%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN451-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:09 AM UTC 2025
% Result : Unsatisfiable 0.67s 0.86s
% Output : Proof 0.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN451-1 : TPTP v9.0.0. Released v2.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:36:11 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.67/0.86 % SZS status Unsatisfiable
% 0.67/0.86 % SZS output start Proof
% 0.67/0.86 tff(c0_1_type, type, (
% 0.67/0.86 c0_1: $i > $o)).
% 0.67/0.86 tff(a731_type, type, (
% 0.67/0.86 a731: $i)).
% 0.67/0.86 tff(c3_1_type, type, (
% 0.67/0.86 c3_1: $i > $o)).
% 0.67/0.86 tff(c1_1_type, type, (
% 0.67/0.86 c1_1: $i > $o)).
% 0.67/0.86 tff(c2_1_type, type, (
% 0.67/0.86 c2_1: $i > $o)).
% 0.67/0.86 tff(ndr1_0_type, type, (
% 0.67/0.86 ndr1_0: $o)).
% 0.67/0.86 tff(hskp1_type, type, (
% 0.67/0.86 hskp1: $o)).
% 0.67/0.86 tff(a750_type, type, (
% 0.67/0.86 a750: $i)).
% 0.67/0.86 tff(hskp27_type, type, (
% 0.67/0.86 hskp27: $o)).
% 0.67/0.86 tff(hskp19_type, type, (
% 0.67/0.86 hskp19: $o)).
% 0.67/0.86 tff(hskp8_type, type, (
% 0.67/0.86 hskp8: $o)).
% 0.67/0.86 tff(a730_type, type, (
% 0.67/0.86 a730: $i)).
% 0.67/0.86 tff(a735_type, type, (
% 0.67/0.86 a735: $i)).
% 0.67/0.86 tff(hskp5_type, type, (
% 0.67/0.86 hskp5: $o)).
% 0.67/0.86 tff(hskp11_type, type, (
% 0.67/0.86 hskp11: $o)).
% 0.67/0.86 tff(hskp25_type, type, (
% 0.67/0.86 hskp25: $o)).
% 0.67/0.86 tff(hskp0_type, type, (
% 0.67/0.86 hskp0: $o)).
% 0.67/0.86 tff(hskp4_type, type, (
% 0.67/0.86 hskp4: $o)).
% 0.67/0.86 tff(a734_type, type, (
% 0.67/0.86 a734: $i)).
% 0.67/0.86 tff(hskp7_type, type, (
% 0.67/0.86 hskp7: $o)).
% 0.67/0.86 tff(a759_type, type, (
% 0.67/0.86 a759: $i)).
% 0.67/0.86 tff(hskp13_type, type, (
% 0.67/0.86 hskp13: $o)).
% 0.67/0.86 tff(a763_type, type, (
% 0.67/0.86 a763: $i)).
% 0.67/0.86 tff(hskp15_type, type, (
% 0.67/0.86 hskp15: $o)).
% 0.67/0.86 tff(a764_type, type, (
% 0.67/0.86 a764: $i)).
% 0.67/0.86 tff(hskp18_type, type, (
% 0.67/0.86 hskp18: $o)).
% 0.67/0.86 tff(a741_type, type, (
% 0.67/0.86 a741: $i)).
% 0.67/0.86 tff(hskp24_type, type, (
% 0.67/0.86 hskp24: $o)).
% 0.67/0.86 tff(hskp23_type, type, (
% 0.67/0.86 hskp23: $o)).
% 0.67/0.86 tff(a738_type, type, (
% 0.67/0.86 a738: $i)).
% 0.67/0.86 tff(hskp6_type, type, (
% 0.67/0.86 hskp6: $o)).
% 0.67/0.86 tff(a746_type, type, (
% 0.67/0.86 a746: $i)).
% 0.67/0.86 tff(hskp9_type, type, (
% 0.67/0.86 hskp9: $o)).
% 0.67/0.86 tff(a732_type, type, (
% 0.67/0.86 a732: $i)).
% 0.67/0.86 tff(hskp2_type, type, (
% 0.67/0.86 hskp2: $o)).
% 0.67/0.86 tff(a793_type, type, (
% 0.67/0.86 a793: $i)).
% 0.67/0.86 tff(hskp21_type, type, (
% 0.67/0.86 hskp21: $o)).
% 0.67/0.86 tff(a766_type, type, (
% 0.67/0.86 a766: $i)).
% 0.67/0.86 tff(hskp17_type, type, (
% 0.67/0.86 hskp17: $o)).
% 0.67/0.86 tff(a744_type, type, (
% 0.67/0.86 a744: $i)).
% 0.67/0.86 tff(a777_type, type, (
% 0.67/0.86 a777: $i)).
% 0.67/0.86 tff(a798_type, type, (
% 0.67/0.86 a798: $i)).
% 0.67/0.86 tff(hskp16_type, type, (
% 0.67/0.86 hskp16: $o)).
% 0.67/0.86 tff(a729_type, type, (
% 0.67/0.86 a729: $i)).
% 0.67/0.86 tff(a802_type, type, (
% 0.67/0.86 a802: $i)).
% 0.67/0.86 tff(a748_type, type, (
% 0.67/0.86 a748: $i)).
% 0.67/0.86 tff(hskp10_type, type, (
% 0.67/0.86 hskp10: $o)).
% 0.67/0.86 tff(a755_type, type, (
% 0.67/0.86 a755: $i)).
% 0.67/0.86 tff(hskp12_type, type, (
% 0.67/0.86 hskp12: $o)).
% 0.67/0.86 tff(a733_type, type, (
% 0.67/0.86 a733: $i)).
% 0.67/0.86 tff(hskp3_type, type, (
% 0.67/0.86 hskp3: $o)).
% 0.67/0.86 tff(a749_type, type, (
% 0.67/0.86 a749: $i)).
% 0.67/0.86 tff(a775_type, type, (
% 0.67/0.86 a775: $i)).
% 0.67/0.86 tff(a779_type, type, (
% 0.67/0.86 a779: $i)).
% 0.67/0.86 tff(hskp20_type, type, (
% 0.67/0.86 hskp20: $o)).
% 0.67/0.86 tff(a762_type, type, (
% 0.67/0.86 a762: $i)).
% 0.67/0.86 tff(hskp14_type, type, (
% 0.67/0.86 hskp14: $o)).
% 0.67/0.86 tff(a784_type, type, (
% 0.67/0.86 a784: $i)).
% 0.67/0.86 tff(hskp28_type, type, (
% 0.67/0.86 hskp28: $o)).
% 0.67/0.86 tff(1,plain,
% 0.67/0.86 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)))),
% 0.67/0.86 inference(bind,[status(th)],[])).
% 0.67/0.86 tff(2,plain,
% 0.67/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.67/0.86 inference(quant_intro,[status(thm)],[1])).
% 0.67/0.86 tff(3,plain,
% 0.67/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(4,plain,
% 0.67/0.86 (^[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)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))))),
% 0.67/0.86 inference(bind,[status(th)],[])).
% 0.67/0.86 tff(5,plain,
% 0.67/0.86 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.67/0.86 inference(quant_intro,[status(thm)],[4])).
% 0.67/0.86 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 0.67/0.86 tff(7,plain,
% 0.67/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.67/0.86 tff(8,plain,
% 0.67/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.67/0.86 tff(9,plain,(
% 0.67/0.86 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.67/0.86 inference(skolemize,[status(sab)],[8])).
% 0.67/0.86 tff(10,plain,
% 0.67/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.67/0.86 tff(11,plain,
% 0.67/0.86 (^[V: $i, U: $i] : refl((hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))),
% 0.67/0.86 inference(bind,[status(th)],[])).
% 0.67/0.86 tff(12,plain,
% 0.67/0.86 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.67/0.86 inference(quant_intro,[status(thm)],[11])).
% 0.67/0.86 tff(13,plain,
% 0.67/0.86 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(14,plain,
% 0.67/0.86 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_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)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_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)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp25) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp25))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp25) <=> (hskp25 | (~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)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp25) <=> (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))))),
% 0.67/0.86 inference(bind,[status(th)],[])).
% 0.67/0.86 tff(15,plain,
% 0.67/0.86 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp25) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.67/0.86 inference(quant_intro,[status(thm)],[14])).
% 0.67/0.86 tff(16,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 0.67/0.86 tff(17,plain,
% 0.67/0.86 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.67/0.86 tff(18,plain,
% 0.67/0.86 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.67/0.86 tff(19,plain,(
% 0.67/0.86 ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.67/0.86 inference(skolemize,[status(sab)],[18])).
% 0.67/0.86 tff(20,plain,
% 0.67/0.86 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.67/0.86 tff(21,assumption,(~hskp11), introduced(assumption)).
% 0.67/0.86 tff(22,assumption,(~c0_1(a734)), introduced(assumption)).
% 0.67/0.86 tff(23,plain,
% 0.67/0.86 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.67/0.86 inference(bind,[status(th)],[])).
% 0.67/0.86 tff(24,plain,
% 0.67/0.86 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.67/0.86 inference(quant_intro,[status(thm)],[23])).
% 0.67/0.86 tff(25,plain,
% 0.67/0.86 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(26,plain,
% 0.67/0.86 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp13) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp13))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.67/0.86 inference(bind,[status(th)],[])).
% 0.67/0.86 tff(27,plain,
% 0.67/0.86 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.67/0.86 inference(quant_intro,[status(thm)],[26])).
% 0.67/0.86 tff(28,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 0.67/0.86 tff(29,plain,
% 0.67/0.86 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.67/0.86 tff(30,plain,
% 0.67/0.86 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.67/0.86 tff(31,plain,(
% 0.67/0.86 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.67/0.86 inference(skolemize,[status(sab)],[30])).
% 0.67/0.86 tff(32,plain,
% 0.67/0.86 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.67/0.86 tff(33,assumption,(~c3_1(a734)), introduced(assumption)).
% 0.67/0.86 tff(34,plain,
% 0.67/0.86 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.67/0.86 inference(bind,[status(th)],[])).
% 0.67/0.86 tff(35,plain,
% 0.67/0.86 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.67/0.86 inference(quant_intro,[status(thm)],[34])).
% 0.67/0.86 tff(36,plain,
% 0.67/0.86 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(37,plain,
% 0.67/0.86 (^[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)) | (~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))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp11))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.67/0.86 inference(bind,[status(th)],[])).
% 0.67/0.86 tff(38,plain,
% 0.67/0.86 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.67/0.86 inference(quant_intro,[status(thm)],[37])).
% 0.67/0.86 tff(39,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 0.67/0.86 tff(40,plain,
% 0.67/0.86 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.67/0.86 tff(41,plain,
% 0.67/0.86 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.67/0.86 tff(42,plain,(
% 0.67/0.86 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.67/0.86 inference(skolemize,[status(sab)],[41])).
% 0.67/0.86 tff(43,plain,
% 0.67/0.86 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.67/0.86 tff(44,assumption,(~c1_1(a734)), introduced(assumption)).
% 0.67/0.86 tff(45,plain,
% 0.67/0.86 (((~hskp4) | c1_1(a734)) <=> ((~hskp4) | c1_1(a734))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(46,axiom,((~hskp4) | c1_1(a734)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 0.67/0.86 tff(47,plain,
% 0.67/0.86 ((~hskp4) | c1_1(a734)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.67/0.86 tff(48,plain,
% 0.67/0.86 ((~hskp4) | c1_1(a734)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[47, 45])).
% 0.67/0.86 tff(49,plain,
% 0.67/0.86 ((~hskp4) | c1_1(a734)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[48, 45])).
% 0.67/0.86 tff(50,plain,
% 0.67/0.86 ((~hskp4) | c1_1(a734)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.67/0.86 tff(51,plain,
% 0.67/0.86 ((~hskp4) | c1_1(a734)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[50, 45])).
% 0.67/0.86 tff(52,plain,
% 0.67/0.86 (~hskp4),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[51, 44])).
% 0.67/0.86 tff(53,assumption,(hskp1), introduced(assumption)).
% 0.67/0.86 tff(54,plain,
% 0.67/0.86 (((~hskp1) | (~c2_1(a731))) <=> ((~hskp1) | (~c2_1(a731)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(55,plain,
% 0.67/0.86 (((~c2_1(a731)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a731)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(56,axiom,((~c2_1(a731)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 0.67/0.86 tff(57,plain,
% 0.67/0.86 ((~hskp1) | (~c2_1(a731))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.67/0.86 tff(58,plain,
% 0.67/0.86 ((~hskp1) | (~c2_1(a731))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[57, 54])).
% 0.67/0.86 tff(59,plain,
% 0.67/0.86 (~c2_1(a731)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[58, 53])).
% 0.67/0.86 tff(60,plain,
% 0.67/0.86 (((~hskp1) | c3_1(a731)) <=> ((~hskp1) | c3_1(a731))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(61,axiom,((~hskp1) | c3_1(a731)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 0.67/0.86 tff(62,plain,
% 0.67/0.86 ((~hskp1) | c3_1(a731)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.67/0.86 tff(63,plain,
% 0.67/0.86 ((~hskp1) | c3_1(a731)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[62, 60])).
% 0.67/0.86 tff(64,plain,
% 0.67/0.86 ((~hskp1) | c3_1(a731)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[63, 60])).
% 0.67/0.86 tff(65,plain,
% 0.67/0.86 ((~hskp1) | c3_1(a731)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.67/0.86 tff(66,plain,
% 0.67/0.86 ((~hskp1) | c3_1(a731)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[65, 60])).
% 0.67/0.86 tff(67,plain,
% 0.67/0.86 (c3_1(a731)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[66, 53])).
% 0.67/0.86 tff(68,plain,
% 0.67/0.86 (((~hskp1) | c1_1(a731)) <=> ((~hskp1) | c1_1(a731))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(69,axiom,((~hskp1) | c1_1(a731)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 0.67/0.86 tff(70,plain,
% 0.67/0.86 ((~hskp1) | c1_1(a731)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.67/0.86 tff(71,plain,
% 0.67/0.86 ((~hskp1) | c1_1(a731)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[70, 68])).
% 0.67/0.86 tff(72,plain,
% 0.67/0.86 ((~hskp1) | c1_1(a731)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[71, 68])).
% 0.67/0.86 tff(73,plain,
% 0.67/0.86 ((~hskp1) | c1_1(a731)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.67/0.86 tff(74,plain,
% 0.67/0.86 ((~hskp1) | c1_1(a731)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[73, 68])).
% 0.67/0.86 tff(75,plain,
% 0.67/0.86 (c1_1(a731)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[74, 53])).
% 0.67/0.86 tff(76,assumption,(~ndr1_0), introduced(assumption)).
% 0.67/0.86 tff(77,plain,
% 0.67/0.86 ((ndr1_0 | (~hskp13)) <=> (ndr1_0 | (~hskp13))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(78,plain,
% 0.67/0.86 (((~hskp13) | ndr1_0) <=> (ndr1_0 | (~hskp13))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(79,axiom,((~hskp13) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause17')).
% 0.67/0.86 tff(80,plain,
% 0.67/0.86 (ndr1_0 | (~hskp13)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.67/0.86 tff(81,plain,
% 0.67/0.86 (ndr1_0 | (~hskp13)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[80, 77])).
% 0.67/0.86 tff(82,plain,
% 0.67/0.86 (~hskp13),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[81, 76])).
% 0.67/0.86 tff(83,plain,
% 0.67/0.86 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(84,plain,
% 0.67/0.86 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(85,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause6')).
% 0.67/0.86 tff(86,plain,
% 0.67/0.86 (ndr1_0 | (~hskp24)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.67/0.86 tff(87,plain,
% 0.67/0.86 (ndr1_0 | (~hskp24)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[86, 83])).
% 0.67/0.86 tff(88,plain,
% 0.67/0.86 (~hskp24),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[87, 76])).
% 0.67/0.86 tff(89,plain,
% 0.67/0.86 ((ndr1_0 | (~hskp23)) <=> (ndr1_0 | (~hskp23))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(90,plain,
% 0.67/0.86 (((~hskp23) | ndr1_0) <=> (ndr1_0 | (~hskp23))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(91,axiom,((~hskp23) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause7')).
% 0.67/0.86 tff(92,plain,
% 0.67/0.86 (ndr1_0 | (~hskp23)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.67/0.86 tff(93,plain,
% 0.67/0.86 (ndr1_0 | (~hskp23)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[92, 89])).
% 0.67/0.86 tff(94,plain,
% 0.67/0.86 (~hskp23),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[93, 76])).
% 0.67/0.86 tff(95,plain,
% 0.67/0.86 ((hskp24 | hskp23 | hskp13) <=> (hskp24 | hskp23 | hskp13)),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(96,plain,
% 0.67/0.86 (((hskp23 | hskp24) | hskp13) <=> (hskp24 | hskp23 | hskp13)),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(97,axiom,((hskp23 | hskp24) | hskp13), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 0.67/0.86 tff(98,plain,
% 0.67/0.86 (hskp24 | hskp23 | hskp13),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.67/0.86 tff(99,plain,
% 0.67/0.86 (hskp24 | hskp23 | hskp13),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[98, 95])).
% 0.67/0.86 tff(100,plain,
% 0.67/0.86 (hskp24 | hskp23 | hskp13),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.67/0.86 tff(101,plain,
% 0.67/0.86 (hskp24 | hskp23 | hskp13),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[100, 95])).
% 0.67/0.86 tff(102,plain,
% 0.67/0.86 (hskp24 | hskp23 | hskp13),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[101, 95])).
% 0.67/0.86 tff(103,plain,
% 0.67/0.86 ($false),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[102, 94, 88, 82])).
% 0.67/0.86 tff(104,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.67/0.86 tff(105,plain,
% 0.67/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a734) | c0_1(a734) | c3_1(a734) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a734) | c0_1(a734) | c3_1(a734) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(106,plain,
% 0.67/0.86 (((~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c1_1(a734) | c0_1(a734) | c3_1(a734)) <=> (c1_1(a734) | c0_1(a734) | c3_1(a734) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(107,plain,
% 0.67/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c1_1(a734) | c0_1(a734) | c3_1(a734))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a734) | c0_1(a734) | c3_1(a734) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731))))),
% 0.67/0.86 inference(monotonicity,[status(thm)],[106])).
% 0.67/0.86 tff(108,plain,
% 0.67/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c1_1(a734) | c0_1(a734) | c3_1(a734))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a734) | c0_1(a734) | c3_1(a734) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)))),
% 0.67/0.86 inference(transitivity,[status(thm)],[107, 105])).
% 0.67/0.86 tff(109,plain,
% 0.67/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c1_1(a734) | c0_1(a734) | c3_1(a734))),
% 0.67/0.86 inference(quant_inst,[status(thm)],[])).
% 0.67/0.86 tff(110,plain,
% 0.67/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a734) | c0_1(a734) | c3_1(a734) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.67/0.86 tff(111,plain,
% 0.67/0.86 (~c0_1(a731)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[110, 104, 44, 75, 67, 22, 33, 59, 10])).
% 0.67/0.86 tff(112,plain,
% 0.67/0.86 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.67/0.86 inference(bind,[status(th)],[])).
% 0.67/0.86 tff(113,plain,
% 0.67/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.67/0.86 inference(quant_intro,[status(thm)],[112])).
% 0.67/0.86 tff(114,plain,
% 0.67/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(115,plain,
% 0.67/0.86 (^[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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | 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(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(116,plain,
% 0.67/0.87 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[115])).
% 0.67/0.87 tff(117,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 0.67/0.87 tff(118,plain,
% 0.67/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.67/0.87 tff(119,plain,
% 0.67/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.67/0.87 tff(120,plain,(
% 0.67/0.87 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.67/0.87 inference(skolemize,[status(sab)],[119])).
% 0.67/0.87 tff(121,plain,
% 0.67/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.67/0.87 tff(122,plain,
% 0.67/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a731))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a731))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(123,plain,
% 0.67/0.87 (((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c2_1(a731) | c0_1(a731) | (~c3_1(a731))) <=> (c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a731))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(124,plain,
% 0.67/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c2_1(a731) | c0_1(a731) | (~c3_1(a731)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a731)))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[123])).
% 0.67/0.87 tff(125,plain,
% 0.67/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c2_1(a731) | c0_1(a731) | (~c3_1(a731)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a731))),
% 0.67/0.87 inference(transitivity,[status(thm)],[124, 122])).
% 0.67/0.87 tff(126,plain,
% 0.67/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c2_1(a731) | c0_1(a731) | (~c3_1(a731)))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(127,plain,
% 0.67/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a731)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.67/0.87 tff(128,plain,
% 0.67/0.87 ($false),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[127, 104, 75, 67, 59, 121, 111])).
% 0.67/0.87 tff(129,plain,((~hskp1) | c1_1(a734) | c0_1(a734) | c3_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.87 tff(130,plain,
% 0.67/0.87 (~hskp1),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[129, 44, 22, 33])).
% 0.67/0.87 tff(131,plain,
% 0.67/0.87 ((hskp7 | hskp4 | hskp1) <=> (hskp7 | hskp4 | hskp1)),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(132,plain,
% 0.67/0.87 (((hskp7 | hskp1) | hskp4) <=> (hskp7 | hskp4 | hskp1)),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(133,plain,
% 0.67/0.87 ((hskp7 | hskp1) <=> (hskp7 | hskp1)),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(134,plain,
% 0.67/0.87 (((hskp7 | hskp1) | hskp4) <=> ((hskp7 | hskp1) | hskp4)),
% 0.67/0.87 inference(monotonicity,[status(thm)],[133])).
% 0.67/0.87 tff(135,plain,
% 0.67/0.87 (((hskp7 | hskp1) | hskp4) <=> (hskp7 | hskp4 | hskp1)),
% 0.67/0.87 inference(transitivity,[status(thm)],[134, 132])).
% 0.67/0.87 tff(136,axiom,((hskp7 | hskp1) | hskp4), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause35')).
% 0.67/0.87 tff(137,plain,
% 0.67/0.87 (hskp7 | hskp4 | hskp1),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.67/0.87 tff(138,plain,
% 0.67/0.87 (hskp7 | hskp4 | hskp1),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[137, 131])).
% 0.67/0.87 tff(139,plain,
% 0.67/0.87 (hskp7 | hskp4 | hskp1),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.67/0.87 tff(140,plain,
% 0.67/0.87 (hskp7 | hskp4 | hskp1),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[139, 131])).
% 0.67/0.87 tff(141,plain,
% 0.67/0.87 (hskp7 | hskp4 | hskp1),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[140, 131])).
% 0.67/0.87 tff(142,plain,
% 0.67/0.87 (hskp7),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[141, 130, 52])).
% 0.67/0.87 tff(143,plain,
% 0.67/0.87 (((~hskp7) | c1_1(a741)) <=> ((~hskp7) | c1_1(a741))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(144,axiom,((~hskp7) | c1_1(a741)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 0.67/0.87 tff(145,plain,
% 0.67/0.87 ((~hskp7) | c1_1(a741)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.67/0.87 tff(146,plain,
% 0.67/0.87 ((~hskp7) | c1_1(a741)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[145, 143])).
% 0.67/0.87 tff(147,plain,
% 0.67/0.87 ((~hskp7) | c1_1(a741)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[146, 143])).
% 0.67/0.87 tff(148,plain,
% 0.67/0.87 ((~hskp7) | c1_1(a741)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[147, 143])).
% 0.67/0.87 tff(149,plain,
% 0.67/0.87 ((~hskp7) | c1_1(a741)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[148, 143])).
% 0.67/0.87 tff(150,plain,
% 0.67/0.87 (c1_1(a741)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[149, 142])).
% 0.67/0.87 tff(151,plain,
% 0.67/0.87 (((~hskp7) | c3_1(a741)) <=> ((~hskp7) | c3_1(a741))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(152,axiom,((~hskp7) | c3_1(a741)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 0.67/0.87 tff(153,plain,
% 0.67/0.87 ((~hskp7) | c3_1(a741)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.67/0.87 tff(154,plain,
% 0.67/0.87 ((~hskp7) | c3_1(a741)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[153, 151])).
% 0.67/0.87 tff(155,plain,
% 0.67/0.87 ((~hskp7) | c3_1(a741)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[154, 151])).
% 0.67/0.87 tff(156,plain,
% 0.67/0.87 ((~hskp7) | c3_1(a741)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.67/0.87 tff(157,plain,
% 0.67/0.87 ((~hskp7) | c3_1(a741)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[156, 151])).
% 0.67/0.87 tff(158,plain,
% 0.67/0.87 (c3_1(a741)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[157, 142])).
% 0.67/0.87 tff(159,plain,
% 0.67/0.87 (((~hskp7) | (~c0_1(a741))) <=> ((~hskp7) | (~c0_1(a741)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(160,plain,
% 0.67/0.87 (((~c0_1(a741)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a741)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(161,axiom,((~c0_1(a741)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 0.67/0.87 tff(162,plain,
% 0.67/0.87 ((~hskp7) | (~c0_1(a741))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.67/0.87 tff(163,plain,
% 0.67/0.87 ((~hskp7) | (~c0_1(a741))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[162, 159])).
% 0.67/0.87 tff(164,plain,
% 0.67/0.87 (~c0_1(a741)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[163, 142])).
% 0.67/0.87 tff(165,assumption,(~c2_1(a741)), introduced(assumption)).
% 0.67/0.87 tff(166,assumption,(~hskp4), introduced(assumption)).
% 0.67/0.87 tff(167,plain,
% 0.67/0.87 (^[U: $i] : refl((hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(168,plain,
% 0.67/0.87 (![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[167])).
% 0.67/0.87 tff(169,plain,
% 0.67/0.87 (![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(170,plain,
% 0.67/0.87 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp6) | hskp4) <=> ((hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp4))), rewrite(((hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp4) <=> (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp6) | hskp4) <=> (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(171,plain,
% 0.67/0.87 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp6) | hskp4) <=> ![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[170])).
% 0.67/0.87 tff(172,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp6) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 0.67/0.87 tff(173,plain,
% 0.67/0.87 (![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.67/0.87 tff(174,plain,
% 0.67/0.87 (![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[173, 169])).
% 0.67/0.87 tff(175,plain,(
% 0.67/0.87 ![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.67/0.87 inference(skolemize,[status(sab)],[174])).
% 0.67/0.87 tff(176,plain,
% 0.67/0.87 (![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[175, 168])).
% 0.67/0.87 tff(177,assumption,(~c0_1(a741)), introduced(assumption)).
% 0.67/0.87 tff(178,assumption,(c3_1(a741)), introduced(assumption)).
% 0.67/0.87 tff(179,plain,
% 0.67/0.87 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp6 | hskp4 | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c3_1(a741)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp6 | hskp4 | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c3_1(a741)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(180,plain,
% 0.67/0.87 ((hskp6 | hskp4 | (~ndr1_0) | c2_1(a741) | c0_1(a741) | (~c3_1(a741))) <=> (hskp6 | hskp4 | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c3_1(a741)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(181,plain,
% 0.67/0.87 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c2_1(a741) | c0_1(a741) | (~c3_1(a741)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp6 | hskp4 | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c3_1(a741))))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[180])).
% 0.67/0.87 tff(182,plain,
% 0.67/0.87 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c2_1(a741) | c0_1(a741) | (~c3_1(a741)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp6 | hskp4 | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c3_1(a741)))),
% 0.67/0.87 inference(transitivity,[status(thm)],[181, 179])).
% 0.67/0.87 tff(183,plain,
% 0.67/0.87 ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c2_1(a741) | c0_1(a741) | (~c3_1(a741)))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(184,plain,
% 0.67/0.87 ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp6 | hskp4 | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c3_1(a741))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.67/0.87 tff(185,plain,
% 0.67/0.87 (hskp6 | hskp4 | c2_1(a741)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[184, 104, 178, 177, 176])).
% 0.67/0.87 tff(186,plain,
% 0.67/0.87 (hskp6),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[185, 165, 166])).
% 0.67/0.87 tff(187,plain,
% 0.67/0.87 (((~hskp6) | (~c2_1(a738))) <=> ((~hskp6) | (~c2_1(a738)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(188,plain,
% 0.67/0.87 (((~c2_1(a738)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a738)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(189,axiom,((~c2_1(a738)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 0.67/0.87 tff(190,plain,
% 0.67/0.87 ((~hskp6) | (~c2_1(a738))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.67/0.87 tff(191,plain,
% 0.67/0.87 ((~hskp6) | (~c2_1(a738))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[190, 187])).
% 0.67/0.87 tff(192,plain,
% 0.67/0.87 (~c2_1(a738)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[191, 186])).
% 0.67/0.87 tff(193,plain,
% 0.67/0.87 (((~hskp6) | (~c0_1(a738))) <=> ((~hskp6) | (~c0_1(a738)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(194,plain,
% 0.67/0.87 (((~c0_1(a738)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a738)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(195,axiom,((~c0_1(a738)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 0.67/0.87 tff(196,plain,
% 0.67/0.87 ((~hskp6) | (~c0_1(a738))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.67/0.87 tff(197,plain,
% 0.67/0.87 ((~hskp6) | (~c0_1(a738))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[196, 193])).
% 0.67/0.87 tff(198,plain,
% 0.67/0.87 (~c0_1(a738)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[197, 186])).
% 0.67/0.87 tff(199,plain,
% 0.67/0.87 (((~hskp6) | c1_1(a738)) <=> ((~hskp6) | c1_1(a738))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(200,axiom,((~hskp6) | c1_1(a738)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 0.67/0.87 tff(201,plain,
% 0.67/0.87 ((~hskp6) | c1_1(a738)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.67/0.87 tff(202,plain,
% 0.67/0.87 ((~hskp6) | c1_1(a738)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[201, 199])).
% 0.67/0.87 tff(203,plain,
% 0.67/0.87 ((~hskp6) | c1_1(a738)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[202, 199])).
% 0.67/0.87 tff(204,plain,
% 0.67/0.87 ((~hskp6) | c1_1(a738)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[203, 199])).
% 0.67/0.87 tff(205,plain,
% 0.67/0.87 ((~hskp6) | c1_1(a738)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[204, 199])).
% 0.67/0.87 tff(206,plain,
% 0.67/0.87 (c1_1(a738)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[205, 186])).
% 0.67/0.87 tff(207,assumption,(c1_1(a741)), introduced(assumption)).
% 0.67/0.87 tff(208,plain,
% 0.67/0.87 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a738) | c2_1(a738) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a741)) | (~c1_1(a738)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a738) | c2_1(a738) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a741)) | (~c1_1(a738)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(209,plain,
% 0.67/0.87 ((hskp11 | (~ndr1_0) | c2_1(a741) | (~c3_1(a741)) | (~c1_1(a741)) | c0_1(a738) | c2_1(a738) | (~c1_1(a738))) <=> (hskp11 | c0_1(a738) | c2_1(a738) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a741)) | (~c1_1(a738)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(210,plain,
% 0.67/0.87 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a741) | (~c3_1(a741)) | (~c1_1(a741)) | c0_1(a738) | c2_1(a738) | (~c1_1(a738)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a738) | c2_1(a738) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a741)) | (~c1_1(a738))))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[209])).
% 0.67/0.87 tff(211,plain,
% 0.67/0.87 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a741) | (~c3_1(a741)) | (~c1_1(a741)) | c0_1(a738) | c2_1(a738) | (~c1_1(a738)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a738) | c2_1(a738) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a741)) | (~c1_1(a738)))),
% 0.67/0.87 inference(transitivity,[status(thm)],[210, 208])).
% 0.67/0.87 tff(212,plain,
% 0.67/0.87 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a741) | (~c3_1(a741)) | (~c1_1(a741)) | c0_1(a738) | c2_1(a738) | (~c1_1(a738)))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(213,plain,
% 0.67/0.87 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a738) | c2_1(a738) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a741)) | (~c1_1(a738))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.67/0.87 tff(214,plain,
% 0.67/0.87 ($false),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[213, 104, 21, 207, 178, 206, 198, 192, 43, 165])).
% 0.67/0.87 tff(215,plain,(c2_1(a741) | hskp11 | (~c1_1(a741)) | (~c3_1(a741)) | hskp4 | c0_1(a741)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.87 tff(216,plain,
% 0.67/0.87 (c2_1(a741)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[215, 164, 150, 158, 52, 21])).
% 0.67/0.87 tff(217,assumption,(~hskp0), introduced(assumption)).
% 0.67/0.87 tff(218,plain,
% 0.67/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a741) | c2_1(a731) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a731))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a741) | c2_1(a731) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a731))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(219,plain,
% 0.67/0.87 (((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741)) | c2_1(a731) | c0_1(a731) | (~c3_1(a731))) <=> (c0_1(a741) | c2_1(a731) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a731))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(220,plain,
% 0.67/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741)) | c2_1(a731) | c0_1(a731) | (~c3_1(a731)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a741) | c2_1(a731) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a731)))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[219])).
% 0.67/0.87 tff(221,plain,
% 0.67/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741)) | c2_1(a731) | c0_1(a731) | (~c3_1(a731)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a741) | c2_1(a731) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a731))),
% 0.67/0.87 inference(transitivity,[status(thm)],[220, 218])).
% 0.67/0.87 tff(222,plain,
% 0.67/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741)) | c2_1(a731) | c0_1(a731) | (~c3_1(a731)))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(223,plain,
% 0.67/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a741) | c2_1(a731) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a731)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.67/0.87 tff(224,plain,
% 0.67/0.87 ($false),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[223, 104, 207, 178, 75, 67, 177, 59, 121, 111])).
% 0.67/0.87 tff(225,plain,((~hskp1) | (~c1_1(a741)) | (~c3_1(a741)) | c0_1(a741) | c1_1(a734) | c0_1(a734) | c3_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.87 tff(226,plain,
% 0.67/0.87 (~hskp1),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[225, 44, 178, 177, 207, 22, 33])).
% 0.67/0.87 tff(227,plain,
% 0.67/0.87 (^[U: $i] : refl((hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(228,plain,
% 0.67/0.87 (![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[227])).
% 0.67/0.87 tff(229,plain,
% 0.67/0.87 (![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(230,plain,
% 0.67/0.87 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp1) <=> ((hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite(((hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp1) <=> (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(231,plain,
% 0.67/0.87 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp1) <=> ![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[230])).
% 0.67/0.87 tff(232,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 0.67/0.87 tff(233,plain,
% 0.67/0.87 (![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.67/0.87 tff(234,plain,
% 0.67/0.87 (![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[233, 229])).
% 0.67/0.87 tff(235,plain,(
% 0.67/0.87 ![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.67/0.87 inference(skolemize,[status(sab)],[234])).
% 0.67/0.87 tff(236,plain,
% 0.67/0.87 (![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[235, 228])).
% 0.67/0.87 tff(237,plain,
% 0.67/0.87 (((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | c1_1(a734) | c0_1(a734) | (~ndr1_0) | c2_1(a734))) <=> ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | hskp1 | c1_1(a734) | c0_1(a734) | (~ndr1_0) | c2_1(a734))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(238,plain,
% 0.71/0.87 ((hskp0 | hskp1 | (~ndr1_0) | c2_1(a734) | c1_1(a734) | c0_1(a734)) <=> (hskp0 | hskp1 | c1_1(a734) | c0_1(a734) | (~ndr1_0) | c2_1(a734))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(239,plain,
% 0.71/0.87 (((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | (~ndr1_0) | c2_1(a734) | c1_1(a734) | c0_1(a734))) <=> ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | c1_1(a734) | c0_1(a734) | (~ndr1_0) | c2_1(a734)))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[238])).
% 0.71/0.87 tff(240,plain,
% 0.71/0.87 (((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | (~ndr1_0) | c2_1(a734) | c1_1(a734) | c0_1(a734))) <=> ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | hskp1 | c1_1(a734) | c0_1(a734) | (~ndr1_0) | c2_1(a734))),
% 0.71/0.87 inference(transitivity,[status(thm)],[239, 237])).
% 0.71/0.87 tff(241,plain,
% 0.71/0.87 ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | (~ndr1_0) | c2_1(a734) | c1_1(a734) | c0_1(a734))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(242,plain,
% 0.71/0.87 ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | hskp1 | c1_1(a734) | c0_1(a734) | (~ndr1_0) | c2_1(a734)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.71/0.87 tff(243,plain,
% 0.71/0.87 (hskp0 | hskp1 | c1_1(a734) | c2_1(a734)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[242, 104, 22, 236])).
% 0.71/0.87 tff(244,plain,
% 0.71/0.87 (c2_1(a734)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[243, 226, 217, 44])).
% 0.71/0.87 tff(245,plain,
% 0.71/0.87 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(246,plain,
% 0.71/0.87 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[245])).
% 0.71/0.87 tff(247,plain,
% 0.71/0.87 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(248,plain,
% 0.71/0.87 (^[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))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | 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) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(249,plain,
% 0.71/0.87 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[248])).
% 0.71/0.87 tff(250,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 0.71/0.87 tff(251,plain,
% 0.71/0.87 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.71/0.87 tff(252,plain,
% 0.71/0.87 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[251, 247])).
% 0.71/0.87 tff(253,plain,(
% 0.71/0.87 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.87 inference(skolemize,[status(sab)],[252])).
% 0.71/0.87 tff(254,plain,
% 0.71/0.87 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[253, 246])).
% 0.71/0.87 tff(255,assumption,(~hskp1), introduced(assumption)).
% 0.71/0.87 tff(256,assumption,(~hskp2), introduced(assumption)).
% 0.71/0.87 tff(257,plain,
% 0.71/0.87 (^[U: $i] : refl((hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(258,plain,
% 0.71/0.87 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[257])).
% 0.71/0.87 tff(259,plain,
% 0.71/0.88 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(260,plain,
% 0.71/0.88 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp1) | hskp2) <=> ((hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp2))), rewrite(((hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp1) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(261,plain,
% 0.71/0.88 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp1) | hskp2) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[260])).
% 0.71/0.88 tff(262,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp1) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 0.71/0.88 tff(263,plain,
% 0.71/0.88 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.71/0.88 tff(264,plain,
% 0.71/0.88 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[263, 259])).
% 0.71/0.88 tff(265,plain,(
% 0.71/0.88 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.71/0.88 inference(skolemize,[status(sab)],[264])).
% 0.71/0.88 tff(266,plain,
% 0.71/0.88 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[265, 258])).
% 0.71/0.88 tff(267,plain,
% 0.71/0.88 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c1_1(a734) | c0_1(a734) | (~ndr1_0) | (~c2_1(a734)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c1_1(a734) | c0_1(a734) | (~ndr1_0) | (~c2_1(a734)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(268,plain,
% 0.71/0.88 ((hskp2 | hskp1 | (~ndr1_0) | c1_1(a734) | c0_1(a734) | (~c2_1(a734))) <=> (hskp2 | hskp1 | c1_1(a734) | c0_1(a734) | (~ndr1_0) | (~c2_1(a734)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(269,plain,
% 0.71/0.88 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c1_1(a734) | c0_1(a734) | (~c2_1(a734)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c1_1(a734) | c0_1(a734) | (~ndr1_0) | (~c2_1(a734))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[268])).
% 0.71/0.88 tff(270,plain,
% 0.71/0.88 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c1_1(a734) | c0_1(a734) | (~c2_1(a734)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c1_1(a734) | c0_1(a734) | (~ndr1_0) | (~c2_1(a734)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[269, 267])).
% 0.71/0.88 tff(271,plain,
% 0.71/0.88 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c1_1(a734) | c0_1(a734) | (~c2_1(a734)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(272,plain,
% 0.71/0.88 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c1_1(a734) | c0_1(a734) | (~ndr1_0) | (~c2_1(a734))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.71/0.88 tff(273,plain,
% 0.71/0.88 (hskp2 | hskp1 | c1_1(a734) | (~c2_1(a734))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[272, 104, 22, 266])).
% 0.71/0.88 tff(274,plain,
% 0.71/0.88 (~c2_1(a734)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[273, 255, 44, 256])).
% 0.71/0.88 tff(275,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[243, 274, 255, 217, 44])).
% 0.71/0.88 tff(276,plain,(hskp1 | hskp0 | c1_1(a734) | c0_1(a734) | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.71/0.88 tff(277,plain,
% 0.71/0.88 (hskp2),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[276, 226, 44, 22, 217])).
% 0.71/0.88 tff(278,plain,
% 0.71/0.88 (((~hskp2) | (~c2_1(a732))) <=> ((~hskp2) | (~c2_1(a732)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(279,plain,
% 0.71/0.88 (((~c2_1(a732)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a732)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(280,axiom,((~c2_1(a732)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 0.71/0.88 tff(281,plain,
% 0.71/0.88 ((~hskp2) | (~c2_1(a732))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.71/0.88 tff(282,plain,
% 0.71/0.88 ((~hskp2) | (~c2_1(a732))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[281, 278])).
% 0.71/0.88 tff(283,plain,
% 0.71/0.88 (~c2_1(a732)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[282, 277])).
% 0.71/0.88 tff(284,plain,
% 0.71/0.88 (((~hskp2) | (~c0_1(a732))) <=> ((~hskp2) | (~c0_1(a732)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(285,plain,
% 0.71/0.88 (((~c0_1(a732)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a732)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(286,axiom,((~c0_1(a732)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 0.71/0.88 tff(287,plain,
% 0.71/0.88 ((~hskp2) | (~c0_1(a732))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.71/0.88 tff(288,plain,
% 0.71/0.88 ((~hskp2) | (~c0_1(a732))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[287, 284])).
% 0.71/0.88 tff(289,plain,
% 0.71/0.88 (~c0_1(a732)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[288, 277])).
% 0.71/0.88 tff(290,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | c1_1(a734) | c0_1(a734) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c2_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp0 | c1_1(a734) | c0_1(a734) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c2_1(a734)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(291,plain,
% 0.71/0.88 ((hskp0 | (~ndr1_0) | c2_1(a732) | c0_1(a732) | (~c1_1(a732)) | c1_1(a734) | c0_1(a734) | (~c2_1(a734))) <=> (hskp0 | c1_1(a734) | c0_1(a734) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c2_1(a734)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(292,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a732) | c0_1(a732) | (~c1_1(a732)) | c1_1(a734) | c0_1(a734) | (~c2_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | c1_1(a734) | c0_1(a734) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c2_1(a734))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[291])).
% 0.71/0.88 tff(293,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a732) | c0_1(a732) | (~c1_1(a732)) | c1_1(a734) | c0_1(a734) | (~c2_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp0 | c1_1(a734) | c0_1(a734) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c2_1(a734)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[292, 290])).
% 0.71/0.88 tff(294,plain,
% 0.71/0.88 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a732) | c0_1(a732) | (~c1_1(a732)) | c1_1(a734) | c0_1(a734) | (~c2_1(a734)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(295,plain,
% 0.71/0.88 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp0 | c1_1(a734) | c0_1(a734) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c2_1(a734))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.71/0.88 tff(296,plain,
% 0.71/0.88 (~c1_1(a732)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[295, 217, 104, 44, 22, 289, 283, 254, 244])).
