1293, 540, 851])).
% 0.86/1.01 tff(1302,plain,
% 0.86/1.01 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.86/1.01 inference(bind,[status(th)],[])).
% 0.86/1.01 tff(1303,plain,
% 0.86/1.01 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.86/1.01 inference(quant_intro,[status(thm)],[1302])).
% 0.86/1.01 tff(1304,plain,
% 0.86/1.01 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.86/1.01 inference(rewrite,[status(thm)],[])).
% 0.86/1.01 tff(1305,plain,
% 0.86/1.01 (^[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))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.86/1.01 inference(bind,[status(th)],[])).
% 0.86/1.01 tff(1306,plain,
% 0.86/1.01 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.86/1.01 inference(quant_intro,[status(thm)],[1305])).
% 0.86/1.01 tff(1307,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 0.86/1.01 tff(1308,plain,
% 0.86/1.01 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.86/1.01 inference(modus_ponens,[status(thm)],[1307, 1306])).
% 0.86/1.01 tff(1309,plain,
% 0.86/1.01 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.86/1.01 inference(modus_ponens,[status(thm)],[1308, 1304])).
% 0.86/1.01 tff(1310,plain,(
% 0.86/1.01 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.86/1.01 inference(skolemize,[status(sab)],[1309])).
% 0.86/1.01 tff(1311,plain,
% 0.86/1.01 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.86/1.01 inference(modus_ponens,[status(thm)],[1310, 1303])).
% 0.86/1.01 tff(1312,plain,
% 0.86/1.01 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300)))),
% 0.86/1.01 inference(rewrite,[status(thm)],[])).
% 0.86/1.01 tff(1313,plain,
% 0.86/1.01 ((hskp21 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300))) <=> (hskp21 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300)))),
% 0.86/1.01 inference(rewrite,[status(thm)],[])).
% 0.86/1.01 tff(1314,plain,
% 0.86/1.01 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300))))),
% 0.86/1.01 inference(monotonicity,[status(thm)],[1313])).
% 0.86/1.01 tff(1315,plain,
% 0.86/1.01 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300)))),
% 0.86/1.01 inference(transitivity,[status(thm)],[1314, 1312])).
% 0.86/1.01 tff(1316,plain,
% 0.86/1.01 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300)))),
% 0.86/1.01 inference(quant_inst,[status(thm)],[])).
% 0.86/1.01 tff(1317,plain,
% 0.86/1.01 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300))),
% 0.86/1.01 inference(modus_ponens,[status(thm)],[1316, 1315])).
% 0.86/1.01 tff(1318,plain,
% 0.86/1.01 (hskp21),
% 0.86/1.01 inference(unit_resolution,[status(thm)],[1317, 129, 849, 1270, 1269, 848, 1311, 1275, 851])).
% 0.86/1.01 tff(1319,plain,
% 0.86/1.01 (((~hskp21) | (~c0_1(a330))) <=> ((~hskp21) | (~c0_1(a330)))),
% 0.86/1.01 inference(rewrite,[status(thm)],[])).
% 0.86/1.01 tff(1320,plain,
% 0.86/1.01 (((~c0_1(a330)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a330)))),
% 0.86/1.01 inference(rewrite,[status(thm)],[])).
% 0.86/1.01 tff(1321,axiom,((~c0_1(a330)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 0.86/1.01 tff(1322,plain,
% 0.86/1.01 ((~hskp21) | (~c0_1(a330))),
% 0.86/1.01 inference(modus_ponens,[status(thm)],[1321, 1320])).
% 0.86/1.01 tff(1323,plain,
% 0.86/1.01 ((~hskp21) | (~c0_1(a330))),
% 0.86/1.01 inference(modus_ponens,[status(thm)],[1322, 1319])).
% 0.86/1.01 tff(1324,plain,
% 0.86/1.01 (~c0_1(a330)),
% 0.86/1.01 inference(unit_resolution,[status(thm)],[1323, 1318])).
% 0.86/1.01 tff(1325,plain,
% 0.86/1.01 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300)))),
% 0.86/1.01 inference(rewrite,[status(thm)],[])).
% 0.86/1.01 tff(1326,plain,
% 0.86/1.01 ((hskp22 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300))) <=> (hskp22 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(1327,plain,
% 0.86/1.02 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300))))),
% 0.86/1.02 inference(monotonicity,[status(thm)],[1326])).
% 0.86/1.02 tff(1328,plain,
% 0.86/1.02 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300)))),
% 0.86/1.02 inference(transitivity,[status(thm)],[1327, 1325])).
% 0.86/1.02 tff(1329,plain,
% 0.86/1.02 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300)))),
% 0.86/1.02 inference(quant_inst,[status(thm)],[])).
% 0.86/1.02 tff(1330,plain,
% 0.86/1.02 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[1329, 1328])).
% 0.86/1.02 tff(1331,plain,
% 0.86/1.02 (hskp22),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[1330, 129, 849, 1270, 1269, 848, 1233, 1275, 851])).
% 0.86/1.02 tff(1332,plain,
% 0.86/1.02 (~c3_1(a331)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[82, 1331])).
% 0.86/1.02 tff(1333,plain,
% 0.86/1.02 (~c2_1(a331)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[70, 1331])).
% 0.86/1.02 tff(1334,plain,
% 0.86/1.02 (~c1_1(a331)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[76, 1331])).
% 0.86/1.02 tff(1335,plain,
% 0.86/1.02 (((~hskp21) | (~c2_1(a330))) <=> ((~hskp21) | (~c2_1(a330)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(1336,plain,
% 0.86/1.02 (((~c2_1(a330)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a330)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(1337,axiom,((~c2_1(a330)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 0.86/1.02 tff(1338,plain,
% 0.86/1.02 ((~hskp21) | (~c2_1(a330))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[1337, 1336])).
% 0.86/1.02 tff(1339,plain,
% 0.86/1.02 ((~hskp21) | (~c2_1(a330))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[1338, 1335])).
% 0.86/1.02 tff(1340,plain,
% 0.86/1.02 (~c2_1(a330)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[1339, 1318])).
% 0.86/1.02 tff(1341,plain,
% 0.86/1.02 (((~hskp21) | c3_1(a330)) <=> ((~hskp21) | c3_1(a330))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(1342,axiom,((~hskp21) | c3_1(a330)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 0.86/1.02 tff(1343,plain,
% 0.86/1.02 ((~hskp21) | c3_1(a330)),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[1342, 1341])).
% 0.86/1.02 tff(1344,plain,
% 0.86/1.02 ((~hskp21) | c3_1(a330)),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[1343, 1341])).
% 0.86/1.02 tff(1345,plain,
% 0.86/1.02 ((~hskp21) | c3_1(a330)),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[1344, 1341])).
% 0.86/1.02 tff(1346,plain,
% 0.86/1.02 ((~hskp21) | c3_1(a330)),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[1345, 1341])).
% 0.86/1.02 tff(1347,plain,
% 0.86/1.02 ((~hskp21) | c3_1(a330)),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[1346, 1341])).
% 0.86/1.02 tff(1348,plain,
% 0.86/1.02 (c3_1(a330)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[1347, 1318])).
% 0.86/1.02 tff(1349,assumption,(~c1_1(a294)), introduced(assumption)).
% 0.86/1.02 tff(1350,assumption,(c2_1(a294)), introduced(assumption)).
% 0.86/1.02 tff(1351,assumption,(c0_1(a294)), introduced(assumption)).
% 0.86/1.02 tff(1352,plain,
% 0.86/1.02 (hskp16),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[803, 129, 1222, 1221, 1351, 1350, 1220, 1349, 273])).
% 0.86/1.02 tff(1353,plain,
% 0.86/1.02 (~c3_1(a315)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[438, 1352])).
% 0.86/1.02 tff(1354,plain,
% 0.86/1.02 (~c0_1(a315)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[420, 1352])).
% 0.86/1.02 tff(1355,plain,
% 0.86/1.02 (c2_1(a315)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[414, 1352])).
% 0.86/1.02 tff(1356,plain,
% 0.86/1.02 (~c1_1(a315)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[432, 53, 276, 287, 275, 1354, 1355])).
% 0.86/1.02 tff(1357,assumption,(~c0_1(a330)), introduced(assumption)).
% 0.86/1.02 tff(1358,assumption,(c3_1(a308)), introduced(assumption)).
% 0.86/1.02 tff(1359,assumption,(~c2_1(a311)), introduced(assumption)).
% 0.86/1.02 tff(1360,assumption,(~c3_1(a311)), introduced(assumption)).
% 0.86/1.02 tff(1361,assumption,(~c3_1(a315)), introduced(assumption)).
% 0.86/1.02 tff(1362,assumption,(c0_1(a311)), introduced(assumption)).
% 0.86/1.02 tff(1363,plain,
% 0.86/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(1364,plain,
% 0.86/1.02 (((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315))) <=> (c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(1365,plain,
% 0.86/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315))))),
% 0.86/1.02 inference(monotonicity,[status(thm)],[1364])).
% 0.86/1.02 tff(1366,plain,
% 0.86/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315)))),
% 0.86/1.02 inference(transitivity,[status(thm)],[1365, 1363])).
% 0.86/1.02 tff(1367,plain,
% 0.86/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))),
% 0.86/1.02 inference(quant_inst,[status(thm)],[])).
% 0.86/1.02 tff(1368,plain,
% 0.86/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[1367, 1366])).
% 0.86/1.02 tff(1369,plain,
% 0.86/1.02 ($false),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[1368, 129, 424, 1362, 1195, 423, 1361, 1360, 1193, 540, 1358, 1359])).
% 0.86/1.02 tff(1370,plain,(c2_1(a311) | (~c2_1(a315)) | (~c0_1(a311)) | (~c0_1(a308)) | c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a308) | (~c3_1(a308))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.02 tff(1371,plain,
% 0.86/1.02 (c2_1(a311)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[1370, 1237, 1355, 1195, 1354, 1353, 1236, 1193, 1358])).
% 0.86/1.02 tff(1372,assumption,(~c2_1(a330)), introduced(assumption)).
% 0.86/1.02 tff(1373,assumption,(c3_1(a330)), introduced(assumption)).
% 0.86/1.02 tff(1374,plain,
% 0.86/1.02 (c1_1(a311)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[767, 1235])).
% 0.86/1.02 tff(1375,assumption,(c2_1(a311)), introduced(assumption)).
% 0.86/1.02 tff(1376,assumption,(~hskp4), introduced(assumption)).
% 0.86/1.02 tff(1377,plain,
% 0.86/1.02 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a330) | (~ndr1_0) | (~c1_1(a330)) | (~c3_1(a330)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a330) | (~ndr1_0) | (~c1_1(a330)) | (~c3_1(a330)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(1378,plain,
% 0.86/1.02 ((hskp4 | (~ndr1_0) | c0_1(a330) | (~c1_1(a330)) | (~c3_1(a330)) | c2_1(a331) | c1_1(a331) | c3_1(a331)) <=> (hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a330) | (~ndr1_0) | (~c1_1(a330)) | (~c3_1(a330)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(1379,plain,
% 0.86/1.02 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c0_1(a330) | (~c1_1(a330)) | (~c3_1(a330)) | c2_1(a331) | c1_1(a331) | c3_1(a331))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a330) | (~ndr1_0) | (~c1_1(a330)) | (~c3_1(a330))))),
% 0.86/1.02 inference(monotonicity,[status(thm)],[1378])).
% 0.86/1.02 tff(1380,plain,
% 0.86/1.02 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c0_1(a330) | (~c1_1(a330)) | (~c3_1(a330)) | c2_1(a331) | c1_1(a331) | c3_1(a331))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a330) | (~ndr1_0) | (~c1_1(a330)) | (~c3_1(a330)))),
% 0.86/1.02 inference(transitivity,[status(thm)],[1379, 1377])).
% 0.86/1.02 tff(1381,plain,
% 0.86/1.02 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c0_1(a330) | (~c1_1(a330)) | (~c3_1(a330)) | c2_1(a331) | c1_1(a331) | c3_1(a331))),
% 0.86/1.02 inference(quant_inst,[status(thm)],[])).
% 0.86/1.02 tff(1382,plain,
% 0.86/1.02 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a330) | (~ndr1_0) | (~c1_1(a330)) | (~c3_1(a330))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[1381, 1380])).
% 0.86/1.02 tff(1383,plain,
% 0.86/1.02 (hskp4 | (~c1_1(a330))),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[1382, 129, 1373, 95, 148, 94, 1357, 42])).
% 0.86/1.02 tff(1384,plain,
% 0.86/1.02 (~c1_1(a330)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[1383, 1376])).
% 0.86/1.02 tff(1385,assumption,(c1_1(a311)), introduced(assumption)).
% 0.86/1.02 tff(1386,assumption,(~c1_1(a315)), introduced(assumption)).
% 0.86/1.02 tff(1387,plain,
% 0.86/1.02 (^[U: $i] : refl((hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 0.86/1.02 inference(bind,[status(th)],[])).
% 0.86/1.02 tff(1388,plain,
% 0.86/1.02 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.86/1.02 inference(quant_intro,[status(thm)],[1387])).
