%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN445-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:39:08 AM UTC 2025
% Result : Unsatisfiable 0.58s 0.75s
% Output : Proof 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN445-1 : TPTP v9.0.0. Released v2.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:35:07 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.58/0.75 % SZS status Unsatisfiable
% 0.58/0.75 % SZS output start Proof
% 0.58/0.75 tff(c2_1_type, type, (
% 0.58/0.75 c2_1: $i > $o)).
% 0.58/0.75 tff(a309_type, type, (
% 0.58/0.75 a309: $i)).
% 0.58/0.75 tff(hskp11_type, type, (
% 0.58/0.75 hskp11: $o)).
% 0.58/0.75 tff(c0_1_type, type, (
% 0.58/0.75 c0_1: $i > $o)).
% 0.58/0.75 tff(a333_type, type, (
% 0.58/0.75 a333: $i)).
% 0.58/0.75 tff(c1_1_type, type, (
% 0.58/0.75 c1_1: $i > $o)).
% 0.58/0.75 tff(c3_1_type, type, (
% 0.58/0.75 c3_1: $i > $o)).
% 0.58/0.75 tff(ndr1_0_type, type, (
% 0.58/0.75 ndr1_0: $o)).
% 0.58/0.75 tff(a297_type, type, (
% 0.58/0.75 a297: $i)).
% 0.58/0.75 tff(hskp2_type, type, (
% 0.58/0.75 hskp2: $o)).
% 0.58/0.75 tff(hskp0_type, type, (
% 0.58/0.75 hskp0: $o)).
% 0.58/0.75 tff(a294_type, type, (
% 0.58/0.75 a294: $i)).
% 0.58/0.75 tff(a308_type, type, (
% 0.58/0.75 a308: $i)).
% 0.58/0.75 tff(hskp10_type, type, (
% 0.58/0.75 hskp10: $o)).
% 0.58/0.75 tff(hskp3_type, type, (
% 0.58/0.75 hskp3: $o)).
% 0.58/0.75 tff(a336_type, type, (
% 0.58/0.75 a336: $i)).
% 0.58/0.75 tff(hskp21_type, type, (
% 0.58/0.75 hskp21: $o)).
% 0.58/0.75 tff(a295_type, type, (
% 0.58/0.75 a295: $i)).
% 0.58/0.75 tff(hskp1_type, type, (
% 0.58/0.75 hskp1: $o)).
% 0.58/0.75 tff(a303_type, type, (
% 0.58/0.75 a303: $i)).
% 0.58/0.75 tff(hskp7_type, type, (
% 0.58/0.75 hskp7: $o)).
% 0.58/0.75 tff(a321_type, type, (
% 0.58/0.75 a321: $i)).
% 0.58/0.75 tff(hskp29_type, type, (
% 0.58/0.75 hskp29: $o)).
% 0.58/0.75 tff(hskp27_type, type, (
% 0.58/0.75 hskp27: $o)).
% 0.58/0.75 tff(hskp16_type, type, (
% 0.58/0.75 hskp16: $o)).
% 0.58/0.75 tff(hskp26_type, type, (
% 0.58/0.75 hskp26: $o)).
% 0.58/0.75 tff(a349_type, type, (
% 0.58/0.75 a349: $i)).
% 0.58/0.75 tff(hskp20_type, type, (
% 0.58/0.75 hskp20: $o)).
% 0.58/0.75 tff(a299_type, type, (
% 0.58/0.75 a299: $i)).
% 0.58/0.75 tff(a300_type, type, (
% 0.58/0.75 a300: $i)).
% 0.58/0.75 tff(hskp4_type, type, (
% 0.58/0.75 hskp4: $o)).
% 0.58/0.75 tff(a310_type, type, (
% 0.58/0.75 a310: $i)).
% 0.58/0.75 tff(hskp12_type, type, (
% 0.58/0.75 hskp12: $o)).
% 0.58/0.75 tff(a338_type, type, (
% 0.58/0.75 a338: $i)).
% 0.58/0.75 tff(hskp22_type, type, (
% 0.58/0.75 hskp22: $o)).
% 0.58/0.75 tff(a315_type, type, (
% 0.58/0.75 a315: $i)).
% 0.58/0.75 tff(hskp14_type, type, (
% 0.58/0.75 hskp14: $o)).
% 0.58/0.75 tff(a323_type, type, (
% 0.58/0.75 a323: $i)).
% 0.58/0.75 tff(hskp17_type, type, (
% 0.58/0.75 hskp17: $o)).
% 0.58/0.75 tff(1,plain,
% 0.58/0.75 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 0.58/0.75 inference(bind,[status(th)],[])).
% 0.58/0.75 tff(2,plain,
% 0.58/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.58/0.75 inference(quant_intro,[status(thm)],[1])).
% 0.58/0.75 tff(3,plain,
% 0.58/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(4,plain,
% 0.58/0.75 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c1_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c1_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c0_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 0.58/0.75 inference(bind,[status(th)],[])).
% 0.58/0.75 tff(5,plain,
% 0.58/0.75 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.58/0.75 inference(quant_intro,[status(thm)],[4])).
% 0.58/0.75 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 0.58/0.75 tff(7,plain,
% 0.58/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.58/0.75 tff(8,plain,
% 0.58/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.58/0.75 tff(9,plain,(
% 0.58/0.75 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.58/0.75 inference(skolemize,[status(sab)],[8])).
% 0.58/0.75 tff(10,plain,
% 0.58/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.58/0.75 tff(11,assumption,(hskp0), introduced(assumption)).
% 0.58/0.75 tff(12,plain,
% 0.58/0.75 (((~hskp0) | (~c3_1(a294))) <=> ((~hskp0) | (~c3_1(a294)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(13,plain,
% 0.58/0.75 (((~c3_1(a294)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a294)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(14,axiom,((~c3_1(a294)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 0.58/0.75 tff(15,plain,
% 0.58/0.75 ((~hskp0) | (~c3_1(a294))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.58/0.75 tff(16,plain,
% 0.58/0.75 ((~hskp0) | (~c3_1(a294))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.58/0.75 tff(17,plain,
% 0.58/0.75 (~c3_1(a294)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[16, 11])).
% 0.58/0.75 tff(18,plain,
% 0.58/0.75 (((~hskp0) | (~c2_1(a294))) <=> ((~hskp0) | (~c2_1(a294)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(19,plain,
% 0.58/0.75 (((~c2_1(a294)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a294)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(20,axiom,((~c2_1(a294)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 0.58/0.75 tff(21,plain,
% 0.58/0.75 ((~hskp0) | (~c2_1(a294))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.58/0.75 tff(22,plain,
% 0.58/0.75 ((~hskp0) | (~c2_1(a294))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.58/0.75 tff(23,plain,
% 0.58/0.75 (~c2_1(a294)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[22, 11])).
% 0.58/0.75 tff(24,plain,
% 0.58/0.75 (((~hskp0) | (~c0_1(a294))) <=> ((~hskp0) | (~c0_1(a294)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(25,plain,
% 0.58/0.75 (((~c0_1(a294)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a294)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(26,axiom,((~c0_1(a294)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 0.58/0.75 tff(27,plain,
% 0.58/0.75 ((~hskp0) | (~c0_1(a294))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.58/0.75 tff(28,plain,
% 0.58/0.75 ((~hskp0) | (~c0_1(a294))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.58/0.75 tff(29,plain,
% 0.58/0.75 (~c0_1(a294)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[28, 11])).
% 0.58/0.75 tff(30,plain,
% 0.58/0.75 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.58/0.75 inference(bind,[status(th)],[])).
% 0.58/0.75 tff(31,plain,
% 0.58/0.75 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.58/0.75 inference(quant_intro,[status(thm)],[30])).
% 0.58/0.75 tff(32,plain,
% 0.58/0.75 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(33,plain,
% 0.58/0.75 (^[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) | c3_1(U) | 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) | c3_1(U) | c0_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) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_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) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c0_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)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.58/0.76 inference(bind,[status(th)],[])).
% 0.58/0.76 tff(34,plain,
% 0.58/0.76 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.58/0.76 inference(quant_intro,[status(thm)],[33])).
% 0.58/0.76 tff(35,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)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 0.58/0.76 tff(36,plain,
% 0.58/0.76 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.58/0.76 tff(37,plain,
% 0.58/0.76 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.58/0.76 tff(38,plain,(
% 0.58/0.76 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.58/0.76 inference(skolemize,[status(sab)],[37])).
% 0.58/0.76 tff(39,plain,
% 0.58/0.76 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.58/0.76 tff(40,assumption,(~hskp10), introduced(assumption)).
% 0.58/0.76 tff(41,assumption,(~hskp11), introduced(assumption)).
% 0.58/0.76 tff(42,plain,
% 0.58/0.76 (^[U: $i] : refl((hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U)) <=> (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U)))),
% 0.58/0.76 inference(bind,[status(th)],[])).
% 0.58/0.76 tff(43,plain,
% 0.58/0.76 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U)) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))),
% 0.58/0.76 inference(quant_intro,[status(thm)],[42])).
% 0.58/0.76 tff(44,plain,
% 0.58/0.76 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U)) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(45,plain,
% 0.58/0.76 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U)) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp11) <=> ((hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U)) | hskp11))), rewrite(((hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U)) | hskp11) <=> (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp11) <=> (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))))),
% 0.58/0.76 inference(bind,[status(th)],[])).
% 0.58/0.76 tff(46,plain,
% 0.58/0.76 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp11) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))),
% 0.58/0.76 inference(quant_intro,[status(thm)],[45])).
% 0.58/0.76 tff(47,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 0.58/0.76 tff(48,plain,
% 0.58/0.76 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.58/0.76 tff(49,plain,
% 0.58/0.76 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.58/0.76 tff(50,plain,(
% 0.58/0.76 ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))),
% 0.58/0.76 inference(skolemize,[status(sab)],[49])).
% 0.58/0.76 tff(51,plain,
% 0.58/0.76 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.58/0.76 tff(52,plain,
% 0.58/0.76 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.58/0.76 inference(bind,[status(th)],[])).
% 0.58/0.76 tff(53,plain,
% 0.58/0.76 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.58/0.76 inference(quant_intro,[status(thm)],[52])).
% 0.58/0.76 tff(54,plain,
% 0.58/0.76 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(55,plain,
% 0.58/0.76 (^[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) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_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(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.58/0.76 inference(bind,[status(th)],[])).
% 0.58/0.76 tff(56,plain,
% 0.58/0.76 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.58/0.76 inference(quant_intro,[status(thm)],[55])).
% 0.58/0.76 tff(57,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 0.58/0.76 tff(58,plain,
% 0.58/0.76 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.58/0.76 tff(59,plain,
% 0.58/0.76 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.58/0.76 tff(60,plain,(
% 0.58/0.76 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.58/0.76 inference(skolemize,[status(sab)],[59])).
% 0.58/0.76 tff(61,plain,
% 0.58/0.76 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.58/0.76 tff(62,assumption,(~hskp1), introduced(assumption)).
% 0.58/0.76 tff(63,plain,
% 0.58/0.76 ((hskp10 | hskp7 | hskp1) <=> (hskp10 | hskp7 | hskp1)),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(64,plain,
% 0.58/0.76 (((hskp7 | hskp1) | hskp10) <=> (hskp10 | hskp7 | hskp1)),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(65,plain,
% 0.58/0.76 ((hskp7 | hskp1) <=> (hskp7 | hskp1)),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(66,plain,
% 0.58/0.76 (((hskp7 | hskp1) | hskp10) <=> ((hskp7 | hskp1) | hskp10)),
% 0.58/0.76 inference(monotonicity,[status(thm)],[65])).
% 0.58/0.76 tff(67,plain,
% 0.58/0.76 (((hskp7 | hskp1) | hskp10) <=> (hskp10 | hskp7 | hskp1)),
% 0.58/0.76 inference(transitivity,[status(thm)],[66, 64])).
% 0.58/0.76 tff(68,axiom,((hskp7 | hskp1) | hskp10), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 0.58/0.76 tff(69,plain,
% 0.58/0.76 (hskp10 | hskp7 | hskp1),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.58/0.76 tff(70,plain,
% 0.58/0.76 (hskp10 | hskp7 | hskp1),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[69, 63])).
% 0.58/0.76 tff(71,plain,
% 0.58/0.76 (hskp10 | hskp7 | hskp1),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.58/0.76 tff(72,plain,
% 0.58/0.76 (hskp10 | hskp7 | hskp1),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[71, 63])).
% 0.58/0.76 tff(73,plain,
% 0.58/0.76 (hskp10 | hskp7 | hskp1),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[72, 63])).
% 0.58/0.76 tff(74,plain,
% 0.58/0.76 (hskp7),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[73, 62, 40])).
% 0.58/0.76 tff(75,plain,
% 0.58/0.76 (((~hskp7) | c0_1(a303)) <=> ((~hskp7) | c0_1(a303))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(76,axiom,((~hskp7) | c0_1(a303)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 0.58/0.76 tff(77,plain,
% 0.58/0.76 ((~hskp7) | c0_1(a303)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.58/0.76 tff(78,plain,
% 0.58/0.76 ((~hskp7) | c0_1(a303)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[77, 75])).
% 0.58/0.76 tff(79,plain,
% 0.58/0.76 ((~hskp7) | c0_1(a303)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[78, 75])).
% 0.58/0.76 tff(80,plain,
% 0.58/0.76 ((~hskp7) | c0_1(a303)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.58/0.76 tff(81,plain,
% 0.58/0.76 ((~hskp7) | c0_1(a303)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[80, 75])).
% 0.58/0.76 tff(82,plain,
% 0.58/0.76 (c0_1(a303)),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[81, 74])).
% 0.58/0.76 tff(83,plain,
% 0.58/0.76 (((~hskp7) | (~c2_1(a303))) <=> ((~hskp7) | (~c2_1(a303)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(84,plain,
% 0.58/0.76 (((~c2_1(a303)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a303)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(85,axiom,((~c2_1(a303)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 0.58/0.76 tff(86,plain,
% 0.58/0.76 ((~hskp7) | (~c2_1(a303))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.58/0.76 tff(87,plain,
% 0.58/0.76 ((~hskp7) | (~c2_1(a303))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[86, 83])).
% 0.58/0.76 tff(88,plain,
% 0.58/0.76 (~c2_1(a303)),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[87, 74])).
% 0.58/0.76 tff(89,plain,
% 0.58/0.76 (((~hskp7) | c1_1(a303)) <=> ((~hskp7) | c1_1(a303))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(90,axiom,((~hskp7) | c1_1(a303)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.58/0.76 tff(91,plain,
% 0.58/0.76 ((~hskp7) | c1_1(a303)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.58/0.76 tff(92,plain,
% 0.58/0.76 ((~hskp7) | c1_1(a303)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[91, 89])).
% 0.58/0.76 tff(93,plain,
% 0.58/0.76 ((~hskp7) | c1_1(a303)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[92, 89])).
% 0.58/0.76 tff(94,plain,
% 0.58/0.76 ((~hskp7) | c1_1(a303)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.58/0.76 tff(95,plain,
% 0.58/0.76 ((~hskp7) | c1_1(a303)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[94, 89])).
% 0.58/0.76 tff(96,plain,
% 0.58/0.76 (c1_1(a303)),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[95, 74])).
% 0.58/0.76 tff(97,assumption,(~hskp21), introduced(assumption)).
% 0.58/0.76 tff(98,plain,
% 0.58/0.76 (^[U: $i] : refl((hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 0.58/0.76 inference(bind,[status(th)],[])).
% 0.58/0.76 tff(99,plain,
% 0.58/0.76 (![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.58/0.76 inference(quant_intro,[status(thm)],[98])).
% 0.58/0.76 tff(100,plain,
% 0.58/0.76 (![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(101,plain,
% 0.58/0.76 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp21) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp21))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 0.58/0.76 inference(bind,[status(th)],[])).
% 0.58/0.76 tff(102,plain,
% 0.58/0.76 (![U: $i] : (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp21) <=> ![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.58/0.76 inference(quant_intro,[status(thm)],[101])).
% 0.58/0.76 tff(103,axiom,(![U: $i] : (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.58/0.76 tff(104,plain,
% 0.58/0.76 (![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.58/0.76 tff(105,plain,
% 0.58/0.76 (![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.58/0.76 tff(106,plain,(
% 0.58/0.76 ![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.58/0.76 inference(skolemize,[status(sab)],[105])).
% 0.58/0.76 tff(107,plain,
% 0.58/0.76 (![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.58/0.76 tff(108,assumption,(~c2_1(a303)), introduced(assumption)).
% 0.58/0.76 tff(109,assumption,(c0_1(a303)), introduced(assumption)).
% 0.58/0.76 tff(110,assumption,(~ndr1_0), introduced(assumption)).
% 0.58/0.76 tff(111,plain,
% 0.58/0.76 ((ndr1_0 | (~hskp10)) <=> (ndr1_0 | (~hskp10))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(112,plain,
% 0.58/0.76 (((~hskp10) | ndr1_0) <=> (ndr1_0 | (~hskp10))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(113,axiom,((~hskp10) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause21')).
% 0.58/0.76 tff(114,plain,
% 0.58/0.76 (ndr1_0 | (~hskp10)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.58/0.76 tff(115,plain,
% 0.58/0.76 (ndr1_0 | (~hskp10)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[114, 111])).
% 0.58/0.76 tff(116,plain,
% 0.58/0.76 (~hskp10),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[115, 110])).
% 0.58/0.76 tff(117,plain,
% 0.58/0.76 (((~hskp29) | ndr1_0) <=> ((~hskp29) | ndr1_0)),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(118,axiom,((~hskp29) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 0.58/0.76 tff(119,plain,
% 0.58/0.76 ((~hskp29) | ndr1_0),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.58/0.76 tff(120,plain,
% 0.58/0.76 ((~hskp29) | ndr1_0),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[119, 117])).
% 0.58/0.76 tff(121,plain,
% 0.58/0.76 ((~hskp29) | ndr1_0),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[120, 117])).
% 0.58/0.76 tff(122,plain,
% 0.58/0.76 ((~hskp29) | ndr1_0),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.58/0.76 tff(123,plain,
% 0.58/0.76 ((~hskp29) | ndr1_0),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[122, 117])).
% 0.58/0.76 tff(124,plain,
% 0.58/0.76 (~hskp29),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[123, 110])).
% 0.58/0.76 tff(125,plain,
% 0.58/0.76 ((ndr1_0 | (~hskp27)) <=> (ndr1_0 | (~hskp27))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(126,plain,
% 0.58/0.76 (((~hskp27) | ndr1_0) <=> (ndr1_0 | (~hskp27))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(127,axiom,((~hskp27) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause4')).
% 0.58/0.76 tff(128,plain,
% 0.58/0.76 (ndr1_0 | (~hskp27)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.58/0.76 tff(129,plain,
% 0.58/0.76 (ndr1_0 | (~hskp27)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[128, 125])).
% 0.58/0.76 tff(130,plain,
% 0.58/0.76 (~hskp27),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[129, 110])).
% 0.58/0.76 tff(131,plain,
% 0.58/0.76 ((hskp29 | hskp27 | hskp10) <=> (hskp29 | hskp27 | hskp10)),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(132,plain,
% 0.58/0.76 (((hskp29 | hskp27) | hskp10) <=> (hskp29 | hskp27 | hskp10)),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(133,plain,
% 0.58/0.76 ((hskp29 | hskp27) <=> (hskp29 | hskp27)),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(134,plain,
% 0.58/0.76 (((hskp29 | hskp27) | hskp10) <=> ((hskp29 | hskp27) | hskp10)),
% 0.58/0.76 inference(monotonicity,[status(thm)],[133])).
% 0.58/0.76 tff(135,plain,
% 0.58/0.76 (((hskp29 | hskp27) | hskp10) <=> (hskp29 | hskp27 | hskp10)),
% 0.58/0.76 inference(transitivity,[status(thm)],[134, 132])).
% 0.58/0.76 tff(136,axiom,((hskp29 | hskp27) | hskp10), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 0.58/0.76 tff(137,plain,
% 0.58/0.76 (hskp29 | hskp27 | hskp10),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.58/0.76 tff(138,plain,
% 0.58/0.76 (hskp29 | hskp27 | hskp10),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[137, 131])).
% 0.58/0.76 tff(139,plain,
% 0.58/0.76 (hskp29 | hskp27 | hskp10),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.58/0.76 tff(140,plain,
% 0.58/0.76 (hskp29 | hskp27 | hskp10),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[139, 131])).
% 0.58/0.76 tff(141,plain,
% 0.58/0.76 (hskp29 | hskp27 | hskp10),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[140, 131])).
% 0.58/0.76 tff(142,plain,
% 0.58/0.76 ($false),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[141, 130, 124, 116])).
% 0.58/0.76 tff(143,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.58/0.76 tff(144,plain,
% 0.58/0.76 (((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp21 | c2_1(a303) | (~ndr1_0) | c3_1(a303) | (~c0_1(a303)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp21 | c2_1(a303) | (~ndr1_0) | c3_1(a303) | (~c0_1(a303)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(145,plain,
% 0.58/0.76 ((hskp21 | (~ndr1_0) | c2_1(a303) | c3_1(a303) | (~c0_1(a303))) <=> (hskp21 | c2_1(a303) | (~ndr1_0) | c3_1(a303) | (~c0_1(a303)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(146,plain,
% 0.58/0.76 (((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp21 | (~ndr1_0) | c2_1(a303) | c3_1(a303) | (~c0_1(a303)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp21 | c2_1(a303) | (~ndr1_0) | c3_1(a303) | (~c0_1(a303))))),
% 0.58/0.76 inference(monotonicity,[status(thm)],[145])).
% 0.58/0.76 tff(147,plain,
% 0.58/0.76 (((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp21 | (~ndr1_0) | c2_1(a303) | c3_1(a303) | (~c0_1(a303)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp21 | c2_1(a303) | (~ndr1_0) | c3_1(a303) | (~c0_1(a303)))),
% 0.58/0.76 inference(transitivity,[status(thm)],[146, 144])).
% 0.58/0.76 tff(148,plain,
% 0.58/0.76 ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp21 | (~ndr1_0) | c2_1(a303) | c3_1(a303) | (~c0_1(a303)))),
% 0.58/0.76 inference(quant_inst,[status(thm)],[])).
% 0.58/0.76 tff(149,plain,
% 0.58/0.76 ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp21 | c2_1(a303) | (~ndr1_0) | c3_1(a303) | (~c0_1(a303))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.58/0.76 tff(150,plain,
% 0.58/0.76 (hskp21 | c3_1(a303)),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[149, 143, 109, 108, 107])).
% 0.58/0.76 tff(151,plain,
% 0.58/0.76 (c3_1(a303)),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[150, 97])).
% 0.58/0.76 tff(152,plain,
% 0.58/0.76 (^[V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 0.58/0.76 inference(bind,[status(th)],[])).