% 0.71/0.88 tff(297,plain,
% 0.71/0.88 (((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | c0_1(a732) | c2_1(a732) | (~ndr1_0) | c1_1(a732))) <=> ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | hskp1 | c0_1(a732) | c2_1(a732) | (~ndr1_0) | c1_1(a732))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(298,plain,
% 0.71/0.88 ((hskp0 | hskp1 | (~ndr1_0) | c2_1(a732) | c1_1(a732) | c0_1(a732)) <=> (hskp0 | hskp1 | c0_1(a732) | c2_1(a732) | (~ndr1_0) | c1_1(a732))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(299,plain,
% 0.71/0.88 (((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | (~ndr1_0) | c2_1(a732) | c1_1(a732) | c0_1(a732))) <=> ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | c0_1(a732) | c2_1(a732) | (~ndr1_0) | c1_1(a732)))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[298])).
% 0.71/0.88 tff(300,plain,
% 0.71/0.88 (((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | (~ndr1_0) | c2_1(a732) | c1_1(a732) | c0_1(a732))) <=> ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | hskp1 | c0_1(a732) | c2_1(a732) | (~ndr1_0) | c1_1(a732))),
% 0.71/0.88 inference(transitivity,[status(thm)],[299, 297])).
% 0.71/0.88 tff(301,plain,
% 0.71/0.88 ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | (~ndr1_0) | c2_1(a732) | c1_1(a732) | c0_1(a732))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(302,plain,
% 0.71/0.88 ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | hskp1 | c0_1(a732) | c2_1(a732) | (~ndr1_0) | c1_1(a732)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.71/0.88 tff(303,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[302, 217, 104, 226, 289, 283, 236, 296])).
% 0.71/0.88 tff(304,plain,(c1_1(a734) | hskp0 | c0_1(a734) | (~c3_1(a741)) | c0_1(a741) | (~c1_1(a741)) | c3_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.88 tff(305,plain,
% 0.71/0.88 (c1_1(a734)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[304, 217, 22, 178, 177, 207, 33])).
% 0.71/0.88 tff(306,plain,
% 0.71/0.88 (^[U: $i] : refl((hskp0 | hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp0 | hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(307,plain,
% 0.71/0.88 (![U: $i] : (hskp0 | hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp0 | hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[306])).
% 0.71/0.88 tff(308,plain,
% 0.71/0.88 (![U: $i] : (hskp0 | hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp0 | hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(309,plain,
% 0.71/0.88 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp0) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp0))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp0) | hskp9) <=> ((hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp9))), rewrite(((hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp9) <=> (hskp0 | hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp0) | hskp9) <=> (hskp0 | hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(310,plain,
% 0.71/0.88 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp0) | hskp9) <=> ![U: $i] : (hskp0 | hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[309])).
% 0.71/0.88 tff(311,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp0) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 0.71/0.88 tff(312,plain,
% 0.71/0.88 (![U: $i] : (hskp0 | hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.71/0.88 tff(313,plain,
% 0.71/0.88 (![U: $i] : (hskp0 | hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[312, 308])).
% 0.71/0.88 tff(314,plain,(
% 0.71/0.88 ![U: $i] : (hskp0 | hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.71/0.88 inference(skolemize,[status(sab)],[313])).
% 0.71/0.88 tff(315,plain,
% 0.71/0.88 (![U: $i] : (hskp0 | hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[314, 307])).
% 0.71/0.88 tff(316,plain,
% 0.71/0.88 (((~![U: $i] : (hskp0 | hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp0 | hskp9 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c1_1(a734)))) <=> ((~![U: $i] : (hskp0 | hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp0 | hskp9 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c1_1(a734)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(317,plain,
% 0.71/0.88 ((hskp0 | hskp9 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c1_1(a734))) <=> (hskp0 | hskp9 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c1_1(a734)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(318,plain,
% 0.71/0.88 (((~![U: $i] : (hskp0 | hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp0 | hskp9 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c1_1(a734)))) <=> ((~![U: $i] : (hskp0 | hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp0 | hskp9 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c1_1(a734))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[317])).
% 0.71/0.88 tff(319,plain,
% 0.71/0.88 (((~![U: $i] : (hskp0 | hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp0 | hskp9 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c1_1(a734)))) <=> ((~![U: $i] : (hskp0 | hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp0 | hskp9 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c1_1(a734)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[318, 316])).
% 0.71/0.88 tff(320,plain,
% 0.71/0.88 ((~![U: $i] : (hskp0 | hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp0 | hskp9 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c1_1(a734)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(321,plain,
% 0.71/0.88 ((~![U: $i] : (hskp0 | hskp9 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp0 | hskp9 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c1_1(a734))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.71/0.88 tff(322,plain,
% 0.71/0.88 (hskp0 | hskp9 | c0_1(a734) | (~c1_1(a734))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[321, 104, 33, 315])).
% 0.71/0.88 tff(323,plain,
% 0.71/0.88 (hskp9),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[322, 305, 217, 22])).
% 0.71/0.88 tff(324,plain,
% 0.71/0.88 (((~hskp9) | (~c2_1(a746))) <=> ((~hskp9) | (~c2_1(a746)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(325,plain,
% 0.71/0.88 (((~c2_1(a746)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a746)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(326,axiom,((~c2_1(a746)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.71/0.88 tff(327,plain,
% 0.71/0.88 ((~hskp9) | (~c2_1(a746))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.71/0.88 tff(328,plain,
% 0.71/0.88 ((~hskp9) | (~c2_1(a746))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[327, 324])).
% 0.71/0.88 tff(329,plain,
% 0.71/0.88 (~c2_1(a746)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[328, 323])).
% 0.71/0.88 tff(330,plain,
% 0.71/0.88 (((~hskp9) | (~c0_1(a746))) <=> ((~hskp9) | (~c0_1(a746)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(331,plain,
% 0.71/0.88 (((~c0_1(a746)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a746)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(332,axiom,((~c0_1(a746)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 0.71/0.88 tff(333,plain,
% 0.71/0.88 ((~hskp9) | (~c0_1(a746))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[332, 331])).
% 0.71/0.88 tff(334,plain,
% 0.71/0.88 ((~hskp9) | (~c0_1(a746))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[333, 330])).
% 0.71/0.88 tff(335,plain,
% 0.71/0.88 (~c0_1(a746)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[334, 323])).
% 0.71/0.88 tff(336,plain,
% 0.71/0.88 (((~hskp9) | c3_1(a746)) <=> ((~hskp9) | c3_1(a746))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(337,axiom,((~hskp9) | c3_1(a746)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 0.71/0.88 tff(338,plain,
% 0.71/0.88 ((~hskp9) | c3_1(a746)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.71/0.88 tff(339,plain,
% 0.71/0.88 ((~hskp9) | c3_1(a746)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[338, 336])).
% 0.71/0.88 tff(340,plain,
% 0.71/0.88 ((~hskp9) | c3_1(a746)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[339, 336])).
% 0.71/0.88 tff(341,plain,
% 0.71/0.88 ((~hskp9) | c3_1(a746)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[340, 336])).
% 0.71/0.88 tff(342,plain,
% 0.71/0.88 ((~hskp9) | c3_1(a746)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[341, 336])).
% 0.71/0.88 tff(343,plain,
% 0.71/0.88 (c3_1(a746)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[342, 323])).
% 0.71/0.88 tff(344,plain,
% 0.71/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a746) | c2_1(a746) | (~ndr1_0) | (~c3_1(a746)) | (~c1_1(a746)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a746) | c2_1(a746) | (~ndr1_0) | (~c3_1(a746)) | (~c1_1(a746)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(345,plain,
% 0.71/0.88 (((~ndr1_0) | c2_1(a746) | (~c3_1(a746)) | (~c1_1(a746)) | c0_1(a746) | (~c3_1(a746)) | (~c1_1(a746)) | c2_1(a746) | c0_1(a746) | (~c3_1(a746))) <=> (c0_1(a746) | c2_1(a746) | (~ndr1_0) | (~c3_1(a746)) | (~c1_1(a746)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(346,plain,
% 0.71/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a746) | (~c3_1(a746)) | (~c1_1(a746)) | c0_1(a746) | (~c3_1(a746)) | (~c1_1(a746)) | c2_1(a746) | c0_1(a746) | (~c3_1(a746)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a746) | c2_1(a746) | (~ndr1_0) | (~c3_1(a746)) | (~c1_1(a746))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[345])).
% 0.71/0.88 tff(347,plain,
% 0.71/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a746) | (~c3_1(a746)) | (~c1_1(a746)) | c0_1(a746) | (~c3_1(a746)) | (~c1_1(a746)) | c2_1(a746) | c0_1(a746) | (~c3_1(a746)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a746) | c2_1(a746) | (~ndr1_0) | (~c3_1(a746)) | (~c1_1(a746)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[346, 344])).
% 0.71/0.88 tff(348,plain,
% 0.71/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a746) | (~c3_1(a746)) | (~c1_1(a746)) | c0_1(a746) | (~c3_1(a746)) | (~c1_1(a746)) | c2_1(a746) | c0_1(a746) | (~c3_1(a746)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(349,plain,
% 0.71/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a746) | c2_1(a746) | (~ndr1_0) | (~c3_1(a746)) | (~c1_1(a746))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.71/0.88 tff(350,plain,
% 0.71/0.88 (~c1_1(a746)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[349, 104, 343, 335, 329, 121])).
% 0.71/0.88 tff(351,plain,
% 0.71/0.88 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(352,plain,
% 0.71/0.88 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[351])).
% 0.71/0.88 tff(353,plain,
% 0.71/0.88 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(354,plain,
% 0.71/0.88 (^[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)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | 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) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp11) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp11))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(355,plain,
% 0.71/0.88 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[354])).
% 0.71/0.88 tff(356,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 0.71/0.88 tff(357,plain,
% 0.71/0.88 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[356, 355])).
% 0.71/0.88 tff(358,plain,
% 0.71/0.88 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[357, 353])).
% 0.71/0.88 tff(359,plain,(
% 0.71/0.88 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.71/0.88 inference(skolemize,[status(sab)],[358])).
% 0.71/0.88 tff(360,plain,
% 0.71/0.88 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[359, 352])).
% 0.71/0.88 tff(361,plain,
% 0.71/0.88 (((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | c0_1(a746) | c2_1(a746) | (~ndr1_0) | c1_1(a746))) <=> ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | hskp1 | c0_1(a746) | c2_1(a746) | (~ndr1_0) | c1_1(a746))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(362,plain,
% 0.71/0.88 ((hskp0 | hskp1 | (~ndr1_0) | c2_1(a746) | c1_1(a746) | c0_1(a746)) <=> (hskp0 | hskp1 | c0_1(a746) | c2_1(a746) | (~ndr1_0) | c1_1(a746))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(363,plain,
% 0.71/0.88 (((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | (~ndr1_0) | c2_1(a746) | c1_1(a746) | c0_1(a746))) <=> ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | c0_1(a746) | c2_1(a746) | (~ndr1_0) | c1_1(a746)))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[362])).
% 0.71/0.88 tff(364,plain,
% 0.71/0.88 (((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | (~ndr1_0) | c2_1(a746) | c1_1(a746) | c0_1(a746))) <=> ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | hskp1 | c0_1(a746) | c2_1(a746) | (~ndr1_0) | c1_1(a746))),
% 0.71/0.88 inference(transitivity,[status(thm)],[363, 361])).
% 0.71/0.88 tff(365,plain,
% 0.71/0.88 ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | (~ndr1_0) | c2_1(a746) | c1_1(a746) | c0_1(a746))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(366,plain,
% 0.71/0.88 ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | hskp1 | c0_1(a746) | c2_1(a746) | (~ndr1_0) | c1_1(a746)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.71/0.88 tff(367,plain,
% 0.71/0.88 (hskp1),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[366, 217, 104, 335, 329, 236, 350])).
% 0.71/0.88 tff(368,plain,
% 0.71/0.88 (~c2_1(a731)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[58, 367])).
% 0.71/0.88 tff(369,plain,
% 0.71/0.88 (c3_1(a731)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[66, 367])).
% 0.71/0.88 tff(370,plain,
% 0.71/0.88 (c1_1(a731)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[74, 367])).
% 0.71/0.88 tff(371,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a746) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c3_1(a746)) | c1_1(a746))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a746) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c3_1(a746)) | c1_1(a746))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(372,plain,
% 0.71/0.88 ((hskp11 | (~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c1_1(a746) | c2_1(a746) | (~c3_1(a746))) <=> (hskp11 | c2_1(a746) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c3_1(a746)) | c1_1(a746))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(373,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c1_1(a746) | c2_1(a746) | (~c3_1(a746)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a746) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c3_1(a746)) | c1_1(a746)))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[372])).
% 0.71/0.88 tff(374,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c1_1(a746) | c2_1(a746) | (~c3_1(a746)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a746) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c3_1(a746)) | c1_1(a746))),
% 0.71/0.88 inference(transitivity,[status(thm)],[373, 371])).
% 0.71/0.88 tff(375,plain,
% 0.71/0.88 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c1_1(a746) | c2_1(a746) | (~c3_1(a746)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(376,plain,
% 0.71/0.88 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a746) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c3_1(a746)) | c1_1(a746)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.71/0.88 tff(377,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[376, 104, 21, 343, 370, 369, 329, 368, 360, 350])).
% 0.71/0.88 tff(378,plain,(hskp0 | hskp11 | c0_1(a734) | c3_1(a734) | (~c3_1(a741)) | c0_1(a741) | (~c1_1(a741))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.88 tff(379,plain,
% 0.71/0.88 (hskp0),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[378, 158, 21, 22, 33, 164, 150])).
% 0.71/0.88 tff(380,plain,
% 0.71/0.88 (((~hskp0) | (~c1_1(a730))) <=> ((~hskp0) | (~c1_1(a730)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(381,plain,
% 0.71/0.88 (((~c1_1(a730)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a730)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(382,axiom,((~c1_1(a730)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 0.71/0.88 tff(383,plain,
% 0.71/0.88 ((~hskp0) | (~c1_1(a730))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[382, 381])).
% 0.71/0.88 tff(384,plain,
% 0.71/0.88 ((~hskp0) | (~c1_1(a730))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[383, 380])).
% 0.71/0.88 tff(385,plain,
% 0.71/0.88 (~c1_1(a730)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[384, 379])).
% 0.71/0.88 tff(386,plain,
% 0.71/0.88 (^[U: $i] : refl((hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(387,plain,
% 0.71/0.88 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[386])).
% 0.71/0.88 tff(388,plain,
% 0.71/0.88 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(389,plain,
% 0.71/0.88 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp5) <=> ((hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp5))), rewrite(((hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp5) <=> (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp5) <=> (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(390,plain,
% 0.71/0.89 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp5) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[389])).
% 0.71/0.89 tff(391,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 0.71/0.89 tff(392,plain,
% 0.71/0.89 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.71/0.89 tff(393,plain,
% 0.71/0.89 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[392, 388])).
% 0.71/0.89 tff(394,plain,(
% 0.71/0.89 ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.71/0.89 inference(skolemize,[status(sab)],[393])).
% 0.71/0.89 tff(395,plain,
% 0.71/0.89 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[394, 387])).
% 0.71/0.89 tff(396,assumption,(~hskp5), introduced(assumption)).
% 0.71/0.89 tff(397,plain,
% 0.71/0.89 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | c1_1(a734) | c0_1(a734) | c3_1(a734) | (~ndr1_0))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp5 | hskp4 | c1_1(a734) | c0_1(a734) | c3_1(a734) | (~ndr1_0))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(398,plain,
% 0.71/0.89 ((hskp5 | hskp4 | (~ndr1_0) | c1_1(a734) | c0_1(a734) | c3_1(a734)) <=> (hskp5 | hskp4 | c1_1(a734) | c0_1(a734) | c3_1(a734) | (~ndr1_0))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(399,plain,
% 0.71/0.89 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c1_1(a734) | c0_1(a734) | c3_1(a734))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | c1_1(a734) | c0_1(a734) | c3_1(a734) | (~ndr1_0)))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[398])).
% 0.71/0.89 tff(400,plain,
% 0.71/0.89 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c1_1(a734) | c0_1(a734) | c3_1(a734))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp5 | hskp4 | c1_1(a734) | c0_1(a734) | c3_1(a734) | (~ndr1_0))),
% 0.71/0.89 inference(transitivity,[status(thm)],[399, 397])).
% 0.71/0.89 tff(401,plain,
% 0.71/0.89 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c1_1(a734) | c0_1(a734) | c3_1(a734))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(402,plain,
% 0.71/0.89 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp5 | hskp4 | c1_1(a734) | c0_1(a734) | c3_1(a734) | (~ndr1_0)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.71/0.89 tff(403,plain,
% 0.71/0.89 (hskp4 | c1_1(a734) | c0_1(a734)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[402, 104, 396, 33, 395])).
% 0.71/0.89 tff(404,plain,
% 0.71/0.89 ($false),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[403, 52, 44, 22])).
% 0.71/0.89 tff(405,plain,(c1_1(a734) | c0_1(a734) | hskp5 | c3_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.89 tff(406,plain,
% 0.71/0.89 (hskp5),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[405, 44, 33, 22])).
% 0.71/0.89 tff(407,plain,
% 0.71/0.89 (((~hskp5) | c3_1(a735)) <=> ((~hskp5) | c3_1(a735))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(408,axiom,((~hskp5) | c3_1(a735)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 0.71/0.89 tff(409,plain,
% 0.71/0.89 ((~hskp5) | c3_1(a735)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[408, 407])).
% 0.71/0.89 tff(410,plain,
% 0.71/0.89 ((~hskp5) | c3_1(a735)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[409, 407])).
% 0.71/0.89 tff(411,plain,
% 0.71/0.89 ((~hskp5) | c3_1(a735)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[410, 407])).
% 0.71/0.89 tff(412,plain,
% 0.71/0.89 ((~hskp5) | c3_1(a735)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[411, 407])).
% 0.71/0.89 tff(413,plain,
% 0.71/0.89 ((~hskp5) | c3_1(a735)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[412, 407])).
% 0.71/0.89 tff(414,plain,
% 0.71/0.89 (c3_1(a735)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[413, 406])).
% 0.71/0.89 tff(415,plain,
% 0.71/0.89 (((~hskp5) | c2_1(a735)) <=> ((~hskp5) | c2_1(a735))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(416,axiom,((~hskp5) | c2_1(a735)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.71/0.89 tff(417,plain,
% 0.71/0.89 ((~hskp5) | c2_1(a735)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[416, 415])).
% 0.71/0.89 tff(418,plain,
% 0.71/0.89 ((~hskp5) | c2_1(a735)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[417, 415])).
% 0.71/0.89 tff(419,plain,
% 0.71/0.89 ((~hskp5) | c2_1(a735)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[418, 415])).
% 0.71/0.89 tff(420,plain,
% 0.71/0.89 ((~hskp5) | c2_1(a735)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[419, 415])).
% 0.71/0.89 tff(421,plain,
% 0.71/0.89 ((~hskp5) | c2_1(a735)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[420, 415])).
% 0.71/0.89 tff(422,plain,
% 0.71/0.89 (c2_1(a735)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[421, 406])).
% 0.71/0.89 tff(423,plain,
% 0.71/0.89 (((~hskp5) | (~c0_1(a735))) <=> ((~hskp5) | (~c0_1(a735)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(424,plain,
% 0.71/0.89 (((~c0_1(a735)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a735)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(425,axiom,((~c0_1(a735)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 0.71/0.89 tff(426,plain,
% 0.71/0.89 ((~hskp5) | (~c0_1(a735))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[425, 424])).
% 0.71/0.89 tff(427,plain,
% 0.71/0.89 ((~hskp5) | (~c0_1(a735))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[426, 423])).
% 0.71/0.89 tff(428,plain,
% 0.71/0.89 (~c0_1(a735)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[427, 406])).
% 0.71/0.89 tff(429,plain,
% 0.71/0.89 (((~hskp0) | c3_1(a730)) <=> ((~hskp0) | c3_1(a730))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(430,axiom,((~hskp0) | c3_1(a730)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 0.71/0.89 tff(431,plain,
% 0.71/0.89 ((~hskp0) | c3_1(a730)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[430, 429])).
% 0.71/0.89 tff(432,plain,
% 0.71/0.89 ((~hskp0) | c3_1(a730)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[431, 429])).
% 0.71/0.89 tff(433,plain,
% 0.71/0.89 ((~hskp0) | c3_1(a730)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[432, 429])).
% 0.71/0.89 tff(434,plain,
% 0.71/0.89 ((~hskp0) | c3_1(a730)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[433, 429])).
% 0.71/0.89 tff(435,plain,
% 0.71/0.89 ((~hskp0) | c3_1(a730)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[434, 429])).
% 0.71/0.89 tff(436,plain,
% 0.71/0.89 (c3_1(a730)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[435, 379])).
% 0.71/0.89 tff(437,plain,
% 0.71/0.89 (((~hskp0) | c0_1(a730)) <=> ((~hskp0) | c0_1(a730))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(438,axiom,((~hskp0) | c0_1(a730)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 0.71/0.89 tff(439,plain,
% 0.71/0.89 ((~hskp0) | c0_1(a730)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.71/0.89 tff(440,plain,
% 0.71/0.89 ((~hskp0) | c0_1(a730)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[439, 437])).
% 0.71/0.89 tff(441,plain,
% 0.71/0.89 ((~hskp0) | c0_1(a730)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[440, 437])).
% 0.71/0.89 tff(442,plain,
% 0.71/0.89 ((~hskp0) | c0_1(a730)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[441, 437])).
% 0.71/0.89 tff(443,plain,
% 0.71/0.89 ((~hskp0) | c0_1(a730)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[442, 437])).
% 0.71/0.89 tff(444,plain,
% 0.71/0.89 (c0_1(a730)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[443, 379])).
% 0.71/0.89 tff(445,assumption,(c2_1(a730)), introduced(assumption)).
% 0.71/0.89 tff(446,plain,
% 0.71/0.89 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(447,plain,
% 0.71/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[446])).
% 0.71/0.89 tff(448,plain,
% 0.71/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(449,plain,
% 0.71/0.89 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(450,plain,
% 0.71/0.89 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[449])).
% 0.71/0.89 tff(451,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 0.71/0.89 tff(452,plain,
% 0.71/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[451, 450])).
% 0.71/0.89 tff(453,plain,
% 0.71/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[452, 448])).
% 0.71/0.89 tff(454,plain,(
% 0.71/0.89 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.71/0.89 inference(skolemize,[status(sab)],[453])).
% 0.71/0.89 tff(455,plain,
% 0.71/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[454, 447])).
% 0.71/0.89 tff(456,assumption,(~c1_1(a730)), introduced(assumption)).
% 0.71/0.89 tff(457,assumption,(~c0_1(a735)), introduced(assumption)).
% 0.71/0.89 tff(458,plain,
% 0.71/0.89 (^[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))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(459,plain,
% 0.71/0.89 (![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)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[458])).
% 0.71/0.89 tff(460,plain,
% 0.71/0.89 (![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)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(461,plain,
% 0.71/0.89 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | 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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(462,plain,
% 0.71/0.89 (![U: $i] : (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp21) <=> ![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[461])).
% 0.71/0.89 tff(463,axiom,(![U: $i] : (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 0.71/0.89 tff(464,plain,
% 0.71/0.89 (![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[463, 462])).
% 0.71/0.89 tff(465,plain,
% 0.71/0.89 (![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[464, 460])).
% 0.71/0.89 tff(466,plain,(
% 0.71/0.89 ![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.89 inference(skolemize,[status(sab)],[465])).
% 0.71/0.89 tff(467,plain,
% 0.71/0.89 (![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[466, 459])).
% 0.71/0.89 tff(468,assumption,(c3_1(a730)), introduced(assumption)).
% 0.71/0.89 tff(469,assumption,(c0_1(a730)), introduced(assumption)).
% 0.71/0.89 tff(470,plain,
% 0.71/0.89 (((~![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | (~ndr1_0) | (~c2_1(a730)) | (~c0_1(a730)) | (~c3_1(a730)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | (~ndr1_0) | (~c2_1(a730)) | (~c0_1(a730)) | (~c3_1(a730)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(471,plain,
% 0.71/0.89 ((hskp21 | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c0_1(a730))) <=> (hskp21 | (~ndr1_0) | (~c2_1(a730)) | (~c0_1(a730)) | (~c3_1(a730)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(472,plain,
% 0.71/0.89 (((~![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c0_1(a730)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | (~ndr1_0) | (~c2_1(a730)) | (~c0_1(a730)) | (~c3_1(a730))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[471])).
% 0.71/0.89 tff(473,plain,
% 0.71/0.89 (((~![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c0_1(a730)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | (~ndr1_0) | (~c2_1(a730)) | (~c0_1(a730)) | (~c3_1(a730)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[472, 470])).
% 0.71/0.89 tff(474,plain,
% 0.71/0.89 ((~![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c0_1(a730)))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(475,plain,
% 0.71/0.89 ((~![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | (~ndr1_0) | (~c2_1(a730)) | (~c0_1(a730)) | (~c3_1(a730))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[474, 473])).
% 0.71/0.89 tff(476,plain,
% 0.71/0.89 (hskp21 | (~c2_1(a730))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[475, 104, 469, 468, 467])).
% 0.71/0.89 tff(477,plain,
% 0.71/0.89 (hskp21),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[476, 445])).
% 0.71/0.89 tff(478,plain,
% 0.71/0.89 (((~hskp21) | (~c2_1(a793))) <=> ((~hskp21) | (~c2_1(a793)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(479,plain,
% 0.71/0.89 (((~c2_1(a793)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a793)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(480,axiom,((~c2_1(a793)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 0.71/0.89 tff(481,plain,
% 0.71/0.89 ((~hskp21) | (~c2_1(a793))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[480, 479])).
% 0.71/0.89 tff(482,plain,
% 0.71/0.89 ((~hskp21) | (~c2_1(a793))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[481, 478])).
% 0.71/0.89 tff(483,plain,
% 0.71/0.89 (~c2_1(a793)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[482, 477])).
% 0.71/0.89 tff(484,assumption,(c3_1(a735)), introduced(assumption)).
% 0.71/0.89 tff(485,assumption,(c2_1(a735)), introduced(assumption)).
% 0.71/0.89 tff(486,plain,
% 0.71/0.89 (((~hskp21) | c3_1(a793)) <=> ((~hskp21) | c3_1(a793))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(487,axiom,((~hskp21) | c3_1(a793)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 0.71/0.89 tff(488,plain,
% 0.71/0.89 ((~hskp21) | c3_1(a793)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[487, 486])).
% 0.71/0.89 tff(489,plain,
% 0.71/0.89 ((~hskp21) | c3_1(a793)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[488, 486])).
% 0.71/0.89 tff(490,plain,
% 0.71/0.89 ((~hskp21) | c3_1(a793)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[489, 486])).
% 0.71/0.89 tff(491,plain,
% 0.71/0.89 ((~hskp21) | c3_1(a793)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[490, 486])).
% 0.71/0.89 tff(492,plain,
% 0.71/0.89 ((~hskp21) | c3_1(a793)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[491, 486])).
% 0.71/0.89 tff(493,plain,
% 0.71/0.89 (c3_1(a793)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[492, 477])).
% 0.71/0.89 tff(494,plain,
% 0.71/0.89 (((~hskp21) | c0_1(a793)) <=> ((~hskp21) | c0_1(a793))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(495,axiom,((~hskp21) | c0_1(a793)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 0.71/0.89 tff(496,plain,
% 0.71/0.89 ((~hskp21) | c0_1(a793)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[495, 494])).
% 0.71/0.89 tff(497,plain,
% 0.71/0.89 ((~hskp21) | c0_1(a793)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[496, 494])).
% 0.71/0.89 tff(498,plain,
% 0.71/0.89 ((~hskp21) | c0_1(a793)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[497, 494])).
% 0.71/0.89 tff(499,plain,
% 0.71/0.89 ((~hskp21) | c0_1(a793)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[498, 494])).
% 0.71/0.89 tff(500,plain,
% 0.71/0.89 ((~hskp21) | c0_1(a793)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[499, 494])).
% 0.71/0.89 tff(501,plain,
% 0.71/0.89 (c0_1(a793)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[500, 477])).
% 0.71/0.89 tff(502,plain,
% 0.71/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a793) | c0_1(a735) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c3_1(a735)) | (~c2_1(a735)) | (~c3_1(a793)) | (~c0_1(a793)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a793) | c0_1(a735) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c3_1(a735)) | (~c2_1(a735)) | (~c3_1(a793)) | (~c0_1(a793)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(503,plain,
% 0.71/0.89 (((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a735) | (~c3_1(a735)) | (~c2_1(a735))) <=> (c2_1(a793) | c0_1(a735) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c3_1(a735)) | (~c2_1(a735)) | (~c3_1(a793)) | (~c0_1(a793)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(504,plain,
% 0.71/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a735) | (~c3_1(a735)) | (~c2_1(a735)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a793) | c0_1(a735) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c3_1(a735)) | (~c2_1(a735)) | (~c3_1(a793)) | (~c0_1(a793))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[503])).
% 0.71/0.89 tff(505,plain,
% 0.71/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a735) | (~c3_1(a735)) | (~c2_1(a735)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a793) | c0_1(a735) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c3_1(a735)) | (~c2_1(a735)) | (~c3_1(a793)) | (~c0_1(a793)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[504, 502])).
% 0.71/0.89 tff(506,plain,
% 0.71/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a735) | (~c3_1(a735)) | (~c2_1(a735)))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(507,plain,
% 0.71/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a793) | c0_1(a735) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c3_1(a735)) | (~c2_1(a735)) | (~c3_1(a793)) | (~c0_1(a793))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[506, 505])).
% 0.71/0.89 tff(508,plain,
% 0.71/0.89 ($false),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[507, 104, 501, 493, 485, 484, 468, 483, 457, 456, 455, 445])).
% 0.71/0.89 tff(509,plain,((~c2_1(a730)) | (~c2_1(a735)) | (~c3_1(a735)) | (~c3_1(a730)) | c0_1(a735) | c1_1(a730) | (~c0_1(a730))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.89 tff(510,plain,
% 0.71/0.89 (~c2_1(a730)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[509, 444, 414, 436, 428, 385, 422])).
% 0.71/0.89 tff(511,assumption,(~c2_1(a730)), introduced(assumption)).
% 0.71/0.89 tff(512,plain,
% 0.71/0.89 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c0_1(a735) | (~ndr1_0) | (~c2_1(a735)) | c1_1(a735))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a735) | (~ndr1_0) | (~c2_1(a735)) | c1_1(a735))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(513,plain,
% 0.71/0.89 ((hskp2 | hskp1 | (~ndr1_0) | c1_1(a735) | c0_1(a735) | (~c2_1(a735))) <=> (hskp2 | hskp1 | c0_1(a735) | (~ndr1_0) | (~c2_1(a735)) | c1_1(a735))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(514,plain,
% 0.71/0.89 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c1_1(a735) | c0_1(a735) | (~c2_1(a735)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c0_1(a735) | (~ndr1_0) | (~c2_1(a735)) | c1_1(a735)))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[513])).
% 0.71/0.89 tff(515,plain,
% 0.71/0.89 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c1_1(a735) | c0_1(a735) | (~c2_1(a735)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a735) | (~ndr1_0) | (~c2_1(a735)) | c1_1(a735))),
% 0.71/0.89 inference(transitivity,[status(thm)],[514, 512])).
% 0.71/0.89 tff(516,plain,
% 0.71/0.89 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c1_1(a735) | c0_1(a735) | (~c2_1(a735)))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(517,plain,
% 0.71/0.89 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a735) | (~ndr1_0) | (~c2_1(a735)) | c1_1(a735)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[516, 515])).
% 0.71/0.89 tff(518,plain,
% 0.71/0.89 (hskp2 | hskp1 | c1_1(a735)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[517, 104, 485, 457, 266])).
% 0.71/0.89 tff(519,plain,
% 0.71/0.89 (c1_1(a735)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[518, 256, 255])).
% 0.71/0.89 tff(520,assumption,(c1_1(a735)), introduced(assumption)).
% 0.71/0.89 tff(521,plain,
% 0.71/0.89 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(522,plain,
% 0.71/0.89 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[521])).
% 0.71/0.89 tff(523,plain,
% 0.71/0.89 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(524,plain,
% 0.71/0.89 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(525,plain,
% 0.71/0.89 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[524])).
% 0.71/0.89 tff(526,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 0.71/0.89 tff(527,plain,
% 0.71/0.89 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[526, 525])).
% 0.71/0.89 tff(528,plain,
% 0.71/0.89 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[527, 523])).
% 0.71/0.89 tff(529,plain,(
% 0.71/0.89 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.71/0.89 inference(skolemize,[status(sab)],[528])).
% 0.71/0.89 tff(530,plain,
% 0.71/0.89 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[529, 522])).
% 0.71/0.89 tff(531,plain,
% 0.71/0.89 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c0_1(a735) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a735)) | (~c1_1(a735)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c0_1(a735) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a735)) | (~c1_1(a735)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(532,plain,
% 0.71/0.89 ((hskp2 | (~ndr1_0) | c2_1(a730) | c1_1(a730) | (~c0_1(a730)) | c0_1(a735) | (~c3_1(a735)) | (~c1_1(a735))) <=> (hskp2 | c0_1(a735) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a735)) | (~c1_1(a735)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(533,plain,
% 0.71/0.89 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a730) | c1_1(a730) | (~c0_1(a730)) | c0_1(a735) | (~c3_1(a735)) | (~c1_1(a735)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c0_1(a735) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a735)) | (~c1_1(a735))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[532])).
% 0.71/0.89 tff(534,plain,
% 0.71/0.89 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a730) | c1_1(a730) | (~c0_1(a730)) | c0_1(a735) | (~c3_1(a735)) | (~c1_1(a735)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c0_1(a735) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a735)) | (~c1_1(a735)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[533, 531])).
% 0.71/0.89 tff(535,plain,
% 0.71/0.89 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a730) | c1_1(a730) | (~c0_1(a730)) | c0_1(a735) | (~c3_1(a735)) | (~c1_1(a735)))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(536,plain,
% 0.71/0.89 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c0_1(a735) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a735)) | (~c1_1(a735))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[535, 534])).
% 0.71/0.89 tff(537,plain,
% 0.71/0.89 ($false),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[536, 104, 256, 484, 469, 457, 456, 530, 511, 520])).
% 0.71/0.89 tff(538,plain,(c2_1(a730) | hskp2 | (~c3_1(a735)) | (~c0_1(a730)) | c0_1(a735) | c1_1(a730) | (~c1_1(a735))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.89 tff(539,plain,
% 0.71/0.89 ($false),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[538, 519, 256, 484, 469, 457, 456, 511])).
% 0.71/0.89 tff(540,plain,(hskp2 | (~c3_1(a735)) | (~c0_1(a730)) | c0_1(a735) | c1_1(a730) | c2_1(a730) | hskp1 | (~c2_1(a735))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.89 tff(541,plain,
% 0.71/0.89 (hskp2),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[540, 444, 422, 428, 385, 510, 130, 414])).
% 0.71/0.89 tff(542,plain,
% 0.71/0.89 (((~hskp2) | (~c3_1(a732))) <=> ((~hskp2) | (~c3_1(a732)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(543,plain,
% 0.71/0.89 (((~c3_1(a732)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a732)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(544,axiom,((~c3_1(a732)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 0.71/0.89 tff(545,plain,
% 0.71/0.89 ((~hskp2) | (~c3_1(a732))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[544, 543])).
% 0.71/0.89 tff(546,plain,
% 0.71/0.89 ((~hskp2) | (~c3_1(a732))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[545, 542])).
% 0.71/0.89 tff(547,plain,
% 0.71/0.89 (~c3_1(a732)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[546, 541])).
% 0.71/0.89 tff(548,plain,
% 0.71/0.89 (~c2_1(a732)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[282, 541])).
% 0.71/0.89 tff(549,plain,
% 0.71/0.89 (~c0_1(a732)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[288, 541])).
% 0.71/0.89 tff(550,plain,
% 0.71/0.89 (^[U: $i] : refl((hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(551,plain,
% 0.71/0.89 (![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[550])).
% 0.71/0.89 tff(552,plain,
% 0.71/0.89 (![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(553,plain,
% 0.71/0.89 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | 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) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp11) <=> ((hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp11))), rewrite(((hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp11) <=> (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp11) <=> (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(554,plain,
% 0.71/0.90 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp11) <=> ![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[553])).
% 0.71/0.90 tff(555,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 0.71/0.90 tff(556,plain,
% 0.71/0.90 (![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[555, 554])).
% 0.71/0.90 tff(557,plain,
% 0.71/0.90 (![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[556, 552])).
% 0.71/0.90 tff(558,plain,(
% 0.71/0.90 ![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.71/0.90 inference(skolemize,[status(sab)],[557])).
% 0.71/0.90 tff(559,plain,
% 0.71/0.90 (![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[558, 551])).
% 0.71/0.90 tff(560,assumption,(~hskp27), introduced(assumption)).
% 0.71/0.90 tff(561,assumption,(c2_1(a741)), introduced(assumption)).
% 0.71/0.90 tff(562,plain,
% 0.71/0.90 (^[U: $i] : refl((hskp27 | hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp27 | hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(563,plain,
% 0.71/0.90 (![U: $i] : (hskp27 | hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[562])).
% 0.71/0.90 tff(564,plain,
% 0.71/0.90 (![U: $i] : (hskp27 | hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(565,plain,
% 0.71/0.90 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp27))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp17) <=> ((hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp17))), rewrite(((hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp17) <=> (hskp27 | hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp17) <=> (hskp27 | hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(566,plain,
% 0.71/0.90 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp17) <=> ![U: $i] : (hskp27 | hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[565])).
% 0.71/0.90 tff(567,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 0.71/0.90 tff(568,plain,
% 0.71/0.90 (![U: $i] : (hskp27 | hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[567, 566])).
% 0.71/0.90 tff(569,plain,
% 0.71/0.90 (![U: $i] : (hskp27 | hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[568, 564])).
% 0.71/0.90 tff(570,plain,(
% 0.71/0.90 ![U: $i] : (hskp27 | hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.71/0.90 inference(skolemize,[status(sab)],[569])).
% 0.71/0.90 tff(571,plain,
% 0.71/0.90 (![U: $i] : (hskp27 | hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[570, 563])).
% 0.71/0.90 tff(572,plain,
% 0.71/0.90 (((~![U: $i] : (hskp27 | hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp17 | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)))) <=> ((~![U: $i] : (hskp27 | hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp17 | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(573,plain,
% 0.71/0.90 ((hskp27 | hskp17 | (~ndr1_0) | c0_1(a741) | (~c2_1(a741)) | (~c1_1(a741))) <=> (hskp27 | hskp17 | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(574,plain,
% 0.71/0.90 (((~![U: $i] : (hskp27 | hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp17 | (~ndr1_0) | c0_1(a741) | (~c2_1(a741)) | (~c1_1(a741)))) <=> ((~![U: $i] : (hskp27 | hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp17 | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[573])).
% 0.71/0.90 tff(575,plain,
% 0.71/0.90 (((~![U: $i] : (hskp27 | hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp17 | (~ndr1_0) | c0_1(a741) | (~c2_1(a741)) | (~c1_1(a741)))) <=> ((~![U: $i] : (hskp27 | hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp17 | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)))),
% 0.71/0.90 inference(transitivity,[status(thm)],[574, 572])).
% 0.71/0.90 tff(576,plain,
% 0.71/0.90 ((~![U: $i] : (hskp27 | hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp17 | (~ndr1_0) | c0_1(a741) | (~c2_1(a741)) | (~c1_1(a741)))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(577,plain,
% 0.71/0.90 ((~![U: $i] : (hskp27 | hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp17 | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[576, 575])).
% 0.71/0.90 tff(578,plain,
% 0.71/0.90 (hskp27 | hskp17),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[577, 104, 207, 177, 571, 561])).
% 0.71/0.90 tff(579,plain,
% 0.71/0.90 (hskp17),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[578, 560])).
% 0.71/0.90 tff(580,plain,
% 0.71/0.90 (((~hskp17) | c2_1(a766)) <=> ((~hskp17) | c2_1(a766))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(581,axiom,((~hskp17) | c2_1(a766)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 0.71/0.90 tff(582,plain,
% 0.71/0.90 ((~hskp17) | c2_1(a766)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[581, 580])).
% 0.71/0.90 tff(583,plain,
% 0.71/0.90 ((~hskp17) | c2_1(a766)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[582, 580])).
% 0.71/0.90 tff(584,plain,
% 0.71/0.90 ((~hskp17) | c2_1(a766)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[583, 580])).
% 0.71/0.90 tff(585,plain,
% 0.71/0.90 ((~hskp17) | c2_1(a766)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[584, 580])).
% 0.71/0.90 tff(586,plain,
% 0.71/0.90 ((~hskp17) | c2_1(a766)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[585, 580])).
% 0.71/0.90 tff(587,plain,
% 0.71/0.90 (c2_1(a766)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[586, 579])).
% 0.71/0.90 tff(588,plain,
% 0.71/0.90 (((~hskp17) | c1_1(a766)) <=> ((~hskp17) | c1_1(a766))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(589,axiom,((~hskp17) | c1_1(a766)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 0.71/0.90 tff(590,plain,
% 0.71/0.90 ((~hskp17) | c1_1(a766)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[589, 588])).
% 0.71/0.90 tff(591,plain,
% 0.71/0.90 ((~hskp17) | c1_1(a766)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[590, 588])).
% 0.71/0.90 tff(592,plain,
% 0.71/0.90 ((~hskp17) | c1_1(a766)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[591, 588])).
% 0.71/0.90 tff(593,plain,
% 0.71/0.90 ((~hskp17) | c1_1(a766)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[592, 588])).
% 0.71/0.90 tff(594,plain,
% 0.71/0.90 ((~hskp17) | c1_1(a766)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[593, 588])).
% 0.71/0.90 tff(595,plain,
% 0.71/0.90 (c1_1(a766)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[594, 579])).
% 0.71/0.90 tff(596,plain,
% 0.71/0.90 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp11 | (~ndr1_0) | c3_1(a766) | (~c2_1(a766)) | (~c1_1(a766)))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp11 | (~ndr1_0) | c3_1(a766) | (~c2_1(a766)) | (~c1_1(a766)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(597,plain,
% 0.71/0.90 ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp11 | (~ndr1_0) | c3_1(a766) | (~c2_1(a766)) | (~c1_1(a766)))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(598,plain,
% 0.71/0.90 ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp11 | (~ndr1_0) | c3_1(a766) | (~c2_1(a766)) | (~c1_1(a766))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[597, 596])).
% 0.71/0.90 tff(599,plain,
% 0.71/0.90 (c3_1(a766)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[598, 104, 560, 21, 595, 587, 559])).
% 0.71/0.90 tff(600,plain,
% 0.71/0.90 (^[U: $i] : refl((hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(601,plain,
% 0.71/0.90 (![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[600])).
% 0.71/0.90 tff(602,plain,
% 0.71/0.90 (![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(603,plain,
% 0.71/0.90 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp27) | hskp11) <=> ((hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp11))), rewrite(((hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp11) <=> (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp27) | hskp11) <=> (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(604,plain,
% 0.71/0.90 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp27) | hskp11) <=> ![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[603])).
