%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN506-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:39:23 AM UTC 2025
% Result : Unsatisfiable 0.57s 0.74s
% Output : Proof 0.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN506-1 : TPTP v9.0.0. Released v2.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n012.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:36:25 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.57/0.74 % SZS status Unsatisfiable
% 0.57/0.74 % SZS output start Proof
% 0.57/0.74 tff(c2_1_type, type, (
% 0.57/0.74 c2_1: $i > $o)).
% 0.57/0.74 tff(a359_type, type, (
% 0.57/0.74 a359: $i)).
% 0.57/0.74 tff(hskp21_type, type, (
% 0.57/0.74 hskp21: $o)).
% 0.57/0.74 tff(c3_1_type, type, (
% 0.57/0.74 c3_1: $i > $o)).
% 0.57/0.74 tff(c1_1_type, type, (
% 0.57/0.74 c1_1: $i > $o)).
% 0.57/0.74 tff(c0_1_type, type, (
% 0.57/0.74 c0_1: $i > $o)).
% 0.57/0.74 tff(ndr1_0_type, type, (
% 0.57/0.74 ndr1_0: $o)).
% 0.57/0.74 tff(a323_type, type, (
% 0.57/0.74 a323: $i)).
% 0.57/0.74 tff(hskp1_type, type, (
% 0.57/0.74 hskp1: $o)).
% 0.57/0.74 tff(a419_type, type, (
% 0.57/0.74 a419: $i)).
% 0.57/0.74 tff(hskp25_type, type, (
% 0.57/0.74 hskp25: $o)).
% 0.57/0.74 tff(a349_type, type, (
% 0.57/0.74 a349: $i)).
% 0.57/0.74 tff(hskp16_type, type, (
% 0.57/0.74 hskp16: $o)).
% 0.57/0.74 tff(a338_type, type, (
% 0.57/0.74 a338: $i)).
% 0.57/0.74 tff(hskp11_type, type, (
% 0.57/0.74 hskp11: $o)).
% 0.57/0.74 tff(a343_type, type, (
% 0.57/0.74 a343: $i)).
% 0.57/0.74 tff(hskp28_type, type, (
% 0.57/0.74 hskp28: $o)).
% 0.57/0.74 tff(hskp24_type, type, (
% 0.57/0.74 hskp24: $o)).
% 0.57/0.74 tff(hskp26_type, type, (
% 0.57/0.74 hskp26: $o)).
% 0.57/0.74 tff(hskp2_type, type, (
% 0.57/0.74 hskp2: $o)).
% 0.57/0.74 tff(a327_type, type, (
% 0.57/0.74 a327: $i)).
% 0.57/0.74 tff(hskp5_type, type, (
% 0.57/0.74 hskp5: $o)).
% 0.57/0.74 tff(a367_type, type, (
% 0.57/0.74 a367: $i)).
% 0.57/0.74 tff(a348_type, type, (
% 0.57/0.74 a348: $i)).
% 0.57/0.74 tff(hskp15_type, type, (
% 0.57/0.74 hskp15: $o)).
% 0.57/0.74 tff(a347_type, type, (
% 0.57/0.74 a347: $i)).
% 0.57/0.74 tff(hskp14_type, type, (
% 0.57/0.74 hskp14: $o)).
% 0.57/0.74 tff(a346_type, type, (
% 0.57/0.74 a346: $i)).
% 0.57/0.74 tff(hskp13_type, type, (
% 0.57/0.74 hskp13: $o)).
% 0.57/0.74 tff(a324_type, type, (
% 0.57/0.74 a324: $i)).
% 0.57/0.74 tff(hskp22_type, type, (
% 0.57/0.74 hskp22: $o)).
% 0.57/0.74 tff(a401_type, type, (
% 0.57/0.74 a401: $i)).
% 0.57/0.74 tff(a333_type, type, (
% 0.57/0.74 a333: $i)).
% 0.57/0.74 tff(a330_type, type, (
% 0.57/0.74 a330: $i)).
% 0.57/0.74 tff(hskp7_type, type, (
% 0.57/0.74 hskp7: $o)).
% 0.57/0.74 tff(a353_type, type, (
% 0.57/0.74 a353: $i)).
% 0.57/0.74 tff(hskp17_type, type, (
% 0.57/0.74 hskp17: $o)).
% 0.57/0.74 tff(a329_type, type, (
% 0.57/0.74 a329: $i)).
% 0.57/0.74 tff(hskp6_type, type, (
% 0.57/0.74 hskp6: $o)).
% 0.57/0.74 tff(a337_type, type, (
% 0.57/0.74 a337: $i)).
% 0.57/0.74 tff(hskp10_type, type, (
% 0.57/0.74 hskp10: $o)).
% 0.57/0.74 tff(a345_type, type, (
% 0.57/0.74 a345: $i)).
% 0.57/0.74 tff(hskp12_type, type, (
% 0.57/0.74 hskp12: $o)).
% 0.57/0.74 tff(1,plain,
% 0.57/0.74 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(2,plain,
% 0.57/0.74 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[1])).
% 0.57/0.74 tff(3,plain,
% 0.57/0.74 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(4,plain,
% 0.57/0.74 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | 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)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(5,plain,
% 0.57/0.74 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[4])).
% 0.57/0.74 tff(6,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 0.57/0.74 tff(7,plain,
% 0.57/0.74 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.57/0.74 tff(8,plain,
% 0.57/0.74 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.57/0.74 tff(9,plain,(
% 0.57/0.74 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.57/0.74 inference(skolemize,[status(sab)],[8])).
% 0.57/0.74 tff(10,plain,
% 0.57/0.74 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.57/0.74 tff(11,plain,
% 0.57/0.74 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(12,plain,
% 0.57/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[11])).
% 0.57/0.74 tff(13,plain,
% 0.57/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(14,plain,
% 0.57/0.74 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(15,plain,
% 0.57/0.74 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[14])).
% 0.57/0.74 tff(16,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 0.57/0.74 tff(17,plain,
% 0.57/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.57/0.74 tff(18,plain,
% 0.57/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.57/0.74 tff(19,plain,(
% 0.57/0.74 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.57/0.74 inference(skolemize,[status(sab)],[18])).
% 0.57/0.74 tff(20,plain,
% 0.57/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.57/0.74 tff(21,assumption,(~hskp25), introduced(assumption)).
% 0.57/0.74 tff(22,plain,
% 0.57/0.74 ((hskp25 | hskp16) <=> (hskp25 | hskp16)),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(23,axiom,(hskp25 | hskp16), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.57/0.74 tff(24,plain,
% 0.57/0.74 (hskp25 | hskp16),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.57/0.74 tff(25,plain,
% 0.57/0.74 (hskp25 | hskp16),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[24, 22])).
% 0.57/0.74 tff(26,plain,
% 0.57/0.74 (hskp25 | hskp16),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.57/0.74 tff(27,plain,
% 0.57/0.74 (hskp25 | hskp16),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.57/0.74 tff(28,plain,
% 0.57/0.74 (hskp25 | hskp16),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[27, 22])).
% 0.57/0.74 tff(29,plain,
% 0.57/0.74 (hskp16),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[28, 21])).
% 0.57/0.74 tff(30,plain,
% 0.57/0.74 (((~hskp16) | (~c2_1(a349))) <=> ((~hskp16) | (~c2_1(a349)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(31,plain,
% 0.57/0.74 (((~c2_1(a349)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a349)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(32,axiom,((~c2_1(a349)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 0.57/0.74 tff(33,plain,
% 0.57/0.74 ((~hskp16) | (~c2_1(a349))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.57/0.74 tff(34,plain,
% 0.57/0.74 ((~hskp16) | (~c2_1(a349))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[33, 30])).
% 0.57/0.74 tff(35,plain,
% 0.57/0.74 (~c2_1(a349)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[34, 29])).
% 0.57/0.74 tff(36,plain,
% 0.57/0.74 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(37,plain,
% 0.57/0.74 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[36])).
% 0.57/0.74 tff(38,plain,
% 0.57/0.74 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(39,plain,
% 0.57/0.74 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(40,plain,
% 0.57/0.74 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[39])).
% 0.57/0.74 tff(41,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 0.57/0.74 tff(42,plain,
% 0.57/0.74 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.57/0.74 tff(43,plain,
% 0.57/0.74 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.57/0.74 tff(44,plain,(
% 0.57/0.74 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.57/0.74 inference(skolemize,[status(sab)],[43])).
% 0.57/0.74 tff(45,plain,
% 0.57/0.74 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.57/0.74 tff(46,assumption,(~hskp1), introduced(assumption)).
% 0.57/0.74 tff(47,plain,
% 0.57/0.74 ((hskp25 | hskp11 | hskp1) <=> (hskp25 | hskp11 | hskp1)),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(48,plain,
% 0.57/0.74 (((hskp25 | hskp11) | hskp1) <=> (hskp25 | hskp11 | hskp1)),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(49,plain,
% 0.57/0.74 ((hskp25 | hskp11) <=> (hskp25 | hskp11)),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(50,plain,
% 0.57/0.74 (((hskp25 | hskp11) | hskp1) <=> ((hskp25 | hskp11) | hskp1)),
% 0.57/0.74 inference(monotonicity,[status(thm)],[49])).
% 0.57/0.74 tff(51,plain,
% 0.57/0.74 (((hskp25 | hskp11) | hskp1) <=> (hskp25 | hskp11 | hskp1)),
% 0.57/0.74 inference(transitivity,[status(thm)],[50, 48])).
% 0.57/0.74 tff(52,axiom,((hskp25 | hskp11) | hskp1), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 0.57/0.74 tff(53,plain,
% 0.57/0.74 (hskp25 | hskp11 | hskp1),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.57/0.74 tff(54,plain,
% 0.57/0.74 (hskp25 | hskp11 | hskp1),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[53, 47])).
% 0.57/0.74 tff(55,plain,
% 0.57/0.74 (hskp25 | hskp11 | hskp1),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.57/0.74 tff(56,plain,
% 0.57/0.74 (hskp25 | hskp11 | hskp1),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[55, 47])).
% 0.57/0.74 tff(57,plain,
% 0.57/0.74 (hskp25 | hskp11 | hskp1),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[56, 47])).
% 0.57/0.74 tff(58,plain,
% 0.57/0.74 (hskp11),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[57, 46, 21])).
% 0.57/0.74 tff(59,plain,
% 0.57/0.74 (((~hskp11) | (~c2_1(a338))) <=> ((~hskp11) | (~c2_1(a338)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(60,plain,
% 0.57/0.74 (((~c2_1(a338)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a338)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(61,axiom,((~c2_1(a338)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 0.57/0.74 tff(62,plain,
% 0.57/0.74 ((~hskp11) | (~c2_1(a338))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.57/0.74 tff(63,plain,
% 0.57/0.74 ((~hskp11) | (~c2_1(a338))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[62, 59])).
% 0.57/0.74 tff(64,plain,
% 0.57/0.74 (~c2_1(a338)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[63, 58])).
% 0.57/0.74 tff(65,plain,
% 0.57/0.74 (((~hskp11) | (~c1_1(a338))) <=> ((~hskp11) | (~c1_1(a338)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(66,plain,
% 0.57/0.74 (((~c1_1(a338)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a338)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(67,axiom,((~c1_1(a338)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 0.57/0.74 tff(68,plain,
% 0.57/0.74 ((~hskp11) | (~c1_1(a338))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.57/0.74 tff(69,plain,
% 0.57/0.74 ((~hskp11) | (~c1_1(a338))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[68, 65])).
% 0.57/0.74 tff(70,plain,
% 0.57/0.74 (~c1_1(a338)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[69, 58])).
% 0.57/0.74 tff(71,plain,
% 0.57/0.74 (((~hskp11) | (~c0_1(a338))) <=> ((~hskp11) | (~c0_1(a338)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(72,plain,
% 0.57/0.74 (((~c0_1(a338)) | (~hskp11)) <=> ((~hskp11) | (~c0_1(a338)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(73,axiom,((~c0_1(a338)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 0.57/0.74 tff(74,plain,
% 0.57/0.74 ((~hskp11) | (~c0_1(a338))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.57/0.74 tff(75,plain,
% 0.57/0.74 ((~hskp11) | (~c0_1(a338))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[74, 71])).
% 0.57/0.74 tff(76,plain,
% 0.57/0.74 (~c0_1(a338)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[75, 58])).
% 0.57/0.74 tff(77,plain,
% 0.57/0.74 (((~hskp16) | c3_1(a349)) <=> ((~hskp16) | c3_1(a349))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(78,axiom,((~hskp16) | c3_1(a349)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 0.57/0.74 tff(79,plain,
% 0.57/0.74 ((~hskp16) | c3_1(a349)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.57/0.74 tff(80,plain,
% 0.57/0.74 ((~hskp16) | c3_1(a349)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[79, 77])).
% 0.57/0.74 tff(81,plain,
% 0.57/0.74 ((~hskp16) | c3_1(a349)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[80, 77])).
% 0.57/0.74 tff(82,plain,
% 0.57/0.74 ((~hskp16) | c3_1(a349)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.57/0.74 tff(83,plain,
% 0.57/0.74 ((~hskp16) | c3_1(a349)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[82, 77])).
% 0.57/0.74 tff(84,plain,
% 0.57/0.74 (c3_1(a349)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[83, 29])).
% 0.57/0.74 tff(85,plain,
% 0.57/0.74 (((~hskp16) | c1_1(a349)) <=> ((~hskp16) | c1_1(a349))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(86,axiom,((~hskp16) | c1_1(a349)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 0.57/0.74 tff(87,plain,
% 0.57/0.74 ((~hskp16) | c1_1(a349)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.57/0.74 tff(88,plain,
% 0.57/0.74 ((~hskp16) | c1_1(a349)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[87, 85])).
% 0.57/0.74 tff(89,plain,
% 0.57/0.74 ((~hskp16) | c1_1(a349)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[88, 85])).
% 0.57/0.74 tff(90,plain,
% 0.57/0.74 ((~hskp16) | c1_1(a349)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.57/0.74 tff(91,plain,
% 0.57/0.74 ((~hskp16) | c1_1(a349)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[90, 85])).
% 0.57/0.74 tff(92,plain,
% 0.57/0.74 (c1_1(a349)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[91, 29])).
% 0.57/0.74 tff(93,plain,
% 0.57/0.74 (^[U: $i] : refl((hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(94,plain,
% 0.57/0.74 (![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[93])).
% 0.57/0.74 tff(95,plain,
% 0.57/0.74 (![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(96,plain,
% 0.57/0.74 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(97,plain,
% 0.57/0.74 (![U: $i] : (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[96])).
% 0.57/0.74 tff(98,axiom,(![U: $i] : (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 0.57/0.74 tff(99,plain,
% 0.57/0.74 (![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.57/0.74 tff(100,plain,
% 0.57/0.74 (![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.57/0.74 tff(101,plain,(
% 0.57/0.74 ![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.57/0.74 inference(skolemize,[status(sab)],[100])).
% 0.57/0.74 tff(102,plain,
% 0.57/0.74 (![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.57/0.74 tff(103,assumption,(~ndr1_0), introduced(assumption)).
% 0.57/0.74 tff(104,plain,
% 0.57/0.74 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(105,plain,
% 0.57/0.74 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(106,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause7')).
% 0.57/0.74 tff(107,plain,
% 0.57/0.74 (ndr1_0 | (~hskp24)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.57/0.74 tff(108,plain,
% 0.57/0.74 (ndr1_0 | (~hskp24)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[107, 104])).
% 0.57/0.74 tff(109,plain,
% 0.57/0.74 (~hskp24),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[108, 103])).
% 0.57/0.74 tff(110,plain,
% 0.57/0.74 ((ndr1_0 | (~hskp26)) <=> (ndr1_0 | (~hskp26))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(111,plain,
% 0.57/0.74 (((~hskp26) | ndr1_0) <=> (ndr1_0 | (~hskp26))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(112,axiom,((~hskp26) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 0.57/0.74 tff(113,plain,
% 0.57/0.74 (ndr1_0 | (~hskp26)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.57/0.74 tff(114,plain,
% 0.57/0.74 (ndr1_0 | (~hskp26)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[113, 110])).
% 0.57/0.74 tff(115,plain,
% 0.57/0.74 (~hskp26),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[114, 103])).
% 0.57/0.74 tff(116,plain,
% 0.57/0.74 ((ndr1_0 | (~hskp2)) <=> (ndr1_0 | (~hskp2))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(117,plain,
% 0.57/0.74 (((~hskp2) | ndr1_0) <=> (ndr1_0 | (~hskp2))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(118,axiom,((~hskp2) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause29')).
% 0.57/0.74 tff(119,plain,
% 0.57/0.74 (ndr1_0 | (~hskp2)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.57/0.74 tff(120,plain,
% 0.57/0.74 (ndr1_0 | (~hskp2)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[119, 116])).
% 0.57/0.74 tff(121,plain,
% 0.57/0.74 (~hskp2),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[120, 103])).
% 0.57/0.74 tff(122,plain,
% 0.57/0.74 ((hskp24 | hskp26 | hskp2) <=> (hskp24 | hskp26 | hskp2)),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(123,plain,
% 0.57/0.74 (((hskp24 | hskp26) | hskp2) <=> (hskp24 | hskp26 | hskp2)),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(124,plain,
% 0.57/0.74 ((hskp26 | hskp24) <=> (hskp24 | hskp26)),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(125,plain,
% 0.57/0.74 (((hskp26 | hskp24) | hskp2) <=> ((hskp24 | hskp26) | hskp2)),
% 0.57/0.74 inference(monotonicity,[status(thm)],[124])).
% 0.57/0.74 tff(126,plain,
% 0.57/0.74 (((hskp26 | hskp24) | hskp2) <=> (hskp24 | hskp26 | hskp2)),
% 0.57/0.74 inference(transitivity,[status(thm)],[125, 123])).
% 0.57/0.74 tff(127,axiom,((hskp26 | hskp24) | hskp2), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 0.57/0.74 tff(128,plain,
% 0.57/0.74 (hskp24 | hskp26 | hskp2),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.57/0.74 tff(129,plain,
% 0.57/0.74 (hskp24 | hskp26 | hskp2),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[128, 122])).
% 0.57/0.74 tff(130,plain,
% 0.57/0.74 (hskp24 | hskp26 | hskp2),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.57/0.74 tff(131,plain,
% 0.57/0.74 (hskp24 | hskp26 | hskp2),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[130, 122])).
% 0.57/0.74 tff(132,plain,
% 0.57/0.74 (hskp24 | hskp26 | hskp2),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[131, 122])).
% 0.57/0.74 tff(133,plain,
% 0.57/0.74 ($false),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[132, 121, 115, 109])).
% 0.57/0.74 tff(134,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.57/0.74 tff(135,plain,
% 0.57/0.74 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(136,plain,
% 0.57/0.74 ((hskp28 | (~ndr1_0) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349))) <=> (hskp28 | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(137,plain,
% 0.57/0.74 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349))))),
% 0.57/0.74 inference(monotonicity,[status(thm)],[136])).
% 0.57/0.74 tff(138,plain,
% 0.57/0.74 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349)))),
% 0.57/0.74 inference(transitivity,[status(thm)],[137, 135])).
% 0.57/0.74 tff(139,plain,
% 0.57/0.74 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(140,plain,
% 0.57/0.74 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.57/0.74 tff(141,plain,
% 0.57/0.74 (hskp28),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[140, 134, 92, 84, 35, 102])).
% 0.57/0.74 tff(142,plain,
% 0.57/0.74 (((~hskp28) | c2_1(a343)) <=> ((~hskp28) | c2_1(a343))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(143,axiom,((~hskp28) | c2_1(a343)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 0.57/0.74 tff(144,plain,
% 0.57/0.74 ((~hskp28) | c2_1(a343)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.57/0.74 tff(145,plain,
% 0.57/0.74 ((~hskp28) | c2_1(a343)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[144, 142])).
% 0.57/0.74 tff(146,plain,
% 0.57/0.74 ((~hskp28) | c2_1(a343)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[145, 142])).
% 0.57/0.74 tff(147,plain,
% 0.57/0.74 ((~hskp28) | c2_1(a343)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.57/0.74 tff(148,plain,
% 0.57/0.74 ((~hskp28) | c2_1(a343)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[147, 142])).
% 0.57/0.74 tff(149,plain,
% 0.57/0.74 (c2_1(a343)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[148, 141])).
% 0.57/0.74 tff(150,plain,
% 0.57/0.74 (((~hskp28) | c1_1(a343)) <=> ((~hskp28) | c1_1(a343))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(151,axiom,((~hskp28) | c1_1(a343)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 0.57/0.74 tff(152,plain,
% 0.57/0.74 ((~hskp28) | c1_1(a343)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.57/0.74 tff(153,plain,
% 0.57/0.74 ((~hskp28) | c1_1(a343)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[152, 150])).
% 0.57/0.74 tff(154,plain,
% 0.57/0.74 ((~hskp28) | c1_1(a343)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[153, 150])).
% 0.57/0.74 tff(155,plain,
% 0.57/0.74 ((~hskp28) | c1_1(a343)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[154, 150])).
% 0.57/0.74 tff(156,plain,
% 0.57/0.74 ((~hskp28) | c1_1(a343)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[155, 150])).
% 0.57/0.74 tff(157,plain,
% 0.57/0.74 (c1_1(a343)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[156, 141])).
% 0.57/0.74 tff(158,plain,
% 0.57/0.74 (((~hskp28) | c0_1(a343)) <=> ((~hskp28) | c0_1(a343))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(159,axiom,((~hskp28) | c0_1(a343)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 0.57/0.74 tff(160,plain,
% 0.57/0.74 ((~hskp28) | c0_1(a343)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.57/0.74 tff(161,plain,
% 0.57/0.74 ((~hskp28) | c0_1(a343)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[160, 158])).
% 0.57/0.74 tff(162,plain,
% 0.57/0.74 ((~hskp28) | c0_1(a343)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[161, 158])).
% 0.57/0.74 tff(163,plain,
% 0.57/0.74 ((~hskp28) | c0_1(a343)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.57/0.74 tff(164,plain,
% 0.57/0.74 ((~hskp28) | c0_1(a343)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[163, 158])).
% 0.57/0.74 tff(165,plain,
% 0.57/0.74 (c0_1(a343)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[164, 141])).
% 0.57/0.74 tff(166,plain,
% 0.57/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a349) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a338)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a349) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a338)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(167,plain,
% 0.57/0.74 (((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a338) | c1_1(a338) | (~c3_1(a338))) <=> (c2_1(a349) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a338)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(168,plain,
% 0.57/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a338) | c1_1(a338) | (~c3_1(a338)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a349) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a338)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 0.57/0.74 inference(monotonicity,[status(thm)],[167])).
% 0.57/0.74 tff(169,plain,
% 0.57/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a338) | c1_1(a338) | (~c3_1(a338)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a349) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a338)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.57/0.74 inference(transitivity,[status(thm)],[168, 166])).
% 0.57/0.74 tff(170,plain,
% 0.57/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a338) | c1_1(a338) | (~c3_1(a338)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(171,plain,
% 0.57/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a349) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a338)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.57/0.75 tff(172,plain,
% 0.57/0.75 (~c3_1(a338)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[171, 134, 165, 157, 149, 92, 84, 35, 70, 64, 20])).
% 0.57/0.75 tff(173,plain,
% 0.57/0.75 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(174,plain,
% 0.57/0.75 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[173])).
% 0.57/0.75 tff(175,plain,
% 0.57/0.75 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(176,plain,
% 0.57/0.75 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(177,plain,
% 0.57/0.75 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[176])).
% 0.57/0.75 tff(178,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 0.57/0.75 tff(179,plain,
% 0.57/0.75 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.57/0.75 tff(180,plain,
% 0.57/0.75 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.57/0.75 tff(181,plain,(
% 0.57/0.75 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.57/0.75 inference(skolemize,[status(sab)],[180])).
% 0.57/0.75 tff(182,plain,
% 0.57/0.75 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[181, 174])).
% 0.57/0.75 tff(183,plain,
% 0.57/0.75 (^[U: $i] : refl((hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(184,plain,
% 0.57/0.75 (![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[183])).
% 0.57/0.75 tff(185,plain,
% 0.57/0.75 (![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(186,plain,
% 0.57/0.75 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp15))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(187,plain,
% 0.57/0.75 (![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) <=> ![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[186])).
% 0.57/0.75 tff(188,axiom,(![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 0.57/0.75 tff(189,plain,
% 0.57/0.75 (![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.57/0.75 tff(190,plain,
% 0.57/0.75 (![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[189, 185])).
% 0.57/0.75 tff(191,plain,(
% 0.57/0.75 ![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.57/0.75 inference(skolemize,[status(sab)],[190])).
% 0.57/0.75 tff(192,plain,
% 0.57/0.75 (![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[191, 184])).
% 0.57/0.75 tff(193,assumption,(~hskp5), introduced(assumption)).
% 0.57/0.75 tff(194,plain,
% 0.57/0.75 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(195,plain,
% 0.57/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[194])).
% 0.57/0.75 tff(196,plain,
% 0.57/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(197,plain,
% 0.57/0.75 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(198,plain,
% 0.57/0.75 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[197])).
% 0.57/0.75 tff(199,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 0.57/0.75 tff(200,plain,
% 0.57/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.57/0.75 tff(201,plain,
% 0.57/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[200, 196])).
% 0.57/0.75 tff(202,plain,(
% 0.57/0.75 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.57/0.75 inference(skolemize,[status(sab)],[201])).
% 0.57/0.75 tff(203,plain,
% 0.57/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[202, 195])).
% 0.57/0.75 tff(204,assumption,(~hskp14), introduced(assumption)).
% 0.57/0.75 tff(205,plain,
% 0.57/0.75 (^[U: $i] : refl((hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(206,plain,
% 0.57/0.75 (![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[205])).
% 0.57/0.75 tff(207,plain,
% 0.57/0.75 (![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(208,plain,
% 0.57/0.75 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp14) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp14))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp14) <=> (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp14) <=> (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(209,plain,
% 0.57/0.75 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp14) <=> ![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[208])).
% 0.57/0.75 tff(210,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.57/0.75 tff(211,plain,
% 0.57/0.75 (![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.57/0.75 tff(212,plain,
% 0.57/0.75 (![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[211, 207])).
% 0.57/0.75 tff(213,plain,(
% 0.57/0.75 ![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.57/0.75 inference(skolemize,[status(sab)],[212])).
% 0.57/0.75 tff(214,plain,
% 0.57/0.75 (![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[213, 206])).
% 0.57/0.75 tff(215,plain,
% 0.57/0.75 (^[U: $i] : refl((hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(216,plain,
% 0.57/0.75 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[215])).
% 0.57/0.75 tff(217,plain,
% 0.57/0.75 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(218,plain,
% 0.57/0.75 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp1) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp1) <=> (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(219,plain,
% 0.57/0.75 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp1) <=> ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[218])).