% 0.58/0.76 tff(153,plain,
% 0.58/0.76 (![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.58/0.76 inference(quant_intro,[status(thm)],[152])).
% 0.58/0.76 tff(154,plain,
% 0.58/0.76 (![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(155,plain,
% 0.58/0.76 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 0.58/0.76 inference(bind,[status(th)],[])).
% 0.58/0.76 tff(156,plain,
% 0.58/0.76 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.58/0.76 inference(quant_intro,[status(thm)],[155])).
% 0.58/0.76 tff(157,axiom,(![V: $i, U: $i] : (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 0.58/0.76 tff(158,plain,
% 0.58/0.76 (![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.58/0.76 tff(159,plain,
% 0.58/0.76 (![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[158, 154])).
% 0.58/0.76 tff(160,plain,(
% 0.58/0.76 ![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.58/0.76 inference(skolemize,[status(sab)],[159])).
% 0.58/0.76 tff(161,plain,
% 0.58/0.76 (![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[160, 153])).
% 0.58/0.76 tff(162,assumption,(c1_1(a303)), introduced(assumption)).
% 0.58/0.76 tff(163,assumption,(hskp26), introduced(assumption)).
% 0.58/0.76 tff(164,plain,
% 0.58/0.76 (((~hskp26) | (~c3_1(a349))) <=> ((~hskp26) | (~c3_1(a349)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(165,plain,
% 0.58/0.76 (((~c3_1(a349)) | (~hskp26)) <=> ((~hskp26) | (~c3_1(a349)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(166,axiom,((~c3_1(a349)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.58/0.76 tff(167,plain,
% 0.58/0.76 ((~hskp26) | (~c3_1(a349))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.58/0.76 tff(168,plain,
% 0.58/0.76 ((~hskp26) | (~c3_1(a349))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[167, 164])).
% 0.58/0.76 tff(169,plain,
% 0.58/0.76 (~c3_1(a349)),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[168, 163])).
% 0.58/0.76 tff(170,plain,
% 0.58/0.76 (((~hskp26) | (~c2_1(a349))) <=> ((~hskp26) | (~c2_1(a349)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(171,plain,
% 0.58/0.76 (((~c2_1(a349)) | (~hskp26)) <=> ((~hskp26) | (~c2_1(a349)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(172,axiom,((~c2_1(a349)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 0.58/0.76 tff(173,plain,
% 0.58/0.76 ((~hskp26) | (~c2_1(a349))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.58/0.76 tff(174,plain,
% 0.58/0.76 ((~hskp26) | (~c2_1(a349))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[173, 170])).
% 0.58/0.76 tff(175,plain,
% 0.58/0.76 (~c2_1(a349)),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[174, 163])).
% 0.58/0.76 tff(176,plain,
% 0.58/0.76 (((~hskp26) | c0_1(a349)) <=> ((~hskp26) | c0_1(a349))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(177,axiom,((~hskp26) | c0_1(a349)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 0.58/0.76 tff(178,plain,
% 0.58/0.76 ((~hskp26) | c0_1(a349)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.58/0.76 tff(179,plain,
% 0.58/0.76 ((~hskp26) | c0_1(a349)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[178, 176])).
% 0.58/0.76 tff(180,plain,
% 0.58/0.76 ((~hskp26) | c0_1(a349)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[179, 176])).
% 0.58/0.76 tff(181,plain,
% 0.58/0.76 ((~hskp26) | c0_1(a349)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[180, 176])).
% 0.58/0.76 tff(182,plain,
% 0.58/0.76 ((~hskp26) | c0_1(a349)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[181, 176])).
% 0.58/0.76 tff(183,plain,
% 0.58/0.76 (c0_1(a349)),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[182, 163])).
% 0.58/0.76 tff(184,plain,
% 0.58/0.76 (((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp21 | c2_1(a349) | c3_1(a349) | (~ndr1_0) | (~c0_1(a349)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp21 | c2_1(a349) | c3_1(a349) | (~ndr1_0) | (~c0_1(a349)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(185,plain,
% 0.58/0.76 ((hskp21 | (~ndr1_0) | c2_1(a349) | c3_1(a349) | (~c0_1(a349))) <=> (hskp21 | c2_1(a349) | c3_1(a349) | (~ndr1_0) | (~c0_1(a349)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(186,plain,
% 0.58/0.76 (((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp21 | (~ndr1_0) | c2_1(a349) | c3_1(a349) | (~c0_1(a349)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp21 | c2_1(a349) | c3_1(a349) | (~ndr1_0) | (~c0_1(a349))))),
% 0.58/0.76 inference(monotonicity,[status(thm)],[185])).
% 0.58/0.77 tff(187,plain,
% 0.58/0.77 (((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp21 | (~ndr1_0) | c2_1(a349) | c3_1(a349) | (~c0_1(a349)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp21 | c2_1(a349) | c3_1(a349) | (~ndr1_0) | (~c0_1(a349)))),
% 0.58/0.77 inference(transitivity,[status(thm)],[186, 184])).
% 0.58/0.77 tff(188,plain,
% 0.58/0.77 ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp21 | (~ndr1_0) | c2_1(a349) | c3_1(a349) | (~c0_1(a349)))),
% 0.58/0.77 inference(quant_inst,[status(thm)],[])).
% 0.58/0.77 tff(189,plain,
% 0.58/0.77 ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp21 | c2_1(a349) | c3_1(a349) | (~ndr1_0) | (~c0_1(a349))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.58/0.77 tff(190,plain,
% 0.58/0.77 ($false),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[189, 143, 97, 183, 175, 169, 107])).
% 0.58/0.77 tff(191,plain,((~hskp26) | hskp21), inference(lemma,lemma(discharge,[]))).
% 0.58/0.77 tff(192,plain,
% 0.58/0.77 (~hskp26),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[191, 97])).
% 0.58/0.77 tff(193,plain,
% 0.58/0.77 ((hskp26 | hskp16) <=> (hskp26 | hskp16)),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(194,axiom,(hskp26 | hskp16), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.58/0.77 tff(195,plain,
% 0.58/0.77 (hskp26 | hskp16),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.58/0.77 tff(196,plain,
% 0.58/0.77 (hskp26 | hskp16),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[195, 193])).
% 0.58/0.77 tff(197,plain,
% 0.58/0.77 (hskp26 | hskp16),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[196, 193])).
% 0.58/0.77 tff(198,plain,
% 0.58/0.77 (hskp26 | hskp16),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[197, 193])).
% 0.58/0.77 tff(199,plain,
% 0.58/0.77 (hskp26 | hskp16),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[198, 193])).
% 0.58/0.77 tff(200,plain,
% 0.58/0.77 (hskp16),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[199, 192])).
% 0.58/0.77 tff(201,plain,
% 0.58/0.77 (((~hskp16) | c3_1(a321)) <=> ((~hskp16) | c3_1(a321))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(202,axiom,((~hskp16) | c3_1(a321)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 0.58/0.77 tff(203,plain,
% 0.58/0.77 ((~hskp16) | c3_1(a321)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.58/0.77 tff(204,plain,
% 0.58/0.77 ((~hskp16) | c3_1(a321)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[203, 201])).
% 0.58/0.77 tff(205,plain,
% 0.58/0.77 ((~hskp16) | c3_1(a321)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[204, 201])).
% 0.58/0.77 tff(206,plain,
% 0.58/0.77 ((~hskp16) | c3_1(a321)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[205, 201])).
% 0.58/0.77 tff(207,plain,
% 0.58/0.77 ((~hskp16) | c3_1(a321)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[206, 201])).
% 0.58/0.77 tff(208,plain,
% 0.58/0.77 (c3_1(a321)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[207, 200])).
% 0.58/0.77 tff(209,plain,
% 0.58/0.77 (((~hskp16) | c2_1(a321)) <=> ((~hskp16) | c2_1(a321))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(210,axiom,((~hskp16) | c2_1(a321)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 0.58/0.77 tff(211,plain,
% 0.58/0.77 ((~hskp16) | c2_1(a321)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.58/0.77 tff(212,plain,
% 0.58/0.77 ((~hskp16) | c2_1(a321)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[211, 209])).
% 0.58/0.77 tff(213,plain,
% 0.58/0.77 ((~hskp16) | c2_1(a321)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[212, 209])).
% 0.58/0.77 tff(214,plain,
% 0.58/0.77 ((~hskp16) | c2_1(a321)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[213, 209])).
% 0.58/0.77 tff(215,plain,
% 0.58/0.77 ((~hskp16) | c2_1(a321)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[214, 209])).
% 0.58/0.77 tff(216,plain,
% 0.58/0.77 (c2_1(a321)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[215, 200])).
% 0.58/0.77 tff(217,plain,
% 0.58/0.77 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (c2_1(a303) | (~ndr1_0) | (~c1_1(a303)) | (~c3_1(a303)) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | c2_1(a303) | (~ndr1_0) | (~c1_1(a303)) | (~c3_1(a303)) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(218,plain,
% 0.58/0.77 (((~ndr1_0) | (~c3_1(a321)) | (~c0_1(a321)) | (~c2_1(a321)) | c2_1(a303) | (~c1_1(a303)) | (~c3_1(a303))) <=> (c2_1(a303) | (~ndr1_0) | (~c1_1(a303)) | (~c3_1(a303)) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(219,plain,
% 0.58/0.77 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | ((~ndr1_0) | (~c3_1(a321)) | (~c0_1(a321)) | (~c2_1(a321)) | c2_1(a303) | (~c1_1(a303)) | (~c3_1(a303)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (c2_1(a303) | (~ndr1_0) | (~c1_1(a303)) | (~c3_1(a303)) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321))))),
% 0.58/0.77 inference(monotonicity,[status(thm)],[218])).
% 0.58/0.77 tff(220,plain,
% 0.58/0.77 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | ((~ndr1_0) | (~c3_1(a321)) | (~c0_1(a321)) | (~c2_1(a321)) | c2_1(a303) | (~c1_1(a303)) | (~c3_1(a303)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | c2_1(a303) | (~ndr1_0) | (~c1_1(a303)) | (~c3_1(a303)) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321)))),
% 0.58/0.77 inference(transitivity,[status(thm)],[219, 217])).
% 0.58/0.77 tff(221,plain,
% 0.58/0.77 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | ((~ndr1_0) | (~c3_1(a321)) | (~c0_1(a321)) | (~c2_1(a321)) | c2_1(a303) | (~c1_1(a303)) | (~c3_1(a303)))),
% 0.58/0.77 inference(quant_inst,[status(thm)],[])).
% 0.58/0.77 tff(222,plain,
% 0.58/0.77 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | c2_1(a303) | (~ndr1_0) | (~c1_1(a303)) | (~c3_1(a303)) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.58/0.77 tff(223,plain,
% 0.58/0.77 (~c0_1(a321)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[222, 143, 216, 208, 162, 108, 161, 151])).
% 0.58/0.77 tff(224,plain,
% 0.58/0.77 (((~hskp16) | (~c1_1(a321))) <=> ((~hskp16) | (~c1_1(a321)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(225,plain,
% 0.58/0.77 (((~c1_1(a321)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a321)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(226,axiom,((~c1_1(a321)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.58/0.77 tff(227,plain,
% 0.58/0.77 ((~hskp16) | (~c1_1(a321))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.58/0.77 tff(228,plain,
% 0.58/0.77 ((~hskp16) | (~c1_1(a321))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[227, 224])).
% 0.58/0.77 tff(229,plain,
% 0.58/0.77 (~c1_1(a321)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[228, 200])).
% 0.58/0.77 tff(230,plain,
% 0.58/0.77 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a321) | (~ndr1_0) | c0_1(a321) | (~c2_1(a321)) | (~c3_1(a321)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a321) | (~ndr1_0) | c0_1(a321) | (~c2_1(a321)) | (~c3_1(a321)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(231,plain,
% 0.58/0.77 ((hskp1 | (~ndr1_0) | c1_1(a321) | (~c3_1(a321)) | (~c2_1(a321)) | c1_1(a321) | c0_1(a321) | (~c2_1(a321))) <=> (hskp1 | c1_1(a321) | (~ndr1_0) | c0_1(a321) | (~c2_1(a321)) | (~c3_1(a321)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(232,plain,
% 0.58/0.77 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a321) | (~c3_1(a321)) | (~c2_1(a321)) | c1_1(a321) | c0_1(a321) | (~c2_1(a321)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a321) | (~ndr1_0) | c0_1(a321) | (~c2_1(a321)) | (~c3_1(a321))))),
% 0.58/0.77 inference(monotonicity,[status(thm)],[231])).
% 0.58/0.77 tff(233,plain,
% 0.58/0.77 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a321) | (~c3_1(a321)) | (~c2_1(a321)) | c1_1(a321) | c0_1(a321) | (~c2_1(a321)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a321) | (~ndr1_0) | c0_1(a321) | (~c2_1(a321)) | (~c3_1(a321)))),
% 0.58/0.77 inference(transitivity,[status(thm)],[232, 230])).
% 0.58/0.77 tff(234,plain,
% 0.58/0.77 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a321) | (~c3_1(a321)) | (~c2_1(a321)) | c1_1(a321) | c0_1(a321) | (~c2_1(a321)))),
% 0.58/0.77 inference(quant_inst,[status(thm)],[])).
% 0.58/0.77 tff(235,plain,
% 0.58/0.77 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a321) | (~ndr1_0) | c0_1(a321) | (~c2_1(a321)) | (~c3_1(a321))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.58/0.77 tff(236,plain,
% 0.58/0.77 ($false),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[235, 143, 62, 216, 208, 229, 61, 223])).
% 0.58/0.77 tff(237,plain,(hskp21 | hskp1 | (~c1_1(a303)) | c2_1(a303) | (~c0_1(a303))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.77 tff(238,plain,
% 0.58/0.77 (hskp21),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[237, 62, 96, 88, 82])).
% 0.58/0.77 tff(239,plain,
% 0.58/0.77 (((~hskp21) | (~c1_1(a336))) <=> ((~hskp21) | (~c1_1(a336)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(240,plain,
% 0.58/0.77 (((~c1_1(a336)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a336)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(241,axiom,((~c1_1(a336)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 0.58/0.77 tff(242,plain,
% 0.58/0.77 ((~hskp21) | (~c1_1(a336))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.58/0.77 tff(243,plain,
% 0.58/0.77 ((~hskp21) | (~c1_1(a336))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[242, 239])).
% 0.58/0.77 tff(244,plain,
% 0.58/0.77 (~c1_1(a336)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[243, 238])).
% 0.58/0.77 tff(245,plain,
% 0.58/0.77 (((~hskp21) | (~c0_1(a336))) <=> ((~hskp21) | (~c0_1(a336)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(246,plain,
% 0.58/0.77 (((~c0_1(a336)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a336)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(247,axiom,((~c0_1(a336)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 0.58/0.77 tff(248,plain,
% 0.58/0.77 ((~hskp21) | (~c0_1(a336))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.58/0.77 tff(249,plain,
% 0.58/0.77 ((~hskp21) | (~c0_1(a336))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[248, 245])).
% 0.58/0.77 tff(250,plain,
% 0.58/0.77 (~c0_1(a336)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[249, 238])).
% 0.58/0.77 tff(251,plain,
% 0.58/0.77 (((~hskp21) | c3_1(a336)) <=> ((~hskp21) | c3_1(a336))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(252,axiom,((~hskp21) | c3_1(a336)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 0.58/0.77 tff(253,plain,
% 0.58/0.77 ((~hskp21) | c3_1(a336)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.58/0.77 tff(254,plain,
% 0.58/0.77 ((~hskp21) | c3_1(a336)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[253, 251])).
% 0.58/0.77 tff(255,plain,
% 0.58/0.77 ((~hskp21) | c3_1(a336)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[254, 251])).
% 0.58/0.77 tff(256,plain,
% 0.58/0.77 ((~hskp21) | c3_1(a336)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[255, 251])).
% 0.58/0.77 tff(257,plain,
% 0.58/0.77 ((~hskp21) | c3_1(a336)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[256, 251])).
% 0.58/0.77 tff(258,plain,
% 0.58/0.77 (c3_1(a336)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[257, 238])).
% 0.58/0.77 tff(259,plain,
% 0.58/0.77 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a336) | c1_1(a336) | (~ndr1_0) | (~c2_1(a336)) | (~c3_1(a336)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a336) | c1_1(a336) | (~ndr1_0) | (~c2_1(a336)) | (~c3_1(a336)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(260,plain,
% 0.58/0.77 ((hskp1 | (~ndr1_0) | c1_1(a336) | (~c3_1(a336)) | (~c2_1(a336)) | c1_1(a336) | c0_1(a336) | (~c2_1(a336))) <=> (hskp1 | c0_1(a336) | c1_1(a336) | (~ndr1_0) | (~c2_1(a336)) | (~c3_1(a336)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(261,plain,
% 0.58/0.77 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a336) | (~c3_1(a336)) | (~c2_1(a336)) | c1_1(a336) | c0_1(a336) | (~c2_1(a336)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a336) | c1_1(a336) | (~ndr1_0) | (~c2_1(a336)) | (~c3_1(a336))))),
% 0.58/0.77 inference(monotonicity,[status(thm)],[260])).
% 0.58/0.77 tff(262,plain,
% 0.58/0.77 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a336) | (~c3_1(a336)) | (~c2_1(a336)) | c1_1(a336) | c0_1(a336) | (~c2_1(a336)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a336) | c1_1(a336) | (~ndr1_0) | (~c2_1(a336)) | (~c3_1(a336)))),
% 0.58/0.77 inference(transitivity,[status(thm)],[261, 259])).
% 0.58/0.77 tff(263,plain,
% 0.58/0.77 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a336) | (~c3_1(a336)) | (~c2_1(a336)) | c1_1(a336) | c0_1(a336) | (~c2_1(a336)))),
% 0.58/0.77 inference(quant_inst,[status(thm)],[])).
% 0.58/0.77 tff(264,plain,
% 0.58/0.77 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a336) | c1_1(a336) | (~ndr1_0) | (~c2_1(a336)) | (~c3_1(a336))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.58/0.77 tff(265,plain,
% 0.58/0.77 (~c2_1(a336)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[264, 143, 62, 258, 250, 244, 61])).
% 0.58/0.77 tff(266,plain,
% 0.58/0.77 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.58/0.77 inference(bind,[status(th)],[])).
% 0.58/0.77 tff(267,plain,
% 0.58/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.58/0.77 inference(quant_intro,[status(thm)],[266])).
% 0.58/0.77 tff(268,plain,
% 0.58/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(269,plain,
% 0.58/0.77 (^[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)) | 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)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_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))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | 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)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.58/0.77 inference(bind,[status(th)],[])).
% 0.58/0.77 tff(270,plain,
% 0.58/0.77 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.58/0.77 inference(quant_intro,[status(thm)],[269])).
% 0.58/0.77 tff(271,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 0.58/0.77 tff(272,plain,
% 0.58/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.58/0.77 tff(273,plain,
% 0.58/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[272, 268])).
% 0.58/0.77 tff(274,plain,(
% 0.58/0.77 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.58/0.77 inference(skolemize,[status(sab)],[273])).
% 0.58/0.77 tff(275,plain,
% 0.58/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[274, 267])).
% 0.58/0.77 tff(276,plain,
% 0.58/0.77 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))) | (hskp11 | hskp10 | c0_1(a336) | (~ndr1_0) | c2_1(a336) | (~c3_1(a336)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))) | hskp11 | hskp10 | c0_1(a336) | (~ndr1_0) | c2_1(a336) | (~c3_1(a336)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(277,plain,
% 0.58/0.77 ((hskp11 | hskp10 | (~ndr1_0) | c2_1(a336) | (~c3_1(a336)) | c0_1(a336)) <=> (hskp11 | hskp10 | c0_1(a336) | (~ndr1_0) | c2_1(a336) | (~c3_1(a336)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(278,plain,
% 0.58/0.77 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c2_1(a336) | (~c3_1(a336)) | c0_1(a336))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))) | (hskp11 | hskp10 | c0_1(a336) | (~ndr1_0) | c2_1(a336) | (~c3_1(a336))))),
% 0.58/0.77 inference(monotonicity,[status(thm)],[277])).
% 0.58/0.77 tff(279,plain,
% 0.58/0.77 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c2_1(a336) | (~c3_1(a336)) | c0_1(a336))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))) | hskp11 | hskp10 | c0_1(a336) | (~ndr1_0) | c2_1(a336) | (~c3_1(a336)))),
% 0.58/0.77 inference(transitivity,[status(thm)],[278, 276])).
% 0.58/0.77 tff(280,plain,
% 0.58/0.77 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c2_1(a336) | (~c3_1(a336)) | c0_1(a336))),
% 0.58/0.77 inference(quant_inst,[status(thm)],[])).
% 0.58/0.77 tff(281,plain,
% 0.58/0.77 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))) | hskp11 | hskp10 | c0_1(a336) | (~ndr1_0) | c2_1(a336) | (~c3_1(a336))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.58/0.77 tff(282,plain,
% 0.58/0.77 (hskp11 | c2_1(a336)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[281, 143, 40, 258, 250, 51])).
% 0.58/0.77 tff(283,plain,
% 0.58/0.77 (hskp11),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[282, 265])).
% 0.58/0.77 tff(284,plain,
% 0.58/0.77 (((~hskp11) | (~c2_1(a309))) <=> ((~hskp11) | (~c2_1(a309)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(285,plain,
% 0.58/0.77 (((~c2_1(a309)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a309)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(286,axiom,((~c2_1(a309)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.58/0.77 tff(287,plain,
% 0.58/0.77 ((~hskp11) | (~c2_1(a309))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.58/0.77 tff(288,plain,
% 0.58/0.77 ((~hskp11) | (~c2_1(a309))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[287, 284])).
% 0.58/0.77 tff(289,plain,
% 0.58/0.77 (~c2_1(a309)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[288, 283])).
% 0.58/0.77 tff(290,plain,
% 0.58/0.77 (((~hskp11) | c3_1(a309)) <=> ((~hskp11) | c3_1(a309))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(291,axiom,((~hskp11) | c3_1(a309)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 0.58/0.77 tff(292,plain,
% 0.58/0.77 ((~hskp11) | c3_1(a309)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.58/0.77 tff(293,plain,
% 0.58/0.77 ((~hskp11) | c3_1(a309)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[292, 290])).
% 0.58/0.77 tff(294,plain,
% 0.58/0.77 ((~hskp11) | c3_1(a309)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[293, 290])).
% 0.58/0.77 tff(295,plain,
% 0.58/0.77 ((~hskp11) | c3_1(a309)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[294, 290])).
% 0.58/0.77 tff(296,plain,
% 0.58/0.77 ((~hskp11) | c3_1(a309)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[295, 290])).
% 0.58/0.77 tff(297,plain,
% 0.58/0.77 (c3_1(a309)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[296, 283])).