% 0.71/0.90 tff(605,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp27) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.71/0.90 tff(606,plain,
% 0.71/0.90 (![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[605, 604])).
% 0.71/0.90 tff(607,plain,
% 0.71/0.90 (![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[606, 602])).
% 0.71/0.90 tff(608,plain,(
% 0.71/0.90 ![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.71/0.90 inference(skolemize,[status(sab)],[607])).
% 0.71/0.90 tff(609,plain,
% 0.71/0.90 (![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[608, 601])).
% 0.71/0.90 tff(610,plain,
% 0.71/0.90 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(611,plain,
% 0.71/0.90 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[610])).
% 0.71/0.90 tff(612,plain,
% 0.71/0.90 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(613,plain,
% 0.71/0.90 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp8))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(614,plain,
% 0.71/0.90 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[613])).
% 0.71/0.90 tff(615,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 0.71/0.90 tff(616,plain,
% 0.71/0.90 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[615, 614])).
% 0.71/0.90 tff(617,plain,
% 0.71/0.90 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[616, 612])).
% 0.71/0.90 tff(618,plain,(
% 0.71/0.90 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.71/0.90 inference(skolemize,[status(sab)],[617])).
% 0.71/0.90 tff(619,plain,
% 0.71/0.90 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[618, 611])).
% 0.71/0.90 tff(620,assumption,(~c3_1(a732)), introduced(assumption)).
% 0.71/0.90 tff(621,assumption,(~c2_1(a732)), introduced(assumption)).
% 0.71/0.90 tff(622,assumption,(~c0_1(a732)), introduced(assumption)).
% 0.71/0.90 tff(623,plain,
% 0.71/0.90 (^[U: $i] : refl((hskp27 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp27 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(624,plain,
% 0.71/0.90 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[623])).
% 0.71/0.90 tff(625,plain,
% 0.71/0.90 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(626,plain,
% 0.71/0.90 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp27) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp27))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp27) | hskp19) <=> ((hskp27 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp19))), rewrite(((hskp27 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp19) <=> (hskp27 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp27) | hskp19) <=> (hskp27 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(627,plain,
% 0.71/0.90 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp27) | hskp19) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[626])).
% 0.71/0.90 tff(628,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp27) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 0.71/0.90 tff(629,plain,
% 0.71/0.90 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[628, 627])).
% 0.71/0.90 tff(630,plain,
% 0.71/0.90 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[629, 625])).
% 0.71/0.90 tff(631,plain,(
% 0.71/0.90 ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.90 inference(skolemize,[status(sab)],[630])).
% 0.71/0.90 tff(632,plain,
% 0.71/0.90 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[631, 624])).
% 0.71/0.90 tff(633,plain,
% 0.71/0.90 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp19 | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp19 | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(634,plain,
% 0.71/0.90 ((hskp27 | hskp19 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730))) <=> (hskp27 | hskp19 | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(635,plain,
% 0.71/0.90 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp19 | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[634])).
% 0.71/0.90 tff(636,plain,
% 0.71/0.90 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp19 | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)))),
% 0.71/0.90 inference(transitivity,[status(thm)],[635, 633])).
% 0.71/0.90 tff(637,plain,
% 0.71/0.90 ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(638,plain,
% 0.71/0.90 ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp19 | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[637, 636])).
% 0.71/0.90 tff(639,plain,
% 0.71/0.90 (hskp27 | hskp19),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[638, 104, 469, 468, 456, 632])).
% 0.71/0.90 tff(640,plain,
% 0.71/0.90 (hskp19),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[639, 560])).
% 0.71/0.90 tff(641,plain,
% 0.71/0.90 (((~hskp19) | (~c3_1(a777))) <=> ((~hskp19) | (~c3_1(a777)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(642,plain,
% 0.71/0.90 (((~c3_1(a777)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a777)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(643,axiom,((~c3_1(a777)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 0.71/0.90 tff(644,plain,
% 0.71/0.90 ((~hskp19) | (~c3_1(a777))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[643, 642])).
% 0.71/0.90 tff(645,plain,
% 0.71/0.90 ((~hskp19) | (~c3_1(a777))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[644, 641])).
% 0.71/0.90 tff(646,plain,
% 0.71/0.90 (~c3_1(a777)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[645, 640])).
% 0.71/0.90 tff(647,plain,
% 0.71/0.90 (((~hskp19) | (~c0_1(a777))) <=> ((~hskp19) | (~c0_1(a777)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(648,plain,
% 0.71/0.90 (((~c0_1(a777)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a777)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(649,axiom,((~c0_1(a777)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 0.71/0.90 tff(650,plain,
% 0.71/0.90 ((~hskp19) | (~c0_1(a777))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[649, 648])).
% 0.71/0.90 tff(651,plain,
% 0.71/0.90 ((~hskp19) | (~c0_1(a777))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[650, 647])).
% 0.71/0.90 tff(652,plain,
% 0.71/0.90 (~c0_1(a777)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[651, 640])).
% 0.71/0.90 tff(653,plain,
% 0.71/0.90 (((~hskp19) | c2_1(a777)) <=> ((~hskp19) | c2_1(a777))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(654,axiom,((~hskp19) | c2_1(a777)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 0.71/0.90 tff(655,plain,
% 0.71/0.90 ((~hskp19) | c2_1(a777)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[654, 653])).
% 0.71/0.90 tff(656,plain,
% 0.71/0.90 ((~hskp19) | c2_1(a777)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[655, 653])).
% 0.71/0.90 tff(657,plain,
% 0.71/0.90 ((~hskp19) | c2_1(a777)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[656, 653])).
% 0.71/0.90 tff(658,plain,
% 0.71/0.90 ((~hskp19) | c2_1(a777)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[657, 653])).
% 0.71/0.90 tff(659,plain,
% 0.71/0.90 ((~hskp19) | c2_1(a777)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[658, 653])).
% 0.71/0.90 tff(660,plain,
% 0.71/0.90 (c2_1(a777)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[659, 640])).
% 0.71/0.90 tff(661,plain,
% 0.71/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c0_1(a777) | c3_1(a777) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a777)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a777) | c3_1(a777) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a777)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(662,plain,
% 0.71/0.90 ((hskp8 | (~ndr1_0) | c0_1(a777) | c3_1(a777) | (~c2_1(a777)) | c3_1(a732) | c0_1(a732) | c2_1(a732)) <=> (hskp8 | c0_1(a777) | c3_1(a777) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a777)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(663,plain,
% 0.71/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a777) | c3_1(a777) | (~c2_1(a777)) | c3_1(a732) | c0_1(a732) | c2_1(a732))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c0_1(a777) | c3_1(a777) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a777))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[662])).
% 0.71/0.90 tff(664,plain,
% 0.71/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a777) | c3_1(a777) | (~c2_1(a777)) | c3_1(a732) | c0_1(a732) | c2_1(a732))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a777) | c3_1(a777) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a777)))),
% 0.71/0.90 inference(transitivity,[status(thm)],[663, 661])).
% 0.71/0.90 tff(665,plain,
% 0.71/0.90 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a777) | c3_1(a777) | (~c2_1(a777)) | c3_1(a732) | c0_1(a732) | c2_1(a732))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(666,plain,
% 0.71/0.90 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a777) | c3_1(a777) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a777))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[665, 664])).
% 0.71/0.90 tff(667,plain,
% 0.71/0.90 (hskp8),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[666, 104, 660, 652, 646, 622, 621, 620, 619])).
% 0.71/0.90 tff(668,plain,
% 0.71/0.90 (((~hskp8) | (~c0_1(a744))) <=> ((~hskp8) | (~c0_1(a744)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(669,plain,
% 0.71/0.90 (((~c0_1(a744)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a744)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(670,axiom,((~c0_1(a744)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 0.71/0.90 tff(671,plain,
% 0.71/0.90 ((~hskp8) | (~c0_1(a744))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[670, 669])).
% 0.71/0.90 tff(672,plain,
% 0.71/0.90 ((~hskp8) | (~c0_1(a744))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[671, 668])).
% 0.71/0.90 tff(673,plain,
% 0.71/0.90 (~c0_1(a744)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[672, 667])).
% 0.71/0.90 tff(674,plain,
% 0.71/0.90 (((~hskp8) | c3_1(a744)) <=> ((~hskp8) | c3_1(a744))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(675,axiom,((~hskp8) | c3_1(a744)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.71/0.90 tff(676,plain,
% 0.71/0.90 ((~hskp8) | c3_1(a744)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[675, 674])).
% 0.71/0.90 tff(677,plain,
% 0.71/0.90 ((~hskp8) | c3_1(a744)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[676, 674])).
% 0.71/0.90 tff(678,plain,
% 0.71/0.90 ((~hskp8) | c3_1(a744)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[677, 674])).
% 0.71/0.90 tff(679,plain,
% 0.71/0.90 ((~hskp8) | c3_1(a744)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[678, 674])).
% 0.71/0.90 tff(680,plain,
% 0.71/0.90 ((~hskp8) | c3_1(a744)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[679, 674])).
% 0.71/0.90 tff(681,plain,
% 0.71/0.90 (c3_1(a744)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[680, 667])).
% 0.71/0.90 tff(682,plain,
% 0.71/0.90 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp27 | hskp11 | c0_1(a744) | (~ndr1_0) | c2_1(a744) | (~c3_1(a744)))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp27 | hskp11 | c0_1(a744) | (~ndr1_0) | c2_1(a744) | (~c3_1(a744)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(683,plain,
% 0.71/0.90 ((hskp27 | hskp11 | (~ndr1_0) | c2_1(a744) | c0_1(a744) | (~c3_1(a744))) <=> (hskp27 | hskp11 | c0_1(a744) | (~ndr1_0) | c2_1(a744) | (~c3_1(a744)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(684,plain,
% 0.71/0.90 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp27 | hskp11 | (~ndr1_0) | c2_1(a744) | c0_1(a744) | (~c3_1(a744)))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp27 | hskp11 | c0_1(a744) | (~ndr1_0) | c2_1(a744) | (~c3_1(a744))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[683])).
% 0.71/0.90 tff(685,plain,
% 0.71/0.90 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp27 | hskp11 | (~ndr1_0) | c2_1(a744) | c0_1(a744) | (~c3_1(a744)))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp27 | hskp11 | c0_1(a744) | (~ndr1_0) | c2_1(a744) | (~c3_1(a744)))),
% 0.71/0.90 inference(transitivity,[status(thm)],[684, 682])).
% 0.71/0.90 tff(686,plain,
% 0.71/0.90 ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp27 | hskp11 | (~ndr1_0) | c2_1(a744) | c0_1(a744) | (~c3_1(a744)))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(687,plain,
% 0.71/0.90 ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp27 | hskp11 | c0_1(a744) | (~ndr1_0) | c2_1(a744) | (~c3_1(a744))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[686, 685])).
% 0.71/0.90 tff(688,plain,
% 0.71/0.90 (c2_1(a744)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[687, 104, 560, 21, 681, 673, 609])).
% 0.71/0.90 tff(689,plain,
% 0.71/0.90 (((~hskp8) | (~c1_1(a744))) <=> ((~hskp8) | (~c1_1(a744)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(690,plain,
% 0.71/0.90 (((~c1_1(a744)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a744)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(691,axiom,((~c1_1(a744)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 0.71/0.90 tff(692,plain,
% 0.71/0.90 ((~hskp8) | (~c1_1(a744))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[691, 690])).
% 0.71/0.90 tff(693,plain,
% 0.71/0.90 ((~hskp8) | (~c1_1(a744))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[692, 689])).
% 0.71/0.90 tff(694,plain,
% 0.71/0.90 (~c1_1(a744)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[693, 667])).
% 0.71/0.90 tff(695,plain,
% 0.71/0.90 (((~hskp17) | (~c0_1(a766))) <=> ((~hskp17) | (~c0_1(a766)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(696,plain,
% 0.71/0.90 (((~c0_1(a766)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a766)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(697,axiom,((~c0_1(a766)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 0.71/0.90 tff(698,plain,
% 0.71/0.90 ((~hskp17) | (~c0_1(a766))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[697, 696])).
% 0.71/0.90 tff(699,plain,
% 0.71/0.90 ((~hskp17) | (~c0_1(a766))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[698, 695])).
% 0.71/0.90 tff(700,plain,
% 0.71/0.90 (~c0_1(a766)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[699, 579])).
% 0.71/0.90 tff(701,plain,
% 0.71/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a766) | c1_1(a744) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a744)) | (~c3_1(a744)) | (~c3_1(a766)) | (~c2_1(a766)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a766) | c1_1(a744) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a744)) | (~c3_1(a744)) | (~c3_1(a766)) | (~c2_1(a766)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(702,plain,
% 0.71/0.90 (((~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a744) | (~c2_1(a744)) | (~c3_1(a744)) | c0_1(a766) | (~c3_1(a766)) | (~c2_1(a766))) <=> (c0_1(a766) | c1_1(a744) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a744)) | (~c3_1(a744)) | (~c3_1(a766)) | (~c2_1(a766)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(703,plain,
% 0.71/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a744) | (~c2_1(a744)) | (~c3_1(a744)) | c0_1(a766) | (~c3_1(a766)) | (~c2_1(a766)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a766) | c1_1(a744) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a744)) | (~c3_1(a744)) | (~c3_1(a766)) | (~c2_1(a766))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[702])).
% 0.71/0.90 tff(704,plain,
% 0.71/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a744) | (~c2_1(a744)) | (~c3_1(a744)) | c0_1(a766) | (~c3_1(a766)) | (~c2_1(a766)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a766) | c1_1(a744) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a744)) | (~c3_1(a744)) | (~c3_1(a766)) | (~c2_1(a766)))),
% 0.71/0.90 inference(transitivity,[status(thm)],[703, 701])).
% 0.71/0.90 tff(705,plain,
% 0.71/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a744) | (~c2_1(a744)) | (~c3_1(a744)) | c0_1(a766) | (~c3_1(a766)) | (~c2_1(a766)))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(706,plain,
% 0.71/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a766) | c1_1(a744) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a744)) | (~c3_1(a744)) | (~c3_1(a766)) | (~c2_1(a766))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[705, 704])).
% 0.71/0.90 tff(707,plain,
% 0.71/0.90 ($false),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[706, 104, 587, 681, 469, 468, 700, 694, 455, 688, 511, 599])).
% 0.71/0.90 tff(708,plain,(hskp27 | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a730) | hskp11 | c0_1(a732) | c2_1(a732) | c3_1(a732) | c1_1(a730) | (~c1_1(a741)) | c0_1(a741) | (~c2_1(a741))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.90 tff(709,plain,
% 0.71/0.90 (hskp27),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[708, 444, 436, 510, 21, 549, 548, 547, 385, 150, 164, 216])).
% 0.71/0.90 tff(710,plain,
% 0.71/0.90 (((~hskp27) | c0_1(a750)) <=> ((~hskp27) | c0_1(a750))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(711,axiom,((~hskp27) | c0_1(a750)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 0.71/0.90 tff(712,plain,
% 0.71/0.90 ((~hskp27) | c0_1(a750)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[711, 710])).
% 0.71/0.90 tff(713,plain,
% 0.71/0.90 ((~hskp27) | c0_1(a750)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[712, 710])).
% 0.71/0.90 tff(714,plain,
% 0.71/0.90 ((~hskp27) | c0_1(a750)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[713, 710])).
% 0.71/0.90 tff(715,plain,
% 0.71/0.90 ((~hskp27) | c0_1(a750)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[714, 710])).
% 0.71/0.91 tff(716,plain,
% 0.71/0.91 ((~hskp27) | c0_1(a750)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[715, 710])).
% 0.71/0.91 tff(717,plain,
% 0.71/0.91 (c0_1(a750)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[716, 709])).
% 0.71/0.91 tff(718,plain,
% 0.71/0.91 (((~hskp27) | c2_1(a750)) <=> ((~hskp27) | c2_1(a750))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(719,axiom,((~hskp27) | c2_1(a750)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 0.71/0.91 tff(720,plain,
% 0.71/0.91 ((~hskp27) | c2_1(a750)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[719, 718])).
% 0.71/0.91 tff(721,plain,
% 0.71/0.91 ((~hskp27) | c2_1(a750)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[720, 718])).
% 0.71/0.91 tff(722,plain,
% 0.71/0.91 ((~hskp27) | c2_1(a750)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[721, 718])).
% 0.71/0.91 tff(723,plain,
% 0.71/0.91 ((~hskp27) | c2_1(a750)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[722, 718])).
% 0.71/0.91 tff(724,plain,
% 0.71/0.91 ((~hskp27) | c2_1(a750)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[723, 718])).
% 0.71/0.91 tff(725,plain,
% 0.71/0.91 (c2_1(a750)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[724, 709])).
% 0.71/0.91 tff(726,plain,
% 0.71/0.91 (((~hskp27) | c1_1(a750)) <=> ((~hskp27) | c1_1(a750))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(727,axiom,((~hskp27) | c1_1(a750)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 0.71/0.91 tff(728,plain,
% 0.71/0.91 ((~hskp27) | c1_1(a750)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[727, 726])).
% 0.71/0.91 tff(729,plain,
% 0.71/0.91 ((~hskp27) | c1_1(a750)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[728, 726])).
% 0.71/0.91 tff(730,plain,
% 0.71/0.91 ((~hskp27) | c1_1(a750)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[729, 726])).
% 0.71/0.91 tff(731,plain,
% 0.71/0.91 ((~hskp27) | c1_1(a750)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[730, 726])).
% 0.71/0.91 tff(732,plain,
% 0.71/0.91 ((~hskp27) | c1_1(a750)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[731, 726])).
% 0.71/0.91 tff(733,plain,
% 0.71/0.91 (c1_1(a750)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[732, 709])).
% 0.71/0.91 tff(734,plain,
% 0.71/0.91 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 0.71/0.91 inference(bind,[status(th)],[])).
% 0.71/0.91 tff(735,plain,
% 0.71/0.91 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.71/0.91 inference(quant_intro,[status(thm)],[734])).
% 0.71/0.91 tff(736,plain,
% 0.71/0.91 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(737,plain,
% 0.71/0.91 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp1))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.71/0.91 inference(bind,[status(th)],[])).
% 0.71/0.91 tff(738,plain,
% 0.71/0.91 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.71/0.91 inference(quant_intro,[status(thm)],[737])).
% 0.71/0.91 tff(739,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 0.71/0.91 tff(740,plain,
% 0.71/0.91 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[739, 738])).
% 0.71/0.91 tff(741,plain,
% 0.71/0.91 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[740, 736])).
% 0.71/0.91 tff(742,plain,(
% 0.71/0.91 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.71/0.91 inference(skolemize,[status(sab)],[741])).
% 0.71/0.91 tff(743,plain,
% 0.71/0.91 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[742, 735])).
% 0.71/0.91 tff(744,assumption,(c0_1(a750)), introduced(assumption)).
% 0.71/0.91 tff(745,plain,
% 0.71/0.91 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 0.71/0.91 inference(bind,[status(th)],[])).
% 0.71/0.91 tff(746,plain,
% 0.71/0.91 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.71/0.91 inference(quant_intro,[status(thm)],[745])).
% 0.71/0.91 tff(747,plain,
% 0.71/0.91 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(748,plain,
% 0.71/0.91 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp16))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 0.71/0.91 inference(bind,[status(th)],[])).
% 0.71/0.91 tff(749,plain,
% 0.71/0.91 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.71/0.91 inference(quant_intro,[status(thm)],[748])).
% 0.71/0.91 tff(750,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 0.71/0.91 tff(751,plain,
% 0.71/0.91 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[750, 749])).
% 0.71/0.91 tff(752,plain,
% 0.71/0.91 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[751, 747])).
% 0.71/0.91 tff(753,plain,(
% 0.71/0.91 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.71/0.91 inference(skolemize,[status(sab)],[752])).
% 0.71/0.91 tff(754,plain,
% 0.71/0.91 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[753, 746])).
% 0.71/0.91 tff(755,assumption,(hskp25), introduced(assumption)).
% 0.71/0.91 tff(756,plain,
% 0.71/0.91 (((~hskp25) | c3_1(a729)) <=> ((~hskp25) | c3_1(a729))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(757,axiom,((~hskp25) | c3_1(a729)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 0.71/0.91 tff(758,plain,
% 0.71/0.91 ((~hskp25) | c3_1(a729)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[757, 756])).
% 0.71/0.91 tff(759,plain,
% 0.71/0.91 ((~hskp25) | c3_1(a729)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[758, 756])).
% 0.71/0.91 tff(760,plain,
% 0.71/0.91 ((~hskp25) | c3_1(a729)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[759, 756])).
% 0.71/0.91 tff(761,plain,
% 0.71/0.91 ((~hskp25) | c3_1(a729)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[760, 756])).
% 0.71/0.91 tff(762,plain,
% 0.71/0.91 ((~hskp25) | c3_1(a729)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[761, 756])).
% 0.71/0.91 tff(763,plain,
% 0.71/0.91 (c3_1(a729)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[762, 755])).
% 0.71/0.91 tff(764,plain,
% 0.71/0.91 (((~hskp25) | c2_1(a729)) <=> ((~hskp25) | c2_1(a729))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(765,axiom,((~hskp25) | c2_1(a729)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 0.71/0.91 tff(766,plain,
% 0.71/0.91 ((~hskp25) | c2_1(a729)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[765, 764])).
% 0.71/0.91 tff(767,plain,
% 0.71/0.91 ((~hskp25) | c2_1(a729)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[766, 764])).
% 0.71/0.91 tff(768,plain,
% 0.71/0.91 ((~hskp25) | c2_1(a729)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[767, 764])).
% 0.71/0.91 tff(769,plain,
% 0.71/0.91 ((~hskp25) | c2_1(a729)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[768, 764])).
% 0.71/0.91 tff(770,plain,
% 0.71/0.91 ((~hskp25) | c2_1(a729)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[769, 764])).
% 0.71/0.91 tff(771,plain,
% 0.71/0.91 (c2_1(a729)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[770, 755])).
% 0.71/0.91 tff(772,plain,
% 0.71/0.91 (((~hskp25) | c0_1(a729)) <=> ((~hskp25) | c0_1(a729))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(773,axiom,((~hskp25) | c0_1(a729)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 0.71/0.91 tff(774,plain,
% 0.71/0.91 ((~hskp25) | c0_1(a729)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[773, 772])).
% 0.71/0.91 tff(775,plain,
% 0.71/0.91 ((~hskp25) | c0_1(a729)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[774, 772])).
% 0.71/0.91 tff(776,plain,
% 0.71/0.91 ((~hskp25) | c0_1(a729)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[775, 772])).
% 0.71/0.91 tff(777,plain,
% 0.71/0.91 ((~hskp25) | c0_1(a729)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[776, 772])).
% 0.71/0.91 tff(778,plain,
% 0.71/0.91 ((~hskp25) | c0_1(a729)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[777, 772])).
% 0.71/0.91 tff(779,plain,
% 0.71/0.91 (c0_1(a729)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[778, 755])).
% 0.71/0.91 tff(780,plain,
% 0.71/0.91 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(781,plain,
% 0.71/0.91 ((hskp16 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c0_1(a741) | (~c2_1(a741)) | (~c1_1(a741))) <=> (hskp16 | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(782,plain,
% 0.71/0.91 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c0_1(a741) | (~c2_1(a741)) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729))))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[781])).
% 0.71/0.91 tff(783,plain,
% 0.71/0.91 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c0_1(a741) | (~c2_1(a741)) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)))),
% 0.71/0.91 inference(transitivity,[status(thm)],[782, 780])).
% 0.71/0.91 tff(784,plain,
% 0.71/0.91 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c0_1(a741) | (~c2_1(a741)) | (~c1_1(a741)))),
% 0.71/0.91 inference(quant_inst,[status(thm)],[])).
% 0.71/0.91 tff(785,plain,
% 0.71/0.91 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[784, 783])).
% 0.71/0.91 tff(786,plain,
% 0.71/0.91 (hskp16),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[785, 104, 779, 771, 763, 207, 177, 754, 561])).
% 0.71/0.91 tff(787,plain,
% 0.71/0.91 (((~hskp16) | (~c3_1(a764))) <=> ((~hskp16) | (~c3_1(a764)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(788,plain,
% 0.71/0.91 (((~c3_1(a764)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a764)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(789,axiom,((~c3_1(a764)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 0.71/0.91 tff(790,plain,
% 0.71/0.91 ((~hskp16) | (~c3_1(a764))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[789, 788])).
% 0.71/0.91 tff(791,plain,
% 0.71/0.91 ((~hskp16) | (~c3_1(a764))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[790, 787])).
% 0.71/0.91 tff(792,plain,
% 0.71/0.91 (~c3_1(a764)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[791, 786])).
% 0.71/0.91 tff(793,plain,
% 0.71/0.91 (((~hskp16) | c2_1(a764)) <=> ((~hskp16) | c2_1(a764))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(794,axiom,((~hskp16) | c2_1(a764)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 0.71/0.91 tff(795,plain,
% 0.71/0.91 ((~hskp16) | c2_1(a764)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[794, 793])).
% 0.71/0.91 tff(796,plain,
% 0.71/0.91 ((~hskp16) | c2_1(a764)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[795, 793])).
% 0.71/0.91 tff(797,plain,
% 0.71/0.91 ((~hskp16) | c2_1(a764)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[796, 793])).
% 0.71/0.91 tff(798,plain,
% 0.71/0.91 ((~hskp16) | c2_1(a764)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[797, 793])).
% 0.71/0.91 tff(799,plain,
% 0.71/0.91 ((~hskp16) | c2_1(a764)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[798, 793])).
% 0.71/0.91 tff(800,plain,
% 0.71/0.91 (c2_1(a764)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[799, 786])).
% 0.71/0.91 tff(801,assumption,(c2_1(a750)), introduced(assumption)).
% 0.71/0.91 tff(802,assumption,(c1_1(a750)), introduced(assumption)).
% 0.71/0.91 tff(803,plain,
% 0.71/0.91 (((~hskp16) | c0_1(a764)) <=> ((~hskp16) | c0_1(a764))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(804,axiom,((~hskp16) | c0_1(a764)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 0.71/0.91 tff(805,plain,
% 0.71/0.91 ((~hskp16) | c0_1(a764)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[804, 803])).
% 0.71/0.91 tff(806,plain,
% 0.71/0.91 ((~hskp16) | c0_1(a764)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[805, 803])).
% 0.71/0.91 tff(807,plain,
% 0.71/0.91 ((~hskp16) | c0_1(a764)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[806, 803])).
% 0.71/0.91 tff(808,plain,
% 0.71/0.91 ((~hskp16) | c0_1(a764)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[807, 803])).
% 0.71/0.91 tff(809,plain,
% 0.71/0.91 ((~hskp16) | c0_1(a764)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[808, 803])).
% 0.71/0.91 tff(810,plain,
% 0.71/0.91 (c0_1(a764)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[809, 786])).
% 0.71/0.91 tff(811,plain,
% 0.71/0.91 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | c3_1(a764) | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | (~c0_1(a764)) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp1 | c3_1(a764) | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(812,plain,
% 0.71/0.91 ((hskp1 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764))) <=> (hskp1 | c3_1(a764) | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(813,plain,
% 0.71/0.91 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | c3_1(a764) | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | (~c0_1(a764)) | (~c1_1(a764))))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[812])).
% 0.71/0.91 tff(814,plain,
% 0.71/0.91 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp1 | c3_1(a764) | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 0.71/0.91 inference(transitivity,[status(thm)],[813, 811])).
% 0.71/0.91 tff(815,plain,
% 0.71/0.91 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)))),
% 0.71/0.91 inference(quant_inst,[status(thm)],[])).
% 0.71/0.91 tff(816,plain,
% 0.71/0.91 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp1 | c3_1(a764) | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | (~c0_1(a764)) | (~c1_1(a764))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[815, 814])).
% 0.71/0.91 tff(817,plain,
% 0.71/0.91 (~c1_1(a764)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[816, 104, 255, 779, 771, 763, 810, 792, 743])).
% 0.71/0.91 tff(818,assumption,(~c1_1(a764)), introduced(assumption)).
% 0.71/0.91 tff(819,plain,
% 0.71/0.91 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))))),
% 0.71/0.91 inference(bind,[status(th)],[])).
% 0.71/0.91 tff(820,plain,
% 0.71/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.71/0.91 inference(quant_intro,[status(thm)],[819])).
% 0.71/0.91 tff(821,plain,
% 0.71/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(822,plain,
% 0.71/0.91 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))))),
% 0.71/0.91 inference(bind,[status(th)],[])).
% 0.71/0.91 tff(823,plain,
% 0.71/0.91 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.71/0.91 inference(quant_intro,[status(thm)],[822])).
% 0.71/0.91 tff(824,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 0.71/0.91 tff(825,plain,
% 0.71/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[824, 823])).
% 0.71/0.91 tff(826,plain,
% 0.71/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[825, 821])).
% 0.71/0.91 tff(827,plain,(
% 0.71/0.91 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.71/0.91 inference(skolemize,[status(sab)],[826])).
% 0.71/0.91 tff(828,plain,
% 0.71/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[827, 820])).
% 0.71/0.91 tff(829,assumption,(~c3_1(a764)), introduced(assumption)).
% 0.71/0.91 tff(830,assumption,(hskp24), introduced(assumption)).
% 0.71/0.91 tff(831,plain,
% 0.71/0.91 (((~hskp24) | (~c3_1(a802))) <=> ((~hskp24) | (~c3_1(a802)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(832,plain,
% 0.71/0.91 (((~c3_1(a802)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a802)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(833,axiom,((~c3_1(a802)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.71/0.91 tff(834,plain,
% 0.71/0.91 ((~hskp24) | (~c3_1(a802))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[833, 832])).
% 0.71/0.91 tff(835,plain,
% 0.71/0.91 ((~hskp24) | (~c3_1(a802))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[834, 831])).
% 0.71/0.91 tff(836,plain,
% 0.71/0.91 (~c3_1(a802)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[835, 830])).
% 0.71/0.91 tff(837,plain,
% 0.71/0.91 (((~hskp24) | (~c2_1(a802))) <=> ((~hskp24) | (~c2_1(a802)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(838,plain,
% 0.71/0.91 (((~c2_1(a802)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a802)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(839,axiom,((~c2_1(a802)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 0.71/0.91 tff(840,plain,
% 0.71/0.91 ((~hskp24) | (~c2_1(a802))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[839, 838])).
% 0.71/0.91 tff(841,plain,
% 0.71/0.91 ((~hskp24) | (~c2_1(a802))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[840, 837])).
% 0.71/0.91 tff(842,plain,
% 0.71/0.91 (~c2_1(a802)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[841, 830])).
% 0.71/0.91 tff(843,assumption,(c2_1(a764)), introduced(assumption)).
% 0.71/0.91 tff(844,plain,
% 0.71/0.91 (((~hskp24) | c0_1(a802)) <=> ((~hskp24) | c0_1(a802))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(845,axiom,((~hskp24) | c0_1(a802)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 0.71/0.91 tff(846,plain,
% 0.71/0.91 ((~hskp24) | c0_1(a802)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[845, 844])).
% 0.71/0.91 tff(847,plain,
% 0.71/0.91 ((~hskp24) | c0_1(a802)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[846, 844])).
% 0.71/0.91 tff(848,plain,
% 0.71/0.91 ((~hskp24) | c0_1(a802)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[847, 844])).
% 0.71/0.91 tff(849,plain,
% 0.71/0.91 ((~hskp24) | c0_1(a802)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[848, 844])).
% 0.71/0.91 tff(850,plain,
% 0.71/0.91 ((~hskp24) | c0_1(a802)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[849, 844])).
% 0.71/0.91 tff(851,plain,
% 0.71/0.91 (c0_1(a802)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[850, 830])).
% 0.71/0.91 tff(852,plain,
% 0.71/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a802) | c3_1(a802) | c3_1(a764) | (~ndr1_0) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | c1_1(a764) | (~c2_1(a764)) | (~c0_1(a802)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a802) | c3_1(a802) | c3_1(a764) | (~ndr1_0) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | c1_1(a764) | (~c2_1(a764)) | (~c0_1(a802)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(853,plain,
% 0.71/0.91 (((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a802) | c2_1(a802) | (~c0_1(a802)) | c1_1(a764) | c3_1(a764) | (~c2_1(a764))) <=> (c2_1(a802) | c3_1(a802) | c3_1(a764) | (~ndr1_0) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | c1_1(a764) | (~c2_1(a764)) | (~c0_1(a802)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(854,plain,
% 0.71/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a802) | c2_1(a802) | (~c0_1(a802)) | c1_1(a764) | c3_1(a764) | (~c2_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a802) | c3_1(a802) | c3_1(a764) | (~ndr1_0) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | c1_1(a764) | (~c2_1(a764)) | (~c0_1(a802))))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[853])).
% 0.71/0.91 tff(855,plain,
% 0.71/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a802) | c2_1(a802) | (~c0_1(a802)) | c1_1(a764) | c3_1(a764) | (~c2_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a802) | c3_1(a802) | c3_1(a764) | (~ndr1_0) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | c1_1(a764) | (~c2_1(a764)) | (~c0_1(a802)))),
% 0.71/0.91 inference(transitivity,[status(thm)],[854, 852])).
% 0.71/0.91 tff(856,plain,
% 0.71/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a802) | c2_1(a802) | (~c0_1(a802)) | c1_1(a764) | c3_1(a764) | (~c2_1(a764)))),
% 0.71/0.91 inference(quant_inst,[status(thm)],[])).
% 0.71/0.91 tff(857,plain,
% 0.71/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a802) | c3_1(a802) | c3_1(a764) | (~ndr1_0) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | c1_1(a764) | (~c2_1(a764)) | (~c0_1(a802))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[856, 855])).
% 0.71/0.91 tff(858,plain,
% 0.71/0.91 ($false),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[857, 104, 744, 802, 801, 851, 843, 842, 836, 829, 828, 818])).
% 0.71/0.91 tff(859,plain,((~hskp24) | (~c0_1(a750)) | (~c1_1(a750)) | (~c2_1(a750)) | (~c2_1(a764)) | c3_1(a764) | c1_1(a764)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.91 tff(860,plain,
% 0.71/0.91 (~hskp24),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[859, 817, 802, 801, 800, 792, 744])).
% 0.71/0.91 tff(861,plain,
% 0.71/0.91 (((~![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(862,plain,
% 0.71/0.91 ((~![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)))),
% 0.71/0.91 inference(quant_inst,[status(thm)],[])).
% 0.71/0.91 tff(863,plain,
% 0.71/0.91 ((~![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[862, 861])).
% 0.71/0.91 tff(864,plain,
% 0.71/0.91 (hskp21),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[863, 104, 779, 771, 763, 467])).
% 0.71/0.91 tff(865,plain,
% 0.71/0.91 (~c2_1(a793)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[482, 864])).
% 0.71/0.91 tff(866,plain,
% 0.71/0.91 (c3_1(a793)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[492, 864])).
% 0.71/0.91 tff(867,plain,
% 0.71/0.91 (c0_1(a793)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[500, 864])).
% 0.71/0.91 tff(868,assumption,(hskp13), introduced(assumption)).
% 0.71/0.91 tff(869,plain,
% 0.71/0.91 (((~hskp13) | (~c1_1(a759))) <=> ((~hskp13) | (~c1_1(a759)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(870,plain,
% 0.71/0.91 (((~c1_1(a759)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a759)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(871,axiom,((~c1_1(a759)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 0.71/0.91 tff(872,plain,
% 0.71/0.91 ((~hskp13) | (~c1_1(a759))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[871, 870])).
% 0.71/0.91 tff(873,plain,
% 0.71/0.91 ((~hskp13) | (~c1_1(a759))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[872, 869])).
% 0.71/0.91 tff(874,plain,
% 0.71/0.91 (~c1_1(a759)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[873, 868])).
% 0.71/0.91 tff(875,assumption,(~c2_1(a793)), introduced(assumption)).
% 0.71/0.91 tff(876,plain,
% 0.71/0.91 (((~hskp13) | c3_1(a759)) <=> ((~hskp13) | c3_1(a759))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(877,axiom,((~hskp13) | c3_1(a759)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 0.71/0.91 tff(878,plain,
% 0.71/0.91 ((~hskp13) | c3_1(a759)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[877, 876])).
% 0.71/0.91 tff(879,plain,
% 0.71/0.91 ((~hskp13) | c3_1(a759)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[878, 876])).
% 0.71/0.91 tff(880,plain,
% 0.71/0.91 ((~hskp13) | c3_1(a759)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[879, 876])).
% 0.71/0.91 tff(881,plain,
% 0.71/0.91 ((~hskp13) | c3_1(a759)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[880, 876])).
% 0.71/0.91 tff(882,plain,
% 0.71/0.91 ((~hskp13) | c3_1(a759)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[881, 876])).
% 0.71/0.91 tff(883,plain,
% 0.71/0.91 (c3_1(a759)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[882, 868])).
% 0.71/0.91 tff(884,plain,
% 0.71/0.91 (((~hskp13) | c2_1(a759)) <=> ((~hskp13) | c2_1(a759))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(885,axiom,((~hskp13) | c2_1(a759)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 0.71/0.91 tff(886,plain,
% 0.71/0.91 ((~hskp13) | c2_1(a759)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[885, 884])).
% 0.71/0.91 tff(887,plain,
% 0.71/0.91 ((~hskp13) | c2_1(a759)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[886, 884])).
% 0.71/0.91 tff(888,plain,
% 0.71/0.91 ((~hskp13) | c2_1(a759)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[887, 884])).
% 0.71/0.91 tff(889,plain,
% 0.71/0.91 ((~hskp13) | c2_1(a759)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[888, 884])).
% 0.71/0.91 tff(890,plain,
% 0.71/0.91 ((~hskp13) | c2_1(a759)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[889, 884])).
% 0.71/0.91 tff(891,plain,
% 0.71/0.91 (c2_1(a759)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[890, 868])).
% 0.71/0.91 tff(892,assumption,(c3_1(a793)), introduced(assumption)).
% 0.71/0.91 tff(893,assumption,(c0_1(a793)), introduced(assumption)).
% 0.71/0.91 tff(894,plain,
% 0.71/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a793) | c1_1(a759) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | (~c2_1(a759)) | (~c3_1(a759)) | (~c3_1(a793)) | (~c0_1(a793)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a793) | c1_1(a759) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | (~c2_1(a759)) | (~c3_1(a759)) | (~c3_1(a793)) | (~c0_1(a793)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(895,plain,
% 0.71/0.91 (((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a759) | (~c2_1(a759)) | (~c3_1(a759)) | c0_1(a741) | (~c3_1(a741)) | (~c2_1(a741))) <=> (c2_1(a793) | c1_1(a759) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | (~c2_1(a759)) | (~c3_1(a759)) | (~c3_1(a793)) | (~c0_1(a793)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(896,plain,
% 0.71/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a759) | (~c2_1(a759)) | (~c3_1(a759)) | c0_1(a741) | (~c3_1(a741)) | (~c2_1(a741)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a793) | c1_1(a759) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | (~c2_1(a759)) | (~c3_1(a759)) | (~c3_1(a793)) | (~c0_1(a793))))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[895])).
% 0.71/0.91 tff(897,plain,
% 0.71/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a759) | (~c2_1(a759)) | (~c3_1(a759)) | c0_1(a741) | (~c3_1(a741)) | (~c2_1(a741)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a793) | c1_1(a759) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | (~c2_1(a759)) | (~c3_1(a759)) | (~c3_1(a793)) | (~c0_1(a793)))),
% 0.71/0.91 inference(transitivity,[status(thm)],[896, 894])).
% 0.71/0.91 tff(898,plain,
% 0.71/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a759) | (~c2_1(a759)) | (~c3_1(a759)) | c0_1(a741) | (~c3_1(a741)) | (~c2_1(a741)))),
% 0.71/0.92 inference(quant_inst,[status(thm)],[])).
% 0.71/0.92 tff(899,plain,
% 0.71/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a793) | c1_1(a759) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | (~c2_1(a759)) | (~c3_1(a759)) | (~c3_1(a793)) | (~c0_1(a793))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[898, 897])).
% 0.71/0.92 tff(900,plain,
% 0.71/0.92 ($false),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[899, 104, 893, 892, 891, 883, 178, 875, 874, 177, 455, 561])).
% 0.71/0.92 tff(901,plain,((~hskp13) | (~c0_1(a793)) | (~c3_1(a793)) | (~c3_1(a741)) | c2_1(a793) | c0_1(a741) | (~c2_1(a741))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.92 tff(902,plain,
% 0.71/0.92 (~hskp13),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[901, 867, 866, 178, 865, 177, 561])).
% 0.71/0.92 tff(903,plain,
% 0.71/0.92 (hskp23),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[102, 902, 860])).
% 0.71/0.92 tff(904,plain,
% 0.71/0.92 (((~hskp23) | (~c3_1(a798))) <=> ((~hskp23) | (~c3_1(a798)))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(905,plain,
% 0.71/0.92 (((~c3_1(a798)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a798)))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(906,axiom,((~c3_1(a798)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 0.71/0.92 tff(907,plain,
% 0.71/0.92 ((~hskp23) | (~c3_1(a798))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[906, 905])).
% 0.71/0.92 tff(908,plain,
% 0.71/0.92 ((~hskp23) | (~c3_1(a798))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[907, 904])).
% 0.71/0.92 tff(909,plain,
% 0.71/0.92 (~c3_1(a798)),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[908, 903])).
% 0.71/0.92 tff(910,plain,
% 0.71/0.92 (((~hskp23) | c1_1(a798)) <=> ((~hskp23) | c1_1(a798))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(911,axiom,((~hskp23) | c1_1(a798)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 0.71/0.92 tff(912,plain,
% 0.71/0.92 ((~hskp23) | c1_1(a798)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[911, 910])).
% 0.71/0.92 tff(913,plain,
% 0.71/0.92 ((~hskp23) | c1_1(a798)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[912, 910])).
% 0.71/0.92 tff(914,plain,
% 0.71/0.92 ((~hskp23) | c1_1(a798)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[913, 910])).
% 0.71/0.92 tff(915,plain,
% 0.71/0.92 ((~hskp23) | c1_1(a798)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[914, 910])).
% 0.71/0.92 tff(916,plain,
% 0.71/0.92 ((~hskp23) | c1_1(a798)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[915, 910])).
% 0.71/0.92 tff(917,plain,
% 0.71/0.92 (c1_1(a798)),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[916, 903])).
% 0.71/0.92 tff(918,plain,
% 0.71/0.92 (((~hskp23) | c0_1(a798)) <=> ((~hskp23) | c0_1(a798))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(919,axiom,((~hskp23) | c0_1(a798)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 0.71/0.92 tff(920,plain,
% 0.71/0.92 ((~hskp23) | c0_1(a798)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[919, 918])).
% 0.71/0.92 tff(921,plain,
% 0.71/0.92 ((~hskp23) | c0_1(a798)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[920, 918])).