% 0.57/0.75 tff(220,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 0.57/0.75 tff(221,plain,
% 0.57/0.75 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.57/0.75 tff(222,plain,
% 0.57/0.75 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[221, 217])).
% 0.57/0.75 tff(223,plain,(
% 0.57/0.75 ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.57/0.75 inference(skolemize,[status(sab)],[222])).
% 0.57/0.75 tff(224,plain,
% 0.57/0.75 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[223, 216])).
% 0.57/0.75 tff(225,assumption,(~hskp2), introduced(assumption)).
% 0.57/0.75 tff(226,plain,
% 0.57/0.75 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(227,plain,
% 0.57/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | 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)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[226])).
% 0.57/0.75 tff(228,plain,
% 0.57/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | 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)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(229,plain,
% 0.57/0.75 (^[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(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_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) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(230,plain,
% 0.57/0.75 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_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)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[229])).
% 0.57/0.75 tff(231,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 0.57/0.75 tff(232,plain,
% 0.57/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.57/0.75 tff(233,plain,
% 0.57/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[232, 228])).
% 0.57/0.75 tff(234,plain,(
% 0.57/0.75 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.57/0.75 inference(skolemize,[status(sab)],[233])).
% 0.57/0.75 tff(235,plain,
% 0.57/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[234, 227])).
% 0.57/0.75 tff(236,plain,
% 0.57/0.75 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(237,plain,
% 0.57/0.75 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[236])).
% 0.57/0.75 tff(238,plain,
% 0.57/0.75 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(239,plain,
% 0.57/0.75 (^[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) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(240,plain,
% 0.57/0.75 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[239])).
% 0.57/0.75 tff(241,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 0.57/0.75 tff(242,plain,
% 0.57/0.75 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.57/0.75 tff(243,plain,
% 0.57/0.75 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[242, 238])).
% 0.57/0.75 tff(244,plain,(
% 0.57/0.75 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.57/0.75 inference(skolemize,[status(sab)],[243])).
% 0.57/0.75 tff(245,plain,
% 0.57/0.75 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[244, 237])).
% 0.57/0.75 tff(246,assumption,(hskp25), introduced(assumption)).
% 0.57/0.75 tff(247,plain,
% 0.57/0.75 (((~hskp25) | (~c2_1(a419))) <=> ((~hskp25) | (~c2_1(a419)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(248,plain,
% 0.57/0.75 (((~c2_1(a419)) | (~hskp25)) <=> ((~hskp25) | (~c2_1(a419)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(249,axiom,((~c2_1(a419)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.57/0.75 tff(250,plain,
% 0.57/0.75 ((~hskp25) | (~c2_1(a419))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.57/0.75 tff(251,plain,
% 0.57/0.75 ((~hskp25) | (~c2_1(a419))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[250, 247])).
% 0.57/0.75 tff(252,plain,
% 0.57/0.75 (~c2_1(a419)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[251, 246])).
% 0.57/0.75 tff(253,plain,
% 0.57/0.75 (((~hskp25) | (~c1_1(a419))) <=> ((~hskp25) | (~c1_1(a419)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(254,plain,
% 0.57/0.75 (((~c1_1(a419)) | (~hskp25)) <=> ((~hskp25) | (~c1_1(a419)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(255,axiom,((~c1_1(a419)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 0.57/0.75 tff(256,plain,
% 0.57/0.75 ((~hskp25) | (~c1_1(a419))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.57/0.75 tff(257,plain,
% 0.57/0.75 ((~hskp25) | (~c1_1(a419))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[256, 253])).
% 0.57/0.75 tff(258,plain,
% 0.57/0.75 (~c1_1(a419)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[257, 246])).
% 0.57/0.75 tff(259,plain,
% 0.57/0.75 (((~hskp25) | c0_1(a419)) <=> ((~hskp25) | c0_1(a419))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(260,axiom,((~hskp25) | c0_1(a419)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 0.57/0.75 tff(261,plain,
% 0.57/0.75 ((~hskp25) | c0_1(a419)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.57/0.75 tff(262,plain,
% 0.57/0.75 ((~hskp25) | c0_1(a419)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[261, 259])).
% 0.57/0.75 tff(263,plain,
% 0.57/0.75 ((~hskp25) | c0_1(a419)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[262, 259])).
% 0.57/0.75 tff(264,plain,
% 0.57/0.75 ((~hskp25) | c0_1(a419)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[263, 259])).
% 0.57/0.75 tff(265,plain,
% 0.57/0.75 ((~hskp25) | c0_1(a419)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[264, 259])).
% 0.57/0.75 tff(266,plain,
% 0.57/0.75 (c0_1(a419)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[265, 246])).
% 0.57/0.75 tff(267,plain,
% 0.57/0.75 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c3_1(a419)) | (~c0_1(a419)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c3_1(a419)) | (~c0_1(a419)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(268,plain,
% 0.57/0.75 ((hskp2 | (~ndr1_0) | c2_1(a419) | (~c0_1(a419)) | (~c3_1(a419)) | c2_1(a419) | c1_1(a419) | (~c3_1(a419))) <=> (hskp2 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c3_1(a419)) | (~c0_1(a419)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(269,plain,
% 0.57/0.75 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a419) | (~c0_1(a419)) | (~c3_1(a419)) | c2_1(a419) | c1_1(a419) | (~c3_1(a419)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c3_1(a419)) | (~c0_1(a419))))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[268])).
% 0.57/0.75 tff(270,plain,
% 0.57/0.75 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a419) | (~c0_1(a419)) | (~c3_1(a419)) | c2_1(a419) | c1_1(a419) | (~c3_1(a419)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c3_1(a419)) | (~c0_1(a419)))),
% 0.57/0.75 inference(transitivity,[status(thm)],[269, 267])).
% 0.57/0.75 tff(271,plain,
% 0.57/0.75 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a419) | (~c0_1(a419)) | (~c3_1(a419)) | c2_1(a419) | c1_1(a419) | (~c3_1(a419)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(272,plain,
% 0.57/0.75 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c3_1(a419)) | (~c0_1(a419))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.57/0.75 tff(273,plain,
% 0.57/0.75 (~c3_1(a419)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[272, 134, 225, 266, 258, 252, 245])).
% 0.57/0.75 tff(274,plain,
% 0.57/0.75 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp14 | hskp5 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(275,plain,
% 0.57/0.75 ((hskp14 | hskp5 | (~ndr1_0) | c2_1(a419) | c1_1(a419) | c3_1(a419)) <=> (hskp14 | hskp5 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(276,plain,
% 0.57/0.75 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | (~ndr1_0) | c2_1(a419) | c1_1(a419) | c3_1(a419))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419)))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[275])).
% 0.57/0.75 tff(277,plain,
% 0.57/0.75 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | (~ndr1_0) | c2_1(a419) | c1_1(a419) | c3_1(a419))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp14 | hskp5 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419))),
% 0.57/0.75 inference(transitivity,[status(thm)],[276, 274])).
% 0.57/0.75 tff(278,plain,
% 0.57/0.75 ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | (~ndr1_0) | c2_1(a419) | c1_1(a419) | c3_1(a419))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(279,plain,
% 0.57/0.75 ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp14 | hskp5 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.57/0.75 tff(280,plain,
% 0.57/0.75 (hskp14 | c3_1(a419)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[279, 134, 193, 258, 252, 214])).
% 0.57/0.75 tff(281,plain,
% 0.57/0.75 (hskp14),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[280, 273])).
% 0.57/0.75 tff(282,plain,
% 0.57/0.75 (((~hskp14) | (~c1_1(a347))) <=> ((~hskp14) | (~c1_1(a347)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(283,plain,
% 0.57/0.76 (((~c1_1(a347)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a347)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(284,axiom,((~c1_1(a347)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 0.57/0.76 tff(285,plain,
% 0.57/0.76 ((~hskp14) | (~c1_1(a347))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.57/0.76 tff(286,plain,
% 0.57/0.76 ((~hskp14) | (~c1_1(a347))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[285, 282])).
% 0.57/0.76 tff(287,plain,
% 0.57/0.76 (~c1_1(a347)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[286, 281])).
% 0.57/0.76 tff(288,plain,
% 0.57/0.76 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(289,plain,
% 0.57/0.76 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[288])).
% 0.57/0.76 tff(290,plain,
% 0.57/0.76 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(291,plain,
% 0.57/0.76 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | 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)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(292,plain,
% 0.57/0.76 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[291])).
% 0.57/0.76 tff(293,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 0.57/0.76 tff(294,plain,
% 0.57/0.76 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.57/0.76 tff(295,plain,
% 0.57/0.76 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[294, 290])).
% 0.57/0.76 tff(296,plain,(
% 0.57/0.76 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.57/0.76 inference(skolemize,[status(sab)],[295])).
% 0.57/0.76 tff(297,plain,
% 0.57/0.76 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[296, 289])).
% 0.57/0.76 tff(298,plain,
% 0.57/0.76 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419) | (~c0_1(a419)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419) | (~c0_1(a419)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(299,plain,
% 0.57/0.76 ((hskp22 | (~ndr1_0) | c2_1(a419) | c3_1(a419) | (~c0_1(a419)) | c1_1(a419) | c3_1(a419) | (~c0_1(a419))) <=> (hskp22 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419) | (~c0_1(a419)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(300,plain,
% 0.57/0.76 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a419) | c3_1(a419) | (~c0_1(a419)) | c1_1(a419) | c3_1(a419) | (~c0_1(a419)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419) | (~c0_1(a419))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[299])).
% 0.57/0.76 tff(301,plain,
% 0.57/0.76 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a419) | c3_1(a419) | (~c0_1(a419)) | c1_1(a419) | c3_1(a419) | (~c0_1(a419)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419) | (~c0_1(a419)))),
% 0.57/0.76 inference(transitivity,[status(thm)],[300, 298])).
% 0.57/0.76 tff(302,plain,
% 0.57/0.76 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a419) | c3_1(a419) | (~c0_1(a419)) | c1_1(a419) | c3_1(a419) | (~c0_1(a419)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(303,plain,
% 0.57/0.76 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419) | (~c0_1(a419))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.57/0.76 tff(304,plain,
% 0.57/0.76 (hskp22 | c3_1(a419)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[303, 134, 266, 258, 252, 297])).
% 0.57/0.76 tff(305,plain,
% 0.57/0.76 (hskp22),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[304, 273])).
% 0.57/0.76 tff(306,plain,
% 0.57/0.76 (((~hskp22) | (~c2_1(a367))) <=> ((~hskp22) | (~c2_1(a367)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(307,plain,
% 0.57/0.76 (((~c2_1(a367)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a367)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(308,axiom,((~c2_1(a367)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 0.57/0.76 tff(309,plain,
% 0.57/0.76 ((~hskp22) | (~c2_1(a367))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.57/0.76 tff(310,plain,
% 0.57/0.76 ((~hskp22) | (~c2_1(a367))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[309, 306])).
% 0.57/0.76 tff(311,plain,
% 0.57/0.76 (~c2_1(a367)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[310, 305])).
% 0.57/0.76 tff(312,plain,
% 0.57/0.76 (((~hskp14) | c3_1(a347)) <=> ((~hskp14) | c3_1(a347))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(313,axiom,((~hskp14) | c3_1(a347)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 0.57/0.76 tff(314,plain,
% 0.57/0.76 ((~hskp14) | c3_1(a347)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.57/0.76 tff(315,plain,
% 0.57/0.76 ((~hskp14) | c3_1(a347)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[314, 312])).
% 0.57/0.76 tff(316,plain,
% 0.57/0.76 ((~hskp14) | c3_1(a347)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[315, 312])).
% 0.57/0.76 tff(317,plain,
% 0.57/0.76 ((~hskp14) | c3_1(a347)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[316, 312])).
% 0.57/0.76 tff(318,plain,
% 0.57/0.76 ((~hskp14) | c3_1(a347)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[317, 312])).
% 0.57/0.76 tff(319,plain,
% 0.57/0.76 (c3_1(a347)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[318, 281])).
% 0.57/0.76 tff(320,plain,
% 0.57/0.76 (((~hskp14) | c2_1(a347)) <=> ((~hskp14) | c2_1(a347))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(321,axiom,((~hskp14) | c2_1(a347)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 0.57/0.76 tff(322,plain,
% 0.57/0.76 ((~hskp14) | c2_1(a347)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.57/0.76 tff(323,plain,
% 0.57/0.76 ((~hskp14) | c2_1(a347)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[322, 320])).
% 0.57/0.76 tff(324,plain,
% 0.57/0.76 ((~hskp14) | c2_1(a347)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[323, 320])).
% 0.57/0.76 tff(325,plain,
% 0.57/0.76 ((~hskp14) | c2_1(a347)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[324, 320])).
% 0.57/0.76 tff(326,plain,
% 0.57/0.76 ((~hskp14) | c2_1(a347)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[325, 320])).
% 0.57/0.76 tff(327,plain,
% 0.57/0.76 (c2_1(a347)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[326, 281])).
% 0.57/0.76 tff(328,plain,
% 0.57/0.76 (((~hskp22) | c3_1(a367)) <=> ((~hskp22) | c3_1(a367))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(329,axiom,((~hskp22) | c3_1(a367)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 0.57/0.76 tff(330,plain,
% 0.57/0.76 ((~hskp22) | c3_1(a367)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.57/0.76 tff(331,plain,
% 0.57/0.76 ((~hskp22) | c3_1(a367)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[330, 328])).
% 0.57/0.76 tff(332,plain,
% 0.57/0.76 ((~hskp22) | c3_1(a367)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[331, 328])).
% 0.57/0.76 tff(333,plain,
% 0.57/0.76 ((~hskp22) | c3_1(a367)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[332, 328])).
% 0.57/0.76 tff(334,plain,
% 0.57/0.76 ((~hskp22) | c3_1(a367)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[333, 328])).
% 0.57/0.76 tff(335,plain,
% 0.57/0.76 (c3_1(a367)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[334, 305])).
% 0.57/0.76 tff(336,plain,
% 0.57/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a419)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a419)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(337,plain,
% 0.57/0.76 (((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367))) <=> (c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a419)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(338,plain,
% 0.57/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a419))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[337])).
% 0.57/0.76 tff(339,plain,
% 0.57/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a419)))),
% 0.57/0.76 inference(transitivity,[status(thm)],[338, 336])).
% 0.57/0.76 tff(340,plain,
% 0.57/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(341,plain,
% 0.57/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a419))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.57/0.76 tff(342,plain,
% 0.57/0.76 (c0_1(a367)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[341, 134, 266, 335, 327, 319, 258, 252, 311, 287, 235])).
% 0.57/0.76 tff(343,plain,
% 0.57/0.76 (((~hskp22) | (~c1_1(a367))) <=> ((~hskp22) | (~c1_1(a367)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(344,plain,
% 0.57/0.76 (((~c1_1(a367)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a367)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(345,axiom,((~c1_1(a367)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 0.57/0.76 tff(346,plain,
% 0.57/0.76 ((~hskp22) | (~c1_1(a367))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.57/0.76 tff(347,plain,
% 0.57/0.76 ((~hskp22) | (~c1_1(a367))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[346, 343])).
% 0.57/0.76 tff(348,plain,
% 0.57/0.76 (~c1_1(a367)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[347, 305])).
% 0.57/0.76 tff(349,plain,
% 0.57/0.76 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(350,plain,
% 0.57/0.76 ((hskp2 | (~ndr1_0) | c2_1(a367) | (~c0_1(a367)) | (~c3_1(a367)) | c2_1(a367) | c1_1(a367) | (~c3_1(a367))) <=> (hskp2 | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(351,plain,
% 0.57/0.76 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a367) | (~c0_1(a367)) | (~c3_1(a367)) | c2_1(a367) | c1_1(a367) | (~c3_1(a367)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[350])).
% 0.57/0.76 tff(352,plain,
% 0.57/0.76 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a367) | (~c0_1(a367)) | (~c3_1(a367)) | c2_1(a367) | c1_1(a367) | (~c3_1(a367)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)))),
% 0.57/0.76 inference(transitivity,[status(thm)],[351, 349])).
% 0.57/0.76 tff(353,plain,
% 0.57/0.76 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a367) | (~c0_1(a367)) | (~c3_1(a367)) | c2_1(a367) | c1_1(a367) | (~c3_1(a367)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(354,plain,
% 0.57/0.76 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.57/0.76 tff(355,plain,
% 0.57/0.76 ($false),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[354, 134, 225, 335, 348, 311, 245, 342])).
% 0.57/0.76 tff(356,plain,((~hskp25) | hskp2 | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.57/0.76 tff(357,plain,
% 0.57/0.76 (~hskp25),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[356, 225, 193])).
% 0.57/0.76 tff(358,assumption,(~hskp24), introduced(assumption)).
% 0.57/0.76 tff(359,plain,
% 0.57/0.76 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(360,plain,
% 0.57/0.76 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[359])).
% 0.57/0.76 tff(361,plain,
% 0.57/0.76 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(362,plain,
% 0.57/0.76 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(363,plain,
% 0.57/0.76 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[362])).
% 0.57/0.76 tff(364,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 0.57/0.76 tff(365,plain,
% 0.57/0.76 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.57/0.76 tff(366,plain,
% 0.57/0.76 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[365, 361])).
% 0.57/0.76 tff(367,plain,(
% 0.57/0.76 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.57/0.76 inference(skolemize,[status(sab)],[366])).
% 0.57/0.76 tff(368,plain,
% 0.57/0.76 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[367, 360])).
% 0.57/0.76 tff(369,plain,
% 0.57/0.76 ((hskp24 | hskp7) <=> (hskp24 | hskp7)),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(370,axiom,(hskp24 | hskp7), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 0.57/0.76 tff(371,plain,
% 0.57/0.76 (hskp24 | hskp7),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.57/0.76 tff(372,plain,
% 0.57/0.76 (hskp7),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[371, 358])).
% 0.57/0.76 tff(373,plain,
% 0.57/0.76 (((~hskp7) | (~c1_1(a330))) <=> ((~hskp7) | (~c1_1(a330)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(374,plain,
% 0.57/0.76 (((~c1_1(a330)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a330)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(375,axiom,((~c1_1(a330)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 0.57/0.76 tff(376,plain,
% 0.57/0.76 ((~hskp7) | (~c1_1(a330))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.57/0.76 tff(377,plain,
% 0.57/0.76 ((~hskp7) | (~c1_1(a330))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[376, 373])).
% 0.57/0.76 tff(378,plain,
% 0.57/0.76 (~c1_1(a330)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[377, 372])).
% 0.57/0.76 tff(379,plain,
% 0.57/0.76 (((~hskp7) | (~c0_1(a330))) <=> ((~hskp7) | (~c0_1(a330)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(380,plain,
% 0.57/0.76 (((~c0_1(a330)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a330)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(381,axiom,((~c0_1(a330)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 0.57/0.76 tff(382,plain,
% 0.57/0.76 ((~hskp7) | (~c0_1(a330))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[381, 380])).
% 0.57/0.76 tff(383,plain,
% 0.57/0.76 ((~hskp7) | (~c0_1(a330))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[382, 379])).
% 0.57/0.76 tff(384,plain,
% 0.57/0.76 (~c0_1(a330)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[383, 372])).
% 0.57/0.76 tff(385,plain,
% 0.57/0.76 (^[U: $i] : refl((hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(386,plain,
% 0.57/0.76 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[385])).
% 0.57/0.76 tff(387,plain,
% 0.57/0.76 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(388,plain,
% 0.57/0.76 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp17) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp17))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp17) | hskp24) <=> ((hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp24))), rewrite(((hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp24) <=> (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp17) | hskp24) <=> (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(389,plain,
% 0.57/0.76 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp17) | hskp24) <=> ![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[388])).
% 0.57/0.76 tff(390,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp17) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 0.57/0.76 tff(391,plain,
% 0.57/0.76 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[390, 389])).
% 0.57/0.76 tff(392,plain,
% 0.57/0.76 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[391, 387])).
% 0.57/0.76 tff(393,plain,(
% 0.57/0.76 ![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 0.57/0.76 inference(skolemize,[status(sab)],[392])).
% 0.57/0.76 tff(394,plain,
% 0.57/0.76 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[393, 386])).
% 0.57/0.76 tff(395,assumption,(hskp16), introduced(assumption)).
% 0.57/0.76 tff(396,plain,
% 0.57/0.76 (~c2_1(a349)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[34, 395])).
% 0.57/0.76 tff(397,plain,
% 0.57/0.76 (c3_1(a349)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[83, 395])).
% 0.57/0.76 tff(398,plain,
% 0.57/0.76 (c1_1(a349)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[91, 395])).
% 0.57/0.76 tff(399,plain,
% 0.57/0.76 (hskp28),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[140, 134, 398, 397, 396, 102])).
% 0.57/0.76 tff(400,plain,
% 0.57/0.76 (c2_1(a343)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[148, 399])).
% 0.57/0.76 tff(401,plain,
% 0.57/0.76 (c1_1(a343)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[156, 399])).
% 0.57/0.76 tff(402,plain,
% 0.57/0.76 (c0_1(a343)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[164, 399])).
% 0.57/0.76 tff(403,plain,
% 0.57/0.76 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | (~ndr1_0) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(404,plain,
% 0.57/0.76 ((hskp24 | hskp17 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343))) <=> (hskp24 | hskp17 | (~ndr1_0) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(405,plain,
% 0.57/0.76 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[404])).
% 0.57/0.76 tff(406,plain,
% 0.57/0.76 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | (~ndr1_0) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.57/0.76 inference(transitivity,[status(thm)],[405, 403])).
% 0.57/0.76 tff(407,plain,
% 0.57/0.76 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(408,plain,
% 0.57/0.76 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | (~ndr1_0) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.57/0.76 tff(409,plain,
% 0.57/0.76 (hskp17),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[408, 358, 134, 402, 401, 400, 394])).
% 0.57/0.76 tff(410,plain,
% 0.57/0.76 (((~hskp17) | (~c0_1(a353))) <=> ((~hskp17) | (~c0_1(a353)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(411,plain,
% 0.57/0.76 (((~c0_1(a353)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a353)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(412,axiom,((~c0_1(a353)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 0.57/0.76 tff(413,plain,
% 0.57/0.76 ((~hskp17) | (~c0_1(a353))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.57/0.76 tff(414,plain,
% 0.57/0.76 ((~hskp17) | (~c0_1(a353))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[413, 410])).
% 0.57/0.76 tff(415,plain,
% 0.57/0.76 (~c0_1(a353)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[414, 409])).
% 0.57/0.76 tff(416,plain,
% 0.57/0.76 (((~hskp17) | c2_1(a353)) <=> ((~hskp17) | c2_1(a353))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(417,axiom,((~hskp17) | c2_1(a353)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 0.57/0.76 tff(418,plain,
% 0.57/0.76 ((~hskp17) | c2_1(a353)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[417, 416])).
% 0.57/0.76 tff(419,plain,
% 0.57/0.76 ((~hskp17) | c2_1(a353)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[418, 416])).
% 0.57/0.76 tff(420,plain,
% 0.57/0.76 ((~hskp17) | c2_1(a353)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[419, 416])).
% 0.57/0.76 tff(421,plain,
% 0.57/0.76 ((~hskp17) | c2_1(a353)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[420, 416])).
% 0.57/0.76 tff(422,plain,
% 0.57/0.76 ((~hskp17) | c2_1(a353)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[421, 416])).
% 0.57/0.76 tff(423,plain,
% 0.57/0.76 (c2_1(a353)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[422, 409])).
% 0.57/0.76 tff(424,plain,
% 0.57/0.76 (((~hskp17) | c1_1(a353)) <=> ((~hskp17) | c1_1(a353))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(425,axiom,((~hskp17) | c1_1(a353)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 0.57/0.76 tff(426,plain,
% 0.57/0.76 ((~hskp17) | c1_1(a353)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[425, 424])).
% 0.57/0.76 tff(427,plain,
% 0.57/0.76 ((~hskp17) | c1_1(a353)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[426, 424])).
% 0.57/0.76 tff(428,plain,
% 0.57/0.76 ((~hskp17) | c1_1(a353)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[427, 424])).
% 0.57/0.76 tff(429,plain,
% 0.57/0.76 ((~hskp17) | c1_1(a353)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[428, 424])).
% 0.57/0.76 tff(430,plain,
% 0.57/0.76 ((~hskp17) | c1_1(a353)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[429, 424])).
% 0.57/0.76 tff(431,plain,
% 0.57/0.76 (c1_1(a353)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[430, 409])).
% 0.57/0.76 tff(432,plain,
% 0.57/0.76 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a353) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c2_1(a330)) | (~c1_1(a353)) | (~c2_1(a353)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a353) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c2_1(a330)) | (~c1_1(a353)) | (~c2_1(a353)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(433,plain,
% 0.57/0.76 ((hskp5 | (~ndr1_0) | c0_1(a353) | (~c2_1(a353)) | (~c1_1(a353)) | c1_1(a330) | c0_1(a330) | (~c2_1(a330))) <=> (hskp5 | c0_1(a353) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c2_1(a330)) | (~c1_1(a353)) | (~c2_1(a353)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(434,plain,
% 0.57/0.76 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a353) | (~c2_1(a353)) | (~c1_1(a353)) | c1_1(a330) | c0_1(a330) | (~c2_1(a330)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a353) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c2_1(a330)) | (~c1_1(a353)) | (~c2_1(a353))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[433])).
% 0.57/0.76 tff(435,plain,
% 0.57/0.76 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a353) | (~c2_1(a353)) | (~c1_1(a353)) | c1_1(a330) | c0_1(a330) | (~c2_1(a330)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a353) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c2_1(a330)) | (~c1_1(a353)) | (~c2_1(a353)))),
% 0.57/0.76 inference(transitivity,[status(thm)],[434, 432])).
% 0.57/0.76 tff(436,plain,
% 0.57/0.76 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a353) | (~c2_1(a353)) | (~c1_1(a353)) | c1_1(a330) | c0_1(a330) | (~c2_1(a330)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(437,plain,
% 0.57/0.76 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a353) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c2_1(a330)) | (~c1_1(a353)) | (~c2_1(a353))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.57/0.76 tff(438,plain,
% 0.57/0.76 (~c2_1(a330)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[437, 134, 193, 431, 423, 415, 384, 378, 368])).
% 0.57/0.76 tff(439,plain,
% 0.57/0.76 (((~hskp7) | c3_1(a330)) <=> ((~hskp7) | c3_1(a330))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(440,axiom,((~hskp7) | c3_1(a330)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 0.57/0.76 tff(441,plain,
% 0.57/0.76 ((~hskp7) | c3_1(a330)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[440, 439])).
% 0.57/0.77 tff(442,plain,
% 0.57/0.77 ((~hskp7) | c3_1(a330)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[441, 439])).
% 0.57/0.77 tff(443,plain,
% 0.57/0.77 ((~hskp7) | c3_1(a330)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[442, 439])).
% 0.57/0.77 tff(444,plain,
% 0.57/0.77 ((~hskp7) | c3_1(a330)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[443, 439])).