% 0.58/0.77 tff(298,plain,
% 0.58/0.77 (((~hskp11) | c1_1(a309)) <=> ((~hskp11) | c1_1(a309))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(299,axiom,((~hskp11) | c1_1(a309)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 0.58/0.77 tff(300,plain,
% 0.58/0.77 ((~hskp11) | c1_1(a309)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.58/0.77 tff(301,plain,
% 0.58/0.77 ((~hskp11) | c1_1(a309)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[300, 298])).
% 0.58/0.77 tff(302,plain,
% 0.58/0.77 ((~hskp11) | c1_1(a309)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[301, 298])).
% 0.58/0.77 tff(303,plain,
% 0.58/0.77 ((~hskp11) | c1_1(a309)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[302, 298])).
% 0.58/0.77 tff(304,plain,
% 0.58/0.77 ((~hskp11) | c1_1(a309)),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[303, 298])).
% 0.58/0.77 tff(305,plain,
% 0.58/0.77 (c1_1(a309)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[304, 283])).
% 0.58/0.77 tff(306,plain,
% 0.58/0.77 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.58/0.77 inference(bind,[status(th)],[])).
% 0.58/0.77 tff(307,plain,
% 0.58/0.77 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.58/0.77 inference(quant_intro,[status(thm)],[306])).
% 0.58/0.77 tff(308,plain,
% 0.58/0.77 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(309,plain,
% 0.58/0.77 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_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) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.58/0.78 inference(bind,[status(th)],[])).
% 0.58/0.78 tff(310,plain,
% 0.58/0.78 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.58/0.78 inference(quant_intro,[status(thm)],[309])).
% 0.58/0.78 tff(311,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 0.58/0.78 tff(312,plain,
% 0.58/0.78 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.58/0.78 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.58/0.78 tff(313,plain,
% 0.58/0.78 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.58/0.78 inference(modus_ponens,[status(thm)],[312, 308])).
% 0.58/0.78 tff(314,plain,(
% 0.58/0.78 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.58/0.78 inference(skolemize,[status(sab)],[313])).
% 0.58/0.78 tff(315,plain,
% 0.58/0.78 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.58/0.78 inference(modus_ponens,[status(thm)],[314, 307])).
% 0.58/0.78 tff(316,assumption,(~c2_1(a309)), introduced(assumption)).
% 0.58/0.78 tff(317,assumption,(hskp21), introduced(assumption)).
% 0.58/0.78 tff(318,plain,
% 0.58/0.78 (~c1_1(a336)),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[243, 317])).
% 0.58/0.78 tff(319,plain,
% 0.58/0.78 (~c0_1(a336)),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[249, 317])).
% 0.58/0.78 tff(320,assumption,(c3_1(a309)), introduced(assumption)).
% 0.58/0.78 tff(321,assumption,(c1_1(a309)), introduced(assumption)).
% 0.58/0.78 tff(322,plain,
% 0.58/0.78 (c3_1(a336)),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[257, 317])).
% 0.58/0.78 tff(323,assumption,(~hskp0), introduced(assumption)).
% 0.58/0.78 tff(324,plain,
% 0.58/0.78 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c0_1(a336) | c1_1(a336) | c2_1(a309) | (~ndr1_0) | (~c1_1(a309)) | (~c3_1(a309)) | (~c3_1(a336)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c0_1(a336) | c1_1(a336) | c2_1(a309) | (~ndr1_0) | (~c1_1(a309)) | (~c3_1(a309)) | (~c3_1(a336)))),
% 0.58/0.78 inference(rewrite,[status(thm)],[])).
% 0.58/0.78 tff(325,plain,
% 0.58/0.78 ((hskp0 | (~ndr1_0) | c2_1(a309) | (~c3_1(a309)) | (~c1_1(a309)) | c1_1(a336) | c0_1(a336) | (~c3_1(a336))) <=> (hskp0 | c0_1(a336) | c1_1(a336) | c2_1(a309) | (~ndr1_0) | (~c1_1(a309)) | (~c3_1(a309)) | (~c3_1(a336)))),
% 0.58/0.78 inference(rewrite,[status(thm)],[])).
% 0.58/0.78 tff(326,plain,
% 0.58/0.78 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a309) | (~c3_1(a309)) | (~c1_1(a309)) | c1_1(a336) | c0_1(a336) | (~c3_1(a336)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c0_1(a336) | c1_1(a336) | c2_1(a309) | (~ndr1_0) | (~c1_1(a309)) | (~c3_1(a309)) | (~c3_1(a336))))),
% 0.58/0.78 inference(monotonicity,[status(thm)],[325])).
% 0.58/0.78 tff(327,plain,
% 0.58/0.78 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a309) | (~c3_1(a309)) | (~c1_1(a309)) | c1_1(a336) | c0_1(a336) | (~c3_1(a336)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c0_1(a336) | c1_1(a336) | c2_1(a309) | (~ndr1_0) | (~c1_1(a309)) | (~c3_1(a309)) | (~c3_1(a336)))),
% 0.58/0.78 inference(transitivity,[status(thm)],[326, 324])).
% 0.58/0.78 tff(328,plain,
% 0.58/0.78 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a309) | (~c3_1(a309)) | (~c1_1(a309)) | c1_1(a336) | c0_1(a336) | (~c3_1(a336)))),
% 0.58/0.78 inference(quant_inst,[status(thm)],[])).
% 0.58/0.78 tff(329,plain,
% 0.58/0.78 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c0_1(a336) | c1_1(a336) | c2_1(a309) | (~ndr1_0) | (~c1_1(a309)) | (~c3_1(a309)) | (~c3_1(a336))),
% 0.58/0.78 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.58/0.78 tff(330,plain,
% 0.58/0.78 ($false),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[329, 143, 323, 322, 321, 320, 319, 318, 316, 315])).
% 0.58/0.78 tff(331,plain,((~hskp21) | hskp0 | (~c1_1(a309)) | (~c3_1(a309)) | c2_1(a309)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.78 tff(332,plain,
% 0.58/0.78 (hskp0),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[331, 305, 238, 297, 289])).
% 0.58/0.78 tff(333,plain,
% 0.58/0.78 (~c3_1(a294)),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[16, 332])).
% 0.58/0.78 tff(334,plain,
% 0.58/0.78 (~c2_1(a294)),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[22, 332])).
% 0.58/0.78 tff(335,plain,
% 0.58/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a336) | c1_1(a336) | c2_1(a309) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a309)) | (~c3_1(a309)) | c2_1(a336))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a336) | c1_1(a336) | c2_1(a309) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a309)) | (~c3_1(a309)) | c2_1(a336))),
% 0.58/0.78 inference(rewrite,[status(thm)],[])).
% 0.58/0.78 tff(336,plain,
% 0.58/0.78 (((~ndr1_0) | c2_1(a309) | (~c3_1(a309)) | (~c1_1(a309)) | c2_1(a294) | c1_1(a294) | c3_1(a294) | c2_1(a336) | c1_1(a336) | c0_1(a336)) <=> (c0_1(a336) | c1_1(a336) | c2_1(a309) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a309)) | (~c3_1(a309)) | c2_1(a336))),
% 0.58/0.78 inference(rewrite,[status(thm)],[])).
% 0.58/0.78 tff(337,plain,
% 0.58/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a309) | (~c3_1(a309)) | (~c1_1(a309)) | c2_1(a294) | c1_1(a294) | c3_1(a294) | c2_1(a336) | c1_1(a336) | c0_1(a336))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a336) | c1_1(a336) | c2_1(a309) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a309)) | (~c3_1(a309)) | c2_1(a336)))),
% 0.58/0.78 inference(monotonicity,[status(thm)],[336])).
% 0.58/0.78 tff(338,plain,
% 0.58/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a309) | (~c3_1(a309)) | (~c1_1(a309)) | c2_1(a294) | c1_1(a294) | c3_1(a294) | c2_1(a336) | c1_1(a336) | c0_1(a336))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a336) | c1_1(a336) | c2_1(a309) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a309)) | (~c3_1(a309)) | c2_1(a336))),
% 0.58/0.78 inference(transitivity,[status(thm)],[337, 335])).
% 0.58/0.78 tff(339,plain,
% 0.58/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a309) | (~c3_1(a309)) | (~c1_1(a309)) | c2_1(a294) | c1_1(a294) | c3_1(a294) | c2_1(a336) | c1_1(a336) | c0_1(a336))),
% 0.58/0.78 inference(quant_inst,[status(thm)],[])).
% 0.58/0.78 tff(340,plain,
% 0.58/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a336) | c1_1(a336) | c2_1(a309) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a309)) | (~c3_1(a309)) | c2_1(a336)),
% 0.58/0.78 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.58/0.78 tff(341,plain,
% 0.58/0.78 (c1_1(a294)),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[340, 143, 305, 297, 250, 244, 289, 334, 333, 275, 265])).
% 0.58/0.78 tff(342,plain,
% 0.58/0.78 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))))),
% 0.58/0.78 inference(bind,[status(th)],[])).
% 0.58/0.78 tff(343,plain,
% 0.58/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.58/0.78 inference(quant_intro,[status(thm)],[342])).
% 0.58/0.78 tff(344,plain,
% 0.58/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.58/0.78 inference(rewrite,[status(thm)],[])).
% 0.58/0.78 tff(345,plain,
% 0.58/0.78 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(V)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(V)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))))),
% 0.58/0.78 inference(bind,[status(th)],[])).
% 0.58/0.78 tff(346,plain,
% 0.58/0.78 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.58/0.78 inference(quant_intro,[status(thm)],[345])).
% 0.58/0.78 tff(347,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 0.58/0.78 tff(348,plain,
% 0.58/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.58/0.78 inference(modus_ponens,[status(thm)],[347, 346])).
% 0.58/0.78 tff(349,plain,
% 0.58/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.58/0.78 inference(modus_ponens,[status(thm)],[348, 344])).
% 0.58/0.78 tff(350,plain,(
% 0.58/0.78 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.58/0.78 inference(skolemize,[status(sab)],[349])).
% 0.58/0.78 tff(351,plain,
% 0.58/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.58/0.78 inference(modus_ponens,[status(thm)],[350, 343])).
% 0.58/0.78 tff(352,plain,
% 0.58/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a309) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | (~c1_1(a309)) | (~c3_1(a309)) | (~c0_1(a309)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a309) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | (~c1_1(a309)) | (~c3_1(a309)) | (~c0_1(a309)))),
% 0.58/0.78 inference(rewrite,[status(thm)],[])).
% 0.58/0.78 tff(353,plain,
% 0.58/0.78 (((~ndr1_0) | (~c3_1(a309)) | (~c0_1(a309)) | (~c1_1(a309)) | c2_1(a309) | (~c1_1(a309)) | (~c3_1(a309)) | c2_1(a294) | c3_1(a294) | (~c1_1(a294))) <=> (c2_1(a309) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | (~c1_1(a309)) | (~c3_1(a309)) | (~c0_1(a309)))),
% 0.58/0.78 inference(rewrite,[status(thm)],[])).
% 0.58/0.78 tff(354,plain,
% 0.58/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a309)) | (~c0_1(a309)) | (~c1_1(a309)) | c2_1(a309) | (~c1_1(a309)) | (~c3_1(a309)) | c2_1(a294) | c3_1(a294) | (~c1_1(a294)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a309) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | (~c1_1(a309)) | (~c3_1(a309)) | (~c0_1(a309))))),
% 0.58/0.78 inference(monotonicity,[status(thm)],[353])).
% 0.58/0.78 tff(355,plain,
% 0.58/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a309)) | (~c0_1(a309)) | (~c1_1(a309)) | c2_1(a309) | (~c1_1(a309)) | (~c3_1(a309)) | c2_1(a294) | c3_1(a294) | (~c1_1(a294)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a309) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | (~c1_1(a309)) | (~c3_1(a309)) | (~c0_1(a309)))),
% 0.58/0.78 inference(transitivity,[status(thm)],[354, 352])).
% 0.58/0.78 tff(356,plain,
% 0.58/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a309)) | (~c0_1(a309)) | (~c1_1(a309)) | c2_1(a309) | (~c1_1(a309)) | (~c3_1(a309)) | c2_1(a294) | c3_1(a294) | (~c1_1(a294)))),
% 0.58/0.78 inference(quant_inst,[status(thm)],[])).
% 0.58/0.78 tff(357,plain,
% 0.58/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a309) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | (~c1_1(a309)) | (~c3_1(a309)) | (~c0_1(a309))),
% 0.58/0.78 inference(modus_ponens,[status(thm)],[356, 355])).
% 0.58/0.78 tff(358,plain,
% 0.58/0.78 (~c0_1(a309)),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[357, 143, 305, 297, 289, 334, 333, 351, 341])).
% 0.58/0.78 tff(359,plain,
% 0.58/0.78 (~c0_1(a294)),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[28, 332])).
% 0.58/0.78 tff(360,plain,
% 0.58/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a309) | c0_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | c0_1(a309) | (~c1_1(a309)) | (~c3_1(a309)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a309) | c0_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | c0_1(a309) | (~c1_1(a309)) | (~c3_1(a309)))),
% 0.58/0.78 inference(rewrite,[status(thm)],[])).
% 0.58/0.78 tff(361,plain,
% 0.58/0.78 (((~ndr1_0) | (~c3_1(a309)) | c0_1(a309) | (~c1_1(a309)) | c0_1(a294) | (~c1_1(a294)) | c3_1(a294) | c2_1(a309) | c0_1(a309) | (~c1_1(a309))) <=> (c2_1(a309) | c0_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | c0_1(a309) | (~c1_1(a309)) | (~c3_1(a309)))),
% 0.58/0.78 inference(rewrite,[status(thm)],[])).
% 0.58/0.78 tff(362,plain,
% 0.58/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a309)) | c0_1(a309) | (~c1_1(a309)) | c0_1(a294) | (~c1_1(a294)) | c3_1(a294) | c2_1(a309) | c0_1(a309) | (~c1_1(a309)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a309) | c0_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | c0_1(a309) | (~c1_1(a309)) | (~c3_1(a309))))),
% 0.58/0.78 inference(monotonicity,[status(thm)],[361])).
% 0.58/0.78 tff(363,plain,
% 0.58/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a309)) | c0_1(a309) | (~c1_1(a309)) | c0_1(a294) | (~c1_1(a294)) | c3_1(a294) | c2_1(a309) | c0_1(a309) | (~c1_1(a309)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a309) | c0_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | c0_1(a309) | (~c1_1(a309)) | (~c3_1(a309)))),
% 0.58/0.78 inference(transitivity,[status(thm)],[362, 360])).
% 0.58/0.78 tff(364,plain,
% 0.58/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a309)) | c0_1(a309) | (~c1_1(a309)) | c0_1(a294) | (~c1_1(a294)) | c3_1(a294) | c2_1(a309) | c0_1(a309) | (~c1_1(a309)))),
% 0.58/0.78 inference(quant_inst,[status(thm)],[])).
% 0.58/0.78 tff(365,plain,
% 0.58/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a309) | c0_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | c0_1(a309) | (~c1_1(a309)) | (~c3_1(a309))),
% 0.58/0.78 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.58/0.78 tff(366,plain,
% 0.58/0.78 ($false),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[365, 143, 305, 297, 289, 359, 333, 10, 358, 341])).
% 0.58/0.78 tff(367,plain,(hskp1 | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.58/0.78 tff(368,plain,
% 0.58/0.78 (hskp1),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[367, 40])).
% 0.58/0.78 tff(369,plain,
% 0.58/0.78 (((~hskp1) | (~c1_1(a295))) <=> ((~hskp1) | (~c1_1(a295)))),
% 0.58/0.78 inference(rewrite,[status(thm)],[])).
% 0.58/0.78 tff(370,plain,
% 0.58/0.78 (((~c1_1(a295)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a295)))),
% 0.58/0.78 inference(rewrite,[status(thm)],[])).
% 0.58/0.78 tff(371,axiom,((~c1_1(a295)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 0.58/0.78 tff(372,plain,
% 0.58/0.78 ((~hskp1) | (~c1_1(a295))),
% 0.58/0.78 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.58/0.78 tff(373,plain,
% 0.58/0.78 ((~hskp1) | (~c1_1(a295))),
% 0.58/0.78 inference(modus_ponens,[status(thm)],[372, 369])).
% 0.58/0.78 tff(374,plain,
% 0.58/0.78 (~c1_1(a295)),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[373, 368])).
% 0.58/0.78 tff(375,plain,
% 0.58/0.78 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 0.58/0.78 inference(bind,[status(th)],[])).
% 0.58/0.78 tff(376,plain,
% 0.58/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.58/0.78 inference(quant_intro,[status(thm)],[375])).
% 0.58/0.78 tff(377,plain,
% 0.58/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.58/0.78 inference(rewrite,[status(thm)],[])).
% 0.58/0.78 tff(378,plain,
% 0.58/0.78 (^[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) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_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) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_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) | (~c3_1(U)) | (~c2_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) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_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) | 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) | (~c3_1(U)) | (~c2_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)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 0.58/0.79 inference(bind,[status(th)],[])).
% 0.58/0.79 tff(379,plain,
% 0.58/0.79 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.58/0.79 inference(quant_intro,[status(thm)],[378])).
% 0.58/0.79 tff(380,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 0.58/0.79 tff(381,plain,
% 0.58/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[380, 379])).
% 0.58/0.79 tff(382,plain,
% 0.58/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[381, 377])).
% 0.58/0.79 tff(383,plain,(
% 0.58/0.79 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.58/0.79 inference(skolemize,[status(sab)],[382])).
% 0.58/0.79 tff(384,plain,
% 0.58/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[383, 376])).
% 0.58/0.79 tff(385,assumption,(~c1_1(a295)), introduced(assumption)).
% 0.58/0.79 tff(386,assumption,(hskp20), introduced(assumption)).
% 0.58/0.79 tff(387,plain,
% 0.58/0.79 (((~hskp20) | (~c3_1(a333))) <=> ((~hskp20) | (~c3_1(a333)))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(388,plain,
% 0.58/0.79 (((~c3_1(a333)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a333)))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(389,axiom,((~c3_1(a333)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 0.58/0.79 tff(390,plain,
% 0.58/0.79 ((~hskp20) | (~c3_1(a333))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.58/0.79 tff(391,plain,
% 0.58/0.79 ((~hskp20) | (~c3_1(a333))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[390, 387])).
% 0.58/0.79 tff(392,plain,
% 0.58/0.79 (~c3_1(a333)),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[391, 386])).
% 0.58/0.79 tff(393,plain,
% 0.58/0.79 (((~hskp20) | (~c2_1(a333))) <=> ((~hskp20) | (~c2_1(a333)))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(394,plain,
% 0.58/0.79 (((~c2_1(a333)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a333)))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(395,axiom,((~c2_1(a333)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 0.58/0.79 tff(396,plain,
% 0.58/0.79 ((~hskp20) | (~c2_1(a333))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[395, 394])).
% 0.58/0.79 tff(397,plain,
% 0.58/0.79 ((~hskp20) | (~c2_1(a333))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[396, 393])).
% 0.58/0.79 tff(398,plain,
% 0.58/0.79 (~c2_1(a333)),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[397, 386])).
% 0.58/0.79 tff(399,plain,
% 0.58/0.79 (((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp21 | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c0_1(a333)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp21 | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c0_1(a333)))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(400,plain,
% 0.58/0.79 ((hskp21 | (~ndr1_0) | c2_1(a333) | c3_1(a333) | (~c0_1(a333))) <=> (hskp21 | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c0_1(a333)))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(401,plain,
% 0.58/0.79 (((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp21 | (~ndr1_0) | c2_1(a333) | c3_1(a333) | (~c0_1(a333)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp21 | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c0_1(a333))))),
% 0.58/0.79 inference(monotonicity,[status(thm)],[400])).
% 0.58/0.79 tff(402,plain,
% 0.58/0.79 (((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp21 | (~ndr1_0) | c2_1(a333) | c3_1(a333) | (~c0_1(a333)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp21 | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c0_1(a333)))),
% 0.58/0.79 inference(transitivity,[status(thm)],[401, 399])).
% 0.58/0.79 tff(403,plain,
% 0.58/0.79 ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp21 | (~ndr1_0) | c2_1(a333) | c3_1(a333) | (~c0_1(a333)))),
% 0.58/0.79 inference(quant_inst,[status(thm)],[])).
% 0.58/0.79 tff(404,plain,
% 0.58/0.79 ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp21 | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c0_1(a333))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[403, 402])).
% 0.58/0.79 tff(405,plain,
% 0.58/0.79 (~c0_1(a333)),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[404, 143, 97, 398, 392, 107])).
% 0.58/0.79 tff(406,assumption,(~c1_1(a321)), introduced(assumption)).
% 0.58/0.79 tff(407,assumption,(c3_1(a321)), introduced(assumption)).
% 0.58/0.79 tff(408,assumption,(c2_1(a321)), introduced(assumption)).
% 0.58/0.79 tff(409,plain,
% 0.58/0.79 (((~hskp20) | c1_1(a333)) <=> ((~hskp20) | c1_1(a333))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(410,axiom,((~hskp20) | c1_1(a333)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 0.58/0.79 tff(411,plain,
% 0.58/0.79 ((~hskp20) | c1_1(a333)),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[410, 409])).
% 0.58/0.79 tff(412,plain,
% 0.58/0.79 ((~hskp20) | c1_1(a333)),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[411, 409])).
% 0.58/0.79 tff(413,plain,
% 0.58/0.79 ((~hskp20) | c1_1(a333)),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[412, 409])).
% 0.58/0.79 tff(414,plain,
% 0.58/0.79 ((~hskp20) | c1_1(a333)),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[413, 409])).
% 0.58/0.79 tff(415,plain,
% 0.58/0.79 ((~hskp20) | c1_1(a333)),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[414, 409])).
% 0.58/0.79 tff(416,plain,
% 0.58/0.79 (c1_1(a333)),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[415, 386])).
% 0.58/0.79 tff(417,plain,
% 0.58/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a333) | c3_1(a333) | c1_1(a321) | (~ndr1_0) | (~c2_1(a321)) | (~c3_1(a321)) | (~c1_1(a333)) | c0_1(a333))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a333) | c3_1(a333) | c1_1(a321) | (~ndr1_0) | (~c2_1(a321)) | (~c3_1(a321)) | (~c1_1(a333)) | c0_1(a333))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(418,plain,
% 0.58/0.79 (((~ndr1_0) | c1_1(a321) | (~c3_1(a321)) | (~c2_1(a321)) | c2_1(a333) | c0_1(a333) | (~c1_1(a333)) | c2_1(a333) | c0_1(a333) | c3_1(a333)) <=> (c2_1(a333) | c3_1(a333) | c1_1(a321) | (~ndr1_0) | (~c2_1(a321)) | (~c3_1(a321)) | (~c1_1(a333)) | c0_1(a333))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(419,plain,
% 0.58/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a321) | (~c3_1(a321)) | (~c2_1(a321)) | c2_1(a333) | c0_1(a333) | (~c1_1(a333)) | c2_1(a333) | c0_1(a333) | c3_1(a333))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a333) | c3_1(a333) | c1_1(a321) | (~ndr1_0) | (~c2_1(a321)) | (~c3_1(a321)) | (~c1_1(a333)) | c0_1(a333)))),
% 0.58/0.79 inference(monotonicity,[status(thm)],[418])).