% 0.86/1.02 tff(1389,plain,
% 0.86/1.02 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(1390,plain,
% 0.86/1.02 (^[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)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp4))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp28) <=> ((hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp28))), rewrite(((hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp28) <=> (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp28) <=> (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 0.86/1.02 inference(bind,[status(th)],[])).
% 0.86/1.02 tff(1391,plain,
% 0.86/1.02 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp28) <=> ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.86/1.02 inference(quant_intro,[status(thm)],[1390])).
% 0.86/1.02 tff(1392,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 0.86/1.02 tff(1393,plain,
% 0.86/1.02 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[1392, 1391])).
% 0.86/1.02 tff(1394,plain,
% 0.86/1.02 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[1393, 1389])).
% 0.86/1.02 tff(1395,plain,(
% 0.86/1.02 ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.86/1.02 inference(skolemize,[status(sab)],[1394])).
% 0.86/1.02 tff(1396,plain,
% 0.86/1.02 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[1395, 1388])).
% 0.86/1.02 tff(1397,plain,
% 0.86/1.02 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp28 | hskp4 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp28 | hskp4 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(1398,plain,
% 0.86/1.02 ((hskp28 | hskp4 | (~ndr1_0) | c3_1(a315) | c1_1(a315) | c0_1(a315)) <=> (hskp28 | hskp4 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(1399,plain,
% 0.86/1.02 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp28 | hskp4 | (~ndr1_0) | c3_1(a315) | c1_1(a315) | c0_1(a315))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp28 | hskp4 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315)))),
% 0.86/1.02 inference(monotonicity,[status(thm)],[1398])).
% 0.86/1.02 tff(1400,plain,
% 0.86/1.02 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp28 | hskp4 | (~ndr1_0) | c3_1(a315) | c1_1(a315) | c0_1(a315))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp28 | hskp4 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315))),
% 0.86/1.02 inference(transitivity,[status(thm)],[1399, 1397])).
% 0.86/1.02 tff(1401,plain,
% 0.86/1.02 ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp28 | hskp4 | (~ndr1_0) | c3_1(a315) | c1_1(a315) | c0_1(a315))),
% 0.86/1.02 inference(quant_inst,[status(thm)],[])).
% 0.86/1.02 tff(1402,plain,
% 0.86/1.02 ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp28 | hskp4 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315)),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 0.86/1.02 tff(1403,plain,
% 0.86/1.02 (hskp28 | hskp4 | c1_1(a315)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[1402, 129, 423, 1361, 1396])).
% 0.86/1.02 tff(1404,plain,
% 0.86/1.02 (hskp28),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[1403, 1376, 1386])).
% 0.86/1.02 tff(1405,plain,
% 0.86/1.02 (c3_1(a296)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[1063, 1404])).
% 0.86/1.02 tff(1406,plain,
% 0.86/1.02 (c2_1(a296)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[1071, 1404])).
% 0.86/1.02 tff(1407,plain,
% 0.86/1.02 (c1_1(a296)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[1079, 1404])).
% 0.86/1.02 tff(1408,plain,
% 0.86/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c2_1(a330) | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | c1_1(a330) | (~c3_1(a330)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c2_1(a330) | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | c1_1(a330) | (~c3_1(a330)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(1409,plain,
% 0.86/1.02 (((~ndr1_0) | (~c2_1(a296)) | (~c1_1(a296)) | (~c3_1(a296)) | c3_1(a311) | (~c2_1(a311)) | (~c1_1(a311)) | c2_1(a330) | (~c3_1(a330)) | c1_1(a330)) <=> (c2_1(a330) | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | c1_1(a330) | (~c3_1(a330)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(1410,plain,
% 0.86/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a296)) | (~c1_1(a296)) | (~c3_1(a296)) | c3_1(a311) | (~c2_1(a311)) | (~c1_1(a311)) | c2_1(a330) | (~c3_1(a330)) | c1_1(a330))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c2_1(a330) | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | c1_1(a330) | (~c3_1(a330)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296))))),
% 0.86/1.02 inference(monotonicity,[status(thm)],[1409])).
% 0.86/1.02 tff(1411,plain,
% 0.86/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a296)) | (~c1_1(a296)) | (~c3_1(a296)) | c3_1(a311) | (~c2_1(a311)) | (~c1_1(a311)) | c2_1(a330) | (~c3_1(a330)) | c1_1(a330))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c2_1(a330) | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | c1_1(a330) | (~c3_1(a330)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296)))),
% 0.86/1.02 inference(transitivity,[status(thm)],[1410, 1408])).
% 0.86/1.02 tff(1412,plain,
% 0.86/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a296)) | (~c1_1(a296)) | (~c3_1(a296)) | c3_1(a311) | (~c2_1(a311)) | (~c1_1(a311)) | c2_1(a330) | (~c3_1(a330)) | c1_1(a330))),
% 0.86/1.02 inference(quant_inst,[status(thm)],[])).
% 0.86/1.02 tff(1413,plain,
% 0.86/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c2_1(a330) | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | c1_1(a330) | (~c3_1(a330)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[1412, 1411])).
% 0.86/1.02 tff(1414,plain,
% 0.86/1.02 ($false),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[1413, 129, 1407, 1406, 1405, 1373, 1385, 1372, 1360, 1001, 1384, 1375])).
% 0.86/1.02 tff(1415,plain,(hskp4 | (~c3_1(a330)) | (~c1_1(a311)) | c2_1(a330) | c3_1(a311) | (~c2_1(a311)) | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a330) | c1_1(a315) | c0_1(a315) | c3_1(a315)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.02 tff(1416,plain,
% 0.86/1.02 (hskp4),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[1415, 1374, 1373, 1372, 1236, 1371, 95, 148, 94, 1357, 1356, 1354, 1353])).
% 0.86/1.02 tff(1417,plain,
% 0.86/1.02 (~c3_1(a295)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[925, 1416])).
% 0.86/1.02 tff(1418,plain,
% 0.86/1.02 (hskp7),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[795, 129, 1237, 1374, 1351, 1350, 1236, 1349, 52])).
% 0.86/1.02 tff(1419,plain,
% 0.86/1.02 (c3_1(a299)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[692, 1418])).
% 0.86/1.02 tff(1420,plain,
% 0.86/1.02 (~c2_1(a299)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[709, 1418])).
% 0.86/1.02 tff(1421,plain,
% 0.86/1.02 (c0_1(a299)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[684, 1418])).
% 0.86/1.02 tff(1422,plain,
% 0.86/1.02 (c0_1(a295)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[963, 1416])).
% 0.86/1.02 tff(1423,plain,
% 0.86/1.02 (~c2_1(a295)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[931, 1416])).
% 0.86/1.02 tff(1424,assumption,(hskp16), introduced(assumption)).
% 0.86/1.02 tff(1425,plain,
% 0.86/1.02 (~c3_1(a315)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[438, 1424])).
% 0.86/1.02 tff(1426,plain,
% 0.86/1.02 (~c0_1(a315)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[420, 1424])).
% 0.86/1.02 tff(1427,assumption,(c0_1(a295)), introduced(assumption)).
% 0.86/1.02 tff(1428,assumption,(c3_1(a299)), introduced(assumption)).
% 0.86/1.02 tff(1429,assumption,(c0_1(a299)), introduced(assumption)).
% 0.86/1.02 tff(1430,plain,
% 0.86/1.02 (c2_1(a315)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[414, 1424])).
% 0.86/1.02 tff(1431,plain,
% 0.86/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c2_1(a299) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a299) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(1432,plain,
% 0.86/1.02 (((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315))) <=> (c0_1(a315) | c3_1(a315) | c2_1(a299) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(1433,plain,
% 0.86/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c2_1(a299) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315))))),
% 0.86/1.02 inference(monotonicity,[status(thm)],[1432])).
% 0.86/1.02 tff(1434,plain,
% 0.86/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a299) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315)))),
% 0.86/1.02 inference(transitivity,[status(thm)],[1433, 1431])).
% 0.86/1.02 tff(1435,plain,
% 0.86/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))),
% 0.86/1.02 inference(quant_inst,[status(thm)],[])).
% 0.86/1.02 tff(1436,plain,
% 0.86/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a299) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[1435, 1434])).
% 0.86/1.02 tff(1437,plain,
% 0.86/1.02 ($false),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[1436, 129, 1430, 1429, 1428, 1427, 1426, 1425, 694, 1143, 1142, 540])).
% 0.86/1.02 tff(1438,plain,((~hskp16) | (~c0_1(a299)) | (~c3_1(a299)) | (~c0_1(a295)) | c2_1(a299) | c2_1(a295) | c3_1(a295)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.02 tff(1439,plain,
% 0.86/1.02 ($false),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[1438, 1423, 1422, 1352, 1421, 1420, 1419, 1417])).
% 0.86/1.02 tff(1440,plain,(hskp29 | (~c3_1(a330)) | c2_1(a330) | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a330) | (~c0_1(a308)) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a294)) | (~c2_1(a294)) | c1_1(a294) | (~c0_1(a300)) | (~c3_1(a300)) | c1_1(a300) | (~c1_1(a341)) | c2_1(a341) | c0_1(a341)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.02 tff(1441,plain,
% 0.86/1.02 (hskp29),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[1440, 1348, 1340, 1334, 1333, 1332, 1324, 1294, 1293, 1301, 1270, 1269, 1268, 850, 849, 848, 276, 287, 275])).
% 0.86/1.02 tff(1442,plain,
% 0.86/1.02 (c3_1(a301)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[349, 1441])).
% 0.86/1.02 tff(1443,plain,
% 0.86/1.02 (c2_1(a301)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[326, 1441])).
% 0.86/1.02 tff(1444,plain,
% 0.86/1.02 (c0_1(a301)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[334, 1441])).
% 0.86/1.02 tff(1445,plain,
% 0.86/1.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(1446,plain,
% 0.86/1.02 ((hskp5 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315))) <=> (hskp5 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(1447,plain,
% 0.86/1.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))))),
% 0.86/1.02 inference(monotonicity,[status(thm)],[1446])).
% 0.86/1.02 tff(1448,plain,
% 0.86/1.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.86/1.02 inference(transitivity,[status(thm)],[1447, 1445])).
% 0.86/1.02 tff(1449,plain,
% 0.86/1.02 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)))),
% 0.86/1.02 inference(quant_inst,[status(thm)],[])).
% 0.86/1.02 tff(1450,plain,
% 0.86/1.02 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[1449, 1448])).
% 0.86/1.02 tff(1451,plain,
% 0.86/1.02 (hskp5),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[1450, 129, 1444, 1443, 1442, 1274, 1273, 1272, 21])).
% 0.86/1.02 tff(1452,plain,
% 0.86/1.02 (~c0_1(a297)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[365, 1451])).
% 0.86/1.02 tff(1453,plain,
% 0.86/1.02 (c2_1(a297)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[381, 1451])).
% 0.86/1.02 tff(1454,plain,
% 0.86/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a341) | c3_1(a341) | c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c2_1(a315)) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c2_1(a315)) | (~c1_1(a341)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(1455,plain,
% 0.86/1.03 (((~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c3_1(a297)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341))) <=> (c0_1(a341) | c3_1(a341) | c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c2_1(a315)) | (~c1_1(a341)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(1456,plain,
% 0.86/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c3_1(a297)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a341) | c3_1(a341) | c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c2_1(a315)) | (~c1_1(a341))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[1455])).
% 0.86/1.03 tff(1457,plain,
% 0.86/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c3_1(a297)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c2_1(a315)) | (~c1_1(a341)))),
% 0.86/1.03 inference(transitivity,[status(thm)],[1456, 1454])).
% 0.86/1.03 tff(1458,plain,
% 0.86/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c3_1(a297)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(1459,plain,
% 0.86/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c2_1(a315)) | (~c1_1(a341))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1458, 1457])).
% 0.86/1.03 tff(1460,plain,
% 0.86/1.03 (~c3_1(a297)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1459, 129, 276, 1274, 1453, 275, 274, 1273, 1272, 1452, 263])).
% 0.86/1.03 tff(1461,plain,
% 0.86/1.03 (~c1_1(a308)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1189, 1292])).
% 0.86/1.03 tff(1462,plain,
% 0.86/1.03 (c1_1(a297)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[373, 1451])).
% 0.86/1.03 tff(1463,plain,
% 0.86/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(1464,plain,
% 0.86/1.03 (((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a308) | (~c3_1(a308)) | c1_1(a308)) <=> (c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(1465,plain,
% 0.86/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a308) | (~c3_1(a308)) | c1_1(a308))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[1464])).
% 0.86/1.03 tff(1466,plain,
% 0.86/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a308) | (~c3_1(a308)) | c1_1(a308))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))),
% 0.86/1.03 inference(transitivity,[status(thm)],[1465, 1463])).
% 0.86/1.03 tff(1467,plain,
% 0.86/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a308) | (~c3_1(a308)) | c1_1(a308))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(1468,plain,
% 0.86/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1467, 1466])).
% 0.86/1.03 tff(1469,plain,
% 0.86/1.03 (~c1_1(a301)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1468, 129, 1443, 1442, 1462, 1453, 1461, 1293, 1001, 1301, 1460])).
% 0.86/1.03 tff(1470,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[356, 129, 1444, 1443, 1442, 276, 275, 274, 11, 1469])).