% 0.57/0.77 tff(445,plain,
% 0.57/0.77 ((~hskp7) | c3_1(a330)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[444, 439])).
% 0.57/0.77 tff(446,plain,
% 0.57/0.77 (c3_1(a330)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[445, 372])).
% 0.57/0.77 tff(447,plain,
% 0.57/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a349) | c1_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a349) | c1_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(448,plain,
% 0.57/0.77 (((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a330) | c1_1(a330) | (~c3_1(a330))) <=> (c2_1(a349) | c1_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(449,plain,
% 0.57/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a330) | c1_1(a330) | (~c3_1(a330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a349) | c1_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 0.57/0.77 inference(monotonicity,[status(thm)],[448])).
% 0.57/0.77 tff(450,plain,
% 0.57/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a330) | c1_1(a330) | (~c3_1(a330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a349) | c1_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.57/0.77 inference(transitivity,[status(thm)],[449, 447])).
% 0.57/0.77 tff(451,plain,
% 0.57/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a330) | c1_1(a330) | (~c3_1(a330)))),
% 0.57/0.77 inference(quant_inst,[status(thm)],[])).
% 0.57/0.77 tff(452,plain,
% 0.57/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a349) | c1_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[451, 450])).
% 0.57/0.77 tff(453,plain,
% 0.57/0.77 ($false),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[452, 134, 402, 401, 400, 398, 397, 446, 396, 378, 20, 438])).
% 0.57/0.77 tff(454,plain,((~hskp16) | hskp5 | hskp24), inference(lemma,lemma(discharge,[]))).
% 0.57/0.77 tff(455,plain,
% 0.57/0.77 (~hskp16),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[454, 358, 193])).
% 0.57/0.77 tff(456,plain,
% 0.57/0.77 (^[U: $i] : refl((hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) <=> (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))),
% 0.57/0.77 inference(bind,[status(th)],[])).
% 0.57/0.77 tff(457,plain,
% 0.57/0.77 (![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))),
% 0.57/0.77 inference(quant_intro,[status(thm)],[456])).
% 0.57/0.77 tff(458,plain,
% 0.57/0.77 (![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(459,plain,
% 0.57/0.77 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | hskp5))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) | hskp16) <=> ((hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | hskp16))), rewrite(((hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | hskp16) <=> (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) | hskp16) <=> (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))))),
% 0.57/0.77 inference(bind,[status(th)],[])).
% 0.57/0.77 tff(460,plain,
% 0.57/0.77 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) | hskp16) <=> ![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))),
% 0.57/0.77 inference(quant_intro,[status(thm)],[459])).
% 0.57/0.77 tff(461,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 0.57/0.77 tff(462,plain,
% 0.57/0.77 (![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[461, 460])).
% 0.57/0.77 tff(463,plain,
% 0.57/0.77 (![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[462, 458])).
% 0.57/0.77 tff(464,plain,(
% 0.57/0.77 ![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))),
% 0.57/0.77 inference(skolemize,[status(sab)],[463])).
% 0.57/0.77 tff(465,plain,
% 0.57/0.77 (![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[464, 457])).
% 0.57/0.77 tff(466,plain,
% 0.57/0.77 (hskp26),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[132, 358, 225])).
% 0.57/0.77 tff(467,plain,
% 0.57/0.77 (((~hskp26) | c3_1(a333)) <=> ((~hskp26) | c3_1(a333))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(468,axiom,((~hskp26) | c3_1(a333)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 0.57/0.77 tff(469,plain,
% 0.57/0.77 ((~hskp26) | c3_1(a333)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[468, 467])).
% 0.57/0.77 tff(470,plain,
% 0.57/0.77 ((~hskp26) | c3_1(a333)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[469, 467])).
% 0.57/0.77 tff(471,plain,
% 0.57/0.77 ((~hskp26) | c3_1(a333)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[470, 467])).
% 0.57/0.77 tff(472,plain,
% 0.57/0.77 ((~hskp26) | c3_1(a333)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[471, 467])).
% 0.57/0.77 tff(473,plain,
% 0.57/0.77 ((~hskp26) | c3_1(a333)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[472, 467])).
% 0.57/0.77 tff(474,plain,
% 0.57/0.77 (c3_1(a333)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[473, 466])).
% 0.57/0.77 tff(475,plain,
% 0.57/0.77 (((~hskp26) | c0_1(a333)) <=> ((~hskp26) | c0_1(a333))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(476,axiom,((~hskp26) | c0_1(a333)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 0.57/0.77 tff(477,plain,
% 0.57/0.77 ((~hskp26) | c0_1(a333)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.57/0.77 tff(478,plain,
% 0.57/0.77 ((~hskp26) | c0_1(a333)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[477, 475])).
% 0.57/0.77 tff(479,plain,
% 0.57/0.77 ((~hskp26) | c0_1(a333)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[478, 475])).
% 0.57/0.77 tff(480,plain,
% 0.57/0.77 ((~hskp26) | c0_1(a333)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[479, 475])).
% 0.57/0.77 tff(481,plain,
% 0.57/0.77 ((~hskp26) | c0_1(a333)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[480, 475])).
% 0.57/0.77 tff(482,plain,
% 0.57/0.77 (c0_1(a333)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[481, 466])).
% 0.57/0.77 tff(483,plain,
% 0.57/0.77 (((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp5 | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)))) <=> ((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp5 | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(484,plain,
% 0.57/0.77 ((hskp16 | hskp5 | (~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333))) <=> (hskp16 | hskp5 | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(485,plain,
% 0.57/0.77 (((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)))) <=> ((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp5 | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333))))),
% 0.57/0.77 inference(monotonicity,[status(thm)],[484])).
% 0.57/0.77 tff(486,plain,
% 0.57/0.77 (((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)))) <=> ((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp5 | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)))),
% 0.57/0.77 inference(transitivity,[status(thm)],[485, 483])).
% 0.57/0.77 tff(487,plain,
% 0.57/0.77 ((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)))),
% 0.57/0.77 inference(quant_inst,[status(thm)],[])).
% 0.57/0.77 tff(488,plain,
% 0.57/0.77 ((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp5 | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[487, 486])).
% 0.57/0.77 tff(489,plain,
% 0.57/0.77 (hskp16 | (~c2_1(a333))),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[488, 134, 193, 482, 474, 465])).
% 0.57/0.77 tff(490,plain,
% 0.57/0.77 (~c2_1(a333)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[489, 455])).
% 0.57/0.77 tff(491,plain,
% 0.57/0.77 (hskp25),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[28, 455])).
% 0.57/0.77 tff(492,plain,
% 0.57/0.77 (~c2_1(a419)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[251, 491])).
% 0.57/0.77 tff(493,plain,
% 0.57/0.77 (~c1_1(a419)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[257, 491])).
% 0.57/0.77 tff(494,plain,
% 0.57/0.77 (((~hskp26) | c1_1(a333)) <=> ((~hskp26) | c1_1(a333))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(495,axiom,((~hskp26) | c1_1(a333)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 0.57/0.77 tff(496,plain,
% 0.57/0.77 ((~hskp26) | c1_1(a333)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[495, 494])).
% 0.57/0.77 tff(497,plain,
% 0.57/0.77 ((~hskp26) | c1_1(a333)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[496, 494])).
% 0.57/0.77 tff(498,plain,
% 0.57/0.77 ((~hskp26) | c1_1(a333)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[497, 494])).
% 0.57/0.77 tff(499,plain,
% 0.57/0.77 ((~hskp26) | c1_1(a333)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[498, 494])).
% 0.57/0.77 tff(500,plain,
% 0.57/0.77 ((~hskp26) | c1_1(a333)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[499, 494])).
% 0.57/0.77 tff(501,plain,
% 0.57/0.77 (c1_1(a333)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[500, 466])).
% 0.57/0.77 tff(502,plain,
% 0.57/0.77 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(503,plain,
% 0.57/0.77 ((hskp28 | (~ndr1_0) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333))) <=> (hskp28 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(504,plain,
% 0.57/0.77 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333))))),
% 0.57/0.77 inference(monotonicity,[status(thm)],[503])).
% 0.57/0.77 tff(505,plain,
% 0.57/0.77 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)))),
% 0.57/0.77 inference(transitivity,[status(thm)],[504, 502])).
% 0.57/0.77 tff(506,plain,
% 0.57/0.77 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)))),
% 0.57/0.77 inference(quant_inst,[status(thm)],[])).
% 0.57/0.77 tff(507,plain,
% 0.57/0.77 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[506, 505])).
% 0.57/0.77 tff(508,plain,
% 0.57/0.77 (hskp28 | c2_1(a333)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[507, 134, 501, 474, 102])).
% 0.57/0.77 tff(509,plain,
% 0.57/0.77 (hskp28),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[508, 490])).
% 0.57/0.77 tff(510,plain,
% 0.57/0.77 (c2_1(a343)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[148, 509])).
% 0.57/0.77 tff(511,plain,
% 0.57/0.77 (c1_1(a343)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[156, 509])).
% 0.57/0.77 tff(512,plain,
% 0.57/0.77 (c0_1(a343)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[164, 509])).
% 0.57/0.77 tff(513,plain,
% 0.57/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a419)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a419)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(514,plain,
% 0.57/0.77 (((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c2_1(a419) | c1_1(a419) | (~c3_1(a419))) <=> (c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a419)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(515,plain,
% 0.57/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c2_1(a419) | c1_1(a419) | (~c3_1(a419)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a419)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 0.57/0.77 inference(monotonicity,[status(thm)],[514])).
% 0.57/0.77 tff(516,plain,
% 0.57/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c2_1(a419) | c1_1(a419) | (~c3_1(a419)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a419)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.57/0.77 inference(transitivity,[status(thm)],[515, 513])).
% 0.57/0.77 tff(517,plain,
% 0.57/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c2_1(a419) | c1_1(a419) | (~c3_1(a419)))),
% 0.57/0.77 inference(quant_inst,[status(thm)],[])).
% 0.57/0.77 tff(518,plain,
% 0.57/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a419)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[517, 516])).
% 0.57/0.77 tff(519,plain,
% 0.57/0.77 (~c3_1(a419)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[518, 134, 512, 511, 510, 501, 474, 493, 492, 20, 490])).
% 0.57/0.77 tff(520,plain,
% 0.57/0.77 (c0_1(a419)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[265, 491])).
% 0.57/0.77 tff(521,plain,
% 0.57/0.77 (hskp22 | c3_1(a419)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[303, 134, 520, 493, 492, 297])).
% 0.57/0.77 tff(522,plain,
% 0.57/0.77 (hskp22),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[521, 519])).
% 0.57/0.77 tff(523,plain,
% 0.57/0.77 (~c2_1(a367)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[310, 522])).
% 0.57/0.77 tff(524,plain,
% 0.57/0.77 (c3_1(a367)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[334, 522])).
% 0.57/0.77 tff(525,plain,
% 0.57/0.77 (~c1_1(a367)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[347, 522])).
% 0.57/0.77 tff(526,plain,
% 0.57/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a367)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a367)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(527,plain,
% 0.57/0.77 (((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c2_1(a367) | c1_1(a367) | (~c3_1(a367))) <=> (c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a367)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(528,plain,
% 0.57/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c2_1(a367) | c1_1(a367) | (~c3_1(a367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a367)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 0.57/0.77 inference(monotonicity,[status(thm)],[527])).
% 0.57/0.77 tff(529,plain,
% 0.57/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c2_1(a367) | c1_1(a367) | (~c3_1(a367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a367)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.57/0.77 inference(transitivity,[status(thm)],[528, 526])).
% 0.57/0.77 tff(530,plain,
% 0.57/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c2_1(a367) | c1_1(a367) | (~c3_1(a367)))),
% 0.57/0.77 inference(quant_inst,[status(thm)],[])).
% 0.57/0.77 tff(531,plain,
% 0.57/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a367)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[530, 529])).
% 0.57/0.77 tff(532,plain,
% 0.57/0.77 (c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a367)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[531, 20])).
% 0.57/0.77 tff(533,plain,
% 0.57/0.77 ($false),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[532, 525, 524, 134, 510, 501, 474, 512, 511, 523, 490])).
% 0.57/0.77 tff(534,plain,(hskp24 | hskp5 | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.57/0.77 tff(535,plain,
% 0.57/0.77 (hskp24),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[534, 225, 193])).
% 0.57/0.77 tff(536,plain,
% 0.57/0.77 (((~hskp24) | (~c2_1(a401))) <=> ((~hskp24) | (~c2_1(a401)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(537,plain,
% 0.57/0.77 (((~c2_1(a401)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a401)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(538,axiom,((~c2_1(a401)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 0.57/0.77 tff(539,plain,
% 0.57/0.77 ((~hskp24) | (~c2_1(a401))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[538, 537])).
% 0.57/0.77 tff(540,plain,
% 0.57/0.77 ((~hskp24) | (~c2_1(a401))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[539, 536])).
% 0.57/0.77 tff(541,plain,
% 0.57/0.77 (~c2_1(a401)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[540, 535])).
% 0.57/0.77 tff(542,plain,
% 0.57/0.77 (((~hskp24) | (~c0_1(a401))) <=> ((~hskp24) | (~c0_1(a401)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(543,plain,
% 0.57/0.77 (((~c0_1(a401)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a401)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(544,axiom,((~c0_1(a401)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 0.57/0.77 tff(545,plain,
% 0.57/0.77 ((~hskp24) | (~c0_1(a401))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[544, 543])).
% 0.57/0.77 tff(546,plain,
% 0.57/0.77 ((~hskp24) | (~c0_1(a401))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[545, 542])).
% 0.57/0.77 tff(547,plain,
% 0.57/0.77 (~c0_1(a401)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[546, 535])).
% 0.57/0.77 tff(548,plain,
% 0.57/0.77 (((~hskp24) | c1_1(a401)) <=> ((~hskp24) | c1_1(a401))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(549,axiom,((~hskp24) | c1_1(a401)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 0.57/0.77 tff(550,plain,
% 0.57/0.77 ((~hskp24) | c1_1(a401)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[549, 548])).
% 0.57/0.77 tff(551,plain,
% 0.57/0.77 ((~hskp24) | c1_1(a401)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[550, 548])).
% 0.57/0.77 tff(552,plain,
% 0.57/0.77 ((~hskp24) | c1_1(a401)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[551, 548])).
% 0.57/0.77 tff(553,plain,
% 0.57/0.77 ((~hskp24) | c1_1(a401)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[552, 548])).
% 0.57/0.77 tff(554,plain,
% 0.57/0.77 ((~hskp24) | c1_1(a401)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[553, 548])).
% 0.57/0.77 tff(555,plain,
% 0.57/0.77 (c1_1(a401)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[554, 535])).
% 0.57/0.77 tff(556,plain,
% 0.57/0.77 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.57/0.77 inference(bind,[status(th)],[])).
% 0.57/0.77 tff(557,plain,
% 0.57/0.77 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.57/0.77 inference(quant_intro,[status(thm)],[556])).
% 0.57/0.77 tff(558,plain,
% 0.57/0.77 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(559,plain,
% 0.57/0.77 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.57/0.77 inference(bind,[status(th)],[])).
% 0.57/0.77 tff(560,plain,
% 0.57/0.77 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.57/0.77 inference(quant_intro,[status(thm)],[559])).
% 0.57/0.77 tff(561,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 0.57/0.77 tff(562,plain,
% 0.57/0.77 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[561, 560])).
% 0.57/0.77 tff(563,plain,
% 0.57/0.77 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[562, 558])).
% 0.57/0.77 tff(564,plain,(
% 0.57/0.77 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.57/0.77 inference(skolemize,[status(sab)],[563])).
% 0.57/0.77 tff(565,plain,
% 0.57/0.77 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[564, 557])).
% 0.57/0.77 tff(566,assumption,(hskp14), introduced(assumption)).
% 0.57/0.77 tff(567,plain,
% 0.57/0.77 (~c1_1(a347)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[286, 566])).
% 0.57/0.77 tff(568,assumption,(~c2_1(a401)), introduced(assumption)).
% 0.57/0.77 tff(569,assumption,(~c0_1(a401)), introduced(assumption)).
% 0.57/0.77 tff(570,plain,
% 0.57/0.77 (c3_1(a347)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[318, 566])).
% 0.57/0.77 tff(571,plain,
% 0.57/0.77 (c2_1(a347)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[326, 566])).
% 0.57/0.77 tff(572,assumption,(c1_1(a401)), introduced(assumption)).
% 0.57/0.77 tff(573,plain,
% 0.57/0.77 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a401) | c2_1(a401) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c1_1(a401)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a401) | c2_1(a401) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c1_1(a401)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(574,plain,
% 0.57/0.77 ((hskp5 | (~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401))) <=> (hskp5 | c0_1(a401) | c2_1(a401) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c1_1(a401)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(575,plain,
% 0.57/0.77 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a401) | c2_1(a401) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c1_1(a401))))),
% 0.57/0.77 inference(monotonicity,[status(thm)],[574])).
% 0.57/0.77 tff(576,plain,
% 0.57/0.77 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a401) | c2_1(a401) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c1_1(a401)))),
% 0.57/0.77 inference(transitivity,[status(thm)],[575, 573])).
% 0.57/0.77 tff(577,plain,
% 0.57/0.77 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))),
% 0.57/0.77 inference(quant_inst,[status(thm)],[])).
% 0.57/0.77 tff(578,plain,
% 0.57/0.77 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a401) | c2_1(a401) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c1_1(a401))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[577, 576])).
% 0.57/0.77 tff(579,plain,
% 0.57/0.77 ($false),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[578, 134, 193, 572, 571, 570, 569, 568, 567, 565])).
% 0.57/0.77 tff(580,plain,((~hskp14) | hskp5 | (~c1_1(a401)) | c0_1(a401) | c2_1(a401)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.77 tff(581,plain,
% 0.57/0.77 (~hskp14),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[580, 555, 193, 547, 541])).
% 0.57/0.77 tff(582,assumption,(hskp1), introduced(assumption)).
% 0.57/0.77 tff(583,plain,
% 0.57/0.77 (((~hskp1) | (~c3_1(a323))) <=> ((~hskp1) | (~c3_1(a323)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(584,plain,
% 0.57/0.77 (((~c3_1(a323)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a323)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(585,axiom,((~c3_1(a323)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 0.57/0.77 tff(586,plain,
% 0.57/0.77 ((~hskp1) | (~c3_1(a323))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[585, 584])).
% 0.57/0.77 tff(587,plain,
% 0.57/0.77 ((~hskp1) | (~c3_1(a323))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[586, 583])).
% 0.57/0.77 tff(588,plain,
% 0.57/0.77 (~c3_1(a323)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[587, 582])).
% 0.57/0.77 tff(589,plain,
% 0.57/0.77 (((~hskp1) | (~c2_1(a323))) <=> ((~hskp1) | (~c2_1(a323)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(590,plain,
% 0.57/0.77 (((~c2_1(a323)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a323)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(591,axiom,((~c2_1(a323)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 0.57/0.78 tff(592,plain,
% 0.57/0.78 ((~hskp1) | (~c2_1(a323))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[591, 590])).
% 0.57/0.78 tff(593,plain,
% 0.57/0.78 ((~hskp1) | (~c2_1(a323))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[592, 589])).
% 0.57/0.78 tff(594,plain,
% 0.57/0.78 (~c2_1(a323)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[593, 582])).
% 0.57/0.78 tff(595,plain,
% 0.57/0.78 (((~hskp1) | (~c1_1(a323))) <=> ((~hskp1) | (~c1_1(a323)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(596,plain,
% 0.57/0.78 (((~c1_1(a323)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a323)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(597,axiom,((~c1_1(a323)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 0.57/0.78 tff(598,plain,
% 0.57/0.78 ((~hskp1) | (~c1_1(a323))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[597, 596])).
% 0.57/0.78 tff(599,plain,
% 0.57/0.78 ((~hskp1) | (~c1_1(a323))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[598, 595])).
% 0.57/0.78 tff(600,plain,
% 0.57/0.78 (~c1_1(a323)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[599, 582])).
% 0.57/0.78 tff(601,plain,
% 0.57/0.78 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp14 | hskp5 | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(602,plain,
% 0.57/0.78 ((hskp14 | hskp5 | (~ndr1_0) | c2_1(a323) | c1_1(a323) | c3_1(a323)) <=> (hskp14 | hskp5 | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(603,plain,
% 0.57/0.78 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | (~ndr1_0) | c2_1(a323) | c1_1(a323) | c3_1(a323))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0)))),
% 0.57/0.78 inference(monotonicity,[status(thm)],[602])).
% 0.57/0.78 tff(604,plain,
% 0.57/0.78 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | (~ndr1_0) | c2_1(a323) | c1_1(a323) | c3_1(a323))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp14 | hskp5 | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0))),
% 0.57/0.78 inference(transitivity,[status(thm)],[603, 601])).
% 0.57/0.78 tff(605,plain,
% 0.57/0.78 ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | (~ndr1_0) | c2_1(a323) | c1_1(a323) | c3_1(a323))),
% 0.57/0.78 inference(quant_inst,[status(thm)],[])).
% 0.57/0.78 tff(606,plain,
% 0.57/0.78 ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp14 | hskp5 | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0)),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[605, 604])).
% 0.57/0.78 tff(607,plain,
% 0.57/0.78 ($false),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[606, 134, 204, 193, 600, 594, 588, 214])).
% 0.57/0.78 tff(608,plain,((~hskp1) | hskp14 | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.57/0.78 tff(609,plain,
% 0.57/0.78 (~hskp1),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[608, 581, 193])).
% 0.57/0.78 tff(610,plain,
% 0.57/0.78 (hskp11),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[57, 609, 357])).
% 0.57/0.78 tff(611,plain,
% 0.57/0.78 (~c2_1(a338)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[63, 610])).
% 0.57/0.78 tff(612,plain,
% 0.57/0.78 (~c1_1(a338)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[69, 610])).
% 0.57/0.78 tff(613,plain,
% 0.57/0.78 (~c0_1(a338)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[75, 610])).
% 0.57/0.78 tff(614,plain,
% 0.57/0.78 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp1 | c0_1(a338) | c1_1(a338) | c2_1(a338) | (~ndr1_0))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp5 | hskp1 | c0_1(a338) | c1_1(a338) | c2_1(a338) | (~ndr1_0))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(615,plain,
% 0.57/0.78 ((hskp5 | hskp1 | (~ndr1_0) | c2_1(a338) | c1_1(a338) | c0_1(a338)) <=> (hskp5 | hskp1 | c0_1(a338) | c1_1(a338) | c2_1(a338) | (~ndr1_0))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(616,plain,
% 0.57/0.78 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a338) | c1_1(a338) | c0_1(a338))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp1 | c0_1(a338) | c1_1(a338) | c2_1(a338) | (~ndr1_0)))),
% 0.57/0.78 inference(monotonicity,[status(thm)],[615])).
% 0.57/0.78 tff(617,plain,
% 0.57/0.78 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a338) | c1_1(a338) | c0_1(a338))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp5 | hskp1 | c0_1(a338) | c1_1(a338) | c2_1(a338) | (~ndr1_0))),
% 0.57/0.78 inference(transitivity,[status(thm)],[616, 614])).
% 0.57/0.78 tff(618,plain,
% 0.57/0.78 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a338) | c1_1(a338) | c0_1(a338))),
% 0.57/0.78 inference(quant_inst,[status(thm)],[])).
% 0.57/0.78 tff(619,plain,
% 0.57/0.78 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp5 | hskp1 | c0_1(a338) | c1_1(a338) | c2_1(a338) | (~ndr1_0)),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[618, 617])).
% 0.57/0.78 tff(620,plain,
% 0.57/0.78 ($false),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[619, 134, 193, 609, 613, 612, 611, 224])).
% 0.57/0.78 tff(621,plain,(hskp2 | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.57/0.78 tff(622,plain,
% 0.57/0.78 (hskp2),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[621, 193])).
% 0.57/0.78 tff(623,plain,
% 0.57/0.78 (((~hskp2) | (~c3_1(a324))) <=> ((~hskp2) | (~c3_1(a324)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(624,plain,
% 0.57/0.78 (((~c3_1(a324)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a324)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(625,axiom,((~c3_1(a324)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 0.57/0.78 tff(626,plain,
% 0.57/0.78 ((~hskp2) | (~c3_1(a324))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[625, 624])).
% 0.57/0.78 tff(627,plain,
% 0.57/0.78 ((~hskp2) | (~c3_1(a324))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[626, 623])).
% 0.57/0.78 tff(628,plain,
% 0.57/0.78 (~c3_1(a324)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[627, 622])).
% 0.57/0.78 tff(629,plain,
% 0.57/0.78 (((~hskp2) | (~c1_1(a324))) <=> ((~hskp2) | (~c1_1(a324)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(630,plain,
% 0.57/0.78 (((~c1_1(a324)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a324)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(631,axiom,((~c1_1(a324)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 0.57/0.78 tff(632,plain,
% 0.57/0.78 ((~hskp2) | (~c1_1(a324))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[631, 630])).
% 0.57/0.78 tff(633,plain,
% 0.57/0.78 ((~hskp2) | (~c1_1(a324))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[632, 629])).
% 0.57/0.78 tff(634,plain,
% 0.57/0.78 (~c1_1(a324)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[633, 622])).
% 0.57/0.78 tff(635,plain,
% 0.57/0.78 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | c1_1(a324) | c3_1(a324) | (~ndr1_0) | c2_1(a324))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp14 | hskp5 | c1_1(a324) | c3_1(a324) | (~ndr1_0) | c2_1(a324))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(636,plain,
% 0.57/0.78 ((hskp14 | hskp5 | (~ndr1_0) | c2_1(a324) | c1_1(a324) | c3_1(a324)) <=> (hskp14 | hskp5 | c1_1(a324) | c3_1(a324) | (~ndr1_0) | c2_1(a324))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(637,plain,
% 0.57/0.78 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | (~ndr1_0) | c2_1(a324) | c1_1(a324) | c3_1(a324))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | c1_1(a324) | c3_1(a324) | (~ndr1_0) | c2_1(a324)))),
% 0.57/0.78 inference(monotonicity,[status(thm)],[636])).
% 0.57/0.78 tff(638,plain,
% 0.57/0.78 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | (~ndr1_0) | c2_1(a324) | c1_1(a324) | c3_1(a324))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp14 | hskp5 | c1_1(a324) | c3_1(a324) | (~ndr1_0) | c2_1(a324))),
% 0.57/0.78 inference(transitivity,[status(thm)],[637, 635])).
% 0.57/0.78 tff(639,plain,
% 0.57/0.78 ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | (~ndr1_0) | c2_1(a324) | c1_1(a324) | c3_1(a324))),
% 0.57/0.78 inference(quant_inst,[status(thm)],[])).
% 0.57/0.78 tff(640,plain,
% 0.57/0.78 ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp14 | hskp5 | c1_1(a324) | c3_1(a324) | (~ndr1_0) | c2_1(a324)),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[639, 638])).