% 0.58/0.79 tff(420,plain,
% 0.58/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a321) | (~c3_1(a321)) | (~c2_1(a321)) | c2_1(a333) | c0_1(a333) | (~c1_1(a333)) | c2_1(a333) | c0_1(a333) | c3_1(a333))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a333) | c3_1(a333) | c1_1(a321) | (~ndr1_0) | (~c2_1(a321)) | (~c3_1(a321)) | (~c1_1(a333)) | c0_1(a333))),
% 0.58/0.79 inference(transitivity,[status(thm)],[419, 417])).
% 0.58/0.79 tff(421,plain,
% 0.58/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a321) | (~c3_1(a321)) | (~c2_1(a321)) | c2_1(a333) | c0_1(a333) | (~c1_1(a333)) | c2_1(a333) | c0_1(a333) | c3_1(a333))),
% 0.58/0.79 inference(quant_inst,[status(thm)],[])).
% 0.58/0.79 tff(422,plain,
% 0.58/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a333) | c3_1(a333) | c1_1(a321) | (~ndr1_0) | (~c2_1(a321)) | (~c3_1(a321)) | (~c1_1(a333)) | c0_1(a333)),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.58/0.79 tff(423,plain,
% 0.58/0.79 ($false),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[422, 143, 416, 408, 407, 398, 392, 406, 384, 405])).
% 0.58/0.79 tff(424,plain,((~hskp20) | (~c2_1(a321)) | (~c3_1(a321)) | c1_1(a321) | hskp21), inference(lemma,lemma(discharge,[]))).
% 0.58/0.79 tff(425,plain,
% 0.58/0.79 (~hskp20),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[424, 208, 97, 229, 216])).
% 0.58/0.79 tff(426,assumption,(~hskp20), introduced(assumption)).
% 0.58/0.79 tff(427,plain,
% 0.58/0.79 (^[U: $i] : refl((hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))),
% 0.58/0.79 inference(bind,[status(th)],[])).
% 0.58/0.79 tff(428,plain,
% 0.58/0.79 (![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.58/0.79 inference(quant_intro,[status(thm)],[427])).
% 0.58/0.79 tff(429,plain,
% 0.58/0.79 (![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(430,plain,
% 0.58/0.79 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp11))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp20) <=> ((hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp20))), rewrite(((hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp20) <=> (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp20) <=> (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))))),
% 0.58/0.79 inference(bind,[status(th)],[])).
% 0.58/0.79 tff(431,plain,
% 0.58/0.79 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp20) <=> ![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.58/0.79 inference(quant_intro,[status(thm)],[430])).
% 0.58/0.79 tff(432,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 0.58/0.79 tff(433,plain,
% 0.58/0.79 (![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[432, 431])).
% 0.58/0.79 tff(434,plain,
% 0.58/0.79 (![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[433, 429])).
% 0.58/0.79 tff(435,plain,(
% 0.58/0.79 ![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.58/0.79 inference(skolemize,[status(sab)],[434])).
% 0.58/0.79 tff(436,plain,
% 0.58/0.79 (![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[435, 428])).
% 0.58/0.79 tff(437,plain,
% 0.58/0.79 (((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp20 | hskp11 | c1_1(a321) | (~ndr1_0) | (~c2_1(a321)) | (~c0_1(a321)))) <=> ((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp20 | hskp11 | c1_1(a321) | (~ndr1_0) | (~c2_1(a321)) | (~c0_1(a321)))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(438,plain,
% 0.58/0.79 ((hskp20 | hskp11 | (~ndr1_0) | c1_1(a321) | (~c0_1(a321)) | (~c2_1(a321))) <=> (hskp20 | hskp11 | c1_1(a321) | (~ndr1_0) | (~c2_1(a321)) | (~c0_1(a321)))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(439,plain,
% 0.58/0.79 (((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp20 | hskp11 | (~ndr1_0) | c1_1(a321) | (~c0_1(a321)) | (~c2_1(a321)))) <=> ((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp20 | hskp11 | c1_1(a321) | (~ndr1_0) | (~c2_1(a321)) | (~c0_1(a321))))),
% 0.58/0.79 inference(monotonicity,[status(thm)],[438])).
% 0.58/0.79 tff(440,plain,
% 0.58/0.79 (((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp20 | hskp11 | (~ndr1_0) | c1_1(a321) | (~c0_1(a321)) | (~c2_1(a321)))) <=> ((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp20 | hskp11 | c1_1(a321) | (~ndr1_0) | (~c2_1(a321)) | (~c0_1(a321)))),
% 0.58/0.79 inference(transitivity,[status(thm)],[439, 437])).
% 0.58/0.79 tff(441,plain,
% 0.58/0.79 ((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp20 | hskp11 | (~ndr1_0) | c1_1(a321) | (~c0_1(a321)) | (~c2_1(a321)))),
% 0.58/0.79 inference(quant_inst,[status(thm)],[])).
% 0.58/0.79 tff(442,plain,
% 0.58/0.79 ((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp20 | hskp11 | c1_1(a321) | (~ndr1_0) | (~c2_1(a321)) | (~c0_1(a321))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[441, 440])).
% 0.58/0.79 tff(443,plain,
% 0.58/0.79 (hskp20 | hskp11 | (~c0_1(a321))),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[442, 143, 408, 406, 436])).
% 0.58/0.79 tff(444,plain,
% 0.58/0.79 (~c0_1(a321)),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[443, 41, 426])).
% 0.58/0.79 tff(445,plain,
% 0.58/0.79 (hskp1 | c0_1(a321)),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[235, 143, 408, 407, 406, 61])).
% 0.58/0.79 tff(446,plain,
% 0.58/0.79 (hskp1),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[445, 444])).
% 0.58/0.79 tff(447,plain,
% 0.58/0.79 (((~hskp1) | c0_1(a295)) <=> ((~hskp1) | c0_1(a295))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(448,axiom,((~hskp1) | c0_1(a295)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 0.58/0.79 tff(449,plain,
% 0.58/0.79 ((~hskp1) | c0_1(a295)),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[448, 447])).
% 0.58/0.79 tff(450,plain,
% 0.58/0.79 ((~hskp1) | c0_1(a295)),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[449, 447])).
% 0.58/0.79 tff(451,plain,
% 0.58/0.79 ((~hskp1) | c0_1(a295)),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[450, 447])).
% 0.58/0.79 tff(452,plain,
% 0.58/0.79 ((~hskp1) | c0_1(a295)),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[451, 447])).
% 0.58/0.79 tff(453,plain,
% 0.58/0.79 ((~hskp1) | c0_1(a295)),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[452, 447])).
% 0.58/0.79 tff(454,plain,
% 0.58/0.79 (c0_1(a295)),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[453, 446])).
% 0.58/0.79 tff(455,plain,
% 0.58/0.79 (((~hskp1) | c2_1(a295)) <=> ((~hskp1) | c2_1(a295))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(456,axiom,((~hskp1) | c2_1(a295)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 0.58/0.79 tff(457,plain,
% 0.58/0.79 ((~hskp1) | c2_1(a295)),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[456, 455])).
% 0.58/0.79 tff(458,plain,
% 0.58/0.79 ((~hskp1) | c2_1(a295)),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[457, 455])).
% 0.58/0.79 tff(459,plain,
% 0.58/0.79 ((~hskp1) | c2_1(a295)),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[458, 455])).
% 0.58/0.79 tff(460,plain,
% 0.58/0.79 ((~hskp1) | c2_1(a295)),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[459, 455])).
% 0.58/0.79 tff(461,plain,
% 0.58/0.79 ((~hskp1) | c2_1(a295)),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[460, 455])).
% 0.58/0.79 tff(462,plain,
% 0.58/0.79 (c2_1(a295)),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[461, 446])).
% 0.58/0.79 tff(463,plain,
% 0.58/0.79 (((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp20 | hskp11 | c1_1(a295) | (~ndr1_0) | (~c2_1(a295)) | (~c0_1(a295)))) <=> ((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp20 | hskp11 | c1_1(a295) | (~ndr1_0) | (~c2_1(a295)) | (~c0_1(a295)))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(464,plain,
% 0.58/0.79 ((hskp20 | hskp11 | (~ndr1_0) | c1_1(a295) | (~c0_1(a295)) | (~c2_1(a295))) <=> (hskp20 | hskp11 | c1_1(a295) | (~ndr1_0) | (~c2_1(a295)) | (~c0_1(a295)))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(465,plain,
% 0.58/0.79 (((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp20 | hskp11 | (~ndr1_0) | c1_1(a295) | (~c0_1(a295)) | (~c2_1(a295)))) <=> ((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp20 | hskp11 | c1_1(a295) | (~ndr1_0) | (~c2_1(a295)) | (~c0_1(a295))))),
% 0.58/0.79 inference(monotonicity,[status(thm)],[464])).
% 0.58/0.79 tff(466,plain,
% 0.58/0.79 (((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp20 | hskp11 | (~ndr1_0) | c1_1(a295) | (~c0_1(a295)) | (~c2_1(a295)))) <=> ((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp20 | hskp11 | c1_1(a295) | (~ndr1_0) | (~c2_1(a295)) | (~c0_1(a295)))),
% 0.58/0.79 inference(transitivity,[status(thm)],[465, 463])).
% 0.58/0.79 tff(467,plain,
% 0.58/0.79 ((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp20 | hskp11 | (~ndr1_0) | c1_1(a295) | (~c0_1(a295)) | (~c2_1(a295)))),
% 0.58/0.79 inference(quant_inst,[status(thm)],[])).
% 0.58/0.79 tff(468,plain,
% 0.58/0.79 ((~![U: $i] : (hskp20 | hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp20 | hskp11 | c1_1(a295) | (~ndr1_0) | (~c2_1(a295)) | (~c0_1(a295))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[467, 466])).
% 0.58/0.79 tff(469,plain,
% 0.58/0.79 (hskp20 | hskp11 | (~c2_1(a295)) | (~c0_1(a295))),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[468, 143, 385, 436])).
% 0.58/0.79 tff(470,plain,
% 0.58/0.79 ($false),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[469, 462, 454, 426, 41])).
% 0.58/0.79 tff(471,plain,(hskp11 | hskp20 | c1_1(a295) | (~c2_1(a321)) | (~c3_1(a321)) | c1_1(a321)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.79 tff(472,plain,
% 0.58/0.79 (hskp11),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[471, 425, 385, 216, 208, 229])).
% 0.58/0.79 tff(473,plain,
% 0.58/0.79 (~c2_1(a309)),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[288, 472])).
% 0.58/0.79 tff(474,plain,
% 0.58/0.79 (c3_1(a309)),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[296, 472])).
% 0.58/0.79 tff(475,plain,
% 0.58/0.79 (c1_1(a309)),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[304, 472])).
% 0.58/0.79 tff(476,plain,
% 0.58/0.79 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (c2_1(a309) | (~ndr1_0) | (~c1_1(a309)) | (~c3_1(a309)) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | c2_1(a309) | (~ndr1_0) | (~c1_1(a309)) | (~c3_1(a309)) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321)))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(477,plain,
% 0.58/0.79 (((~ndr1_0) | (~c3_1(a321)) | (~c0_1(a321)) | (~c2_1(a321)) | c2_1(a309) | (~c1_1(a309)) | (~c3_1(a309))) <=> (c2_1(a309) | (~ndr1_0) | (~c1_1(a309)) | (~c3_1(a309)) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321)))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(478,plain,
% 0.58/0.79 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | ((~ndr1_0) | (~c3_1(a321)) | (~c0_1(a321)) | (~c2_1(a321)) | c2_1(a309) | (~c1_1(a309)) | (~c3_1(a309)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (c2_1(a309) | (~ndr1_0) | (~c1_1(a309)) | (~c3_1(a309)) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321))))),
% 0.58/0.79 inference(monotonicity,[status(thm)],[477])).
% 0.58/0.79 tff(479,plain,
% 0.58/0.79 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | ((~ndr1_0) | (~c3_1(a321)) | (~c0_1(a321)) | (~c2_1(a321)) | c2_1(a309) | (~c1_1(a309)) | (~c3_1(a309)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | c2_1(a309) | (~ndr1_0) | (~c1_1(a309)) | (~c3_1(a309)) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321)))),
% 0.58/0.79 inference(transitivity,[status(thm)],[478, 476])).
% 0.58/0.79 tff(480,plain,
% 0.58/0.79 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | ((~ndr1_0) | (~c3_1(a321)) | (~c0_1(a321)) | (~c2_1(a321)) | c2_1(a309) | (~c1_1(a309)) | (~c3_1(a309)))),
% 0.58/0.79 inference(quant_inst,[status(thm)],[])).
% 0.58/0.79 tff(481,plain,
% 0.58/0.79 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | c2_1(a309) | (~ndr1_0) | (~c1_1(a309)) | (~c3_1(a309)) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[480, 479])).
% 0.58/0.79 tff(482,plain,
% 0.58/0.79 (~c0_1(a321)),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[481, 143, 216, 208, 475, 474, 473, 161])).
% 0.58/0.79 tff(483,plain,
% 0.58/0.79 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a321) | c2_1(a309) | (~ndr1_0) | (~c1_1(a309)) | (~c3_1(a309)) | c0_1(a321) | (~c3_1(a321)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a321) | c2_1(a309) | (~ndr1_0) | (~c1_1(a309)) | (~c3_1(a309)) | c0_1(a321) | (~c3_1(a321)))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(484,plain,
% 0.58/0.79 ((hskp0 | (~ndr1_0) | c2_1(a309) | (~c3_1(a309)) | (~c1_1(a309)) | c1_1(a321) | c0_1(a321) | (~c3_1(a321))) <=> (hskp0 | c1_1(a321) | c2_1(a309) | (~ndr1_0) | (~c1_1(a309)) | (~c3_1(a309)) | c0_1(a321) | (~c3_1(a321)))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(485,plain,
% 0.58/0.79 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a309) | (~c3_1(a309)) | (~c1_1(a309)) | c1_1(a321) | c0_1(a321) | (~c3_1(a321)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a321) | c2_1(a309) | (~ndr1_0) | (~c1_1(a309)) | (~c3_1(a309)) | c0_1(a321) | (~c3_1(a321))))),
% 0.58/0.79 inference(monotonicity,[status(thm)],[484])).
% 0.58/0.79 tff(486,plain,
% 0.58/0.79 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a309) | (~c3_1(a309)) | (~c1_1(a309)) | c1_1(a321) | c0_1(a321) | (~c3_1(a321)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a321) | c2_1(a309) | (~ndr1_0) | (~c1_1(a309)) | (~c3_1(a309)) | c0_1(a321) | (~c3_1(a321)))),
% 0.58/0.79 inference(transitivity,[status(thm)],[485, 483])).
% 0.58/0.79 tff(487,plain,
% 0.58/0.79 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a309) | (~c3_1(a309)) | (~c1_1(a309)) | c1_1(a321) | c0_1(a321) | (~c3_1(a321)))),
% 0.58/0.79 inference(quant_inst,[status(thm)],[])).
% 0.58/0.79 tff(488,plain,
% 0.58/0.79 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a321) | c2_1(a309) | (~ndr1_0) | (~c1_1(a309)) | (~c3_1(a309)) | c0_1(a321) | (~c3_1(a321))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[487, 486])).
% 0.58/0.79 tff(489,plain,
% 0.58/0.79 (hskp0),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[488, 143, 208, 475, 474, 229, 473, 315, 482])).
% 0.58/0.79 tff(490,plain,
% 0.58/0.79 (~c3_1(a294)),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[16, 489])).
% 0.58/0.79 tff(491,plain,
% 0.58/0.79 (~c2_1(a294)),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[22, 489])).
% 0.58/0.79 tff(492,plain,
% 0.58/0.79 (~c0_1(a294)),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[28, 489])).
% 0.58/0.79 tff(493,plain,
% 0.58/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a321) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | (~c2_1(a321)) | (~c3_1(a321)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a321) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | (~c2_1(a321)) | (~c3_1(a321)))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(494,plain,
% 0.58/0.79 (((~ndr1_0) | c1_1(a321) | (~c3_1(a321)) | (~c2_1(a321)) | c2_1(a294) | c0_1(a294) | (~c1_1(a294)) | c2_1(a294) | c0_1(a294) | c3_1(a294)) <=> (c1_1(a321) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | (~c2_1(a321)) | (~c3_1(a321)))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(495,plain,
% 0.58/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a321) | (~c3_1(a321)) | (~c2_1(a321)) | c2_1(a294) | c0_1(a294) | (~c1_1(a294)) | c2_1(a294) | c0_1(a294) | c3_1(a294))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a321) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | (~c2_1(a321)) | (~c3_1(a321))))),
% 0.58/0.79 inference(monotonicity,[status(thm)],[494])).
% 0.58/0.79 tff(496,plain,
% 0.58/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a321) | (~c3_1(a321)) | (~c2_1(a321)) | c2_1(a294) | c0_1(a294) | (~c1_1(a294)) | c2_1(a294) | c0_1(a294) | c3_1(a294))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a321) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | (~c2_1(a321)) | (~c3_1(a321)))),
% 0.58/0.79 inference(transitivity,[status(thm)],[495, 493])).
% 0.58/0.79 tff(497,plain,
% 0.58/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a321) | (~c3_1(a321)) | (~c2_1(a321)) | c2_1(a294) | c0_1(a294) | (~c1_1(a294)) | c2_1(a294) | c0_1(a294) | c3_1(a294))),
% 0.58/0.79 inference(quant_inst,[status(thm)],[])).
% 0.58/0.79 tff(498,plain,
% 0.58/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a321) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | (~c2_1(a321)) | (~c3_1(a321))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[497, 496])).
% 0.65/0.80 tff(499,plain,
% 0.65/0.80 (~c1_1(a294)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[498, 143, 216, 208, 229, 492, 491, 490, 384])).
% 0.65/0.80 tff(500,plain,
% 0.65/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a309) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a309)) | (~c3_1(a309)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a309) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a309)) | (~c3_1(a309)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(501,plain,
% 0.65/0.80 (((~ndr1_0) | c2_1(a309) | (~c3_1(a309)) | (~c1_1(a309)) | c2_1(a294) | c1_1(a294) | c3_1(a294) | c2_1(a294) | c1_1(a294) | c0_1(a294)) <=> (c2_1(a309) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a309)) | (~c3_1(a309)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(502,plain,
% 0.65/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a309) | (~c3_1(a309)) | (~c1_1(a309)) | c2_1(a294) | c1_1(a294) | c3_1(a294) | c2_1(a294) | c1_1(a294) | c0_1(a294))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a309) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a309)) | (~c3_1(a309))))),
% 0.65/0.80 inference(monotonicity,[status(thm)],[501])).
% 0.65/0.80 tff(503,plain,
% 0.65/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a309) | (~c3_1(a309)) | (~c1_1(a309)) | c2_1(a294) | c1_1(a294) | c3_1(a294) | c2_1(a294) | c1_1(a294) | c0_1(a294))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a309) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a309)) | (~c3_1(a309)))),
% 0.65/0.80 inference(transitivity,[status(thm)],[502, 500])).
% 0.65/0.80 tff(504,plain,
% 0.65/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a309) | (~c3_1(a309)) | (~c1_1(a309)) | c2_1(a294) | c1_1(a294) | c3_1(a294) | c2_1(a294) | c1_1(a294) | c0_1(a294))),
% 0.65/0.80 inference(quant_inst,[status(thm)],[])).
% 0.65/0.80 tff(505,plain,
% 0.65/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a309) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a309)) | (~c3_1(a309))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[504, 503])).
% 0.65/0.80 tff(506,plain,
% 0.65/0.80 ($false),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[505, 143, 475, 474, 473, 492, 491, 490, 275, 499])).
% 0.65/0.80 tff(507,plain,(hskp21 | c1_1(a295)), inference(lemma,lemma(discharge,[]))).
% 0.65/0.80 tff(508,plain,
% 0.65/0.80 (hskp21),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[507, 374])).
% 0.65/0.80 tff(509,plain,
% 0.65/0.80 (~c0_1(a336)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[249, 508])).
% 0.65/0.80 tff(510,plain,
% 0.65/0.80 (c3_1(a336)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[257, 508])).
% 0.65/0.80 tff(511,plain,
% 0.65/0.80 (hskp11 | c2_1(a336)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[281, 143, 40, 510, 509, 51])).
% 0.65/0.80 tff(512,plain,
% 0.65/0.80 (c2_1(a336)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[511, 41])).
% 0.65/0.80 tff(513,plain,
% 0.65/0.80 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 0.65/0.80 inference(bind,[status(th)],[])).
% 0.65/0.80 tff(514,plain,
% 0.65/0.80 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.65/0.80 inference(quant_intro,[status(thm)],[513])).
% 0.65/0.80 tff(515,plain,
% 0.65/0.80 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(516,plain,
% 0.65/0.80 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 0.65/0.80 inference(bind,[status(th)],[])).
% 0.65/0.80 tff(517,plain,
% 0.65/0.80 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.65/0.80 inference(quant_intro,[status(thm)],[516])).
% 0.65/0.80 tff(518,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 0.65/0.80 tff(519,plain,
% 0.65/0.80 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[518, 517])).
% 0.65/0.80 tff(520,plain,
% 0.65/0.80 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[519, 515])).
% 0.65/0.80 tff(521,plain,(
% 0.65/0.80 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.65/0.80 inference(skolemize,[status(sab)],[520])).
% 0.65/0.80 tff(522,plain,
% 0.65/0.80 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[521, 514])).
% 0.65/0.80 tff(523,plain,
% 0.65/0.80 (c2_1(a295)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[461, 368])).
% 0.65/0.80 tff(524,plain,
% 0.65/0.80 (c0_1(a295)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[453, 368])).
% 0.65/0.80 tff(525,plain,
% 0.65/0.80 (hskp20 | hskp11),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[468, 143, 524, 523, 374, 436])).
% 0.65/0.80 tff(526,plain,
% 0.65/0.80 (hskp20),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[525, 41])).
% 0.65/0.80 tff(527,plain,
% 0.65/0.80 (~c3_1(a333)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[391, 526])).
% 0.65/0.80 tff(528,plain,
% 0.65/0.80 (~c2_1(a333)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[397, 526])).
% 0.65/0.80 tff(529,plain,
% 0.65/0.80 (c1_1(a333)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[415, 526])).
% 0.65/0.80 tff(530,assumption,(~c2_1(a299)), introduced(assumption)).
% 0.65/0.80 tff(531,assumption,(~c0_1(a336)), introduced(assumption)).
% 0.65/0.80 tff(532,assumption,(c3_1(a336)), introduced(assumption)).
% 0.65/0.80 tff(533,plain,
% 0.65/0.80 (hskp11 | c2_1(a336)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[281, 143, 40, 532, 531, 51])).