% 0.71/0.92 tff(922,plain,
% 0.71/0.92 ((~hskp23) | c0_1(a798)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[921, 918])).
% 0.71/0.92 tff(923,plain,
% 0.71/0.92 ((~hskp23) | c0_1(a798)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[922, 918])).
% 0.71/0.92 tff(924,plain,
% 0.71/0.92 ((~hskp23) | c0_1(a798)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[923, 918])).
% 0.71/0.92 tff(925,plain,
% 0.71/0.92 (c0_1(a798)),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[924, 903])).
% 0.71/0.92 tff(926,plain,
% 0.71/0.92 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | c3_1(a798) | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | (~c0_1(a798)) | (~c1_1(a798)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp1 | c3_1(a798) | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | (~c0_1(a798)) | (~c1_1(a798)))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(927,plain,
% 0.71/0.92 ((hskp1 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c3_1(a798) | (~c1_1(a798)) | (~c0_1(a798))) <=> (hskp1 | c3_1(a798) | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | (~c0_1(a798)) | (~c1_1(a798)))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(928,plain,
% 0.71/0.92 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c3_1(a798) | (~c1_1(a798)) | (~c0_1(a798)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | c3_1(a798) | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | (~c0_1(a798)) | (~c1_1(a798))))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[927])).
% 0.71/0.92 tff(929,plain,
% 0.71/0.92 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c3_1(a798) | (~c1_1(a798)) | (~c0_1(a798)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp1 | c3_1(a798) | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | (~c0_1(a798)) | (~c1_1(a798)))),
% 0.71/0.92 inference(transitivity,[status(thm)],[928, 926])).
% 0.71/0.92 tff(930,plain,
% 0.71/0.92 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c3_1(a798) | (~c1_1(a798)) | (~c0_1(a798)))),
% 0.71/0.92 inference(quant_inst,[status(thm)],[])).
% 0.71/0.92 tff(931,plain,
% 0.71/0.92 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp1 | c3_1(a798) | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | (~c0_1(a798)) | (~c1_1(a798))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[930, 929])).
% 0.71/0.92 tff(932,plain,
% 0.71/0.92 ($false),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[931, 104, 255, 779, 771, 763, 925, 917, 909, 743])).
% 0.71/0.92 tff(933,plain,((~hskp25) | hskp1 | (~c3_1(a741)) | c0_1(a741) | (~c2_1(a741)) | (~c1_1(a750)) | (~c2_1(a750)) | (~c0_1(a750)) | (~c1_1(a741))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.92 tff(934,plain,
% 0.71/0.92 (~hskp25),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[933, 130, 158, 164, 216, 733, 725, 717, 150])).
% 0.71/0.92 tff(935,plain,
% 0.71/0.92 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | c1_1(a734) | c0_1(a734) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a734))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c1_1(a734) | c0_1(a734) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a734))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(936,plain,
% 0.71/0.92 ((hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a734) | c0_1(a734) | c2_1(a734)) <=> (hskp25 | c1_1(a734) | c0_1(a734) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a734))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(937,plain,
% 0.71/0.92 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a734) | c0_1(a734) | c2_1(a734))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | c1_1(a734) | c0_1(a734) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a734)))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[936])).
% 0.71/0.92 tff(938,plain,
% 0.71/0.92 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a734) | c0_1(a734) | c2_1(a734))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c1_1(a734) | c0_1(a734) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a734))),
% 0.71/0.92 inference(transitivity,[status(thm)],[937, 935])).
% 0.71/0.92 tff(939,plain,
% 0.71/0.92 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a734) | c0_1(a734) | c2_1(a734))),
% 0.71/0.92 inference(quant_inst,[status(thm)],[])).
% 0.71/0.92 tff(940,plain,
% 0.71/0.92 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c1_1(a734) | c0_1(a734) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a734)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[939, 938])).
% 0.71/0.92 tff(941,plain,
% 0.71/0.92 (hskp25 | c2_1(a734)),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[940, 104, 44, 444, 436, 22, 385, 20])).
% 0.71/0.92 tff(942,plain,
% 0.71/0.92 (c2_1(a734)),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[941, 934])).
% 0.71/0.92 tff(943,plain,
% 0.71/0.92 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.71/0.92 inference(bind,[status(th)],[])).
% 0.71/0.92 tff(944,plain,
% 0.71/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.92 inference(quant_intro,[status(thm)],[943])).
% 0.71/0.92 tff(945,plain,
% 0.71/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(946,plain,
% 0.71/0.92 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.71/0.92 inference(bind,[status(th)],[])).
% 0.71/0.92 tff(947,plain,
% 0.71/0.92 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_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)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.92 inference(quant_intro,[status(thm)],[946])).
% 0.71/0.92 tff(948,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 0.71/0.92 tff(949,plain,
% 0.71/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[948, 947])).
% 0.71/0.92 tff(950,plain,
% 0.71/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[949, 945])).
% 0.71/0.92 tff(951,plain,(
% 0.71/0.92 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.92 inference(skolemize,[status(sab)],[950])).
% 0.71/0.92 tff(952,plain,
% 0.71/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[951, 944])).
% 0.71/0.92 tff(953,plain,
% 0.71/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a734) | c3_1(a734) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | c1_1(a732) | (~c2_1(a734)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a734) | c3_1(a734) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | c1_1(a732) | (~c2_1(a734)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(954,plain,
% 0.71/0.92 (((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a734) | c0_1(a734) | (~c2_1(a734)) | c2_1(a732) | c1_1(a732) | c0_1(a732)) <=> (c0_1(a734) | c3_1(a734) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | c1_1(a732) | (~c2_1(a734)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(955,plain,
% 0.71/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a734) | c0_1(a734) | (~c2_1(a734)) | c2_1(a732) | c1_1(a732) | c0_1(a732))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a734) | c3_1(a734) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | c1_1(a732) | (~c2_1(a734)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750))))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[954])).
% 0.71/0.92 tff(956,plain,
% 0.71/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a734) | c0_1(a734) | (~c2_1(a734)) | c2_1(a732) | c1_1(a732) | c0_1(a732))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a734) | c3_1(a734) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | c1_1(a732) | (~c2_1(a734)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)))),
% 0.71/0.92 inference(transitivity,[status(thm)],[955, 953])).
% 0.71/0.92 tff(957,plain,
% 0.71/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a734) | c0_1(a734) | (~c2_1(a734)) | c2_1(a732) | c1_1(a732) | c0_1(a732))),
% 0.71/0.92 inference(quant_inst,[status(thm)],[])).
% 0.71/0.92 tff(958,plain,
% 0.71/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a734) | c3_1(a734) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | c1_1(a732) | (~c2_1(a734)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[957, 956])).
% 0.71/0.92 tff(959,plain,
% 0.71/0.92 (c1_1(a732) | (~c2_1(a734))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[958, 104, 717, 733, 725, 22, 33, 549, 548, 952])).
% 0.71/0.92 tff(960,plain,
% 0.71/0.92 (c1_1(a732)),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[959, 942])).
% 0.71/0.92 tff(961,plain,
% 0.71/0.92 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.71/0.92 inference(bind,[status(th)],[])).
% 0.71/0.92 tff(962,plain,
% 0.71/0.92 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.71/0.92 inference(quant_intro,[status(thm)],[961])).
% 0.71/0.92 tff(963,plain,
% 0.71/0.92 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(964,plain,
% 0.71/0.92 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp10))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.71/0.92 inference(bind,[status(th)],[])).
% 0.71/0.92 tff(965,plain,
% 0.71/0.92 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.71/0.92 inference(quant_intro,[status(thm)],[964])).
% 0.71/0.92 tff(966,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 0.71/0.92 tff(967,plain,
% 0.71/0.92 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[966, 965])).
% 0.71/0.92 tff(968,plain,
% 0.71/0.92 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[967, 963])).
% 0.71/0.92 tff(969,plain,(
% 0.71/0.92 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.71/0.92 inference(skolemize,[status(sab)],[968])).
% 0.71/0.92 tff(970,plain,
% 0.71/0.92 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[969, 962])).
% 0.71/0.92 tff(971,plain,
% 0.71/0.92 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a741) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | (~c1_1(a732)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a741) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | (~c1_1(a732)))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(972,plain,
% 0.71/0.92 ((hskp10 | (~ndr1_0) | c0_1(a741) | (~c2_1(a741)) | (~c3_1(a741)) | c0_1(a732) | c2_1(a732) | (~c1_1(a732))) <=> (hskp10 | c0_1(a741) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | (~c1_1(a732)))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(973,plain,
% 0.71/0.92 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a741) | (~c2_1(a741)) | (~c3_1(a741)) | c0_1(a732) | c2_1(a732) | (~c1_1(a732)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a741) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | (~c1_1(a732))))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[972])).
% 0.71/0.92 tff(974,plain,
% 0.71/0.92 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a741) | (~c2_1(a741)) | (~c3_1(a741)) | c0_1(a732) | c2_1(a732) | (~c1_1(a732)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a741) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | (~c1_1(a732)))),
% 0.71/0.92 inference(transitivity,[status(thm)],[973, 971])).
% 0.71/0.92 tff(975,plain,
% 0.71/0.92 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a741) | (~c2_1(a741)) | (~c3_1(a741)) | c0_1(a732) | c2_1(a732) | (~c1_1(a732)))),
% 0.71/0.92 inference(quant_inst,[status(thm)],[])).
% 0.71/0.92 tff(976,plain,
% 0.71/0.92 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a741) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | (~c1_1(a732))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[975, 974])).
% 0.71/0.92 tff(977,plain,
% 0.71/0.92 (hskp10 | (~c1_1(a732))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[976, 104, 158, 164, 549, 548, 970, 216])).
% 0.71/0.92 tff(978,plain,
% 0.71/0.92 (hskp10),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[977, 960])).
% 0.71/0.92 tff(979,plain,
% 0.71/0.92 (((~hskp10) | (~c2_1(a748))) <=> ((~hskp10) | (~c2_1(a748)))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(980,plain,
% 0.71/0.92 (((~c2_1(a748)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a748)))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(981,axiom,((~c2_1(a748)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 0.71/0.92 tff(982,plain,
% 0.71/0.92 ((~hskp10) | (~c2_1(a748))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[981, 980])).
% 0.71/0.92 tff(983,plain,
% 0.71/0.92 ((~hskp10) | (~c2_1(a748))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[982, 979])).
% 0.71/0.92 tff(984,plain,
% 0.71/0.92 (~c2_1(a748)),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[983, 978])).
% 0.71/0.92 tff(985,plain,
% 0.71/0.92 (((~hskp10) | (~c1_1(a748))) <=> ((~hskp10) | (~c1_1(a748)))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(986,plain,
% 0.71/0.92 (((~c1_1(a748)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a748)))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(987,axiom,((~c1_1(a748)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 0.71/0.92 tff(988,plain,
% 0.71/0.92 ((~hskp10) | (~c1_1(a748))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[987, 986])).
% 0.71/0.92 tff(989,plain,
% 0.71/0.92 ((~hskp10) | (~c1_1(a748))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[988, 985])).
% 0.71/0.92 tff(990,plain,
% 0.71/0.92 (~c1_1(a748)),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[989, 978])).
% 0.71/0.92 tff(991,plain,
% 0.71/0.92 (((~hskp10) | (~c0_1(a748))) <=> ((~hskp10) | (~c0_1(a748)))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(992,plain,
% 0.71/0.92 (((~c0_1(a748)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a748)))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(993,axiom,((~c0_1(a748)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 0.71/0.92 tff(994,plain,
% 0.71/0.92 ((~hskp10) | (~c0_1(a748))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[993, 992])).
% 0.71/0.92 tff(995,plain,
% 0.71/0.92 ((~hskp10) | (~c0_1(a748))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[994, 991])).
% 0.71/0.92 tff(996,plain,
% 0.71/0.92 (~c0_1(a748)),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[995, 978])).
% 0.71/0.92 tff(997,plain,
% 0.71/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a748) | c1_1(a748) | c2_1(a748) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a748) | c1_1(a748) | c2_1(a748) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(998,plain,
% 0.71/0.92 (((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a734) | c0_1(a734) | (~c2_1(a734)) | c2_1(a748) | c1_1(a748) | c0_1(a748)) <=> (c0_1(a748) | c1_1(a748) | c2_1(a748) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(999,plain,
% 0.71/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a734) | c0_1(a734) | (~c2_1(a734)) | c2_1(a748) | c1_1(a748) | c0_1(a748))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a748) | c1_1(a748) | c2_1(a748) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750))))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[998])).
% 0.71/0.92 tff(1000,plain,
% 0.71/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a734) | c0_1(a734) | (~c2_1(a734)) | c2_1(a748) | c1_1(a748) | c0_1(a748))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a748) | c1_1(a748) | c2_1(a748) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)))),
% 0.71/0.92 inference(transitivity,[status(thm)],[999, 997])).
% 0.71/0.92 tff(1001,plain,
% 0.71/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a734) | c0_1(a734) | (~c2_1(a734)) | c2_1(a748) | c1_1(a748) | c0_1(a748))),
% 0.71/0.92 inference(quant_inst,[status(thm)],[])).
% 0.71/0.92 tff(1002,plain,
% 0.71/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a748) | c1_1(a748) | c2_1(a748) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[1001, 1000])).
% 0.71/0.92 tff(1003,plain,
% 0.71/0.92 ($false),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1002, 104, 717, 733, 725, 996, 990, 984, 22, 33, 952, 942])).
% 0.71/0.92 tff(1004,plain,(c1_1(a734) | c0_1(a734) | c3_1(a734) | hskp11), inference(lemma,lemma(discharge,[]))).
% 0.71/0.92 tff(1005,plain,
% 0.71/0.92 (c1_1(a734)),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1004, 33, 22, 21])).
% 0.71/0.92 tff(1006,assumption,(c1_1(a734)), introduced(assumption)).
% 0.71/0.92 tff(1007,plain,
% 0.71/0.92 (hskp0 | hskp9 | c3_1(a734) | (~c1_1(a734))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[321, 104, 22, 315])).
% 0.71/0.92 tff(1008,plain,
% 0.71/0.92 (hskp9),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1007, 217, 1006, 33])).
% 0.71/0.92 tff(1009,plain,
% 0.71/0.92 (~c2_1(a746)),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[328, 1008])).
% 0.71/0.92 tff(1010,plain,
% 0.71/0.92 (~c0_1(a746)),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[334, 1008])).
% 0.71/0.92 tff(1011,plain,
% 0.71/0.92 (c3_1(a746)),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[342, 1008])).
% 0.71/0.92 tff(1012,plain,
% 0.71/0.92 (~c1_1(a746)),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[349, 104, 1011, 1010, 1009, 121])).
% 0.71/0.92 tff(1013,plain,
% 0.71/0.92 ($false),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[366, 217, 104, 255, 1010, 1009, 236, 1012])).
% 0.71/0.92 tff(1014,plain,(hskp0 | hskp1 | (~c1_1(a734)) | c3_1(a734) | c0_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.92 tff(1015,plain,
% 0.71/0.92 (hskp0),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1014, 255, 1005, 33, 22])).
% 0.71/0.92 tff(1016,plain,
% 0.71/0.92 (~c1_1(a730)),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[384, 1015])).
% 0.71/0.92 tff(1017,assumption,(~c1_1(a741)), introduced(assumption)).
% 0.71/0.92 tff(1018,plain,
% 0.71/0.92 (~hskp7),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[149, 1017])).
% 0.71/0.92 tff(1019,plain,
% 0.71/0.92 (^[U: $i] : refl((hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 0.71/0.93 inference(bind,[status(th)],[])).
% 0.71/0.93 tff(1020,plain,
% 0.71/0.93 (![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.71/0.93 inference(quant_intro,[status(thm)],[1019])).
% 0.71/0.93 tff(1021,plain,
% 0.71/0.93 (![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.71/0.93 inference(rewrite,[status(thm)],[])).
% 0.71/0.93 tff(1022,plain,
% 0.71/0.93 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp12) | hskp7) <=> ((hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp7))), rewrite(((hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp7) <=> (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp12) | hskp7) <=> (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 0.71/0.93 inference(bind,[status(th)],[])).
% 0.71/0.93 tff(1023,plain,
% 0.71/0.93 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp12) | hskp7) <=> ![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.71/0.93 inference(quant_intro,[status(thm)],[1022])).
% 0.71/0.93 tff(1024,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp12) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 0.71/0.93 tff(1025,plain,
% 0.71/0.93 (![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[1024, 1023])).
% 0.71/0.93 tff(1026,plain,
% 0.71/0.93 (![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[1025, 1021])).
% 0.71/0.93 tff(1027,plain,(
% 0.71/0.93 ![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.71/0.93 inference(skolemize,[status(sab)],[1026])).
% 0.71/0.93 tff(1028,plain,
% 0.71/0.93 (![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[1027, 1020])).
% 0.71/0.93 tff(1029,assumption,(~hskp7), introduced(assumption)).
% 0.71/0.93 tff(1030,assumption,(~hskp12), introduced(assumption)).
% 0.71/0.93 tff(1031,plain,
% 0.71/0.93 (hskp1),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[141, 52, 1029])).
% 0.71/0.93 tff(1032,plain,
% 0.71/0.93 (c3_1(a731)),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[66, 1031])).
% 0.71/0.93 tff(1033,assumption,(~c2_1(a731)), introduced(assumption)).
% 0.71/0.93 tff(1034,plain,
% 0.71/0.93 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | c0_1(a731))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp7 | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | c0_1(a731))),
% 0.71/0.93 inference(rewrite,[status(thm)],[])).
% 0.71/0.93 tff(1035,plain,
% 0.71/0.93 ((hskp12 | hskp7 | (~ndr1_0) | c2_1(a731) | c0_1(a731) | (~c3_1(a731))) <=> (hskp12 | hskp7 | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | c0_1(a731))),
% 0.71/0.93 inference(rewrite,[status(thm)],[])).
% 0.71/0.93 tff(1036,plain,
% 0.71/0.93 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c2_1(a731) | c0_1(a731) | (~c3_1(a731)))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | c0_1(a731)))),
% 0.71/0.93 inference(monotonicity,[status(thm)],[1035])).
% 0.71/0.93 tff(1037,plain,
% 0.71/0.93 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c2_1(a731) | c0_1(a731) | (~c3_1(a731)))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp7 | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | c0_1(a731))),
% 0.71/0.93 inference(transitivity,[status(thm)],[1036, 1034])).
% 0.71/0.93 tff(1038,plain,
% 0.71/0.93 ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c2_1(a731) | c0_1(a731) | (~c3_1(a731)))),
% 0.71/0.93 inference(quant_inst,[status(thm)],[])).
% 0.71/0.93 tff(1039,plain,
% 0.71/0.93 ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp7 | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | c0_1(a731)),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 0.71/0.93 tff(1040,plain,
% 0.71/0.93 ((~c3_1(a731)) | c0_1(a731)),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[1039, 104, 1030, 1029, 1033, 1028])).
% 0.71/0.93 tff(1041,plain,
% 0.71/0.93 (c0_1(a731)),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[1040, 1032])).
% 0.71/0.93 tff(1042,plain,
% 0.71/0.93 (c1_1(a731)),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[74, 1031])).
% 0.71/0.93 tff(1043,plain,
% 0.71/0.93 ($false),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[110, 104, 44, 1042, 1032, 22, 33, 1033, 10, 1041])).
% 0.71/0.93 tff(1044,plain,(c1_1(a734) | c0_1(a734) | c3_1(a734) | c2_1(a731) | hskp12 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.71/0.93 tff(1045,plain,
% 0.71/0.93 (c2_1(a731)),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[1044, 44, 33, 22, 1030, 1029])).
% 0.71/0.93 tff(1046,plain,
% 0.71/0.93 ($false),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[58, 1031, 1045])).
% 0.71/0.93 tff(1047,plain,(c1_1(a734) | hskp7 | c3_1(a734) | c0_1(a734) | hskp12), inference(lemma,lemma(discharge,[]))).
% 0.71/0.93 tff(1048,plain,
% 0.71/0.93 (c1_1(a734)),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[1047, 22, 1029, 33, 1030])).
% 0.71/0.93 tff(1049,assumption,(hskp9), introduced(assumption)).
% 0.71/0.93 tff(1050,plain,
% 0.71/0.93 (~c2_1(a746)),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[328, 1049])).
% 0.71/0.93 tff(1051,plain,
% 0.71/0.93 (~c0_1(a746)),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[334, 1049])).
% 0.71/0.93 tff(1052,plain,
% 0.71/0.93 (c3_1(a746)),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[342, 1049])).
% 0.71/0.93 tff(1053,plain,
% 0.71/0.93 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | c0_1(a746) | c2_1(a746) | (~ndr1_0) | (~c3_1(a746)))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp7 | c0_1(a746) | c2_1(a746) | (~ndr1_0) | (~c3_1(a746)))),
% 0.71/0.93 inference(rewrite,[status(thm)],[])).
% 0.71/0.93 tff(1054,plain,
% 0.71/0.93 ((hskp12 | hskp7 | (~ndr1_0) | c2_1(a746) | c0_1(a746) | (~c3_1(a746))) <=> (hskp12 | hskp7 | c0_1(a746) | c2_1(a746) | (~ndr1_0) | (~c3_1(a746)))),
% 0.71/0.93 inference(rewrite,[status(thm)],[])).
% 0.71/0.93 tff(1055,plain,
% 0.71/0.93 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c2_1(a746) | c0_1(a746) | (~c3_1(a746)))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | c0_1(a746) | c2_1(a746) | (~ndr1_0) | (~c3_1(a746))))),
% 0.71/0.93 inference(monotonicity,[status(thm)],[1054])).
% 0.71/0.93 tff(1056,plain,
% 0.71/0.93 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c2_1(a746) | c0_1(a746) | (~c3_1(a746)))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp7 | c0_1(a746) | c2_1(a746) | (~ndr1_0) | (~c3_1(a746)))),
% 0.71/0.93 inference(transitivity,[status(thm)],[1055, 1053])).
% 0.71/0.93 tff(1057,plain,
% 0.71/0.93 ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c2_1(a746) | c0_1(a746) | (~c3_1(a746)))),
% 0.71/0.93 inference(quant_inst,[status(thm)],[])).
% 0.71/0.93 tff(1058,plain,
% 0.71/0.93 ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp7 | c0_1(a746) | c2_1(a746) | (~ndr1_0) | (~c3_1(a746))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[1057, 1056])).
% 0.71/0.93 tff(1059,plain,
% 0.71/0.93 ($false),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[1058, 104, 1030, 1029, 1052, 1051, 1050, 1028])).
% 0.71/0.93 tff(1060,plain,((~hskp9) | hskp12 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.71/0.93 tff(1061,plain,
% 0.71/0.93 (~hskp9),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[1060, 1029, 1030])).
% 0.71/0.93 tff(1062,plain,
% 0.71/0.93 (hskp0 | c0_1(a734) | (~c1_1(a734))),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[321, 104, 1061, 33, 315])).
% 0.71/0.93 tff(1063,plain,
% 0.71/0.93 (hskp0),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[1062, 1048, 22])).
% 0.71/0.93 tff(1064,plain,
% 0.71/0.93 (c0_1(a730)),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[443, 1063])).
% 0.71/0.93 tff(1065,plain,
% 0.71/0.93 (~c1_1(a730)),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[384, 1063])).
% 0.71/0.93 tff(1066,plain,
% 0.71/0.93 (^[U: $i] : refl((hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.71/0.93 inference(bind,[status(th)],[])).
% 0.71/0.93 tff(1067,plain,
% 0.71/0.93 (![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.71/0.93 inference(quant_intro,[status(thm)],[1066])).
% 0.71/0.93 tff(1068,plain,
% 0.71/0.93 (![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.71/0.93 inference(rewrite,[status(thm)],[])).
% 0.71/0.93 tff(1069,plain,
% 0.71/0.93 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp18))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp11) <=> ((hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp11))), rewrite(((hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp11) <=> (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp11) <=> (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.71/0.93 inference(bind,[status(th)],[])).
% 0.71/0.93 tff(1070,plain,
% 0.71/0.93 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp11) <=> ![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.71/0.93 inference(quant_intro,[status(thm)],[1069])).
% 0.71/0.93 tff(1071,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 0.71/0.93 tff(1072,plain,
% 0.71/0.93 (![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[1071, 1070])).
% 0.71/0.93 tff(1073,plain,
% 0.71/0.93 (![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[1072, 1068])).
% 0.71/0.93 tff(1074,plain,(
% 0.71/0.93 ![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.71/0.93 inference(skolemize,[status(sab)],[1073])).
% 0.71/0.93 tff(1075,plain,
% 0.71/0.93 (![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[1074, 1067])).
% 0.71/0.93 tff(1076,plain,
% 0.71/0.93 (^[U: $i] : refl((hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 0.71/0.93 inference(bind,[status(th)],[])).
% 0.71/0.93 tff(1077,plain,
% 0.71/0.93 (![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.71/0.93 inference(quant_intro,[status(thm)],[1076])).
% 0.71/0.93 tff(1078,plain,
% 0.71/0.93 (![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.71/0.93 inference(rewrite,[status(thm)],[])).
% 0.71/0.93 tff(1079,plain,
% 0.71/0.93 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp9) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp9))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp9) <=> (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp9) <=> (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 0.71/0.93 inference(bind,[status(th)],[])).
% 0.71/0.93 tff(1080,plain,
% 0.71/0.93 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp9) <=> ![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.71/0.93 inference(quant_intro,[status(thm)],[1079])).
% 0.71/0.93 tff(1081,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 0.71/0.93 tff(1082,plain,
% 0.71/0.93 (![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[1081, 1080])).
% 0.71/0.93 tff(1083,plain,
% 0.71/0.93 (![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[1082, 1078])).
% 0.71/0.93 tff(1084,plain,(
% 0.71/0.93 ![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.71/0.93 inference(skolemize,[status(sab)],[1083])).
% 0.71/0.93 tff(1085,plain,
% 0.71/0.93 (![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[1084, 1077])).
% 0.71/0.93 tff(1086,plain,
% 0.71/0.93 (((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | c2_1(a734))) <=> ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp5 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | c2_1(a734))),
% 0.71/0.93 inference(rewrite,[status(thm)],[])).
% 0.71/0.93 tff(1087,plain,
% 0.71/0.93 ((hskp9 | hskp5 | (~ndr1_0) | c2_1(a734) | c0_1(a734) | c3_1(a734)) <=> (hskp9 | hskp5 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | c2_1(a734))),
% 0.71/0.93 inference(rewrite,[status(thm)],[])).
% 0.71/0.93 tff(1088,plain,
% 0.71/0.93 (((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | (~ndr1_0) | c2_1(a734) | c0_1(a734) | c3_1(a734))) <=> ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | c2_1(a734)))),
% 0.71/0.93 inference(monotonicity,[status(thm)],[1087])).
% 0.71/0.93 tff(1089,plain,
% 0.71/0.93 (((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | (~ndr1_0) | c2_1(a734) | c0_1(a734) | c3_1(a734))) <=> ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp5 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | c2_1(a734))),
% 0.71/0.93 inference(transitivity,[status(thm)],[1088, 1086])).
% 0.71/0.93 tff(1090,plain,
% 0.71/0.93 ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | (~ndr1_0) | c2_1(a734) | c0_1(a734) | c3_1(a734))),
% 0.71/0.93 inference(quant_inst,[status(thm)],[])).
% 0.71/0.93 tff(1091,plain,
% 0.71/0.93 ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp5 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | c2_1(a734)),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[1090, 1089])).
% 0.71/0.93 tff(1092,plain,
% 0.71/0.93 (hskp5 | c0_1(a734) | c2_1(a734)),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[1091, 104, 1061, 33, 1085])).
% 0.71/0.93 tff(1093,plain,
% 0.71/0.93 (c2_1(a734)),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[1092, 396, 22])).
% 0.71/0.93 tff(1094,assumption,(~c0_1(a744)), introduced(assumption)).
% 0.71/0.93 tff(1095,assumption,(~c1_1(a744)), introduced(assumption)).
% 0.71/0.93 tff(1096,assumption,(~c3_1(a744)), introduced(assumption)).
% 0.71/0.93 tff(1097,plain,
% 0.71/0.93 (c0_1(a731)),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[1039, 104, 1030, 1029, 67, 59, 1028])).
% 0.71/0.93 tff(1098,plain,
% 0.71/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a744) | c0_1(a744) | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c3_1(a744) | c0_1(a744) | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)))),
% 0.71/0.93 inference(rewrite,[status(thm)],[])).
% 0.71/0.93 tff(1099,plain,
% 0.71/0.93 (((~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c1_1(a744) | c0_1(a744) | c3_1(a744)) <=> (c3_1(a744) | c0_1(a744) | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)))),
% 0.71/0.93 inference(rewrite,[status(thm)],[])).
% 0.71/0.93 tff(1100,plain,
% 0.71/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c1_1(a744) | c0_1(a744) | c3_1(a744))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a744) | c0_1(a744) | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731))))),
% 0.71/0.93 inference(monotonicity,[status(thm)],[1099])).
% 0.71/0.93 tff(1101,plain,
% 0.71/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c1_1(a744) | c0_1(a744) | c3_1(a744))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c3_1(a744) | c0_1(a744) | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)))),
% 0.71/0.93 inference(transitivity,[status(thm)],[1100, 1098])).
% 0.71/0.93 tff(1102,plain,
% 0.71/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c1_1(a744) | c0_1(a744) | c3_1(a744))),
% 0.71/0.93 inference(quant_inst,[status(thm)],[])).
% 0.71/0.93 tff(1103,plain,
% 0.71/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c3_1(a744) | c0_1(a744) | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[1102, 1101])).
% 0.71/0.93 tff(1104,plain,
% 0.71/0.93 (c3_1(a744) | (~c0_1(a731))),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[1103, 104, 75, 67, 1094, 1095, 59, 10])).
% 0.77/0.93 tff(1105,plain,
% 0.77/0.93 (c3_1(a744)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1104, 1097])).
% 0.77/0.93 tff(1106,plain,
% 0.77/0.93 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | c0_1(a744) | (~ndr1_0) | c2_1(a744) | (~c3_1(a744)))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp7 | c0_1(a744) | (~ndr1_0) | c2_1(a744) | (~c3_1(a744)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1107,plain,
% 0.77/0.93 ((hskp12 | hskp7 | (~ndr1_0) | c2_1(a744) | c0_1(a744) | (~c3_1(a744))) <=> (hskp12 | hskp7 | c0_1(a744) | (~ndr1_0) | c2_1(a744) | (~c3_1(a744)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1108,plain,
% 0.77/0.93 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c2_1(a744) | c0_1(a744) | (~c3_1(a744)))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | c0_1(a744) | (~ndr1_0) | c2_1(a744) | (~c3_1(a744))))),
% 0.77/0.93 inference(monotonicity,[status(thm)],[1107])).
% 0.77/0.93 tff(1109,plain,
% 0.77/0.93 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c2_1(a744) | c0_1(a744) | (~c3_1(a744)))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp7 | c0_1(a744) | (~ndr1_0) | c2_1(a744) | (~c3_1(a744)))),
% 0.77/0.93 inference(transitivity,[status(thm)],[1108, 1106])).
% 0.77/0.93 tff(1110,plain,
% 0.77/0.93 ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c2_1(a744) | c0_1(a744) | (~c3_1(a744)))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(1111,plain,
% 0.77/0.93 ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp7 | c0_1(a744) | (~ndr1_0) | c2_1(a744) | (~c3_1(a744))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1110, 1109])).
% 0.77/0.93 tff(1112,plain,
% 0.77/0.93 (c2_1(a744) | (~c3_1(a744))),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1111, 104, 1030, 1029, 1094, 1028])).
% 0.77/0.93 tff(1113,plain,
% 0.77/0.93 (c2_1(a744)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1112, 1105])).
% 0.77/0.93 tff(1114,plain,
% 0.77/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a744) | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c0_1(a731)) | (~c2_1(a744)) | (~c3_1(a744)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a744) | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c0_1(a731)) | (~c2_1(a744)) | (~c3_1(a744)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1115,plain,
% 0.77/0.93 (((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c0_1(a731)) | c1_1(a744) | (~c2_1(a744)) | (~c3_1(a744)) | c0_1(a744) | (~c3_1(a744)) | (~c2_1(a744))) <=> (c0_1(a744) | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c0_1(a731)) | (~c2_1(a744)) | (~c3_1(a744)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1116,plain,
% 0.77/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c0_1(a731)) | c1_1(a744) | (~c2_1(a744)) | (~c3_1(a744)) | c0_1(a744) | (~c3_1(a744)) | (~c2_1(a744)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a744) | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c0_1(a731)) | (~c2_1(a744)) | (~c3_1(a744))))),
% 0.77/0.93 inference(monotonicity,[status(thm)],[1115])).
% 0.77/0.93 tff(1117,plain,
% 0.77/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c0_1(a731)) | c1_1(a744) | (~c2_1(a744)) | (~c3_1(a744)) | c0_1(a744) | (~c3_1(a744)) | (~c2_1(a744)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a744) | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c0_1(a731)) | (~c2_1(a744)) | (~c3_1(a744)))),
% 0.77/0.93 inference(transitivity,[status(thm)],[1116, 1114])).
% 0.77/0.93 tff(1118,plain,
% 0.77/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c0_1(a731)) | c1_1(a744) | (~c2_1(a744)) | (~c3_1(a744)) | c0_1(a744) | (~c3_1(a744)) | (~c2_1(a744)))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(1119,plain,
% 0.77/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a744) | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c0_1(a731)) | (~c2_1(a744)) | (~c3_1(a744))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1118, 1117])).
% 0.77/0.93 tff(1120,plain,
% 0.77/0.93 ((~c2_1(a744)) | (~c3_1(a744))),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1119, 104, 67, 1094, 1095, 59, 455, 1097])).
% 0.77/0.93 tff(1121,plain,
% 0.77/0.93 ($false),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1120, 1113, 1105])).
% 0.77/0.93 tff(1122,plain,((~hskp1) | c0_1(a744) | c1_1(a744) | hskp12 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.77/0.93 tff(1123,plain,
% 0.77/0.93 (~hskp1),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1122, 1095, 1094, 1030, 1029])).
% 0.77/0.93 tff(1124,assumption,(hskp2), introduced(assumption)).
% 0.77/0.93 tff(1125,plain,
% 0.77/0.93 (~c3_1(a732)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[546, 1124])).
% 0.77/0.93 tff(1126,plain,
% 0.77/0.93 (~c0_1(a732)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[288, 1124])).
% 0.77/0.93 tff(1127,plain,
% 0.77/0.93 (~c2_1(a732)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[282, 1124])).
% 0.77/0.93 tff(1128,plain,
% 0.77/0.93 (c1_1(a734)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1044, 1033, 33, 22, 1030, 1029])).
% 0.77/0.93 tff(1129,plain,
% 0.77/0.93 (~hskp8),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[680, 1096])).
% 0.77/0.93 tff(1130,plain,
% 0.77/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c0_1(a734) | c3_1(a734) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a734) | c3_1(a734) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a734)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1131,plain,
% 0.77/0.93 ((hskp8 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c3_1(a732) | c0_1(a732) | c2_1(a732)) <=> (hskp8 | c0_1(a734) | c3_1(a734) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a734)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1132,plain,
% 0.77/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c3_1(a732) | c0_1(a732) | c2_1(a732))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c0_1(a734) | c3_1(a734) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a734))))),
% 0.77/0.93 inference(monotonicity,[status(thm)],[1131])).
% 0.77/0.93 tff(1133,plain,
% 0.77/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c3_1(a732) | c0_1(a732) | c2_1(a732))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a734) | c3_1(a734) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a734)))),
% 0.77/0.93 inference(transitivity,[status(thm)],[1132, 1130])).
% 0.77/0.93 tff(1134,plain,
% 0.77/0.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c3_1(a732) | c0_1(a732) | c2_1(a732))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(1135,plain,
% 0.77/0.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a734) | c3_1(a734) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a734))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1134, 1133])).
% 0.77/0.93 tff(1136,plain,
% 0.77/0.93 (hskp8 | c0_1(a732) | (~c2_1(a734))),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1135, 104, 22, 33, 621, 620, 619])).
% 0.77/0.93 tff(1137,plain,
% 0.77/0.93 (~c2_1(a734)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1136, 1129, 622])).
% 0.77/0.93 tff(1138,plain,
% 0.77/0.93 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.77/0.93 inference(bind,[status(th)],[])).
% 0.77/0.93 tff(1139,plain,
% 0.77/0.93 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.93 inference(quant_intro,[status(thm)],[1138])).
% 0.77/0.93 tff(1140,plain,
% 0.77/0.93 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1141,plain,
% 0.77/0.93 (^[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(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)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_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)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.77/0.93 inference(bind,[status(th)],[])).
% 0.77/0.93 tff(1142,plain,
% 0.77/0.93 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[1141])).
% 0.77/0.94 tff(1143,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 0.77/0.94 tff(1144,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1143, 1142])).
% 0.77/0.94 tff(1145,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1144, 1140])).
% 0.77/0.94 tff(1146,plain,(
% 0.77/0.94 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.94 inference(skolemize,[status(sab)],[1145])).
% 0.77/0.94 tff(1147,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1146, 1139])).
% 0.77/0.94 tff(1148,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | c3_1(a744) | c0_1(a744) | c1_1(a744) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c3_1(a744) | c0_1(a744) | c1_1(a744) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1149,plain,
% 0.77/0.94 ((hskp3 | (~ndr1_0) | c2_1(a734) | c3_1(a734) | (~c1_1(a734)) | c3_1(a744) | c1_1(a744) | c0_1(a744)) <=> (hskp3 | c3_1(a744) | c0_1(a744) | c1_1(a744) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1150,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a734) | c3_1(a734) | (~c1_1(a734)) | c3_1(a744) | c1_1(a744) | c0_1(a744))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | c3_1(a744) | c0_1(a744) | c1_1(a744) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1149])).
% 0.77/0.94 tff(1151,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a734) | c3_1(a734) | (~c1_1(a734)) | c3_1(a744) | c1_1(a744) | c0_1(a744))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c3_1(a744) | c0_1(a744) | c1_1(a744) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1150, 1148])).
% 0.77/0.94 tff(1152,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a734) | c3_1(a734) | (~c1_1(a734)) | c3_1(a744) | c1_1(a744) | c0_1(a744))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1153,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c3_1(a744) | c0_1(a744) | c1_1(a744) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1152, 1151])).
% 0.77/0.94 tff(1154,plain,
% 0.77/0.94 (hskp3),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1153, 104, 1096, 1006, 1094, 1095, 33, 1147, 1137])).
% 0.77/0.94 tff(1155,plain,
% 0.77/0.94 (((~hskp3) | (~c0_1(a733))) <=> ((~hskp3) | (~c0_1(a733)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1156,plain,
% 0.77/0.94 (((~c0_1(a733)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a733)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1157,axiom,((~c0_1(a733)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 0.77/0.94 tff(1158,plain,
% 0.77/0.94 ((~hskp3) | (~c0_1(a733))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1157, 1156])).
% 0.77/0.94 tff(1159,plain,
% 0.77/0.94 ((~hskp3) | (~c0_1(a733))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1158, 1155])).
% 0.77/0.94 tff(1160,plain,
% 0.77/0.94 (~c0_1(a733)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1159, 1154])).
% 0.77/0.94 tff(1161,plain,
% 0.77/0.94 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(1162,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[1161])).
% 0.77/0.94 tff(1163,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1164,plain,
% 0.77/0.94 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_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)) | hskp5) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp5))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_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)) | hskp5) <=> (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(1165,plain,
% 0.77/0.94 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[1164])).
% 0.77/0.94 tff(1166,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)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 0.77/0.94 tff(1167,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1166, 1165])).
% 0.77/0.94 tff(1168,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1167, 1163])).
% 0.77/0.94 tff(1169,plain,(
% 0.77/0.94 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.77/0.94 inference(skolemize,[status(sab)],[1168])).
% 0.77/0.94 tff(1170,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1169, 1162])).
% 0.77/0.94 tff(1171,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1172,plain,
% 0.77/0.94 ((hskp5 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c1_1(a734)) | c0_1(a734) | c2_1(a734) | (~c1_1(a734))) <=> (hskp5 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1173,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c1_1(a734)) | c0_1(a734) | c2_1(a734) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1172])).
% 0.77/0.94 tff(1174,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c1_1(a734)) | c0_1(a734) | c2_1(a734) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1173, 1171])).
% 0.77/0.94 tff(1175,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c1_1(a734)) | c0_1(a734) | c2_1(a734) | (~c1_1(a734)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1176,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1175, 1174])).
% 0.77/0.94 tff(1177,plain,
% 0.77/0.94 (hskp5 | c3_1(a734) | c2_1(a734) | (~c1_1(a734))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1176, 104, 22, 1170])).
% 0.77/0.94 tff(1178,plain,
% 0.77/0.94 (hskp5),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1177, 1137, 33, 1006])).
% 0.77/0.94 tff(1179,plain,
% 0.77/0.94 (c2_1(a735)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[421, 1178])).
% 0.77/0.94 tff(1180,plain,
% 0.77/0.94 ((hskp0 | hskp8) <=> (hskp0 | hskp8)),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1181,axiom,(hskp0 | hskp8), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.77/0.94 tff(1182,plain,
% 0.77/0.94 (hskp0 | hskp8),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1181, 1180])).
% 0.77/0.94 tff(1183,plain,
% 0.77/0.94 (hskp0),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1182, 1129])).
% 0.77/0.94 tff(1184,plain,
% 0.77/0.94 (~c1_1(a730)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[384, 1183])).
% 0.77/0.94 tff(1185,plain,
% 0.77/0.94 (c3_1(a735)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[413, 1178])).
% 0.77/0.94 tff(1186,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a735) | c0_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c3_1(a735)) | (~c2_1(a735)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a735) | c0_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c3_1(a735)) | (~c2_1(a735)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1187,plain,
% 0.77/0.94 ((hskp10 | (~ndr1_0) | c0_1(a735) | (~c2_1(a735)) | (~c3_1(a735)) | c0_1(a734) | c2_1(a734) | (~c1_1(a734))) <=> (hskp10 | c0_1(a735) | c0_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c3_1(a735)) | (~c2_1(a735)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1188,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a735) | (~c2_1(a735)) | (~c3_1(a735)) | c0_1(a734) | c2_1(a734) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a735) | c0_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c3_1(a735)) | (~c2_1(a735))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1187])).
% 0.77/0.94 tff(1189,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a735) | (~c2_1(a735)) | (~c3_1(a735)) | c0_1(a734) | c2_1(a734) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a735) | c0_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c3_1(a735)) | (~c2_1(a735)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1188, 1186])).
% 0.77/0.94 tff(1190,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a735) | (~c2_1(a735)) | (~c3_1(a735)) | c0_1(a734) | c2_1(a734) | (~c1_1(a734)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1191,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a735) | c0_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c3_1(a735)) | (~c2_1(a735))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1190, 1189])).