% 0.57/0.78 tff(641,plain,
% 0.57/0.78 (hskp14 | c2_1(a324)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[640, 134, 193, 634, 628, 214])).
% 0.57/0.78 tff(642,plain,
% 0.57/0.78 (c2_1(a324)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[641, 204])).
% 0.57/0.78 tff(643,plain,
% 0.57/0.78 (^[U: $i] : refl((hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 0.57/0.78 inference(bind,[status(th)],[])).
% 0.57/0.78 tff(644,plain,
% 0.57/0.78 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.57/0.78 inference(quant_intro,[status(thm)],[643])).
% 0.57/0.78 tff(645,plain,
% 0.57/0.78 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(646,plain,
% 0.57/0.78 (^[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) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp13) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp13))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp13) | hskp14) <=> ((hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp14))), rewrite(((hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp14) <=> (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp13) | hskp14) <=> (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 0.57/0.78 inference(bind,[status(th)],[])).
% 0.57/0.78 tff(647,plain,
% 0.57/0.78 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp13) | hskp14) <=> ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.57/0.78 inference(quant_intro,[status(thm)],[646])).
% 0.57/0.78 tff(648,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp13) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 0.57/0.78 tff(649,plain,
% 0.57/0.78 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[648, 647])).
% 0.57/0.78 tff(650,plain,
% 0.57/0.78 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[649, 645])).
% 0.57/0.78 tff(651,plain,(
% 0.57/0.78 ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.57/0.78 inference(skolemize,[status(sab)],[650])).
% 0.57/0.78 tff(652,plain,
% 0.57/0.78 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[651, 644])).
% 0.57/0.78 tff(653,plain,
% 0.57/0.78 (((~hskp2) | (~c0_1(a324))) <=> ((~hskp2) | (~c0_1(a324)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(654,plain,
% 0.57/0.78 (((~c0_1(a324)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a324)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(655,axiom,((~c0_1(a324)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 0.57/0.78 tff(656,plain,
% 0.57/0.78 ((~hskp2) | (~c0_1(a324))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[655, 654])).
% 0.57/0.78 tff(657,plain,
% 0.57/0.78 ((~hskp2) | (~c0_1(a324))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[656, 653])).
% 0.57/0.78 tff(658,plain,
% 0.57/0.78 (~c0_1(a324)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[657, 622])).
% 0.57/0.78 tff(659,plain,
% 0.57/0.78 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | c0_1(a324) | c3_1(a324) | (~ndr1_0) | (~c2_1(a324)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp13 | c0_1(a324) | c3_1(a324) | (~ndr1_0) | (~c2_1(a324)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(660,plain,
% 0.57/0.78 ((hskp14 | hskp13 | (~ndr1_0) | c0_1(a324) | c3_1(a324) | (~c2_1(a324))) <=> (hskp14 | hskp13 | c0_1(a324) | c3_1(a324) | (~ndr1_0) | (~c2_1(a324)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(661,plain,
% 0.57/0.78 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a324) | c3_1(a324) | (~c2_1(a324)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | c0_1(a324) | c3_1(a324) | (~ndr1_0) | (~c2_1(a324))))),
% 0.57/0.78 inference(monotonicity,[status(thm)],[660])).
% 0.57/0.78 tff(662,plain,
% 0.57/0.78 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a324) | c3_1(a324) | (~c2_1(a324)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp13 | c0_1(a324) | c3_1(a324) | (~ndr1_0) | (~c2_1(a324)))),
% 0.57/0.78 inference(transitivity,[status(thm)],[661, 659])).
% 0.57/0.78 tff(663,plain,
% 0.57/0.78 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a324) | c3_1(a324) | (~c2_1(a324)))),
% 0.57/0.78 inference(quant_inst,[status(thm)],[])).
% 0.57/0.78 tff(664,plain,
% 0.57/0.78 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp13 | c0_1(a324) | c3_1(a324) | (~ndr1_0) | (~c2_1(a324))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[663, 662])).
% 0.57/0.78 tff(665,plain,
% 0.57/0.78 (hskp14 | hskp13 | (~c2_1(a324))),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[664, 134, 658, 628, 652])).
% 0.57/0.78 tff(666,plain,
% 0.57/0.78 (hskp13),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[665, 642, 204])).
% 0.57/0.78 tff(667,plain,
% 0.57/0.78 (((~hskp13) | (~c3_1(a346))) <=> ((~hskp13) | (~c3_1(a346)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(668,plain,
% 0.57/0.78 (((~c3_1(a346)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a346)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(669,axiom,((~c3_1(a346)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.57/0.78 tff(670,plain,
% 0.57/0.78 ((~hskp13) | (~c3_1(a346))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[669, 668])).
% 0.57/0.78 tff(671,plain,
% 0.57/0.78 ((~hskp13) | (~c3_1(a346))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[670, 667])).
% 0.57/0.78 tff(672,plain,
% 0.57/0.78 (~c3_1(a346)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[671, 666])).
% 0.57/0.78 tff(673,plain,
% 0.57/0.78 (c3_1(a419)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[279, 134, 204, 193, 493, 492, 214])).
% 0.57/0.78 tff(674,plain,
% 0.57/0.78 (~hskp1),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[608, 204, 193])).
% 0.57/0.78 tff(675,plain,
% 0.57/0.78 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp1 | c0_1(a330) | c1_1(a330) | (~ndr1_0) | c2_1(a330))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp5 | hskp1 | c0_1(a330) | c1_1(a330) | (~ndr1_0) | c2_1(a330))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(676,plain,
% 0.57/0.78 ((hskp5 | hskp1 | (~ndr1_0) | c2_1(a330) | c1_1(a330) | c0_1(a330)) <=> (hskp5 | hskp1 | c0_1(a330) | c1_1(a330) | (~ndr1_0) | c2_1(a330))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(677,plain,
% 0.57/0.78 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a330) | c1_1(a330) | c0_1(a330))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp1 | c0_1(a330) | c1_1(a330) | (~ndr1_0) | c2_1(a330)))),
% 0.57/0.78 inference(monotonicity,[status(thm)],[676])).
% 0.57/0.78 tff(678,plain,
% 0.57/0.78 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a330) | c1_1(a330) | c0_1(a330))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp5 | hskp1 | c0_1(a330) | c1_1(a330) | (~ndr1_0) | c2_1(a330))),
% 0.57/0.78 inference(transitivity,[status(thm)],[677, 675])).
% 0.57/0.78 tff(679,plain,
% 0.57/0.78 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a330) | c1_1(a330) | c0_1(a330))),
% 0.57/0.78 inference(quant_inst,[status(thm)],[])).
% 0.57/0.78 tff(680,plain,
% 0.57/0.78 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp5 | hskp1 | c0_1(a330) | c1_1(a330) | (~ndr1_0) | c2_1(a330)),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[679, 678])).
% 0.57/0.78 tff(681,plain,
% 0.57/0.78 (c2_1(a330)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[680, 134, 193, 674, 384, 378, 224])).
% 0.57/0.78 tff(682,plain,
% 0.57/0.78 (^[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)) | c0_1(W) | c1_1(W) | (~c2_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(W))))),
% 0.57/0.78 inference(bind,[status(th)],[])).
% 0.57/0.78 tff(683,plain,
% 0.57/0.78 (![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)) | c0_1(W) | c1_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)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.57/0.78 inference(quant_intro,[status(thm)],[682])).
% 0.57/0.78 tff(684,plain,
% 0.57/0.78 (![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)) | c0_1(W) | c1_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)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(685,plain,
% 0.57/0.78 (^[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))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_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)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_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)) | (~c2_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_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)) | (~c2_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)) | (~c2_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) | (~c2_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_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) | (~c2_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | 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)) | c0_1(W) | (~c2_1(W))) | c1_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) | (~c2_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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | 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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))))),
% 0.57/0.78 inference(bind,[status(th)],[])).
% 0.57/0.78 tff(686,plain,
% 0.57/0.78 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.57/0.78 inference(quant_intro,[status(thm)],[685])).
% 0.57/0.78 tff(687,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 0.57/0.78 tff(688,plain,
% 0.57/0.78 (![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[687, 686])).
% 0.57/0.78 tff(689,plain,
% 0.57/0.78 (![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[688, 684])).
% 0.57/0.78 tff(690,plain,(
% 0.57/0.78 ![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.57/0.78 inference(skolemize,[status(sab)],[689])).
% 0.57/0.78 tff(691,plain,
% 0.57/0.78 (![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[690, 683])).
% 0.57/0.78 tff(692,plain,
% 0.57/0.78 (((~![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a419) | c1_1(a330) | c0_1(a324) | c1_1(a324) | (~ndr1_0) | (~c2_1(a324)) | (~c2_1(a330)) | (~c3_1(a330)) | (~c3_1(a419)) | (~c0_1(a419)))) <=> ((~![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a419) | c1_1(a330) | c0_1(a324) | c1_1(a324) | (~ndr1_0) | (~c2_1(a324)) | (~c2_1(a330)) | (~c3_1(a330)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(693,plain,
% 0.57/0.78 (((~ndr1_0) | c1_1(a330) | (~c2_1(a330)) | (~c3_1(a330)) | c1_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c0_1(a324) | c1_1(a324) | (~c2_1(a324))) <=> (c1_1(a419) | c1_1(a330) | c0_1(a324) | c1_1(a324) | (~ndr1_0) | (~c2_1(a324)) | (~c2_1(a330)) | (~c3_1(a330)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(694,plain,
% 0.57/0.78 (((~![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a330) | (~c2_1(a330)) | (~c3_1(a330)) | c1_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c0_1(a324) | c1_1(a324) | (~c2_1(a324)))) <=> ((~![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a419) | c1_1(a330) | c0_1(a324) | c1_1(a324) | (~ndr1_0) | (~c2_1(a324)) | (~c2_1(a330)) | (~c3_1(a330)) | (~c3_1(a419)) | (~c0_1(a419))))),
% 0.57/0.78 inference(monotonicity,[status(thm)],[693])).
% 0.57/0.78 tff(695,plain,
% 0.57/0.78 (((~![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a330) | (~c2_1(a330)) | (~c3_1(a330)) | c1_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c0_1(a324) | c1_1(a324) | (~c2_1(a324)))) <=> ((~![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a419) | c1_1(a330) | c0_1(a324) | c1_1(a324) | (~ndr1_0) | (~c2_1(a324)) | (~c2_1(a330)) | (~c3_1(a330)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 0.57/0.78 inference(transitivity,[status(thm)],[694, 692])).
% 0.57/0.78 tff(696,plain,
% 0.57/0.78 ((~![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a330) | (~c2_1(a330)) | (~c3_1(a330)) | c1_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c0_1(a324) | c1_1(a324) | (~c2_1(a324)))),
% 0.57/0.78 inference(quant_inst,[status(thm)],[])).
% 0.57/0.78 tff(697,plain,
% 0.57/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a419) | c1_1(a330) | c0_1(a324) | c1_1(a324) | (~ndr1_0) | (~c2_1(a324)) | (~c2_1(a330)) | (~c3_1(a330)) | (~c3_1(a419)) | (~c0_1(a419))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[696, 695])).
% 0.57/0.78 tff(698,plain,
% 0.57/0.78 ($false),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[697, 134, 520, 446, 493, 378, 658, 634, 691, 642, 681, 673])).
% 0.57/0.78 tff(699,plain,(hskp24 | hskp14 | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.57/0.78 tff(700,plain,
% 0.57/0.78 (hskp24),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[699, 204, 193])).
% 0.57/0.78 tff(701,plain,
% 0.57/0.78 (~c2_1(a401)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[540, 700])).
% 0.57/0.78 tff(702,plain,
% 0.57/0.78 (~c0_1(a401)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[546, 700])).
% 0.57/0.78 tff(703,plain,
% 0.57/0.78 (((~hskp13) | c2_1(a346)) <=> ((~hskp13) | c2_1(a346))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(704,axiom,((~hskp13) | c2_1(a346)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 0.57/0.78 tff(705,plain,
% 0.57/0.78 ((~hskp13) | c2_1(a346)),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[704, 703])).
% 0.57/0.78 tff(706,plain,
% 0.57/0.78 ((~hskp13) | c2_1(a346)),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[705, 703])).
% 0.57/0.78 tff(707,plain,
% 0.57/0.78 ((~hskp13) | c2_1(a346)),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[706, 703])).
% 0.57/0.78 tff(708,plain,
% 0.57/0.78 ((~hskp13) | c2_1(a346)),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[707, 703])).
% 0.57/0.78 tff(709,plain,
% 0.57/0.78 ((~hskp13) | c2_1(a346)),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[708, 703])).
% 0.57/0.78 tff(710,plain,
% 0.57/0.78 (c2_1(a346)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[709, 666])).
% 0.57/0.78 tff(711,plain,
% 0.57/0.78 (((~hskp13) | c0_1(a346)) <=> ((~hskp13) | c0_1(a346))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(712,axiom,((~hskp13) | c0_1(a346)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 0.57/0.78 tff(713,plain,
% 0.57/0.78 ((~hskp13) | c0_1(a346)),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[712, 711])).
% 0.57/0.78 tff(714,plain,
% 0.57/0.78 ((~hskp13) | c0_1(a346)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[713, 711])).
% 0.63/0.78 tff(715,plain,
% 0.63/0.78 ((~hskp13) | c0_1(a346)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[714, 711])).
% 0.63/0.78 tff(716,plain,
% 0.63/0.78 ((~hskp13) | c0_1(a346)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[715, 711])).
% 0.63/0.78 tff(717,plain,
% 0.63/0.78 ((~hskp13) | c0_1(a346)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[716, 711])).
% 0.63/0.78 tff(718,plain,
% 0.63/0.78 (c0_1(a346)),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[717, 666])).
% 0.63/0.78 tff(719,plain,
% 0.63/0.78 (c1_1(a401)),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[554, 700])).
% 0.63/0.78 tff(720,plain,
% 0.63/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a401) | c2_1(a401) | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a401)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a401) | c2_1(a401) | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a401)))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(721,plain,
% 0.63/0.78 (((~ndr1_0) | (~c2_1(a346)) | (~c0_1(a346)) | (~c1_1(a346)) | c3_1(a346) | (~c1_1(a346)) | (~c2_1(a346)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401))) <=> (c0_1(a401) | c2_1(a401) | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a401)))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(722,plain,
% 0.63/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a346)) | (~c0_1(a346)) | (~c1_1(a346)) | c3_1(a346) | (~c1_1(a346)) | (~c2_1(a346)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a401) | c2_1(a401) | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a401))))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[721])).
% 0.63/0.78 tff(723,plain,
% 0.63/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a346)) | (~c0_1(a346)) | (~c1_1(a346)) | c3_1(a346) | (~c1_1(a346)) | (~c2_1(a346)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a401) | c2_1(a401) | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a401)))),
% 0.63/0.78 inference(transitivity,[status(thm)],[722, 720])).
% 0.63/0.78 tff(724,plain,
% 0.63/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a346)) | (~c0_1(a346)) | (~c1_1(a346)) | c3_1(a346) | (~c1_1(a346)) | (~c2_1(a346)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))),
% 0.63/0.78 inference(quant_inst,[status(thm)],[])).
% 0.63/0.78 tff(725,plain,
% 0.63/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a401) | c2_1(a401) | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a401))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[724, 723])).
% 0.63/0.78 tff(726,plain,
% 0.63/0.78 (~c1_1(a346)),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[725, 134, 719, 718, 710, 702, 701, 672, 203])).
% 0.63/0.78 tff(727,plain,
% 0.63/0.78 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(728,plain,
% 0.63/0.78 ((hskp5 | (~ndr1_0) | c1_1(a346) | (~c2_1(a346)) | (~c0_1(a346)) | c1_1(a346) | c3_1(a346) | (~c2_1(a346))) <=> (hskp5 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(729,plain,
% 0.63/0.79 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a346) | (~c2_1(a346)) | (~c0_1(a346)) | c1_1(a346) | c3_1(a346) | (~c2_1(a346)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346))))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[728])).
% 0.63/0.79 tff(730,plain,
% 0.63/0.79 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a346) | (~c2_1(a346)) | (~c0_1(a346)) | c1_1(a346) | c3_1(a346) | (~c2_1(a346)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)))),
% 0.63/0.79 inference(transitivity,[status(thm)],[729, 727])).
% 0.63/0.79 tff(731,plain,
% 0.63/0.79 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a346) | (~c2_1(a346)) | (~c0_1(a346)) | c1_1(a346) | c3_1(a346) | (~c2_1(a346)))),
% 0.63/0.79 inference(quant_inst,[status(thm)],[])).
% 0.63/0.79 tff(732,plain,
% 0.63/0.79 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[731, 730])).
% 0.63/0.79 tff(733,plain,
% 0.63/0.79 ($false),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[732, 134, 193, 718, 710, 672, 182, 726])).
% 0.63/0.79 tff(734,plain,(hskp14 | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.63/0.79 tff(735,plain,
% 0.63/0.79 (hskp14),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[734, 193])).
% 0.63/0.79 tff(736,plain,
% 0.63/0.79 (~c1_1(a347)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[286, 735])).
% 0.63/0.79 tff(737,plain,
% 0.63/0.79 (c3_1(a347)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[318, 735])).
% 0.63/0.79 tff(738,plain,
% 0.63/0.79 (c2_1(a347)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[326, 735])).
% 0.63/0.79 tff(739,plain,
% 0.63/0.79 (((~![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp15 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp15 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(740,plain,
% 0.63/0.79 ((hskp15 | (~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347))) <=> (hskp15 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(741,plain,
% 0.63/0.79 (((~![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp15 | (~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp15 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347))))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[740])).
% 0.63/0.79 tff(742,plain,
% 0.63/0.79 (((~![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp15 | (~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp15 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)))),
% 0.63/0.79 inference(transitivity,[status(thm)],[741, 739])).
% 0.63/0.79 tff(743,plain,
% 0.63/0.79 ((~![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp15 | (~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)))),
% 0.63/0.79 inference(quant_inst,[status(thm)],[])).
% 0.63/0.79 tff(744,plain,
% 0.63/0.79 ((~![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp15 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[743, 742])).
% 0.63/0.79 tff(745,plain,
% 0.63/0.79 (hskp15),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[744, 134, 738, 737, 736, 192])).
% 0.63/0.79 tff(746,plain,
% 0.63/0.79 (((~hskp15) | (~c3_1(a348))) <=> ((~hskp15) | (~c3_1(a348)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(747,plain,
% 0.63/0.79 (((~c3_1(a348)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a348)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(748,axiom,((~c3_1(a348)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 0.63/0.79 tff(749,plain,
% 0.63/0.79 ((~hskp15) | (~c3_1(a348))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[748, 747])).
% 0.63/0.79 tff(750,plain,
% 0.63/0.79 ((~hskp15) | (~c3_1(a348))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[749, 746])).
% 0.63/0.79 tff(751,plain,
% 0.63/0.79 (~c3_1(a348)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[750, 745])).
% 0.63/0.79 tff(752,plain,
% 0.63/0.79 (((~hskp15) | (~c1_1(a348))) <=> ((~hskp15) | (~c1_1(a348)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(753,plain,
% 0.63/0.79 (((~c1_1(a348)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a348)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(754,axiom,((~c1_1(a348)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 0.63/0.79 tff(755,plain,
% 0.63/0.79 ((~hskp15) | (~c1_1(a348))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[754, 753])).
% 0.63/0.79 tff(756,plain,
% 0.63/0.79 ((~hskp15) | (~c1_1(a348))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[755, 752])).
% 0.63/0.79 tff(757,plain,
% 0.63/0.79 (~c1_1(a348)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[756, 745])).
% 0.63/0.79 tff(758,plain,
% 0.63/0.79 (((~hskp15) | c0_1(a348)) <=> ((~hskp15) | c0_1(a348))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(759,axiom,((~hskp15) | c0_1(a348)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 0.63/0.79 tff(760,plain,
% 0.63/0.79 ((~hskp15) | c0_1(a348)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[759, 758])).
% 0.63/0.79 tff(761,plain,
% 0.63/0.79 ((~hskp15) | c0_1(a348)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[760, 758])).
% 0.63/0.79 tff(762,plain,
% 0.63/0.79 ((~hskp15) | c0_1(a348)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[761, 758])).
% 0.63/0.79 tff(763,plain,
% 0.63/0.79 ((~hskp15) | c0_1(a348)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[762, 758])).
% 0.63/0.79 tff(764,plain,
% 0.63/0.79 ((~hskp15) | c0_1(a348)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[763, 758])).
% 0.63/0.79 tff(765,plain,
% 0.63/0.79 (c0_1(a348)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[764, 745])).
% 0.63/0.79 tff(766,plain,
% 0.63/0.79 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | (~c2_1(a348)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | (~c2_1(a348)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(767,plain,
% 0.63/0.79 ((hskp5 | (~ndr1_0) | c1_1(a348) | (~c2_1(a348)) | (~c0_1(a348)) | c1_1(a348) | c3_1(a348) | (~c2_1(a348))) <=> (hskp5 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | (~c2_1(a348)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(768,plain,
% 0.63/0.79 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a348) | (~c2_1(a348)) | (~c0_1(a348)) | c1_1(a348) | c3_1(a348) | (~c2_1(a348)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | (~c2_1(a348))))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[767])).
% 0.63/0.79 tff(769,plain,
% 0.63/0.79 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a348) | (~c2_1(a348)) | (~c0_1(a348)) | c1_1(a348) | c3_1(a348) | (~c2_1(a348)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | (~c2_1(a348)))),
% 0.63/0.79 inference(transitivity,[status(thm)],[768, 766])).
% 0.63/0.79 tff(770,plain,
% 0.63/0.79 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a348) | (~c2_1(a348)) | (~c0_1(a348)) | c1_1(a348) | c3_1(a348) | (~c2_1(a348)))),
% 0.63/0.79 inference(quant_inst,[status(thm)],[])).
% 0.63/0.79 tff(771,plain,
% 0.63/0.79 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | (~c2_1(a348))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[770, 769])).
% 0.63/0.79 tff(772,plain,
% 0.63/0.79 (~c2_1(a348)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[771, 134, 193, 765, 757, 751, 182])).
% 0.63/0.79 tff(773,plain,
% 0.63/0.79 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | c2_1(a348))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | c2_1(a348))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(774,plain,
% 0.63/0.79 ((hskp22 | (~ndr1_0) | c2_1(a348) | c3_1(a348) | (~c0_1(a348)) | c1_1(a348) | c3_1(a348) | (~c0_1(a348))) <=> (hskp22 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | c2_1(a348))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(775,plain,
% 0.63/0.79 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a348) | c3_1(a348) | (~c0_1(a348)) | c1_1(a348) | c3_1(a348) | (~c0_1(a348)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | c2_1(a348)))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[774])).
% 0.63/0.79 tff(776,plain,
% 0.63/0.79 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a348) | c3_1(a348) | (~c0_1(a348)) | c1_1(a348) | c3_1(a348) | (~c0_1(a348)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | c2_1(a348))),
% 0.63/0.79 inference(transitivity,[status(thm)],[775, 773])).
% 0.63/0.79 tff(777,plain,
% 0.63/0.79 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a348) | c3_1(a348) | (~c0_1(a348)) | c1_1(a348) | c3_1(a348) | (~c0_1(a348)))),
% 0.63/0.79 inference(quant_inst,[status(thm)],[])).
% 0.63/0.79 tff(778,plain,
% 0.63/0.79 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | c2_1(a348)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[777, 776])).
% 0.63/0.79 tff(779,plain,
% 0.63/0.79 (hskp22),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[778, 134, 765, 757, 751, 297, 772])).
% 0.63/0.79 tff(780,plain,
% 0.63/0.79 (~c2_1(a367)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[310, 779])).
% 0.63/0.79 tff(781,plain,
% 0.63/0.79 (c3_1(a367)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[334, 779])).
% 0.63/0.79 tff(782,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a367) | c1_1(a348) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a348)) | c2_1(a348))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a367) | c1_1(a348) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a348)) | c2_1(a348))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(783,plain,
% 0.63/0.79 (((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a348) | c1_1(a348) | (~c0_1(a348)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367))) <=> (c2_1(a367) | c1_1(a348) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a348)) | c2_1(a348))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(784,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a348) | c1_1(a348) | (~c0_1(a348)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a367) | c1_1(a348) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a348)) | c2_1(a348)))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[783])).
% 0.63/0.79 tff(785,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a348) | c1_1(a348) | (~c0_1(a348)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a367) | c1_1(a348) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a348)) | c2_1(a348))),
% 0.63/0.79 inference(transitivity,[status(thm)],[784, 782])).
% 0.63/0.79 tff(786,plain,
% 0.63/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a348) | c1_1(a348) | (~c0_1(a348)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367)))),
% 0.63/0.79 inference(quant_inst,[status(thm)],[])).
% 0.63/0.79 tff(787,plain,
% 0.63/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a367) | c1_1(a348) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a348)) | c2_1(a348)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[786, 785])).
% 0.63/0.79 tff(788,plain,
% 0.63/0.79 (c0_1(a367)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[787, 134, 781, 765, 738, 737, 780, 757, 736, 235, 772])).
% 0.63/0.79 tff(789,plain,
% 0.63/0.79 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))))),
% 0.63/0.79 inference(bind,[status(th)],[])).
% 0.63/0.79 tff(790,plain,
% 0.63/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.63/0.79 inference(quant_intro,[status(thm)],[789])).
% 0.63/0.79 tff(791,plain,
% 0.63/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(792,plain,
% 0.63/0.79 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_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)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_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)) | (~c0_1(U)) | (~c3_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))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))))),
% 0.63/0.79 inference(bind,[status(th)],[])).
% 0.63/0.79 tff(793,plain,
% 0.63/0.79 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.63/0.79 inference(quant_intro,[status(thm)],[792])).
% 0.63/0.79 tff(794,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 0.63/0.79 tff(795,plain,
% 0.63/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[794, 793])).
% 0.63/0.79 tff(796,plain,
% 0.63/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[795, 791])).
% 0.63/0.79 tff(797,plain,(
% 0.63/0.79 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.63/0.79 inference(skolemize,[status(sab)],[796])).
% 0.63/0.79 tff(798,plain,
% 0.63/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[797, 790])).
% 0.63/0.79 tff(799,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a367) | c3_1(a348) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a347)) | (~c0_1(a348)) | c2_1(a348))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a367) | c3_1(a348) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a347)) | (~c0_1(a348)) | c2_1(a348))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(800,plain,
% 0.63/0.79 (((~ndr1_0) | (~c2_1(a347)) | (~c0_1(a347)) | (~c3_1(a347)) | c2_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c2_1(a348) | c3_1(a348) | (~c0_1(a348))) <=> (c2_1(a367) | c3_1(a348) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a347)) | (~c0_1(a348)) | c2_1(a348))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(801,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a347)) | (~c0_1(a347)) | (~c3_1(a347)) | c2_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c2_1(a348) | c3_1(a348) | (~c0_1(a348)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a367) | c3_1(a348) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a347)) | (~c0_1(a348)) | c2_1(a348)))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[800])).