% 0.65/0.80 tff(534,plain,
% 0.65/0.80 (c2_1(a336)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[533, 41])).
% 0.65/0.80 tff(535,assumption,(~c1_1(a336)), introduced(assumption)).
% 0.65/0.80 tff(536,plain,
% 0.65/0.80 (hskp1 | (~c2_1(a336))),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[264, 143, 532, 531, 535, 61])).
% 0.65/0.80 tff(537,plain,
% 0.65/0.80 (hskp1),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[536, 534])).
% 0.65/0.80 tff(538,plain,
% 0.65/0.80 (c0_1(a295)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[453, 537])).
% 0.65/0.80 tff(539,plain,
% 0.65/0.80 (c2_1(a295)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[461, 537])).
% 0.65/0.80 tff(540,plain,
% 0.65/0.80 (hskp20),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[469, 539, 41, 538])).
% 0.65/0.80 tff(541,plain,
% 0.65/0.80 (~c3_1(a333)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[391, 540])).
% 0.65/0.80 tff(542,plain,
% 0.65/0.80 (~c2_1(a333)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[397, 540])).
% 0.65/0.80 tff(543,plain,
% 0.65/0.80 (c1_1(a333)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[415, 540])).
% 0.65/0.80 tff(544,plain,
% 0.65/0.80 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp3 | c0_1(a336) | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c1_1(a333)) | (~c2_1(a336)) | (~c3_1(a336)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp3 | c0_1(a336) | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c1_1(a333)) | (~c2_1(a336)) | (~c3_1(a336)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(545,plain,
% 0.65/0.80 ((hskp3 | (~ndr1_0) | c2_1(a333) | c3_1(a333) | (~c1_1(a333)) | c0_1(a336) | (~c2_1(a336)) | (~c3_1(a336))) <=> (hskp3 | c0_1(a336) | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c1_1(a333)) | (~c2_1(a336)) | (~c3_1(a336)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(546,plain,
% 0.65/0.80 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a333) | c3_1(a333) | (~c1_1(a333)) | c0_1(a336) | (~c2_1(a336)) | (~c3_1(a336)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp3 | c0_1(a336) | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c1_1(a333)) | (~c2_1(a336)) | (~c3_1(a336))))),
% 0.65/0.80 inference(monotonicity,[status(thm)],[545])).
% 0.65/0.80 tff(547,plain,
% 0.65/0.80 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a333) | c3_1(a333) | (~c1_1(a333)) | c0_1(a336) | (~c2_1(a336)) | (~c3_1(a336)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp3 | c0_1(a336) | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c1_1(a333)) | (~c2_1(a336)) | (~c3_1(a336)))),
% 0.65/0.80 inference(transitivity,[status(thm)],[546, 544])).
% 0.65/0.80 tff(548,plain,
% 0.65/0.80 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a333) | c3_1(a333) | (~c1_1(a333)) | c0_1(a336) | (~c2_1(a336)) | (~c3_1(a336)))),
% 0.65/0.80 inference(quant_inst,[status(thm)],[])).
% 0.65/0.80 tff(549,plain,
% 0.65/0.80 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp3 | c0_1(a336) | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c1_1(a333)) | (~c2_1(a336)) | (~c3_1(a336))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[548, 547])).
% 0.65/0.80 tff(550,plain,
% 0.65/0.80 (hskp3),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[549, 143, 532, 543, 531, 542, 541, 522, 534])).
% 0.65/0.80 tff(551,plain,
% 0.65/0.80 (((~hskp3) | c3_1(a299)) <=> ((~hskp3) | c3_1(a299))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(552,axiom,((~hskp3) | c3_1(a299)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 0.65/0.80 tff(553,plain,
% 0.65/0.80 ((~hskp3) | c3_1(a299)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[552, 551])).
% 0.65/0.80 tff(554,plain,
% 0.65/0.80 ((~hskp3) | c3_1(a299)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[553, 551])).
% 0.65/0.80 tff(555,plain,
% 0.65/0.80 ((~hskp3) | c3_1(a299)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[554, 551])).
% 0.65/0.80 tff(556,plain,
% 0.65/0.80 ((~hskp3) | c3_1(a299)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[555, 551])).
% 0.65/0.80 tff(557,plain,
% 0.65/0.80 ((~hskp3) | c3_1(a299)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[556, 551])).
% 0.65/0.80 tff(558,plain,
% 0.65/0.80 (c3_1(a299)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[557, 550])).
% 0.65/0.80 tff(559,plain,
% 0.65/0.80 (((~hskp3) | c0_1(a299)) <=> ((~hskp3) | c0_1(a299))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(560,axiom,((~hskp3) | c0_1(a299)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 0.65/0.80 tff(561,plain,
% 0.65/0.80 ((~hskp3) | c0_1(a299)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[560, 559])).
% 0.65/0.80 tff(562,plain,
% 0.65/0.80 ((~hskp3) | c0_1(a299)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[561, 559])).
% 0.65/0.80 tff(563,plain,
% 0.65/0.80 ((~hskp3) | c0_1(a299)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[562, 559])).
% 0.65/0.80 tff(564,plain,
% 0.65/0.80 ((~hskp3) | c0_1(a299)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[563, 559])).
% 0.65/0.80 tff(565,plain,
% 0.65/0.80 ((~hskp3) | c0_1(a299)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[564, 559])).
% 0.65/0.80 tff(566,plain,
% 0.65/0.80 (c0_1(a299)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[565, 550])).
% 0.65/0.80 tff(567,plain,
% 0.65/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a333) | c3_1(a333) | c2_1(a299) | (~ndr1_0) | (~c1_1(a299)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c1_1(a333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a333) | c3_1(a333) | c2_1(a299) | (~ndr1_0) | (~c1_1(a299)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c1_1(a333)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(568,plain,
% 0.65/0.80 (((~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c1_1(a299)) | c2_1(a299) | (~c1_1(a299)) | (~c3_1(a299)) | c2_1(a333) | c3_1(a333) | (~c1_1(a333))) <=> (c2_1(a333) | c3_1(a333) | c2_1(a299) | (~ndr1_0) | (~c1_1(a299)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c1_1(a333)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(569,plain,
% 0.65/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c1_1(a299)) | c2_1(a299) | (~c1_1(a299)) | (~c3_1(a299)) | c2_1(a333) | c3_1(a333) | (~c1_1(a333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a333) | c3_1(a333) | c2_1(a299) | (~ndr1_0) | (~c1_1(a299)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c1_1(a333))))),
% 0.65/0.80 inference(monotonicity,[status(thm)],[568])).
% 0.65/0.80 tff(570,plain,
% 0.65/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c1_1(a299)) | c2_1(a299) | (~c1_1(a299)) | (~c3_1(a299)) | c2_1(a333) | c3_1(a333) | (~c1_1(a333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a333) | c3_1(a333) | c2_1(a299) | (~ndr1_0) | (~c1_1(a299)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c1_1(a333)))),
% 0.65/0.80 inference(transitivity,[status(thm)],[569, 567])).
% 0.65/0.80 tff(571,plain,
% 0.65/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c1_1(a299)) | c2_1(a299) | (~c1_1(a299)) | (~c3_1(a299)) | c2_1(a333) | c3_1(a333) | (~c1_1(a333)))),
% 0.65/0.80 inference(quant_inst,[status(thm)],[])).
% 0.65/0.80 tff(572,plain,
% 0.65/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a333) | c3_1(a333) | c2_1(a299) | (~ndr1_0) | (~c1_1(a299)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c1_1(a333))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[571, 570])).
% 0.65/0.80 tff(573,plain,
% 0.65/0.80 (~c1_1(a299)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[572, 143, 543, 566, 558, 542, 541, 530, 351])).
% 0.65/0.80 tff(574,plain,
% 0.65/0.80 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 0.65/0.80 inference(bind,[status(th)],[])).
% 0.65/0.80 tff(575,plain,
% 0.65/0.80 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.65/0.80 inference(quant_intro,[status(thm)],[574])).
% 0.65/0.80 tff(576,plain,
% 0.65/0.80 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(577,plain,
% 0.65/0.80 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 0.65/0.80 inference(bind,[status(th)],[])).
% 0.65/0.80 tff(578,plain,
% 0.65/0.80 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.65/0.80 inference(quant_intro,[status(thm)],[577])).
% 0.65/0.80 tff(579,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 0.65/0.80 tff(580,plain,
% 0.65/0.80 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[579, 578])).
% 0.65/0.80 tff(581,plain,
% 0.65/0.80 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[580, 576])).
% 0.65/0.80 tff(582,plain,(
% 0.65/0.80 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.65/0.80 inference(skolemize,[status(sab)],[581])).
% 0.65/0.80 tff(583,plain,
% 0.65/0.80 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[582, 575])).
% 0.65/0.80 tff(584,plain,
% 0.65/0.80 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp4 | c1_1(a295) | (~ndr1_0) | (~c2_1(a295)) | (~c0_1(a295)) | c1_1(a299) | (~c3_1(a299)) | (~c0_1(a299)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp4 | c1_1(a295) | (~ndr1_0) | (~c2_1(a295)) | (~c0_1(a295)) | c1_1(a299) | (~c3_1(a299)) | (~c0_1(a299)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(585,plain,
% 0.65/0.80 ((hskp4 | (~ndr1_0) | c1_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c1_1(a295) | (~c0_1(a295)) | (~c2_1(a295))) <=> (hskp4 | c1_1(a295) | (~ndr1_0) | (~c2_1(a295)) | (~c0_1(a295)) | c1_1(a299) | (~c3_1(a299)) | (~c0_1(a299)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(586,plain,
% 0.65/0.80 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c1_1(a295) | (~c0_1(a295)) | (~c2_1(a295)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp4 | c1_1(a295) | (~ndr1_0) | (~c2_1(a295)) | (~c0_1(a295)) | c1_1(a299) | (~c3_1(a299)) | (~c0_1(a299))))),
% 0.65/0.80 inference(monotonicity,[status(thm)],[585])).
% 0.65/0.80 tff(587,plain,
% 0.65/0.80 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c1_1(a295) | (~c0_1(a295)) | (~c2_1(a295)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp4 | c1_1(a295) | (~ndr1_0) | (~c2_1(a295)) | (~c0_1(a295)) | c1_1(a299) | (~c3_1(a299)) | (~c0_1(a299)))),
% 0.65/0.80 inference(transitivity,[status(thm)],[586, 584])).
% 0.65/0.80 tff(588,plain,
% 0.65/0.80 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c1_1(a295) | (~c0_1(a295)) | (~c2_1(a295)))),
% 0.65/0.80 inference(quant_inst,[status(thm)],[])).
% 0.65/0.80 tff(589,plain,
% 0.65/0.80 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp4 | c1_1(a295) | (~ndr1_0) | (~c2_1(a295)) | (~c0_1(a295)) | c1_1(a299) | (~c3_1(a299)) | (~c0_1(a299))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[588, 587])).
% 0.65/0.80 tff(590,plain,
% 0.65/0.80 (hskp4),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[589, 143, 566, 558, 538, 539, 385, 583, 573])).
% 0.65/0.80 tff(591,plain,
% 0.65/0.80 (((~hskp4) | (~c2_1(a300))) <=> ((~hskp4) | (~c2_1(a300)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(592,plain,
% 0.65/0.80 (((~c2_1(a300)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a300)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(593,axiom,((~c2_1(a300)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 0.65/0.80 tff(594,plain,
% 0.65/0.80 ((~hskp4) | (~c2_1(a300))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[593, 592])).
% 0.65/0.80 tff(595,plain,
% 0.65/0.80 ((~hskp4) | (~c2_1(a300))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[594, 591])).
% 0.65/0.80 tff(596,plain,
% 0.65/0.80 (~c2_1(a300)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[595, 590])).
% 0.65/0.80 tff(597,plain,
% 0.65/0.80 (((~hskp4) | (~c0_1(a300))) <=> ((~hskp4) | (~c0_1(a300)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(598,plain,
% 0.65/0.80 (((~c0_1(a300)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a300)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(599,axiom,((~c0_1(a300)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 0.65/0.80 tff(600,plain,
% 0.65/0.80 ((~hskp4) | (~c0_1(a300))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[599, 598])).
% 0.65/0.80 tff(601,plain,
% 0.65/0.80 ((~hskp4) | (~c0_1(a300))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[600, 597])).
% 0.65/0.80 tff(602,plain,
% 0.65/0.80 (~c0_1(a300)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[601, 590])).
% 0.65/0.80 tff(603,plain,
% 0.65/0.80 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))) | (hskp11 | hskp10 | c0_1(a300) | c2_1(a300) | (~ndr1_0) | (~c3_1(a300)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))) | hskp11 | hskp10 | c0_1(a300) | c2_1(a300) | (~ndr1_0) | (~c3_1(a300)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(604,plain,
% 0.65/0.80 ((hskp11 | hskp10 | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | c0_1(a300)) <=> (hskp11 | hskp10 | c0_1(a300) | c2_1(a300) | (~ndr1_0) | (~c3_1(a300)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(605,plain,
% 0.65/0.80 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | c0_1(a300))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))) | (hskp11 | hskp10 | c0_1(a300) | c2_1(a300) | (~ndr1_0) | (~c3_1(a300))))),
% 0.65/0.80 inference(monotonicity,[status(thm)],[604])).
% 0.65/0.80 tff(606,plain,
% 0.65/0.80 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | c0_1(a300))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))) | hskp11 | hskp10 | c0_1(a300) | c2_1(a300) | (~ndr1_0) | (~c3_1(a300)))),
% 0.65/0.80 inference(transitivity,[status(thm)],[605, 603])).
% 0.65/0.80 tff(607,plain,
% 0.65/0.80 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | c0_1(a300))),
% 0.65/0.80 inference(quant_inst,[status(thm)],[])).
% 0.65/0.80 tff(608,plain,
% 0.65/0.80 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | c0_1(U))) | hskp11 | hskp10 | c0_1(a300) | c2_1(a300) | (~ndr1_0) | (~c3_1(a300))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[607, 606])).
% 0.65/0.80 tff(609,plain,
% 0.65/0.80 (~c3_1(a300)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[608, 143, 41, 40, 602, 596, 51])).
% 0.65/0.80 tff(610,plain,
% 0.65/0.80 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W)))),
% 0.65/0.80 inference(bind,[status(th)],[])).
% 0.65/0.80 tff(611,plain,
% 0.65/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.65/0.80 inference(quant_intro,[status(thm)],[610])).
% 0.65/0.80 tff(612,plain,
% 0.65/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(613,plain,
% 0.65/0.80 (^[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) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))))),
% 0.65/0.80 inference(bind,[status(th)],[])).
% 0.65/0.80 tff(614,plain,
% 0.65/0.80 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.65/0.80 inference(quant_intro,[status(thm)],[613])).
% 0.65/0.80 tff(615,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 0.65/0.80 tff(616,plain,
% 0.65/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[615, 614])).
% 0.65/0.80 tff(617,plain,
% 0.65/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[616, 612])).
% 0.65/0.80 tff(618,plain,(
% 0.65/0.80 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.65/0.80 inference(skolemize,[status(sab)],[617])).
% 0.65/0.80 tff(619,plain,
% 0.65/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[618, 611])).
% 0.65/0.80 tff(620,plain,
% 0.65/0.80 (((~hskp4) | (~c1_1(a300))) <=> ((~hskp4) | (~c1_1(a300)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(621,plain,
% 0.65/0.80 (((~c1_1(a300)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a300)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(622,axiom,((~c1_1(a300)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 0.65/0.80 tff(623,plain,
% 0.65/0.80 ((~hskp4) | (~c1_1(a300))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[622, 621])).
% 0.65/0.80 tff(624,plain,
% 0.65/0.80 ((~hskp4) | (~c1_1(a300))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[623, 620])).
% 0.65/0.80 tff(625,plain,
% 0.65/0.80 (~c1_1(a300)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[624, 590])).
% 0.65/0.80 tff(626,plain,
% 0.65/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a336) | c0_1(a300) | c1_1(a300) | c2_1(a300) | (~ndr1_0) | c3_1(a300) | (~c2_1(a336)) | (~c3_1(a336)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a336) | c0_1(a300) | c1_1(a300) | c2_1(a300) | (~ndr1_0) | c3_1(a300) | (~c2_1(a336)) | (~c3_1(a336)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(627,plain,
% 0.65/0.80 (((~ndr1_0) | (~c3_1(a336)) | c0_1(a336) | (~c2_1(a336)) | c2_1(a300) | c0_1(a300) | c3_1(a300) | c1_1(a300) | c0_1(a300) | c3_1(a300)) <=> (c0_1(a336) | c0_1(a300) | c1_1(a300) | c2_1(a300) | (~ndr1_0) | c3_1(a300) | (~c2_1(a336)) | (~c3_1(a336)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(628,plain,
% 0.65/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a336)) | c0_1(a336) | (~c2_1(a336)) | c2_1(a300) | c0_1(a300) | c3_1(a300) | c1_1(a300) | c0_1(a300) | c3_1(a300))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a336) | c0_1(a300) | c1_1(a300) | c2_1(a300) | (~ndr1_0) | c3_1(a300) | (~c2_1(a336)) | (~c3_1(a336))))),
% 0.65/0.80 inference(monotonicity,[status(thm)],[627])).
% 0.65/0.80 tff(629,plain,
% 0.65/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a336)) | c0_1(a336) | (~c2_1(a336)) | c2_1(a300) | c0_1(a300) | c3_1(a300) | c1_1(a300) | c0_1(a300) | c3_1(a300))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a336) | c0_1(a300) | c1_1(a300) | c2_1(a300) | (~ndr1_0) | c3_1(a300) | (~c2_1(a336)) | (~c3_1(a336)))),
% 0.65/0.81 inference(transitivity,[status(thm)],[628, 626])).
% 0.65/0.81 tff(630,plain,
% 0.65/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a336)) | c0_1(a336) | (~c2_1(a336)) | c2_1(a300) | c0_1(a300) | c3_1(a300) | c1_1(a300) | c0_1(a300) | c3_1(a300))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(631,plain,
% 0.65/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a336) | c0_1(a300) | c1_1(a300) | c2_1(a300) | (~ndr1_0) | c3_1(a300) | (~c2_1(a336)) | (~c3_1(a336))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[630, 629])).
% 0.65/0.81 tff(632,plain,
% 0.65/0.81 ($false),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[631, 143, 532, 531, 602, 625, 596, 619, 534, 609])).
% 0.65/0.81 tff(633,plain,(hskp11 | (~c3_1(a336)) | c0_1(a336) | hskp10 | c1_1(a295) | c2_1(a299) | c1_1(a336)), inference(lemma,lemma(discharge,[]))).
% 0.65/0.81 tff(634,plain,
% 0.65/0.81 (hskp11),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[633, 322, 319, 40, 385, 530, 318])).
% 0.65/0.81 tff(635,plain,
% 0.65/0.81 (~c2_1(a309)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[288, 634])).
% 0.65/0.81 tff(636,plain,
% 0.65/0.81 (c3_1(a309)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[296, 634])).
% 0.65/0.81 tff(637,plain,
% 0.65/0.81 (c1_1(a309)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[304, 634])).
% 0.65/0.81 tff(638,plain,
% 0.65/0.81 (hskp0),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[331, 637, 317, 636, 635])).
% 0.65/0.81 tff(639,plain,
% 0.65/0.81 (~c3_1(a294)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[16, 638])).
% 0.65/0.81 tff(640,plain,
% 0.65/0.81 (~c2_1(a294)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[22, 638])).
% 0.65/0.81 tff(641,plain,
% 0.65/0.81 (~c0_1(a294)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[28, 638])).
% 0.65/0.81 tff(642,plain,
% 0.65/0.81 (c1_1(a294)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[505, 143, 637, 636, 635, 641, 640, 639, 275])).
% 0.65/0.81 tff(643,plain,
% 0.65/0.81 ((~c1_1(a294)) | (~c0_1(a309))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[357, 143, 637, 636, 635, 640, 639, 351])).
% 0.65/0.81 tff(644,plain,
% 0.65/0.81 (~c0_1(a309)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[643, 642])).
% 0.65/0.81 tff(645,plain,
% 0.65/0.81 ((~c1_1(a294)) | c0_1(a309)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[365, 143, 637, 636, 635, 641, 639, 10])).
% 0.65/0.81 tff(646,plain,
% 0.65/0.81 ($false),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[645, 644, 642])).
% 0.65/0.81 tff(647,plain,((~hskp21) | hskp10 | c1_1(a295) | c2_1(a299)), inference(lemma,lemma(discharge,[]))).
% 0.65/0.81 tff(648,plain,
% 0.65/0.81 (c2_1(a299)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[647, 508, 40, 374])).
% 0.65/0.81 tff(649,plain,
% 0.65/0.81 (((~hskp3) | (~c2_1(a299))) <=> ((~hskp3) | (~c2_1(a299)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(650,plain,
% 0.65/0.81 (((~c2_1(a299)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a299)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(651,axiom,((~c2_1(a299)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 0.65/0.81 tff(652,plain,
% 0.65/0.81 ((~hskp3) | (~c2_1(a299))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[651, 650])).
% 0.65/0.81 tff(653,plain,
% 0.65/0.81 ((~hskp3) | (~c2_1(a299))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[652, 649])).
% 0.65/0.81 tff(654,plain,
% 0.65/0.81 (~hskp3),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[653, 648])).
% 0.65/0.81 tff(655,plain,
% 0.65/0.81 ($false),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[549, 143, 654, 510, 529, 509, 528, 527, 522, 512])).
% 0.65/0.81 tff(656,plain,(hskp11 | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.65/0.81 tff(657,plain,
% 0.65/0.81 (hskp11),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[656, 40])).
% 0.65/0.81 tff(658,plain,
% 0.65/0.81 (~c2_1(a309)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[288, 657])).
% 0.65/0.81 tff(659,plain,
% 0.65/0.81 (c3_1(a309)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[296, 657])).
% 0.65/0.81 tff(660,plain,
% 0.65/0.81 (c1_1(a309)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[304, 657])).
% 0.65/0.81 tff(661,plain,
% 0.65/0.81 (hskp0),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[331, 660, 508, 659, 658])).
% 0.65/0.81 tff(662,plain,
% 0.65/0.81 (~c3_1(a294)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[16, 661])).
% 0.65/0.81 tff(663,plain,
% 0.65/0.81 (~c2_1(a294)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[22, 661])).
% 0.65/0.81 tff(664,plain,
% 0.65/0.81 (~c0_1(a294)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[28, 661])).
% 0.65/0.81 tff(665,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(666,plain,
% 0.65/0.81 ((hskp3 | (~ndr1_0) | c3_1(a294) | c0_1(a294) | (~c1_1(a294)) | c2_1(a294) | c0_1(a294) | (~c1_1(a294))) <=> (hskp3 | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(667,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a294) | c0_1(a294) | (~c1_1(a294)) | c2_1(a294) | c0_1(a294) | (~c1_1(a294)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[666])).