% 0.86/1.03 tff(1471,plain,(c2_1(a341) | (~c1_1(a341)) | c0_1(a341) | c3_1(a341)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(1472,plain,
% 0.86/1.03 (c2_1(a341)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1471, 253, 245, 239])).
% 0.86/1.03 tff(1473,plain,
% 0.86/1.03 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 0.86/1.03 inference(bind,[status(th)],[])).
% 0.86/1.03 tff(1474,plain,
% 0.86/1.03 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.86/1.03 inference(quant_intro,[status(thm)],[1473])).
% 0.86/1.03 tff(1475,plain,
% 0.86/1.03 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(1476,plain,
% 0.86/1.03 (^[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)) | (~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))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp9) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp9))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.86/1.03 inference(bind,[status(th)],[])).
% 0.86/1.03 tff(1477,plain,
% 0.86/1.03 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.86/1.03 inference(quant_intro,[status(thm)],[1476])).
% 0.86/1.03 tff(1478,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause185')).
% 0.86/1.03 tff(1479,plain,
% 0.86/1.03 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1478, 1477])).
% 0.86/1.03 tff(1480,plain,
% 0.86/1.03 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1479, 1475])).
% 0.86/1.03 tff(1481,plain,(
% 0.86/1.03 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.86/1.03 inference(skolemize,[status(sab)],[1480])).
% 0.86/1.03 tff(1482,plain,
% 0.86/1.03 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1481, 1474])).
% 0.86/1.03 tff(1483,plain,
% 0.86/1.03 (hskp3),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1266, 253, 245, 239])).
% 0.86/1.03 tff(1484,plain,
% 0.86/1.03 (~c1_1(a294)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[718, 1483])).
% 0.86/1.03 tff(1485,plain,
% 0.86/1.03 (c2_1(a294)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[726, 1483])).
% 0.86/1.03 tff(1486,plain,
% 0.86/1.03 (c0_1(a294)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[734, 1483])).
% 0.86/1.03 tff(1487,plain,
% 0.86/1.03 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp9 | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a341)) | (~c2_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp9 | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(1488,plain,
% 0.86/1.03 ((hskp9 | (~ndr1_0) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294))) <=> (hskp9 | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(1489,plain,
% 0.86/1.03 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp9 | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a341)) | (~c2_1(a341))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[1488])).
% 0.86/1.03 tff(1490,plain,
% 0.86/1.03 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp9 | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 0.86/1.03 inference(transitivity,[status(thm)],[1489, 1487])).
% 0.86/1.03 tff(1491,plain,
% 0.86/1.03 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(1492,plain,
% 0.86/1.03 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp9 | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a341)) | (~c2_1(a341))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1491, 1490])).
% 0.86/1.03 tff(1493,plain,
% 0.86/1.03 (hskp9 | (~c2_1(a341))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1492, 129, 253, 1486, 1485, 239, 1484, 1482])).
% 0.86/1.03 tff(1494,plain,
% 0.86/1.03 (hskp9),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1493, 1472])).
% 0.86/1.03 tff(1495,plain,
% 0.86/1.03 (~c2_1(a304)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[893, 1494])).
% 0.86/1.03 tff(1496,plain,
% 0.86/1.03 (c1_1(a304)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[901, 1494])).
% 0.86/1.03 tff(1497,plain,
% 0.86/1.03 (c0_1(a304)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[909, 1494])).
% 0.86/1.03 tff(1498,plain,
% 0.86/1.03 (c2_1(a341)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1471, 276, 275, 274])).
% 0.86/1.03 tff(1499,plain,
% 0.86/1.03 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.86/1.03 inference(bind,[status(th)],[])).
% 0.86/1.03 tff(1500,plain,
% 0.86/1.03 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.86/1.03 inference(quant_intro,[status(thm)],[1499])).
% 0.86/1.03 tff(1501,plain,
% 0.86/1.03 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(1502,plain,
% 0.86/1.03 (^[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)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.86/1.03 inference(bind,[status(th)],[])).
% 0.86/1.03 tff(1503,plain,
% 0.86/1.03 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.86/1.03 inference(quant_intro,[status(thm)],[1502])).
% 0.86/1.03 tff(1504,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 0.86/1.03 tff(1505,plain,
% 0.86/1.03 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1504, 1503])).
% 0.86/1.03 tff(1506,plain,
% 0.86/1.03 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1505, 1501])).
% 0.86/1.03 tff(1507,plain,(
% 0.86/1.03 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.86/1.03 inference(skolemize,[status(sab)],[1506])).
% 0.86/1.03 tff(1508,plain,
% 0.86/1.03 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1507, 1500])).
% 0.86/1.03 tff(1509,plain,
% 0.86/1.03 (^[U: $i] : refl((hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.86/1.03 inference(bind,[status(th)],[])).
% 0.86/1.03 tff(1510,plain,
% 0.86/1.03 (![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.86/1.03 inference(quant_intro,[status(thm)],[1509])).
% 0.86/1.03 tff(1511,plain,
% 0.86/1.03 (![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(1512,plain,
% 0.86/1.03 (^[U: $i] : 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)) | hskp20) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp20))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.86/1.03 inference(bind,[status(th)],[])).
% 0.86/1.03 tff(1513,plain,
% 0.86/1.03 (![U: $i] : (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp20) <=> ![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.86/1.03 inference(quant_intro,[status(thm)],[1512])).
% 0.86/1.03 tff(1514,axiom,(![U: $i] : (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 0.86/1.03 tff(1515,plain,
% 0.86/1.03 (![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1514, 1513])).
% 0.86/1.03 tff(1516,plain,
% 0.86/1.03 (![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1515, 1511])).
% 0.86/1.03 tff(1517,plain,(
% 0.86/1.03 ![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.86/1.03 inference(skolemize,[status(sab)],[1516])).
% 0.86/1.03 tff(1518,plain,
% 0.86/1.03 (![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1517, 1510])).
% 0.86/1.03 tff(1519,plain,
% 0.86/1.03 (((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(1520,plain,
% 0.86/1.03 ((hskp20 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294))) <=> (hskp20 | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(1521,plain,
% 0.86/1.03 (((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[1520])).
% 0.86/1.03 tff(1522,plain,
% 0.86/1.03 (((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)))),
% 0.86/1.03 inference(transitivity,[status(thm)],[1521, 1519])).
% 0.86/1.03 tff(1523,plain,
% 0.86/1.03 ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(1524,plain,
% 0.86/1.03 ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1523, 1522])).
% 0.86/1.03 tff(1525,plain,
% 0.86/1.03 (hskp20 | c3_1(a294)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1524, 129, 1270, 1269, 1518])).
% 0.86/1.03 tff(1526,plain,
% 0.86/1.03 (hskp20),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1525, 1275])).
% 0.86/1.03 tff(1527,plain,
% 0.86/1.03 (((~hskp20) | (~c2_1(a329))) <=> ((~hskp20) | (~c2_1(a329)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(1528,plain,
% 0.86/1.03 (((~c2_1(a329)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a329)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(1529,axiom,((~c2_1(a329)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 0.86/1.03 tff(1530,plain,
% 0.86/1.03 ((~hskp20) | (~c2_1(a329))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1529, 1528])).
% 0.86/1.03 tff(1531,plain,
% 0.86/1.03 ((~hskp20) | (~c2_1(a329))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1530, 1527])).
% 0.86/1.03 tff(1532,plain,
% 0.86/1.03 (~c2_1(a329)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1531, 1526])).
% 0.86/1.03 tff(1533,plain,
% 0.86/1.03 (((~hskp20) | (~c1_1(a329))) <=> ((~hskp20) | (~c1_1(a329)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(1534,plain,
% 0.86/1.03 (((~c1_1(a329)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a329)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(1535,axiom,((~c1_1(a329)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 0.86/1.03 tff(1536,plain,
% 0.86/1.03 ((~hskp20) | (~c1_1(a329))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1535, 1534])).
% 0.86/1.03 tff(1537,plain,
% 0.86/1.03 ((~hskp20) | (~c1_1(a329))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1536, 1533])).
% 0.86/1.03 tff(1538,plain,
% 0.86/1.03 (~c1_1(a329)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1537, 1526])).
% 0.86/1.03 tff(1539,plain,
% 0.86/1.03 (((~hskp20) | (~c0_1(a329))) <=> ((~hskp20) | (~c0_1(a329)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(1540,plain,
% 0.86/1.03 (((~c0_1(a329)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a329)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(1541,axiom,((~c0_1(a329)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 0.86/1.03 tff(1542,plain,
% 0.86/1.03 ((~hskp20) | (~c0_1(a329))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1541, 1540])).
% 0.86/1.03 tff(1543,plain,
% 0.86/1.03 ((~hskp20) | (~c0_1(a329))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1542, 1539])).
% 0.86/1.03 tff(1544,plain,
% 0.86/1.03 (~c0_1(a329)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1543, 1526])).
% 0.86/1.03 tff(1545,plain,
% 0.86/1.03 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a329) | c1_1(a329) | c2_1(a329) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a329) | c1_1(a329) | c2_1(a329) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(1546,plain,
% 0.86/1.03 ((hskp0 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c2_1(a329) | c1_1(a329) | c0_1(a329)) <=> (hskp0 | c0_1(a329) | c1_1(a329) | c2_1(a329) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(1547,plain,
% 0.86/1.03 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c2_1(a329) | c1_1(a329) | c0_1(a329))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a329) | c1_1(a329) | c2_1(a329) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[1546])).
% 0.86/1.03 tff(1548,plain,
% 0.86/1.03 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c2_1(a329) | c1_1(a329) | c0_1(a329))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a329) | c1_1(a329) | c2_1(a329) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)))),
% 0.86/1.03 inference(transitivity,[status(thm)],[1547, 1545])).
% 0.86/1.03 tff(1549,plain,
% 0.86/1.03 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c2_1(a329) | c1_1(a329) | c0_1(a329))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(1550,plain,
% 0.86/1.03 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a329) | c1_1(a329) | c2_1(a329) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1549, 1548])).
% 0.86/1.03 tff(1551,plain,
% 0.86/1.03 (hskp0),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1550, 129, 1270, 1544, 1538, 1532, 1268, 1508, 1275])).
% 0.86/1.03 tff(1552,plain,
% 0.86/1.03 (~c2_1(a291)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[475, 1551])).
% 0.86/1.03 tff(1553,plain,
% 0.86/1.03 (c1_1(a291)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[483, 1551])).
% 0.86/1.03 tff(1554,plain,
% 0.86/1.03 (hskp29 | c0_1(a291) | (~c2_1(a341))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[490, 129, 276, 1553, 275, 1552, 63])).
% 0.86/1.03 tff(1555,plain,
% 0.86/1.03 (c0_1(a291)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1554, 53, 1498])).
% 0.86/1.03 tff(1556,plain,
% 0.86/1.03 (c0_1(a337)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1040, 53, 1498])).
% 0.86/1.03 tff(1557,plain,
% 0.86/1.03 (~c3_1(a291)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[497, 1551])).
% 0.86/1.03 tff(1558,plain,
% 0.86/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(1559,plain,
% 0.86/1.03 (((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341))) <=> (c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(1560,plain,
% 0.86/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[1559])).
% 0.86/1.03 tff(1561,plain,
% 0.86/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))),
% 0.86/1.03 inference(transitivity,[status(thm)],[1560, 1558])).
% 0.86/1.03 tff(1562,plain,
% 0.86/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(1563,plain,
% 0.86/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1562, 1561])).
% 0.86/1.03 tff(1564,plain,
% 0.86/1.03 ((~c0_1(a291)) | (~c0_1(a337)) | (~c2_1(a341))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1563, 129, 832, 275, 274, 824, 1552, 1557, 540])).
% 0.86/1.03 tff(1565,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1564, 1556, 1555, 1498])).
% 0.86/1.03 tff(1566,plain,(hskp29 | c0_1(a341) | c3_1(a341) | (~c1_1(a341))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(1567,plain,
% 0.86/1.03 (hskp29),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1566, 245, 239, 253])).
% 0.86/1.03 tff(1568,plain,
% 0.86/1.03 (c3_1(a301)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[349, 1567])).
% 0.86/1.03 tff(1569,plain,
% 0.86/1.03 (c2_1(a301)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[326, 1567])).
% 0.86/1.03 tff(1570,plain,
% 0.86/1.03 (c0_1(a301)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[334, 1567])).
% 0.86/1.03 tff(1571,plain,
% 0.86/1.03 (hskp4),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[919, 129, 1570, 1569, 1568, 1497, 1496, 1495, 876])).
% 0.86/1.03 tff(1572,plain,
% 0.86/1.03 (~c3_1(a295)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[925, 1571])).
% 0.86/1.03 tff(1573,plain,
% 0.86/1.03 (~c2_1(a295)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[931, 1571])).
% 0.86/1.03 tff(1574,plain,
% 0.86/1.03 (~c3_1(a294)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[741, 129, 253, 1486, 1485, 245, 239, 1484, 11])).
% 0.86/1.03 tff(1575,plain,
% 0.86/1.03 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp13 | c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a341)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(1576,plain,
% 0.86/1.03 ((hskp13 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c0_1(a341) | c3_1(a341) | (~c2_1(a341))) <=> (hskp13 | c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a341)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(1577,plain,
% 0.86/1.03 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c0_1(a341) | c3_1(a341) | (~c2_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a341))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[1576])).