% 0.63/0.79 tff(802,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a347)) | (~c0_1(a347)) | (~c3_1(a347)) | c2_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c2_1(a348) | c3_1(a348) | (~c0_1(a348)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a367) | c3_1(a348) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a347)) | (~c0_1(a348)) | c2_1(a348))),
% 0.63/0.79 inference(transitivity,[status(thm)],[801, 799])).
% 0.63/0.79 tff(803,plain,
% 0.63/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a347)) | (~c0_1(a347)) | (~c3_1(a347)) | c2_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c2_1(a348) | c3_1(a348) | (~c0_1(a348)))),
% 0.63/0.79 inference(quant_inst,[status(thm)],[])).
% 0.63/0.79 tff(804,plain,
% 0.63/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a367) | c3_1(a348) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a347)) | (~c0_1(a348)) | c2_1(a348)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[803, 802])).
% 0.63/0.79 tff(805,plain,
% 0.63/0.79 ((~c0_1(a367)) | (~c0_1(a347))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[804, 134, 781, 765, 738, 737, 780, 751, 798, 772])).
% 0.63/0.79 tff(806,plain,
% 0.63/0.79 (~c0_1(a347)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[805, 788])).
% 0.63/0.79 tff(807,plain,
% 0.63/0.79 (~c1_1(a367)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[347, 779])).
% 0.63/0.79 tff(808,plain,
% 0.63/0.79 (((~![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | c0_1(a347))) <=> ((~![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | c0_1(a347))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(809,plain,
% 0.63/0.79 (((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c1_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c0_1(a347) | c1_1(a347) | (~c2_1(a347))) <=> (c1_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | c0_1(a347))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(810,plain,
% 0.63/0.79 (((~![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c1_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c0_1(a347) | c1_1(a347) | (~c2_1(a347)))) <=> ((~![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | c0_1(a347)))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[809])).
% 0.63/0.79 tff(811,plain,
% 0.63/0.79 (((~![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c1_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c0_1(a347) | c1_1(a347) | (~c2_1(a347)))) <=> ((~![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | c0_1(a347))),
% 0.63/0.79 inference(transitivity,[status(thm)],[810, 808])).
% 0.63/0.79 tff(812,plain,
% 0.63/0.79 ((~![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c1_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c0_1(a347) | c1_1(a347) | (~c2_1(a347)))),
% 0.63/0.79 inference(quant_inst,[status(thm)],[])).
% 0.63/0.79 tff(813,plain,
% 0.63/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | c0_1(a347)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[812, 811])).
% 0.63/0.79 tff(814,plain,
% 0.63/0.79 ($false),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[813, 134, 781, 738, 737, 807, 736, 691, 806, 788])).
% 0.63/0.79 tff(815,plain,(hskp5), inference(lemma,lemma(discharge,[]))).
% 0.63/0.79 tff(816,plain,
% 0.63/0.79 (((~hskp5) | (~c3_1(a327))) <=> ((~hskp5) | (~c3_1(a327)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(817,plain,
% 0.63/0.79 (((~c3_1(a327)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a327)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(818,axiom,((~c3_1(a327)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 0.63/0.79 tff(819,plain,
% 0.63/0.79 ((~hskp5) | (~c3_1(a327))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[818, 817])).
% 0.63/0.79 tff(820,plain,
% 0.63/0.79 ((~hskp5) | (~c3_1(a327))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[819, 816])).
% 0.63/0.79 tff(821,plain,
% 0.63/0.79 (~c3_1(a327)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[820, 815])).
% 0.63/0.79 tff(822,plain,
% 0.63/0.79 (((~hskp5) | c1_1(a327)) <=> ((~hskp5) | c1_1(a327))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(823,axiom,((~hskp5) | c1_1(a327)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 0.63/0.79 tff(824,plain,
% 0.63/0.79 ((~hskp5) | c1_1(a327)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[823, 822])).
% 0.63/0.79 tff(825,plain,
% 0.63/0.79 ((~hskp5) | c1_1(a327)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[824, 822])).
% 0.63/0.79 tff(826,plain,
% 0.63/0.79 ((~hskp5) | c1_1(a327)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[825, 822])).
% 0.63/0.79 tff(827,plain,
% 0.63/0.79 ((~hskp5) | c1_1(a327)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[826, 822])).
% 0.63/0.79 tff(828,plain,
% 0.63/0.79 ((~hskp5) | c1_1(a327)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[827, 822])).
% 0.63/0.79 tff(829,plain,
% 0.63/0.79 (c1_1(a327)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[828, 815])).
% 0.63/0.79 tff(830,plain,
% 0.63/0.79 (((~hskp5) | c0_1(a327)) <=> ((~hskp5) | c0_1(a327))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(831,axiom,((~hskp5) | c0_1(a327)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.63/0.79 tff(832,plain,
% 0.63/0.79 ((~hskp5) | c0_1(a327)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[831, 830])).
% 0.63/0.79 tff(833,plain,
% 0.63/0.79 ((~hskp5) | c0_1(a327)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[832, 830])).
% 0.63/0.79 tff(834,plain,
% 0.63/0.79 ((~hskp5) | c0_1(a327)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[833, 830])).
% 0.63/0.79 tff(835,plain,
% 0.63/0.79 ((~hskp5) | c0_1(a327)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[834, 830])).
% 0.63/0.80 tff(836,plain,
% 0.63/0.80 ((~hskp5) | c0_1(a327)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[835, 830])).
% 0.63/0.80 tff(837,plain,
% 0.63/0.80 (c0_1(a327)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[836, 815])).
% 0.63/0.80 tff(838,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | c1_1(a338) | c2_1(a338) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c3_1(a338))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c1_1(a338) | c2_1(a338) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c3_1(a338))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(839,plain,
% 0.63/0.80 ((hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a338) | c1_1(a338) | c3_1(a338)) <=> (hskp21 | c1_1(a338) | c2_1(a338) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c3_1(a338))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(840,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a338) | c1_1(a338) | c3_1(a338))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | c1_1(a338) | c2_1(a338) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c3_1(a338)))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[839])).
% 0.63/0.80 tff(841,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a338) | c1_1(a338) | c3_1(a338))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c1_1(a338) | c2_1(a338) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c3_1(a338))),
% 0.63/0.80 inference(transitivity,[status(thm)],[840, 838])).
% 0.63/0.80 tff(842,plain,
% 0.63/0.80 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a338) | c1_1(a338) | c3_1(a338))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(843,plain,
% 0.63/0.80 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c1_1(a338) | c2_1(a338) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c3_1(a338)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[842, 841])).
% 0.63/0.80 tff(844,plain,
% 0.63/0.80 (hskp21),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[843, 134, 837, 829, 70, 64, 821, 10, 172])).
% 0.63/0.80 tff(845,plain,
% 0.63/0.80 (((~hskp21) | (~c2_1(a359))) <=> ((~hskp21) | (~c2_1(a359)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(846,plain,
% 0.63/0.80 (((~c2_1(a359)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a359)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(847,axiom,((~c2_1(a359)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 0.63/0.80 tff(848,plain,
% 0.63/0.80 ((~hskp21) | (~c2_1(a359))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[847, 846])).
% 0.63/0.80 tff(849,plain,
% 0.63/0.80 ((~hskp21) | (~c2_1(a359))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[848, 845])).
% 0.63/0.80 tff(850,plain,
% 0.63/0.80 (~c2_1(a359)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[849, 844])).
% 0.63/0.80 tff(851,plain,
% 0.63/0.80 (((~hskp21) | (~c0_1(a359))) <=> ((~hskp21) | (~c0_1(a359)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(852,plain,
% 0.63/0.80 (((~c0_1(a359)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a359)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(853,axiom,((~c0_1(a359)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 0.63/0.80 tff(854,plain,
% 0.63/0.80 ((~hskp21) | (~c0_1(a359))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[853, 852])).
% 0.63/0.80 tff(855,plain,
% 0.63/0.80 ((~hskp21) | (~c0_1(a359))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[854, 851])).
% 0.63/0.80 tff(856,plain,
% 0.63/0.80 (~c0_1(a359)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[855, 844])).
% 0.63/0.80 tff(857,plain,
% 0.63/0.80 (((~hskp21) | c3_1(a359)) <=> ((~hskp21) | c3_1(a359))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(858,axiom,((~hskp21) | c3_1(a359)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 0.63/0.80 tff(859,plain,
% 0.63/0.80 ((~hskp21) | c3_1(a359)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[858, 857])).
% 0.63/0.80 tff(860,plain,
% 0.63/0.80 ((~hskp21) | c3_1(a359)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[859, 857])).
% 0.63/0.80 tff(861,plain,
% 0.63/0.80 ((~hskp21) | c3_1(a359)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[860, 857])).
% 0.63/0.80 tff(862,plain,
% 0.63/0.80 ((~hskp21) | c3_1(a359)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[861, 857])).
% 0.63/0.80 tff(863,plain,
% 0.63/0.80 ((~hskp21) | c3_1(a359)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[862, 857])).
% 0.63/0.80 tff(864,plain,
% 0.63/0.80 (c3_1(a359)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[863, 844])).
% 0.63/0.80 tff(865,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a359) | c2_1(a359) | c0_1(a338) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a359)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a359) | c2_1(a359) | c0_1(a338) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a359)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(866,plain,
% 0.63/0.80 ((hskp1 | (~ndr1_0) | c2_1(a359) | c0_1(a359) | (~c3_1(a359)) | c2_1(a338) | c1_1(a338) | c0_1(a338)) <=> (hskp1 | c0_1(a359) | c2_1(a359) | c0_1(a338) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a359)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(867,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a359) | c0_1(a359) | (~c3_1(a359)) | c2_1(a338) | c1_1(a338) | c0_1(a338))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a359) | c2_1(a359) | c0_1(a338) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a359))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[866])).
% 0.63/0.80 tff(868,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a359) | c0_1(a359) | (~c3_1(a359)) | c2_1(a338) | c1_1(a338) | c0_1(a338))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a359) | c2_1(a359) | c0_1(a338) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a359)))),
% 0.63/0.80 inference(transitivity,[status(thm)],[867, 865])).
% 0.63/0.80 tff(869,plain,
% 0.63/0.80 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a359) | c0_1(a359) | (~c3_1(a359)) | c2_1(a338) | c1_1(a338) | c0_1(a338))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(870,plain,
% 0.63/0.80 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a359) | c2_1(a359) | c0_1(a338) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a359))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[869, 868])).
% 0.63/0.80 tff(871,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[870, 134, 46, 864, 856, 850, 76, 70, 64, 45])).
% 0.63/0.80 tff(872,plain,(hskp1 | hskp25), inference(lemma,lemma(discharge,[]))).
% 0.63/0.80 tff(873,plain,
% 0.63/0.80 (hskp1),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[872, 21])).
% 0.63/0.80 tff(874,plain,
% 0.63/0.80 (~c3_1(a323)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[587, 873])).
% 0.63/0.80 tff(875,plain,
% 0.63/0.80 (~c2_1(a323)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[593, 873])).
% 0.63/0.80 tff(876,plain,
% 0.63/0.80 (~c1_1(a323)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[599, 873])).
% 0.63/0.80 tff(877,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | c3_1(a327) | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c3_1(a327) | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(878,plain,
% 0.63/0.80 ((hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a323) | c1_1(a323) | c3_1(a323)) <=> (hskp21 | c3_1(a327) | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(879,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a323) | c1_1(a323) | c3_1(a323))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | c3_1(a327) | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[878])).
% 0.63/0.80 tff(880,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a323) | c1_1(a323) | c3_1(a323))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c3_1(a327) | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)))),
% 0.63/0.80 inference(transitivity,[status(thm)],[879, 877])).
% 0.63/0.80 tff(881,plain,
% 0.63/0.80 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a323) | c1_1(a323) | c3_1(a323))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(882,plain,
% 0.63/0.80 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c3_1(a327) | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[881, 880])).
% 0.63/0.80 tff(883,plain,
% 0.63/0.80 (hskp21),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[882, 134, 837, 829, 821, 876, 875, 874, 10])).
% 0.63/0.80 tff(884,plain,
% 0.63/0.80 (~c2_1(a359)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[849, 883])).
% 0.63/0.80 tff(885,plain,
% 0.63/0.80 (c3_1(a359)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[863, 883])).
% 0.63/0.80 tff(886,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a359) | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349)) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a359) | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349)) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(887,plain,
% 0.63/0.80 (((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a359) | c1_1(a359) | (~c3_1(a359))) <=> (c2_1(a359) | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349)) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(888,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a359) | c1_1(a359) | (~c3_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a359) | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349)) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[887])).
% 0.63/0.80 tff(889,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a359) | c1_1(a359) | (~c3_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a359) | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349)) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.63/0.80 inference(transitivity,[status(thm)],[888, 886])).
% 0.63/0.80 tff(890,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a359) | c1_1(a359) | (~c3_1(a359)))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(891,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a359) | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349)) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[890, 889])).
% 0.63/0.80 tff(892,plain,
% 0.63/0.80 (c1_1(a359)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[891, 134, 165, 157, 149, 885, 92, 84, 884, 35, 20])).
% 0.63/0.80 tff(893,plain,
% 0.63/0.80 (~c0_1(a359)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[855, 883])).
% 0.63/0.80 tff(894,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a359) | c2_1(a359) | c3_1(a327) | (~ndr1_0) | (~c1_1(a327)) | (~c2_1(a327)) | (~c1_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | c3_1(a327) | (~ndr1_0) | (~c1_1(a327)) | (~c2_1(a327)) | (~c1_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(895,plain,
% 0.63/0.80 (((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a327) | (~c1_1(a327)) | (~c2_1(a327)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359))) <=> (c0_1(a359) | c2_1(a359) | c3_1(a327) | (~ndr1_0) | (~c1_1(a327)) | (~c2_1(a327)) | (~c1_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(896,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a327) | (~c1_1(a327)) | (~c2_1(a327)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a359) | c2_1(a359) | c3_1(a327) | (~ndr1_0) | (~c1_1(a327)) | (~c2_1(a327)) | (~c1_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[895])).
% 0.63/0.80 tff(897,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a327) | (~c1_1(a327)) | (~c2_1(a327)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | c3_1(a327) | (~ndr1_0) | (~c1_1(a327)) | (~c2_1(a327)) | (~c1_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.63/0.80 inference(transitivity,[status(thm)],[896, 894])).
% 0.63/0.80 tff(898,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a327) | (~c1_1(a327)) | (~c2_1(a327)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(899,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | c3_1(a327) | (~ndr1_0) | (~c1_1(a327)) | (~c2_1(a327)) | (~c1_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[898, 897])).
% 0.63/0.80 tff(900,plain,
% 0.63/0.80 (~c2_1(a327)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[899, 134, 165, 157, 149, 829, 893, 884, 821, 203, 892])).
% 0.63/0.80 tff(901,plain,
% 0.63/0.80 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(902,plain,
% 0.63/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.63/0.80 inference(quant_intro,[status(thm)],[901])).
% 0.63/0.80 tff(903,plain,
% 0.63/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(904,plain,
% 0.63/0.80 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(905,plain,
% 0.63/0.80 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.63/0.80 inference(quant_intro,[status(thm)],[904])).
% 0.63/0.80 tff(906,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 0.63/0.80 tff(907,plain,
% 0.63/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[906, 905])).
% 0.63/0.80 tff(908,plain,
% 0.63/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[907, 903])).
% 0.63/0.80 tff(909,plain,(
% 0.63/0.80 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.63/0.80 inference(skolemize,[status(sab)],[908])).
% 0.63/0.80 tff(910,plain,
% 0.63/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[909, 902])).
% 0.63/0.80 tff(911,plain,
% 0.63/0.80 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(912,plain,
% 0.63/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.63/0.80 inference(quant_intro,[status(thm)],[911])).
% 0.63/0.80 tff(913,plain,
% 0.63/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(914,plain,
% 0.63/0.80 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(915,plain,
% 0.63/0.80 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.63/0.80 inference(quant_intro,[status(thm)],[914])).
% 0.63/0.80 tff(916,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 0.63/0.80 tff(917,plain,
% 0.63/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[916, 915])).
% 0.63/0.80 tff(918,plain,
% 0.63/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[917, 913])).
% 0.63/0.80 tff(919,plain,(
% 0.63/0.80 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.63/0.80 inference(skolemize,[status(sab)],[918])).
% 0.63/0.80 tff(920,plain,
% 0.63/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[919, 912])).
% 0.63/0.80 tff(921,plain,
% 0.63/0.80 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(922,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.63/0.80 inference(quant_intro,[status(thm)],[921])).
% 0.63/0.80 tff(923,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(924,plain,
% 0.63/0.80 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp6))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(925,plain,
% 0.63/0.80 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.63/0.80 inference(quant_intro,[status(thm)],[924])).
% 0.63/0.80 tff(926,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 0.63/0.80 tff(927,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[926, 925])).
% 0.63/0.80 tff(928,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[927, 923])).
% 0.63/0.80 tff(929,plain,(
% 0.63/0.80 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.63/0.80 inference(skolemize,[status(sab)],[928])).
% 0.63/0.80 tff(930,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[929, 922])).
% 0.63/0.80 tff(931,plain,
% 0.63/0.80 (^[U: $i] : refl((hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(932,plain,
% 0.63/0.80 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[931])).
% 0.63/0.81 tff(933,plain,
% 0.63/0.81 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(934,plain,
% 0.63/0.81 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp2) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp2))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp2) | hskp1) <=> ((hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp1))), rewrite(((hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp1) <=> (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp2) | hskp1) <=> (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(935,plain,
% 0.63/0.81 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp2) | hskp1) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[934])).
% 0.63/0.81 tff(936,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp2) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 0.63/0.81 tff(937,plain,
% 0.63/0.81 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[936, 935])).
% 0.63/0.81 tff(938,plain,
% 0.63/0.81 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[937, 933])).
% 0.63/0.81 tff(939,plain,(
% 0.63/0.81 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.63/0.81 inference(skolemize,[status(sab)],[938])).
% 0.63/0.81 tff(940,plain,
% 0.63/0.81 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[939, 932])).
% 0.63/0.81 tff(941,plain,
% 0.63/0.81 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | (~c0_1(a343)) | c3_1(a343) | (~c2_1(a343)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp2 | hskp1 | (~ndr1_0) | (~c0_1(a343)) | c3_1(a343) | (~c2_1(a343)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(942,plain,
% 0.63/0.81 ((hskp2 | hskp1 | (~ndr1_0) | c3_1(a343) | (~c2_1(a343)) | (~c0_1(a343))) <=> (hskp2 | hskp1 | (~ndr1_0) | (~c0_1(a343)) | c3_1(a343) | (~c2_1(a343)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(943,plain,
% 0.63/0.81 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a343) | (~c2_1(a343)) | (~c0_1(a343)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | (~c0_1(a343)) | c3_1(a343) | (~c2_1(a343))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[942])).
% 0.63/0.81 tff(944,plain,
% 0.63/0.81 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a343) | (~c2_1(a343)) | (~c0_1(a343)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp2 | hskp1 | (~ndr1_0) | (~c0_1(a343)) | c3_1(a343) | (~c2_1(a343)))),
% 0.63/0.81 inference(transitivity,[status(thm)],[943, 941])).
% 0.63/0.81 tff(945,plain,
% 0.63/0.81 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a343) | (~c2_1(a343)) | (~c0_1(a343)))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(946,plain,
% 0.63/0.81 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp2 | hskp1 | (~ndr1_0) | (~c0_1(a343)) | c3_1(a343) | (~c2_1(a343))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[945, 944])).
% 0.63/0.81 tff(947,plain,
% 0.63/0.81 (hskp2 | hskp1 | c3_1(a343)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[946, 134, 165, 149, 940])).
% 0.63/0.81 tff(948,plain,
% 0.63/0.81 (c3_1(a343)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[947, 46, 225])).
% 0.63/0.81 tff(949,plain,
% 0.63/0.81 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp2 | hskp1 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c2_1(a327)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp2 | hskp1 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c2_1(a327)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(950,plain,
% 0.63/0.81 ((hskp2 | hskp1 | (~ndr1_0) | c3_1(a327) | (~c2_1(a327)) | (~c0_1(a327))) <=> (hskp2 | hskp1 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c2_1(a327)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(951,plain,
% 0.63/0.81 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a327) | (~c2_1(a327)) | (~c0_1(a327)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp2 | hskp1 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c2_1(a327))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[950])).
% 0.63/0.81 tff(952,plain,
% 0.63/0.81 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a327) | (~c2_1(a327)) | (~c0_1(a327)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp2 | hskp1 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c2_1(a327)))),
% 0.63/0.81 inference(transitivity,[status(thm)],[951, 949])).
% 0.63/0.81 tff(953,plain,
% 0.63/0.81 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a327) | (~c2_1(a327)) | (~c0_1(a327)))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(954,plain,
% 0.63/0.81 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp2 | hskp1 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c2_1(a327))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[953, 952])).
% 0.63/0.81 tff(955,plain,
% 0.63/0.81 (hskp2 | hskp1 | (~c2_1(a327))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[954, 134, 837, 821, 940])).
% 0.63/0.81 tff(956,plain,
% 0.63/0.81 (~c2_1(a327)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[955, 46, 225])).
% 0.63/0.81 tff(957,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a349) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a349)) | (~c3_1(a349)) | (~c0_1(a343)) | (~c3_1(a343)) | (~c2_1(a343)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a349) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a349)) | (~c3_1(a349)) | (~c0_1(a343)) | (~c3_1(a343)) | (~c2_1(a343)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(958,plain,
% 0.63/0.81 (((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c3_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c0_1(a349)) | c2_1(a327) | c3_1(a327) | (~c0_1(a327))) <=> (c2_1(a349) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a349)) | (~c3_1(a349)) | (~c0_1(a343)) | (~c3_1(a343)) | (~c2_1(a343)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(959,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c3_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c0_1(a349)) | c2_1(a327) | c3_1(a327) | (~c0_1(a327)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a349) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a349)) | (~c3_1(a349)) | (~c0_1(a343)) | (~c3_1(a343)) | (~c2_1(a343))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[958])).
% 0.63/0.81 tff(960,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c3_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c0_1(a349)) | c2_1(a327) | c3_1(a327) | (~c0_1(a327)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a349) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a349)) | (~c3_1(a349)) | (~c0_1(a343)) | (~c3_1(a343)) | (~c2_1(a343)))),
% 0.63/0.81 inference(transitivity,[status(thm)],[959, 957])).
% 0.63/0.81 tff(961,plain,
% 0.63/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c3_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c0_1(a349)) | c2_1(a327) | c3_1(a327) | (~c0_1(a327)))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(962,plain,
% 0.63/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a349) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a349)) | (~c3_1(a349)) | (~c0_1(a343)) | (~c3_1(a343)) | (~c2_1(a343))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[961, 960])).
% 0.63/0.81 tff(963,plain,
% 0.63/0.81 (~c0_1(a349)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[962, 134, 165, 149, 84, 837, 35, 821, 798, 956, 948])).
% 0.63/0.81 tff(964,plain,
% 0.63/0.81 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c2_1(a349) | c0_1(a338) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | c0_1(a349) | (~c3_1(a349)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c2_1(a349) | c0_1(a338) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | c0_1(a349) | (~c3_1(a349)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(965,plain,
% 0.63/0.81 ((hskp1 | (~ndr1_0) | c2_1(a349) | c0_1(a349) | (~c3_1(a349)) | c2_1(a338) | c1_1(a338) | c0_1(a338)) <=> (hskp1 | c2_1(a349) | c0_1(a338) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | c0_1(a349) | (~c3_1(a349)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(966,plain,
% 0.63/0.81 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a349) | c0_1(a349) | (~c3_1(a349)) | c2_1(a338) | c1_1(a338) | c0_1(a338))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c2_1(a349) | c0_1(a338) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | c0_1(a349) | (~c3_1(a349))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[965])).
% 0.63/0.81 tff(967,plain,
% 0.63/0.81 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a349) | c0_1(a349) | (~c3_1(a349)) | c2_1(a338) | c1_1(a338) | c0_1(a338))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c2_1(a349) | c0_1(a338) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | c0_1(a349) | (~c3_1(a349)))),
% 0.63/0.81 inference(transitivity,[status(thm)],[966, 964])).
% 0.63/0.81 tff(968,plain,
% 0.63/0.81 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a349) | c0_1(a349) | (~c3_1(a349)) | c2_1(a338) | c1_1(a338) | c0_1(a338))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(969,plain,
% 0.63/0.81 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c2_1(a349) | c0_1(a338) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | c0_1(a349) | (~c3_1(a349))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[968, 967])).
% 0.63/0.81 tff(970,plain,
% 0.63/0.81 ($false),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[969, 134, 46, 84, 35, 76, 70, 64, 45, 963])).
% 0.63/0.81 tff(971,plain,(hskp1 | hskp2 | hskp25), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(972,plain,
% 0.63/0.81 (hskp1),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[971, 225, 21])).
% 0.63/0.81 tff(973,plain,
% 0.63/0.81 (~c3_1(a323)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[587, 972])).
% 0.63/0.81 tff(974,plain,
% 0.63/0.81 (~c2_1(a323)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[593, 972])).
% 0.63/0.81 tff(975,plain,
% 0.63/0.81 (~c1_1(a323)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[599, 972])).
% 0.63/0.81 tff(976,plain,
% 0.63/0.81 (hskp21),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[882, 134, 837, 829, 821, 975, 974, 973, 10])).
% 0.63/0.81 tff(977,plain,
% 0.63/0.81 (~c2_1(a359)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[849, 976])).
% 0.63/0.81 tff(978,plain,
% 0.63/0.81 (c3_1(a359)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[863, 976])).
% 0.63/0.81 tff(979,plain,
% 0.63/0.81 (c1_1(a359)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[891, 134, 165, 157, 149, 978, 92, 84, 977, 35, 20])).
% 0.63/0.81 tff(980,plain,
% 0.63/0.81 (~c0_1(a359)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[855, 976])).
% 0.63/0.81 tff(981,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a359) | c2_1(a359) | c1_1(a323) | c2_1(a323) | (~ndr1_0) | (~c0_1(a323)) | (~c3_1(a359)) | (~c1_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a359) | c2_1(a359) | c1_1(a323) | c2_1(a323) | (~ndr1_0) | (~c0_1(a323)) | (~c3_1(a359)) | (~c1_1(a359)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(982,plain,
% 0.63/0.81 (((~ndr1_0) | c2_1(a359) | (~c3_1(a359)) | (~c1_1(a359)) | c2_1(a323) | c1_1(a323) | (~c0_1(a323)) | c0_1(a359) | (~c1_1(a359)) | (~c3_1(a359))) <=> (c0_1(a359) | c2_1(a359) | c1_1(a323) | c2_1(a323) | (~ndr1_0) | (~c0_1(a323)) | (~c3_1(a359)) | (~c1_1(a359)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(983,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a359) | (~c3_1(a359)) | (~c1_1(a359)) | c2_1(a323) | c1_1(a323) | (~c0_1(a323)) | c0_1(a359) | (~c1_1(a359)) | (~c3_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a359) | c2_1(a359) | c1_1(a323) | c2_1(a323) | (~ndr1_0) | (~c0_1(a323)) | (~c3_1(a359)) | (~c1_1(a359))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[982])).