% 0.65/0.81 tff(668,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a294) | c0_1(a294) | (~c1_1(a294)) | c2_1(a294) | c0_1(a294) | (~c1_1(a294)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)))),
% 0.65/0.81 inference(transitivity,[status(thm)],[667, 665])).
% 0.65/0.81 tff(669,plain,
% 0.65/0.81 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a294) | c0_1(a294) | (~c1_1(a294)) | c2_1(a294) | c0_1(a294) | (~c1_1(a294)))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(670,plain,
% 0.65/0.81 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[669, 668])).
% 0.65/0.81 tff(671,plain,
% 0.65/0.81 (~c1_1(a294)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[670, 143, 654, 664, 663, 662, 39])).
% 0.65/0.81 tff(672,plain,
% 0.65/0.81 ($false),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[505, 143, 660, 659, 658, 664, 663, 662, 275, 671])).
% 0.65/0.81 tff(673,plain,(hskp10), inference(lemma,lemma(discharge,[]))).
% 0.65/0.81 tff(674,plain,
% 0.65/0.81 (((~hskp10) | (~c0_1(a308))) <=> ((~hskp10) | (~c0_1(a308)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(675,plain,
% 0.65/0.81 (((~c0_1(a308)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a308)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(676,axiom,((~c0_1(a308)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 0.65/0.81 tff(677,plain,
% 0.65/0.81 ((~hskp10) | (~c0_1(a308))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[676, 675])).
% 0.65/0.81 tff(678,plain,
% 0.65/0.81 ((~hskp10) | (~c0_1(a308))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[677, 674])).
% 0.65/0.81 tff(679,plain,
% 0.65/0.81 (~c0_1(a308)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[678, 673])).
% 0.65/0.81 tff(680,plain,
% 0.65/0.81 (((~hskp10) | c3_1(a308)) <=> ((~hskp10) | c3_1(a308))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(681,axiom,((~hskp10) | c3_1(a308)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.65/0.81 tff(682,plain,
% 0.65/0.81 ((~hskp10) | c3_1(a308)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[681, 680])).
% 0.65/0.81 tff(683,plain,
% 0.65/0.81 ((~hskp10) | c3_1(a308)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[682, 680])).
% 0.65/0.81 tff(684,plain,
% 0.65/0.81 ((~hskp10) | c3_1(a308)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[683, 680])).
% 0.65/0.81 tff(685,plain,
% 0.65/0.81 ((~hskp10) | c3_1(a308)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[684, 680])).
% 0.65/0.81 tff(686,plain,
% 0.65/0.81 ((~hskp10) | c3_1(a308)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[685, 680])).
% 0.65/0.81 tff(687,plain,
% 0.65/0.81 (c3_1(a308)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[686, 673])).
% 0.65/0.81 tff(688,plain,
% 0.65/0.81 (((~hskp10) | c1_1(a308)) <=> ((~hskp10) | c1_1(a308))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(689,axiom,((~hskp10) | c1_1(a308)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 0.65/0.81 tff(690,plain,
% 0.65/0.81 ((~hskp10) | c1_1(a308)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[689, 688])).
% 0.65/0.81 tff(691,plain,
% 0.65/0.81 ((~hskp10) | c1_1(a308)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[690, 688])).
% 0.65/0.81 tff(692,plain,
% 0.65/0.81 ((~hskp10) | c1_1(a308)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[691, 688])).
% 0.65/0.81 tff(693,plain,
% 0.65/0.81 ((~hskp10) | c1_1(a308)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[692, 688])).
% 0.65/0.81 tff(694,plain,
% 0.65/0.81 ((~hskp10) | c1_1(a308)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[693, 688])).
% 0.65/0.81 tff(695,plain,
% 0.65/0.81 (c1_1(a308)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[694, 673])).
% 0.65/0.81 tff(696,plain,
% 0.65/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a308) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | (~c1_1(a308)) | (~c3_1(a308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a308) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | (~c1_1(a308)) | (~c3_1(a308)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(697,plain,
% 0.65/0.81 (((~ndr1_0) | (~c3_1(a308)) | c0_1(a308) | (~c1_1(a308)) | c0_1(a294) | (~c1_1(a294)) | c3_1(a294) | c2_1(a294) | c0_1(a294) | (~c1_1(a294))) <=> (c0_1(a308) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | (~c1_1(a308)) | (~c3_1(a308)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(698,plain,
% 0.65/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a308)) | c0_1(a308) | (~c1_1(a308)) | c0_1(a294) | (~c1_1(a294)) | c3_1(a294) | c2_1(a294) | c0_1(a294) | (~c1_1(a294)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a308) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | (~c1_1(a308)) | (~c3_1(a308))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[697])).
% 0.65/0.81 tff(699,plain,
% 0.65/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a308)) | c0_1(a308) | (~c1_1(a308)) | c0_1(a294) | (~c1_1(a294)) | c3_1(a294) | c2_1(a294) | c0_1(a294) | (~c1_1(a294)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a308) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | (~c1_1(a308)) | (~c3_1(a308)))),
% 0.65/0.81 inference(transitivity,[status(thm)],[698, 696])).
% 0.65/0.81 tff(700,plain,
% 0.65/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a308)) | c0_1(a308) | (~c1_1(a308)) | c0_1(a294) | (~c1_1(a294)) | c3_1(a294) | c2_1(a294) | c0_1(a294) | (~c1_1(a294)))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(701,plain,
% 0.65/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a308) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | (~c1_1(a294)) | (~c1_1(a308)) | (~c3_1(a308))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[700, 699])).
% 0.65/0.81 tff(702,plain,
% 0.65/0.81 (~c1_1(a294)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[701, 143, 695, 687, 679, 29, 23, 17, 10])).
% 0.65/0.81 tff(703,plain,
% 0.65/0.81 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(704,plain,
% 0.65/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[703])).
% 0.65/0.81 tff(705,plain,
% 0.65/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(706,plain,
% 0.65/0.81 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(707,plain,
% 0.65/0.81 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[706])).
% 0.65/0.81 tff(708,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 0.65/0.81 tff(709,plain,
% 0.65/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[708, 707])).
% 0.65/0.81 tff(710,plain,
% 0.65/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[709, 705])).
% 0.65/0.81 tff(711,plain,(
% 0.65/0.81 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.65/0.81 inference(skolemize,[status(sab)],[710])).
% 0.65/0.81 tff(712,plain,
% 0.65/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[711, 704])).
% 0.65/0.81 tff(713,plain,
% 0.65/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a308) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a308)) | (~c2_1(a308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a308) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a308)) | (~c2_1(a308)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(714,plain,
% 0.65/0.81 (((~ndr1_0) | c0_1(a308) | (~c1_1(a308)) | (~c2_1(a308)) | c2_1(a294) | c0_1(a294) | c3_1(a294) | c2_1(a294) | c1_1(a294) | c0_1(a294)) <=> (c0_1(a308) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a308)) | (~c2_1(a308)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(715,plain,
% 0.65/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a308) | (~c1_1(a308)) | (~c2_1(a308)) | c2_1(a294) | c0_1(a294) | c3_1(a294) | c2_1(a294) | c1_1(a294) | c0_1(a294))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a308) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a308)) | (~c2_1(a308))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[714])).
% 0.65/0.81 tff(716,plain,
% 0.65/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a308) | (~c1_1(a308)) | (~c2_1(a308)) | c2_1(a294) | c0_1(a294) | c3_1(a294) | c2_1(a294) | c1_1(a294) | c0_1(a294))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a308) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a308)) | (~c2_1(a308)))),
% 0.65/0.81 inference(transitivity,[status(thm)],[715, 713])).
% 0.65/0.81 tff(717,plain,
% 0.65/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a308) | (~c1_1(a308)) | (~c2_1(a308)) | c2_1(a294) | c0_1(a294) | c3_1(a294) | c2_1(a294) | c1_1(a294) | c0_1(a294))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(718,plain,
% 0.65/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a308) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a308)) | (~c2_1(a308))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[717, 716])).
% 0.65/0.81 tff(719,plain,
% 0.65/0.81 (~c2_1(a308)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[718, 143, 695, 679, 29, 23, 17, 712, 702])).
% 0.65/0.81 tff(720,plain,
% 0.65/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a308)) | c2_1(a308) | (~c3_1(a308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a308)) | c2_1(a308) | (~c3_1(a308)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(721,plain,
% 0.65/0.81 (((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c1_1(a308)) | c2_1(a294) | c1_1(a294) | c3_1(a294) | c2_1(a294) | c1_1(a294) | c0_1(a294)) <=> (c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a308)) | c2_1(a308) | (~c3_1(a308)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(722,plain,
% 0.65/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c1_1(a308)) | c2_1(a294) | c1_1(a294) | c3_1(a294) | c2_1(a294) | c1_1(a294) | c0_1(a294))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a308)) | c2_1(a308) | (~c3_1(a308))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[721])).
% 0.65/0.81 tff(723,plain,
% 0.65/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c1_1(a308)) | c2_1(a294) | c1_1(a294) | c3_1(a294) | c2_1(a294) | c1_1(a294) | c0_1(a294))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a308)) | c2_1(a308) | (~c3_1(a308)))),
% 0.65/0.81 inference(transitivity,[status(thm)],[722, 720])).
% 0.65/0.81 tff(724,plain,
% 0.65/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c1_1(a308)) | c2_1(a294) | c1_1(a294) | c3_1(a294) | c2_1(a294) | c1_1(a294) | c0_1(a294))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(725,plain,
% 0.65/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a294) | c2_1(a294) | c3_1(a294) | (~ndr1_0) | c1_1(a294) | (~c1_1(a308)) | c2_1(a308) | (~c3_1(a308))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[724, 723])).
% 0.65/0.81 tff(726,plain,
% 0.65/0.81 ($false),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[725, 143, 695, 687, 29, 23, 17, 275, 719, 702])).
% 0.65/0.81 tff(727,plain,(~hskp0), inference(lemma,lemma(discharge,[]))).
% 0.65/0.81 tff(728,plain,
% 0.65/0.81 (^[U: $i] : refl((hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U)) <=> (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U)))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(729,plain,
% 0.65/0.81 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[728])).
% 0.65/0.81 tff(730,plain,
% 0.65/0.81 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(731,plain,
% 0.65/0.81 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U)) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp0) <=> ((hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U)) | hskp0))), rewrite(((hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U)) | hskp0) <=> (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp0) <=> (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(732,plain,
% 0.65/0.81 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp0) <=> ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[731])).
% 0.65/0.81 tff(733,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 0.65/0.81 tff(734,plain,
% 0.65/0.81 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[733, 732])).
% 0.65/0.81 tff(735,plain,
% 0.65/0.81 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[734, 730])).
% 0.65/0.81 tff(736,plain,(
% 0.65/0.81 ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U))),
% 0.65/0.81 inference(skolemize,[status(sab)],[735])).
% 0.65/0.81 tff(737,plain,
% 0.65/0.81 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[736, 729])).
% 0.65/0.81 tff(738,plain,
% 0.65/0.81 (c1_1(a295)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[507, 97])).
% 0.65/0.81 tff(739,plain,
% 0.65/0.81 (~hskp1),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[373, 738])).
% 0.65/0.81 tff(740,plain,
% 0.65/0.81 (c0_1(a321)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[235, 143, 739, 216, 208, 229, 61])).
% 0.65/0.81 tff(741,plain,
% 0.65/0.81 (hskp11 | (~c0_1(a321))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[442, 143, 425, 216, 229, 436])).
% 0.65/0.81 tff(742,plain,
% 0.65/0.81 (hskp11),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[741, 740])).
% 0.65/0.81 tff(743,plain,
% 0.65/0.81 (~c2_1(a309)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[288, 742])).
% 0.65/0.81 tff(744,plain,
% 0.65/0.81 (c3_1(a309)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[296, 742])).
% 0.65/0.81 tff(745,plain,
% 0.65/0.81 (c1_1(a309)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[304, 742])).
% 0.65/0.81 tff(746,plain,
% 0.65/0.81 ($false),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[481, 143, 216, 208, 745, 744, 743, 161, 740])).
% 0.65/0.81 tff(747,plain,(hskp21), inference(lemma,lemma(discharge,[]))).
% 0.65/0.81 tff(748,plain,
% 0.65/0.81 (~c1_1(a336)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[243, 747])).
% 0.65/0.81 tff(749,plain,
% 0.65/0.81 (~c0_1(a336)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[249, 747])).
% 0.65/0.81 tff(750,plain,
% 0.65/0.81 (c3_1(a336)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[257, 747])).
% 0.65/0.81 tff(751,plain,
% 0.65/0.81 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U))) | (hskp2 | hskp0 | c0_1(a336) | c1_1(a336) | (~ndr1_0) | (~c3_1(a336)))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U))) | hskp2 | hskp0 | c0_1(a336) | c1_1(a336) | (~ndr1_0) | (~c3_1(a336)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(752,plain,
% 0.65/0.81 ((hskp2 | hskp0 | (~ndr1_0) | c1_1(a336) | (~c3_1(a336)) | c0_1(a336)) <=> (hskp2 | hskp0 | c0_1(a336) | c1_1(a336) | (~ndr1_0) | (~c3_1(a336)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(753,plain,
% 0.65/0.81 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a336) | (~c3_1(a336)) | c0_1(a336))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U))) | (hskp2 | hskp0 | c0_1(a336) | c1_1(a336) | (~ndr1_0) | (~c3_1(a336))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[752])).
% 0.65/0.81 tff(754,plain,
% 0.65/0.81 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a336) | (~c3_1(a336)) | c0_1(a336))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U))) | hskp2 | hskp0 | c0_1(a336) | c1_1(a336) | (~ndr1_0) | (~c3_1(a336)))),
% 0.65/0.81 inference(transitivity,[status(thm)],[753, 751])).
% 0.65/0.81 tff(755,plain,
% 0.65/0.81 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a336) | (~c3_1(a336)) | c0_1(a336))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(756,plain,
% 0.65/0.81 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c0_1(U))) | hskp2 | hskp0 | c0_1(a336) | c1_1(a336) | (~ndr1_0) | (~c3_1(a336))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[755, 754])).
% 0.65/0.81 tff(757,plain,
% 0.65/0.81 (hskp2 | hskp0),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[756, 143, 750, 749, 748, 737])).
% 0.65/0.81 tff(758,plain,
% 0.65/0.81 (hskp2),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[757, 727])).
% 0.65/0.81 tff(759,plain,
% 0.65/0.81 (((~hskp2) | (~c3_1(a297))) <=> ((~hskp2) | (~c3_1(a297)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(760,plain,
% 0.65/0.81 (((~c3_1(a297)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a297)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(761,axiom,((~c3_1(a297)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 0.65/0.81 tff(762,plain,
% 0.65/0.81 ((~hskp2) | (~c3_1(a297))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[761, 760])).
% 0.65/0.81 tff(763,plain,
% 0.65/0.81 ((~hskp2) | (~c3_1(a297))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[762, 759])).
% 0.65/0.81 tff(764,plain,
% 0.65/0.81 (~c3_1(a297)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[763, 758])).
% 0.65/0.81 tff(765,plain,
% 0.65/0.81 (((~hskp2) | (~c0_1(a297))) <=> ((~hskp2) | (~c0_1(a297)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(766,plain,
% 0.65/0.81 (((~c0_1(a297)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a297)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(767,axiom,((~c0_1(a297)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 0.65/0.81 tff(768,plain,
% 0.65/0.81 ((~hskp2) | (~c0_1(a297))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[767, 766])).
% 0.65/0.81 tff(769,plain,
% 0.65/0.81 ((~hskp2) | (~c0_1(a297))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[768, 765])).
% 0.65/0.81 tff(770,plain,
% 0.65/0.81 (~c0_1(a297)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[769, 758])).
% 0.65/0.81 tff(771,plain,
% 0.65/0.81 (hskp2),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[757, 323])).
% 0.65/0.81 tff(772,plain,
% 0.65/0.81 (~c3_1(a297)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[763, 771])).
% 0.65/0.81 tff(773,plain,
% 0.65/0.81 (~c0_1(a297)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[769, 771])).
% 0.65/0.81 tff(774,assumption,(~hskp16), introduced(assumption)).
% 0.65/0.81 tff(775,plain,
% 0.65/0.81 (^[U: $i] : refl((hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(776,plain,
% 0.65/0.81 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[775])).
% 0.65/0.81 tff(777,plain,
% 0.65/0.81 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(778,plain,
% 0.65/0.81 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp16))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(779,plain,
% 0.65/0.81 (![U: $i] : (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) <=> ![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[778])).
% 0.65/0.81 tff(780,axiom,(![U: $i] : (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 0.65/0.81 tff(781,plain,
% 0.65/0.81 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[780, 779])).
% 0.65/0.81 tff(782,plain,
% 0.65/0.81 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[781, 777])).
% 0.65/0.81 tff(783,plain,(
% 0.65/0.81 ![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.65/0.81 inference(skolemize,[status(sab)],[782])).
% 0.65/0.81 tff(784,plain,
% 0.65/0.81 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[783, 776])).
% 0.65/0.81 tff(785,plain,
% 0.65/0.81 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp16 | c1_1(a336) | (~ndr1_0) | c2_1(a336) | (~c3_1(a336)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp16 | c1_1(a336) | (~ndr1_0) | c2_1(a336) | (~c3_1(a336)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(786,plain,
% 0.65/0.81 ((hskp16 | (~ndr1_0) | c2_1(a336) | c1_1(a336) | (~c3_1(a336))) <=> (hskp16 | c1_1(a336) | (~ndr1_0) | c2_1(a336) | (~c3_1(a336)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(787,plain,
% 0.65/0.81 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a336) | c1_1(a336) | (~c3_1(a336)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp16 | c1_1(a336) | (~ndr1_0) | c2_1(a336) | (~c3_1(a336))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[786])).
% 0.65/0.81 tff(788,plain,
% 0.65/0.81 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a336) | c1_1(a336) | (~c3_1(a336)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp16 | c1_1(a336) | (~ndr1_0) | c2_1(a336) | (~c3_1(a336)))),
% 0.65/0.81 inference(transitivity,[status(thm)],[787, 785])).
% 0.65/0.81 tff(789,plain,
% 0.65/0.81 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a336) | c1_1(a336) | (~c3_1(a336)))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(790,plain,
% 0.65/0.81 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp16 | c1_1(a336) | (~ndr1_0) | c2_1(a336) | (~c3_1(a336))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[789, 788])).
% 0.65/0.81 tff(791,plain,
% 0.65/0.81 (hskp16 | c2_1(a336)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[790, 143, 750, 748, 784])).
% 0.65/0.82 tff(792,plain,
% 0.65/0.82 (c2_1(a336)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[791, 774])).
% 0.65/0.82 tff(793,plain,
% 0.65/0.82 (hskp1 | (~c2_1(a336))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[264, 143, 750, 749, 748, 61])).
% 0.65/0.82 tff(794,plain,
% 0.65/0.82 (hskp1),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[793, 792])).
% 0.65/0.82 tff(795,plain,
% 0.65/0.82 (c2_1(a295)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[461, 794])).
% 0.65/0.82 tff(796,plain,
% 0.65/0.82 (c0_1(a295)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[453, 794])).
% 0.65/0.82 tff(797,plain,
% 0.65/0.82 (hskp20 | (~c2_1(a295)) | (~c0_1(a295))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[468, 143, 41, 385, 436])).
% 0.65/0.82 tff(798,plain,
% 0.65/0.82 (hskp20),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[797, 796, 795])).
% 0.65/0.82 tff(799,plain,
% 0.65/0.82 (~c2_1(a333)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[397, 798])).
% 0.65/0.82 tff(800,plain,
% 0.65/0.82 (((~hskp2) | c1_1(a297)) <=> ((~hskp2) | c1_1(a297))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(801,axiom,((~hskp2) | c1_1(a297)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 0.65/0.82 tff(802,plain,
% 0.65/0.82 ((~hskp2) | c1_1(a297)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[801, 800])).
% 0.65/0.82 tff(803,plain,
% 0.65/0.82 ((~hskp2) | c1_1(a297)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[802, 800])).
% 0.65/0.82 tff(804,plain,
% 0.65/0.82 ((~hskp2) | c1_1(a297)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[803, 800])).
% 0.65/0.82 tff(805,plain,
% 0.65/0.82 ((~hskp2) | c1_1(a297)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[804, 800])).
% 0.65/0.82 tff(806,plain,
% 0.65/0.82 ((~hskp2) | c1_1(a297)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[805, 800])).
% 0.65/0.82 tff(807,plain,
% 0.65/0.82 (c1_1(a297)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[806, 771])).
% 0.65/0.82 tff(808,plain,
% 0.65/0.82 (c1_1(a333)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[415, 798])).
% 0.65/0.82 tff(809,plain,
% 0.65/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a333) | c0_1(a308) | c0_1(a297) | c3_1(a297) | (~ndr1_0) | (~c1_1(a297)) | (~c1_1(a308)) | (~c3_1(a308)) | (~c1_1(a333)) | c0_1(a333))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a333) | c0_1(a308) | c0_1(a297) | c3_1(a297) | (~ndr1_0) | (~c1_1(a297)) | (~c1_1(a308)) | (~c3_1(a308)) | (~c1_1(a333)) | c0_1(a333))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(810,plain,
% 0.65/0.82 (((~ndr1_0) | (~c3_1(a308)) | c0_1(a308) | (~c1_1(a308)) | c0_1(a297) | (~c1_1(a297)) | c3_1(a297) | c2_1(a333) | c0_1(a333) | (~c1_1(a333))) <=> (c2_1(a333) | c0_1(a308) | c0_1(a297) | c3_1(a297) | (~ndr1_0) | (~c1_1(a297)) | (~c1_1(a308)) | (~c3_1(a308)) | (~c1_1(a333)) | c0_1(a333))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(811,plain,
% 0.65/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a308)) | c0_1(a308) | (~c1_1(a308)) | c0_1(a297) | (~c1_1(a297)) | c3_1(a297) | c2_1(a333) | c0_1(a333) | (~c1_1(a333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a333) | c0_1(a308) | c0_1(a297) | c3_1(a297) | (~ndr1_0) | (~c1_1(a297)) | (~c1_1(a308)) | (~c3_1(a308)) | (~c1_1(a333)) | c0_1(a333)))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[810])).
% 0.65/0.82 tff(812,plain,
% 0.65/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a308)) | c0_1(a308) | (~c1_1(a308)) | c0_1(a297) | (~c1_1(a297)) | c3_1(a297) | c2_1(a333) | c0_1(a333) | (~c1_1(a333)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a333) | c0_1(a308) | c0_1(a297) | c3_1(a297) | (~ndr1_0) | (~c1_1(a297)) | (~c1_1(a308)) | (~c3_1(a308)) | (~c1_1(a333)) | c0_1(a333))),
% 0.65/0.82 inference(transitivity,[status(thm)],[811, 809])).