% 0.86/1.03 tff(1578,plain,
% 0.86/1.03 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c0_1(a341) | c3_1(a341) | (~c2_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp13 | c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a341)))),
% 0.86/1.03 inference(transitivity,[status(thm)],[1577, 1575])).
% 0.86/1.03 tff(1579,plain,
% 0.86/1.03 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c0_1(a341) | c3_1(a341) | (~c2_1(a341)))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(1580,plain,
% 0.86/1.03 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp13 | c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a341))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[1579, 1578])).
% 0.86/1.03 tff(1581,plain,
% 0.86/1.03 (hskp13 | (~c2_1(a341))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1580, 129, 1486, 245, 239, 1484, 1285, 1574])).
% 0.86/1.03 tff(1582,plain,
% 0.86/1.03 (hskp13),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1581, 1472])).
% 0.86/1.03 tff(1583,plain,
% 0.86/1.03 (~c2_1(a308)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[955, 1582])).
% 0.86/1.03 tff(1584,plain,
% 0.86/1.03 (c0_1(a295)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[963, 1571])).
% 0.86/1.03 tff(1585,plain,
% 0.86/1.03 (c0_1(a308)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[971, 1582])).
% 0.86/1.03 tff(1586,plain,
% 0.86/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a308)) | (~c0_1(a308)) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a308)) | (~c0_1(a308)) | (~c2_1(a341)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1587,plain,
% 0.86/1.04 (((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341))) <=> (c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a308)) | (~c0_1(a308)) | (~c2_1(a341)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1588,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a308)) | (~c0_1(a308)) | (~c2_1(a341))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[1587])).
% 0.86/1.04 tff(1589,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a308)) | (~c0_1(a308)) | (~c2_1(a341)))),
% 0.86/1.04 inference(transitivity,[status(thm)],[1588, 1586])).
% 0.86/1.04 tff(1590,plain,
% 0.86/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(1591,plain,
% 0.86/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a308)) | (~c0_1(a308)) | (~c2_1(a341))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1590, 1589])).
% 0.86/1.04 tff(1592,plain,
% 0.86/1.04 (~c3_1(a308)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1591, 129, 1585, 1584, 245, 239, 1583, 1573, 1572, 540, 1472])).
% 0.86/1.04 tff(1593,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a304) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a304)) | (~c0_1(a304)) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a304) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a304)) | (~c0_1(a304)) | (~c2_1(a341)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1594,plain,
% 0.86/1.04 (((~ndr1_0) | c2_1(a304) | (~c3_1(a304)) | (~c0_1(a304)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341))) <=> (c0_1(a341) | c3_1(a341) | c2_1(a304) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a304)) | (~c0_1(a304)) | (~c2_1(a341)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1595,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a304) | (~c3_1(a304)) | (~c0_1(a304)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a304) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a304)) | (~c0_1(a304)) | (~c2_1(a341))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[1594])).
% 0.86/1.04 tff(1596,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a304) | (~c3_1(a304)) | (~c0_1(a304)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a304) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a304)) | (~c0_1(a304)) | (~c2_1(a341)))),
% 0.86/1.04 inference(transitivity,[status(thm)],[1595, 1593])).
% 0.86/1.04 tff(1597,plain,
% 0.86/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a304) | (~c3_1(a304)) | (~c0_1(a304)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(1598,plain,
% 0.86/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a304) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a304)) | (~c0_1(a304)) | (~c2_1(a341))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1597, 1596])).
% 0.86/1.04 tff(1599,plain,
% 0.86/1.04 (~c3_1(a304)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1598, 129, 1497, 1584, 245, 239, 1495, 1573, 1572, 540, 1472])).
% 0.86/1.04 tff(1600,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a304)) | c3_1(a304) | (~c0_1(a304)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a304)) | c3_1(a304) | (~c0_1(a304)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1601,plain,
% 0.86/1.04 ((hskp7 | (~ndr1_0) | c3_1(a304) | (~c1_1(a304)) | (~c0_1(a304)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294))) <=> (hskp7 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a304)) | c3_1(a304) | (~c0_1(a304)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1602,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c3_1(a304) | (~c1_1(a304)) | (~c0_1(a304)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a304)) | c3_1(a304) | (~c0_1(a304))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[1601])).
% 0.86/1.04 tff(1603,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c3_1(a304) | (~c1_1(a304)) | (~c0_1(a304)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a304)) | c3_1(a304) | (~c0_1(a304)))),
% 0.86/1.04 inference(transitivity,[status(thm)],[1602, 1600])).
% 0.86/1.04 tff(1604,plain,
% 0.86/1.04 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c3_1(a304) | (~c1_1(a304)) | (~c0_1(a304)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(1605,plain,
% 0.86/1.04 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a304)) | c3_1(a304) | (~c0_1(a304))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1604, 1603])).
% 0.86/1.04 tff(1606,plain,
% 0.86/1.04 (hskp7),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1605, 129, 1497, 1496, 1486, 1485, 1484, 52, 1599])).
% 0.86/1.04 tff(1607,plain,
% 0.86/1.04 (~c2_1(a299)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[709, 1606])).
% 0.86/1.04 tff(1608,plain,
% 0.86/1.04 (c3_1(a299)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[692, 1606])).
% 0.86/1.04 tff(1609,plain,
% 0.86/1.04 (c0_1(a299)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[684, 1606])).
% 0.86/1.04 tff(1610,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a341)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1611,plain,
% 0.86/1.04 (((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341))) <=> (c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a341)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1612,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a341))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[1611])).
% 0.86/1.04 tff(1613,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a341)))),
% 0.86/1.04 inference(transitivity,[status(thm)],[1612, 1610])).
% 0.86/1.04 tff(1614,plain,
% 0.86/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(1615,plain,
% 0.86/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a341))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1614, 1613])).
% 0.86/1.04 tff(1616,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1615, 129, 1585, 1609, 1608, 245, 239, 1583, 1607, 540, 1472, 1592])).
% 0.86/1.04 tff(1617,plain,(~hskp24), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(1618,plain,
% 0.86/1.04 (hskp31 | hskp27),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[127, 1617])).
% 0.86/1.04 tff(1619,plain,
% 0.86/1.04 (hskp27),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1618, 232])).
% 0.86/1.04 tff(1620,plain,
% 0.86/1.04 (((~hskp27) | (~c2_1(a368))) <=> ((~hskp27) | (~c2_1(a368)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1621,plain,
% 0.86/1.04 (((~c2_1(a368)) | (~hskp27)) <=> ((~hskp27) | (~c2_1(a368)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1622,axiom,((~c2_1(a368)) | (~hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 0.86/1.04 tff(1623,plain,
% 0.86/1.04 ((~hskp27) | (~c2_1(a368))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1622, 1621])).
% 0.86/1.04 tff(1624,plain,
% 0.86/1.04 ((~hskp27) | (~c2_1(a368))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1623, 1620])).
% 0.86/1.04 tff(1625,plain,
% 0.86/1.04 (~c2_1(a368)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1624, 1619])).
% 0.86/1.04 tff(1626,plain,
% 0.86/1.04 (((~hskp27) | (~c0_1(a368))) <=> ((~hskp27) | (~c0_1(a368)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1627,plain,
% 0.86/1.04 (((~c0_1(a368)) | (~hskp27)) <=> ((~hskp27) | (~c0_1(a368)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1628,axiom,((~c0_1(a368)) | (~hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 0.86/1.04 tff(1629,plain,
% 0.86/1.04 ((~hskp27) | (~c0_1(a368))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1628, 1627])).
% 0.86/1.04 tff(1630,plain,
% 0.86/1.04 ((~hskp27) | (~c0_1(a368))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1629, 1626])).
% 0.86/1.04 tff(1631,plain,
% 0.86/1.04 (~c0_1(a368)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1630, 1619])).
% 0.86/1.04 tff(1632,plain,
% 0.86/1.04 (((~hskp27) | c1_1(a368)) <=> ((~hskp27) | c1_1(a368))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1633,axiom,((~hskp27) | c1_1(a368)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 0.86/1.04 tff(1634,plain,
% 0.86/1.04 ((~hskp27) | c1_1(a368)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1633, 1632])).
% 0.86/1.04 tff(1635,plain,
% 0.86/1.04 ((~hskp27) | c1_1(a368)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1634, 1632])).
% 0.86/1.04 tff(1636,plain,
% 0.86/1.04 ((~hskp27) | c1_1(a368)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1635, 1632])).
% 0.86/1.04 tff(1637,plain,
% 0.86/1.04 ((~hskp27) | c1_1(a368)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1636, 1632])).
% 0.86/1.04 tff(1638,plain,
% 0.86/1.04 ((~hskp27) | c1_1(a368)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1637, 1632])).
% 0.86/1.04 tff(1639,plain,
% 0.86/1.04 (c1_1(a368)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1638, 1619])).
% 0.86/1.04 tff(1640,assumption,(~c2_1(a368)), introduced(assumption)).
% 0.86/1.04 tff(1641,assumption,(~c0_1(a368)), introduced(assumption)).
% 0.86/1.04 tff(1642,assumption,(c1_1(a368)), introduced(assumption)).
% 0.86/1.04 tff(1643,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a368)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a368)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1644,plain,
% 0.86/1.04 ((hskp29 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a368) | c0_1(a368) | (~c1_1(a368))) <=> (hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a368)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1645,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a368) | c0_1(a368) | (~c1_1(a368)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a368))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[1644])).
% 0.86/1.04 tff(1646,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a368) | c0_1(a368) | (~c1_1(a368)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a368)))),
% 0.86/1.04 inference(transitivity,[status(thm)],[1645, 1643])).
% 0.86/1.04 tff(1647,plain,
% 0.86/1.04 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a368) | c0_1(a368) | (~c1_1(a368)))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(1648,plain,
% 0.86/1.04 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a368))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1647, 1646])).
% 0.86/1.04 tff(1649,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1648, 129, 53, 1642, 374, 382, 1641, 1640, 366, 63])).
% 0.86/1.04 tff(1650,plain,((~hskp5) | hskp29 | (~c1_1(a368)) | c0_1(a368) | c2_1(a368)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(1651,plain,
% 0.86/1.04 (~hskp5),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1650, 1639, 53, 1631, 1625])).
% 0.86/1.04 tff(1652,plain,
% 0.86/1.04 (hskp16),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[406, 1651, 160])).
% 0.86/1.04 tff(1653,plain,
% 0.86/1.04 (~c0_1(a315)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[420, 1652])).
% 0.86/1.04 tff(1654,plain,
% 0.86/1.04 (c2_1(a315)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[414, 1652])).
% 0.86/1.04 tff(1655,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a368)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a368)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1656,plain,
% 0.86/1.04 ((hskp29 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a368) | c0_1(a368) | (~c1_1(a368))) <=> (hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a368)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1657,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a368) | c0_1(a368) | (~c1_1(a368)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a368))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[1656])).
% 0.86/1.04 tff(1658,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a368) | c0_1(a368) | (~c1_1(a368)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a368)))),
% 0.86/1.04 inference(transitivity,[status(thm)],[1657, 1655])).
% 0.86/1.04 tff(1659,plain,
% 0.86/1.04 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a368) | c0_1(a368) | (~c1_1(a368)))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(1660,plain,
% 0.86/1.04 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a368))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1659, 1658])).
% 0.86/1.04 tff(1661,plain,
% 0.86/1.04 (~c1_1(a315)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1660, 129, 53, 1639, 1654, 1631, 1625, 1653, 63])).
% 0.86/1.04 tff(1662,plain,
% 0.86/1.04 (~c3_1(a315)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[438, 1652])).
% 0.86/1.04 tff(1663,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[445, 129, 64, 1653, 1662, 93, 1661])).
% 0.86/1.04 tff(1664,plain,(hskp3 | hskp29), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(1665,plain,
% 0.86/1.04 (hskp3),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1664, 53])).
% 0.86/1.04 tff(1666,plain,
% 0.86/1.04 (~c1_1(a294)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[718, 1665])).
% 0.86/1.04 tff(1667,plain,
% 0.86/1.04 (c2_1(a294)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[726, 1665])).
% 0.86/1.04 tff(1668,plain,
% 0.86/1.04 (c0_1(a294)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[734, 1665])).
% 0.86/1.04 tff(1669,plain,
% 0.86/1.04 (((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp24 | hskp16 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp24 | hskp16 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1670,plain,
% 0.86/1.04 ((hskp24 | hskp16 | (~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294))) <=> (hskp24 | hskp16 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1671,plain,
% 0.86/1.04 (((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp24 | hskp16 | (~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp24 | hskp16 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[1670])).
% 0.86/1.04 tff(1672,plain,
% 0.86/1.04 (((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp24 | hskp16 | (~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp24 | hskp16 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)))),
% 0.86/1.04 inference(transitivity,[status(thm)],[1671, 1669])).
% 0.86/1.04 tff(1673,plain,
% 0.86/1.04 ((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp24 | hskp16 | (~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(1674,plain,
% 0.86/1.04 ((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp24 | hskp16 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1673, 1672])).