% 0.63/0.81 tff(984,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a359) | (~c3_1(a359)) | (~c1_1(a359)) | c2_1(a323) | c1_1(a323) | (~c0_1(a323)) | c0_1(a359) | (~c1_1(a359)) | (~c3_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a359) | c2_1(a359) | c1_1(a323) | c2_1(a323) | (~ndr1_0) | (~c0_1(a323)) | (~c3_1(a359)) | (~c1_1(a359)))),
% 0.63/0.81 inference(transitivity,[status(thm)],[983, 981])).
% 0.63/0.81 tff(985,plain,
% 0.63/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a359) | (~c3_1(a359)) | (~c1_1(a359)) | c2_1(a323) | c1_1(a323) | (~c0_1(a323)) | c0_1(a359) | (~c1_1(a359)) | (~c3_1(a359)))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(986,plain,
% 0.63/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a359) | c2_1(a359) | c1_1(a323) | c2_1(a323) | (~ndr1_0) | (~c0_1(a323)) | (~c3_1(a359)) | (~c1_1(a359))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[985, 984])).
% 0.63/0.81 tff(987,plain,
% 0.63/0.81 ((~c0_1(a323)) | (~c1_1(a359))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[986, 134, 978, 980, 977, 975, 974, 920])).
% 0.63/0.81 tff(988,plain,
% 0.63/0.81 (~c0_1(a323)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[987, 979])).
% 0.63/0.81 tff(989,plain,
% 0.63/0.81 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(990,plain,
% 0.63/0.81 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[989])).
% 0.63/0.81 tff(991,plain,
% 0.63/0.81 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(992,plain,
% 0.63/0.81 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(993,plain,
% 0.63/0.81 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[992])).
% 0.63/0.81 tff(994,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 0.63/0.81 tff(995,plain,
% 0.63/0.81 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[994, 993])).
% 0.63/0.81 tff(996,plain,
% 0.63/0.81 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[995, 991])).
% 0.63/0.81 tff(997,plain,(
% 0.63/0.81 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.63/0.81 inference(skolemize,[status(sab)],[996])).
% 0.63/0.81 tff(998,plain,
% 0.63/0.81 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[997, 990])).
% 0.63/0.81 tff(999,plain,
% 0.63/0.81 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c1_1(a323) | c3_1(a323) | (~ndr1_0) | c0_1(a323) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c1_1(a323) | c3_1(a323) | (~ndr1_0) | c0_1(a323) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1000,plain,
% 0.63/0.81 ((hskp6 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c1_1(a323) | c0_1(a323) | c3_1(a323)) <=> (hskp6 | c1_1(a323) | c3_1(a323) | (~ndr1_0) | c0_1(a323) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1001,plain,
% 0.63/0.81 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c1_1(a323) | c0_1(a323) | c3_1(a323))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c1_1(a323) | c3_1(a323) | (~ndr1_0) | c0_1(a323) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[1000])).
% 0.63/0.81 tff(1002,plain,
% 0.63/0.81 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c1_1(a323) | c0_1(a323) | c3_1(a323))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c1_1(a323) | c3_1(a323) | (~ndr1_0) | c0_1(a323) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.63/0.81 inference(transitivity,[status(thm)],[1001, 999])).
% 0.63/0.81 tff(1003,plain,
% 0.63/0.81 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c1_1(a323) | c0_1(a323) | c3_1(a323))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(1004,plain,
% 0.63/0.81 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c1_1(a323) | c3_1(a323) | (~ndr1_0) | c0_1(a323) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1003, 1002])).
% 0.63/0.81 tff(1005,plain,
% 0.63/0.81 (hskp6 | c0_1(a323)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1004, 134, 165, 157, 149, 975, 973, 930])).
% 0.63/0.81 tff(1006,plain,
% 0.63/0.81 (hskp6),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1005, 988])).
% 0.63/0.81 tff(1007,plain,
% 0.63/0.81 (((~hskp6) | (~c3_1(a329))) <=> ((~hskp6) | (~c3_1(a329)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1008,plain,
% 0.63/0.81 (((~c3_1(a329)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a329)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1009,axiom,((~c3_1(a329)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 0.63/0.81 tff(1010,plain,
% 0.63/0.81 ((~hskp6) | (~c3_1(a329))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1009, 1008])).
% 0.63/0.81 tff(1011,plain,
% 0.63/0.81 ((~hskp6) | (~c3_1(a329))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1010, 1007])).
% 0.63/0.81 tff(1012,plain,
% 0.63/0.81 (~c3_1(a329)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1011, 1006])).
% 0.63/0.81 tff(1013,plain,
% 0.63/0.81 (((~hskp6) | (~c1_1(a329))) <=> ((~hskp6) | (~c1_1(a329)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1014,plain,
% 0.63/0.81 (((~c1_1(a329)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a329)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1015,axiom,((~c1_1(a329)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 0.63/0.81 tff(1016,plain,
% 0.63/0.81 ((~hskp6) | (~c1_1(a329))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1015, 1014])).
% 0.63/0.81 tff(1017,plain,
% 0.63/0.81 ((~hskp6) | (~c1_1(a329))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1016, 1013])).
% 0.63/0.81 tff(1018,plain,
% 0.63/0.81 (~c1_1(a329)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1017, 1006])).
% 0.63/0.81 tff(1019,plain,
% 0.63/0.81 (((~hskp6) | c2_1(a329)) <=> ((~hskp6) | c2_1(a329))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1020,axiom,((~hskp6) | c2_1(a329)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 0.63/0.81 tff(1021,plain,
% 0.63/0.81 ((~hskp6) | c2_1(a329)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1020, 1019])).
% 0.63/0.81 tff(1022,plain,
% 0.63/0.81 ((~hskp6) | c2_1(a329)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1021, 1019])).
% 0.63/0.81 tff(1023,plain,
% 0.63/0.81 ((~hskp6) | c2_1(a329)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1022, 1019])).
% 0.63/0.81 tff(1024,plain,
% 0.63/0.81 ((~hskp6) | c2_1(a329)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1023, 1019])).
% 0.63/0.81 tff(1025,plain,
% 0.63/0.81 ((~hskp6) | c2_1(a329)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1024, 1019])).
% 0.63/0.81 tff(1026,plain,
% 0.63/0.81 (c2_1(a329)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1025, 1006])).
% 0.63/0.81 tff(1027,plain,
% 0.63/0.81 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a329) | c3_1(a329) | c1_1(a323) | c2_1(a323) | (~ndr1_0) | c0_1(a323) | (~c2_1(a329)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a329) | c3_1(a329) | c1_1(a323) | c2_1(a323) | (~ndr1_0) | c0_1(a323) | (~c2_1(a329)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1028,plain,
% 0.63/0.81 ((hskp2 | (~ndr1_0) | c1_1(a329) | c3_1(a329) | (~c2_1(a329)) | c2_1(a323) | c1_1(a323) | c0_1(a323)) <=> (hskp2 | c1_1(a329) | c3_1(a329) | c1_1(a323) | c2_1(a323) | (~ndr1_0) | c0_1(a323) | (~c2_1(a329)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1029,plain,
% 0.63/0.81 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a329) | c3_1(a329) | (~c2_1(a329)) | c2_1(a323) | c1_1(a323) | c0_1(a323))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a329) | c3_1(a329) | c1_1(a323) | c2_1(a323) | (~ndr1_0) | c0_1(a323) | (~c2_1(a329))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[1028])).
% 0.63/0.81 tff(1030,plain,
% 0.63/0.81 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a329) | c3_1(a329) | (~c2_1(a329)) | c2_1(a323) | c1_1(a323) | c0_1(a323))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a329) | c3_1(a329) | c1_1(a323) | c2_1(a323) | (~ndr1_0) | c0_1(a323) | (~c2_1(a329)))),
% 0.63/0.81 inference(transitivity,[status(thm)],[1029, 1027])).
% 0.63/0.81 tff(1031,plain,
% 0.63/0.81 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a329) | c3_1(a329) | (~c2_1(a329)) | c2_1(a323) | c1_1(a323) | c0_1(a323))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(1032,plain,
% 0.63/0.81 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a329) | c3_1(a329) | c1_1(a323) | c2_1(a323) | (~ndr1_0) | c0_1(a323) | (~c2_1(a329))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1031, 1030])).
% 0.63/0.81 tff(1033,plain,
% 0.63/0.81 ($false),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1032, 134, 225, 1026, 1018, 1012, 975, 974, 998, 988])).
% 0.63/0.81 tff(1034,plain,(hskp2 | hskp25), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(1035,plain,
% 0.63/0.81 (hskp2),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1034, 21])).
% 0.63/0.81 tff(1036,plain,
% 0.63/0.81 (~c3_1(a324)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[627, 1035])).
% 0.63/0.81 tff(1037,plain,
% 0.63/0.81 (~c1_1(a324)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[633, 1035])).
% 0.63/0.82 tff(1038,plain,
% 0.63/0.82 (~c0_1(a324)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[657, 1035])).
% 0.63/0.82 tff(1039,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c0_1(a324) | c1_1(a324) | c3_1(a324) | (~ndr1_0) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a324) | c1_1(a324) | c3_1(a324) | (~ndr1_0) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1040,plain,
% 0.63/0.82 ((hskp6 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c1_1(a324) | c0_1(a324) | c3_1(a324)) <=> (hskp6 | c0_1(a324) | c1_1(a324) | c3_1(a324) | (~ndr1_0) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1041,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c1_1(a324) | c0_1(a324) | c3_1(a324))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c0_1(a324) | c1_1(a324) | c3_1(a324) | (~ndr1_0) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1040])).
% 0.63/0.82 tff(1042,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c1_1(a324) | c0_1(a324) | c3_1(a324))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a324) | c1_1(a324) | c3_1(a324) | (~ndr1_0) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1041, 1039])).
% 0.63/0.82 tff(1043,plain,
% 0.63/0.82 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c1_1(a324) | c0_1(a324) | c3_1(a324))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1044,plain,
% 0.63/0.82 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a324) | c1_1(a324) | c3_1(a324) | (~ndr1_0) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1043, 1042])).
% 0.63/0.82 tff(1045,plain,
% 0.63/0.82 (hskp6),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1044, 134, 165, 157, 149, 1038, 1037, 1036, 930])).
% 0.63/0.82 tff(1046,plain,
% 0.63/0.82 (~c1_1(a329)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1017, 1045])).
% 0.63/0.82 tff(1047,plain,
% 0.63/0.82 (c2_1(a329)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1025, 1045])).
% 0.63/0.82 tff(1048,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a359) | c2_1(a359) | c1_1(a329) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a329)) | (~c2_1(a329)) | (~c1_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | c1_1(a329) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a329)) | (~c2_1(a329)) | (~c1_1(a359)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1049,plain,
% 0.63/0.82 (((~ndr1_0) | c2_1(a327) | c3_1(a327) | (~c0_1(a327)) | c1_1(a329) | (~c0_1(a329)) | (~c2_1(a329)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359))) <=> (c0_1(a359) | c2_1(a359) | c1_1(a329) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a329)) | (~c2_1(a329)) | (~c1_1(a359)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1050,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a327) | c3_1(a327) | (~c0_1(a327)) | c1_1(a329) | (~c0_1(a329)) | (~c2_1(a329)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a359) | c2_1(a359) | c1_1(a329) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a329)) | (~c2_1(a329)) | (~c1_1(a359))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1049])).
% 0.63/0.82 tff(1051,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a327) | c3_1(a327) | (~c0_1(a327)) | c1_1(a329) | (~c0_1(a329)) | (~c2_1(a329)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | c1_1(a329) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a329)) | (~c2_1(a329)) | (~c1_1(a359)))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1050, 1048])).
% 0.63/0.82 tff(1052,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a327) | c3_1(a327) | (~c0_1(a327)) | c1_1(a329) | (~c0_1(a329)) | (~c2_1(a329)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1053,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | c1_1(a329) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a329)) | (~c2_1(a329)) | (~c1_1(a359))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1052, 1051])).
% 0.63/0.82 tff(1054,plain,
% 0.63/0.82 (~c0_1(a329)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1053, 134, 1047, 837, 893, 884, 1046, 821, 910, 900, 892])).
% 0.63/0.82 tff(1055,plain,
% 0.63/0.82 (~c3_1(a329)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1011, 1045])).
% 0.63/0.82 tff(1056,plain,
% 0.63/0.82 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | c3_1(a329) | (~ndr1_0) | c0_1(a329) | (~c2_1(a329)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp13 | c3_1(a329) | (~ndr1_0) | c0_1(a329) | (~c2_1(a329)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1057,plain,
% 0.63/0.82 ((hskp14 | hskp13 | (~ndr1_0) | c0_1(a329) | c3_1(a329) | (~c2_1(a329))) <=> (hskp14 | hskp13 | c3_1(a329) | (~ndr1_0) | c0_1(a329) | (~c2_1(a329)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1058,plain,
% 0.63/0.82 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a329) | c3_1(a329) | (~c2_1(a329)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | c3_1(a329) | (~ndr1_0) | c0_1(a329) | (~c2_1(a329))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1057])).
% 0.63/0.82 tff(1059,plain,
% 0.63/0.82 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a329) | c3_1(a329) | (~c2_1(a329)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp13 | c3_1(a329) | (~ndr1_0) | c0_1(a329) | (~c2_1(a329)))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1058, 1056])).
% 0.63/0.82 tff(1060,plain,
% 0.63/0.82 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a329) | c3_1(a329) | (~c2_1(a329)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1061,plain,
% 0.63/0.82 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp13 | c3_1(a329) | (~ndr1_0) | c0_1(a329) | (~c2_1(a329))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1060, 1059])).
% 0.63/0.82 tff(1062,plain,
% 0.63/0.82 (hskp13 | c0_1(a329)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1061, 134, 204, 1047, 1055, 652])).
% 0.63/0.82 tff(1063,plain,
% 0.63/0.82 (hskp13),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1062, 1054])).
% 0.63/0.82 tff(1064,plain,
% 0.63/0.82 (~c3_1(a346)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[671, 1063])).
% 0.63/0.82 tff(1065,plain,
% 0.63/0.82 (c2_1(a346)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[709, 1063])).
% 0.63/0.82 tff(1066,plain,
% 0.63/0.82 (c0_1(a346)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[717, 1063])).
% 0.63/0.82 tff(1067,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a359) | c2_1(a359) | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a359)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1068,plain,
% 0.63/0.82 (((~ndr1_0) | (~c2_1(a346)) | (~c0_1(a346)) | (~c1_1(a346)) | c3_1(a346) | (~c1_1(a346)) | (~c2_1(a346)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359))) <=> (c0_1(a359) | c2_1(a359) | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a359)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1069,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a346)) | (~c0_1(a346)) | (~c1_1(a346)) | c3_1(a346) | (~c1_1(a346)) | (~c2_1(a346)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a359) | c2_1(a359) | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a359))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1068])).
% 0.63/0.82 tff(1070,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a346)) | (~c0_1(a346)) | (~c1_1(a346)) | c3_1(a346) | (~c1_1(a346)) | (~c2_1(a346)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a359)))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1069, 1067])).
% 0.63/0.82 tff(1071,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a346)) | (~c0_1(a346)) | (~c1_1(a346)) | c3_1(a346) | (~c1_1(a346)) | (~c2_1(a346)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1072,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a359))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1071, 1070])).
% 0.63/0.82 tff(1073,plain,
% 0.63/0.82 (~c1_1(a346)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1072, 134, 1066, 1065, 893, 884, 1064, 203, 892])).
% 0.63/0.82 tff(1074,plain,
% 0.63/0.82 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(1075,plain,
% 0.63/0.82 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[1074])).
% 0.63/0.82 tff(1076,plain,
% 0.63/0.82 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1077,plain,
% 0.63/0.82 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp10) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(1078,plain,
% 0.63/0.82 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[1077])).
% 0.63/0.82 tff(1079,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 0.63/0.82 tff(1080,plain,
% 0.63/0.82 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1079, 1078])).
% 0.63/0.82 tff(1081,plain,
% 0.63/0.82 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1080, 1076])).
% 0.63/0.82 tff(1082,plain,(
% 0.63/0.82 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.63/0.82 inference(skolemize,[status(sab)],[1081])).
% 0.63/0.82 tff(1083,plain,
% 0.63/0.82 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1082, 1075])).
% 0.63/0.82 tff(1084,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp10 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp10 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1085,plain,
% 0.63/0.82 ((hskp10 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a327) | c3_1(a327) | (~c0_1(a327))) <=> (hskp10 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1086,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a327) | c3_1(a327) | (~c0_1(a327)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp10 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1085])).
% 0.63/0.82 tff(1087,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a327) | c3_1(a327) | (~c0_1(a327)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp10 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1086, 1084])).
% 0.63/0.82 tff(1088,plain,
% 0.63/0.82 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a327) | c3_1(a327) | (~c0_1(a327)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1089,plain,
% 0.63/0.82 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp10 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1088, 1087])).
% 0.63/0.82 tff(1090,plain,
% 0.63/0.82 (hskp10),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1089, 134, 165, 157, 149, 837, 821, 1083, 900])).
% 0.63/0.82 tff(1091,plain,
% 0.63/0.82 (((~hskp10) | (~c3_1(a337))) <=> ((~hskp10) | (~c3_1(a337)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1092,plain,
% 0.63/0.82 (((~c3_1(a337)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a337)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1093,axiom,((~c3_1(a337)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 0.63/0.82 tff(1094,plain,
% 0.63/0.82 ((~hskp10) | (~c3_1(a337))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1093, 1092])).
% 0.63/0.82 tff(1095,plain,
% 0.63/0.82 ((~hskp10) | (~c3_1(a337))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1094, 1091])).
% 0.63/0.82 tff(1096,plain,
% 0.63/0.82 (~c3_1(a337)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1095, 1090])).
% 0.63/0.82 tff(1097,plain,
% 0.63/0.82 (((~hskp10) | (~c2_1(a337))) <=> ((~hskp10) | (~c2_1(a337)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1098,plain,
% 0.63/0.82 (((~c2_1(a337)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a337)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1099,axiom,((~c2_1(a337)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 0.63/0.82 tff(1100,plain,
% 0.63/0.82 ((~hskp10) | (~c2_1(a337))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1099, 1098])).
% 0.63/0.82 tff(1101,plain,
% 0.63/0.82 ((~hskp10) | (~c2_1(a337))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1100, 1097])).
% 0.63/0.82 tff(1102,plain,
% 0.63/0.82 (~c2_1(a337)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1101, 1090])).
% 0.63/0.82 tff(1103,plain,
% 0.63/0.82 (((~hskp10) | c0_1(a337)) <=> ((~hskp10) | c0_1(a337))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1104,axiom,((~hskp10) | c0_1(a337)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.63/0.82 tff(1105,plain,
% 0.63/0.82 ((~hskp10) | c0_1(a337)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1104, 1103])).
% 0.63/0.82 tff(1106,plain,
% 0.63/0.82 ((~hskp10) | c0_1(a337)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1105, 1103])).
% 0.63/0.82 tff(1107,plain,
% 0.63/0.82 ((~hskp10) | c0_1(a337)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1106, 1103])).
% 0.63/0.82 tff(1108,plain,
% 0.63/0.82 ((~hskp10) | c0_1(a337)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1107, 1103])).
% 0.63/0.82 tff(1109,plain,
% 0.63/0.82 ((~hskp10) | c0_1(a337)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1108, 1103])).
% 0.63/0.82 tff(1110,plain,
% 0.63/0.82 (c0_1(a337)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1109, 1090])).
% 0.63/0.82 tff(1111,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a359) | c2_1(a359) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)) | (~c1_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)) | (~c1_1(a359)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1112,plain,
% 0.63/0.82 (((~ndr1_0) | c2_1(a337) | c3_1(a337) | (~c0_1(a337)) | c1_1(a346) | (~c0_1(a346)) | (~c2_1(a346)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359))) <=> (c0_1(a359) | c2_1(a359) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)) | (~c1_1(a359)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1113,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a337) | c3_1(a337) | (~c0_1(a337)) | c1_1(a346) | (~c0_1(a346)) | (~c2_1(a346)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a359) | c2_1(a359) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)) | (~c1_1(a359))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1112])).
% 0.63/0.82 tff(1114,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a337) | c3_1(a337) | (~c0_1(a337)) | c1_1(a346) | (~c0_1(a346)) | (~c2_1(a346)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)) | (~c1_1(a359)))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1113, 1111])).
% 0.63/0.82 tff(1115,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a337) | c3_1(a337) | (~c0_1(a337)) | c1_1(a346) | (~c0_1(a346)) | (~c2_1(a346)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1116,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)) | (~c1_1(a359))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1115, 1114])).
% 0.63/0.82 tff(1117,plain,
% 0.63/0.82 ($false),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1116, 134, 1066, 1065, 1110, 893, 884, 1102, 1096, 910, 892, 1073])).
% 0.63/0.82 tff(1118,plain,(hskp25 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.63/0.82 tff(1119,plain,
% 0.63/0.82 (hskp25),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1118, 204])).
% 0.63/0.82 tff(1120,plain,
% 0.63/0.82 (~c2_1(a419)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[251, 1119])).
% 0.63/0.82 tff(1121,plain,
% 0.63/0.82 (~c1_1(a419)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[257, 1119])).
% 0.63/0.82 tff(1122,plain,
% 0.63/0.82 (c0_1(a419)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[265, 1119])).
% 0.63/0.82 tff(1123,assumption,(~c2_1(a419)), introduced(assumption)).
% 0.63/0.82 tff(1124,assumption,(~c1_1(a419)), introduced(assumption)).
% 0.63/0.82 tff(1125,assumption,(c0_1(a419)), introduced(assumption)).
% 0.63/0.82 tff(1126,assumption,(hskp21), introduced(assumption)).
% 0.63/0.82 tff(1127,plain,
% 0.63/0.82 (~c2_1(a359)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[849, 1126])).
% 0.63/0.82 tff(1128,plain,
% 0.63/0.82 (~c0_1(a359)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[855, 1126])).
% 0.63/0.82 tff(1129,plain,
% 0.63/0.82 (c3_1(a359)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[863, 1126])).
% 0.63/0.82 tff(1130,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359) | (~ndr1_0) | (~c3_1(a359)) | (~c1_1(a359)) | (~c0_1(a419)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359) | (~ndr1_0) | (~c3_1(a359)) | (~c1_1(a359)) | (~c0_1(a419)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1131,plain,
% 0.63/0.82 (((~ndr1_0) | c2_1(a359) | (~c3_1(a359)) | (~c1_1(a359)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c0_1(a359) | (~c1_1(a359)) | (~c3_1(a359))) <=> (c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359) | (~ndr1_0) | (~c3_1(a359)) | (~c1_1(a359)) | (~c0_1(a419)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1132,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a359) | (~c3_1(a359)) | (~c1_1(a359)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c0_1(a359) | (~c1_1(a359)) | (~c3_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359) | (~ndr1_0) | (~c3_1(a359)) | (~c1_1(a359)) | (~c0_1(a419))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1131])).
% 0.63/0.82 tff(1133,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a359) | (~c3_1(a359)) | (~c1_1(a359)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c0_1(a359) | (~c1_1(a359)) | (~c3_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359) | (~ndr1_0) | (~c3_1(a359)) | (~c1_1(a359)) | (~c0_1(a419)))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1132, 1130])).
% 0.63/0.82 tff(1134,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a359) | (~c3_1(a359)) | (~c1_1(a359)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c0_1(a359) | (~c1_1(a359)) | (~c3_1(a359)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1135,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359) | (~ndr1_0) | (~c3_1(a359)) | (~c1_1(a359)) | (~c0_1(a419))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1134, 1133])).
% 0.63/0.82 tff(1136,plain,
% 0.63/0.82 (~c1_1(a359)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1135, 134, 1125, 1129, 1124, 1123, 1128, 1127, 920])).
% 0.63/0.82 tff(1137,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a359) | c2_1(a359) | (~ndr1_0) | c1_1(a359) | (~c3_1(a359)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a359) | c2_1(a359) | (~ndr1_0) | c1_1(a359) | (~c3_1(a359)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1138,plain,
% 0.63/0.82 ((hskp1 | (~ndr1_0) | c2_1(a359) | c0_1(a359) | (~c3_1(a359)) | c2_1(a359) | c1_1(a359) | c0_1(a359)) <=> (hskp1 | c0_1(a359) | c2_1(a359) | (~ndr1_0) | c1_1(a359) | (~c3_1(a359)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1139,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a359) | c0_1(a359) | (~c3_1(a359)) | c2_1(a359) | c1_1(a359) | c0_1(a359))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a359) | c2_1(a359) | (~ndr1_0) | c1_1(a359) | (~c3_1(a359))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1138])).
% 0.63/0.82 tff(1140,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a359) | c0_1(a359) | (~c3_1(a359)) | c2_1(a359) | c1_1(a359) | c0_1(a359))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a359) | c2_1(a359) | (~ndr1_0) | c1_1(a359) | (~c3_1(a359)))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1139, 1137])).
% 0.63/0.82 tff(1141,plain,
% 0.63/0.82 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a359) | c0_1(a359) | (~c3_1(a359)) | c2_1(a359) | c1_1(a359) | c0_1(a359))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1142,plain,
% 0.63/0.82 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a359) | c2_1(a359) | (~ndr1_0) | c1_1(a359) | (~c3_1(a359))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1141, 1140])).
% 0.63/0.82 tff(1143,plain,
% 0.63/0.82 ($false),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1142, 134, 46, 1129, 1128, 1127, 45, 1136])).
% 0.63/0.82 tff(1144,plain,((~hskp21) | hskp1 | (~c0_1(a419)) | c1_1(a419) | c2_1(a419)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.82 tff(1145,plain,
% 0.63/0.82 (~hskp21),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1144, 46, 1125, 1124, 1123])).
% 0.63/0.82 tff(1146,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | c1_1(a419) | c2_1(a419) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c3_1(a419))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c1_1(a419) | c2_1(a419) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c3_1(a419))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1147,plain,
% 0.63/0.82 ((hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a419) | c1_1(a419) | c3_1(a419)) <=> (hskp21 | c1_1(a419) | c2_1(a419) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c3_1(a419))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1148,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a419) | c1_1(a419) | c3_1(a419))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | c1_1(a419) | c2_1(a419) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c3_1(a419)))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1147])).
% 0.63/0.82 tff(1149,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a419) | c1_1(a419) | c3_1(a419))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c1_1(a419) | c2_1(a419) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c3_1(a419))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1148, 1146])).
% 0.63/0.82 tff(1150,plain,
% 0.63/0.82 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a419) | c1_1(a419) | c3_1(a419))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(1151,plain,
% 0.63/0.83 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c1_1(a419) | c2_1(a419) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c3_1(a419)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1150, 1149])).