% 0.77/0.94 tff(1192,plain,
% 0.77/0.94 (hskp10 | c2_1(a734) | (~c1_1(a734)) | (~c3_1(a735)) | (~c2_1(a735))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1191, 104, 457, 22, 970])).
% 0.77/0.94 tff(1193,plain,
% 0.77/0.94 (hskp10),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1192, 1185, 1006, 1179, 1137])).
% 0.77/0.94 tff(1194,plain,
% 0.77/0.94 (~c2_1(a748)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[983, 1193])).
% 0.77/0.94 tff(1195,plain,
% 0.77/0.94 (~c1_1(a748)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[989, 1193])).
% 0.77/0.94 tff(1196,plain,
% 0.77/0.94 (~c0_1(a748)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[995, 1193])).
% 0.77/0.94 tff(1197,plain,
% 0.77/0.94 (c3_1(a730)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[435, 1183])).
% 0.77/0.94 tff(1198,plain,
% 0.77/0.94 (c0_1(a730)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[443, 1183])).
% 0.77/0.94 tff(1199,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | c0_1(a748) | c1_1(a748) | c2_1(a748) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c0_1(a748) | c1_1(a748) | c2_1(a748) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1200,plain,
% 0.77/0.94 ((hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a748) | c0_1(a748) | c2_1(a748)) <=> (hskp25 | c0_1(a748) | c1_1(a748) | c2_1(a748) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1201,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a748) | c0_1(a748) | c2_1(a748))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | c0_1(a748) | c1_1(a748) | c2_1(a748) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1200])).
% 0.77/0.94 tff(1202,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a748) | c0_1(a748) | c2_1(a748))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c0_1(a748) | c1_1(a748) | c2_1(a748) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1201, 1199])).
% 0.77/0.94 tff(1203,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a748) | c0_1(a748) | c2_1(a748))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1204,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c0_1(a748) | c1_1(a748) | c2_1(a748) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1203, 1202])).
% 0.77/0.94 tff(1205,plain,
% 0.77/0.94 (hskp25),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1204, 104, 1198, 1197, 1196, 1195, 1194, 1184, 20])).
% 0.77/0.94 tff(1206,plain,
% 0.77/0.94 (c3_1(a729)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[762, 1205])).
% 0.77/0.94 tff(1207,plain,
% 0.77/0.94 (c2_1(a729)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[770, 1205])).
% 0.77/0.94 tff(1208,plain,
% 0.77/0.94 (c0_1(a729)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[778, 1205])).
% 0.77/0.94 tff(1209,plain,
% 0.77/0.94 (hskp21),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[863, 104, 1208, 1207, 1206, 467])).
% 0.77/0.94 tff(1210,plain,
% 0.77/0.94 (~c2_1(a793)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[482, 1209])).
% 0.77/0.94 tff(1211,plain,
% 0.77/0.94 (((~hskp3) | (~c1_1(a733))) <=> ((~hskp3) | (~c1_1(a733)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1212,plain,
% 0.77/0.94 (((~c1_1(a733)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a733)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1213,axiom,((~c1_1(a733)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 0.77/0.94 tff(1214,plain,
% 0.77/0.94 ((~hskp3) | (~c1_1(a733))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1213, 1212])).
% 0.77/0.94 tff(1215,plain,
% 0.77/0.94 ((~hskp3) | (~c1_1(a733))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1214, 1211])).
% 0.77/0.94 tff(1216,plain,
% 0.77/0.94 (~c1_1(a733)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1215, 1154])).
% 0.77/0.94 tff(1217,plain,
% 0.77/0.94 (c0_1(a793)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[500, 1209])).
% 0.77/0.94 tff(1218,plain,
% 0.77/0.94 (c3_1(a793)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[492, 1209])).
% 0.77/0.94 tff(1219,assumption,(ndr1_0), introduced(assumption)).
% 0.77/0.94 tff(1220,plain,
% 0.77/0.94 (hskp8 | (~ndr1_0) | (~c2_1(a734))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1135, 22, 33, 622, 621, 620, 619])).
% 0.77/0.94 tff(1221,plain,
% 0.77/0.94 (~c2_1(a734)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1220, 1129, 1219])).
% 0.77/0.94 tff(1222,plain,
% 0.77/0.94 (hskp3),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1153, 1219, 1096, 1006, 1094, 1095, 33, 1147, 1221])).
% 0.77/0.94 tff(1223,plain,
% 0.77/0.94 (((~hskp3) | c2_1(a733)) <=> ((~hskp3) | c2_1(a733))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1224,axiom,((~hskp3) | c2_1(a733)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 0.77/0.94 tff(1225,plain,
% 0.77/0.94 ((~hskp3) | c2_1(a733)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1224, 1223])).
% 0.77/0.94 tff(1226,plain,
% 0.77/0.94 ((~hskp3) | c2_1(a733)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1225, 1223])).
% 0.77/0.94 tff(1227,plain,
% 0.77/0.94 ((~hskp3) | c2_1(a733)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1226, 1223])).
% 0.77/0.94 tff(1228,plain,
% 0.77/0.94 ((~hskp3) | c2_1(a733)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1227, 1223])).
% 0.77/0.94 tff(1229,plain,
% 0.77/0.94 ((~hskp3) | c2_1(a733)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1228, 1223])).
% 0.77/0.94 tff(1230,plain,
% 0.77/0.94 (c2_1(a733)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1229, 1222])).
% 0.77/0.94 tff(1231,assumption,(~c0_1(a733)), introduced(assumption)).
% 0.77/0.94 tff(1232,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c0_1(a733) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | c3_1(a733) | (~c2_1(a733)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a733) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | c3_1(a733) | (~c2_1(a733)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1233,plain,
% 0.77/0.94 ((hskp8 | (~ndr1_0) | c0_1(a733) | c3_1(a733) | (~c2_1(a733)) | c3_1(a732) | c0_1(a732) | c2_1(a732)) <=> (hskp8 | c0_1(a733) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | c3_1(a733) | (~c2_1(a733)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1234,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a733) | c3_1(a733) | (~c2_1(a733)) | c3_1(a732) | c0_1(a732) | c2_1(a732))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c0_1(a733) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | c3_1(a733) | (~c2_1(a733))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1233])).
% 0.77/0.94 tff(1235,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a733) | c3_1(a733) | (~c2_1(a733)) | c3_1(a732) | c0_1(a732) | c2_1(a732))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a733) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | c3_1(a733) | (~c2_1(a733)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1234, 1232])).
% 0.77/0.94 tff(1236,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a733) | c3_1(a733) | (~c2_1(a733)) | c3_1(a732) | c0_1(a732) | c2_1(a732))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1237,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a733) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | c3_1(a733) | (~c2_1(a733))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1236, 1235])).
% 0.77/0.94 tff(1238,plain,
% 0.77/0.94 (hskp8 | (~ndr1_0) | c3_1(a733) | (~c2_1(a733))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1237, 1231, 622, 621, 620, 619])).
% 0.77/0.94 tff(1239,plain,
% 0.77/0.94 (c3_1(a733)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1238, 1230, 1219, 1129])).
% 0.77/0.94 tff(1240,assumption,(~c1_1(a733)), introduced(assumption)).
% 0.77/0.94 tff(1241,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a793) | c0_1(a735) | c1_1(a733) | (~ndr1_0) | (~c3_1(a733)) | (~c2_1(a733)) | (~c3_1(a735)) | (~c2_1(a735)) | (~c3_1(a793)) | (~c0_1(a793)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a793) | c0_1(a735) | c1_1(a733) | (~ndr1_0) | (~c3_1(a733)) | (~c2_1(a733)) | (~c3_1(a735)) | (~c2_1(a735)) | (~c3_1(a793)) | (~c0_1(a793)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1242,plain,
% 0.77/0.94 (((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a733) | (~c2_1(a733)) | (~c3_1(a733)) | c0_1(a735) | (~c3_1(a735)) | (~c2_1(a735))) <=> (c2_1(a793) | c0_1(a735) | c1_1(a733) | (~ndr1_0) | (~c3_1(a733)) | (~c2_1(a733)) | (~c3_1(a735)) | (~c2_1(a735)) | (~c3_1(a793)) | (~c0_1(a793)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1243,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a733) | (~c2_1(a733)) | (~c3_1(a733)) | c0_1(a735) | (~c3_1(a735)) | (~c2_1(a735)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a793) | c0_1(a735) | c1_1(a733) | (~ndr1_0) | (~c3_1(a733)) | (~c2_1(a733)) | (~c3_1(a735)) | (~c2_1(a735)) | (~c3_1(a793)) | (~c0_1(a793))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1242])).
% 0.77/0.94 tff(1244,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a733) | (~c2_1(a733)) | (~c3_1(a733)) | c0_1(a735) | (~c3_1(a735)) | (~c2_1(a735)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a793) | c0_1(a735) | c1_1(a733) | (~ndr1_0) | (~c3_1(a733)) | (~c2_1(a733)) | (~c3_1(a735)) | (~c2_1(a735)) | (~c3_1(a793)) | (~c0_1(a793)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1243, 1241])).
% 0.77/0.94 tff(1245,plain,
% 0.77/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a733) | (~c2_1(a733)) | (~c3_1(a733)) | c0_1(a735) | (~c3_1(a735)) | (~c2_1(a735)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1246,plain,
% 0.77/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a793) | c0_1(a735) | c1_1(a733) | (~ndr1_0) | (~c3_1(a733)) | (~c2_1(a733)) | (~c3_1(a735)) | (~c2_1(a735)) | (~c3_1(a793)) | (~c0_1(a793))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 0.77/0.94 tff(1247,plain,
% 0.77/0.94 ((~c3_1(a733)) | (~c2_1(a733))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1246, 1219, 893, 892, 485, 484, 875, 457, 1240, 455])).
% 0.77/0.94 tff(1248,plain,
% 0.77/0.94 ($false),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1247, 1239, 1230])).
% 0.77/0.94 tff(1249,plain,(c3_1(a744) | (~ndr1_0) | (~c0_1(a793)) | (~c3_1(a793)) | (~c2_1(a735)) | (~c3_1(a735)) | c2_1(a793) | c0_1(a735) | c1_1(a733) | c0_1(a733) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~c1_1(a734)) | c0_1(a744) | c1_1(a744) | c3_1(a734) | c0_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.94 tff(1250,plain,
% 0.77/0.94 ($false),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1249, 1218, 1217, 1006, 1096, 1216, 1185, 1210, 457, 1179, 1160, 622, 621, 620, 104, 1094, 1095, 33, 22])).
% 0.77/0.94 tff(1251,plain,(c3_1(a744) | (~c1_1(a734)) | c0_1(a735) | c0_1(a732) | c2_1(a732) | c3_1(a732) | c0_1(a744) | c1_1(a744) | c3_1(a734) | c0_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.94 tff(1252,plain,
% 0.77/0.94 (c3_1(a744)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1251, 1128, 457, 622, 621, 620, 1094, 1095, 33, 22])).
% 0.77/0.94 tff(1253,plain,
% 0.77/0.94 (c2_1(a744)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1112, 1252])).
% 0.77/0.94 tff(1254,plain,
% 0.77/0.94 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(1255,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[1254])).
% 0.77/0.94 tff(1256,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1257,plain,
% 0.77/0.94 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(1258,plain,
% 0.77/0.94 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[1257])).
% 0.77/0.94 tff(1259,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 0.77/0.94 tff(1260,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1259, 1258])).
% 0.77/0.94 tff(1261,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1260, 1256])).
% 0.77/0.94 tff(1262,plain,(
% 0.77/0.94 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.77/0.94 inference(skolemize,[status(sab)],[1261])).
% 0.77/0.94 tff(1263,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1262, 1255])).
% 0.77/0.94 tff(1264,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a744) | c1_1(a744) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c3_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a744) | c1_1(a744) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c3_1(a744)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1265,plain,
% 0.77/0.94 ((hskp7 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c1_1(a744) | c0_1(a744) | (~c3_1(a744))) <=> (hskp7 | c0_1(a744) | c1_1(a744) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c3_1(a744)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1266,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c1_1(a744) | c0_1(a744) | (~c3_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a744) | c1_1(a744) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c3_1(a744))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[1265])).
% 0.77/0.95 tff(1267,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c1_1(a744) | c0_1(a744) | (~c3_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a744) | c1_1(a744) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c3_1(a744)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[1266, 1264])).
% 0.77/0.95 tff(1268,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c1_1(a744) | c0_1(a744) | (~c3_1(a744)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1269,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a744) | c1_1(a744) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c3_1(a744))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1268, 1267])).
% 0.77/0.95 tff(1270,plain,
% 0.77/0.95 (c3_1(a734) | (~c2_1(a734)) | (~c3_1(a744))),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1269, 104, 1029, 1094, 1095, 22, 1263])).
% 0.77/0.95 tff(1271,plain,
% 0.77/0.95 (~c2_1(a734)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1270, 1252, 33])).
% 0.77/0.95 tff(1272,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a744) | c0_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c2_1(a744)) | (~c3_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a744) | c0_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c2_1(a744)) | (~c3_1(a744)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1273,plain,
% 0.77/0.95 ((hskp10 | (~ndr1_0) | c0_1(a744) | (~c2_1(a744)) | (~c3_1(a744)) | c0_1(a734) | c2_1(a734) | (~c1_1(a734))) <=> (hskp10 | c0_1(a744) | c0_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c2_1(a744)) | (~c3_1(a744)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1274,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a744) | (~c2_1(a744)) | (~c3_1(a744)) | c0_1(a734) | c2_1(a734) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a744) | c0_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c2_1(a744)) | (~c3_1(a744))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[1273])).
% 0.77/0.95 tff(1275,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a744) | (~c2_1(a744)) | (~c3_1(a744)) | c0_1(a734) | c2_1(a734) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a744) | c0_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c2_1(a744)) | (~c3_1(a744)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[1274, 1272])).
% 0.77/0.95 tff(1276,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a744) | (~c2_1(a744)) | (~c3_1(a744)) | c0_1(a734) | c2_1(a734) | (~c1_1(a734)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1277,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a744) | c0_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c2_1(a744)) | (~c3_1(a744))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1276, 1275])).
% 0.77/0.95 tff(1278,plain,
% 0.77/0.95 (hskp10 | c2_1(a734) | (~c1_1(a734)) | (~c2_1(a744)) | (~c3_1(a744))),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1277, 104, 1094, 22, 970])).
% 0.77/0.95 tff(1279,plain,
% 0.77/0.95 (hskp10),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1278, 1271, 1128, 1253, 1252])).
% 0.77/0.95 tff(1280,plain,
% 0.77/0.95 (~c2_1(a748)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[983, 1279])).
% 0.77/0.95 tff(1281,plain,
% 0.77/0.95 (~c1_1(a748)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[989, 1279])).
% 0.77/0.95 tff(1282,plain,
% 0.77/0.95 (~c0_1(a748)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[995, 1279])).
% 0.77/0.95 tff(1283,plain,
% 0.77/0.95 (hskp8),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1182, 217])).
% 0.77/0.95 tff(1284,plain,
% 0.77/0.95 ((ndr1_0 | (~hskp8)) <=> (ndr1_0 | (~hskp8))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1285,plain,
% 0.77/0.95 (((~hskp8) | ndr1_0) <=> (ndr1_0 | (~hskp8))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1286,axiom,((~hskp8) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause22')).
% 0.77/0.95 tff(1287,plain,
% 0.77/0.95 (ndr1_0 | (~hskp8)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1286, 1285])).
% 0.77/0.95 tff(1288,plain,
% 0.77/0.95 (ndr1_0 | (~hskp8)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1287, 1284])).
% 0.77/0.95 tff(1289,plain,
% 0.77/0.95 (ndr1_0),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1288, 1283])).
% 0.77/0.95 tff(1290,plain,
% 0.77/0.95 (c3_1(a744)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[680, 1283])).
% 0.77/0.95 tff(1291,plain,
% 0.77/0.95 ((~ndr1_0) | c2_1(a744) | (~c3_1(a744))),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1111, 1030, 1029, 1094, 1028])).
% 0.77/0.95 tff(1292,plain,
% 0.77/0.95 (c2_1(a744)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1291, 1290, 1289])).
% 0.77/0.95 tff(1293,assumption,(~c1_1(a748)), introduced(assumption)).
% 0.77/0.95 tff(1294,assumption,(~c0_1(a748)), introduced(assumption)).
% 0.77/0.95 tff(1295,assumption,(~c2_1(a748)), introduced(assumption)).
% 0.77/0.95 tff(1296,plain,
% 0.77/0.95 (((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | c0_1(a748) | c1_1(a748) | c2_1(a748) | (~ndr1_0))) <=> ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | hskp1 | c0_1(a748) | c1_1(a748) | c2_1(a748) | (~ndr1_0))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1297,plain,
% 0.77/0.95 ((hskp0 | hskp1 | (~ndr1_0) | c2_1(a748) | c1_1(a748) | c0_1(a748)) <=> (hskp0 | hskp1 | c0_1(a748) | c1_1(a748) | c2_1(a748) | (~ndr1_0))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1298,plain,
% 0.77/0.95 (((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | (~ndr1_0) | c2_1(a748) | c1_1(a748) | c0_1(a748))) <=> ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | c0_1(a748) | c1_1(a748) | c2_1(a748) | (~ndr1_0)))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[1297])).
% 0.77/0.95 tff(1299,plain,
% 0.77/0.95 (((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | (~ndr1_0) | c2_1(a748) | c1_1(a748) | c0_1(a748))) <=> ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | hskp1 | c0_1(a748) | c1_1(a748) | c2_1(a748) | (~ndr1_0))),
% 0.77/0.95 inference(transitivity,[status(thm)],[1298, 1296])).
% 0.77/0.95 tff(1300,plain,
% 0.77/0.95 ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | (~ndr1_0) | c2_1(a748) | c1_1(a748) | c0_1(a748))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1301,plain,
% 0.77/0.95 ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | hskp1 | c0_1(a748) | c1_1(a748) | c2_1(a748) | (~ndr1_0)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1300, 1299])).
% 0.77/0.95 tff(1302,plain,
% 0.77/0.95 (hskp0 | hskp1 | c0_1(a748) | c1_1(a748) | (~ndr1_0)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1301, 1295, 236])).
% 0.77/0.95 tff(1303,plain,
% 0.77/0.95 (hskp1),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1302, 1289, 217, 1294, 1293])).
% 0.77/0.95 tff(1304,plain,
% 0.77/0.95 (c3_1(a731)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[66, 1303])).
% 0.77/0.95 tff(1305,plain,
% 0.77/0.95 (c1_1(a731)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[74, 1303])).
% 0.77/0.95 tff(1306,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | c0_1(a744) | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | c0_1(a731) | (~c2_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a744) | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | c0_1(a731) | (~c2_1(a744)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1307,plain,
% 0.77/0.95 ((hskp0 | (~ndr1_0) | c2_1(a731) | c0_1(a731) | (~c1_1(a731)) | c1_1(a744) | c0_1(a744) | (~c2_1(a744))) <=> (hskp0 | c0_1(a744) | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | c0_1(a731) | (~c2_1(a744)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1308,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a731) | c0_1(a731) | (~c1_1(a731)) | c1_1(a744) | c0_1(a744) | (~c2_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | c0_1(a744) | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | c0_1(a731) | (~c2_1(a744))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[1307])).
% 0.77/0.95 tff(1309,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a731) | c0_1(a731) | (~c1_1(a731)) | c1_1(a744) | c0_1(a744) | (~c2_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a744) | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | c0_1(a731) | (~c2_1(a744)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[1308, 1306])).
% 0.77/0.95 tff(1310,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a731) | c0_1(a731) | (~c1_1(a731)) | c1_1(a744) | c0_1(a744) | (~c2_1(a744)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1311,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a744) | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | c0_1(a731) | (~c2_1(a744))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1310, 1309])).
% 0.77/0.95 tff(1312,plain,
% 0.77/0.95 (hskp0 | c0_1(a744) | (~ndr1_0) | (~c1_1(a731)) | c0_1(a731) | (~c2_1(a744))),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1311, 1095, 1033, 254])).
% 0.77/0.95 tff(1313,plain,
% 0.77/0.95 (c0_1(a731)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1312, 1305, 217, 1094, 1289, 1292])).
% 0.77/0.95 tff(1314,plain,
% 0.77/0.95 ((~ndr1_0) | (~c3_1(a731)) | (~c0_1(a731)) | (~c2_1(a744)) | (~c3_1(a744))),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1119, 1094, 1095, 1033, 455])).
% 0.77/0.95 tff(1315,plain,
% 0.77/0.95 ($false),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1314, 1313, 1304, 1289, 1290, 1292])).
% 0.77/0.95 tff(1316,plain,(hskp0 | c0_1(a744) | c1_1(a744) | c2_1(a731) | hskp12 | hskp7 | c0_1(a748) | c1_1(a748) | c2_1(a748)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.95 tff(1317,plain,
% 0.77/0.95 (hskp0),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1316, 1282, 1095, 1033, 1030, 1029, 1094, 1281, 1280])).
% 0.77/0.95 tff(1318,plain,
% 0.77/0.95 (~c1_1(a730)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[384, 1317])).
% 0.77/0.95 tff(1319,plain,
% 0.77/0.95 (c3_1(a730)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[435, 1317])).
% 0.77/0.95 tff(1320,plain,
% 0.77/0.95 (c0_1(a730)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[443, 1317])).
% 0.77/0.95 tff(1321,plain,
% 0.77/0.95 (hskp25),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1204, 104, 1320, 1319, 1282, 1281, 1280, 1318, 20])).
% 0.77/0.95 tff(1322,plain,
% 0.77/0.95 (c3_1(a729)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[762, 1321])).
% 0.77/0.95 tff(1323,plain,
% 0.77/0.95 (c2_1(a729)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[770, 1321])).
% 0.77/0.95 tff(1324,plain,
% 0.77/0.95 (c0_1(a729)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[778, 1321])).
% 0.77/0.95 tff(1325,plain,
% 0.77/0.95 (hskp21),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[863, 104, 1324, 1323, 1322, 467])).
% 0.77/0.95 tff(1326,plain,
% 0.77/0.95 (~c2_1(a793)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[482, 1325])).
% 0.77/0.95 tff(1327,plain,
% 0.77/0.95 (c0_1(a793)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[500, 1325])).
% 0.77/0.95 tff(1328,plain,
% 0.77/0.95 (c3_1(a793)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[492, 1325])).
% 0.77/0.95 tff(1329,assumption,(c3_1(a744)), introduced(assumption)).
% 0.77/0.95 tff(1330,plain,
% 0.77/0.95 (c2_1(a744)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1291, 1329, 1219])).
% 0.77/0.95 tff(1331,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a793) | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c2_1(a744)) | (~c3_1(a744)) | (~c3_1(a793)) | (~c0_1(a793)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a793) | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c2_1(a744)) | (~c3_1(a744)) | (~c3_1(a793)) | (~c0_1(a793)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1332,plain,
% 0.77/0.95 (((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a744) | (~c2_1(a744)) | (~c3_1(a744)) | c0_1(a744) | (~c3_1(a744)) | (~c2_1(a744))) <=> (c2_1(a793) | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c2_1(a744)) | (~c3_1(a744)) | (~c3_1(a793)) | (~c0_1(a793)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1333,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a744) | (~c2_1(a744)) | (~c3_1(a744)) | c0_1(a744) | (~c3_1(a744)) | (~c2_1(a744)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a793) | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c2_1(a744)) | (~c3_1(a744)) | (~c3_1(a793)) | (~c0_1(a793))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[1332])).
% 0.77/0.95 tff(1334,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a744) | (~c2_1(a744)) | (~c3_1(a744)) | c0_1(a744) | (~c3_1(a744)) | (~c2_1(a744)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a793) | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c2_1(a744)) | (~c3_1(a744)) | (~c3_1(a793)) | (~c0_1(a793)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[1333, 1331])).
% 0.77/0.95 tff(1335,plain,
% 0.77/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a744) | (~c2_1(a744)) | (~c3_1(a744)) | c0_1(a744) | (~c3_1(a744)) | (~c2_1(a744)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1336,plain,
% 0.77/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a793) | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c2_1(a744)) | (~c3_1(a744)) | (~c3_1(a793)) | (~c0_1(a793))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1335, 1334])).
% 0.77/0.95 tff(1337,plain,
% 0.77/0.95 ((~c2_1(a744)) | (~c3_1(a744))),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1336, 1219, 893, 892, 875, 1094, 1095, 455])).
% 0.77/0.95 tff(1338,plain,
% 0.77/0.95 ($false),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1337, 1330, 1329])).
% 0.77/0.95 tff(1339,plain,((~c3_1(a744)) | (~ndr1_0) | (~c0_1(a793)) | (~c3_1(a793)) | c2_1(a793) | c0_1(a744) | c1_1(a744) | hskp12 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.77/0.95 tff(1340,plain,
% 0.77/0.95 ($false),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1339, 1328, 1327, 104, 1252, 1326, 1094, 1095, 1030, 1029])).
% 0.77/0.95 tff(1341,plain,(c2_1(a731) | c0_1(a744) | c1_1(a744) | hskp12 | hskp7 | c0_1(a734) | c3_1(a734) | c0_1(a735) | c0_1(a732) | c2_1(a732) | c3_1(a732)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.95 tff(1342,plain,
% 0.77/0.95 (c2_1(a731)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1341, 622, 1095, 1030, 1029, 22, 33, 457, 1094, 621, 620])).
% 0.77/0.95 tff(1343,plain,
% 0.77/0.95 (~hskp1),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[58, 1342])).
% 0.77/0.95 tff(1344,plain,
% 0.77/0.95 (hskp4),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[141, 1343, 1029])).
% 0.77/0.95 tff(1345,plain,
% 0.77/0.95 (c1_1(a734)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[51, 1344])).
% 0.77/0.95 tff(1346,plain,
% 0.77/0.95 (c3_1(a744)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1251, 1345, 457, 622, 621, 620, 1094, 1095, 33, 22])).
% 0.77/0.95 tff(1347,plain,
% 0.77/0.95 (~c2_1(a734)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1270, 1346, 33])).
% 0.77/0.95 tff(1348,plain,
% 0.77/0.95 (c2_1(a744)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1112, 1346])).
% 0.77/0.95 tff(1349,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | c0_1(a744) | c1_1(a744) | c0_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c2_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a744) | c1_1(a744) | c0_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c2_1(a744)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1350,plain,
% 0.77/0.95 ((hskp0 | (~ndr1_0) | c2_1(a734) | c0_1(a734) | (~c1_1(a734)) | c1_1(a744) | c0_1(a744) | (~c2_1(a744))) <=> (hskp0 | c0_1(a744) | c1_1(a744) | c0_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c2_1(a744)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1351,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a734) | c0_1(a734) | (~c1_1(a734)) | c1_1(a744) | c0_1(a744) | (~c2_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | c0_1(a744) | c1_1(a744) | c0_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c2_1(a744))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[1350])).
% 0.77/0.95 tff(1352,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a734) | c0_1(a734) | (~c1_1(a734)) | c1_1(a744) | c0_1(a744) | (~c2_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a744) | c1_1(a744) | c0_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c2_1(a744)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[1351, 1349])).
% 0.77/0.95 tff(1353,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a734) | c0_1(a734) | (~c1_1(a734)) | c1_1(a744) | c0_1(a744) | (~c2_1(a744)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1354,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a744) | c1_1(a744) | c0_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c2_1(a744))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1353, 1352])).
% 0.77/0.95 tff(1355,plain,
% 0.77/0.95 (hskp0),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1354, 104, 1345, 1094, 1095, 22, 254, 1348, 1347])).
% 0.77/0.95 tff(1356,plain,
% 0.77/0.95 (~c1_1(a730)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[384, 1355])).
% 0.77/0.95 tff(1357,plain,
% 0.77/0.95 (hskp10),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1278, 1347, 1345, 1348, 1346])).
% 0.77/0.95 tff(1358,plain,
% 0.77/0.95 (~c2_1(a748)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[983, 1357])).
% 0.77/0.95 tff(1359,plain,
% 0.77/0.95 (~c1_1(a748)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[989, 1357])).
% 0.77/0.95 tff(1360,plain,
% 0.77/0.95 (~c0_1(a748)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[995, 1357])).
% 0.77/0.95 tff(1361,plain,
% 0.77/0.95 (c3_1(a730)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[435, 1355])).
% 0.77/0.95 tff(1362,plain,
% 0.77/0.95 (c0_1(a730)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[443, 1355])).
% 0.77/0.95 tff(1363,plain,
% 0.77/0.95 (hskp25),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1204, 104, 1362, 1361, 1360, 1359, 1358, 1356, 20])).
% 0.77/0.95 tff(1364,plain,
% 0.77/0.95 (c3_1(a729)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[762, 1363])).
% 0.77/0.95 tff(1365,plain,
% 0.77/0.95 (c2_1(a729)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[770, 1363])).
% 0.77/0.95 tff(1366,plain,
% 0.77/0.95 (c0_1(a729)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[778, 1363])).
% 0.77/0.95 tff(1367,plain,
% 0.77/0.95 (hskp21),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[863, 104, 1366, 1365, 1364, 467])).
% 0.77/0.95 tff(1368,plain,
% 0.77/0.95 (~c2_1(a793)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[482, 1367])).
% 0.77/0.95 tff(1369,plain,
% 0.77/0.95 (c0_1(a793)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[500, 1367])).
% 0.77/0.95 tff(1370,plain,
% 0.77/0.95 (c3_1(a793)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[492, 1367])).
% 0.77/0.95 tff(1371,plain,
% 0.77/0.95 ($false),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1339, 1370, 1369, 104, 1346, 1368, 1094, 1095, 1030, 1029])).
% 0.77/0.95 tff(1372,plain,(c0_1(a732) | c0_1(a744) | c1_1(a744) | hskp12 | hskp7 | c0_1(a734) | c3_1(a734) | c0_1(a735) | c2_1(a732) | c3_1(a732)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.95 tff(1373,plain,
% 0.77/0.95 ($false),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1372, 1127, 1126, 1095, 1030, 1029, 22, 33, 457, 1125, 1094])).
% 0.77/0.95 tff(1374,plain,((~hskp2) | c1_1(a744) | hskp12 | hskp7 | c0_1(a734) | c3_1(a734) | c0_1(a735) | c0_1(a744)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.95 tff(1375,plain,
% 0.77/0.95 (~hskp2),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1374, 457, 1030, 1029, 22, 1094, 33, 1095])).
% 0.77/0.95 tff(1376,plain,
% 0.77/0.95 (c1_1(a734)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1047, 33, 1029, 22, 1030])).
% 0.77/0.95 tff(1377,assumption,(~c2_1(a744)), introduced(assumption)).
% 0.77/0.95 tff(1378,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c3_1(a744) | c0_1(a744) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | c2_1(a744))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c3_1(a744) | c0_1(a744) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | c2_1(a744))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1379,plain,
% 0.77/0.95 ((hskp8 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c3_1(a744) | c0_1(a744) | c2_1(a744)) <=> (hskp8 | c3_1(a744) | c0_1(a744) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | c2_1(a744))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1380,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c3_1(a744) | c0_1(a744) | c2_1(a744))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c3_1(a744) | c0_1(a744) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | c2_1(a744)))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[1379])).
% 0.77/0.95 tff(1381,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c3_1(a744) | c0_1(a744) | c2_1(a744))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c3_1(a744) | c0_1(a744) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | c2_1(a744))),
% 0.77/0.95 inference(transitivity,[status(thm)],[1380, 1378])).
% 0.77/0.95 tff(1382,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c3_1(a744) | c0_1(a744) | c2_1(a744))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1383,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c3_1(a744) | c0_1(a744) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | c2_1(a744)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1382, 1381])).
% 0.77/0.95 tff(1384,plain,
% 0.77/0.95 ((~c2_1(a734)) | c2_1(a744)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1383, 1129, 104, 1096, 1094, 22, 33, 619])).
% 0.77/0.95 tff(1385,plain,
% 0.77/0.95 (~c2_1(a734)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1384, 1377])).
% 0.77/0.95 tff(1386,plain,
% 0.77/0.95 (hskp5),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1177, 1385, 33, 1376])).
% 0.77/0.95 tff(1387,plain,
% 0.77/0.95 (c3_1(a735)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[413, 1386])).
% 0.77/0.95 tff(1388,plain,
% 0.77/0.95 (c2_1(a735)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[421, 1386])).
% 0.77/0.95 tff(1389,plain,
% 0.77/0.95 (hskp10),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1192, 1388, 1376, 1385, 1387])).
% 0.77/0.95 tff(1390,plain,
% 0.77/0.95 (~c2_1(a748)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[983, 1389])).
% 0.77/0.95 tff(1391,plain,
% 0.77/0.95 (~c0_1(a748)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[995, 1389])).
% 0.77/0.95 tff(1392,plain,
% 0.77/0.95 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | c0_1(a748) | c2_1(a748) | (~ndr1_0) | (~c3_1(a748)))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp7 | c0_1(a748) | c2_1(a748) | (~ndr1_0) | (~c3_1(a748)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1393,plain,
% 0.77/0.95 ((hskp12 | hskp7 | (~ndr1_0) | c2_1(a748) | c0_1(a748) | (~c3_1(a748))) <=> (hskp12 | hskp7 | c0_1(a748) | c2_1(a748) | (~ndr1_0) | (~c3_1(a748)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1394,plain,
% 0.77/0.95 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c2_1(a748) | c0_1(a748) | (~c3_1(a748)))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | c0_1(a748) | c2_1(a748) | (~ndr1_0) | (~c3_1(a748))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[1393])).
% 0.77/0.95 tff(1395,plain,
% 0.77/0.95 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c2_1(a748) | c0_1(a748) | (~c3_1(a748)))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp7 | c0_1(a748) | c2_1(a748) | (~ndr1_0) | (~c3_1(a748)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[1394, 1392])).
% 0.77/0.95 tff(1396,plain,
% 0.77/0.95 ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c2_1(a748) | c0_1(a748) | (~c3_1(a748)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1397,plain,
% 0.77/0.95 ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp7 | c0_1(a748) | c2_1(a748) | (~ndr1_0) | (~c3_1(a748))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1396, 1395])).
% 0.77/0.95 tff(1398,plain,
% 0.77/0.95 (~c3_1(a748)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1397, 104, 1030, 1029, 1391, 1390, 1028])).
% 0.77/0.95 tff(1399,plain,
% 0.77/0.95 (hskp3),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1153, 104, 1096, 1376, 1094, 1095, 33, 1147, 1385])).
% 0.77/0.95 tff(1400,plain,
% 0.77/0.95 (~c0_1(a733)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1159, 1399])).
% 0.77/0.95 tff(1401,plain,
% 0.77/0.95 (c2_1(a733)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1229, 1399])).
% 0.77/0.95 tff(1402,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c0_1(a748) | c2_1(a748) | c0_1(a733) | (~ndr1_0) | c3_1(a733) | (~c2_1(a733)) | c3_1(a748))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a748) | c2_1(a748) | c0_1(a733) | (~ndr1_0) | c3_1(a733) | (~c2_1(a733)) | c3_1(a748))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1403,plain,
% 0.77/0.95 ((hskp8 | (~ndr1_0) | c0_1(a733) | c3_1(a733) | (~c2_1(a733)) | c3_1(a748) | c0_1(a748) | c2_1(a748)) <=> (hskp8 | c0_1(a748) | c2_1(a748) | c0_1(a733) | (~ndr1_0) | c3_1(a733) | (~c2_1(a733)) | c3_1(a748))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1404,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a733) | c3_1(a733) | (~c2_1(a733)) | c3_1(a748) | c0_1(a748) | c2_1(a748))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c0_1(a748) | c2_1(a748) | c0_1(a733) | (~ndr1_0) | c3_1(a733) | (~c2_1(a733)) | c3_1(a748)))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[1403])).
% 0.79/0.95 tff(1405,plain,
% 0.79/0.95 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a733) | c3_1(a733) | (~c2_1(a733)) | c3_1(a748) | c0_1(a748) | c2_1(a748))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a748) | c2_1(a748) | c0_1(a733) | (~ndr1_0) | c3_1(a733) | (~c2_1(a733)) | c3_1(a748))),
% 0.79/0.95 inference(transitivity,[status(thm)],[1404, 1402])).
% 0.79/0.95 tff(1406,plain,
% 0.79/0.95 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a733) | c3_1(a733) | (~c2_1(a733)) | c3_1(a748) | c0_1(a748) | c2_1(a748))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(1407,plain,
% 0.79/0.95 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a748) | c2_1(a748) | c0_1(a733) | (~ndr1_0) | c3_1(a733) | (~c2_1(a733)) | c3_1(a748)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1406, 1405])).
% 0.79/0.95 tff(1408,plain,
% 0.79/0.95 (c3_1(a733)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1407, 1129, 104, 1401, 1391, 1390, 1400, 619, 1398])).
% 0.79/0.95 tff(1409,plain,
% 0.79/0.95 (~c1_1(a733)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1215, 1399])).
% 0.79/0.95 tff(1410,plain,
% 0.79/0.95 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | c0_1(a744) | c1_1(a744) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a744))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c0_1(a744) | c1_1(a744) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a744))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(1411,plain,
% 0.79/0.95 ((hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a744) | c0_1(a744) | c2_1(a744)) <=> (hskp25 | c0_1(a744) | c1_1(a744) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a744))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(1412,plain,
% 0.79/0.95 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a744) | c0_1(a744) | c2_1(a744))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | c0_1(a744) | c1_1(a744) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a744)))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[1411])).
% 0.79/0.95 tff(1413,plain,
% 0.79/0.95 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a744) | c0_1(a744) | c2_1(a744))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c0_1(a744) | c1_1(a744) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a744))),
% 0.79/0.95 inference(transitivity,[status(thm)],[1412, 1410])).
% 0.79/0.95 tff(1414,plain,
% 0.79/0.95 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a744) | c0_1(a744) | c2_1(a744))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(1415,plain,
% 0.79/0.95 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c0_1(a744) | c1_1(a744) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a744)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1414, 1413])).
% 0.79/0.95 tff(1416,plain,
% 0.79/0.95 (hskp25 | c2_1(a744)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1415, 104, 1198, 1197, 1094, 1095, 1184, 20])).
% 0.79/0.95 tff(1417,plain,
% 0.79/0.95 (hskp25),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1416, 1377])).
% 0.79/0.95 tff(1418,plain,
% 0.79/0.95 (c3_1(a729)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[762, 1417])).
% 0.79/0.96 tff(1419,plain,
% 0.79/0.96 (c2_1(a729)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[770, 1417])).
% 0.79/0.96 tff(1420,plain,
% 0.79/0.96 (c0_1(a729)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[778, 1417])).
% 0.79/0.96 tff(1421,plain,
% 0.79/0.96 (hskp21),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[863, 104, 1420, 1419, 1418, 467])).
% 0.79/0.96 tff(1422,plain,
% 0.79/0.96 (~c2_1(a793)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[482, 1421])).
% 0.79/0.96 tff(1423,plain,
% 0.79/0.96 (c3_1(a793)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[492, 1421])).
% 0.79/0.96 tff(1424,plain,
% 0.79/0.96 (c0_1(a793)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[500, 1421])).
% 0.79/0.96 tff(1425,plain,
% 0.79/0.96 ($false),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1246, 104, 1424, 1423, 1388, 1387, 1401, 1422, 457, 1409, 455, 1408])).
% 0.79/0.96 tff(1426,plain,(c2_1(a744) | c0_1(a735) | c3_1(a744) | c0_1(a744) | c1_1(a744) | c3_1(a734) | hskp12 | hskp7 | c0_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.96 tff(1427,plain,
% 0.79/0.96 (c2_1(a744)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1426, 457, 22, 1094, 1095, 33, 1030, 1029, 1096])).
% 0.79/0.96 tff(1428,plain,
% 0.79/0.96 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c2_1(a744)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c2_1(a744)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1429,plain,
% 0.79/0.96 ((hskp2 | hskp1 | (~ndr1_0) | c1_1(a744) | c0_1(a744) | (~c2_1(a744))) <=> (hskp2 | hskp1 | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c2_1(a744)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1430,plain,
% 0.79/0.96 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c1_1(a744) | c0_1(a744) | (~c2_1(a744)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c2_1(a744))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[1429])).
% 0.79/0.96 tff(1431,plain,
% 0.79/0.96 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c1_1(a744) | c0_1(a744) | (~c2_1(a744)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c2_1(a744)))),
% 0.79/0.96 inference(transitivity,[status(thm)],[1430, 1428])).
% 0.79/0.96 tff(1432,plain,
% 0.79/0.96 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c1_1(a744) | c0_1(a744) | (~c2_1(a744)))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(1433,plain,
% 0.79/0.96 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c2_1(a744))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1432, 1431])).
% 0.79/0.96 tff(1434,plain,
% 0.79/0.96 (hskp2 | hskp1 | c1_1(a744) | (~c2_1(a744))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1433, 104, 1094, 266])).
% 0.79/0.96 tff(1435,plain,
% 0.79/0.96 ($false),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1434, 1427, 1375, 1095, 1123])).
% 0.79/0.96 tff(1436,plain,(c0_1(a735) | c1_1(a744) | c0_1(a744) | c0_1(a734) | c3_1(a734) | hskp12 | hskp7 | c3_1(a744)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.96 tff(1437,plain,
% 0.79/0.96 (c0_1(a735)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1436, 1096, 1094, 22, 33, 1030, 1029, 1095])).
% 0.79/0.96 tff(1438,plain,
% 0.79/0.96 (~hskp5),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[427, 1437])).
% 0.79/0.96 tff(1439,plain,
% 0.79/0.96 (((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | c3_1(a744) | c0_1(a744) | (~ndr1_0) | c2_1(a744))) <=> ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp5 | c3_1(a744) | c0_1(a744) | (~ndr1_0) | c2_1(a744))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1440,plain,
% 0.79/0.96 ((hskp9 | hskp5 | (~ndr1_0) | c2_1(a744) | c0_1(a744) | c3_1(a744)) <=> (hskp9 | hskp5 | c3_1(a744) | c0_1(a744) | (~ndr1_0) | c2_1(a744))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1441,plain,
% 0.79/0.96 (((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | (~ndr1_0) | c2_1(a744) | c0_1(a744) | c3_1(a744))) <=> ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | c3_1(a744) | c0_1(a744) | (~ndr1_0) | c2_1(a744)))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[1440])).
% 0.79/0.96 tff(1442,plain,
% 0.79/0.96 (((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | (~ndr1_0) | c2_1(a744) | c0_1(a744) | c3_1(a744))) <=> ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp5 | c3_1(a744) | c0_1(a744) | (~ndr1_0) | c2_1(a744))),
% 0.79/0.96 inference(transitivity,[status(thm)],[1441, 1439])).
% 0.79/0.96 tff(1443,plain,
% 0.79/0.96 ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | (~ndr1_0) | c2_1(a744) | c0_1(a744) | c3_1(a744))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(1444,plain,
% 0.79/0.96 ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp5 | c3_1(a744) | c0_1(a744) | (~ndr1_0) | c2_1(a744)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1443, 1442])).