% 0.86/1.04 tff(1675,plain,
% 0.86/1.04 (hskp16),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1674, 129, 1617, 1351, 1350, 1349, 31])).
% 0.86/1.04 tff(1676,plain,
% 0.86/1.04 (~c3_1(a315)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[438, 1675])).
% 0.86/1.04 tff(1677,plain,
% 0.86/1.04 (~c0_1(a315)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[420, 1675])).
% 0.86/1.04 tff(1678,plain,
% 0.86/1.04 (c2_1(a315)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[414, 1675])).
% 0.86/1.04 tff(1679,plain,
% 0.86/1.04 (((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp15 | hskp8 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)))) <=> ((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp15 | hskp8 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1680,plain,
% 0.86/1.04 ((hskp15 | hskp8 | (~ndr1_0) | c3_1(a315) | c0_1(a315) | (~c2_1(a315))) <=> (hskp15 | hskp8 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1681,plain,
% 0.86/1.04 (((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp15 | hskp8 | (~ndr1_0) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp15 | hskp8 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[1680])).
% 0.86/1.04 tff(1682,plain,
% 0.86/1.04 (((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp15 | hskp8 | (~ndr1_0) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp15 | hskp8 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)))),
% 0.86/1.04 inference(transitivity,[status(thm)],[1681, 1679])).
% 0.86/1.04 tff(1683,plain,
% 0.86/1.04 ((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp15 | hskp8 | (~ndr1_0) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(1684,plain,
% 0.86/1.04 ((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp15 | hskp8 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1683, 1682])).
% 0.86/1.04 tff(1685,plain,
% 0.86/1.04 (hskp15 | hskp8),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1684, 129, 1678, 1677, 1676, 1022])).
% 0.86/1.04 tff(1686,plain,
% 0.86/1.04 (hskp15),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1685, 583])).
% 0.86/1.04 tff(1687,plain,
% 0.86/1.04 (~c3_1(a311)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[788, 1686])).
% 0.86/1.04 tff(1688,plain,
% 0.86/1.04 (c1_1(a311)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[767, 1686])).
% 0.86/1.04 tff(1689,plain,
% 0.86/1.04 (c0_1(a311)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[775, 1686])).
% 0.86/1.04 tff(1690,plain,
% 0.86/1.04 (hskp7),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[795, 129, 1689, 1688, 1351, 1350, 1687, 1349, 52])).
% 0.86/1.04 tff(1691,plain,
% 0.86/1.04 (~c2_1(a299)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[709, 1690])).
% 0.86/1.04 tff(1692,plain,
% 0.86/1.04 (c3_1(a299)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[692, 1690])).
% 0.86/1.04 tff(1693,plain,
% 0.86/1.04 (c0_1(a299)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[684, 1690])).
% 0.86/1.04 tff(1694,assumption,(~hskp13), introduced(assumption)).
% 0.86/1.04 tff(1695,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[949, 129, 32, 1694, 943, 859, 858, 942])).
% 0.86/1.04 tff(1696,plain,(hskp16 | hskp13 | hskp22), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(1697,plain,
% 0.86/1.04 (hskp16),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1696, 1694, 856])).
% 0.86/1.04 tff(1698,plain,
% 0.86/1.04 (c2_1(a315)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[414, 1697])).
% 0.86/1.04 tff(1699,plain,
% 0.86/1.04 (~c3_1(a315)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[438, 1697])).
% 0.86/1.04 tff(1700,plain,
% 0.86/1.04 ((hskp18 | hskp13 | hskp8) <=> (hskp18 | hskp13 | hskp8)),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1701,plain,
% 0.86/1.04 (((hskp13 | hskp8) | hskp18) <=> (hskp18 | hskp13 | hskp8)),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1702,plain,
% 0.86/1.04 ((hskp8 | hskp13) <=> (hskp13 | hskp8)),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1703,plain,
% 0.86/1.04 (((hskp8 | hskp13) | hskp18) <=> ((hskp13 | hskp8) | hskp18)),
% 0.86/1.04 inference(monotonicity,[status(thm)],[1702])).
% 0.86/1.04 tff(1704,plain,
% 0.86/1.04 (((hskp8 | hskp13) | hskp18) <=> (hskp18 | hskp13 | hskp8)),
% 0.86/1.04 inference(transitivity,[status(thm)],[1703, 1701])).
% 0.86/1.04 tff(1705,axiom,((hskp8 | hskp13) | hskp18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 0.86/1.04 tff(1706,plain,
% 0.86/1.04 (hskp18 | hskp13 | hskp8),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1705, 1704])).
% 0.86/1.04 tff(1707,plain,
% 0.86/1.04 (hskp18 | hskp13 | hskp8),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1706, 1700])).
% 0.86/1.04 tff(1708,plain,
% 0.86/1.04 (hskp18 | hskp13 | hskp8),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1707, 1700])).
% 0.86/1.04 tff(1709,plain,
% 0.86/1.04 (hskp18 | hskp13 | hskp8),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1708, 1700])).
% 0.86/1.04 tff(1710,plain,
% 0.86/1.04 (hskp18 | hskp13 | hskp8),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1709, 1700])).
% 0.86/1.04 tff(1711,plain,
% 0.86/1.04 (hskp18),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1710, 1694, 583])).
% 0.86/1.04 tff(1712,plain,
% 0.86/1.04 (((~hskp18) | (~c3_1(a325))) <=> ((~hskp18) | (~c3_1(a325)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1713,plain,
% 0.86/1.04 (((~c3_1(a325)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a325)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1714,axiom,((~c3_1(a325)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 0.86/1.04 tff(1715,plain,
% 0.86/1.04 ((~hskp18) | (~c3_1(a325))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1714, 1713])).
% 0.86/1.04 tff(1716,plain,
% 0.86/1.04 ((~hskp18) | (~c3_1(a325))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1715, 1712])).
% 0.86/1.04 tff(1717,plain,
% 0.86/1.04 (~c3_1(a325)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1716, 1711])).
% 0.86/1.04 tff(1718,plain,
% 0.86/1.04 (((~hskp18) | (~c1_1(a325))) <=> ((~hskp18) | (~c1_1(a325)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1719,plain,
% 0.86/1.04 (((~c1_1(a325)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a325)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1720,axiom,((~c1_1(a325)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 0.86/1.04 tff(1721,plain,
% 0.86/1.04 ((~hskp18) | (~c1_1(a325))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1720, 1719])).
% 0.86/1.04 tff(1722,plain,
% 0.86/1.04 ((~hskp18) | (~c1_1(a325))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1721, 1718])).
% 0.86/1.04 tff(1723,plain,
% 0.86/1.04 (~c1_1(a325)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1722, 1711])).
% 0.86/1.04 tff(1724,plain,
% 0.86/1.04 (((~hskp18) | c0_1(a325)) <=> ((~hskp18) | c0_1(a325))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1725,axiom,((~hskp18) | c0_1(a325)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 0.86/1.04 tff(1726,plain,
% 0.86/1.04 ((~hskp18) | c0_1(a325)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1725, 1724])).
% 0.86/1.04 tff(1727,plain,
% 0.86/1.04 ((~hskp18) | c0_1(a325)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1726, 1724])).
% 0.86/1.04 tff(1728,plain,
% 0.86/1.04 ((~hskp18) | c0_1(a325)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1727, 1724])).
% 0.86/1.04 tff(1729,plain,
% 0.86/1.04 ((~hskp18) | c0_1(a325)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1728, 1724])).
% 0.86/1.04 tff(1730,plain,
% 0.86/1.04 ((~hskp18) | c0_1(a325)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1729, 1724])).
% 0.86/1.04 tff(1731,plain,
% 0.86/1.04 (c0_1(a325)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1730, 1711])).
% 0.86/1.04 tff(1732,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | c1_1(a325) | c3_1(a325) | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c0_1(a325)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp13 | c1_1(a325) | c3_1(a325) | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c0_1(a325)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1733,plain,
% 0.86/1.04 ((hskp13 | (~ndr1_0) | c3_1(a325) | c1_1(a325) | (~c0_1(a325)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315))) <=> (hskp13 | c1_1(a325) | c3_1(a325) | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c0_1(a325)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(1734,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a325) | c1_1(a325) | (~c0_1(a325)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | c1_1(a325) | c3_1(a325) | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c0_1(a325))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[1733])).
% 0.86/1.04 tff(1735,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a325) | c1_1(a325) | (~c0_1(a325)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp13 | c1_1(a325) | c3_1(a325) | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c0_1(a325)))),
% 0.86/1.04 inference(transitivity,[status(thm)],[1734, 1732])).
% 0.86/1.04 tff(1736,plain,
% 0.86/1.04 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a325) | c1_1(a325) | (~c0_1(a325)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(1737,plain,
% 0.86/1.04 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp13 | c1_1(a325) | c3_1(a325) | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c0_1(a325))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[1736, 1735])).
% 0.86/1.04 tff(1738,plain,
% 0.86/1.04 (c3_1(a315) | (~c2_1(a315))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1737, 129, 1694, 1731, 1723, 1717, 423, 1285])).
% 0.86/1.04 tff(1739,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1738, 1699, 1698])).
% 0.86/1.04 tff(1740,plain,(hskp13 | c0_1(a315) | hskp22 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(1741,plain,
% 0.86/1.04 (hskp13),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1740, 856, 583, 423])).
% 0.86/1.04 tff(1742,plain,
% 0.86/1.04 (c0_1(a308)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[971, 1741])).
% 0.86/1.04 tff(1743,plain,
% 0.86/1.04 (~c2_1(a308)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[955, 1741])).
% 0.86/1.04 tff(1744,plain,
% 0.86/1.05 (hskp15 | hskp8),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1684, 129, 424, 423, 1361, 1022])).
% 0.86/1.05 tff(1745,plain,
% 0.86/1.05 (hskp15),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1744, 583])).
% 0.86/1.05 tff(1746,plain,
% 0.86/1.05 (~c3_1(a311)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[788, 1745])).
% 0.86/1.05 tff(1747,plain,
% 0.86/1.05 (c0_1(a311)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[775, 1745])).
% 0.86/1.05 tff(1748,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(1749,plain,
% 0.86/1.05 (((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315))) <=> (c0_1(a315) | c3_1(a315) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(1750,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[1749])).
% 0.86/1.05 tff(1751,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315)))),
% 0.86/1.05 inference(transitivity,[status(thm)],[1750, 1748])).
% 0.86/1.05 tff(1752,plain,
% 0.86/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(1753,plain,
% 0.86/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[1752, 1751])).
% 0.86/1.05 tff(1754,plain,
% 0.86/1.05 (c3_1(a308)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1753, 129, 424, 1742, 1429, 1428, 423, 1361, 1743, 694, 540])).
% 0.86/1.05 tff(1755,plain,
% 0.86/1.05 (~c1_1(a308)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1189, 1741])).
% 0.86/1.05 tff(1756,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(1757,plain,
% 0.86/1.05 ((hskp22 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a308) | c1_1(a308) | (~c3_1(a308))) <=> (hskp22 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(1758,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a308) | c1_1(a308) | (~c3_1(a308)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[1757])).
% 0.86/1.05 tff(1759,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a308) | c1_1(a308) | (~c3_1(a308)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 0.86/1.05 inference(transitivity,[status(thm)],[1758, 1756])).
% 0.86/1.05 tff(1760,plain,
% 0.86/1.05 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a308) | c1_1(a308) | (~c3_1(a308)))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(1761,plain,
% 0.86/1.05 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[1760, 1759])).
% 0.86/1.05 tff(1762,plain,
% 0.86/1.05 (~c2_1(a311)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1761, 129, 856, 1747, 1746, 1755, 1743, 1233, 1754])).
% 0.86/1.05 tff(1763,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1370, 1762, 1754, 424, 1361, 423, 1747, 1746, 1743, 1742])).
% 0.86/1.05 tff(1764,plain,(hskp22 | (~c2_1(a315)) | c3_1(a315) | c0_1(a315) | (~c0_1(a299)) | (~c3_1(a299)) | c2_1(a299) | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(1765,plain,
% 0.86/1.05 (hskp22),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1764, 1693, 1676, 1677, 1678, 1692, 1691, 583])).
% 0.86/1.05 tff(1766,plain,
% 0.86/1.05 (~c3_1(a331)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[82, 1765])).
% 0.86/1.05 tff(1767,plain,
% 0.86/1.05 (~c2_1(a331)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[70, 1765])).
% 0.86/1.05 tff(1768,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a331) | c3_1(a331) | c0_1(a315) | c3_1(a315) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315)) | (~c0_1(a331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a331) | c3_1(a331) | c0_1(a315) | c3_1(a315) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315)) | (~c0_1(a331)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(1769,plain,
% 0.86/1.05 (((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a331) | c3_1(a331) | (~c0_1(a331)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315))) <=> (c2_1(a331) | c3_1(a331) | c0_1(a315) | c3_1(a315) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315)) | (~c0_1(a331)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(1770,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a331) | c3_1(a331) | (~c0_1(a331)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a331) | c3_1(a331) | c0_1(a315) | c3_1(a315) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315)) | (~c0_1(a331))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[1769])).