% 0.63/0.83 tff(1152,plain,
% 0.63/0.83 (hskp21 | c3_1(a419)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1151, 134, 837, 829, 1124, 1123, 821, 10])).
% 0.63/0.83 tff(1153,plain,
% 0.63/0.83 (c3_1(a419)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1152, 1145])).
% 0.63/0.83 tff(1154,assumption,(c3_1(a419)), introduced(assumption)).
% 0.63/0.83 tff(1155,assumption,(hskp7), introduced(assumption)).
% 0.63/0.83 tff(1156,plain,
% 0.63/0.83 (~c1_1(a330)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[377, 1155])).
% 0.63/0.83 tff(1157,plain,
% 0.63/0.83 (~c0_1(a330)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[383, 1155])).
% 0.63/0.83 tff(1158,plain,
% 0.63/0.83 (c3_1(a330)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[445, 1155])).
% 0.63/0.83 tff(1159,plain,
% 0.63/0.83 (((~![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a419) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c2_1(a330)) | (~c3_1(a330)) | (~c3_1(a419)) | (~c0_1(a419)))) <=> ((~![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a419) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c2_1(a330)) | (~c3_1(a330)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1160,plain,
% 0.63/0.83 (((~ndr1_0) | c1_1(a330) | (~c2_1(a330)) | (~c3_1(a330)) | c1_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c0_1(a330) | c1_1(a330) | (~c2_1(a330))) <=> (c1_1(a419) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c2_1(a330)) | (~c3_1(a330)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1161,plain,
% 0.63/0.83 (((~![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a330) | (~c2_1(a330)) | (~c3_1(a330)) | c1_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c0_1(a330) | c1_1(a330) | (~c2_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)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a419) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c2_1(a330)) | (~c3_1(a330)) | (~c3_1(a419)) | (~c0_1(a419))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[1160])).
% 0.63/0.83 tff(1162,plain,
% 0.63/0.83 (((~![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a330) | (~c2_1(a330)) | (~c3_1(a330)) | c1_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c0_1(a330) | c1_1(a330) | (~c2_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)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a419) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c2_1(a330)) | (~c3_1(a330)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 0.63/0.83 inference(transitivity,[status(thm)],[1161, 1159])).
% 0.63/0.83 tff(1163,plain,
% 0.63/0.83 ((~![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a330) | (~c2_1(a330)) | (~c3_1(a330)) | c1_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c0_1(a330) | c1_1(a330) | (~c2_1(a330)))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(1164,plain,
% 0.63/0.83 ((~![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)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a419) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c2_1(a330)) | (~c3_1(a330)) | (~c3_1(a419)) | (~c0_1(a419))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1163, 1162])).
% 0.63/0.83 tff(1165,plain,
% 0.63/0.83 (~c2_1(a330)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1164, 134, 1125, 1158, 1124, 1157, 1156, 691, 1154])).
% 0.63/0.83 tff(1166,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a330) | c1_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a330) | c1_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1167,plain,
% 0.63/0.83 ((hskp1 | (~ndr1_0) | c2_1(a330) | c0_1(a330) | (~c3_1(a330)) | c2_1(a330) | c1_1(a330) | c0_1(a330)) <=> (hskp1 | c0_1(a330) | c1_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1168,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a330) | c0_1(a330) | (~c3_1(a330)) | c2_1(a330) | c1_1(a330) | c0_1(a330))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a330) | c1_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[1167])).
% 0.63/0.83 tff(1169,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a330) | c0_1(a330) | (~c3_1(a330)) | c2_1(a330) | c1_1(a330) | c0_1(a330))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a330) | c1_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)))),
% 0.63/0.83 inference(transitivity,[status(thm)],[1168, 1166])).
% 0.63/0.83 tff(1170,plain,
% 0.63/0.83 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a330) | c0_1(a330) | (~c3_1(a330)) | c2_1(a330) | c1_1(a330) | c0_1(a330))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(1171,plain,
% 0.63/0.83 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a330) | c1_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1170, 1169])).
% 0.63/0.83 tff(1172,plain,
% 0.63/0.83 ($false),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1171, 134, 46, 1158, 1157, 1156, 45, 1165])).
% 0.63/0.83 tff(1173,plain,((~hskp7) | hskp1 | (~c0_1(a419)) | c1_1(a419) | (~c3_1(a419))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.83 tff(1174,plain,
% 0.63/0.83 (~hskp7),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1173, 46, 1125, 1124, 1153])).
% 0.63/0.83 tff(1175,plain,
% 0.63/0.83 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(1176,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[1175])).
% 0.63/0.83 tff(1177,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1178,plain,
% 0.63/0.83 (^[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)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_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)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_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)) | (~c0_1(U)) | (~c3_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)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_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)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp7) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp7))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(1179,plain,
% 0.63/0.83 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[1178])).
% 0.63/0.83 tff(1180,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)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 0.63/0.83 tff(1181,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1180, 1179])).
% 0.63/0.83 tff(1182,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1181, 1177])).
% 0.63/0.83 tff(1183,plain,(
% 0.63/0.83 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.63/0.83 inference(skolemize,[status(sab)],[1182])).
% 0.63/0.83 tff(1184,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1183, 1176])).
% 0.63/0.83 tff(1185,plain,
% 0.63/0.83 (hskp2 | (~c3_1(a419))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[272, 134, 1125, 1124, 1123, 245])).
% 0.63/0.83 tff(1186,plain,
% 0.63/0.83 (~c3_1(a419)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1185, 225])).
% 0.63/0.83 tff(1187,plain,
% 0.63/0.83 (hskp22 | c3_1(a419)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[303, 134, 1125, 1124, 1123, 297])).
% 0.63/0.83 tff(1188,plain,
% 0.63/0.83 (hskp22),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1187, 1186])).
% 0.63/0.83 tff(1189,plain,
% 0.63/0.83 (~c2_1(a367)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[310, 1188])).
% 0.63/0.83 tff(1190,plain,
% 0.63/0.83 (~c1_1(a367)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[347, 1188])).
% 0.63/0.83 tff(1191,plain,
% 0.63/0.83 (c3_1(a367)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[334, 1188])).
% 0.63/0.83 tff(1192,plain,
% 0.63/0.83 (~c0_1(a367)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[354, 134, 225, 1191, 1190, 1189, 245])).
% 0.63/0.83 tff(1193,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1194,plain,
% 0.63/0.83 ((hskp1 | (~ndr1_0) | c2_1(a367) | c0_1(a367) | (~c3_1(a367)) | c2_1(a367) | c1_1(a367) | c0_1(a367)) <=> (hskp1 | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1195,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a367) | c0_1(a367) | (~c3_1(a367)) | c2_1(a367) | c1_1(a367) | c0_1(a367))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367)))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[1194])).
% 0.63/0.83 tff(1196,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a367) | c0_1(a367) | (~c3_1(a367)) | c2_1(a367) | c1_1(a367) | c0_1(a367))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367))),
% 0.63/0.83 inference(transitivity,[status(thm)],[1195, 1193])).
% 0.63/0.83 tff(1197,plain,
% 0.63/0.83 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a367) | c0_1(a367) | (~c3_1(a367)) | c2_1(a367) | c1_1(a367) | c0_1(a367))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(1198,plain,
% 0.63/0.83 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1197, 1196])).
% 0.63/0.83 tff(1199,plain,
% 0.63/0.83 ($false),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1198, 134, 46, 1191, 1190, 1189, 45, 1192])).
% 0.63/0.83 tff(1200,plain,(hskp2 | hskp1 | (~c0_1(a419)) | c1_1(a419) | c2_1(a419)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.83 tff(1201,plain,
% 0.63/0.83 (hskp2),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1200, 46, 1125, 1124, 1123])).
% 0.63/0.83 tff(1202,plain,
% 0.63/0.83 (~c3_1(a324)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[627, 1201])).
% 0.63/0.83 tff(1203,plain,
% 0.63/0.83 (~c1_1(a324)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[633, 1201])).
% 0.63/0.83 tff(1204,plain,
% 0.63/0.83 (~c0_1(a324)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[657, 1201])).
% 0.63/0.83 tff(1205,assumption,(~hskp21), introduced(assumption)).
% 0.63/0.83 tff(1206,plain,
% 0.63/0.83 (c3_1(a419)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1152, 1205])).
% 0.63/0.83 tff(1207,assumption,(~hskp28), introduced(assumption)).
% 0.63/0.83 tff(1208,plain,
% 0.63/0.83 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(1209,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[1208])).
% 0.63/0.83 tff(1210,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1211,plain,
% 0.63/0.83 (^[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) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(1212,plain,
% 0.63/0.83 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[1211])).
% 0.63/0.83 tff(1213,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 0.63/0.83 tff(1214,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1213, 1212])).
% 0.63/0.83 tff(1215,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1214, 1210])).
% 0.63/0.83 tff(1216,plain,(
% 0.63/0.83 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.63/0.83 inference(skolemize,[status(sab)],[1215])).
% 0.63/0.83 tff(1217,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1216, 1209])).
% 0.63/0.83 tff(1218,assumption,(hskp11), introduced(assumption)).
% 0.63/0.83 tff(1219,plain,
% 0.63/0.83 (~c2_1(a338)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[63, 1218])).
% 0.63/0.83 tff(1220,plain,
% 0.63/0.83 (~c0_1(a338)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[75, 1218])).
% 0.63/0.83 tff(1221,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a419) | c0_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a338)) | (~c3_1(a419)) | (~c0_1(a419)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a419) | c0_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a338)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1222,plain,
% 0.63/0.83 ((hskp28 | (~ndr1_0) | c2_1(a419) | (~c0_1(a419)) | (~c3_1(a419)) | c2_1(a338) | c0_1(a338) | (~c3_1(a338))) <=> (hskp28 | c2_1(a419) | c0_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a338)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1223,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a419) | (~c0_1(a419)) | (~c3_1(a419)) | c2_1(a338) | c0_1(a338) | (~c3_1(a338)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a419) | c0_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a338)) | (~c3_1(a419)) | (~c0_1(a419))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[1222])).
% 0.63/0.83 tff(1224,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a419) | (~c0_1(a419)) | (~c3_1(a419)) | c2_1(a338) | c0_1(a338) | (~c3_1(a338)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a419) | c0_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a338)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 0.63/0.83 inference(transitivity,[status(thm)],[1223, 1221])).
% 0.63/0.83 tff(1225,plain,
% 0.63/0.83 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a419) | (~c0_1(a419)) | (~c3_1(a419)) | c2_1(a338) | c0_1(a338) | (~c3_1(a338)))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(1226,plain,
% 0.63/0.83 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a419) | c0_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a338)) | (~c3_1(a419)) | (~c0_1(a419))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1225, 1224])).
% 0.63/0.83 tff(1227,plain,
% 0.63/0.83 (~c3_1(a338)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1226, 1207, 134, 1125, 1123, 1220, 1219, 1217, 1154])).
% 0.63/0.83 tff(1228,plain,
% 0.63/0.83 (~c1_1(a338)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[69, 1218])).
% 0.63/0.83 tff(1229,plain,
% 0.63/0.83 ($false),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[843, 134, 1205, 837, 829, 1228, 1219, 821, 10, 1227])).
% 0.63/0.83 tff(1230,plain,((~hskp11) | hskp21 | hskp28 | (~c0_1(a419)) | c2_1(a419) | (~c3_1(a419))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.83 tff(1231,plain,
% 0.63/0.83 (~hskp11),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1230, 1207, 1205, 1125, 1123, 1206])).
% 0.63/0.83 tff(1232,assumption,(hskp24), introduced(assumption)).
% 0.63/0.83 tff(1233,plain,
% 0.63/0.83 (~c2_1(a401)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[540, 1232])).
% 0.63/0.83 tff(1234,plain,
% 0.63/0.83 (c1_1(a401)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[554, 1232])).
% 0.63/0.83 tff(1235,plain,
% 0.63/0.83 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | c2_1(a401) | (~ndr1_0) | (~c3_1(a401)) | (~c1_1(a401)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | c2_1(a401) | (~ndr1_0) | (~c3_1(a401)) | (~c1_1(a401)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1236,plain,
% 0.63/0.83 ((hskp28 | (~ndr1_0) | c2_1(a401) | (~c3_1(a401)) | (~c1_1(a401))) <=> (hskp28 | c2_1(a401) | (~ndr1_0) | (~c3_1(a401)) | (~c1_1(a401)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1237,plain,
% 0.63/0.83 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c2_1(a401) | (~c3_1(a401)) | (~c1_1(a401)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | c2_1(a401) | (~ndr1_0) | (~c3_1(a401)) | (~c1_1(a401))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[1236])).
% 0.63/0.83 tff(1238,plain,
% 0.63/0.83 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c2_1(a401) | (~c3_1(a401)) | (~c1_1(a401)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | c2_1(a401) | (~ndr1_0) | (~c3_1(a401)) | (~c1_1(a401)))),
% 0.63/0.83 inference(transitivity,[status(thm)],[1237, 1235])).
% 0.63/0.83 tff(1239,plain,
% 0.63/0.83 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c2_1(a401) | (~c3_1(a401)) | (~c1_1(a401)))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(1240,plain,
% 0.63/0.83 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | c2_1(a401) | (~ndr1_0) | (~c3_1(a401)) | (~c1_1(a401))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1239, 1238])).
% 0.63/0.83 tff(1241,plain,
% 0.63/0.83 (~c3_1(a401)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1240, 1207, 134, 1234, 1233, 102])).
% 0.63/0.83 tff(1242,plain,
% 0.63/0.83 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp11 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(1243,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[1242])).
% 0.63/0.83 tff(1244,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1245,plain,
% 0.63/0.83 (^[V: $i, U: $i] : 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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp11))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(1246,plain,
% 0.63/0.83 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[1245])).
% 0.63/0.83 tff(1247,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 0.63/0.83 tff(1248,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1247, 1246])).
% 0.63/0.83 tff(1249,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1248, 1244])).
% 0.63/0.83 tff(1250,plain,(
% 0.63/0.83 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.63/0.83 inference(skolemize,[status(sab)],[1249])).
% 0.63/0.83 tff(1251,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1250, 1243])).
% 0.63/0.83 tff(1252,plain,
% 0.63/0.83 (~c0_1(a401)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[546, 1232])).
% 0.63/0.83 tff(1253,assumption,(~hskp11), introduced(assumption)).
% 0.63/0.83 tff(1254,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a401) | c2_1(a401) | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a401) | c2_1(a401) | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1255,plain,
% 0.63/0.83 ((hskp11 | (~ndr1_0) | c0_1(a401) | c3_1(a401) | (~c1_1(a401)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401))) <=> (hskp11 | c0_1(a401) | c2_1(a401) | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1256,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a401) | c3_1(a401) | (~c1_1(a401)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a401) | c2_1(a401) | (~ndr1_0) | c3_1(a401) | (~c1_1(a401))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[1255])).
% 0.63/0.83 tff(1257,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a401) | c3_1(a401) | (~c1_1(a401)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a401) | c2_1(a401) | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)))),
% 0.63/0.83 inference(transitivity,[status(thm)],[1256, 1254])).
% 0.63/0.83 tff(1258,plain,
% 0.63/0.83 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a401) | c3_1(a401) | (~c1_1(a401)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(1259,plain,
% 0.63/0.83 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a401) | c2_1(a401) | (~ndr1_0) | c3_1(a401) | (~c1_1(a401))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1258, 1257])).
% 0.63/0.83 tff(1260,plain,
% 0.63/0.83 ($false),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1259, 134, 1253, 1234, 1252, 1233, 1251, 1241])).
% 0.63/0.83 tff(1261,plain,((~hskp24) | hskp11 | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.63/0.83 tff(1262,plain,
% 0.63/0.83 (~hskp24),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1261, 1231, 1207])).
% 0.63/0.83 tff(1263,plain,
% 0.63/0.83 (hskp7),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[371, 1262])).
% 0.63/0.84 tff(1264,plain,
% 0.63/0.84 (~c1_1(a330)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[377, 1263])).
% 0.63/0.84 tff(1265,plain,
% 0.63/0.84 (~c0_1(a330)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[383, 1263])).
% 0.63/0.84 tff(1266,plain,
% 0.63/0.84 (c3_1(a330)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[445, 1263])).
% 0.63/0.84 tff(1267,plain,
% 0.63/0.84 (~c2_1(a330)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1164, 134, 1125, 1266, 1124, 1265, 1264, 691, 1206])).
% 0.63/0.84 tff(1268,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a419) | c0_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c3_1(a419)) | (~c0_1(a419)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a419) | c0_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1269,plain,
% 0.63/0.84 ((hskp28 | (~ndr1_0) | c2_1(a419) | (~c0_1(a419)) | (~c3_1(a419)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330))) <=> (hskp28 | c2_1(a419) | c0_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1270,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a419) | (~c0_1(a419)) | (~c3_1(a419)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a419) | c0_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c3_1(a419)) | (~c0_1(a419))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[1269])).
% 0.63/0.84 tff(1271,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a419) | (~c0_1(a419)) | (~c3_1(a419)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a419) | c0_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 0.63/0.84 inference(transitivity,[status(thm)],[1270, 1268])).
% 0.63/0.84 tff(1272,plain,
% 0.63/0.84 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a419) | (~c0_1(a419)) | (~c3_1(a419)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330)))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(1273,plain,
% 0.63/0.84 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a419) | c0_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c3_1(a419)) | (~c0_1(a419))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1272, 1271])).
% 0.63/0.84 tff(1274,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1273, 1207, 134, 1125, 1266, 1123, 1265, 1217, 1206, 1267])).
% 0.63/0.84 tff(1275,plain,(hskp28 | (~c0_1(a419)) | c2_1(a419) | c1_1(a419) | hskp21), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(1276,plain,
% 0.63/0.84 (hskp28),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1275, 1145, 1123, 1124, 1125])).
% 0.63/0.84 tff(1277,plain,
% 0.63/0.84 (c2_1(a343)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[148, 1276])).
% 0.63/0.84 tff(1278,plain,
% 0.63/0.84 (c0_1(a343)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[164, 1276])).
% 0.63/0.84 tff(1279,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp7 | c0_1(a324) | c1_1(a324) | c3_1(a324) | (~ndr1_0) | (~c0_1(a343)) | (~c3_1(a343)) | (~c2_1(a343)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp7 | c0_1(a324) | c1_1(a324) | c3_1(a324) | (~ndr1_0) | (~c0_1(a343)) | (~c3_1(a343)) | (~c2_1(a343)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1280,plain,
% 0.63/0.84 ((hskp7 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c3_1(a343)) | c1_1(a324) | c0_1(a324) | c3_1(a324)) <=> (hskp7 | c0_1(a324) | c1_1(a324) | c3_1(a324) | (~ndr1_0) | (~c0_1(a343)) | (~c3_1(a343)) | (~c2_1(a343)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1281,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c3_1(a343)) | c1_1(a324) | c0_1(a324) | c3_1(a324))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp7 | c0_1(a324) | c1_1(a324) | c3_1(a324) | (~ndr1_0) | (~c0_1(a343)) | (~c3_1(a343)) | (~c2_1(a343))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[1280])).
% 0.63/0.84 tff(1282,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c3_1(a343)) | c1_1(a324) | c0_1(a324) | c3_1(a324))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp7 | c0_1(a324) | c1_1(a324) | c3_1(a324) | (~ndr1_0) | (~c0_1(a343)) | (~c3_1(a343)) | (~c2_1(a343)))),
% 0.63/0.84 inference(transitivity,[status(thm)],[1281, 1279])).
% 0.63/0.84 tff(1283,plain,
% 0.63/0.84 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c3_1(a343)) | c1_1(a324) | c0_1(a324) | c3_1(a324))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(1284,plain,
% 0.63/0.84 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp7 | c0_1(a324) | c1_1(a324) | c3_1(a324) | (~ndr1_0) | (~c0_1(a343)) | (~c3_1(a343)) | (~c2_1(a343))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1283, 1282])).
% 0.63/0.84 tff(1285,plain,
% 0.63/0.84 (hskp7 | (~c3_1(a343))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1284, 134, 1278, 1277, 1204, 1203, 1202, 1184])).
% 0.63/0.84 tff(1286,plain,
% 0.63/0.84 (~c3_1(a343)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1285, 1174])).
% 0.63/0.84 tff(1287,plain,
% 0.63/0.84 (hskp24),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[371, 1174])).
% 0.63/0.84 tff(1288,plain,
% 0.63/0.84 (~c2_1(a401)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[540, 1287])).
% 0.63/0.84 tff(1289,plain,
% 0.63/0.84 (~c0_1(a401)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[546, 1287])).
% 0.63/0.84 tff(1290,plain,
% 0.63/0.84 (c1_1(a401)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[554, 1287])).
% 0.63/0.84 tff(1291,plain,
% 0.63/0.84 (c1_1(a343)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[156, 1276])).
% 0.63/0.84 tff(1292,plain,
% 0.63/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a401) | c2_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a401) | c2_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1293,plain,
% 0.63/0.84 (((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401))) <=> (c0_1(a401) | c2_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1294,plain,
% 0.63/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a401) | c2_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[1293])).
% 0.63/0.84 tff(1295,plain,
% 0.63/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a401) | c2_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.63/0.84 inference(transitivity,[status(thm)],[1294, 1292])).
% 0.63/0.84 tff(1296,plain,
% 0.63/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(1297,plain,
% 0.63/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a401) | c2_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1296, 1295])).
% 0.63/0.84 tff(1298,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1297, 134, 1278, 1291, 1277, 1290, 1289, 1288, 203, 1286])).
% 0.63/0.84 tff(1299,plain,(hskp1 | (~c0_1(a419)) | c1_1(a419) | c2_1(a419)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(1300,plain,
% 0.63/0.84 (hskp1),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1299, 1122, 1121, 1120])).
% 0.63/0.84 tff(1301,plain,
% 0.63/0.84 (~c3_1(a323)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[587, 1300])).
% 0.63/0.84 tff(1302,plain,
% 0.63/0.84 (~c2_1(a323)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[593, 1300])).
% 0.63/0.84 tff(1303,plain,
% 0.63/0.84 (~c1_1(a323)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[599, 1300])).
% 0.63/0.84 tff(1304,plain,
% 0.63/0.84 (hskp21),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[882, 134, 837, 829, 821, 1303, 1302, 1301, 10])).
% 0.63/0.84 tff(1305,plain,
% 0.63/0.84 (~c2_1(a359)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[849, 1304])).
% 0.63/0.84 tff(1306,plain,
% 0.63/0.84 (~c0_1(a359)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[855, 1304])).
% 0.63/0.84 tff(1307,plain,
% 0.63/0.84 (c3_1(a359)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[863, 1304])).
% 0.63/0.84 tff(1308,plain,
% 0.63/0.84 (~c1_1(a359)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1135, 134, 1122, 1307, 1121, 1120, 1306, 1305, 920])).
% 0.63/0.84 tff(1309,plain,
% 0.63/0.84 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(1310,plain,
% 0.63/0.84 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[1309])).
% 0.63/0.84 tff(1311,plain,
% 0.63/0.84 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1312,plain,
% 0.63/0.84 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp26) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp26))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(1313,plain,
% 0.63/0.84 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[1312])).
% 0.63/0.84 tff(1314,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 0.63/0.84 tff(1315,plain,
% 0.63/0.84 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1314, 1313])).
% 0.63/0.84 tff(1316,plain,
% 0.63/0.84 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1315, 1311])).
% 0.63/0.84 tff(1317,plain,(
% 0.63/0.84 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.63/0.84 inference(skolemize,[status(sab)],[1316])).
% 0.63/0.84 tff(1318,plain,
% 0.63/0.84 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1317, 1310])).
% 0.63/0.84 tff(1319,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c1_1(a419) | c2_1(a419) | c0_1(a359) | (~ndr1_0) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a419)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c1_1(a419) | c2_1(a419) | c0_1(a359) | (~ndr1_0) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a419)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1320,plain,
% 0.63/0.84 ((hskp26 | (~ndr1_0) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c1_1(a359) | c0_1(a359) | (~c3_1(a359))) <=> (hskp26 | c1_1(a419) | c2_1(a419) | c0_1(a359) | (~ndr1_0) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a419)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1321,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c1_1(a359) | c0_1(a359) | (~c3_1(a359)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c1_1(a419) | c2_1(a419) | c0_1(a359) | (~ndr1_0) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a419))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[1320])).
% 0.63/0.84 tff(1322,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c1_1(a359) | c0_1(a359) | (~c3_1(a359)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c1_1(a419) | c2_1(a419) | c0_1(a359) | (~ndr1_0) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a419)))),
% 0.63/0.84 inference(transitivity,[status(thm)],[1321, 1319])).
% 0.63/0.84 tff(1323,plain,
% 0.63/0.84 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c1_1(a359) | c0_1(a359) | (~c3_1(a359)))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(1324,plain,
% 0.63/0.84 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c1_1(a419) | c2_1(a419) | c0_1(a359) | (~ndr1_0) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a419))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1323, 1322])).
% 0.63/0.84 tff(1325,plain,
% 0.63/0.84 (hskp26),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1324, 134, 1122, 1307, 1121, 1120, 1306, 1318, 1308])).
% 0.63/0.84 tff(1326,plain,
% 0.63/0.84 (c3_1(a333)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[473, 1325])).
% 0.63/0.84 tff(1327,plain,
% 0.63/0.84 (c1_1(a333)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[500, 1325])).
% 0.63/0.84 tff(1328,plain,
% 0.63/0.84 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(1329,plain,
% 0.63/0.84 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[1328])).
% 0.63/0.84 tff(1330,plain,
% 0.63/0.84 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1331,plain,
% 0.63/0.84 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | 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))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | 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))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_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)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(1332,plain,
% 0.63/0.84 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[1331])).
% 0.63/0.84 tff(1333,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 0.63/0.84 tff(1334,plain,
% 0.63/0.84 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1333, 1332])).
% 0.63/0.84 tff(1335,plain,
% 0.63/0.84 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1334, 1330])).
% 0.63/0.84 tff(1336,plain,(
% 0.63/0.84 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.63/0.84 inference(skolemize,[status(sab)],[1335])).
% 0.63/0.84 tff(1337,plain,
% 0.63/0.84 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1336, 1329])).
% 0.63/0.84 tff(1338,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp12 | c2_1(a359) | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0) | c1_1(a359) | (~c3_1(a359)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp12 | c2_1(a359) | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0) | c1_1(a359) | (~c3_1(a359)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1339,plain,
% 0.63/0.84 ((hskp12 | (~ndr1_0) | c2_1(a359) | c1_1(a359) | (~c3_1(a359)) | c2_1(a323) | c1_1(a323) | c3_1(a323)) <=> (hskp12 | c2_1(a359) | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0) | c1_1(a359) | (~c3_1(a359)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1340,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a359) | c1_1(a359) | (~c3_1(a359)) | c2_1(a323) | c1_1(a323) | c3_1(a323))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp12 | c2_1(a359) | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0) | c1_1(a359) | (~c3_1(a359))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[1339])).