% 0.65/0.82 tff(813,plain,
% 0.65/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a308)) | c0_1(a308) | (~c1_1(a308)) | c0_1(a297) | (~c1_1(a297)) | c3_1(a297) | c2_1(a333) | c0_1(a333) | (~c1_1(a333)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(814,plain,
% 0.65/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a333) | c0_1(a308) | c0_1(a297) | c3_1(a297) | (~ndr1_0) | (~c1_1(a297)) | (~c1_1(a308)) | (~c3_1(a308)) | (~c1_1(a333)) | c0_1(a333)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[813, 812])).
% 0.65/0.82 tff(815,plain,
% 0.65/0.82 (c0_1(a333)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[814, 143, 808, 695, 687, 807, 799, 679, 773, 772, 10])).
% 0.65/0.82 tff(816,plain,
% 0.65/0.82 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(817,plain,
% 0.65/0.82 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[816])).
% 0.65/0.82 tff(818,plain,
% 0.65/0.82 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(819,plain,
% 0.65/0.82 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(820,plain,
% 0.65/0.82 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[819])).
% 0.65/0.82 tff(821,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 0.65/0.82 tff(822,plain,
% 0.65/0.82 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[821, 820])).
% 0.65/0.82 tff(823,plain,
% 0.65/0.82 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[822, 818])).
% 0.65/0.82 tff(824,plain,(
% 0.65/0.82 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.65/0.82 inference(skolemize,[status(sab)],[823])).
% 0.65/0.82 tff(825,plain,
% 0.65/0.82 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[824, 817])).
% 0.65/0.82 tff(826,plain,
% 0.65/0.82 (^[U: $i] : refl((hskp16 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp16 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(827,plain,
% 0.65/0.82 (![U: $i] : (hskp16 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp16 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[826])).
% 0.65/0.82 tff(828,plain,
% 0.65/0.82 (![U: $i] : (hskp16 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp16 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(829,plain,
% 0.65/0.82 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp11))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) | hskp16) <=> ((hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp16))), rewrite(((hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp16) <=> (hskp16 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) | hskp16) <=> (hskp16 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(830,plain,
% 0.65/0.82 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) | hskp16) <=> ![U: $i] : (hskp16 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[829])).
% 0.65/0.82 tff(831,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 0.65/0.82 tff(832,plain,
% 0.65/0.82 (![U: $i] : (hskp16 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[831, 830])).
% 0.65/0.82 tff(833,plain,
% 0.65/0.82 (![U: $i] : (hskp16 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[832, 828])).
% 0.65/0.82 tff(834,plain,(
% 0.65/0.82 ![U: $i] : (hskp16 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.65/0.82 inference(skolemize,[status(sab)],[833])).
% 0.65/0.82 tff(835,plain,
% 0.65/0.82 (![U: $i] : (hskp16 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[834, 827])).
% 0.65/0.82 tff(836,plain,
% 0.65/0.82 (((~![U: $i] : (hskp16 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp11 | c1_1(a295) | (~ndr1_0) | c3_1(a295) | (~c2_1(a295)))) <=> ((~![U: $i] : (hskp16 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp11 | c1_1(a295) | (~ndr1_0) | c3_1(a295) | (~c2_1(a295)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(837,plain,
% 0.65/0.82 ((hskp16 | hskp11 | (~ndr1_0) | c1_1(a295) | c3_1(a295) | (~c2_1(a295))) <=> (hskp16 | hskp11 | c1_1(a295) | (~ndr1_0) | c3_1(a295) | (~c2_1(a295)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(838,plain,
% 0.65/0.82 (((~![U: $i] : (hskp16 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp11 | (~ndr1_0) | c1_1(a295) | c3_1(a295) | (~c2_1(a295)))) <=> ((~![U: $i] : (hskp16 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp11 | c1_1(a295) | (~ndr1_0) | c3_1(a295) | (~c2_1(a295))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[837])).
% 0.65/0.82 tff(839,plain,
% 0.65/0.82 (((~![U: $i] : (hskp16 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp11 | (~ndr1_0) | c1_1(a295) | c3_1(a295) | (~c2_1(a295)))) <=> ((~![U: $i] : (hskp16 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp11 | c1_1(a295) | (~ndr1_0) | c3_1(a295) | (~c2_1(a295)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[838, 836])).
% 0.65/0.82 tff(840,plain,
% 0.65/0.82 ((~![U: $i] : (hskp16 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp11 | (~ndr1_0) | c1_1(a295) | c3_1(a295) | (~c2_1(a295)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(841,plain,
% 0.65/0.82 ((~![U: $i] : (hskp16 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp11 | c1_1(a295) | (~ndr1_0) | c3_1(a295) | (~c2_1(a295))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[840, 839])).
% 0.65/0.82 tff(842,plain,
% 0.65/0.82 (hskp16 | c3_1(a295) | (~c2_1(a295))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[841, 143, 41, 385, 835])).
% 0.65/0.82 tff(843,plain,
% 0.65/0.82 (c3_1(a295)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[842, 795, 774])).
% 0.65/0.82 tff(844,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp4 | c1_1(a295) | (~ndr1_0) | (~c3_1(a295)) | (~c2_1(a295)) | (~c0_1(a295)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp4 | c1_1(a295) | (~ndr1_0) | (~c3_1(a295)) | (~c2_1(a295)) | (~c0_1(a295)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(845,plain,
% 0.65/0.82 ((hskp4 | (~ndr1_0) | c1_1(a295) | (~c3_1(a295)) | (~c0_1(a295)) | c1_1(a295) | (~c0_1(a295)) | (~c2_1(a295))) <=> (hskp4 | c1_1(a295) | (~ndr1_0) | (~c3_1(a295)) | (~c2_1(a295)) | (~c0_1(a295)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(846,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a295) | (~c3_1(a295)) | (~c0_1(a295)) | c1_1(a295) | (~c0_1(a295)) | (~c2_1(a295)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp4 | c1_1(a295) | (~ndr1_0) | (~c3_1(a295)) | (~c2_1(a295)) | (~c0_1(a295))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[845])).
% 0.65/0.82 tff(847,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a295) | (~c3_1(a295)) | (~c0_1(a295)) | c1_1(a295) | (~c0_1(a295)) | (~c2_1(a295)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp4 | c1_1(a295) | (~ndr1_0) | (~c3_1(a295)) | (~c2_1(a295)) | (~c0_1(a295)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[846, 844])).
% 0.65/0.82 tff(848,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a295) | (~c3_1(a295)) | (~c0_1(a295)) | c1_1(a295) | (~c0_1(a295)) | (~c2_1(a295)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(849,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp4 | c1_1(a295) | (~ndr1_0) | (~c3_1(a295)) | (~c2_1(a295)) | (~c0_1(a295))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[848, 847])).
% 0.65/0.82 tff(850,plain,
% 0.65/0.82 (hskp4 | (~c3_1(a295)) | (~c2_1(a295)) | (~c0_1(a295))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[849, 143, 385, 583])).
% 0.65/0.82 tff(851,plain,
% 0.65/0.82 (hskp4),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[850, 843, 795, 796])).
% 0.65/0.82 tff(852,plain,
% 0.65/0.82 (~c2_1(a300)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[595, 851])).
% 0.65/0.82 tff(853,plain,
% 0.65/0.82 (~c1_1(a300)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[624, 851])).
% 0.65/0.82 tff(854,plain,
% 0.65/0.82 (~c0_1(a300)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[601, 851])).
% 0.65/0.82 tff(855,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c2_1(a333) | c0_1(a300) | c1_1(a300) | c2_1(a300) | (~ndr1_0) | (~c1_1(a333)) | (~c0_1(a333)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a333) | c0_1(a300) | c1_1(a300) | c2_1(a300) | (~ndr1_0) | (~c1_1(a333)) | (~c0_1(a333)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(856,plain,
% 0.65/0.82 ((hskp0 | (~ndr1_0) | c2_1(a333) | (~c0_1(a333)) | (~c1_1(a333)) | c2_1(a300) | c1_1(a300) | c0_1(a300)) <=> (hskp0 | c2_1(a333) | c0_1(a300) | c1_1(a300) | c2_1(a300) | (~ndr1_0) | (~c1_1(a333)) | (~c0_1(a333)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(857,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a333) | (~c0_1(a333)) | (~c1_1(a333)) | c2_1(a300) | c1_1(a300) | c0_1(a300))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c2_1(a333) | c0_1(a300) | c1_1(a300) | c2_1(a300) | (~ndr1_0) | (~c1_1(a333)) | (~c0_1(a333))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[856])).
% 0.65/0.82 tff(858,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a333) | (~c0_1(a333)) | (~c1_1(a333)) | c2_1(a300) | c1_1(a300) | c0_1(a300))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a333) | c0_1(a300) | c1_1(a300) | c2_1(a300) | (~ndr1_0) | (~c1_1(a333)) | (~c0_1(a333)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[857, 855])).
% 0.65/0.82 tff(859,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a333) | (~c0_1(a333)) | (~c1_1(a333)) | c2_1(a300) | c1_1(a300) | c0_1(a300))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(860,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a333) | c0_1(a300) | c1_1(a300) | c2_1(a300) | (~ndr1_0) | (~c1_1(a333)) | (~c0_1(a333))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[859, 858])).
% 0.65/0.82 tff(861,plain,
% 0.65/0.82 ($false),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[860, 143, 323, 808, 799, 854, 853, 852, 825, 815])).
% 0.65/0.82 tff(862,plain,(hskp16 | hskp0 | c1_1(a295) | hskp11), inference(lemma,lemma(discharge,[]))).
% 0.65/0.82 tff(863,plain,
% 0.65/0.82 (hskp16),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[862, 323, 385, 41])).
% 0.65/0.82 tff(864,plain,
% 0.65/0.82 (~c1_1(a321)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[228, 863])).
% 0.65/0.82 tff(865,plain,
% 0.65/0.82 (c3_1(a321)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[207, 863])).
% 0.65/0.82 tff(866,plain,
% 0.65/0.82 (c2_1(a321)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[215, 863])).
% 0.65/0.82 tff(867,plain,
% 0.65/0.82 (hskp20),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[471, 866, 385, 41, 865, 864])).
% 0.65/0.82 tff(868,plain,
% 0.65/0.82 (~c2_1(a333)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[397, 867])).
% 0.65/0.82 tff(869,plain,
% 0.65/0.82 (c1_1(a333)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[415, 867])).
% 0.65/0.82 tff(870,plain,
% 0.65/0.82 (c0_1(a333)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[814, 143, 869, 695, 687, 807, 868, 679, 773, 772, 10])).
% 0.65/0.82 tff(871,plain,
% 0.65/0.82 (^[U: $i] : refl((hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(872,plain,
% 0.65/0.82 (![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[871])).
% 0.65/0.82 tff(873,plain,
% 0.65/0.82 (![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(874,plain,
% 0.65/0.82 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | 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)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | 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) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(875,plain,
% 0.65/0.82 (![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) <=> ![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[874])).
% 0.65/0.82 tff(876,axiom,(![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 0.65/0.82 tff(877,plain,
% 0.65/0.82 (![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[876, 875])).
% 0.65/0.82 tff(878,plain,
% 0.65/0.82 (![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[877, 873])).
% 0.65/0.82 tff(879,plain,(
% 0.65/0.82 ![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.65/0.82 inference(skolemize,[status(sab)],[878])).
% 0.65/0.82 tff(880,plain,
% 0.65/0.82 (![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[879, 872])).
% 0.65/0.82 tff(881,plain,
% 0.65/0.82 (~c3_1(a333)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[391, 867])).
% 0.65/0.82 tff(882,plain,
% 0.65/0.82 (((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp22 | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c1_1(a333)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp22 | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c1_1(a333)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(883,plain,
% 0.65/0.82 ((hskp22 | (~ndr1_0) | c2_1(a333) | c3_1(a333) | (~c1_1(a333))) <=> (hskp22 | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c1_1(a333)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(884,plain,
% 0.65/0.82 (((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp22 | (~ndr1_0) | c2_1(a333) | c3_1(a333) | (~c1_1(a333)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp22 | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c1_1(a333))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[883])).
% 0.65/0.82 tff(885,plain,
% 0.65/0.82 (((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp22 | (~ndr1_0) | c2_1(a333) | c3_1(a333) | (~c1_1(a333)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp22 | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c1_1(a333)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[884, 882])).
% 0.65/0.82 tff(886,plain,
% 0.65/0.82 ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp22 | (~ndr1_0) | c2_1(a333) | c3_1(a333) | (~c1_1(a333)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(887,plain,
% 0.65/0.82 ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp22 | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c1_1(a333))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[886, 885])).
% 0.65/0.82 tff(888,plain,
% 0.65/0.82 (hskp22),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[887, 143, 869, 868, 881, 880])).
% 0.65/0.82 tff(889,plain,
% 0.65/0.82 (((~hskp22) | (~c2_1(a338))) <=> ((~hskp22) | (~c2_1(a338)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(890,plain,
% 0.65/0.82 (((~c2_1(a338)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a338)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(891,axiom,((~c2_1(a338)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 0.65/0.82 tff(892,plain,
% 0.65/0.82 ((~hskp22) | (~c2_1(a338))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[891, 890])).
% 0.65/0.82 tff(893,plain,
% 0.65/0.82 ((~hskp22) | (~c2_1(a338))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[892, 889])).
% 0.65/0.82 tff(894,plain,
% 0.65/0.82 (~c2_1(a338)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[893, 888])).
% 0.65/0.82 tff(895,plain,
% 0.65/0.82 (((~hskp22) | (~c1_1(a338))) <=> ((~hskp22) | (~c1_1(a338)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(896,plain,
% 0.65/0.82 (((~c1_1(a338)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a338)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(897,axiom,((~c1_1(a338)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 0.65/0.82 tff(898,plain,
% 0.65/0.82 ((~hskp22) | (~c1_1(a338))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[897, 896])).
% 0.65/0.82 tff(899,plain,
% 0.65/0.82 ((~hskp22) | (~c1_1(a338))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[898, 895])).
% 0.65/0.82 tff(900,plain,
% 0.65/0.82 (~c1_1(a338)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[899, 888])).
% 0.65/0.82 tff(901,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a338) | c2_1(a338) | c2_1(a333) | (~ndr1_0) | (~c1_1(a333)) | (~c0_1(a333)) | c0_1(a338))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a338) | c2_1(a338) | c2_1(a333) | (~ndr1_0) | (~c1_1(a333)) | (~c0_1(a333)) | c0_1(a338))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(902,plain,
% 0.65/0.82 ((hskp0 | (~ndr1_0) | c2_1(a333) | (~c0_1(a333)) | (~c1_1(a333)) | c2_1(a338) | c1_1(a338) | c0_1(a338)) <=> (hskp0 | c1_1(a338) | c2_1(a338) | c2_1(a333) | (~ndr1_0) | (~c1_1(a333)) | (~c0_1(a333)) | c0_1(a338))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(903,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a333) | (~c0_1(a333)) | (~c1_1(a333)) | c2_1(a338) | c1_1(a338) | c0_1(a338))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a338) | c2_1(a338) | c2_1(a333) | (~ndr1_0) | (~c1_1(a333)) | (~c0_1(a333)) | c0_1(a338)))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[902])).
% 0.65/0.82 tff(904,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a333) | (~c0_1(a333)) | (~c1_1(a333)) | c2_1(a338) | c1_1(a338) | c0_1(a338))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a338) | c2_1(a338) | c2_1(a333) | (~ndr1_0) | (~c1_1(a333)) | (~c0_1(a333)) | c0_1(a338))),
% 0.65/0.82 inference(transitivity,[status(thm)],[903, 901])).
% 0.65/0.82 tff(905,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a333) | (~c0_1(a333)) | (~c1_1(a333)) | c2_1(a338) | c1_1(a338) | c0_1(a338))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(906,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a338) | c2_1(a338) | c2_1(a333) | (~ndr1_0) | (~c1_1(a333)) | (~c0_1(a333)) | c0_1(a338)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[905, 904])).
% 0.65/0.82 tff(907,plain,
% 0.65/0.82 (c0_1(a338)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[906, 143, 323, 869, 900, 894, 868, 825, 870])).
% 0.65/0.82 tff(908,plain,
% 0.65/0.82 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(909,plain,
% 0.65/0.82 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[908])).
% 0.65/0.82 tff(910,plain,
% 0.65/0.82 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(911,plain,
% 0.65/0.82 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(912,plain,
% 0.65/0.83 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[911])).
% 0.65/0.83 tff(913,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 0.65/0.83 tff(914,plain,
% 0.65/0.83 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[913, 912])).
% 0.65/0.83 tff(915,plain,
% 0.65/0.83 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[914, 910])).
% 0.65/0.83 tff(916,plain,(
% 0.65/0.83 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.65/0.83 inference(skolemize,[status(sab)],[915])).
% 0.65/0.83 tff(917,plain,
% 0.65/0.83 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[916, 909])).
% 0.65/0.83 tff(918,plain,
% 0.65/0.83 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(919,plain,
% 0.65/0.83 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[918])).
% 0.65/0.83 tff(920,plain,
% 0.65/0.83 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(921,plain,
% 0.65/0.83 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp11) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp11))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(922,plain,
% 0.65/0.83 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[921])).
% 0.65/0.83 tff(923,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 0.65/0.83 tff(924,plain,
% 0.65/0.83 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[923, 922])).
% 0.65/0.83 tff(925,plain,
% 0.65/0.83 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[924, 920])).
% 0.65/0.83 tff(926,plain,(
% 0.65/0.83 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.65/0.83 inference(skolemize,[status(sab)],[925])).
% 0.65/0.83 tff(927,plain,
% 0.65/0.83 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[926, 919])).
% 0.65/0.83 tff(928,plain,
% 0.65/0.83 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(929,plain,
% 0.65/0.83 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[928])).
% 0.65/0.83 tff(930,plain,
% 0.65/0.83 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(931,plain,
% 0.65/0.83 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | 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)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c1_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) | (~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)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c1_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) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(932,plain,
% 0.65/0.83 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[931])).
% 0.65/0.83 tff(933,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 0.65/0.83 tff(934,plain,
% 0.65/0.83 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[933, 932])).
% 0.65/0.83 tff(935,plain,
% 0.65/0.83 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[934, 930])).
% 0.65/0.83 tff(936,plain,(
% 0.65/0.83 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.65/0.83 inference(skolemize,[status(sab)],[935])).
% 0.65/0.83 tff(937,plain,
% 0.65/0.83 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[936, 929])).
% 0.65/0.83 tff(938,plain,
% 0.65/0.83 (((~hskp22) | (~c3_1(a338))) <=> ((~hskp22) | (~c3_1(a338)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(939,plain,
% 0.65/0.83 (((~c3_1(a338)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a338)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(940,axiom,((~c3_1(a338)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 0.65/0.83 tff(941,plain,
% 0.65/0.83 ((~hskp22) | (~c3_1(a338))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[940, 939])).
% 0.65/0.83 tff(942,plain,
% 0.65/0.83 ((~hskp22) | (~c3_1(a338))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[941, 938])).
% 0.65/0.83 tff(943,plain,
% 0.65/0.83 (~c3_1(a338)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[942, 888])).
% 0.65/0.83 tff(944,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp17 | c1_1(a338) | c3_1(a338) | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c1_1(a333)) | (~c0_1(a338)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a338) | c3_1(a338) | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c1_1(a333)) | (~c0_1(a338)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(945,plain,
% 0.65/0.83 ((hskp17 | (~ndr1_0) | c2_1(a333) | c3_1(a333) | (~c1_1(a333)) | c1_1(a338) | c3_1(a338) | (~c0_1(a338))) <=> (hskp17 | c1_1(a338) | c3_1(a338) | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c1_1(a333)) | (~c0_1(a338)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(946,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a333) | c3_1(a333) | (~c1_1(a333)) | c1_1(a338) | c3_1(a338) | (~c0_1(a338)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp17 | c1_1(a338) | c3_1(a338) | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c1_1(a333)) | (~c0_1(a338))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[945])).
% 0.65/0.83 tff(947,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a333) | c3_1(a333) | (~c1_1(a333)) | c1_1(a338) | c3_1(a338) | (~c0_1(a338)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a338) | c3_1(a338) | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c1_1(a333)) | (~c0_1(a338)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[946, 944])).
% 0.65/0.83 tff(948,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a333) | c3_1(a333) | (~c1_1(a333)) | c1_1(a338) | c3_1(a338) | (~c0_1(a338)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(949,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a338) | c3_1(a338) | c2_1(a333) | c3_1(a333) | (~ndr1_0) | (~c1_1(a333)) | (~c0_1(a338))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[948, 947])).
% 0.65/0.83 tff(950,plain,
% 0.65/0.83 (hskp17 | (~c0_1(a338))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[949, 143, 869, 900, 943, 868, 881, 937])).
% 0.65/0.83 tff(951,plain,
% 0.65/0.83 (hskp17),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[950, 907])).
% 0.65/0.83 tff(952,plain,
% 0.65/0.83 (((~hskp17) | (~c3_1(a323))) <=> ((~hskp17) | (~c3_1(a323)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(953,plain,
% 0.65/0.83 (((~c3_1(a323)) | (~hskp17)) <=> ((~hskp17) | (~c3_1(a323)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(954,axiom,((~c3_1(a323)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 0.65/0.83 tff(955,plain,
% 0.65/0.83 ((~hskp17) | (~c3_1(a323))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[954, 953])).
% 0.65/0.83 tff(956,plain,
% 0.65/0.83 ((~hskp17) | (~c3_1(a323))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[955, 952])).
% 0.65/0.83 tff(957,plain,
% 0.65/0.83 (~c3_1(a323)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[956, 951])).
% 0.65/0.83 tff(958,plain,
% 0.65/0.83 (((~hskp17) | c2_1(a323)) <=> ((~hskp17) | c2_1(a323))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(959,axiom,((~hskp17) | c2_1(a323)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 0.65/0.83 tff(960,plain,
% 0.65/0.83 ((~hskp17) | c2_1(a323)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[959, 958])).
% 0.65/0.83 tff(961,plain,
% 0.65/0.83 ((~hskp17) | c2_1(a323)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[960, 958])).
% 0.65/0.83 tff(962,plain,
% 0.65/0.83 ((~hskp17) | c2_1(a323)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[961, 958])).
% 0.65/0.83 tff(963,plain,
% 0.65/0.83 ((~hskp17) | c2_1(a323)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[962, 958])).
% 0.65/0.83 tff(964,plain,
% 0.65/0.83 ((~hskp17) | c2_1(a323)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[963, 958])).
% 0.65/0.83 tff(965,plain,
% 0.65/0.83 (c2_1(a323)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[964, 951])).
% 0.65/0.83 tff(966,plain,
% 0.65/0.83 (((~hskp17) | c0_1(a323)) <=> ((~hskp17) | c0_1(a323))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(967,axiom,((~hskp17) | c0_1(a323)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 0.65/0.83 tff(968,plain,
% 0.65/0.83 ((~hskp17) | c0_1(a323)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[967, 966])).