% 0.86/1.05 tff(1771,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a331) | c3_1(a331) | (~c0_1(a331)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a331) | c3_1(a331) | c0_1(a315) | c3_1(a315) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315)) | (~c0_1(a331)))),
% 0.86/1.05 inference(transitivity,[status(thm)],[1770, 1768])).
% 0.86/1.05 tff(1772,plain,
% 0.86/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a331) | c3_1(a331) | (~c0_1(a331)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(1773,plain,
% 0.86/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a331) | c3_1(a331) | c0_1(a315) | c3_1(a315) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315)) | (~c0_1(a331))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[1772, 1771])).
% 0.86/1.05 tff(1774,plain,
% 0.86/1.05 (~c0_1(a331)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1773, 129, 1678, 1693, 1692, 1767, 1766, 1677, 1676, 1691, 540])).
% 0.86/1.05 tff(1775,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a311) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a311) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(1776,plain,
% 0.86/1.05 ((hskp13 | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311))) <=> (hskp13 | c3_1(a311) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(1777,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a311) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[1776])).
% 0.86/1.05 tff(1778,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a311) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311)))),
% 0.86/1.05 inference(transitivity,[status(thm)],[1777, 1775])).
% 0.86/1.05 tff(1779,plain,
% 0.86/1.05 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311)))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(1780,plain,
% 0.86/1.05 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a311) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[1779, 1778])).
% 0.86/1.05 tff(1781,plain,
% 0.86/1.05 (hskp13 | (~c3_1(a294))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1780, 129, 1362, 1385, 1351, 1350, 1360, 286])).
% 0.86/1.05 tff(1782,plain,
% 0.86/1.05 (~c3_1(a294)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1781, 1694])).
% 0.86/1.05 tff(1783,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1291, 129, 1694, 1678, 1351, 1677, 1676, 1349, 1285, 1782])).
% 0.86/1.05 tff(1784,plain,(hskp13 | (~c0_1(a294)) | c1_1(a294) | (~c0_1(a311)) | (~c1_1(a311)) | (~c2_1(a294)) | c3_1(a311)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(1785,plain,
% 0.86/1.05 (hskp13),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1784, 1689, 1349, 1351, 1688, 1350, 1687])).
% 0.86/1.05 tff(1786,plain,
% 0.86/1.05 (c0_1(a308)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[971, 1785])).
% 0.86/1.05 tff(1787,plain,
% 0.86/1.05 (~c2_1(a308)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[955, 1785])).
% 0.86/1.05 tff(1788,plain,
% 0.86/1.05 (c3_1(a308)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1753, 129, 1678, 1786, 1693, 1692, 1677, 1676, 1787, 1691, 540])).
% 0.86/1.05 tff(1789,plain,
% 0.86/1.05 (c2_1(a311)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1370, 1788, 1678, 1676, 1677, 1689, 1687, 1787, 1786])).
% 0.86/1.05 tff(1790,plain,
% 0.86/1.05 (hskp23 | (~c2_1(a311))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[782, 129, 1689, 1688, 307])).
% 0.86/1.05 tff(1791,plain,
% 0.86/1.05 (hskp23),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1790, 1789])).
% 0.86/1.05 tff(1792,plain,
% 0.86/1.05 (~c2_1(a337)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[823, 1791])).
% 0.86/1.05 tff(1793,plain,
% 0.86/1.05 (c3_1(a337)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[831, 1791])).
% 0.86/1.05 tff(1794,plain,
% 0.86/1.05 (c1_1(a337)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[839, 1791])).
% 0.86/1.05 tff(1795,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c2_1(a337) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331) | (~c1_1(a337)) | (~c3_1(a337)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a337) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331) | (~c1_1(a337)) | (~c3_1(a337)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(1796,plain,
% 0.86/1.05 ((hskp8 | (~ndr1_0) | c2_1(a337) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a331) | c0_1(a331) | c3_1(a331)) <=> (hskp8 | c2_1(a337) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331) | (~c1_1(a337)) | (~c3_1(a337)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(1797,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a337) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a331) | c0_1(a331) | c3_1(a331))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c2_1(a337) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331) | (~c1_1(a337)) | (~c3_1(a337))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[1796])).
% 0.86/1.05 tff(1798,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a337) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a331) | c0_1(a331) | c3_1(a331))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a337) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331) | (~c1_1(a337)) | (~c3_1(a337)))),
% 0.86/1.05 inference(transitivity,[status(thm)],[1797, 1795])).
% 0.86/1.05 tff(1799,plain,
% 0.86/1.05 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a337) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a331) | c0_1(a331) | c3_1(a331))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(1800,plain,
% 0.86/1.05 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a337) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331) | (~c1_1(a337)) | (~c3_1(a337))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[1799, 1798])).
% 0.86/1.05 tff(1801,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1800, 129, 583, 1794, 1793, 1792, 1767, 1766, 297, 1774])).
% 0.86/1.05 tff(1802,plain,(hskp8 | c1_1(a294) | (~c0_1(a294)) | (~c2_1(a294))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(1803,plain,
% 0.86/1.05 (hskp8),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1802, 1666, 1668, 1667])).
% 0.86/1.05 tff(1804,plain,
% 0.86/1.05 (~c1_1(a300)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[504, 1803])).
% 0.86/1.05 tff(1805,plain,
% 0.86/1.05 (c3_1(a300)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[512, 1803])).
% 0.86/1.05 tff(1806,plain,
% 0.86/1.05 (c0_1(a300)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[520, 1803])).
% 0.86/1.05 tff(1807,plain,
% 0.86/1.05 (hskp15),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[759, 129, 53, 1806, 1805, 1804, 317])).
% 0.86/1.05 tff(1808,plain,
% 0.86/1.05 (~c3_1(a311)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[788, 1807])).
% 0.86/1.05 tff(1809,plain,
% 0.86/1.05 (c1_1(a311)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[767, 1807])).
% 0.86/1.05 tff(1810,plain,
% 0.86/1.05 (c0_1(a311)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[775, 1807])).
% 0.86/1.05 tff(1811,plain,
% 0.86/1.05 (hskp7),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[795, 129, 1810, 1809, 1668, 1667, 1808, 1666, 52])).
% 0.86/1.05 tff(1812,plain,
% 0.86/1.05 (c3_1(a299)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[692, 1811])).
% 0.86/1.05 tff(1813,plain,
% 0.86/1.05 (~c2_1(a299)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[709, 1811])).
% 0.86/1.05 tff(1814,plain,
% 0.86/1.05 (c0_1(a299)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[684, 1811])).
% 0.86/1.05 tff(1815,plain,
% 0.86/1.05 (hskp16),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1674, 129, 1617, 1668, 1667, 1666, 31])).
% 0.86/1.05 tff(1816,assumption,(hskp4), introduced(assumption)).
% 0.86/1.05 tff(1817,plain,
% 0.86/1.05 (~c3_1(a295)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[925, 1816])).
% 0.86/1.05 tff(1818,plain,
% 0.86/1.05 (c0_1(a295)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[963, 1816])).
% 0.86/1.05 tff(1819,plain,
% 0.86/1.05 (~c2_1(a295)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[931, 1816])).
% 0.86/1.05 tff(1820,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1438, 1819, 1818, 1424, 1429, 694, 1428, 1817])).
% 0.86/1.05 tff(1821,plain,((~hskp4) | (~hskp16) | (~c0_1(a299)) | c2_1(a299) | (~c3_1(a299))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(1822,plain,
% 0.86/1.05 (~hskp4),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1821, 1815, 1814, 1813, 1812])).
% 0.86/1.05 tff(1823,plain,
% 0.86/1.05 (hskp13),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1784, 1810, 1666, 1668, 1809, 1667, 1808])).
% 0.86/1.05 tff(1824,plain,
% 0.86/1.05 (c0_1(a308)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[971, 1823])).
% 0.86/1.05 tff(1825,plain,
% 0.86/1.05 (~c2_1(a308)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[955, 1823])).
% 0.86/1.05 tff(1826,plain,
% 0.86/1.05 (~c0_1(a315)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[420, 1815])).
% 0.86/1.05 tff(1827,plain,
% 0.86/1.05 (~c3_1(a315)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[438, 1815])).
% 0.86/1.05 tff(1828,plain,
% 0.86/1.05 (c2_1(a315)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[414, 1815])).
% 0.86/1.05 tff(1829,plain,
% 0.86/1.05 (c3_1(a308)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1753, 129, 1828, 1824, 1814, 1812, 1826, 1827, 1825, 1813, 540])).
% 0.86/1.05 tff(1830,plain,
% 0.86/1.05 (c2_1(a311)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1370, 1829, 1828, 1827, 1826, 1810, 1808, 1825, 1824])).
% 0.86/1.05 tff(1831,plain,
% 0.86/1.05 (~c1_1(a308)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1189, 1823])).
% 0.86/1.05 tff(1832,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(1833,plain,
% 0.86/1.05 ((hskp21 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a308) | c1_1(a308) | (~c3_1(a308))) <=> (hskp21 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(1834,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a308) | c1_1(a308) | (~c3_1(a308)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[1833])).
% 0.86/1.05 tff(1835,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a308) | c1_1(a308) | (~c3_1(a308)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 0.86/1.05 inference(transitivity,[status(thm)],[1834, 1832])).
% 0.86/1.05 tff(1836,plain,
% 0.86/1.05 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a308) | c1_1(a308) | (~c3_1(a308)))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(1837,plain,
% 0.86/1.05 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[1836, 1835])).
% 0.86/1.05 tff(1838,plain,
% 0.86/1.05 (hskp21 | (~c3_1(a308)) | (~c2_1(a311))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1837, 129, 1810, 1808, 1831, 1825, 1311])).
% 0.86/1.05 tff(1839,plain,
% 0.86/1.05 (hskp21),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1838, 1829, 1830])).
% 0.86/1.05 tff(1840,plain,
% 0.86/1.05 (c3_1(a330)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1347, 1839])).
% 0.86/1.05 tff(1841,plain,
% 0.86/1.05 (~c2_1(a330)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1339, 1839])).
% 0.86/1.05 tff(1842,plain,
% 0.86/1.05 (~c0_1(a330)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1323, 1839])).
% 0.86/1.05 tff(1843,plain,
% 0.86/1.05 (hskp22 | (~c3_1(a308)) | (~c2_1(a311))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1761, 129, 1810, 1808, 1831, 1825, 1233])).
% 0.86/1.05 tff(1844,plain,
% 0.86/1.05 (hskp22),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1843, 1829, 1830])).
% 0.86/1.05 tff(1845,plain,
% 0.86/1.05 (~c3_1(a331)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[82, 1844])).
% 0.86/1.05 tff(1846,plain,
% 0.86/1.05 (~c2_1(a331)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[70, 1844])).
% 0.86/1.05 tff(1847,plain,
% 0.86/1.05 (~c1_1(a331)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[76, 1844])).
% 0.86/1.05 tff(1848,plain,
% 0.86/1.05 (c1_1(a315)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1415, 1822, 1827, 1809, 1808, 1830, 1847, 1846, 1845, 1842, 1841, 1826, 1840])).
% 0.86/1.05 tff(1849,plain,
% 0.86/1.05 (^[U: $i] : refl((hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 0.86/1.05 inference(bind,[status(th)],[])).
% 0.86/1.05 tff(1850,plain,
% 0.86/1.05 (![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.86/1.05 inference(quant_intro,[status(thm)],[1849])).
% 0.86/1.05 tff(1851,plain,
% 0.86/1.05 (![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(1852,plain,
% 0.86/1.05 (^[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)) | hskp4) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp4))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp4) | hskp11) <=> ((hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp11))), rewrite(((hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp11) <=> (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp4) | hskp11) <=> (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 0.86/1.05 inference(bind,[status(th)],[])).
% 0.86/1.05 tff(1853,plain,
% 0.86/1.05 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp4) | hskp11) <=> ![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.86/1.05 inference(quant_intro,[status(thm)],[1852])).
% 0.86/1.05 tff(1854,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp4) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 0.86/1.05 tff(1855,plain,
% 0.86/1.05 (![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[1854, 1853])).
% 0.86/1.05 tff(1856,plain,
% 0.86/1.05 (![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[1855, 1851])).
% 0.86/1.05 tff(1857,plain,(
% 0.86/1.05 ![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.86/1.05 inference(skolemize,[status(sab)],[1856])).
% 0.86/1.05 tff(1858,plain,
% 0.86/1.05 (![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[1857, 1850])).
% 0.86/1.05 tff(1859,plain,
% 0.86/1.05 (((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp11 | hskp4 | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)))) <=> ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp11 | hskp4 | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(1860,plain,
% 0.86/1.05 ((hskp11 | hskp4 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315))) <=> (hskp11 | hskp4 | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(1861,plain,
% 0.86/1.05 (((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp11 | hskp4 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315)))) <=> ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp11 | hskp4 | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[1860])).
% 0.86/1.05 tff(1862,plain,
% 0.86/1.05 (((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp11 | hskp4 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315)))) <=> ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp11 | hskp4 | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)))),
% 0.86/1.05 inference(transitivity,[status(thm)],[1861, 1859])).
% 0.86/1.05 tff(1863,plain,
% 0.86/1.05 ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp11 | hskp4 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315)))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(1864,plain,
% 0.86/1.05 ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp11 | hskp4 | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[1863, 1862])).