% 0.63/0.84 tff(1341,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a359) | c1_1(a359) | (~c3_1(a359)) | c2_1(a323) | c1_1(a323) | c3_1(a323))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp12 | c2_1(a359) | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0) | c1_1(a359) | (~c3_1(a359)))),
% 0.63/0.84 inference(transitivity,[status(thm)],[1340, 1338])).
% 0.63/0.84 tff(1342,plain,
% 0.63/0.84 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a359) | c1_1(a359) | (~c3_1(a359)) | c2_1(a323) | c1_1(a323) | c3_1(a323))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(1343,plain,
% 0.63/0.84 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp12 | c2_1(a359) | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0) | c1_1(a359) | (~c3_1(a359))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1342, 1341])).
% 0.63/0.84 tff(1344,plain,
% 0.63/0.84 (hskp12),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1343, 134, 1307, 1305, 1303, 1302, 1301, 1337, 1308])).
% 0.63/0.84 tff(1345,plain,
% 0.63/0.84 (((~hskp12) | c3_1(a345)) <=> ((~hskp12) | c3_1(a345))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1346,axiom,((~hskp12) | c3_1(a345)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 0.63/0.84 tff(1347,plain,
% 0.63/0.84 ((~hskp12) | c3_1(a345)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1346, 1345])).
% 0.63/0.84 tff(1348,plain,
% 0.63/0.84 ((~hskp12) | c3_1(a345)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1347, 1345])).
% 0.63/0.84 tff(1349,plain,
% 0.63/0.84 ((~hskp12) | c3_1(a345)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1348, 1345])).
% 0.63/0.84 tff(1350,plain,
% 0.63/0.84 ((~hskp12) | c3_1(a345)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1349, 1345])).
% 0.63/0.84 tff(1351,plain,
% 0.63/0.84 ((~hskp12) | c3_1(a345)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1350, 1345])).
% 0.63/0.84 tff(1352,plain,
% 0.63/0.84 (c3_1(a345)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1351, 1344])).
% 0.63/0.84 tff(1353,plain,
% 0.63/0.84 (((~hskp12) | c0_1(a345)) <=> ((~hskp12) | c0_1(a345))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1354,axiom,((~hskp12) | c0_1(a345)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 0.63/0.84 tff(1355,plain,
% 0.63/0.84 ((~hskp12) | c0_1(a345)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1354, 1353])).
% 0.63/0.84 tff(1356,plain,
% 0.63/0.84 ((~hskp12) | c0_1(a345)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1355, 1353])).
% 0.63/0.84 tff(1357,plain,
% 0.63/0.84 ((~hskp12) | c0_1(a345)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1356, 1353])).
% 0.63/0.84 tff(1358,plain,
% 0.63/0.84 ((~hskp12) | c0_1(a345)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1357, 1353])).
% 0.63/0.84 tff(1359,plain,
% 0.63/0.84 ((~hskp12) | c0_1(a345)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1358, 1353])).
% 0.63/0.84 tff(1360,plain,
% 0.63/0.84 (c0_1(a345)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1359, 1344])).
% 0.63/0.84 tff(1361,plain,
% 0.63/0.84 (((~hskp12) | (~c2_1(a345))) <=> ((~hskp12) | (~c2_1(a345)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1362,plain,
% 0.63/0.84 (((~c2_1(a345)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a345)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1363,axiom,((~c2_1(a345)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 0.63/0.84 tff(1364,plain,
% 0.63/0.84 ((~hskp12) | (~c2_1(a345))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1363, 1362])).
% 0.63/0.84 tff(1365,plain,
% 0.63/0.84 ((~hskp12) | (~c2_1(a345))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1364, 1361])).
% 0.63/0.84 tff(1366,plain,
% 0.63/0.84 (~c2_1(a345)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1365, 1344])).
% 0.63/0.84 tff(1367,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c0_1(a359) | c2_1(a359) | c2_1(a345) | (~ndr1_0) | (~c0_1(a345)) | (~c3_1(a345)) | (~c3_1(a359)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a359) | c2_1(a359) | c2_1(a345) | (~ndr1_0) | (~c0_1(a345)) | (~c3_1(a345)) | (~c3_1(a359)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1368,plain,
% 0.63/0.84 ((hskp28 | (~ndr1_0) | c2_1(a345) | (~c0_1(a345)) | (~c3_1(a345)) | c2_1(a359) | c0_1(a359) | (~c3_1(a359))) <=> (hskp28 | c0_1(a359) | c2_1(a359) | c2_1(a345) | (~ndr1_0) | (~c0_1(a345)) | (~c3_1(a345)) | (~c3_1(a359)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1369,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a345) | (~c0_1(a345)) | (~c3_1(a345)) | c2_1(a359) | c0_1(a359) | (~c3_1(a359)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c0_1(a359) | c2_1(a359) | c2_1(a345) | (~ndr1_0) | (~c0_1(a345)) | (~c3_1(a345)) | (~c3_1(a359))))),
% 0.63/0.85 inference(monotonicity,[status(thm)],[1368])).
% 0.63/0.85 tff(1370,plain,
% 0.63/0.85 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a345) | (~c0_1(a345)) | (~c3_1(a345)) | c2_1(a359) | c0_1(a359) | (~c3_1(a359)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a359) | c2_1(a359) | c2_1(a345) | (~ndr1_0) | (~c0_1(a345)) | (~c3_1(a345)) | (~c3_1(a359)))),
% 0.63/0.85 inference(transitivity,[status(thm)],[1369, 1367])).
% 0.63/0.85 tff(1371,plain,
% 0.63/0.85 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a345) | (~c0_1(a345)) | (~c3_1(a345)) | c2_1(a359) | c0_1(a359) | (~c3_1(a359)))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(1372,plain,
% 0.63/0.85 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a359) | c2_1(a359) | c2_1(a345) | (~ndr1_0) | (~c0_1(a345)) | (~c3_1(a345)) | (~c3_1(a359))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[1371, 1370])).
% 0.63/0.85 tff(1373,plain,
% 0.63/0.85 (hskp28),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1372, 134, 1307, 1360, 1352, 1306, 1305, 1366, 1217])).
% 0.63/0.85 tff(1374,plain,
% 0.63/0.85 (c2_1(a343)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[148, 1373])).
% 0.63/0.85 tff(1375,plain,
% 0.63/0.85 (c1_1(a343)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[156, 1373])).
% 0.63/0.85 tff(1376,plain,
% 0.63/0.85 (c0_1(a343)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[164, 1373])).
% 0.63/0.85 tff(1377,plain,
% 0.63/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a359) | c2_1(a345) | (~ndr1_0) | (~c3_1(a345)) | (~c1_1(a345)) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a359) | c2_1(a345) | (~ndr1_0) | (~c3_1(a345)) | (~c1_1(a345)) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1378,plain,
% 0.63/0.85 (((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a345) | (~c3_1(a345)) | (~c1_1(a345)) | c2_1(a359) | c1_1(a359) | (~c3_1(a359))) <=> (c2_1(a359) | c2_1(a345) | (~ndr1_0) | (~c3_1(a345)) | (~c1_1(a345)) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1379,plain,
% 0.63/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a345) | (~c3_1(a345)) | (~c1_1(a345)) | c2_1(a359) | c1_1(a359) | (~c3_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a359) | c2_1(a345) | (~ndr1_0) | (~c3_1(a345)) | (~c1_1(a345)) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 0.63/0.85 inference(monotonicity,[status(thm)],[1378])).
% 0.63/0.85 tff(1380,plain,
% 0.63/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a345) | (~c3_1(a345)) | (~c1_1(a345)) | c2_1(a359) | c1_1(a359) | (~c3_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a359) | c2_1(a345) | (~ndr1_0) | (~c3_1(a345)) | (~c1_1(a345)) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 0.63/0.85 inference(transitivity,[status(thm)],[1379, 1377])).
% 0.63/0.85 tff(1381,plain,
% 0.63/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a345) | (~c3_1(a345)) | (~c1_1(a345)) | c2_1(a359) | c1_1(a359) | (~c3_1(a359)))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(1382,plain,
% 0.63/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a359) | c2_1(a345) | (~ndr1_0) | (~c3_1(a345)) | (~c1_1(a345)) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[1381, 1380])).
% 0.63/0.85 tff(1383,plain,
% 0.63/0.85 (~c1_1(a345)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1382, 134, 1376, 1375, 1374, 1307, 1352, 1305, 1366, 20, 1308])).
% 0.63/0.85 tff(1384,plain,
% 0.63/0.85 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(1385,plain,
% 0.63/0.85 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[1384])).
% 0.63/0.85 tff(1386,plain,
% 0.63/0.85 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1387,plain,
% 0.63/0.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(1388,plain,
% 0.63/0.85 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[1387])).
% 0.63/0.85 tff(1389,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 0.63/0.85 tff(1390,plain,
% 0.63/0.85 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[1389, 1388])).
% 0.63/0.85 tff(1391,plain,
% 0.63/0.85 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[1390, 1386])).
% 0.63/0.85 tff(1392,plain,(
% 0.63/0.85 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.63/0.85 inference(skolemize,[status(sab)],[1391])).
% 0.63/0.85 tff(1393,plain,
% 0.63/0.85 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[1392, 1385])).
% 0.63/0.85 tff(1394,plain,
% 0.63/0.85 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | c1_1(a345) | (~c0_1(a345)) | (~c3_1(a345)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp14 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | c1_1(a345) | (~c0_1(a345)) | (~c3_1(a345)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1395,plain,
% 0.63/0.85 ((hskp14 | (~ndr1_0) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c1_1(a345) | (~c3_1(a345)) | (~c0_1(a345))) <=> (hskp14 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | c1_1(a345) | (~c0_1(a345)) | (~c3_1(a345)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1396,plain,
% 0.63/0.85 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c1_1(a345) | (~c3_1(a345)) | (~c0_1(a345)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | c1_1(a345) | (~c0_1(a345)) | (~c3_1(a345))))),
% 0.63/0.85 inference(monotonicity,[status(thm)],[1395])).
% 0.63/0.85 tff(1397,plain,
% 0.63/0.85 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c1_1(a345) | (~c3_1(a345)) | (~c0_1(a345)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp14 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | c1_1(a345) | (~c0_1(a345)) | (~c3_1(a345)))),
% 0.63/0.85 inference(transitivity,[status(thm)],[1396, 1394])).
% 0.63/0.85 tff(1398,plain,
% 0.63/0.85 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c1_1(a345) | (~c3_1(a345)) | (~c0_1(a345)))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(1399,plain,
% 0.63/0.85 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp14 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | c1_1(a345) | (~c0_1(a345)) | (~c3_1(a345))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[1398, 1397])).
% 0.63/0.85 tff(1400,plain,
% 0.63/0.85 (hskp14 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | c1_1(a345) | (~c0_1(a345)) | (~c3_1(a345))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1399, 1393])).
% 0.63/0.85 tff(1401,plain,
% 0.63/0.85 (hskp14 | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | c1_1(a345) | (~c0_1(a345)) | (~c3_1(a345))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1400, 134])).
% 0.63/0.85 tff(1402,plain,
% 0.63/0.85 (c2_1(a333)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1401, 1383, 204, 1360, 1352, 1327, 1326])).
% 0.63/0.85 tff(1403,plain,
% 0.63/0.85 (c0_1(a333)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[481, 1325])).
% 0.63/0.85 tff(1404,plain,
% 0.63/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a419) | c2_1(a345) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a345)) | (~c3_1(a345)) | c3_1(a419) | (~c0_1(a419)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a419) | c2_1(a345) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a345)) | (~c3_1(a345)) | c3_1(a419) | (~c0_1(a419)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1405,plain,
% 0.63/0.85 (((~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)) | c2_1(a345) | (~c3_1(a345)) | (~c0_1(a345)) | c2_1(a419) | c3_1(a419) | (~c0_1(a419))) <=> (c2_1(a419) | c2_1(a345) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a345)) | (~c3_1(a345)) | c3_1(a419) | (~c0_1(a419)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1406,plain,
% 0.63/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)) | c2_1(a345) | (~c3_1(a345)) | (~c0_1(a345)) | c2_1(a419) | c3_1(a419) | (~c0_1(a419)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a419) | c2_1(a345) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a345)) | (~c3_1(a345)) | c3_1(a419) | (~c0_1(a419))))),
% 0.63/0.85 inference(monotonicity,[status(thm)],[1405])).
% 0.63/0.85 tff(1407,plain,
% 0.63/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)) | c2_1(a345) | (~c3_1(a345)) | (~c0_1(a345)) | c2_1(a419) | c3_1(a419) | (~c0_1(a419)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a419) | c2_1(a345) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a345)) | (~c3_1(a345)) | c3_1(a419) | (~c0_1(a419)))),
% 0.63/0.85 inference(transitivity,[status(thm)],[1406, 1404])).
% 0.63/0.85 tff(1408,plain,
% 0.63/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)) | c2_1(a345) | (~c3_1(a345)) | (~c0_1(a345)) | c2_1(a419) | c3_1(a419) | (~c0_1(a419)))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(1409,plain,
% 0.63/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a419) | c2_1(a345) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a345)) | (~c3_1(a345)) | c3_1(a419) | (~c0_1(a419))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[1408, 1407])).
% 0.63/0.85 tff(1410,plain,
% 0.63/0.85 (c3_1(a419)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1409, 134, 1403, 1326, 1122, 1360, 1352, 1120, 1366, 798, 1402])).
% 0.63/0.85 tff(1411,plain,
% 0.63/0.85 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(1412,plain,
% 0.63/0.85 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[1411])).
% 0.63/0.85 tff(1413,plain,
% 0.63/0.85 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1414,plain,
% 0.63/0.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_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)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_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)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp10) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(1415,plain,
% 0.63/0.85 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[1414])).
% 0.63/0.85 tff(1416,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 0.69/0.85 tff(1417,plain,
% 0.69/0.85 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[1416, 1415])).
% 0.69/0.85 tff(1418,plain,
% 0.69/0.85 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[1417, 1413])).
% 0.69/0.85 tff(1419,plain,(
% 0.69/0.85 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 0.69/0.85 inference(skolemize,[status(sab)],[1418])).
% 0.69/0.85 tff(1420,plain,
% 0.69/0.85 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[1419, 1412])).
% 0.69/0.85 tff(1421,plain,
% 0.69/0.85 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a333)) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c1_1(a333)) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1422,plain,
% 0.69/0.85 ((hskp10 | (~ndr1_0) | (~c2_1(a333)) | (~c3_1(a333)) | (~c1_1(a333)) | (~c3_1(a333)) | (~c1_1(a333)) | (~c0_1(a333))) <=> (hskp10 | (~ndr1_0) | (~c1_1(a333)) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1423,plain,
% 0.69/0.85 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a333)) | (~c3_1(a333)) | (~c1_1(a333)) | (~c3_1(a333)) | (~c1_1(a333)) | (~c0_1(a333)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a333)) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333))))),
% 0.69/0.85 inference(monotonicity,[status(thm)],[1422])).
% 0.69/0.85 tff(1424,plain,
% 0.69/0.85 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a333)) | (~c3_1(a333)) | (~c1_1(a333)) | (~c3_1(a333)) | (~c1_1(a333)) | (~c0_1(a333)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c1_1(a333)) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)))),
% 0.69/0.85 inference(transitivity,[status(thm)],[1423, 1421])).
% 0.69/0.85 tff(1425,plain,
% 0.69/0.85 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a333)) | (~c3_1(a333)) | (~c1_1(a333)) | (~c3_1(a333)) | (~c1_1(a333)) | (~c0_1(a333)))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(1426,plain,
% 0.69/0.85 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c1_1(a333)) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[1425, 1424])).
% 0.69/0.85 tff(1427,plain,
% 0.69/0.85 (hskp10),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1426, 134, 1403, 1327, 1326, 1420, 1402])).
% 0.69/0.85 tff(1428,plain,
% 0.69/0.85 (~c3_1(a337)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1095, 1427])).
% 0.69/0.85 tff(1429,plain,
% 0.69/0.85 (~c2_1(a337)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1101, 1427])).
% 0.69/0.85 tff(1430,plain,
% 0.69/0.85 (c0_1(a337)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1109, 1427])).
% 0.69/0.85 tff(1431,plain,
% 0.69/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a419) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a337)) | (~c3_1(a419)) | (~c0_1(a419)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a419) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a337)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1432,plain,
% 0.69/0.85 (((~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)) | c2_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c2_1(a337) | c3_1(a337) | (~c0_1(a337))) <=> (c2_1(a419) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a337)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1433,plain,
% 0.69/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)) | c2_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c2_1(a337) | c3_1(a337) | (~c0_1(a337)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a419) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a337)) | (~c3_1(a419)) | (~c0_1(a419))))),
% 0.69/0.85 inference(monotonicity,[status(thm)],[1432])).
% 0.69/0.85 tff(1434,plain,
% 0.69/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)) | c2_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c2_1(a337) | c3_1(a337) | (~c0_1(a337)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a419) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a337)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 0.69/0.85 inference(transitivity,[status(thm)],[1433, 1431])).
% 0.69/0.85 tff(1435,plain,
% 0.69/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)) | c2_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c2_1(a337) | c3_1(a337) | (~c0_1(a337)))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(1436,plain,
% 0.69/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a419) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a337)) | (~c3_1(a419)) | (~c0_1(a419))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[1435, 1434])).
% 0.69/0.85 tff(1437,plain,
% 0.69/0.85 ($false),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1436, 134, 1403, 1326, 1122, 1430, 1120, 1429, 1428, 798, 1402, 1410])).
% 0.69/0.85 tff(1438,plain,(hskp14), inference(lemma,lemma(discharge,[]))).
% 0.69/0.85 tff(1439,plain,
% 0.69/0.85 (~c1_1(a347)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[286, 1438])).
% 0.69/0.85 tff(1440,plain,
% 0.69/0.85 (c3_1(a347)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[318, 1438])).
% 0.69/0.85 tff(1441,plain,
% 0.69/0.85 (c2_1(a347)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[326, 1438])).
% 0.69/0.85 tff(1442,plain,
% 0.69/0.85 (hskp15),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[744, 134, 1441, 1440, 1439, 192])).
% 0.69/0.85 tff(1443,plain,
% 0.69/0.85 (~c1_1(a348)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[756, 1442])).
% 0.69/0.85 tff(1444,plain,
% 0.69/0.85 (c0_1(a348)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[764, 1442])).
% 0.69/0.85 tff(1445,plain,
% 0.69/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a359) | c2_1(a359) | c1_1(a348) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a348)) | (~c2_1(a348)) | (~c1_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | c1_1(a348) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a348)) | (~c2_1(a348)) | (~c1_1(a359)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1446,plain,
% 0.69/0.85 (((~ndr1_0) | c2_1(a327) | c3_1(a327) | (~c0_1(a327)) | c1_1(a348) | (~c0_1(a348)) | (~c2_1(a348)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359))) <=> (c0_1(a359) | c2_1(a359) | c1_1(a348) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a348)) | (~c2_1(a348)) | (~c1_1(a359)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1447,plain,
% 0.69/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a327) | c3_1(a327) | (~c0_1(a327)) | c1_1(a348) | (~c0_1(a348)) | (~c2_1(a348)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a359) | c2_1(a359) | c1_1(a348) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a348)) | (~c2_1(a348)) | (~c1_1(a359))))),
% 0.69/0.85 inference(monotonicity,[status(thm)],[1446])).
% 0.69/0.85 tff(1448,plain,
% 0.69/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a327) | c3_1(a327) | (~c0_1(a327)) | c1_1(a348) | (~c0_1(a348)) | (~c2_1(a348)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | c1_1(a348) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a348)) | (~c2_1(a348)) | (~c1_1(a359)))),
% 0.69/0.85 inference(transitivity,[status(thm)],[1447, 1445])).
% 0.69/0.85 tff(1449,plain,
% 0.69/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a327) | c3_1(a327) | (~c0_1(a327)) | c1_1(a348) | (~c0_1(a348)) | (~c2_1(a348)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(1450,plain,
% 0.69/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | c1_1(a348) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a348)) | (~c2_1(a348)) | (~c1_1(a359))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[1449, 1448])).
% 0.69/0.85 tff(1451,plain,
% 0.69/0.85 (~c2_1(a348)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1450, 134, 1444, 837, 893, 884, 1443, 821, 910, 900, 892])).
% 0.69/0.85 tff(1452,plain,
% 0.69/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a359) | c2_1(a359) | c1_1(a348) | (~ndr1_0) | (~c0_1(a348)) | c2_1(a348) | (~c3_1(a359)) | (~c1_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a359) | c2_1(a359) | c1_1(a348) | (~ndr1_0) | (~c0_1(a348)) | c2_1(a348) | (~c3_1(a359)) | (~c1_1(a359)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1453,plain,
% 0.69/0.85 (((~ndr1_0) | c2_1(a359) | (~c3_1(a359)) | (~c1_1(a359)) | c2_1(a348) | c1_1(a348) | (~c0_1(a348)) | c0_1(a359) | (~c1_1(a359)) | (~c3_1(a359))) <=> (c0_1(a359) | c2_1(a359) | c1_1(a348) | (~ndr1_0) | (~c0_1(a348)) | c2_1(a348) | (~c3_1(a359)) | (~c1_1(a359)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1454,plain,
% 0.69/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a359) | (~c3_1(a359)) | (~c1_1(a359)) | c2_1(a348) | c1_1(a348) | (~c0_1(a348)) | c0_1(a359) | (~c1_1(a359)) | (~c3_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a359) | c2_1(a359) | c1_1(a348) | (~ndr1_0) | (~c0_1(a348)) | c2_1(a348) | (~c3_1(a359)) | (~c1_1(a359))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[1453])).
% 0.69/0.86 tff(1455,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a359) | (~c3_1(a359)) | (~c1_1(a359)) | c2_1(a348) | c1_1(a348) | (~c0_1(a348)) | c0_1(a359) | (~c1_1(a359)) | (~c3_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a359) | c2_1(a359) | c1_1(a348) | (~ndr1_0) | (~c0_1(a348)) | c2_1(a348) | (~c3_1(a359)) | (~c1_1(a359)))),
% 0.69/0.86 inference(transitivity,[status(thm)],[1454, 1452])).
% 0.69/0.86 tff(1456,plain,
% 0.69/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a359) | (~c3_1(a359)) | (~c1_1(a359)) | c2_1(a348) | c1_1(a348) | (~c0_1(a348)) | c0_1(a359) | (~c1_1(a359)) | (~c3_1(a359)))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(1457,plain,
% 0.69/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a359) | c2_1(a359) | c1_1(a348) | (~ndr1_0) | (~c0_1(a348)) | c2_1(a348) | (~c3_1(a359)) | (~c1_1(a359))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1456, 1455])).
% 0.69/0.86 tff(1458,plain,
% 0.69/0.86 ($false),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1457, 134, 885, 1444, 893, 884, 1443, 920, 1451, 892])).
% 0.69/0.86 tff(1459,plain,(hskp25), inference(lemma,lemma(discharge,[]))).
% 0.69/0.86 tff(1460,plain,
% 0.69/0.86 (~c2_1(a419)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[251, 1459])).
% 0.69/0.86 tff(1461,plain,
% 0.69/0.86 (~c1_1(a419)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[257, 1459])).
% 0.69/0.86 tff(1462,plain,
% 0.69/0.86 (c0_1(a419)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[265, 1459])).
% 0.69/0.86 tff(1463,plain,
% 0.69/0.86 (hskp1),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1299, 1462, 1461, 1460])).
% 0.69/0.86 tff(1464,plain,
% 0.69/0.86 (~c3_1(a323)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[587, 1463])).
% 0.69/0.86 tff(1465,plain,
% 0.69/0.86 (~c2_1(a323)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[593, 1463])).
% 0.69/0.86 tff(1466,plain,
% 0.69/0.86 (~c1_1(a323)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[599, 1463])).
% 0.69/0.86 tff(1467,plain,
% 0.69/0.86 (hskp21),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[882, 134, 837, 829, 821, 1466, 1465, 1464, 10])).
% 0.69/0.86 tff(1468,plain,
% 0.69/0.86 (~c2_1(a359)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[849, 1467])).
% 0.69/0.86 tff(1469,plain,
% 0.69/0.86 (c3_1(a359)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[863, 1467])).
% 0.69/0.86 tff(1470,plain,
% 0.69/0.86 (~c0_1(a359)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[855, 1467])).
% 0.69/0.86 tff(1471,assumption,(c3_1(a359)), introduced(assumption)).
% 0.69/0.86 tff(1472,assumption,(ndr1_0), introduced(assumption)).
% 0.69/0.86 tff(1473,assumption,(~c1_1(a347)), introduced(assumption)).
% 0.69/0.86 tff(1474,assumption,(~c2_1(a359)), introduced(assumption)).
% 0.69/0.86 tff(1475,assumption,(~c0_1(a359)), introduced(assumption)).
% 0.69/0.86 tff(1476,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a359)) | (~c0_1(a419)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a359)) | (~c0_1(a419)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(1477,plain,
% 0.69/0.86 (((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a359) | c0_1(a359) | (~c3_1(a359))) <=> (c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a359)) | (~c0_1(a419)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(1478,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a359) | c0_1(a359) | (~c3_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a359)) | (~c0_1(a419))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[1477])).
% 0.69/0.86 tff(1479,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a359) | c0_1(a359) | (~c3_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a359)) | (~c0_1(a419)))),
% 0.69/0.86 inference(transitivity,[status(thm)],[1478, 1476])).
% 0.69/0.86 tff(1480,plain,
% 0.69/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a359) | c0_1(a359) | (~c3_1(a359)))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(1481,plain,
% 0.69/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a359)) | (~c0_1(a419))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1480, 1479])).
% 0.69/0.86 tff(1482,plain,
% 0.69/0.86 (c1_1(a419) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a359)) | (~c0_1(a419))),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1481, 1123, 1475, 1474, 1473, 235])).
% 0.69/0.86 tff(1483,plain,
% 0.69/0.86 ($false),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1482, 570, 571, 1472, 1471, 1125, 1124])).
% 0.69/0.86 tff(1484,plain,((~hskp14) | (~ndr1_0) | (~c3_1(a359)) | (~c0_1(a419)) | c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359) | c1_1(a347)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.86 tff(1485,plain,
% 0.69/0.86 ((~hskp14) | (~c3_1(a359)) | (~c0_1(a419)) | c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359) | c1_1(a347)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1484, 134])).
% 0.69/0.86 tff(1486,plain,
% 0.69/0.86 ((~c3_1(a359)) | (~c0_1(a419)) | c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1485, 1438, 1439])).
% 0.69/0.86 tff(1487,plain,
% 0.69/0.86 ($false),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1486, 1470, 1469, 1461, 1460, 1462, 1468])).
% 0.69/0.86 % SZS output end Proof
% 0.69/0.86 % E exiting
%------------------------------------------------------------------------------