% 0.79/0.96 tff(1445,plain,
% 0.79/0.96 (hskp5 | c3_1(a744) | c2_1(a744)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1444, 104, 1061, 1094, 1085])).
% 0.79/0.96 tff(1446,plain,
% 0.79/0.96 (c2_1(a744)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1445, 1438, 1096])).
% 0.79/0.96 tff(1447,plain,
% 0.79/0.96 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 0.79/0.96 inference(bind,[status(th)],[])).
% 0.79/0.96 tff(1448,plain,
% 0.79/0.96 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.79/0.96 inference(quant_intro,[status(thm)],[1447])).
% 0.79/0.96 tff(1449,plain,
% 0.79/0.96 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1450,plain,
% 0.79/0.96 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 0.79/0.96 inference(bind,[status(th)],[])).
% 0.79/0.96 tff(1451,plain,
% 0.79/0.96 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.79/0.96 inference(quant_intro,[status(thm)],[1450])).
% 0.79/0.96 tff(1452,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 0.79/0.96 tff(1453,plain,
% 0.79/0.96 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1452, 1451])).
% 0.79/0.96 tff(1454,plain,
% 0.79/0.96 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1453, 1449])).
% 0.79/0.96 tff(1455,plain,(
% 0.79/0.96 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.79/0.96 inference(skolemize,[status(sab)],[1454])).
% 0.79/0.96 tff(1456,plain,
% 0.79/0.96 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1455, 1448])).
% 0.79/0.96 tff(1457,plain,
% 0.79/0.96 (c3_1(a730)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[435, 1063])).
% 0.79/0.96 tff(1458,plain,
% 0.79/0.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c3_1(a744) | c1_1(a744) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c3_1(a744) | c1_1(a744) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a744)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1459,plain,
% 0.79/0.96 ((hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a744) | c1_1(a744) | (~c2_1(a744))) <=> (hskp5 | c3_1(a744) | c1_1(a744) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a744)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1460,plain,
% 0.79/0.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a744) | c1_1(a744) | (~c2_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c3_1(a744) | c1_1(a744) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a744))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[1459])).
% 0.79/0.96 tff(1461,plain,
% 0.79/0.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a744) | c1_1(a744) | (~c2_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c3_1(a744) | c1_1(a744) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a744)))),
% 0.79/0.96 inference(transitivity,[status(thm)],[1460, 1458])).
% 0.79/0.96 tff(1462,plain,
% 0.79/0.96 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a744) | c1_1(a744) | (~c2_1(a744)))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(1463,plain,
% 0.79/0.96 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c3_1(a744) | c1_1(a744) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a744))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1462, 1461])).
% 0.79/0.96 tff(1464,plain,
% 0.79/0.96 (hskp5 | (~c2_1(a744))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1463, 104, 1096, 1064, 1457, 1095, 1065, 1456])).
% 0.79/0.96 tff(1465,plain,
% 0.79/0.96 ($false),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1464, 1446, 1438])).
% 0.79/0.96 tff(1466,plain,(c3_1(a744) | c1_1(a744) | c0_1(a744) | c0_1(a734) | c3_1(a734) | hskp12 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.79/0.96 tff(1467,plain,
% 0.79/0.96 (c3_1(a744)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1466, 1095, 1094, 22, 33, 1030, 1029])).
% 0.79/0.96 tff(1468,plain,
% 0.79/0.96 ((~c2_1(a734)) | (~c3_1(a744))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1269, 104, 1029, 1094, 1095, 22, 33, 1263])).
% 0.79/0.96 tff(1469,plain,
% 0.79/0.96 (~c2_1(a734)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1468, 1467])).
% 0.79/0.96 tff(1470,plain,
% 0.79/0.96 (hskp5),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1092, 1469, 22])).
% 0.79/0.96 tff(1471,plain,
% 0.79/0.96 (c2_1(a744)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1112, 1467])).
% 0.79/0.96 tff(1472,plain,
% 0.79/0.96 (hskp2),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1434, 1471, 1095, 1123])).
% 0.79/0.96 tff(1473,plain,
% 0.79/0.96 (c0_1(a735)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1374, 1472, 1030, 1029, 22, 1094, 33, 1095])).
% 0.79/0.96 tff(1474,plain,
% 0.79/0.96 ($false),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[427, 1473, 1470])).
% 0.79/0.96 tff(1475,plain,(c1_1(a744) | hskp12 | hskp7 | c0_1(a734) | c0_1(a744) | c3_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.96 tff(1476,plain,
% 0.79/0.96 (c1_1(a744)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1475, 1094, 1029, 22, 1030, 33])).
% 0.79/0.96 tff(1477,plain,
% 0.79/0.96 (~hskp8),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[693, 1476])).
% 0.79/0.96 tff(1478,assumption,(~c2_1(a734)), introduced(assumption)).
% 0.79/0.96 tff(1479,plain,
% 0.79/0.96 (hskp5),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1177, 1478, 33, 1376])).
% 0.79/0.96 tff(1480,plain,
% 0.79/0.96 (c3_1(a735)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[413, 1479])).
% 0.79/0.96 tff(1481,plain,
% 0.79/0.96 (c2_1(a735)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[421, 1479])).
% 0.79/0.96 tff(1482,plain,
% 0.79/0.96 (hskp10 | c2_1(a734) | (~c3_1(a735)) | (~c2_1(a735))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1191, 104, 1376, 457, 22, 970])).
% 0.79/0.96 tff(1483,plain,
% 0.79/0.96 (hskp10),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1482, 1481, 1480, 1478])).
% 0.79/0.96 tff(1484,plain,
% 0.79/0.96 (~c2_1(a748)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[983, 1483])).
% 0.79/0.96 tff(1485,plain,
% 0.79/0.96 (~c0_1(a748)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[995, 1483])).
% 0.79/0.96 tff(1486,plain,
% 0.79/0.96 (~c3_1(a748)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1397, 104, 1030, 1029, 1485, 1484, 1028])).
% 0.79/0.96 tff(1487,plain,
% 0.79/0.96 (~c1_1(a748)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[989, 1483])).
% 0.79/0.96 tff(1488,plain,
% 0.79/0.96 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | c0_1(a748) | c1_1(a748) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | c3_1(a748))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c0_1(a748) | c1_1(a748) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | c3_1(a748))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1489,plain,
% 0.79/0.96 ((hskp3 | (~ndr1_0) | c2_1(a734) | c3_1(a734) | (~c1_1(a734)) | c3_1(a748) | c1_1(a748) | c0_1(a748)) <=> (hskp3 | c0_1(a748) | c1_1(a748) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | c3_1(a748))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1490,plain,
% 0.79/0.96 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a734) | c3_1(a734) | (~c1_1(a734)) | c3_1(a748) | c1_1(a748) | c0_1(a748))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | c0_1(a748) | c1_1(a748) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | c3_1(a748)))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[1489])).
% 0.79/0.96 tff(1491,plain,
% 0.79/0.96 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a734) | c3_1(a734) | (~c1_1(a734)) | c3_1(a748) | c1_1(a748) | c0_1(a748))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c0_1(a748) | c1_1(a748) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | c3_1(a748))),
% 0.79/0.96 inference(transitivity,[status(thm)],[1490, 1488])).
% 0.79/0.96 tff(1492,plain,
% 0.79/0.96 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a734) | c3_1(a734) | (~c1_1(a734)) | c3_1(a748) | c1_1(a748) | c0_1(a748))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(1493,plain,
% 0.79/0.96 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c0_1(a748) | c1_1(a748) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | c3_1(a748)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1492, 1491])).
% 0.79/0.96 tff(1494,plain,
% 0.79/0.96 (hskp3),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1493, 104, 1376, 1485, 1487, 33, 1147, 1478, 1486])).
% 0.79/0.96 tff(1495,plain,
% 0.79/0.96 (~c1_1(a733)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1215, 1494])).
% 0.79/0.96 tff(1496,assumption,(~hskp8), introduced(assumption)).
% 0.79/0.96 tff(1497,plain,
% 0.79/0.96 (hskp0),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1182, 1496])).
% 0.79/0.96 tff(1498,plain,
% 0.79/0.96 (~c1_1(a730)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[384, 1497])).
% 0.79/0.96 tff(1499,plain,
% 0.79/0.96 (c3_1(a730)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[435, 1497])).
% 0.79/0.96 tff(1500,plain,
% 0.79/0.96 (c0_1(a730)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[443, 1497])).
% 0.79/0.96 tff(1501,plain,
% 0.79/0.96 (hskp25),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1204, 104, 1500, 1499, 1485, 1487, 1484, 1498, 20])).
% 0.79/0.96 tff(1502,plain,
% 0.79/0.96 (c3_1(a729)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[762, 1501])).
% 0.79/0.96 tff(1503,plain,
% 0.79/0.96 (c2_1(a729)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[770, 1501])).
% 0.79/0.96 tff(1504,plain,
% 0.79/0.96 (c0_1(a729)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[778, 1501])).
% 0.79/0.96 tff(1505,plain,
% 0.79/0.96 (hskp21),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[863, 104, 1504, 1503, 1502, 467])).
% 0.79/0.96 tff(1506,plain,
% 0.79/0.96 (~c2_1(a793)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[482, 1505])).
% 0.79/0.96 tff(1507,plain,
% 0.79/0.96 (c2_1(a733)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1229, 1494])).
% 0.79/0.96 tff(1508,plain,
% 0.79/0.96 (c3_1(a793)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[492, 1505])).
% 0.79/0.96 tff(1509,plain,
% 0.79/0.96 (c0_1(a793)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[500, 1505])).
% 0.79/0.96 tff(1510,plain,
% 0.79/0.96 (~c3_1(a733)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1246, 104, 1509, 1508, 1481, 1480, 1507, 1506, 457, 1495, 455])).
% 0.79/0.96 tff(1511,plain,
% 0.79/0.96 (~c0_1(a733)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1159, 1494])).
% 0.79/0.96 tff(1512,plain,
% 0.79/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c0_1(a734) | c3_1(a734) | c0_1(a733) | (~ndr1_0) | c3_1(a733) | (~c2_1(a733)) | c2_1(a734))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a734) | c3_1(a734) | c0_1(a733) | (~ndr1_0) | c3_1(a733) | (~c2_1(a733)) | c2_1(a734))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1513,plain,
% 0.79/0.96 ((hskp8 | (~ndr1_0) | c0_1(a733) | c3_1(a733) | (~c2_1(a733)) | c3_1(a734) | c0_1(a734) | c2_1(a734)) <=> (hskp8 | c0_1(a734) | c3_1(a734) | c0_1(a733) | (~ndr1_0) | c3_1(a733) | (~c2_1(a733)) | c2_1(a734))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1514,plain,
% 0.79/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a733) | c3_1(a733) | (~c2_1(a733)) | c3_1(a734) | c0_1(a734) | c2_1(a734))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c0_1(a734) | c3_1(a734) | c0_1(a733) | (~ndr1_0) | c3_1(a733) | (~c2_1(a733)) | c2_1(a734)))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[1513])).
% 0.79/0.96 tff(1515,plain,
% 0.79/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a733) | c3_1(a733) | (~c2_1(a733)) | c3_1(a734) | c0_1(a734) | c2_1(a734))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a734) | c3_1(a734) | c0_1(a733) | (~ndr1_0) | c3_1(a733) | (~c2_1(a733)) | c2_1(a734))),
% 0.79/0.96 inference(transitivity,[status(thm)],[1514, 1512])).
% 0.79/0.96 tff(1516,plain,
% 0.79/0.96 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a733) | c3_1(a733) | (~c2_1(a733)) | c3_1(a734) | c0_1(a734) | c2_1(a734))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(1517,plain,
% 0.79/0.96 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a734) | c3_1(a734) | c0_1(a733) | (~ndr1_0) | c3_1(a733) | (~c2_1(a733)) | c2_1(a734)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1516, 1515])).
% 0.79/0.96 tff(1518,plain,
% 0.79/0.96 ($false),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1517, 1496, 104, 1507, 22, 33, 1511, 619, 1478, 1510])).
% 0.79/0.96 tff(1519,plain,(c2_1(a734) | hskp8 | c0_1(a734) | c3_1(a734) | c0_1(a735) | hskp12 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.79/0.96 tff(1520,plain,
% 0.79/0.96 (c2_1(a734)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1519, 457, 22, 33, 1477, 1030, 1029])).
% 0.79/0.96 tff(1521,plain,
% 0.79/0.96 ((~c2_1(a734)) | c2_1(a744)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1383, 1477, 104, 1096, 1094, 22, 33, 619])).
% 0.79/0.96 tff(1522,plain,
% 0.79/0.96 (c2_1(a744)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1521, 1520])).
% 0.79/0.96 tff(1523,assumption,(c2_1(a744)), introduced(assumption)).
% 0.79/0.96 tff(1524,plain,
% 0.79/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c3_1(a744) | c0_1(a744) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c3_1(a744) | c0_1(a744) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a744)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1525,plain,
% 0.79/0.96 ((hskp8 | (~ndr1_0) | c0_1(a744) | c3_1(a744) | (~c2_1(a744)) | c3_1(a732) | c0_1(a732) | c2_1(a732)) <=> (hskp8 | c3_1(a744) | c0_1(a744) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a744)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1526,plain,
% 0.79/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a744) | c3_1(a744) | (~c2_1(a744)) | c3_1(a732) | c0_1(a732) | c2_1(a732))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c3_1(a744) | c0_1(a744) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a744))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[1525])).
% 0.79/0.96 tff(1527,plain,
% 0.79/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a744) | c3_1(a744) | (~c2_1(a744)) | c3_1(a732) | c0_1(a732) | c2_1(a732))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c3_1(a744) | c0_1(a744) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a744)))),
% 0.79/0.96 inference(transitivity,[status(thm)],[1526, 1524])).
% 0.79/0.96 tff(1528,plain,
% 0.79/0.96 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a744) | c3_1(a744) | (~c2_1(a744)) | c3_1(a732) | c0_1(a732) | c2_1(a732))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(1529,plain,
% 0.79/0.96 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c3_1(a744) | c0_1(a744) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a744))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1528, 1527])).
% 0.79/0.96 tff(1530,plain,
% 0.79/0.96 ($false),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1529, 1496, 104, 1096, 1094, 1126, 1127, 1125, 619, 1523])).
% 0.79/0.96 tff(1531,plain,((~hskp2) | hskp8 | c3_1(a744) | c0_1(a744) | (~c2_1(a744))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.96 tff(1532,plain,
% 0.79/0.96 (~hskp2),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1531, 1522, 1096, 1094, 1477])).
% 0.79/0.96 tff(1533,assumption,(c2_1(a734)), introduced(assumption)).
% 0.79/0.96 tff(1534,assumption,(c1_1(a744)), introduced(assumption)).
% 0.79/0.96 tff(1535,assumption,(hskp11), introduced(assumption)).
% 0.79/0.96 tff(1536,plain,
% 0.79/0.96 (((~hskp11) | (~c0_1(a749))) <=> ((~hskp11) | (~c0_1(a749)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1537,plain,
% 0.79/0.96 (((~c0_1(a749)) | (~hskp11)) <=> ((~hskp11) | (~c0_1(a749)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1538,axiom,((~c0_1(a749)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.79/0.96 tff(1539,plain,
% 0.79/0.96 ((~hskp11) | (~c0_1(a749))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1538, 1537])).
% 0.79/0.96 tff(1540,plain,
% 0.79/0.96 ((~hskp11) | (~c0_1(a749))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1539, 1536])).
% 0.79/0.96 tff(1541,plain,
% 0.79/0.96 (~c0_1(a749)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1540, 1535])).
% 0.79/0.96 tff(1542,assumption,(~c2_1(a749)), introduced(assumption)).
% 0.79/0.96 tff(1543,assumption,(~c0_1(a749)), introduced(assumption)).
% 0.79/0.96 tff(1544,plain,
% 0.79/0.96 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | c0_1(a749) | (~c3_1(a749)) | (~ndr1_0) | c2_1(a749))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp7 | c0_1(a749) | (~c3_1(a749)) | (~ndr1_0) | c2_1(a749))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1545,plain,
% 0.79/0.96 ((hskp12 | hskp7 | (~ndr1_0) | c2_1(a749) | c0_1(a749) | (~c3_1(a749))) <=> (hskp12 | hskp7 | c0_1(a749) | (~c3_1(a749)) | (~ndr1_0) | c2_1(a749))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1546,plain,
% 0.79/0.96 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c2_1(a749) | c0_1(a749) | (~c3_1(a749)))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | c0_1(a749) | (~c3_1(a749)) | (~ndr1_0) | c2_1(a749)))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[1545])).
% 0.79/0.96 tff(1547,plain,
% 0.79/0.96 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c2_1(a749) | c0_1(a749) | (~c3_1(a749)))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp7 | c0_1(a749) | (~c3_1(a749)) | (~ndr1_0) | c2_1(a749))),
% 0.79/0.96 inference(transitivity,[status(thm)],[1546, 1544])).
% 0.79/0.96 tff(1548,plain,
% 0.79/0.96 ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c2_1(a749) | c0_1(a749) | (~c3_1(a749)))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(1549,plain,
% 0.79/0.96 ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp7 | c0_1(a749) | (~c3_1(a749)) | (~ndr1_0) | c2_1(a749)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1548, 1547])).
% 0.79/0.96 tff(1550,plain,
% 0.79/0.96 ((~c3_1(a749)) | c2_1(a749)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1549, 104, 1030, 1029, 1543, 1028])).
% 0.79/0.96 tff(1551,plain,
% 0.79/0.96 (~c3_1(a749)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1550, 1542])).
% 0.79/0.96 tff(1552,plain,
% 0.79/0.96 (((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | c0_1(a749) | c3_1(a749) | (~ndr1_0) | c2_1(a749))) <=> ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp5 | c0_1(a749) | c3_1(a749) | (~ndr1_0) | c2_1(a749))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1553,plain,
% 0.79/0.96 ((hskp9 | hskp5 | (~ndr1_0) | c2_1(a749) | c0_1(a749) | c3_1(a749)) <=> (hskp9 | hskp5 | c0_1(a749) | c3_1(a749) | (~ndr1_0) | c2_1(a749))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1554,plain,
% 0.79/0.96 (((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | (~ndr1_0) | c2_1(a749) | c0_1(a749) | c3_1(a749))) <=> ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | c0_1(a749) | c3_1(a749) | (~ndr1_0) | c2_1(a749)))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[1553])).
% 0.79/0.96 tff(1555,plain,
% 0.79/0.96 (((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | (~ndr1_0) | c2_1(a749) | c0_1(a749) | c3_1(a749))) <=> ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp5 | c0_1(a749) | c3_1(a749) | (~ndr1_0) | c2_1(a749))),
% 0.79/0.96 inference(transitivity,[status(thm)],[1554, 1552])).
% 0.79/0.96 tff(1556,plain,
% 0.79/0.96 ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | (~ndr1_0) | c2_1(a749) | c0_1(a749) | c3_1(a749))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(1557,plain,
% 0.79/0.96 ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp5 | c0_1(a749) | c3_1(a749) | (~ndr1_0) | c2_1(a749)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1556, 1555])).
% 0.79/0.96 tff(1558,plain,
% 0.79/0.96 (c3_1(a749) | c2_1(a749)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1557, 104, 1061, 396, 1543, 1085])).
% 0.79/0.96 tff(1559,plain,
% 0.79/0.96 ($false),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1558, 1551, 1542])).
% 0.79/0.96 tff(1560,plain,(c2_1(a749) | hskp5 | c0_1(a749) | hskp12 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.79/0.96 tff(1561,plain,
% 0.79/0.96 (c2_1(a749)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1560, 1541, 396, 1030, 1029])).
% 0.79/0.96 tff(1562,plain,
% 0.79/0.96 (((~hskp11) | (~c1_1(a749))) <=> ((~hskp11) | (~c1_1(a749)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1563,plain,
% 0.79/0.96 (((~c1_1(a749)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a749)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1564,axiom,((~c1_1(a749)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 0.79/0.96 tff(1565,plain,
% 0.79/0.96 ((~hskp11) | (~c1_1(a749))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1564, 1563])).
% 0.79/0.96 tff(1566,plain,
% 0.79/0.96 ((~hskp11) | (~c1_1(a749))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1565, 1562])).
% 0.79/0.96 tff(1567,plain,
% 0.79/0.96 (~c1_1(a749)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1566, 1535])).
% 0.79/0.96 tff(1568,plain,
% 0.79/0.96 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c0_1(a749) | c1_1(a749) | (~ndr1_0) | (~c2_1(a749)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a749) | c1_1(a749) | (~ndr1_0) | (~c2_1(a749)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1569,plain,
% 0.79/0.96 ((hskp2 | hskp1 | (~ndr1_0) | c1_1(a749) | c0_1(a749) | (~c2_1(a749))) <=> (hskp2 | hskp1 | c0_1(a749) | c1_1(a749) | (~ndr1_0) | (~c2_1(a749)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1570,plain,
% 0.79/0.96 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c1_1(a749) | c0_1(a749) | (~c2_1(a749)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c0_1(a749) | c1_1(a749) | (~ndr1_0) | (~c2_1(a749))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[1569])).
% 0.79/0.96 tff(1571,plain,
% 0.79/0.96 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c1_1(a749) | c0_1(a749) | (~c2_1(a749)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a749) | c1_1(a749) | (~ndr1_0) | (~c2_1(a749)))),
% 0.79/0.96 inference(transitivity,[status(thm)],[1570, 1568])).
% 0.79/0.96 tff(1572,plain,
% 0.79/0.96 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c1_1(a749) | c0_1(a749) | (~c2_1(a749)))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(1573,plain,
% 0.79/0.96 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a749) | c1_1(a749) | (~ndr1_0) | (~c2_1(a749))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1572, 1571])).
% 0.79/0.96 tff(1574,plain,
% 0.79/0.96 ($false),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1573, 104, 256, 255, 1541, 1567, 266, 1561])).
% 0.79/0.96 tff(1575,plain,((~hskp11) | hskp2 | hskp1 | hskp5 | hskp12 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.79/0.96 tff(1576,plain,
% 0.79/0.96 (~hskp11),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1575, 396, 255, 256, 1030, 1029])).
% 0.79/0.97 tff(1577,plain,
% 0.79/0.97 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp11 | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734)))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp11 | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1578,plain,
% 0.79/0.97 ((hskp27 | hskp11 | (~ndr1_0) | c3_1(a734) | (~c2_1(a734)) | (~c1_1(a734))) <=> (hskp27 | hskp11 | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1579,plain,
% 0.79/0.97 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp11 | (~ndr1_0) | c3_1(a734) | (~c2_1(a734)) | (~c1_1(a734)))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp11 | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[1578])).
% 0.79/0.97 tff(1580,plain,
% 0.79/0.97 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp11 | (~ndr1_0) | c3_1(a734) | (~c2_1(a734)) | (~c1_1(a734)))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp11 | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734)))),
% 0.79/0.97 inference(transitivity,[status(thm)],[1579, 1577])).
% 0.79/0.97 tff(1581,plain,
% 0.79/0.97 ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp11 | (~ndr1_0) | c3_1(a734) | (~c2_1(a734)) | (~c1_1(a734)))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(1582,plain,
% 0.79/0.97 ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp11 | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1581, 1580])).
% 0.79/0.97 tff(1583,plain,
% 0.79/0.97 (hskp27 | hskp11 | (~c2_1(a734)) | (~c1_1(a734))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1582, 104, 33, 559])).
% 0.79/0.97 tff(1584,plain,
% 0.79/0.97 (hskp27),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1583, 1576, 1006, 1533])).
% 0.79/0.97 tff(1585,plain,
% 0.79/0.97 (c2_1(a750)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[724, 1584])).
% 0.79/0.97 tff(1586,plain,
% 0.79/0.97 (c0_1(a750)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[716, 1584])).
% 0.79/0.97 tff(1587,assumption,(c3_1(a750)), introduced(assumption)).
% 0.79/0.97 tff(1588,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a744) | (~c1_1(a744)) | (~ndr1_0) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c2_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a744) | (~c1_1(a744)) | (~ndr1_0) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c2_1(a744)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1589,plain,
% 0.79/0.97 ((hskp16 | (~ndr1_0) | (~c2_1(a750)) | (~c3_1(a750)) | (~c0_1(a750)) | c0_1(a744) | (~c2_1(a744)) | (~c1_1(a744))) <=> (hskp16 | c0_1(a744) | (~c1_1(a744)) | (~ndr1_0) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c2_1(a744)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1590,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a750)) | (~c3_1(a750)) | (~c0_1(a750)) | c0_1(a744) | (~c2_1(a744)) | (~c1_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a744) | (~c1_1(a744)) | (~ndr1_0) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c2_1(a744))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[1589])).
% 0.79/0.97 tff(1591,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a750)) | (~c3_1(a750)) | (~c0_1(a750)) | c0_1(a744) | (~c2_1(a744)) | (~c1_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a744) | (~c1_1(a744)) | (~ndr1_0) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c2_1(a744)))),
% 0.79/0.97 inference(transitivity,[status(thm)],[1590, 1588])).
% 0.79/0.97 tff(1592,plain,
% 0.79/0.97 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a750)) | (~c3_1(a750)) | (~c0_1(a750)) | c0_1(a744) | (~c2_1(a744)) | (~c1_1(a744)))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(1593,plain,
% 0.79/0.97 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a744) | (~c1_1(a744)) | (~ndr1_0) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c2_1(a744))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1592, 1591])).
% 0.79/0.97 tff(1594,plain,
% 0.79/0.97 (hskp16 | (~c3_1(a750))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1593, 104, 744, 801, 1094, 1534, 754, 1523])).
% 0.79/0.97 tff(1595,plain,
% 0.79/0.97 (hskp16),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1594, 1587])).
% 0.79/0.97 tff(1596,plain,
% 0.79/0.97 (~c3_1(a764)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[791, 1595])).
% 0.79/0.97 tff(1597,plain,
% 0.79/0.97 (c0_1(a764)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[809, 1595])).
% 0.79/0.97 tff(1598,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | c3_1(a764) | (~ndr1_0) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c0_1(a764)) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp1 | c3_1(a764) | (~ndr1_0) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1599,plain,
% 0.79/0.97 ((hskp1 | (~ndr1_0) | (~c2_1(a750)) | (~c3_1(a750)) | (~c0_1(a750)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764))) <=> (hskp1 | c3_1(a764) | (~ndr1_0) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1600,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c2_1(a750)) | (~c3_1(a750)) | (~c0_1(a750)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | c3_1(a764) | (~ndr1_0) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c0_1(a764)) | (~c1_1(a764))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[1599])).
% 0.79/0.97 tff(1601,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c2_1(a750)) | (~c3_1(a750)) | (~c0_1(a750)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp1 | c3_1(a764) | (~ndr1_0) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 0.79/0.97 inference(transitivity,[status(thm)],[1600, 1598])).
% 0.79/0.97 tff(1602,plain,
% 0.79/0.97 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c2_1(a750)) | (~c3_1(a750)) | (~c0_1(a750)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(1603,plain,
% 0.79/0.97 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp1 | c3_1(a764) | (~ndr1_0) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c0_1(a764)) | (~c1_1(a764))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1602, 1601])).
% 0.79/0.97 tff(1604,plain,
% 0.79/0.97 (~c1_1(a764)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1603, 104, 255, 744, 801, 1597, 1596, 743, 1587])).
% 0.79/0.97 tff(1605,plain,
% 0.79/0.97 (c2_1(a764)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[799, 1595])).
% 0.79/0.97 tff(1606,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c3_1(a764) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c1_1(a764) | (~c2_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c3_1(a764) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c1_1(a764) | (~c2_1(a764)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1607,plain,
% 0.79/0.97 ((hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a764) | c1_1(a764) | (~c2_1(a764))) <=> (hskp5 | c3_1(a764) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c1_1(a764) | (~c2_1(a764)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1608,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a764) | c1_1(a764) | (~c2_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c3_1(a764) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c1_1(a764) | (~c2_1(a764))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[1607])).
% 0.79/0.97 tff(1609,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a764) | c1_1(a764) | (~c2_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c3_1(a764) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c1_1(a764) | (~c2_1(a764)))),
% 0.79/0.97 inference(transitivity,[status(thm)],[1608, 1606])).
% 0.79/0.97 tff(1610,plain,
% 0.79/0.97 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a764) | c1_1(a764) | (~c2_1(a764)))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(1611,plain,
% 0.79/0.97 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c3_1(a764) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c1_1(a764) | (~c2_1(a764))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1610, 1609])).
% 0.79/0.97 tff(1612,plain,
% 0.79/0.97 ($false),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1611, 104, 396, 1605, 469, 468, 1596, 456, 1456, 1604])).
% 0.79/0.97 tff(1613,plain,((~c3_1(a750)) | hskp5 | (~c0_1(a730)) | (~c3_1(a730)) | c1_1(a730) | hskp1 | (~c0_1(a750)) | (~c2_1(a750)) | c0_1(a744) | (~c1_1(a744)) | (~c2_1(a744))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.97 tff(1614,plain,
% 0.79/0.97 (~c3_1(a750)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1613, 396, 469, 468, 456, 255, 1586, 1585, 1094, 1534, 1523])).
% 0.79/0.97 tff(1615,plain,
% 0.79/0.97 (~hskp8),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[693, 1534])).
% 0.79/0.97 tff(1616,plain,
% 0.79/0.97 (c1_1(a750)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[732, 1584])).
% 0.79/0.97 tff(1617,plain,
% 0.79/0.97 (((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp11 | (~ndr1_0) | (~c0_1(a750)) | c3_1(a750) | (~c1_1(a750)))) <=> ((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp18 | hskp11 | (~ndr1_0) | (~c0_1(a750)) | c3_1(a750) | (~c1_1(a750)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1618,plain,
% 0.79/0.97 ((hskp18 | hskp11 | (~ndr1_0) | c3_1(a750) | (~c1_1(a750)) | (~c0_1(a750))) <=> (hskp18 | hskp11 | (~ndr1_0) | (~c0_1(a750)) | c3_1(a750) | (~c1_1(a750)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1619,plain,
% 0.79/0.97 (((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp11 | (~ndr1_0) | c3_1(a750) | (~c1_1(a750)) | (~c0_1(a750)))) <=> ((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp11 | (~ndr1_0) | (~c0_1(a750)) | c3_1(a750) | (~c1_1(a750))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[1618])).
% 0.79/0.97 tff(1620,plain,
% 0.79/0.97 (((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp11 | (~ndr1_0) | c3_1(a750) | (~c1_1(a750)) | (~c0_1(a750)))) <=> ((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp18 | hskp11 | (~ndr1_0) | (~c0_1(a750)) | c3_1(a750) | (~c1_1(a750)))),
% 0.79/0.97 inference(transitivity,[status(thm)],[1619, 1617])).
% 0.79/0.97 tff(1621,plain,
% 0.79/0.97 ((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp11 | (~ndr1_0) | c3_1(a750) | (~c1_1(a750)) | (~c0_1(a750)))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(1622,plain,
% 0.79/0.97 ((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp18 | hskp11 | (~ndr1_0) | (~c0_1(a750)) | c3_1(a750) | (~c1_1(a750))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1621, 1620])).
% 0.79/0.97 tff(1623,plain,
% 0.79/0.97 (hskp18 | c3_1(a750)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1622, 104, 1576, 1586, 1616, 1075])).
% 0.79/0.97 tff(1624,plain,
% 0.79/0.97 (hskp18),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1623, 1614])).
% 0.79/0.97 tff(1625,assumption,(hskp18), introduced(assumption)).
% 0.79/0.97 tff(1626,plain,
% 0.79/0.97 (((~hskp18) | (~c3_1(a775))) <=> ((~hskp18) | (~c3_1(a775)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1627,plain,
% 0.79/0.97 (((~c3_1(a775)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a775)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1628,axiom,((~c3_1(a775)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 0.79/0.97 tff(1629,plain,
% 0.79/0.97 ((~hskp18) | (~c3_1(a775))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1628, 1627])).
% 0.79/0.97 tff(1630,plain,
% 0.79/0.97 ((~hskp18) | (~c3_1(a775))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1629, 1626])).
% 0.79/0.97 tff(1631,plain,
% 0.79/0.97 (~c3_1(a775)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1630, 1625])).
% 0.79/0.97 tff(1632,plain,
% 0.79/0.97 (((~hskp18) | (~c2_1(a775))) <=> ((~hskp18) | (~c2_1(a775)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1633,plain,
% 0.79/0.97 (((~c2_1(a775)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a775)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1634,axiom,((~c2_1(a775)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 0.79/0.97 tff(1635,plain,
% 0.79/0.97 ((~hskp18) | (~c2_1(a775))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1634, 1633])).
% 0.79/0.97 tff(1636,plain,
% 0.79/0.97 ((~hskp18) | (~c2_1(a775))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1635, 1632])).
% 0.79/0.97 tff(1637,plain,
% 0.79/0.97 (~c2_1(a775)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1636, 1625])).
% 0.79/0.97 tff(1638,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c3_1(a744) | c2_1(a775) | c3_1(a775) | c0_1(a744) | (~ndr1_0) | (~c2_1(a744)) | c0_1(a775))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c3_1(a744) | c2_1(a775) | c3_1(a775) | c0_1(a744) | (~ndr1_0) | (~c2_1(a744)) | c0_1(a775))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1639,plain,
% 0.79/0.97 ((hskp8 | (~ndr1_0) | c0_1(a744) | c3_1(a744) | (~c2_1(a744)) | c3_1(a775) | c0_1(a775) | c2_1(a775)) <=> (hskp8 | c3_1(a744) | c2_1(a775) | c3_1(a775) | c0_1(a744) | (~ndr1_0) | (~c2_1(a744)) | c0_1(a775))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1640,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a744) | c3_1(a744) | (~c2_1(a744)) | c3_1(a775) | c0_1(a775) | c2_1(a775))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c3_1(a744) | c2_1(a775) | c3_1(a775) | c0_1(a744) | (~ndr1_0) | (~c2_1(a744)) | c0_1(a775)))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[1639])).
% 0.79/0.97 tff(1641,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a744) | c3_1(a744) | (~c2_1(a744)) | c3_1(a775) | c0_1(a775) | c2_1(a775))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c3_1(a744) | c2_1(a775) | c3_1(a775) | c0_1(a744) | (~ndr1_0) | (~c2_1(a744)) | c0_1(a775))),
% 0.79/0.97 inference(transitivity,[status(thm)],[1640, 1638])).
% 0.79/0.97 tff(1642,plain,
% 0.79/0.97 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a744) | c3_1(a744) | (~c2_1(a744)) | c3_1(a775) | c0_1(a775) | c2_1(a775))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(1643,plain,
% 0.79/0.97 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c3_1(a744) | c2_1(a775) | c3_1(a775) | c0_1(a744) | (~ndr1_0) | (~c2_1(a744)) | c0_1(a775)),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 0.79/0.97 tff(1644,plain,
% 0.79/0.97 (c0_1(a775)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1643, 1496, 104, 1096, 1637, 1631, 1094, 619, 1523])).
% 0.79/0.97 tff(1645,plain,
% 0.79/0.97 (^[U: $i] : refl((hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 0.79/0.97 inference(bind,[status(th)],[])).
% 0.79/0.97 tff(1646,plain,
% 0.79/0.97 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.79/0.97 inference(quant_intro,[status(thm)],[1645])).
% 0.79/0.97 tff(1647,plain,
% 0.79/0.97 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1648,plain,
% 0.79/0.97 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | 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)) | hskp25) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp25))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) | hskp9) <=> ((hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp9))), rewrite(((hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp9) <=> (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) | hskp9) <=> (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 0.79/0.97 inference(bind,[status(th)],[])).
% 0.79/0.97 tff(1649,plain,
% 0.79/0.97 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) | hskp9) <=> ![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.79/0.97 inference(quant_intro,[status(thm)],[1648])).
% 0.79/0.97 tff(1650,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 0.79/0.97 tff(1651,plain,
% 0.79/0.97 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1650, 1649])).
% 0.79/0.97 tff(1652,plain,
% 0.79/0.97 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1651, 1647])).
% 0.79/0.97 tff(1653,plain,(
% 0.79/0.97 ![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.79/0.97 inference(skolemize,[status(sab)],[1652])).
% 0.79/0.97 tff(1654,plain,
% 0.79/0.97 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1653, 1646])).
% 0.79/0.97 tff(1655,assumption,(~hskp9), introduced(assumption)).
% 0.79/0.97 tff(1656,assumption,(~hskp25), introduced(assumption)).
% 0.79/0.97 tff(1657,plain,
% 0.79/0.97 (((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp9 | c2_1(a775) | c3_1(a775) | (~ndr1_0) | (~c0_1(a775)))) <=> ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp25 | hskp9 | c2_1(a775) | c3_1(a775) | (~ndr1_0) | (~c0_1(a775)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1658,plain,
% 0.79/0.97 ((hskp25 | hskp9 | (~ndr1_0) | c2_1(a775) | c3_1(a775) | (~c0_1(a775))) <=> (hskp25 | hskp9 | c2_1(a775) | c3_1(a775) | (~ndr1_0) | (~c0_1(a775)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1659,plain,
% 0.79/0.97 (((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp9 | (~ndr1_0) | c2_1(a775) | c3_1(a775) | (~c0_1(a775)))) <=> ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp9 | c2_1(a775) | c3_1(a775) | (~ndr1_0) | (~c0_1(a775))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[1658])).
% 0.79/0.97 tff(1660,plain,
% 0.79/0.97 (((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp9 | (~ndr1_0) | c2_1(a775) | c3_1(a775) | (~c0_1(a775)))) <=> ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp25 | hskp9 | c2_1(a775) | c3_1(a775) | (~ndr1_0) | (~c0_1(a775)))),
% 0.79/0.97 inference(transitivity,[status(thm)],[1659, 1657])).
% 0.79/0.97 tff(1661,plain,
% 0.79/0.97 ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp9 | (~ndr1_0) | c2_1(a775) | c3_1(a775) | (~c0_1(a775)))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(1662,plain,
% 0.79/0.97 ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp25 | hskp9 | c2_1(a775) | c3_1(a775) | (~ndr1_0) | (~c0_1(a775))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1661, 1660])).
% 0.79/0.97 tff(1663,plain,
% 0.79/0.97 ($false),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1662, 104, 1656, 1655, 1637, 1631, 1654, 1644])).
% 0.79/0.97 tff(1664,plain,((~hskp18) | hskp25 | hskp9 | hskp8 | c3_1(a744) | c0_1(a744) | (~c2_1(a744))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.97 tff(1665,plain,
% 0.79/0.97 (hskp25),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1664, 1624, 1061, 1615, 1096, 1094, 1523])).
% 0.79/0.97 tff(1666,plain,
% 0.79/0.97 (c3_1(a729)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[762, 1665])).
% 0.79/0.97 tff(1667,plain,
% 0.79/0.97 (c2_1(a729)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[770, 1665])).
% 0.79/0.97 tff(1668,plain,
% 0.79/0.97 (c0_1(a729)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[778, 1665])).
% 0.79/0.97 tff(1669,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a750)) | c3_1(a750) | (~c1_1(a750)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp1 | (~ndr1_0) | (~c0_1(a750)) | c3_1(a750) | (~c1_1(a750)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1670,plain,
% 0.79/0.97 ((hskp1 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c3_1(a750) | (~c1_1(a750)) | (~c0_1(a750))) <=> (hskp1 | (~ndr1_0) | (~c0_1(a750)) | c3_1(a750) | (~c1_1(a750)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1671,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c3_1(a750) | (~c1_1(a750)) | (~c0_1(a750)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a750)) | c3_1(a750) | (~c1_1(a750)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[1670])).
% 0.79/0.97 tff(1672,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c3_1(a750) | (~c1_1(a750)) | (~c0_1(a750)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp1 | (~ndr1_0) | (~c0_1(a750)) | c3_1(a750) | (~c1_1(a750)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)))),
% 0.79/0.97 inference(transitivity,[status(thm)],[1671, 1669])).
% 0.79/0.97 tff(1673,plain,
% 0.79/0.97 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c3_1(a750) | (~c1_1(a750)) | (~c0_1(a750)))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(1674,plain,
% 0.79/0.97 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp1 | (~ndr1_0) | (~c0_1(a750)) | c3_1(a750) | (~c1_1(a750)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1673, 1672])).
% 0.79/0.97 tff(1675,plain,
% 0.79/0.97 ($false),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1674, 104, 255, 1586, 1616, 1668, 1667, 1666, 743, 1614])).
% 0.79/0.97 tff(1676,plain,(hskp5 | hskp1 | c3_1(a744) | c0_1(a744) | (~c2_1(a744)) | (~c0_1(a730)) | (~c3_1(a730)) | c1_1(a730) | (~c1_1(a744)) | (~c1_1(a734)) | (~c2_1(a734)) | c3_1(a734) | hskp2 | hskp12 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.79/0.97 tff(1677,plain,
% 0.79/0.97 (hskp5),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1676, 256, 1096, 1094, 1523, 469, 468, 456, 1534, 1006, 1533, 33, 255, 1030, 1029])).
% 0.79/0.97 tff(1678,plain,
% 0.79/0.97 (c2_1(a735)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[421, 1677])).
% 0.79/0.97 tff(1679,plain,
% 0.79/0.97 (hskp2 | hskp1 | (~c2_1(a735)) | c1_1(a735)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[517, 104, 457, 266])).
% 0.79/0.97 tff(1680,plain,
% 0.79/0.97 (c1_1(a735)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1679, 1678, 255, 256])).
% 0.79/0.97 tff(1681,plain,
% 0.79/0.97 (c3_1(a735)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[413, 1677])).
% 0.79/0.97 tff(1682,plain,
% 0.79/0.97 (c2_1(a730)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[538, 256, 1681, 469, 457, 456, 1680])).
% 0.79/0.97 tff(1683,plain,
% 0.79/0.97 (hskp21),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[476, 1682])).
% 0.79/0.97 tff(1684,plain,
% 0.79/0.97 (~c2_1(a793)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[482, 1683])).
% 0.79/0.97 tff(1685,plain,
% 0.79/0.97 (c3_1(a793)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[492, 1683])).
% 0.79/0.97 tff(1686,plain,
% 0.79/0.97 (c0_1(a793)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[500, 1683])).
% 0.79/0.97 tff(1687,plain,
% 0.79/0.97 ($false),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[507, 104, 1686, 1685, 1678, 1681, 468, 1684, 457, 456, 455, 1682])).
% 0.79/0.97 tff(1688,plain,(hskp2 | (~c3_1(a730)) | c0_1(a735) | c1_1(a730) | (~c0_1(a730)) | hskp1 | c3_1(a744) | c0_1(a744) | (~c2_1(a744)) | (~c1_1(a744)) | (~c1_1(a734)) | (~c2_1(a734)) | c3_1(a734) | hskp12 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.79/0.97 tff(1689,plain,
% 0.79/0.97 (hskp1),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1688, 1532, 457, 1065, 1064, 1457, 1096, 1094, 1522, 1476, 1048, 1520, 33, 1030, 1029])).