% 0.65/0.83 tff(969,plain,
% 0.65/0.83 ((~hskp17) | c0_1(a323)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[968, 966])).
% 0.65/0.83 tff(970,plain,
% 0.65/0.83 ((~hskp17) | c0_1(a323)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[969, 966])).
% 0.65/0.83 tff(971,plain,
% 0.65/0.83 ((~hskp17) | c0_1(a323)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[970, 966])).
% 0.65/0.83 tff(972,plain,
% 0.65/0.83 ((~hskp17) | c0_1(a323)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[971, 966])).
% 0.65/0.83 tff(973,plain,
% 0.65/0.83 (c0_1(a323)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[972, 951])).
% 0.65/0.83 tff(974,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a323) | (~ndr1_0) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321)) | (~c2_1(a323)) | (~c0_1(a323)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a323) | (~ndr1_0) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321)) | (~c2_1(a323)) | (~c0_1(a323)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(975,plain,
% 0.65/0.83 ((hskp11 | (~ndr1_0) | (~c3_1(a321)) | (~c0_1(a321)) | (~c2_1(a321)) | c3_1(a323) | (~c0_1(a323)) | (~c2_1(a323))) <=> (hskp11 | c3_1(a323) | (~ndr1_0) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321)) | (~c2_1(a323)) | (~c0_1(a323)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(976,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c3_1(a321)) | (~c0_1(a321)) | (~c2_1(a321)) | c3_1(a323) | (~c0_1(a323)) | (~c2_1(a323)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a323) | (~ndr1_0) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321)) | (~c2_1(a323)) | (~c0_1(a323))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[975])).
% 0.65/0.83 tff(977,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c3_1(a321)) | (~c0_1(a321)) | (~c2_1(a321)) | c3_1(a323) | (~c0_1(a323)) | (~c2_1(a323)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a323) | (~ndr1_0) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321)) | (~c2_1(a323)) | (~c0_1(a323)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[976, 974])).
% 0.65/0.83 tff(978,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c3_1(a321)) | (~c0_1(a321)) | (~c2_1(a321)) | c3_1(a323) | (~c0_1(a323)) | (~c2_1(a323)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(979,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a323) | (~ndr1_0) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321)) | (~c2_1(a323)) | (~c0_1(a323))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[978, 977])).
% 0.65/0.83 tff(980,plain,
% 0.65/0.83 (~c0_1(a321)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[979, 143, 41, 973, 965, 866, 865, 957, 927])).
% 0.65/0.83 tff(981,plain,
% 0.65/0.83 (^[U: $i] : refl((hskp14 | hskp0 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U))) <=> (hskp14 | hskp0 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(982,plain,
% 0.65/0.83 (![U: $i] : (hskp14 | hskp0 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp14 | hskp0 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[981])).
% 0.65/0.83 tff(983,plain,
% 0.65/0.83 (![U: $i] : (hskp14 | hskp0 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp14 | hskp0 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(984,plain,
% 0.65/0.83 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) <=> (((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U))) | hskp14))), rewrite((((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp0) <=> ((hskp14 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U))) | hskp0))), rewrite(((hskp14 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U))) | hskp0) <=> (hskp14 | hskp0 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp0) <=> (hskp14 | hskp0 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(985,plain,
% 0.65/0.83 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp0) <=> ![U: $i] : (hskp14 | hskp0 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[984])).
% 0.65/0.83 tff(986,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 0.65/0.83 tff(987,plain,
% 0.65/0.83 (![U: $i] : (hskp14 | hskp0 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[986, 985])).
% 0.65/0.83 tff(988,plain,
% 0.65/0.83 (![U: $i] : (hskp14 | hskp0 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[987, 983])).
% 0.65/0.83 tff(989,plain,(
% 0.65/0.83 ![U: $i] : (hskp14 | hskp0 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)))),
% 0.65/0.83 inference(skolemize,[status(sab)],[988])).
% 0.65/0.83 tff(990,plain,
% 0.65/0.83 (![U: $i] : (hskp14 | hskp0 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[989, 982])).
% 0.65/0.83 tff(991,plain,
% 0.65/0.83 (((~![U: $i] : (hskp14 | hskp0 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)))) | (hskp14 | hskp0 | (~ndr1_0) | c0_1(a321) | (~c2_1(a321)) | (~c3_1(a321)))) <=> ((~![U: $i] : (hskp14 | hskp0 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)))) | hskp14 | hskp0 | (~ndr1_0) | c0_1(a321) | (~c2_1(a321)) | (~c3_1(a321)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(992,plain,
% 0.65/0.83 ((hskp14 | hskp0 | (~ndr1_0) | (~c3_1(a321)) | c0_1(a321) | (~c2_1(a321))) <=> (hskp14 | hskp0 | (~ndr1_0) | c0_1(a321) | (~c2_1(a321)) | (~c3_1(a321)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(993,plain,
% 0.65/0.83 (((~![U: $i] : (hskp14 | hskp0 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)))) | (hskp14 | hskp0 | (~ndr1_0) | (~c3_1(a321)) | c0_1(a321) | (~c2_1(a321)))) <=> ((~![U: $i] : (hskp14 | hskp0 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)))) | (hskp14 | hskp0 | (~ndr1_0) | c0_1(a321) | (~c2_1(a321)) | (~c3_1(a321))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[992])).
% 0.65/0.83 tff(994,plain,
% 0.65/0.83 (((~![U: $i] : (hskp14 | hskp0 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)))) | (hskp14 | hskp0 | (~ndr1_0) | (~c3_1(a321)) | c0_1(a321) | (~c2_1(a321)))) <=> ((~![U: $i] : (hskp14 | hskp0 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)))) | hskp14 | hskp0 | (~ndr1_0) | c0_1(a321) | (~c2_1(a321)) | (~c3_1(a321)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[993, 991])).
% 0.65/0.83 tff(995,plain,
% 0.65/0.83 ((~![U: $i] : (hskp14 | hskp0 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)))) | (hskp14 | hskp0 | (~ndr1_0) | (~c3_1(a321)) | c0_1(a321) | (~c2_1(a321)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(996,plain,
% 0.65/0.83 ((~![U: $i] : (hskp14 | hskp0 | (~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c2_1(U)))) | hskp14 | hskp0 | (~ndr1_0) | c0_1(a321) | (~c2_1(a321)) | (~c3_1(a321))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[995, 994])).
% 0.65/0.83 tff(997,plain,
% 0.65/0.83 (hskp14 | c0_1(a321)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[996, 143, 323, 866, 865, 990])).
% 0.65/0.83 tff(998,plain,
% 0.65/0.83 (hskp14),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[997, 980])).
% 0.65/0.83 tff(999,plain,
% 0.65/0.83 (((~hskp14) | (~c0_1(a315))) <=> ((~hskp14) | (~c0_1(a315)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1000,plain,
% 0.65/0.83 (((~c0_1(a315)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a315)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1001,axiom,((~c0_1(a315)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 0.65/0.83 tff(1002,plain,
% 0.65/0.83 ((~hskp14) | (~c0_1(a315))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1001, 1000])).
% 0.65/0.83 tff(1003,plain,
% 0.65/0.83 ((~hskp14) | (~c0_1(a315))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1002, 999])).
% 0.65/0.83 tff(1004,plain,
% 0.65/0.83 (~c0_1(a315)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1003, 998])).
% 0.65/0.83 tff(1005,plain,
% 0.65/0.83 (((~hskp14) | c2_1(a315)) <=> ((~hskp14) | c2_1(a315))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1006,axiom,((~hskp14) | c2_1(a315)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 0.65/0.83 tff(1007,plain,
% 0.65/0.83 ((~hskp14) | c2_1(a315)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1006, 1005])).
% 0.65/0.83 tff(1008,plain,
% 0.65/0.83 ((~hskp14) | c2_1(a315)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1007, 1005])).
% 0.65/0.83 tff(1009,plain,
% 0.65/0.83 ((~hskp14) | c2_1(a315)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1008, 1005])).
% 0.65/0.83 tff(1010,plain,
% 0.65/0.83 ((~hskp14) | c2_1(a315)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1009, 1005])).
% 0.65/0.83 tff(1011,plain,
% 0.65/0.83 ((~hskp14) | c2_1(a315)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1010, 1005])).
% 0.65/0.83 tff(1012,plain,
% 0.65/0.83 (c2_1(a315)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1011, 998])).
% 0.65/0.83 tff(1013,plain,
% 0.65/0.83 (((~hskp14) | c1_1(a315)) <=> ((~hskp14) | c1_1(a315))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1014,axiom,((~hskp14) | c1_1(a315)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 0.65/0.83 tff(1015,plain,
% 0.65/0.83 ((~hskp14) | c1_1(a315)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1014, 1013])).
% 0.65/0.83 tff(1016,plain,
% 0.65/0.83 ((~hskp14) | c1_1(a315)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1015, 1013])).
% 0.65/0.83 tff(1017,plain,
% 0.65/0.83 ((~hskp14) | c1_1(a315)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1016, 1013])).
% 0.65/0.83 tff(1018,plain,
% 0.65/0.83 ((~hskp14) | c1_1(a315)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1017, 1013])).
% 0.65/0.83 tff(1019,plain,
% 0.65/0.83 ((~hskp14) | c1_1(a315)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1018, 1013])).
% 0.65/0.83 tff(1020,plain,
% 0.65/0.83 (c1_1(a315)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1019, 998])).
% 0.65/0.83 tff(1021,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c2_1(a338) | c3_1(a338) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c0_1(a338)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a338) | c3_1(a338) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c0_1(a338)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1022,plain,
% 0.65/0.83 ((hskp12 | (~ndr1_0) | c2_1(a338) | c3_1(a338) | (~c0_1(a338)) | c0_1(a315) | (~c1_1(a315)) | (~c2_1(a315))) <=> (hskp12 | c2_1(a338) | c3_1(a338) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c0_1(a338)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1023,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a338) | c3_1(a338) | (~c0_1(a338)) | c0_1(a315) | (~c1_1(a315)) | (~c2_1(a315)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c2_1(a338) | c3_1(a338) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c0_1(a338))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[1022])).
% 0.65/0.83 tff(1024,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a338) | c3_1(a338) | (~c0_1(a338)) | c0_1(a315) | (~c1_1(a315)) | (~c2_1(a315)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a338) | c3_1(a338) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c0_1(a338)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[1023, 1021])).
% 0.65/0.83 tff(1025,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a338) | c3_1(a338) | (~c0_1(a338)) | c0_1(a315) | (~c1_1(a315)) | (~c2_1(a315)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(1026,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a338) | c3_1(a338) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c0_1(a338))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1025, 1024])).
% 0.65/0.83 tff(1027,plain,
% 0.65/0.83 (hskp12),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1026, 143, 1020, 1012, 894, 943, 1004, 917, 907])).
% 0.65/0.83 tff(1028,plain,
% 0.65/0.83 (((~hskp12) | (~c2_1(a310))) <=> ((~hskp12) | (~c2_1(a310)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1029,plain,
% 0.65/0.83 (((~c2_1(a310)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a310)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1030,axiom,((~c2_1(a310)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 0.65/0.83 tff(1031,plain,
% 0.65/0.83 ((~hskp12) | (~c2_1(a310))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1030, 1029])).
% 0.65/0.83 tff(1032,plain,
% 0.65/0.83 ((~hskp12) | (~c2_1(a310))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1031, 1028])).
% 0.65/0.83 tff(1033,plain,
% 0.65/0.83 (~c2_1(a310)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1032, 1027])).
% 0.65/0.83 tff(1034,plain,
% 0.65/0.83 (((~hskp12) | (~c0_1(a310))) <=> ((~hskp12) | (~c0_1(a310)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1035,plain,
% 0.65/0.83 (((~c0_1(a310)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a310)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1036,axiom,((~c0_1(a310)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 0.65/0.83 tff(1037,plain,
% 0.65/0.83 ((~hskp12) | (~c0_1(a310))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1036, 1035])).
% 0.65/0.83 tff(1038,plain,
% 0.65/0.83 ((~hskp12) | (~c0_1(a310))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1037, 1034])).
% 0.65/0.83 tff(1039,plain,
% 0.65/0.83 (~c0_1(a310)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1038, 1027])).
% 0.65/0.83 tff(1040,plain,
% 0.65/0.83 (((~hskp12) | c3_1(a310)) <=> ((~hskp12) | c3_1(a310))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1041,axiom,((~hskp12) | c3_1(a310)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 0.65/0.83 tff(1042,plain,
% 0.65/0.83 ((~hskp12) | c3_1(a310)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1041, 1040])).
% 0.65/0.83 tff(1043,plain,
% 0.65/0.83 ((~hskp12) | c3_1(a310)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1042, 1040])).
% 0.65/0.83 tff(1044,plain,
% 0.65/0.83 ((~hskp12) | c3_1(a310)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1043, 1040])).
% 0.65/0.83 tff(1045,plain,
% 0.65/0.83 ((~hskp12) | c3_1(a310)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1044, 1040])).
% 0.65/0.83 tff(1046,plain,
% 0.65/0.83 ((~hskp12) | c3_1(a310)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1045, 1040])).
% 0.65/0.83 tff(1047,plain,
% 0.65/0.83 (c3_1(a310)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1046, 1027])).
% 0.65/0.83 tff(1048,plain,
% 0.65/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a310) | c2_1(a310) | c0_1(a297) | c3_1(a297) | (~ndr1_0) | (~c1_1(a297)) | (~c3_1(a310)) | (~c1_1(a310)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a310) | c2_1(a310) | c0_1(a297) | c3_1(a297) | (~ndr1_0) | (~c1_1(a297)) | (~c3_1(a310)) | (~c1_1(a310)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1049,plain,
% 0.65/0.83 (((~ndr1_0) | (~c3_1(a310)) | c0_1(a310) | (~c1_1(a310)) | c0_1(a297) | (~c1_1(a297)) | c3_1(a297) | c2_1(a310) | c0_1(a310) | (~c1_1(a310))) <=> (c0_1(a310) | c2_1(a310) | c0_1(a297) | c3_1(a297) | (~ndr1_0) | (~c1_1(a297)) | (~c3_1(a310)) | (~c1_1(a310)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1050,plain,
% 0.65/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a310)) | c0_1(a310) | (~c1_1(a310)) | c0_1(a297) | (~c1_1(a297)) | c3_1(a297) | c2_1(a310) | c0_1(a310) | (~c1_1(a310)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a310) | c2_1(a310) | c0_1(a297) | c3_1(a297) | (~ndr1_0) | (~c1_1(a297)) | (~c3_1(a310)) | (~c1_1(a310))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[1049])).
% 0.65/0.83 tff(1051,plain,
% 0.65/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a310)) | c0_1(a310) | (~c1_1(a310)) | c0_1(a297) | (~c1_1(a297)) | c3_1(a297) | c2_1(a310) | c0_1(a310) | (~c1_1(a310)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a310) | c2_1(a310) | c0_1(a297) | c3_1(a297) | (~ndr1_0) | (~c1_1(a297)) | (~c3_1(a310)) | (~c1_1(a310)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[1050, 1048])).
% 0.65/0.83 tff(1052,plain,
% 0.65/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a310)) | c0_1(a310) | (~c1_1(a310)) | c0_1(a297) | (~c1_1(a297)) | c3_1(a297) | c2_1(a310) | c0_1(a310) | (~c1_1(a310)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(1053,plain,
% 0.65/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(V) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a310) | c2_1(a310) | c0_1(a297) | c3_1(a297) | (~ndr1_0) | (~c1_1(a297)) | (~c3_1(a310)) | (~c1_1(a310))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1052, 1051])).
% 0.65/0.83 tff(1054,plain,
% 0.65/0.83 (~c1_1(a310)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1053, 143, 1047, 807, 1039, 1033, 773, 772, 10])).
% 0.65/0.83 tff(1055,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c2_1(a333) | c0_1(a310) | c2_1(a310) | (~ndr1_0) | c1_1(a310) | (~c1_1(a333)) | (~c0_1(a333)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a333) | c0_1(a310) | c2_1(a310) | (~ndr1_0) | c1_1(a310) | (~c1_1(a333)) | (~c0_1(a333)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1056,plain,
% 0.65/0.83 ((hskp0 | (~ndr1_0) | c2_1(a333) | (~c0_1(a333)) | (~c1_1(a333)) | c2_1(a310) | c1_1(a310) | c0_1(a310)) <=> (hskp0 | c2_1(a333) | c0_1(a310) | c2_1(a310) | (~ndr1_0) | c1_1(a310) | (~c1_1(a333)) | (~c0_1(a333)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1057,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a333) | (~c0_1(a333)) | (~c1_1(a333)) | c2_1(a310) | c1_1(a310) | c0_1(a310))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c2_1(a333) | c0_1(a310) | c2_1(a310) | (~ndr1_0) | c1_1(a310) | (~c1_1(a333)) | (~c0_1(a333))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[1056])).
% 0.65/0.83 tff(1058,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a333) | (~c0_1(a333)) | (~c1_1(a333)) | c2_1(a310) | c1_1(a310) | c0_1(a310))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a333) | c0_1(a310) | c2_1(a310) | (~ndr1_0) | c1_1(a310) | (~c1_1(a333)) | (~c0_1(a333)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[1057, 1055])).
% 0.65/0.83 tff(1059,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a333) | (~c0_1(a333)) | (~c1_1(a333)) | c2_1(a310) | c1_1(a310) | c0_1(a310))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(1060,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a333) | c0_1(a310) | c2_1(a310) | (~ndr1_0) | c1_1(a310) | (~c1_1(a333)) | (~c0_1(a333))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1059, 1058])).
% 0.65/0.83 tff(1061,plain,
% 0.65/0.83 ($false),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1060, 143, 323, 869, 868, 1039, 1033, 825, 870, 1054])).
% 0.65/0.84 tff(1062,plain,(hskp0 | hskp11 | c1_1(a295)), inference(lemma,lemma(discharge,[]))).
% 0.65/0.84 tff(1063,plain,
% 0.65/0.84 (c1_1(a295)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1062, 41, 727])).
% 0.65/0.84 tff(1064,plain,
% 0.65/0.84 (~hskp1),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[373, 1063])).
% 0.65/0.84 tff(1065,plain,
% 0.65/0.84 (~c2_1(a336)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[793, 1064])).
% 0.65/0.84 tff(1066,plain,
% 0.65/0.84 (hskp16),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[791, 1065])).
% 0.65/0.84 tff(1067,plain,
% 0.65/0.84 (~c1_1(a321)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[228, 1066])).
% 0.65/0.84 tff(1068,plain,
% 0.65/0.84 (c3_1(a321)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[207, 1066])).
% 0.65/0.84 tff(1069,plain,
% 0.65/0.84 (c2_1(a321)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[215, 1066])).
% 0.65/0.84 tff(1070,plain,
% 0.65/0.84 (c0_1(a321)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[235, 143, 1064, 1069, 1068, 1067, 61])).
% 0.65/0.84 tff(1071,plain,
% 0.65/0.84 (hskp20 | (~c0_1(a321))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[442, 143, 41, 1069, 1067, 436])).
% 0.65/0.84 tff(1072,plain,
% 0.65/0.84 (hskp20),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1071, 1070])).
% 0.65/0.84 tff(1073,plain,
% 0.65/0.84 (~c2_1(a333)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[397, 1072])).
% 0.65/0.84 tff(1074,plain,
% 0.65/0.84 (c1_1(a297)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[806, 758])).
% 0.65/0.84 tff(1075,plain,
% 0.65/0.84 (c1_1(a333)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[415, 1072])).
% 0.65/0.84 tff(1076,plain,
% 0.65/0.84 (c0_1(a333)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[814, 143, 1075, 695, 687, 1074, 1073, 679, 770, 764, 10])).
% 0.65/0.84 tff(1077,plain,
% 0.65/0.84 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp4 | c1_1(a321) | (~ndr1_0) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp4 | c1_1(a321) | (~ndr1_0) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(1078,plain,
% 0.65/0.84 ((hskp4 | (~ndr1_0) | c1_1(a321) | (~c3_1(a321)) | (~c0_1(a321)) | c1_1(a321) | (~c0_1(a321)) | (~c2_1(a321))) <=> (hskp4 | c1_1(a321) | (~ndr1_0) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(1079,plain,
% 0.65/0.84 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a321) | (~c3_1(a321)) | (~c0_1(a321)) | c1_1(a321) | (~c0_1(a321)) | (~c2_1(a321)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp4 | c1_1(a321) | (~ndr1_0) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321))))),
% 0.65/0.84 inference(monotonicity,[status(thm)],[1078])).
% 0.65/0.84 tff(1080,plain,
% 0.65/0.84 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a321) | (~c3_1(a321)) | (~c0_1(a321)) | c1_1(a321) | (~c0_1(a321)) | (~c2_1(a321)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp4 | c1_1(a321) | (~ndr1_0) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321)))),
% 0.65/0.84 inference(transitivity,[status(thm)],[1079, 1077])).
% 0.65/0.84 tff(1081,plain,
% 0.65/0.84 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a321) | (~c3_1(a321)) | (~c0_1(a321)) | c1_1(a321) | (~c0_1(a321)) | (~c2_1(a321)))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(1082,plain,
% 0.65/0.84 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp4 | c1_1(a321) | (~ndr1_0) | (~c2_1(a321)) | (~c3_1(a321)) | (~c0_1(a321))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1081, 1080])).
% 0.65/0.84 tff(1083,plain,
% 0.65/0.84 (hskp4 | (~c0_1(a321))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1082, 143, 1069, 1068, 1067, 583])).
% 0.65/0.84 tff(1084,plain,
% 0.65/0.84 (hskp4),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1083, 1070])).
% 0.65/0.84 tff(1085,plain,
% 0.65/0.84 (~c2_1(a300)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[595, 1084])).
% 0.65/0.84 tff(1086,plain,
% 0.65/0.84 (~c1_1(a300)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[624, 1084])).
% 0.65/0.84 tff(1087,plain,
% 0.65/0.84 (~c0_1(a300)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[601, 1084])).
% 0.65/0.84 tff(1088,plain,
% 0.65/0.84 ($false),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[860, 143, 727, 1075, 1073, 1087, 1086, 1085, 825, 1076])).
% 0.65/0.84 tff(1089,plain,(hskp11), inference(lemma,lemma(discharge,[]))).
% 0.65/0.84 tff(1090,plain,
% 0.65/0.84 (~c2_1(a309)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[288, 1089])).
% 0.65/0.84 tff(1091,plain,
% 0.65/0.84 (c1_1(a309)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[304, 1089])).
% 0.65/0.84 tff(1092,plain,
% 0.65/0.84 (c3_1(a309)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[296, 1089])).
% 0.65/0.84 tff(1093,plain,
% 0.65/0.84 ($false),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[331, 1092, 1091, 747, 727, 1090])).
% 0.65/0.84 % SZS output end Proof
% 0.65/0.84 % E exiting
%------------------------------------------------------------------------------