% 0.86/1.05 tff(1865,plain,
% 0.86/1.05 (hskp11 | hskp4 | (~c1_1(a315))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1864, 129, 1828, 1826, 1858])).
% 0.86/1.05 tff(1866,plain,
% 0.86/1.05 (hskp11),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1865, 1848, 1822])).
% 0.86/1.05 tff(1867,plain,
% 0.86/1.05 (~c0_1(a306)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[615, 1866])).
% 0.86/1.05 tff(1868,plain,
% 0.86/1.05 (c3_1(a306)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[623, 1866])).
% 0.86/1.05 tff(1869,plain,
% 0.86/1.05 (c1_1(a306)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[631, 1866])).
% 0.86/1.05 tff(1870,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(1871,plain,
% 0.86/1.05 ((hskp4 | (~ndr1_0) | c0_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c2_1(a331) | c1_1(a331) | c3_1(a331)) <=> (hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(1872,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c0_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c2_1(a331) | c1_1(a331) | c3_1(a331))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[1871])).
% 0.86/1.05 tff(1873,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c0_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c2_1(a331) | c1_1(a331) | c3_1(a331))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306)))),
% 0.86/1.05 inference(transitivity,[status(thm)],[1872, 1870])).
% 0.86/1.05 tff(1874,plain,
% 0.86/1.05 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c0_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c2_1(a331) | c1_1(a331) | c3_1(a331))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(1875,plain,
% 0.86/1.05 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[1874, 1873])).
% 0.86/1.05 tff(1876,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1875, 129, 1822, 1869, 1868, 1847, 1846, 1845, 1867, 42])).
% 0.86/1.05 tff(1877,plain,(hskp29), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(1878,plain,
% 0.86/1.05 (c2_1(a301)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[326, 1877])).
% 0.86/1.05 tff(1879,plain,
% 0.86/1.05 (c0_1(a301)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[334, 1877])).
% 0.86/1.05 tff(1880,plain,
% 0.86/1.05 (((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp24 | hskp16 | (~ndr1_0) | c1_1(a301) | (~c0_1(a301)) | (~c2_1(a301)))) <=> ((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp24 | hskp16 | (~ndr1_0) | c1_1(a301) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(1881,plain,
% 0.86/1.05 ((hskp24 | hskp16 | (~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c0_1(a301))) <=> (hskp24 | hskp16 | (~ndr1_0) | c1_1(a301) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(1882,plain,
% 0.86/1.05 (((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp24 | hskp16 | (~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c0_1(a301)))) <=> ((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp24 | hskp16 | (~ndr1_0) | c1_1(a301) | (~c0_1(a301)) | (~c2_1(a301))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[1881])).
% 0.86/1.05 tff(1883,plain,
% 0.86/1.05 (((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp24 | hskp16 | (~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c0_1(a301)))) <=> ((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp24 | hskp16 | (~ndr1_0) | c1_1(a301) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[1882, 1880])).
% 0.86/1.06 tff(1884,plain,
% 0.86/1.06 ((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp24 | hskp16 | (~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c0_1(a301)))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(1885,plain,
% 0.86/1.06 ((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp24 | hskp16 | (~ndr1_0) | c1_1(a301) | (~c0_1(a301)) | (~c2_1(a301))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[1884, 1883])).
% 0.86/1.06 tff(1886,plain,
% 0.86/1.06 (hskp16 | c1_1(a301)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1885, 129, 1617, 1879, 1878, 31])).
% 0.86/1.06 tff(1887,plain,
% 0.86/1.06 (c1_1(a301)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1886, 32])).
% 0.86/1.06 tff(1888,assumption,(c1_1(a301)), introduced(assumption)).
% 0.86/1.06 tff(1889,plain,
% 0.86/1.06 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(1890,plain,
% 0.86/1.06 ((hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c0_1(a301))) <=> (hskp26 | hskp3 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(1891,plain,
% 0.86/1.06 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c0_1(a301)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[1890])).
% 0.86/1.06 tff(1892,plain,
% 0.86/1.06 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c0_1(a301)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[1891, 1889])).
% 0.86/1.06 tff(1893,plain,
% 0.86/1.06 ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c0_1(a301)))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(1894,plain,
% 0.86/1.06 ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[1893, 1892])).
% 0.86/1.06 tff(1895,plain,
% 0.86/1.06 (hskp26 | hskp3 | (~c1_1(a301))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1894, 129, 1879, 1878, 170])).
% 0.86/1.06 tff(1896,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1895, 223, 64, 1888])).
% 0.86/1.06 tff(1897,plain,(hskp3 | (~c1_1(a301))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(1898,plain,
% 0.86/1.06 (hskp3),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1897, 1887])).
% 0.86/1.06 tff(1899,plain,
% 0.86/1.06 (~c1_1(a294)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[718, 1898])).
% 0.86/1.06 tff(1900,plain,
% 0.86/1.06 (c2_1(a294)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[726, 1898])).
% 0.86/1.06 tff(1901,plain,
% 0.86/1.06 (c0_1(a294)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[734, 1898])).
% 0.86/1.06 tff(1902,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1674, 129, 1617, 32, 1901, 1900, 1899, 31])).
% 0.86/1.06 tff(1903,plain,(hskp16), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(1904,plain,
% 0.86/1.06 (~c3_1(a315)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[438, 1903])).
% 0.86/1.06 tff(1905,plain,
% 0.86/1.06 (~c0_1(a315)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[420, 1903])).
% 0.86/1.06 tff(1906,plain,
% 0.86/1.06 (c2_1(a315)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[414, 1903])).
% 0.86/1.06 tff(1907,plain,
% 0.86/1.06 (c3_1(a301)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[349, 1877])).
% 0.86/1.06 tff(1908,plain,
% 0.86/1.06 (hskp5),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1450, 129, 1879, 1878, 1907, 1906, 1905, 1904, 21])).
% 0.86/1.06 tff(1909,plain,
% 0.86/1.06 (~c0_1(a297)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[365, 1908])).
% 0.86/1.06 tff(1910,plain,
% 0.86/1.06 (~c1_1(a301)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1897, 64])).
% 0.86/1.06 tff(1911,plain,
% 0.86/1.06 (hskp3 | c1_1(a315)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[445, 129, 1905, 1904, 93])).
% 0.86/1.06 tff(1912,plain,
% 0.86/1.06 (c1_1(a315)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1911, 64])).
% 0.86/1.06 tff(1913,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c1_1(a315)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c1_1(a315)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(1914,plain,
% 0.86/1.06 (((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a315) | c0_1(a315) | (~c1_1(a315))) <=> (c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c1_1(a315)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(1915,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a315) | c0_1(a315) | (~c1_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c1_1(a315)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[1914])).
% 0.86/1.06 tff(1916,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a315) | c0_1(a315) | (~c1_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c1_1(a315)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[1915, 1913])).
% 0.86/1.06 tff(1917,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a315) | c0_1(a315) | (~c1_1(a315)))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(1918,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c1_1(a315)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[1917, 1916])).
% 0.86/1.06 tff(1919,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1918, 129, 1879, 1878, 1907, 1905, 1904, 11, 1912, 1910])).
% 0.86/1.06 tff(1920,plain,(hskp3), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(1921,plain,
% 0.86/1.06 (c2_1(a294)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[726, 1920])).
% 0.86/1.06 tff(1922,plain,
% 0.86/1.06 (c0_1(a294)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[734, 1920])).
% 0.86/1.06 tff(1923,plain,
% 0.86/1.06 (~c1_1(a294)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[718, 1920])).
% 0.86/1.06 tff(1924,plain,
% 0.86/1.06 (hskp8),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1802, 1923, 1922, 1921])).
% 0.86/1.06 tff(1925,plain,
% 0.86/1.06 (~c1_1(a300)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[504, 1924])).
% 0.86/1.06 tff(1926,plain,
% 0.86/1.06 (c1_1(a297)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[373, 1908])).
% 0.86/1.06 tff(1927,plain,
% 0.86/1.06 (c3_1(a300)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[512, 1924])).
% 0.86/1.06 tff(1928,plain,
% 0.86/1.06 (c0_1(a300)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[520, 1924])).
% 0.86/1.06 tff(1929,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a300) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c1_1(a297)) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a300) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c1_1(a297)) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(1930,plain,
% 0.86/1.06 (((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a297) | c0_1(a297) | (~c1_1(a297))) <=> (c1_1(a300) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c1_1(a297)) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(1931,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a297) | c0_1(a297) | (~c1_1(a297)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a300) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c1_1(a297)) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[1930])).
% 0.86/1.06 tff(1932,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a297) | c0_1(a297) | (~c1_1(a297)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a300) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c1_1(a297)) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[1931, 1929])).
% 0.86/1.06 tff(1933,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a297) | c0_1(a297) | (~c1_1(a297)))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(1934,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a300) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c1_1(a297)) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[1933, 1932])).
% 0.86/1.06 tff(1935,plain,
% 0.86/1.06 (~c2_1(a300)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1934, 129, 1928, 1927, 1926, 1925, 1909, 11, 1])).
% 0.86/1.06 tff(1936,plain,
% 0.86/1.06 (c2_1(a297)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[381, 1908])).
% 0.86/1.06 tff(1937,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a300) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a300) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(1938,plain,
% 0.86/1.06 (((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300)) <=> (c1_1(a300) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(1939,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a300) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[1938])).
% 0.86/1.06 tff(1940,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a300) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[1939, 1937])).
% 0.86/1.06 tff(1941,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(1942,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a300) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[1941, 1940])).
% 0.86/1.06 tff(1943,plain,
% 0.86/1.06 (~c1_1(a301)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1942, 129, 1878, 1907, 1927, 1926, 1936, 1925, 1001, 1, 1935])).
% 0.86/1.06 tff(1944,assumption,(c3_1(a294)), introduced(assumption)).
% 0.86/1.06 tff(1945,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a300) | c0_1(a297) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c3_1(a297) | (~c1_1(a297)) | (~c3_1(a300)) | (~c0_1(a300)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a300) | c0_1(a297) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c3_1(a297) | (~c1_1(a297)) | (~c3_1(a300)) | (~c0_1(a300)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(1946,plain,
% 0.86/1.06 (((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a297) | c0_1(a297) | (~c1_1(a297))) <=> (c1_1(a300) | c0_1(a297) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c3_1(a297) | (~c1_1(a297)) | (~c3_1(a300)) | (~c0_1(a300)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(1947,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a297) | c0_1(a297) | (~c1_1(a297)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a300) | c0_1(a297) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c3_1(a297) | (~c1_1(a297)) | (~c3_1(a300)) | (~c0_1(a300))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[1946])).
% 0.86/1.06 tff(1948,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a297) | c0_1(a297) | (~c1_1(a297)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a300) | c0_1(a297) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c3_1(a297) | (~c1_1(a297)) | (~c3_1(a300)) | (~c0_1(a300)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[1947, 1945])).
% 0.86/1.06 tff(1949,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a297) | c0_1(a297) | (~c1_1(a297)))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(1950,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a300) | c0_1(a297) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c3_1(a297) | (~c1_1(a297)) | (~c3_1(a300)) | (~c0_1(a300))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[1949, 1948])).
% 0.86/1.06 tff(1951,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1950, 129, 1928, 1927, 1926, 1921, 1925, 1909, 1923, 11, 1, 1944])).
% 0.86/1.06 tff(1952,plain,(c3_1(a297) | (~c3_1(a294))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(1953,plain,
% 0.86/1.06 (~c3_1(a294)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1952, 1])).
% 0.86/1.06 tff(1954,plain,
% 0.86/1.06 (hskp20 | c3_1(a294)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1524, 129, 1922, 1921, 1518])).
% 0.86/1.06 tff(1955,plain,
% 0.86/1.06 (hskp20),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1954, 1953])).
% 0.86/1.06 tff(1956,plain,
% 0.86/1.06 (~c2_1(a329)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1531, 1955])).
% 0.86/1.06 tff(1957,plain,
% 0.86/1.06 (~c1_1(a329)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1537, 1955])).
% 0.86/1.06 tff(1958,plain,
% 0.86/1.06 (~c0_1(a329)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1543, 1955])).
% 0.86/1.06 tff(1959,plain,
% 0.86/1.06 (hskp0),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1550, 129, 1922, 1958, 1957, 1956, 1923, 1508, 1953])).
% 0.86/1.06 tff(1960,plain,
% 0.86/1.06 (~c3_1(a291)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[497, 1959])).
% 0.86/1.06 tff(1961,plain,
% 0.86/1.06 (~c2_1(a291)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[475, 1959])).
% 0.86/1.06 tff(1962,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a315)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(1963,plain,
% 0.86/1.06 (((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315))) <=> (c0_1(a315) | c3_1(a315) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a315)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(1964,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a315))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[1963])).
% 0.86/1.06 tff(1965,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a315)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[1964, 1962])).
% 0.86/1.06 tff(1966,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(1967,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a315))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[1966, 1965])).
% 0.86/1.06 tff(1968,plain,
% 0.86/1.06 (~c0_1(a291)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1967, 129, 1906, 1928, 1927, 1905, 1904, 1961, 1960, 540, 1935])).
% 0.86/1.06 tff(1969,plain,
% 0.86/1.06 (c1_1(a291)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[483, 1959])).