% 0.79/0.97 tff(1690,plain,
% 0.79/0.97 (~c2_1(a731)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[58, 1689])).
% 0.79/0.97 tff(1691,plain,
% 0.79/0.97 (c3_1(a731)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[66, 1689])).
% 0.79/0.97 tff(1692,plain,
% 0.79/0.97 (c0_1(a731)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1039, 104, 1030, 1029, 1691, 1690, 1028])).
% 0.79/0.97 tff(1693,plain,
% 0.79/0.97 (c1_1(a731)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[74, 1689])).
% 0.79/0.97 tff(1694,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | c3_1(a744) | c0_1(a744) | (~c1_1(a744)) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | (~c0_1(a731)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp13 | c3_1(a744) | c0_1(a744) | (~c1_1(a744)) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | (~c0_1(a731)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1695,plain,
% 0.79/0.97 ((hskp13 | (~ndr1_0) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c3_1(a744) | c0_1(a744) | (~c1_1(a744))) <=> (hskp13 | c3_1(a744) | c0_1(a744) | (~c1_1(a744)) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | (~c0_1(a731)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1696,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c3_1(a744) | c0_1(a744) | (~c1_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | c3_1(a744) | c0_1(a744) | (~c1_1(a744)) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | (~c0_1(a731))))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[1695])).
% 0.79/0.98 tff(1697,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c3_1(a744) | c0_1(a744) | (~c1_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp13 | c3_1(a744) | c0_1(a744) | (~c1_1(a744)) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | (~c0_1(a731)))),
% 0.79/0.98 inference(transitivity,[status(thm)],[1696, 1694])).
% 0.79/0.98 tff(1698,plain,
% 0.79/0.98 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c3_1(a744) | c0_1(a744) | (~c1_1(a744)))),
% 0.79/0.98 inference(quant_inst,[status(thm)],[])).
% 0.79/0.98 tff(1699,plain,
% 0.79/0.98 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp13 | c3_1(a744) | c0_1(a744) | (~c1_1(a744)) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | (~c0_1(a731))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1698, 1697])).
% 0.79/0.98 tff(1700,plain,
% 0.79/0.98 (hskp13),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1699, 104, 1096, 1693, 1094, 1476, 1690, 32, 1692])).
% 0.79/0.98 tff(1701,plain,
% 0.79/0.98 (c2_1(a759)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[890, 1700])).
% 0.79/0.98 tff(1702,plain,
% 0.79/0.98 (~c1_1(a759)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[873, 1700])).
% 0.79/0.98 tff(1703,plain,
% 0.79/0.98 (c3_1(a759)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[882, 1700])).
% 0.79/0.98 tff(1704,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c3_1(a744) | c1_1(a759) | c0_1(a744) | (~ndr1_0) | (~c2_1(a744)) | (~c3_1(a759)) | c0_1(a759))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c3_1(a744) | c1_1(a759) | c0_1(a744) | (~ndr1_0) | (~c2_1(a744)) | (~c3_1(a759)) | c0_1(a759))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1705,plain,
% 0.79/0.98 ((hskp7 | (~ndr1_0) | c0_1(a744) | c3_1(a744) | (~c2_1(a744)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759))) <=> (hskp7 | c3_1(a744) | c1_1(a759) | c0_1(a744) | (~ndr1_0) | (~c2_1(a744)) | (~c3_1(a759)) | c0_1(a759))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1706,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a744) | c3_1(a744) | (~c2_1(a744)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c3_1(a744) | c1_1(a759) | c0_1(a744) | (~ndr1_0) | (~c2_1(a744)) | (~c3_1(a759)) | c0_1(a759)))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[1705])).
% 0.79/0.98 tff(1707,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a744) | c3_1(a744) | (~c2_1(a744)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c3_1(a744) | c1_1(a759) | c0_1(a744) | (~ndr1_0) | (~c2_1(a744)) | (~c3_1(a759)) | c0_1(a759))),
% 0.79/0.98 inference(transitivity,[status(thm)],[1706, 1704])).
% 0.79/0.98 tff(1708,plain,
% 0.79/0.98 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a744) | c3_1(a744) | (~c2_1(a744)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759)))),
% 0.79/0.98 inference(quant_inst,[status(thm)],[])).
% 0.79/0.98 tff(1709,plain,
% 0.79/0.98 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c3_1(a744) | c1_1(a759) | c0_1(a744) | (~ndr1_0) | (~c2_1(a744)) | (~c3_1(a759)) | c0_1(a759)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1708, 1707])).
% 0.79/0.98 tff(1710,plain,
% 0.79/0.98 (c0_1(a759)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1709, 104, 1029, 1703, 1096, 1702, 1094, 1263, 1522])).
% 0.79/0.98 tff(1711,assumption,(c0_1(a759)), introduced(assumption)).
% 0.79/0.98 tff(1712,assumption,(~c1_1(a759)), introduced(assumption)).
% 0.79/0.98 tff(1713,plain,
% 0.79/0.98 (^[U: $i] : refl((hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(1714,plain,
% 0.79/0.98 (![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[1713])).
% 0.79/0.98 tff(1715,plain,
% 0.79/0.98 (![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1716,plain,
% 0.79/0.98 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp5) | hskp20) <=> ((hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp20))), rewrite(((hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp20) <=> (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp5) | hskp20) <=> (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(1717,plain,
% 0.79/0.98 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp5) | hskp20) <=> ![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[1716])).
% 0.79/0.98 tff(1718,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp5) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 0.79/0.98 tff(1719,plain,
% 0.79/0.98 (![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1718, 1717])).
% 0.79/0.98 tff(1720,plain,
% 0.79/0.98 (![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1719, 1715])).
% 0.79/0.98 tff(1721,plain,(
% 0.79/0.98 ![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.79/0.98 inference(skolemize,[status(sab)],[1720])).
% 0.79/0.98 tff(1722,plain,
% 0.79/0.98 (![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1721, 1714])).
% 0.79/0.98 tff(1723,assumption,(c3_1(a759)), introduced(assumption)).
% 0.79/0.98 tff(1724,assumption,(c2_1(a759)), introduced(assumption)).
% 0.79/0.98 tff(1725,plain,
% 0.79/0.98 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp20 | hskp5 | c1_1(a759) | (~ndr1_0) | (~c2_1(a759)) | (~c3_1(a759)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp20 | hskp5 | c1_1(a759) | (~ndr1_0) | (~c2_1(a759)) | (~c3_1(a759)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1726,plain,
% 0.79/0.98 ((hskp20 | hskp5 | (~ndr1_0) | c1_1(a759) | (~c2_1(a759)) | (~c3_1(a759))) <=> (hskp20 | hskp5 | c1_1(a759) | (~ndr1_0) | (~c2_1(a759)) | (~c3_1(a759)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1727,plain,
% 0.79/0.98 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c1_1(a759) | (~c2_1(a759)) | (~c3_1(a759)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp20 | hskp5 | c1_1(a759) | (~ndr1_0) | (~c2_1(a759)) | (~c3_1(a759))))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[1726])).
% 0.79/0.98 tff(1728,plain,
% 0.79/0.98 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c1_1(a759) | (~c2_1(a759)) | (~c3_1(a759)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp20 | hskp5 | c1_1(a759) | (~ndr1_0) | (~c2_1(a759)) | (~c3_1(a759)))),
% 0.79/0.98 inference(transitivity,[status(thm)],[1727, 1725])).
% 0.79/0.98 tff(1729,plain,
% 0.79/0.98 ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c1_1(a759) | (~c2_1(a759)) | (~c3_1(a759)))),
% 0.79/0.98 inference(quant_inst,[status(thm)],[])).
% 0.79/0.98 tff(1730,plain,
% 0.79/0.98 ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp20 | hskp5 | c1_1(a759) | (~ndr1_0) | (~c2_1(a759)) | (~c3_1(a759))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1729, 1728])).
% 0.79/0.98 tff(1731,plain,
% 0.79/0.98 (hskp20 | hskp5),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1730, 104, 1724, 1723, 1712, 1722])).
% 0.79/0.98 tff(1732,plain,
% 0.79/0.98 (hskp20),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1731, 396])).
% 0.79/0.98 tff(1733,plain,
% 0.79/0.98 (((~hskp20) | (~c3_1(a779))) <=> ((~hskp20) | (~c3_1(a779)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1734,plain,
% 0.79/0.98 (((~c3_1(a779)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a779)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1735,axiom,((~c3_1(a779)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 0.79/0.98 tff(1736,plain,
% 0.79/0.98 ((~hskp20) | (~c3_1(a779))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1735, 1734])).
% 0.79/0.98 tff(1737,plain,
% 0.79/0.98 ((~hskp20) | (~c3_1(a779))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1736, 1733])).
% 0.79/0.98 tff(1738,plain,
% 0.79/0.98 (~c3_1(a779)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1737, 1732])).
% 0.79/0.98 tff(1739,plain,
% 0.79/0.98 (((~hskp20) | (~c1_1(a779))) <=> ((~hskp20) | (~c1_1(a779)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1740,plain,
% 0.79/0.98 (((~c1_1(a779)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a779)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1741,axiom,((~c1_1(a779)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 0.79/0.98 tff(1742,plain,
% 0.79/0.98 ((~hskp20) | (~c1_1(a779))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1741, 1740])).
% 0.79/0.98 tff(1743,plain,
% 0.79/0.98 ((~hskp20) | (~c1_1(a779))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1742, 1739])).
% 0.79/0.98 tff(1744,plain,
% 0.79/0.98 (~c1_1(a779)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1743, 1732])).
% 0.79/0.98 tff(1745,plain,
% 0.79/0.98 (((~hskp20) | c2_1(a779)) <=> ((~hskp20) | c2_1(a779))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1746,axiom,((~hskp20) | c2_1(a779)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 0.79/0.98 tff(1747,plain,
% 0.79/0.98 ((~hskp20) | c2_1(a779)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1746, 1745])).
% 0.79/0.98 tff(1748,plain,
% 0.79/0.98 ((~hskp20) | c2_1(a779)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1747, 1745])).
% 0.79/0.98 tff(1749,plain,
% 0.79/0.98 ((~hskp20) | c2_1(a779)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1748, 1745])).
% 0.79/0.98 tff(1750,plain,
% 0.79/0.98 ((~hskp20) | c2_1(a779)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1749, 1745])).
% 0.79/0.98 tff(1751,plain,
% 0.79/0.98 ((~hskp20) | c2_1(a779)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1750, 1745])).
% 0.79/0.98 tff(1752,plain,
% 0.79/0.98 (c2_1(a779)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1751, 1732])).
% 0.79/0.98 tff(1753,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a779) | c3_1(a779) | c1_1(a759) | (~ndr1_0) | (~c3_1(a759)) | (~c0_1(a759)) | (~c2_1(a779)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a779) | c3_1(a779) | c1_1(a759) | (~ndr1_0) | (~c3_1(a759)) | (~c0_1(a759)) | (~c2_1(a779)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1754,plain,
% 0.79/0.98 ((hskp5 | (~ndr1_0) | c1_1(a759) | (~c3_1(a759)) | (~c0_1(a759)) | c3_1(a779) | c1_1(a779) | (~c2_1(a779))) <=> (hskp5 | c1_1(a779) | c3_1(a779) | c1_1(a759) | (~ndr1_0) | (~c3_1(a759)) | (~c0_1(a759)) | (~c2_1(a779)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1755,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a759) | (~c3_1(a759)) | (~c0_1(a759)) | c3_1(a779) | c1_1(a779) | (~c2_1(a779)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a779) | c3_1(a779) | c1_1(a759) | (~ndr1_0) | (~c3_1(a759)) | (~c0_1(a759)) | (~c2_1(a779))))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[1754])).
% 0.79/0.98 tff(1756,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a759) | (~c3_1(a759)) | (~c0_1(a759)) | c3_1(a779) | c1_1(a779) | (~c2_1(a779)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a779) | c3_1(a779) | c1_1(a759) | (~ndr1_0) | (~c3_1(a759)) | (~c0_1(a759)) | (~c2_1(a779)))),
% 0.79/0.98 inference(transitivity,[status(thm)],[1755, 1753])).
% 0.79/0.98 tff(1757,plain,
% 0.79/0.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a759) | (~c3_1(a759)) | (~c0_1(a759)) | c3_1(a779) | c1_1(a779) | (~c2_1(a779)))),
% 0.79/0.98 inference(quant_inst,[status(thm)],[])).
% 0.79/0.98 tff(1758,plain,
% 0.79/0.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a779) | c3_1(a779) | c1_1(a759) | (~ndr1_0) | (~c3_1(a759)) | (~c0_1(a759)) | (~c2_1(a779))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1757, 1756])).
% 0.79/0.98 tff(1759,plain,
% 0.79/0.98 ($false),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1758, 104, 396, 1752, 1723, 1744, 1738, 1712, 1456, 1711])).
% 0.79/0.98 tff(1760,plain,(hskp5 | (~c3_1(a759)) | c1_1(a759) | (~c0_1(a759)) | (~c2_1(a759))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.98 tff(1761,plain,
% 0.79/0.98 (hskp5),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1760, 1703, 1702, 1710, 1701])).
% 0.79/0.98 tff(1762,plain,
% 0.79/0.98 (c2_1(a735)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[421, 1761])).
% 0.79/0.98 tff(1763,plain,
% 0.79/0.98 (c3_1(a735)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[413, 1761])).
% 0.79/0.98 tff(1764,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a759) | c0_1(a735) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c0_1(a731)) | (~c3_1(a735)) | (~c2_1(a735)) | (~c2_1(a759)) | (~c3_1(a759)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a759) | c0_1(a735) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c0_1(a731)) | (~c3_1(a735)) | (~c2_1(a735)) | (~c2_1(a759)) | (~c3_1(a759)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1765,plain,
% 0.79/0.98 (((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c0_1(a731)) | c1_1(a759) | (~c2_1(a759)) | (~c3_1(a759)) | c0_1(a735) | (~c3_1(a735)) | (~c2_1(a735))) <=> (c1_1(a759) | c0_1(a735) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c0_1(a731)) | (~c3_1(a735)) | (~c2_1(a735)) | (~c2_1(a759)) | (~c3_1(a759)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1766,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c0_1(a731)) | c1_1(a759) | (~c2_1(a759)) | (~c3_1(a759)) | c0_1(a735) | (~c3_1(a735)) | (~c2_1(a735)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a759) | c0_1(a735) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c0_1(a731)) | (~c3_1(a735)) | (~c2_1(a735)) | (~c2_1(a759)) | (~c3_1(a759))))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[1765])).
% 0.79/0.98 tff(1767,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c0_1(a731)) | c1_1(a759) | (~c2_1(a759)) | (~c3_1(a759)) | c0_1(a735) | (~c3_1(a735)) | (~c2_1(a735)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a759) | c0_1(a735) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c0_1(a731)) | (~c3_1(a735)) | (~c2_1(a735)) | (~c2_1(a759)) | (~c3_1(a759)))),
% 0.79/0.98 inference(transitivity,[status(thm)],[1766, 1764])).
% 0.79/0.98 tff(1768,plain,
% 0.79/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c0_1(a731)) | c1_1(a759) | (~c2_1(a759)) | (~c3_1(a759)) | c0_1(a735) | (~c3_1(a735)) | (~c2_1(a735)))),
% 0.79/0.98 inference(quant_inst,[status(thm)],[])).
% 0.79/0.98 tff(1769,plain,
% 0.79/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a759) | c0_1(a735) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c0_1(a731)) | (~c3_1(a735)) | (~c2_1(a735)) | (~c2_1(a759)) | (~c3_1(a759))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1768, 1767])).
% 0.79/0.98 tff(1770,plain,
% 0.79/0.98 ((~c3_1(a735)) | (~c2_1(a735))),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1769, 104, 1701, 1703, 1691, 1702, 457, 1690, 455, 1692])).
% 0.79/0.98 tff(1771,plain,
% 0.79/0.98 ($false),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1770, 1763, 1762])).
% 0.79/0.98 tff(1772,plain,(c0_1(a735) | hskp7 | c3_1(a744) | c0_1(a744) | hskp12 | c3_1(a734) | c0_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.98 tff(1773,plain,
% 0.79/0.98 (c0_1(a735)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1772, 1096, 1029, 1094, 1030, 33, 22])).
% 0.79/0.98 tff(1774,plain,
% 0.79/0.98 (~hskp5),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[427, 1773])).
% 0.79/0.98 tff(1775,plain,
% 0.79/0.98 (c2_1(a734)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1092, 1774, 22])).
% 0.79/0.98 tff(1776,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c3_1(a744) | c0_1(a744) | (~c1_1(a744)) | (~ndr1_0) | c2_1(a744))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c3_1(a744) | c0_1(a744) | (~c1_1(a744)) | (~ndr1_0) | c2_1(a744))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1777,plain,
% 0.79/0.98 ((hskp5 | (~ndr1_0) | c0_1(a744) | c3_1(a744) | (~c1_1(a744)) | c0_1(a744) | c2_1(a744) | (~c1_1(a744))) <=> (hskp5 | c3_1(a744) | c0_1(a744) | (~c1_1(a744)) | (~ndr1_0) | c2_1(a744))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1778,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a744) | c3_1(a744) | (~c1_1(a744)) | c0_1(a744) | c2_1(a744) | (~c1_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c3_1(a744) | c0_1(a744) | (~c1_1(a744)) | (~ndr1_0) | c2_1(a744)))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[1777])).
% 0.79/0.98 tff(1779,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a744) | c3_1(a744) | (~c1_1(a744)) | c0_1(a744) | c2_1(a744) | (~c1_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c3_1(a744) | c0_1(a744) | (~c1_1(a744)) | (~ndr1_0) | c2_1(a744))),
% 0.79/0.98 inference(transitivity,[status(thm)],[1778, 1776])).
% 0.79/0.98 tff(1780,plain,
% 0.79/0.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a744) | c3_1(a744) | (~c1_1(a744)) | c0_1(a744) | c2_1(a744) | (~c1_1(a744)))),
% 0.79/0.98 inference(quant_inst,[status(thm)],[])).
% 0.79/0.98 tff(1781,plain,
% 0.79/0.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c3_1(a744) | c0_1(a744) | (~c1_1(a744)) | (~ndr1_0) | c2_1(a744)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1780, 1779])).
% 0.79/0.98 tff(1782,plain,
% 0.79/0.98 (hskp5 | c3_1(a744) | (~c1_1(a744)) | c2_1(a744)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1781, 104, 1094, 1170])).
% 0.79/0.98 tff(1783,plain,
% 0.79/0.98 (c2_1(a744)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1782, 1774, 1476, 1096])).
% 0.79/0.98 tff(1784,plain,
% 0.79/0.98 (~hskp2),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1531, 1783, 1096, 1094, 1477])).
% 0.79/0.98 tff(1785,plain,
% 0.79/0.98 (hskp1),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1676, 1784, 1096, 1094, 1783, 1064, 1457, 1065, 1476, 1048, 1775, 33, 1774, 1030, 1029])).
% 0.79/0.98 tff(1786,plain,
% 0.79/0.98 (~c2_1(a731)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[58, 1785])).
% 0.79/0.98 tff(1787,plain,
% 0.79/0.98 (c3_1(a731)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[66, 1785])).
% 0.79/0.98 tff(1788,plain,
% 0.79/0.98 (c0_1(a731)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1039, 104, 1030, 1029, 1787, 1786, 1028])).
% 0.79/0.98 tff(1789,plain,
% 0.79/0.98 (c1_1(a731)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[74, 1785])).
% 0.79/0.98 tff(1790,plain,
% 0.79/0.98 (hskp13 | (~c0_1(a731))),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1699, 104, 1096, 1789, 1094, 1476, 1786, 32])).
% 0.79/0.98 tff(1791,plain,
% 0.79/0.98 (hskp13),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1790, 1788])).
% 0.79/0.98 tff(1792,plain,
% 0.79/0.98 (c3_1(a759)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[882, 1791])).
% 0.79/0.98 tff(1793,plain,
% 0.79/0.98 (c2_1(a759)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[890, 1791])).
% 0.79/0.98 tff(1794,plain,
% 0.79/0.98 (~c1_1(a759)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[873, 1791])).
% 0.79/0.98 tff(1795,plain,
% 0.79/0.98 (~c0_1(a759)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1760, 1794, 1774, 1793, 1792])).
% 0.79/0.98 tff(1796,plain,
% 0.79/0.98 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(1797,plain,
% 0.79/0.98 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[1796])).
% 0.79/0.98 tff(1798,plain,
% 0.79/0.98 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1799,plain,
% 0.79/0.98 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp5))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(1800,plain,
% 0.79/0.98 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[1799])).
% 0.79/0.98 tff(1801,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 0.79/0.98 tff(1802,plain,
% 0.79/0.98 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1801, 1800])).
% 0.79/0.98 tff(1803,plain,
% 0.79/0.98 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1802, 1798])).
% 0.79/0.98 tff(1804,plain,(
% 0.79/0.98 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.79/0.98 inference(skolemize,[status(sab)],[1803])).
% 0.79/0.98 tff(1805,plain,
% 0.79/0.98 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1804, 1797])).
% 0.79/0.98 tff(1806,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a759) | c0_1(a744) | (~c1_1(a744)) | (~ndr1_0) | (~c2_1(a744)) | (~c3_1(a759)) | c0_1(a759))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a759) | c0_1(a744) | (~c1_1(a744)) | (~ndr1_0) | (~c2_1(a744)) | (~c3_1(a759)) | c0_1(a759))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1807,plain,
% 0.79/0.98 ((hskp5 | (~ndr1_0) | c0_1(a744) | (~c2_1(a744)) | (~c1_1(a744)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759))) <=> (hskp5 | c1_1(a759) | c0_1(a744) | (~c1_1(a744)) | (~ndr1_0) | (~c2_1(a744)) | (~c3_1(a759)) | c0_1(a759))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1808,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a744) | (~c2_1(a744)) | (~c1_1(a744)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a759) | c0_1(a744) | (~c1_1(a744)) | (~ndr1_0) | (~c2_1(a744)) | (~c3_1(a759)) | c0_1(a759)))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[1807])).
% 0.79/0.98 tff(1809,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a744) | (~c2_1(a744)) | (~c1_1(a744)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a759) | c0_1(a744) | (~c1_1(a744)) | (~ndr1_0) | (~c2_1(a744)) | (~c3_1(a759)) | c0_1(a759))),
% 0.79/0.98 inference(transitivity,[status(thm)],[1808, 1806])).
% 0.79/0.98 tff(1810,plain,
% 0.79/0.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a744) | (~c2_1(a744)) | (~c1_1(a744)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759)))),
% 0.79/0.98 inference(quant_inst,[status(thm)],[])).
% 0.79/0.98 tff(1811,plain,
% 0.79/0.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a759) | c0_1(a744) | (~c1_1(a744)) | (~ndr1_0) | (~c2_1(a744)) | (~c3_1(a759)) | c0_1(a759)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1810, 1809])).
% 0.79/0.98 tff(1812,plain,
% 0.79/0.98 ($false),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1811, 104, 1774, 1792, 1794, 1094, 1476, 1805, 1783, 1795])).
% 0.79/0.98 tff(1813,plain,(c3_1(a744) | c0_1(a744) | hskp12 | hskp7 | c3_1(a734) | c0_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.98 tff(1814,plain,
% 0.79/0.98 (c3_1(a744)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1813, 1094, 1030, 1029, 33, 22])).
% 0.79/0.98 tff(1815,plain,
% 0.79/0.98 (c2_1(a744)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1112, 1814])).
% 0.79/0.98 tff(1816,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c2_1(a775) | c3_1(a775) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | c0_1(a775))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c2_1(a775) | c3_1(a775) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | c0_1(a775))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1817,plain,
% 0.79/0.98 ((hskp8 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c3_1(a775) | c0_1(a775) | c2_1(a775)) <=> (hskp8 | c2_1(a775) | c3_1(a775) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | c0_1(a775))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1818,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c3_1(a775) | c0_1(a775) | c2_1(a775))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c2_1(a775) | c3_1(a775) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | c0_1(a775)))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[1817])).
% 0.79/0.98 tff(1819,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c3_1(a775) | c0_1(a775) | c2_1(a775))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c2_1(a775) | c3_1(a775) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | c0_1(a775))),
% 0.79/0.98 inference(transitivity,[status(thm)],[1818, 1816])).
% 0.79/0.98 tff(1820,plain,
% 0.79/0.98 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c3_1(a775) | c0_1(a775) | c2_1(a775))),
% 0.79/0.98 inference(quant_inst,[status(thm)],[])).
% 0.79/0.98 tff(1821,plain,
% 0.79/0.98 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c2_1(a775) | c3_1(a775) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | c0_1(a775)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1820, 1819])).
% 0.79/0.98 tff(1822,plain,
% 0.79/0.98 (c0_1(a775)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1821, 1496, 104, 1637, 1631, 22, 33, 619, 1533])).
% 0.79/0.98 tff(1823,plain,
% 0.79/0.98 (((~hskp18) | c1_1(a775)) <=> ((~hskp18) | c1_1(a775))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1824,axiom,((~hskp18) | c1_1(a775)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 0.79/0.98 tff(1825,plain,
% 0.79/0.98 ((~hskp18) | c1_1(a775)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1824, 1823])).
% 0.79/0.98 tff(1826,plain,
% 0.79/0.98 ((~hskp18) | c1_1(a775)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1825, 1823])).
% 0.79/0.98 tff(1827,plain,
% 0.79/0.98 ((~hskp18) | c1_1(a775)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1826, 1823])).
% 0.79/0.98 tff(1828,plain,
% 0.79/0.98 ((~hskp18) | c1_1(a775)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1827, 1823])).
% 0.79/0.98 tff(1829,plain,
% 0.79/0.98 ((~hskp18) | c1_1(a775)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1828, 1823])).
% 0.79/0.98 tff(1830,plain,
% 0.79/0.98 (c1_1(a775)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1829, 1625])).
% 0.79/0.98 tff(1831,plain,
% 0.79/0.98 (hskp25),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1662, 104, 1655, 1637, 1631, 1654, 1822])).
% 0.79/0.98 tff(1832,plain,
% 0.79/0.98 (c3_1(a729)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[762, 1831])).
% 0.79/0.98 tff(1833,plain,
% 0.79/0.98 (c2_1(a729)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[770, 1831])).
% 0.79/0.98 tff(1834,plain,
% 0.79/0.98 (c0_1(a729)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[778, 1831])).
% 0.79/0.98 tff(1835,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | c3_1(a775) | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | (~c0_1(a775)) | (~c1_1(a775)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp1 | c3_1(a775) | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | (~c0_1(a775)) | (~c1_1(a775)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1836,plain,
% 0.79/0.98 ((hskp1 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c3_1(a775) | (~c1_1(a775)) | (~c0_1(a775))) <=> (hskp1 | c3_1(a775) | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | (~c0_1(a775)) | (~c1_1(a775)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1837,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c3_1(a775) | (~c1_1(a775)) | (~c0_1(a775)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | c3_1(a775) | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | (~c0_1(a775)) | (~c1_1(a775))))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[1836])).
% 0.79/0.98 tff(1838,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c3_1(a775) | (~c1_1(a775)) | (~c0_1(a775)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp1 | c3_1(a775) | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | (~c0_1(a775)) | (~c1_1(a775)))),
% 0.79/0.98 inference(transitivity,[status(thm)],[1837, 1835])).
% 0.79/0.98 tff(1839,plain,
% 0.79/0.98 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c3_1(a775) | (~c1_1(a775)) | (~c0_1(a775)))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(1840,plain,
% 0.79/0.99 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp1 | c3_1(a775) | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | (~c0_1(a775)) | (~c1_1(a775))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[1839, 1838])).
% 0.79/0.99 tff(1841,plain,
% 0.79/0.99 ($false),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1840, 104, 255, 1834, 1833, 1832, 1830, 1631, 743, 1822])).
% 0.79/0.99 tff(1842,plain,((~hskp18) | hskp1 | hskp9 | hskp8 | c0_1(a734) | c3_1(a734) | (~c2_1(a734))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.99 tff(1843,plain,
% 0.79/0.99 (~hskp18),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1842, 255, 1061, 1477, 22, 33, 1093])).
% 0.79/0.99 tff(1844,plain,
% 0.79/0.99 (hskp27),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1583, 21, 1006, 1533])).
% 0.79/0.99 tff(1845,plain,
% 0.79/0.99 (c2_1(a750)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[724, 1844])).
% 0.79/0.99 tff(1846,plain,
% 0.79/0.99 (c0_1(a750)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[716, 1844])).
% 0.79/0.99 tff(1847,plain,
% 0.79/0.99 (~c3_1(a750)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1613, 1846, 469, 468, 456, 1523, 255, 1845, 1094, 1534, 396])).
% 0.79/0.99 tff(1848,plain,
% 0.79/0.99 (c1_1(a750)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[732, 1844])).
% 0.79/0.99 tff(1849,assumption,(~hskp18), introduced(assumption)).
% 0.79/0.99 tff(1850,plain,
% 0.79/0.99 ($false),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1622, 104, 1849, 21, 1846, 1848, 1075, 1847])).
% 0.79/0.99 tff(1851,plain,(hskp11 | hskp18 | (~c0_1(a730)) | (~c3_1(a730)) | c1_1(a730) | (~c2_1(a744)) | hskp1 | c0_1(a744) | (~c1_1(a744)) | hskp5 | (~c1_1(a734)) | (~c2_1(a734)) | c3_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.99 tff(1852,plain,
% 0.79/0.99 (hskp11),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1851, 1843, 1064, 1457, 1065, 1815, 255, 1094, 1476, 396, 1048, 1093, 33])).
% 0.79/0.99 tff(1853,plain,
% 0.79/0.99 (~c0_1(a749)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1540, 1852])).
% 0.79/0.99 tff(1854,plain,
% 0.79/0.99 (c2_1(a749)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1560, 1853, 396, 1030, 1029])).
% 0.79/0.99 tff(1855,plain,
% 0.79/0.99 (hskp2),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1575, 1852, 396, 255, 1030, 1029])).
% 0.79/0.99 tff(1856,plain,
% 0.79/0.99 (~c3_1(a732)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[546, 1855])).
% 0.79/0.99 tff(1857,plain,
% 0.79/0.99 (~c2_1(a732)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[282, 1855])).
% 0.79/0.99 tff(1858,plain,
% 0.79/0.99 (~c0_1(a732)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[288, 1855])).
% 0.79/0.99 tff(1859,plain,
% 0.79/0.99 (((~hskp11) | (~c3_1(a749))) <=> ((~hskp11) | (~c3_1(a749)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(1860,plain,
% 0.79/0.99 (((~c3_1(a749)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a749)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(1861,axiom,((~c3_1(a749)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 0.79/0.99 tff(1862,plain,
% 0.79/0.99 ((~hskp11) | (~c3_1(a749))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[1861, 1860])).
% 0.79/0.99 tff(1863,plain,
% 0.79/0.99 ((~hskp11) | (~c3_1(a749))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[1862, 1859])).
% 0.79/0.99 tff(1864,plain,
% 0.79/0.99 (~c3_1(a749)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1863, 1852])).
% 0.79/0.99 tff(1865,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c0_1(a749) | c3_1(a749) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a749)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a749) | c3_1(a749) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a749)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(1866,plain,
% 0.79/0.99 ((hskp8 | (~ndr1_0) | c0_1(a749) | c3_1(a749) | (~c2_1(a749)) | c3_1(a732) | c0_1(a732) | c2_1(a732)) <=> (hskp8 | c0_1(a749) | c3_1(a749) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a749)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(1867,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a749) | c3_1(a749) | (~c2_1(a749)) | c3_1(a732) | c0_1(a732) | c2_1(a732))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c0_1(a749) | c3_1(a749) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a749))))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[1866])).
% 0.79/0.99 tff(1868,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a749) | c3_1(a749) | (~c2_1(a749)) | c3_1(a732) | c0_1(a732) | c2_1(a732))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a749) | c3_1(a749) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a749)))),
% 0.79/0.99 inference(transitivity,[status(thm)],[1867, 1865])).
% 0.79/0.99 tff(1869,plain,
% 0.79/0.99 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a749) | c3_1(a749) | (~c2_1(a749)) | c3_1(a732) | c0_1(a732) | c2_1(a732))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(1870,plain,
% 0.79/0.99 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a749) | c3_1(a749) | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c2_1(a749))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[1869, 1868])).
% 0.79/0.99 tff(1871,plain,
% 0.79/0.99 ($false),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1870, 1477, 104, 1853, 1864, 1858, 1857, 1856, 619, 1854])).
% 0.79/0.99 tff(1872,plain,(hskp1 | hskp5 | hskp12 | hskp7 | c0_1(a744) | c3_1(a734) | c0_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.99 tff(1873,plain,
% 0.79/0.99 (hskp1),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1872, 396, 1030, 1029, 1094, 33, 22])).
% 0.79/0.99 tff(1874,plain,
% 0.79/0.99 (~c2_1(a731)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[58, 1873])).
% 0.79/0.99 tff(1875,plain,
% 0.79/0.99 (c3_1(a731)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[66, 1873])).
% 0.79/0.99 tff(1876,plain,
% 0.79/0.99 (c0_1(a731)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1039, 104, 1030, 1029, 1875, 1874, 1028])).
% 0.79/0.99 tff(1877,plain,
% 0.79/0.99 (c1_1(a731)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[74, 1873])).
% 0.79/0.99 tff(1878,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | c0_1(a734) | c3_1(a734) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | (~c0_1(a731)) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a734) | c3_1(a734) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | (~c0_1(a731)) | (~c1_1(a734)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(1879,plain,
% 0.79/0.99 ((hskp13 | (~ndr1_0) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c3_1(a734) | c0_1(a734) | (~c1_1(a734))) <=> (hskp13 | c0_1(a734) | c3_1(a734) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | (~c0_1(a731)) | (~c1_1(a734)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(1880,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c3_1(a734) | c0_1(a734) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | c0_1(a734) | c3_1(a734) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | (~c0_1(a731)) | (~c1_1(a734))))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[1879])).
% 0.79/0.99 tff(1881,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c3_1(a734) | c0_1(a734) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a734) | c3_1(a734) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | (~c0_1(a731)) | (~c1_1(a734)))),
% 0.79/0.99 inference(transitivity,[status(thm)],[1880, 1878])).
% 0.79/0.99 tff(1882,plain,
% 0.79/0.99 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c3_1(a734) | c0_1(a734) | (~c1_1(a734)))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(1883,plain,
% 0.79/0.99 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a734) | c3_1(a734) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | (~c0_1(a731)) | (~c1_1(a734))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[1882, 1881])).
% 0.79/0.99 tff(1884,plain,
% 0.79/0.99 (hskp13),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1883, 104, 1048, 1877, 22, 33, 1874, 32, 1876])).
% 0.79/0.99 tff(1885,plain,
% 0.79/0.99 (c3_1(a759)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[882, 1884])).
% 0.79/0.99 tff(1886,plain,
% 0.79/0.99 (c2_1(a759)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[890, 1884])).
% 0.79/0.99 tff(1887,plain,
% 0.79/0.99 (~c1_1(a759)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[873, 1884])).
% 0.79/0.99 tff(1888,plain,
% 0.79/0.99 (~c0_1(a759)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1760, 1887, 396, 1886, 1885])).
% 0.79/0.99 tff(1889,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a744) | c2_1(a731) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c3_1(a731)) | (~c0_1(a731)) | (~c2_1(a744)) | (~c3_1(a744)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a744) | c2_1(a731) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c3_1(a731)) | (~c0_1(a731)) | (~c2_1(a744)) | (~c3_1(a744)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(1890,plain,
% 0.79/0.99 (((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c0_1(a731)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a744) | (~c3_1(a744)) | (~c2_1(a744))) <=> (c0_1(a744) | c2_1(a731) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c3_1(a731)) | (~c0_1(a731)) | (~c2_1(a744)) | (~c3_1(a744)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(1891,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c0_1(a731)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a744) | (~c3_1(a744)) | (~c2_1(a744)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a744) | c2_1(a731) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c3_1(a731)) | (~c0_1(a731)) | (~c2_1(a744)) | (~c3_1(a744))))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[1890])).
% 0.79/0.99 tff(1892,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c0_1(a731)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a744) | (~c3_1(a744)) | (~c2_1(a744)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a744) | c2_1(a731) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c3_1(a731)) | (~c0_1(a731)) | (~c2_1(a744)) | (~c3_1(a744)))),
% 0.79/0.99 inference(transitivity,[status(thm)],[1891, 1889])).
% 0.79/0.99 tff(1893,plain,
% 0.79/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c0_1(a731)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a744) | (~c3_1(a744)) | (~c2_1(a744)))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(1894,plain,
% 0.79/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a744) | c2_1(a731) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c3_1(a731)) | (~c0_1(a731)) | (~c2_1(a744)) | (~c3_1(a744))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[1893, 1892])).
% 0.79/0.99 tff(1895,plain,
% 0.79/0.99 (~c2_1(a730)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1894, 104, 1814, 1875, 1457, 1094, 1874, 1065, 455, 1815, 1876])).
% 0.79/0.99 tff(1896,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a731) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c3_1(a731)) | (~c1_1(a731)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a731) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c3_1(a731)) | (~c1_1(a731)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(1897,plain,
% 0.79/0.99 ((hskp11 | (~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c1_1(a730) | c2_1(a730) | (~c3_1(a730))) <=> (hskp11 | c2_1(a731) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c3_1(a731)) | (~c1_1(a731)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(1898,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c1_1(a730) | c2_1(a730) | (~c3_1(a730)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a731) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c3_1(a731)) | (~c1_1(a731))))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[1897])).
% 0.79/0.99 tff(1899,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c1_1(a730) | c2_1(a730) | (~c3_1(a730)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a731) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c3_1(a731)) | (~c1_1(a731)))),
% 0.79/0.99 inference(transitivity,[status(thm)],[1898, 1896])).
% 0.79/0.99 tff(1900,plain,
% 0.79/0.99 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c1_1(a730) | c2_1(a730) | (~c3_1(a730)))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(1901,plain,
% 0.79/0.99 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a731) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c3_1(a731)) | (~c1_1(a731))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[1900, 1899])).
% 0.79/0.99 tff(1902,plain,
% 0.79/0.99 (hskp11),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1901, 104, 1877, 1875, 1457, 1874, 1065, 360, 1895])).
% 0.79/0.99 tff(1903,plain,
% 0.79/0.99 (~c0_1(a749)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1540, 1902])).
% 0.79/0.99 tff(1904,plain,
% 0.79/0.99 (c2_1(a749)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1560, 1903, 396, 1030, 1029])).
% 0.79/0.99 tff(1905,plain,
% 0.79/0.99 (~c3_1(a749)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1863, 1902])).
% 0.79/0.99 tff(1906,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a759) | c0_1(a749) | c3_1(a749) | (~ndr1_0) | (~c2_1(a749)) | (~c3_1(a759)) | c0_1(a759))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a759) | c0_1(a749) | c3_1(a749) | (~ndr1_0) | (~c2_1(a749)) | (~c3_1(a759)) | c0_1(a759))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(1907,plain,
% 0.79/0.99 ((hskp7 | (~ndr1_0) | c0_1(a749) | c3_1(a749) | (~c2_1(a749)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759))) <=> (hskp7 | c1_1(a759) | c0_1(a749) | c3_1(a749) | (~ndr1_0) | (~c2_1(a749)) | (~c3_1(a759)) | c0_1(a759))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(1908,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a749) | c3_1(a749) | (~c2_1(a749)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a759) | c0_1(a749) | c3_1(a749) | (~ndr1_0) | (~c2_1(a749)) | (~c3_1(a759)) | c0_1(a759)))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[1907])).
% 0.79/0.99 tff(1909,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a749) | c3_1(a749) | (~c2_1(a749)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a759) | c0_1(a749) | c3_1(a749) | (~ndr1_0) | (~c2_1(a749)) | (~c3_1(a759)) | c0_1(a759))),
% 0.79/0.99 inference(transitivity,[status(thm)],[1908, 1906])).
% 0.79/0.99 tff(1910,plain,
% 0.79/0.99 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a749) | c3_1(a749) | (~c2_1(a749)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759)))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(1911,plain,
% 0.79/0.99 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a759) | c0_1(a749) | c3_1(a749) | (~ndr1_0) | (~c2_1(a749)) | (~c3_1(a759)) | c0_1(a759)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[1910, 1909])).
% 0.79/0.99 tff(1912,plain,
% 0.79/0.99 ($false),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1911, 104, 1029, 1885, 1887, 1903, 1905, 1263, 1904, 1888])).
% 0.79/0.99 tff(1913,plain,(hskp5 | hskp7 | hskp12 | c0_1(a734) | c3_1(a734) | c0_1(a744)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.99 tff(1914,plain,
% 0.79/0.99 (hskp5),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1913, 1094, 1030, 22, 33, 1029])).
% 0.79/0.99 tff(1915,plain,
% 0.79/0.99 (~c0_1(a735)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[427, 1914])).
% 0.79/0.99 tff(1916,plain,
% 0.79/0.99 (c2_1(a734)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1519, 1915, 22, 33, 1477, 1030, 1029])).
% 0.79/0.99 tff(1917,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a793) | c0_1(a744) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a744)) | (~c3_1(a744)) | (~c3_1(a793)) | (~c0_1(a793)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a793) | c0_1(a744) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a744)) | (~c3_1(a744)) | (~c3_1(a793)) | (~c0_1(a793)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(1918,plain,
% 0.79/0.99 (((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a744) | (~c3_1(a744)) | (~c2_1(a744))) <=> (c2_1(a793) | c0_1(a744) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a744)) | (~c3_1(a744)) | (~c3_1(a793)) | (~c0_1(a793)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(1919,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a744) | (~c3_1(a744)) | (~c2_1(a744)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a793) | c0_1(a744) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a744)) | (~c3_1(a744)) | (~c3_1(a793)) | (~c0_1(a793))))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[1918])).
% 0.79/0.99 tff(1920,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a744) | (~c3_1(a744)) | (~c2_1(a744)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a793) | c0_1(a744) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a744)) | (~c3_1(a744)) | (~c3_1(a793)) | (~c0_1(a793)))),
% 0.79/0.99 inference(transitivity,[status(thm)],[1919, 1917])).
% 0.79/0.99 tff(1921,plain,
% 0.79/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a744) | (~c3_1(a744)) | (~c2_1(a744)))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(1922,plain,
% 0.79/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a793) | c0_1(a744) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a744)) | (~c3_1(a744)) | (~c3_1(a793)) | (~c0_1(a793))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[1921, 1920])).
% 0.79/0.99 tff(1923,plain,
% 0.79/0.99 ($false),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1922, 104, 501, 493, 1329, 468, 483, 1094, 456, 455, 1523, 445])).
% 0.79/0.99 tff(1924,plain,((~c2_1(a730)) | (~c3_1(a744)) | (~c3_1(a730)) | c0_1(a744) | c1_1(a730) | (~c2_1(a744)) | (~c0_1(a730))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.99 tff(1925,plain,
% 0.79/0.99 (~c2_1(a730)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1924, 1814, 1457, 1094, 1065, 1815, 1064])).