% 0.86/1.06 tff(1970,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(1971,plain,
% 0.86/1.06 (((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a291) | c0_1(a291) | (~c1_1(a291))) <=> (c3_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(1972,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a291) | c0_1(a291) | (~c1_1(a291)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[1971])).
% 0.86/1.06 tff(1973,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a291) | c0_1(a291) | (~c1_1(a291)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[1972, 1970])).
% 0.86/1.06 tff(1974,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a291) | c0_1(a291) | (~c1_1(a291)))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(1975,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[1974, 1973])).
% 0.86/1.06 tff(1976,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1975, 129, 1879, 1878, 1907, 1969, 1960, 11, 1968, 1943])).
% 0.86/1.06 tff(1977,plain,(c3_1(a297)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(1978,plain,
% 0.86/1.06 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a297)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a297)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(1979,plain,
% 0.86/1.06 ((hskp7 | (~ndr1_0) | c0_1(a297) | (~c1_1(a297)) | (~c3_1(a297)) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297))) <=> (hskp7 | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a297)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(1980,plain,
% 0.86/1.06 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a297) | (~c1_1(a297)) | (~c3_1(a297)) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a297))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[1979])).
% 0.86/1.06 tff(1981,plain,
% 0.86/1.06 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a297) | (~c1_1(a297)) | (~c3_1(a297)) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a297)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[1980, 1978])).
% 0.86/1.06 tff(1982,plain,
% 0.86/1.06 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a297) | (~c1_1(a297)) | (~c3_1(a297)) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(1983,plain,
% 0.86/1.06 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a297))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[1982, 1981])).
% 0.86/1.06 tff(1984,plain,
% 0.86/1.06 (hskp7 | (~c3_1(a297))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1983, 129, 1926, 1936, 1909, 458])).
% 0.86/1.06 tff(1985,plain,
% 0.86/1.06 (hskp7),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1984, 1977])).
% 0.86/1.06 tff(1986,assumption,(c3_1(a297)), introduced(assumption)).
% 0.86/1.06 tff(1987,plain,
% 0.86/1.06 (hskp7),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1984, 1986])).
% 0.86/1.06 tff(1988,plain,
% 0.86/1.06 (c3_1(a299)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[692, 1987])).
% 0.86/1.06 tff(1989,plain,
% 0.86/1.06 (~c3_1(a294)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1950, 129, 1928, 1927, 1926, 1921, 1925, 1909, 1923, 11, 1])).
% 0.86/1.06 tff(1990,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1330, 129, 856, 1927, 1922, 1921, 1925, 1233, 1989, 1935])).
% 0.86/1.06 tff(1991,plain,(c3_1(a297) | hskp22), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(1992,plain,
% 0.86/1.06 (c3_1(a297)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1991, 856])).
% 0.86/1.06 tff(1993,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a315)) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a315)) | (~c2_1(a315)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(1994,plain,
% 0.86/1.07 (((~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c3_1(a297)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)) | c3_1(a315) | c0_1(a315) | (~c1_1(a315))) <=> (c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a315)) | (~c2_1(a315)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(1995,plain,
% 0.86/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c3_1(a297)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)) | c3_1(a315) | c0_1(a315) | (~c1_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a315)) | (~c2_1(a315))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[1994])).
% 0.86/1.07 tff(1996,plain,
% 0.86/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c3_1(a297)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)) | c3_1(a315) | c0_1(a315) | (~c1_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a315)) | (~c2_1(a315)))),
% 0.86/1.07 inference(transitivity,[status(thm)],[1995, 1993])).
% 0.86/1.07 tff(1997,plain,
% 0.86/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c3_1(a297)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)) | c3_1(a315) | c0_1(a315) | (~c1_1(a315)))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(1998,plain,
% 0.86/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a315)) | (~c2_1(a315))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1997, 1996])).
% 0.86/1.07 tff(1999,plain,
% 0.86/1.07 ((~c3_1(a297)) | (~c1_1(a315))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1998, 129, 1906, 1936, 1905, 1904, 1909, 263])).
% 0.86/1.07 tff(2000,plain,
% 0.86/1.07 (~c1_1(a315)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1999, 1992])).
% 0.86/1.07 tff(2001,plain,
% 0.86/1.07 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(2002,plain,
% 0.86/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[2001])).
% 0.86/1.07 tff(2003,plain,
% 0.86/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(2004,plain,
% 0.86/1.07 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(2005,plain,
% 0.86/1.07 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[2004])).
% 0.86/1.07 tff(2006,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause191')).
% 0.86/1.07 tff(2007,plain,
% 0.86/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[2006, 2005])).
% 0.86/1.07 tff(2008,plain,
% 0.86/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[2007, 2003])).
% 0.86/1.07 tff(2009,plain,(
% 0.86/1.07 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.86/1.07 inference(skolemize,[status(sab)],[2008])).
% 0.86/1.07 tff(2010,plain,
% 0.86/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[2009, 2002])).
% 0.86/1.07 tff(2011,plain,
% 0.86/1.07 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(2012,plain,
% 0.86/1.07 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[2011])).
% 0.86/1.07 tff(2013,plain,
% 0.86/1.07 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(2014,plain,
% 0.86/1.07 (^[V: $i, U: $i] : 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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp21) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp21))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(2015,plain,
% 0.86/1.07 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[2014])).
% 0.86/1.07 tff(2016,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause188')).
% 0.86/1.07 tff(2017,plain,
% 0.86/1.07 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[2016, 2015])).
% 0.86/1.07 tff(2018,plain,
% 0.86/1.07 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[2017, 2013])).
% 0.86/1.07 tff(2019,plain,(
% 0.86/1.07 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.86/1.07 inference(skolemize,[status(sab)],[2018])).
% 0.86/1.07 tff(2020,plain,
% 0.86/1.07 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[2019, 2012])).
% 0.86/1.07 tff(2021,plain,
% 0.86/1.07 (hskp7),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1984, 1992])).
% 0.86/1.07 tff(2022,plain,
% 0.86/1.07 (~c2_1(a299)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[709, 2021])).
% 0.86/1.07 tff(2023,plain,
% 0.86/1.07 (c3_1(a299)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[692, 2021])).
% 0.86/1.07 tff(2024,plain,
% 0.86/1.07 (c0_1(a299)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[684, 2021])).
% 0.86/1.07 tff(2025,plain,
% 0.86/1.07 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(2026,plain,
% 0.86/1.07 ((hskp21 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299))) <=> (hskp21 | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(2027,plain,
% 0.86/1.07 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[2026])).
% 0.86/1.07 tff(2028,plain,
% 0.86/1.07 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 0.86/1.07 inference(transitivity,[status(thm)],[2027, 2025])).
% 0.86/1.07 tff(2029,plain,
% 0.86/1.07 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(2030,plain,
% 0.86/1.07 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[2029, 2028])).
% 0.86/1.07 tff(2031,plain,
% 0.86/1.07 (hskp21),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[2030, 129, 1879, 1878, 1907, 2024, 2023, 2022, 2020])).
% 0.86/1.07 tff(2032,plain,
% 0.86/1.07 (~c2_1(a330)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1339, 2031])).
% 0.86/1.07 tff(2033,plain,
% 0.86/1.07 (~c0_1(a330)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1323, 2031])).
% 0.86/1.07 tff(2034,plain,
% 0.86/1.07 (c3_1(a330)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1347, 2031])).
% 0.86/1.07 tff(2035,plain,
% 0.86/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(2036,plain,
% 0.86/1.07 (((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a315) | c3_1(a315) | (~c2_1(a315)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330))) <=> (c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(2037,plain,
% 0.86/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a315) | c3_1(a315) | (~c2_1(a315)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[2036])).
% 0.86/1.07 tff(2038,plain,
% 0.86/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a315) | c3_1(a315) | (~c2_1(a315)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330)))),
% 0.86/1.07 inference(transitivity,[status(thm)],[2037, 2035])).
% 0.86/1.07 tff(2039,plain,
% 0.86/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a315) | c3_1(a315) | (~c2_1(a315)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330)))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(2040,plain,
% 0.86/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[2039, 2038])).
% 0.86/1.07 tff(2041,plain,
% 0.86/1.07 (~c2_1(a300)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[2040, 129, 2034, 1906, 1927, 2033, 2032, 1904, 1925, 2010, 2000])).
% 0.86/1.07 tff(2042,plain,
% 0.86/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(2043,plain,
% 0.86/1.07 (((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a315) | c3_1(a315) | (~c2_1(a315)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330))) <=> (c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(2044,plain,
% 0.86/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a315) | c3_1(a315) | (~c2_1(a315)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[2043])).
% 0.86/1.07 tff(2045,plain,
% 0.86/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a315) | c3_1(a315) | (~c2_1(a315)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330)))),
% 0.86/1.07 inference(transitivity,[status(thm)],[2044, 2042])).
% 0.86/1.07 tff(2046,plain,
% 0.86/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a315) | c3_1(a315) | (~c2_1(a315)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330)))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(2047,plain,
% 0.86/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[2046, 2045])).
% 0.86/1.07 tff(2048,plain,
% 0.86/1.07 (~c3_1(a294)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[2047, 129, 2034, 1906, 1921, 2033, 2032, 1904, 1923, 2010, 2000])).
% 0.86/1.07 tff(2049,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1330, 129, 856, 1927, 1922, 1921, 1925, 1233, 2048, 2041])).
% 0.86/1.07 tff(2050,plain,(hskp22), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(2051,plain,
% 0.86/1.07 (~c3_1(a331)),
% 0.93/1.08 inference(unit_resolution,[status(thm)],[82, 2050])).
% 0.93/1.08 tff(2052,plain,
% 0.93/1.08 (~c2_1(a331)),
% 0.93/1.08 inference(unit_resolution,[status(thm)],[70, 2050])).
% 0.93/1.08 tff(2053,plain,
% 0.93/1.08 (~c1_1(a331)),
% 0.93/1.08 inference(unit_resolution,[status(thm)],[76, 2050])).
% 0.93/1.08 tff(2054,plain,
% 0.93/1.08 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c1_1(a297)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c1_1(a297)))),
% 0.93/1.08 inference(rewrite,[status(thm)],[])).
% 0.93/1.08 tff(2055,plain,
% 0.93/1.08 ((hskp4 | (~ndr1_0) | c0_1(a297) | (~c1_1(a297)) | (~c3_1(a297)) | c2_1(a331) | c1_1(a331) | c3_1(a331)) <=> (hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c1_1(a297)))),
% 0.93/1.08 inference(rewrite,[status(thm)],[])).
% 0.93/1.08 tff(2056,plain,
% 0.93/1.08 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c0_1(a297) | (~c1_1(a297)) | (~c3_1(a297)) | c2_1(a331) | c1_1(a331) | c3_1(a331))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c1_1(a297))))),
% 0.93/1.08 inference(monotonicity,[status(thm)],[2055])).
% 0.93/1.08 tff(2057,plain,
% 0.93/1.08 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c0_1(a297) | (~c1_1(a297)) | (~c3_1(a297)) | c2_1(a331) | c1_1(a331) | c3_1(a331))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c1_1(a297)))),
% 0.93/1.08 inference(transitivity,[status(thm)],[2056, 2054])).
% 0.93/1.08 tff(2058,plain,
% 0.93/1.08 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c0_1(a297) | (~c1_1(a297)) | (~c3_1(a297)) | c2_1(a331) | c1_1(a331) | c3_1(a331))),
% 0.93/1.08 inference(quant_inst,[status(thm)],[])).
% 0.93/1.08 tff(2059,plain,
% 0.93/1.08 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c1_1(a297))),
% 0.93/1.08 inference(modus_ponens,[status(thm)],[2058, 2057])).
% 0.93/1.08 tff(2060,plain,
% 0.93/1.08 (hskp4 | (~c3_1(a297))),
% 0.93/1.08 inference(unit_resolution,[status(thm)],[2059, 129, 1926, 2053, 2052, 2051, 1909, 42])).
% 0.93/1.08 tff(2061,plain,
% 0.93/1.08 (hskp4),
% 0.93/1.08 inference(unit_resolution,[status(thm)],[2060, 1986])).
% 0.93/1.08 tff(2062,plain,
% 0.93/1.08 (c0_1(a299)),
% 0.93/1.08 inference(unit_resolution,[status(thm)],[684, 1987])).
% 0.93/1.08 tff(2063,plain,
% 0.93/1.08 ($false),
% 0.93/1.08 inference(unit_resolution,[status(thm)],[1821, 2062, 2061, 1903, 694, 1988])).
% 0.93/1.08 tff(2064,plain,((~c3_1(a297)) | c2_1(a299)), inference(lemma,lemma(discharge,[]))).
% 0.93/1.08 tff(2065,plain,
% 0.93/1.08 (c2_1(a299)),
% 0.93/1.08 inference(unit_resolution,[status(thm)],[2064, 1977])).
% 0.93/1.08 tff(2066,plain,
% 0.93/1.08 ($false),
% 0.93/1.08 inference(unit_resolution,[status(thm)],[709, 2065, 1985])).
% 0.93/1.08 % SZS output end Proof
% 0.93/1.08 % E exiting
%------------------------------------------------------------------------------