% 0.79/0.99 tff(1926,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c0_1(a744) | (~c1_1(a744)) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c0_1(a744) | (~c1_1(a744)) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a744)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(1927,plain,
% 0.79/0.99 ((hskp2 | (~ndr1_0) | c2_1(a730) | c1_1(a730) | (~c0_1(a730)) | c0_1(a744) | (~c3_1(a744)) | (~c1_1(a744))) <=> (hskp2 | c0_1(a744) | (~c1_1(a744)) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a744)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(1928,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a730) | c1_1(a730) | (~c0_1(a730)) | c0_1(a744) | (~c3_1(a744)) | (~c1_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c0_1(a744) | (~c1_1(a744)) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a744))))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[1927])).
% 0.79/0.99 tff(1929,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a730) | c1_1(a730) | (~c0_1(a730)) | c0_1(a744) | (~c3_1(a744)) | (~c1_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c0_1(a744) | (~c1_1(a744)) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a744)))),
% 0.79/0.99 inference(transitivity,[status(thm)],[1928, 1926])).
% 0.79/0.99 tff(1930,plain,
% 0.79/0.99 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a730) | c1_1(a730) | (~c0_1(a730)) | c0_1(a744) | (~c3_1(a744)) | (~c1_1(a744)))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(1931,plain,
% 0.79/0.99 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c0_1(a744) | (~c1_1(a744)) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a744))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[1930, 1929])).
% 0.79/0.99 tff(1932,plain,
% 0.79/0.99 (hskp2),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1931, 104, 1814, 1064, 1094, 1476, 1065, 530, 1925])).
% 0.79/0.99 tff(1933,plain,
% 0.79/0.99 (~c3_1(a732)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[546, 1932])).
% 0.79/0.99 tff(1934,plain,
% 0.79/0.99 (~c2_1(a732)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[282, 1932])).
% 0.79/0.99 tff(1935,plain,
% 0.79/0.99 (~c0_1(a732)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[288, 1932])).
% 0.79/0.99 tff(1936,plain,
% 0.79/0.99 ($false),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1135, 1477, 104, 22, 33, 1935, 1934, 1933, 619, 1916])).
% 0.79/0.99 tff(1937,plain,(c0_1(a744) | c0_1(a734) | c3_1(a734) | hskp12 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.79/0.99 tff(1938,plain,
% 0.79/0.99 (c0_1(a744)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1937, 22, 33, 1030, 1029])).
% 0.79/0.99 tff(1939,plain,
% 0.79/0.99 (~hskp8),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[672, 1938])).
% 0.79/0.99 tff(1940,plain,
% 0.79/0.99 (hskp2),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1575, 1535, 396, 255, 1030, 1029])).
% 0.79/0.99 tff(1941,plain,
% 0.79/0.99 (~c3_1(a732)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[546, 1940])).
% 0.79/0.99 tff(1942,plain,
% 0.79/0.99 (~c2_1(a732)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[282, 1940])).
% 0.79/0.99 tff(1943,plain,
% 0.79/0.99 (~c0_1(a732)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[288, 1940])).
% 0.79/0.99 tff(1944,plain,
% 0.79/0.99 (~c3_1(a749)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1863, 1535])).
% 0.79/0.99 tff(1945,plain,
% 0.79/0.99 ($false),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1870, 1496, 104, 1541, 1944, 1943, 1942, 1941, 619, 1561])).
% 0.79/0.99 tff(1946,plain,((~hskp11) | hskp8 | hskp5 | hskp12 | hskp7 | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.79/0.99 tff(1947,plain,
% 0.79/0.99 (~hskp11),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1946, 255, 396, 1030, 1029, 1939])).
% 0.79/0.99 tff(1948,plain,
% 0.79/0.99 (hskp27),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1583, 1947, 1048, 1093])).
% 0.79/0.99 tff(1949,plain,
% 0.79/0.99 (c1_1(a750)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[732, 1948])).
% 0.79/0.99 tff(1950,plain,
% 0.79/0.99 (c0_1(a750)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[716, 1948])).
% 0.79/0.99 tff(1951,plain,
% 0.79/0.99 (~hskp18),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1842, 255, 1061, 1939, 22, 33, 1093])).
% 0.79/0.99 tff(1952,plain,
% 0.79/0.99 (c3_1(a750)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1622, 104, 1951, 1947, 1950, 1949, 1075])).
% 0.79/0.99 tff(1953,plain,
% 0.79/0.99 (c2_1(a750)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[724, 1948])).
% 0.79/0.99 tff(1954,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a734)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(1955,plain,
% 0.79/0.99 ((hskp16 | (~ndr1_0) | (~c2_1(a750)) | (~c3_1(a750)) | (~c0_1(a750)) | c0_1(a734) | (~c2_1(a734)) | (~c1_1(a734))) <=> (hskp16 | c0_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a734)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(1956,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a750)) | (~c3_1(a750)) | (~c0_1(a750)) | c0_1(a734) | (~c2_1(a734)) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a734))))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[1955])).
% 0.79/0.99 tff(1957,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a750)) | (~c3_1(a750)) | (~c0_1(a750)) | c0_1(a734) | (~c2_1(a734)) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a734)))),
% 0.79/0.99 inference(transitivity,[status(thm)],[1956, 1954])).
% 0.79/0.99 tff(1958,plain,
% 0.79/0.99 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a750)) | (~c3_1(a750)) | (~c0_1(a750)) | c0_1(a734) | (~c2_1(a734)) | (~c1_1(a734)))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(1959,plain,
% 0.79/0.99 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a734))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[1958, 1957])).
% 0.79/0.99 tff(1960,plain,
% 0.79/0.99 (hskp16),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1959, 104, 1950, 1953, 1048, 22, 754, 1093, 1952])).
% 0.79/0.99 tff(1961,plain,
% 0.79/0.99 (~c3_1(a764)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[791, 1960])).
% 0.79/0.99 tff(1962,plain,
% 0.79/0.99 (c0_1(a764)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[809, 1960])).
% 0.79/0.99 tff(1963,plain,
% 0.79/0.99 (~c1_1(a764)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1603, 104, 255, 1950, 1953, 1962, 1961, 743, 1952])).
% 0.79/1.00 tff(1964,plain,
% 0.79/1.00 (c2_1(a764)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[799, 1960])).
% 0.79/1.00 tff(1965,plain,
% 0.79/1.00 ($false),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1611, 104, 396, 1964, 1064, 1457, 1961, 1065, 1456, 1963])).
% 0.79/1.00 tff(1966,plain,(hskp1 | hskp5 | c0_1(a734) | c3_1(a734) | hskp12 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.79/1.00 tff(1967,plain,
% 0.79/1.00 (hskp1),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1966, 396, 22, 33, 1030, 1029])).
% 0.79/1.00 tff(1968,plain,
% 0.79/1.00 (~c2_1(a731)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[58, 1967])).
% 0.79/1.00 tff(1969,plain,
% 0.79/1.00 (c3_1(a731)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[66, 1967])).
% 0.79/1.00 tff(1970,plain,
% 0.79/1.00 (c0_1(a731)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1039, 104, 1030, 1029, 1969, 1968, 1028])).
% 0.79/1.00 tff(1971,plain,
% 0.79/1.00 (c1_1(a731)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[74, 1967])).
% 0.79/1.00 tff(1972,plain,
% 0.79/1.00 (hskp13),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1883, 104, 1048, 1971, 22, 33, 1968, 32, 1970])).
% 0.79/1.00 tff(1973,plain,
% 0.79/1.00 (c3_1(a759)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[882, 1972])).
% 0.79/1.00 tff(1974,plain,
% 0.79/1.00 (c2_1(a759)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[890, 1972])).
% 0.79/1.00 tff(1975,plain,
% 0.79/1.00 (~c1_1(a759)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[873, 1972])).
% 0.79/1.00 tff(1976,plain,
% 0.79/1.00 (~c0_1(a759)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1760, 1975, 396, 1974, 1973])).
% 0.79/1.00 tff(1977,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a759) | c0_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734)) | (~c3_1(a759)) | c0_1(a759))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a759) | c0_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734)) | (~c3_1(a759)) | c0_1(a759))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(1978,plain,
% 0.79/1.00 ((hskp5 | (~ndr1_0) | c0_1(a734) | (~c2_1(a734)) | (~c1_1(a734)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759))) <=> (hskp5 | c1_1(a759) | c0_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734)) | (~c3_1(a759)) | c0_1(a759))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(1979,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a734) | (~c2_1(a734)) | (~c1_1(a734)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a759) | c0_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734)) | (~c3_1(a759)) | c0_1(a759)))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[1978])).
% 0.79/1.00 tff(1980,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a734) | (~c2_1(a734)) | (~c1_1(a734)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a759) | c0_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734)) | (~c3_1(a759)) | c0_1(a759))),
% 0.79/1.00 inference(transitivity,[status(thm)],[1979, 1977])).
% 0.79/1.00 tff(1981,plain,
% 0.79/1.00 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a734) | (~c2_1(a734)) | (~c1_1(a734)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759)))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(1982,plain,
% 0.79/1.00 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a759) | c0_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734)) | (~c3_1(a759)) | c0_1(a759)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[1981, 1980])).
% 0.79/1.00 tff(1983,plain,
% 0.79/1.00 ($false),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1982, 104, 396, 1973, 1048, 1975, 22, 1805, 1093, 1976])).
% 0.79/1.00 tff(1984,plain,(hskp5 | c0_1(a734) | c3_1(a734) | hskp12 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.79/1.00 tff(1985,plain,
% 0.79/1.00 (hskp5),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1984, 22, 33, 1030, 1029])).
% 0.79/1.00 tff(1986,plain,
% 0.79/1.00 (~c0_1(a735)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[427, 1985])).
% 0.79/1.00 tff(1987,plain,
% 0.79/1.00 (c3_1(a735)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[413, 1985])).
% 0.79/1.00 tff(1988,plain,
% 0.79/1.00 (c2_1(a735)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[421, 1985])).
% 0.79/1.00 tff(1989,plain,
% 0.79/1.00 (~c2_1(a730)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[509, 1988, 1987, 1457, 1986, 1065, 1064])).
% 0.79/1.00 tff(1990,plain,
% 0.79/1.00 (c2_1(a734)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1519, 1986, 22, 33, 1939, 1030, 1029])).
% 0.79/1.00 tff(1991,plain,
% 0.79/1.00 ($false),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1135, 1496, 104, 22, 33, 1126, 1127, 1125, 619, 1533])).
% 0.79/1.00 tff(1992,plain,((~hskp2) | hskp8 | c0_1(a734) | c3_1(a734) | (~c2_1(a734))), inference(lemma,lemma(discharge,[]))).
% 0.79/1.00 tff(1993,plain,
% 0.79/1.00 (~hskp2),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1992, 1939, 22, 33, 1990])).
% 0.79/1.00 tff(1994,plain,
% 0.79/1.00 (~c1_1(a735)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[538, 1993, 1987, 1064, 1986, 1065, 1989])).
% 0.79/1.00 tff(1995,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a735) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c3_1(a735)) | (~c2_1(a735)) | c1_1(a735))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a735) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c3_1(a735)) | (~c2_1(a735)) | c1_1(a735))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(1996,plain,
% 0.79/1.00 (((~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a735) | (~c2_1(a735)) | (~c3_1(a735)) | c0_1(a735) | (~c3_1(a735)) | (~c2_1(a735))) <=> (c0_1(a735) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c3_1(a735)) | (~c2_1(a735)) | c1_1(a735))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(1997,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a735) | (~c2_1(a735)) | (~c3_1(a735)) | c0_1(a735) | (~c3_1(a735)) | (~c2_1(a735)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a735) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c3_1(a735)) | (~c2_1(a735)) | c1_1(a735)))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[1996])).
% 0.79/1.00 tff(1998,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a735) | (~c2_1(a735)) | (~c3_1(a735)) | c0_1(a735) | (~c3_1(a735)) | (~c2_1(a735)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a735) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c3_1(a735)) | (~c2_1(a735)) | c1_1(a735))),
% 0.79/1.00 inference(transitivity,[status(thm)],[1997, 1995])).
% 0.79/1.00 tff(1999,plain,
% 0.79/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a735) | (~c2_1(a735)) | (~c3_1(a735)) | c0_1(a735) | (~c3_1(a735)) | (~c2_1(a735)))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(2000,plain,
% 0.79/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a735) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c3_1(a735)) | (~c2_1(a735)) | c1_1(a735)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[1999, 1998])).
% 0.79/1.00 tff(2001,plain,
% 0.79/1.00 ($false),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2000, 104, 1988, 1987, 1064, 1457, 1986, 455, 1989, 1994])).
% 0.79/1.00 tff(2002,plain,(c0_1(a734) | c3_1(a734) | hskp12 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.79/1.00 tff(2003,plain,
% 0.79/1.00 (c0_1(a734)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2002, 33, 1030, 1029])).
% 0.79/1.00 tff(2004,plain,
% 0.79/1.00 (((~hskp4) | (~c0_1(a734))) <=> ((~hskp4) | (~c0_1(a734)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2005,plain,
% 0.79/1.00 (((~c0_1(a734)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a734)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2006,axiom,((~c0_1(a734)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 0.79/1.00 tff(2007,plain,
% 0.79/1.00 ((~hskp4) | (~c0_1(a734))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2006, 2005])).
% 0.79/1.00 tff(2008,plain,
% 0.79/1.00 ((~hskp4) | (~c0_1(a734))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2007, 2004])).
% 0.79/1.00 tff(2009,plain,
% 0.79/1.00 (~hskp4),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2008, 2003])).
% 0.79/1.00 tff(2010,plain,
% 0.79/1.00 (hskp1),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[141, 2009, 1029])).
% 0.79/1.00 tff(2011,plain,
% 0.79/1.00 (~c2_1(a731)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[58, 2010])).
% 0.79/1.00 tff(2012,plain,
% 0.79/1.00 (c3_1(a731)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[66, 2010])).
% 0.79/1.00 tff(2013,plain,
% 0.79/1.00 (c0_1(a731)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1039, 104, 1030, 1029, 2012, 2011, 1028])).
% 0.79/1.00 tff(2014,plain,
% 0.79/1.00 (c1_1(a731)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[74, 2010])).
% 0.79/1.00 tff(2015,assumption,(hskp19), introduced(assumption)).
% 0.79/1.00 tff(2016,plain,
% 0.79/1.00 (~c3_1(a777)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[645, 2015])).
% 0.79/1.00 tff(2017,plain,
% 0.79/1.00 (~c0_1(a777)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[651, 2015])).
% 0.79/1.00 tff(2018,plain,
% 0.79/1.00 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | c0_1(a777) | c3_1(a777) | (~ndr1_0) | c1_1(a777))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp5 | hskp4 | c0_1(a777) | c3_1(a777) | (~ndr1_0) | c1_1(a777))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2019,plain,
% 0.79/1.00 ((hskp5 | hskp4 | (~ndr1_0) | c1_1(a777) | c0_1(a777) | c3_1(a777)) <=> (hskp5 | hskp4 | c0_1(a777) | c3_1(a777) | (~ndr1_0) | c1_1(a777))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2020,plain,
% 0.79/1.00 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c1_1(a777) | c0_1(a777) | c3_1(a777))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | c0_1(a777) | c3_1(a777) | (~ndr1_0) | c1_1(a777)))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[2019])).
% 0.79/1.00 tff(2021,plain,
% 0.79/1.00 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c1_1(a777) | c0_1(a777) | c3_1(a777))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp5 | hskp4 | c0_1(a777) | c3_1(a777) | (~ndr1_0) | c1_1(a777))),
% 0.79/1.00 inference(transitivity,[status(thm)],[2020, 2018])).
% 0.79/1.00 tff(2022,plain,
% 0.79/1.00 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c1_1(a777) | c0_1(a777) | c3_1(a777))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(2023,plain,
% 0.79/1.00 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp5 | hskp4 | c0_1(a777) | c3_1(a777) | (~ndr1_0) | c1_1(a777)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2022, 2021])).
% 0.79/1.00 tff(2024,plain,
% 0.79/1.00 (c1_1(a777)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2023, 104, 396, 166, 2017, 2016, 395])).
% 0.79/1.00 tff(2025,assumption,(c0_1(a731)), introduced(assumption)).
% 0.79/1.00 tff(2026,assumption,(c1_1(a731)), introduced(assumption)).
% 0.79/1.00 tff(2027,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | c0_1(a777) | c3_1(a777) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | (~c0_1(a731)) | (~c1_1(a777)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a777) | c3_1(a777) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | (~c0_1(a731)) | (~c1_1(a777)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2028,plain,
% 0.79/1.00 ((hskp13 | (~ndr1_0) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c3_1(a777) | c0_1(a777) | (~c1_1(a777))) <=> (hskp13 | c0_1(a777) | c3_1(a777) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | (~c0_1(a731)) | (~c1_1(a777)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2029,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c3_1(a777) | c0_1(a777) | (~c1_1(a777)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | c0_1(a777) | c3_1(a777) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | (~c0_1(a731)) | (~c1_1(a777))))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[2028])).
% 0.79/1.00 tff(2030,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c3_1(a777) | c0_1(a777) | (~c1_1(a777)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a777) | c3_1(a777) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | (~c0_1(a731)) | (~c1_1(a777)))),
% 0.79/1.00 inference(transitivity,[status(thm)],[2029, 2027])).
% 0.79/1.00 tff(2031,plain,
% 0.79/1.00 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c3_1(a777) | c0_1(a777) | (~c1_1(a777)))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(2032,plain,
% 0.79/1.00 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a777) | c3_1(a777) | c2_1(a731) | (~ndr1_0) | (~c1_1(a731)) | (~c0_1(a731)) | (~c1_1(a777))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2031, 2030])).
% 0.79/1.00 tff(2033,plain,
% 0.79/1.00 (hskp13),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2032, 104, 2026, 2017, 2016, 1033, 32, 2025, 2024])).
% 0.79/1.00 tff(2034,plain,
% 0.79/1.00 (c3_1(a759)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[882, 2033])).
% 0.79/1.00 tff(2035,plain,
% 0.79/1.00 (c2_1(a759)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[890, 2033])).
% 0.79/1.00 tff(2036,plain,
% 0.79/1.00 (~c1_1(a759)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[873, 2033])).
% 0.79/1.00 tff(2037,plain,
% 0.79/1.00 (~c0_1(a759)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1760, 2036, 396, 2035, 2034])).
% 0.79/1.00 tff(2038,plain,
% 0.79/1.00 (c2_1(a777)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[659, 2015])).
% 0.79/1.00 tff(2039,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a777) | c1_1(a759) | (~ndr1_0) | (~c3_1(a759)) | c0_1(a759) | (~c2_1(a777)) | (~c1_1(a777)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a777) | c1_1(a759) | (~ndr1_0) | (~c3_1(a759)) | c0_1(a759) | (~c2_1(a777)) | (~c1_1(a777)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2040,plain,
% 0.79/1.00 ((hskp5 | (~ndr1_0) | c0_1(a777) | (~c2_1(a777)) | (~c1_1(a777)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759))) <=> (hskp5 | c0_1(a777) | c1_1(a759) | (~ndr1_0) | (~c3_1(a759)) | c0_1(a759) | (~c2_1(a777)) | (~c1_1(a777)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2041,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a777) | (~c2_1(a777)) | (~c1_1(a777)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a777) | c1_1(a759) | (~ndr1_0) | (~c3_1(a759)) | c0_1(a759) | (~c2_1(a777)) | (~c1_1(a777))))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[2040])).
% 0.79/1.00 tff(2042,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a777) | (~c2_1(a777)) | (~c1_1(a777)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a777) | c1_1(a759) | (~ndr1_0) | (~c3_1(a759)) | c0_1(a759) | (~c2_1(a777)) | (~c1_1(a777)))),
% 0.79/1.00 inference(transitivity,[status(thm)],[2041, 2039])).
% 0.79/1.00 tff(2043,plain,
% 0.79/1.00 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a777) | (~c2_1(a777)) | (~c1_1(a777)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759)))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(2044,plain,
% 0.79/1.00 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a777) | c1_1(a759) | (~ndr1_0) | (~c3_1(a759)) | c0_1(a759) | (~c2_1(a777)) | (~c1_1(a777))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2043, 2042])).
% 0.79/1.00 tff(2045,plain,
% 0.79/1.00 ($false),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2044, 104, 396, 2038, 2034, 2017, 2036, 1805, 2037, 2024])).
% 0.79/1.00 tff(2046,plain,((~hskp19) | hskp5 | (~c1_1(a731)) | c2_1(a731) | (~c0_1(a731)) | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.79/1.00 tff(2047,plain,
% 0.79/1.00 (~hskp19),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2046, 396, 2014, 2011, 2013, 2009])).
% 0.79/1.00 tff(2048,assumption,(hskp8), introduced(assumption)).
% 0.79/1.00 tff(2049,plain,
% 0.79/1.00 (~c0_1(a744)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[672, 2048])).
% 0.79/1.00 tff(2050,plain,
% 0.79/1.00 (~c1_1(a744)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[693, 2048])).
% 0.79/1.00 tff(2051,plain,
% 0.79/1.00 ($false),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1122, 2050, 2049, 53, 1030, 1029])).
% 0.79/1.00 tff(2052,plain,((~hskp8) | (~hskp1) | hskp12 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.79/1.00 tff(2053,plain,
% 0.79/1.00 (~hskp8),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2052, 2010, 1030, 1029])).
% 0.79/1.00 tff(2054,plain,
% 0.79/1.00 (hskp0),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1182, 2053])).
% 0.79/1.00 tff(2055,plain,
% 0.79/1.00 (~c1_1(a730)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[384, 2054])).
% 0.79/1.00 tff(2056,plain,
% 0.79/1.00 (c3_1(a730)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[435, 2054])).
% 0.79/1.00 tff(2057,plain,
% 0.79/1.00 (c0_1(a730)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[443, 2054])).
% 0.79/1.00 tff(2058,plain,
% 0.79/1.00 (hskp27 | hskp19),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[638, 104, 2057, 2056, 2055, 632])).
% 0.79/1.00 tff(2059,plain,
% 0.79/1.00 (hskp27),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2058, 2047])).
% 0.79/1.00 tff(2060,assumption,(hskp27), introduced(assumption)).
% 0.79/1.00 tff(2061,plain,
% 0.79/1.00 (c2_1(a750)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[724, 2060])).
% 0.79/1.00 tff(2062,plain,
% 0.79/1.00 (c1_1(a750)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[732, 2060])).
% 0.79/1.00 tff(2063,plain,
% 0.79/1.00 (c0_1(a750)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[716, 2060])).
% 0.79/1.00 tff(2064,assumption,(c0_1(a734)), introduced(assumption)).
% 0.79/1.00 tff(2065,assumption,(hskp20), introduced(assumption)).
% 0.79/1.00 tff(2066,plain,
% 0.79/1.00 (~c3_1(a779)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1737, 2065])).
% 0.79/1.00 tff(2067,plain,
% 0.79/1.00 (~c1_1(a779)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1743, 2065])).
% 0.79/1.00 tff(2068,plain,
% 0.79/1.00 (c2_1(a779)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1751, 2065])).
% 0.79/1.00 tff(2069,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a779) | c3_1(a779) | (~c0_1(a734)) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a779)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a779) | c3_1(a779) | (~c0_1(a734)) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a779)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2070,plain,
% 0.79/1.00 (((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a734) | c2_1(a734) | (~c0_1(a734)) | c1_1(a779) | c3_1(a779) | (~c2_1(a779))) <=> (c1_1(a779) | c3_1(a779) | (~c0_1(a734)) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a779)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2071,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a734) | c2_1(a734) | (~c0_1(a734)) | c1_1(a779) | c3_1(a779) | (~c2_1(a779)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a779) | c3_1(a779) | (~c0_1(a734)) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a779))))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[2070])).
% 0.79/1.00 tff(2072,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a734) | c2_1(a734) | (~c0_1(a734)) | c1_1(a779) | c3_1(a779) | (~c2_1(a779)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a779) | c3_1(a779) | (~c0_1(a734)) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a779)))),
% 0.79/1.00 inference(transitivity,[status(thm)],[2071, 2069])).
% 0.79/1.00 tff(2073,plain,
% 0.79/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a734) | c2_1(a734) | (~c0_1(a734)) | c1_1(a779) | c3_1(a779) | (~c2_1(a779)))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(2074,plain,
% 0.79/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a779) | c3_1(a779) | (~c0_1(a734)) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a779))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2073, 2072])).
% 0.79/1.00 tff(2075,plain,
% 0.79/1.00 ($false),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2074, 104, 744, 802, 801, 2068, 2067, 2066, 2064, 33, 828, 1478])).
% 0.79/1.00 tff(2076,plain,((~hskp20) | (~c0_1(a750)) | (~c1_1(a750)) | (~c2_1(a750)) | (~c0_1(a734)) | c3_1(a734) | c2_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.79/1.00 tff(2077,plain,
% 0.79/1.00 (~hskp20),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2076, 2063, 2062, 2061, 2003, 33, 1478])).
% 0.79/1.00 tff(2078,plain,
% 0.79/1.00 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp20 | hskp5 | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp20 | hskp5 | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2079,plain,
% 0.79/1.00 ((hskp20 | hskp5 | (~ndr1_0) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730))) <=> (hskp20 | hskp5 | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2080,plain,
% 0.79/1.00 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp20 | hskp5 | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730))))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[2079])).
% 0.79/1.00 tff(2081,plain,
% 0.79/1.00 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp20 | hskp5 | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)))),
% 0.79/1.00 inference(transitivity,[status(thm)],[2080, 2078])).
% 0.79/1.00 tff(2082,plain,
% 0.79/1.00 ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(2083,plain,
% 0.79/1.00 ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp20 | hskp5 | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2082, 2081])).
% 0.79/1.00 tff(2084,plain,
% 0.79/1.00 (hskp20 | hskp5 | (~c2_1(a730))),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2083, 104, 2056, 2055, 1722])).
% 0.79/1.00 tff(2085,plain,
% 0.79/1.00 (~c2_1(a730)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2084, 2077, 396])).
% 0.79/1.00 tff(2086,plain,
% 0.79/1.00 (hskp11 | c2_1(a730)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1901, 104, 2014, 2012, 2056, 2011, 2055, 360])).
% 0.79/1.00 tff(2087,plain,
% 0.79/1.00 (hskp11),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2086, 2085])).
% 0.79/1.00 tff(2088,plain,
% 0.79/1.00 (~c0_1(a749)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1540, 2087])).
% 0.79/1.00 tff(2089,plain,
% 0.79/1.00 (c2_1(a749)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1560, 2088, 396, 1030, 1029])).
% 0.79/1.00 tff(2090,plain,
% 0.79/1.00 (~c3_1(a749)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1863, 2087])).
% 0.79/1.00 tff(2091,plain,
% 0.79/1.00 (~c1_1(a749)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1566, 2087])).
% 0.79/1.00 tff(2092,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a749) | c3_1(a749) | (~c0_1(a734)) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a749)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a749) | c3_1(a749) | (~c0_1(a734)) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a749)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2093,plain,
% 0.79/1.00 (((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a734) | c2_1(a734) | (~c0_1(a734)) | c1_1(a749) | c3_1(a749) | (~c2_1(a749))) <=> (c1_1(a749) | c3_1(a749) | (~c0_1(a734)) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a749)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2094,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a734) | c2_1(a734) | (~c0_1(a734)) | c1_1(a749) | c3_1(a749) | (~c2_1(a749)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a749) | c3_1(a749) | (~c0_1(a734)) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a749))))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[2093])).
% 0.79/1.00 tff(2095,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a734) | c2_1(a734) | (~c0_1(a734)) | c1_1(a749) | c3_1(a749) | (~c2_1(a749)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a749) | c3_1(a749) | (~c0_1(a734)) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a749)))),
% 0.79/1.00 inference(transitivity,[status(thm)],[2094, 2092])).
% 0.79/1.00 tff(2096,plain,
% 0.79/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a734) | c2_1(a734) | (~c0_1(a734)) | c1_1(a749) | c3_1(a749) | (~c2_1(a749)))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(2097,plain,
% 0.79/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a749) | c3_1(a749) | (~c0_1(a734)) | c3_1(a734) | (~ndr1_0) | c2_1(a734) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a749))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2096, 2095])).
% 0.79/1.00 tff(2098,plain,
% 0.79/1.00 ($false),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2097, 104, 2063, 2062, 2061, 2091, 2090, 2003, 33, 828, 1478, 2089])).
% 0.79/1.00 tff(2099,plain,((~hskp27) | c3_1(a734) | c2_1(a734) | hskp5 | hskp12 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.79/1.00 tff(2100,plain,
% 0.79/1.00 (c2_1(a734)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2099, 2059, 33, 396, 1030, 1029])).
% 0.79/1.00 tff(2101,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a734) | c3_1(a734) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a734) | c3_1(a734) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a734)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2102,plain,
% 0.79/1.00 ((hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a734) | c1_1(a734) | (~c2_1(a734))) <=> (hskp5 | c1_1(a734) | c3_1(a734) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a734)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2103,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a734) | c1_1(a734) | (~c2_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a734) | c3_1(a734) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a734))))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[2102])).
% 0.79/1.00 tff(2104,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a734) | c1_1(a734) | (~c2_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a734) | c3_1(a734) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a734)))),
% 0.79/1.00 inference(transitivity,[status(thm)],[2103, 2101])).
% 0.79/1.00 tff(2105,plain,
% 0.79/1.00 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a734) | c1_1(a734) | (~c2_1(a734)))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(2106,plain,
% 0.79/1.00 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a734) | c3_1(a734) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a734))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2105, 2104])).
% 0.79/1.00 tff(2107,plain,
% 0.79/1.00 (hskp5 | c1_1(a734) | (~c2_1(a734))),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2106, 104, 2057, 2056, 33, 2055, 1456])).
% 0.79/1.00 tff(2108,plain,
% 0.79/1.00 (c1_1(a734)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2107, 2100, 396])).
% 0.79/1.00 tff(2109,plain,
% 0.79/1.00 (c2_1(a750)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[724, 2059])).
% 0.79/1.00 tff(2110,plain,
% 0.79/1.00 (c1_1(a750)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[732, 2059])).
% 0.79/1.00 tff(2111,plain,
% 0.79/1.00 (c0_1(a750)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[716, 2059])).
% 0.79/1.00 tff(2112,plain,
% 0.79/1.00 (((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp11 | (~c0_1(a734)) | c3_1(a734) | (~ndr1_0) | (~c1_1(a734)))) <=> ((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp18 | hskp11 | (~c0_1(a734)) | c3_1(a734) | (~ndr1_0) | (~c1_1(a734)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2113,plain,
% 0.79/1.00 ((hskp18 | hskp11 | (~ndr1_0) | c3_1(a734) | (~c1_1(a734)) | (~c0_1(a734))) <=> (hskp18 | hskp11 | (~c0_1(a734)) | c3_1(a734) | (~ndr1_0) | (~c1_1(a734)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2114,plain,
% 0.79/1.00 (((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp11 | (~ndr1_0) | c3_1(a734) | (~c1_1(a734)) | (~c0_1(a734)))) <=> ((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp11 | (~c0_1(a734)) | c3_1(a734) | (~ndr1_0) | (~c1_1(a734))))),
% 0.79/1.01 inference(monotonicity,[status(thm)],[2113])).
% 0.79/1.01 tff(2115,plain,
% 0.79/1.01 (((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp11 | (~ndr1_0) | c3_1(a734) | (~c1_1(a734)) | (~c0_1(a734)))) <=> ((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp18 | hskp11 | (~c0_1(a734)) | c3_1(a734) | (~ndr1_0) | (~c1_1(a734)))),
% 0.79/1.01 inference(transitivity,[status(thm)],[2114, 2112])).
% 0.79/1.01 tff(2116,plain,
% 0.79/1.01 ((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp11 | (~ndr1_0) | c3_1(a734) | (~c1_1(a734)) | (~c0_1(a734)))),
% 0.79/1.01 inference(quant_inst,[status(thm)],[])).
% 0.79/1.01 tff(2117,plain,
% 0.79/1.01 ((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp18 | hskp11 | (~c0_1(a734)) | c3_1(a734) | (~ndr1_0) | (~c1_1(a734))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2116, 2115])).
% 0.79/1.01 tff(2118,plain,
% 0.79/1.01 (hskp18 | hskp11 | (~c0_1(a734)) | (~c1_1(a734))),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2117, 104, 33, 1075])).
% 0.79/1.01 tff(2119,plain,
% 0.79/1.01 (hskp18),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2118, 21, 2064, 1006])).
% 0.79/1.01 tff(2120,plain,
% 0.79/1.01 (~c3_1(a775)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[1630, 2119])).
% 0.79/1.01 tff(2121,plain,
% 0.79/1.01 (~c2_1(a775)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[1636, 2119])).
% 0.79/1.01 tff(2122,plain,
% 0.79/1.01 (((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | c2_1(a775) | c3_1(a775) | (~ndr1_0) | c0_1(a775))) <=> ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp5 | c2_1(a775) | c3_1(a775) | (~ndr1_0) | c0_1(a775))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2123,plain,
% 0.79/1.01 ((hskp9 | hskp5 | (~ndr1_0) | c2_1(a775) | c0_1(a775) | c3_1(a775)) <=> (hskp9 | hskp5 | c2_1(a775) | c3_1(a775) | (~ndr1_0) | c0_1(a775))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2124,plain,
% 0.79/1.01 (((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | (~ndr1_0) | c2_1(a775) | c0_1(a775) | c3_1(a775))) <=> ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | c2_1(a775) | c3_1(a775) | (~ndr1_0) | c0_1(a775)))),
% 0.79/1.01 inference(monotonicity,[status(thm)],[2123])).
% 0.79/1.01 tff(2125,plain,
% 0.79/1.01 (((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | (~ndr1_0) | c2_1(a775) | c0_1(a775) | c3_1(a775))) <=> ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp5 | c2_1(a775) | c3_1(a775) | (~ndr1_0) | c0_1(a775))),
% 0.79/1.01 inference(transitivity,[status(thm)],[2124, 2122])).
% 0.79/1.01 tff(2126,plain,
% 0.79/1.01 ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | (~ndr1_0) | c2_1(a775) | c0_1(a775) | c3_1(a775))),
% 0.79/1.01 inference(quant_inst,[status(thm)],[])).
% 0.79/1.01 tff(2127,plain,
% 0.79/1.01 ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp5 | c2_1(a775) | c3_1(a775) | (~ndr1_0) | c0_1(a775)),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2126, 2125])).
% 0.79/1.01 tff(2128,plain,
% 0.79/1.01 (c0_1(a775)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2127, 104, 1655, 396, 2121, 2120, 1085])).
% 0.79/1.01 tff(2129,assumption,(c3_1(a731)), introduced(assumption)).
% 0.79/1.01 tff(2130,plain,
% 0.79/1.01 (hskp11 | c2_1(a730)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[1901, 104, 2026, 2129, 468, 1033, 456, 360])).
% 0.79/1.01 tff(2131,plain,
% 0.79/1.01 (c2_1(a730)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2130, 21])).
% 0.79/1.01 tff(2132,plain,
% 0.79/1.01 (hskp20 | hskp5 | (~c2_1(a730))),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2083, 104, 468, 456, 1722])).
% 0.79/1.01 tff(2133,plain,
% 0.79/1.01 (hskp20),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2132, 2131, 396])).
% 0.79/1.01 tff(2134,plain,
% 0.79/1.01 (~c3_1(a779)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[1737, 2133])).
% 0.79/1.01 tff(2135,plain,
% 0.79/1.01 (~c1_1(a779)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[1743, 2133])).
% 0.79/1.01 tff(2136,plain,
% 0.79/1.01 (c2_1(a779)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[1751, 2133])).
% 0.79/1.01 tff(2137,plain,
% 0.79/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a779) | c3_1(a779) | c2_1(a775) | c3_1(a775) | (~ndr1_0) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a775)) | (~c2_1(a779)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a779) | c3_1(a779) | c2_1(a775) | c3_1(a775) | (~ndr1_0) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a775)) | (~c2_1(a779)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2138,plain,
% 0.79/1.01 (((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a775) | c2_1(a775) | (~c0_1(a775)) | c1_1(a779) | c3_1(a779) | (~c2_1(a779))) <=> (c1_1(a779) | c3_1(a779) | c2_1(a775) | c3_1(a775) | (~ndr1_0) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a775)) | (~c2_1(a779)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2139,plain,
% 0.79/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a775) | c2_1(a775) | (~c0_1(a775)) | c1_1(a779) | c3_1(a779) | (~c2_1(a779)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a779) | c3_1(a779) | c2_1(a775) | c3_1(a775) | (~ndr1_0) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a775)) | (~c2_1(a779))))),
% 0.79/1.01 inference(monotonicity,[status(thm)],[2138])).
% 0.79/1.01 tff(2140,plain,
% 0.79/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a775) | c2_1(a775) | (~c0_1(a775)) | c1_1(a779) | c3_1(a779) | (~c2_1(a779)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a779) | c3_1(a779) | c2_1(a775) | c3_1(a775) | (~ndr1_0) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a775)) | (~c2_1(a779)))),
% 0.79/1.01 inference(transitivity,[status(thm)],[2139, 2137])).
% 0.79/1.01 tff(2141,plain,
% 0.79/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a775) | c2_1(a775) | (~c0_1(a775)) | c1_1(a779) | c3_1(a779) | (~c2_1(a779)))),
% 0.79/1.01 inference(quant_inst,[status(thm)],[])).
% 0.79/1.01 tff(2142,plain,
% 0.79/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a779) | c3_1(a779) | c2_1(a775) | c3_1(a775) | (~ndr1_0) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a775)) | (~c2_1(a779))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2141, 2140])).
% 0.79/1.01 tff(2143,plain,
% 0.79/1.01 ($false),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2142, 104, 744, 802, 801, 2136, 2135, 2134, 2121, 2120, 828, 2128])).
% 0.79/1.01 tff(2144,plain,(hskp11 | (~c0_1(a750)) | (~c1_1(a750)) | (~c2_1(a750)) | hskp9 | hskp5 | (~c3_1(a730)) | c1_1(a730) | (~c0_1(a734)) | (~c1_1(a734)) | c3_1(a734) | (~c1_1(a731)) | (~c3_1(a731)) | c2_1(a731)), inference(lemma,lemma(discharge,[]))).
% 0.79/1.01 tff(2145,plain,
% 0.79/1.01 (hskp11),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2144, 2111, 2110, 2109, 1061, 396, 2056, 2055, 2003, 2108, 33, 2014, 2012, 2011])).
% 0.79/1.01 tff(2146,plain,
% 0.79/1.01 (~c3_1(a749)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[1863, 2145])).
% 0.79/1.01 tff(2147,plain,
% 0.79/1.01 (~c1_1(a749)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[1566, 2145])).
% 0.79/1.01 tff(2148,plain,
% 0.79/1.01 (~c0_1(a749)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[1540, 2145])).
% 0.79/1.01 tff(2149,plain,
% 0.79/1.01 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | c0_1(a749) | c1_1(a749) | c3_1(a749) | (~ndr1_0))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp5 | hskp4 | c0_1(a749) | c1_1(a749) | c3_1(a749) | (~ndr1_0))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2150,plain,
% 0.79/1.01 ((hskp5 | hskp4 | (~ndr1_0) | c1_1(a749) | c0_1(a749) | c3_1(a749)) <=> (hskp5 | hskp4 | c0_1(a749) | c1_1(a749) | c3_1(a749) | (~ndr1_0))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2151,plain,
% 0.79/1.01 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c1_1(a749) | c0_1(a749) | c3_1(a749))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | c0_1(a749) | c1_1(a749) | c3_1(a749) | (~ndr1_0)))),
% 0.79/1.01 inference(monotonicity,[status(thm)],[2150])).
% 0.79/1.01 tff(2152,plain,
% 0.79/1.01 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c1_1(a749) | c0_1(a749) | c3_1(a749))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp5 | hskp4 | c0_1(a749) | c1_1(a749) | c3_1(a749) | (~ndr1_0))),
% 0.79/1.01 inference(transitivity,[status(thm)],[2151, 2149])).
% 0.79/1.01 tff(2153,plain,
% 0.79/1.01 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c1_1(a749) | c0_1(a749) | c3_1(a749))),
% 0.79/1.01 inference(quant_inst,[status(thm)],[])).
% 0.79/1.01 tff(2154,plain,
% 0.79/1.01 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp5 | hskp4 | c0_1(a749) | c1_1(a749) | c3_1(a749) | (~ndr1_0)),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2153, 2152])).
% 0.79/1.01 tff(2155,plain,
% 0.79/1.01 ($false),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2154, 104, 396, 2009, 2148, 2147, 2146, 395])).
% 0.79/1.01 tff(2156,plain,(hskp5 | c3_1(a734) | hskp12 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.79/1.01 tff(2157,plain,
% 0.79/1.01 (hskp5),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2156, 33, 1030, 1029])).
% 0.79/1.01 tff(2158,plain,
% 0.79/1.01 (c2_1(a735)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[421, 2157])).
% 0.79/1.01 tff(2159,plain,
% 0.79/1.01 (~c0_1(a735)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[427, 2157])).
% 0.79/1.01 tff(2160,plain,
% 0.79/1.01 (c3_1(a735)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[413, 2157])).
% 0.79/1.01 tff(2161,plain,
% 0.79/1.01 (~c2_1(a730)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[509, 2160, 2057, 2056, 2159, 2055, 2158])).
% 0.79/1.01 tff(2162,plain,
% 0.79/1.01 (hskp11),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2086, 2161])).
% 0.79/1.01 tff(2163,plain,
% 0.79/1.01 (~c3_1(a749)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[1863, 2162])).
% 0.79/1.01 tff(2164,plain,
% 0.79/1.01 (~c1_1(a749)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[1566, 2162])).
% 0.79/1.01 tff(2165,plain,
% 0.79/1.01 (~c0_1(a749)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[1540, 2162])).
% 0.79/1.01 tff(2166,plain,
% 0.79/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a749) | c1_1(a749) | c3_1(a749) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a749) | c1_1(a749) | c3_1(a749) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2167,plain,
% 0.79/1.01 (((~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c1_1(a749) | c0_1(a749) | c3_1(a749)) <=> (c0_1(a749) | c1_1(a749) | c3_1(a749) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2168,plain,
% 0.79/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c1_1(a749) | c0_1(a749) | c3_1(a749))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a749) | c1_1(a749) | c3_1(a749) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731))))),
% 0.79/1.01 inference(monotonicity,[status(thm)],[2167])).
% 0.79/1.01 tff(2169,plain,
% 0.79/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c1_1(a749) | c0_1(a749) | c3_1(a749))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a749) | c1_1(a749) | c3_1(a749) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)))),
% 0.79/1.01 inference(transitivity,[status(thm)],[2168, 2166])).
% 0.79/1.01 tff(2170,plain,
% 0.79/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c1_1(a749) | c0_1(a749) | c3_1(a749))),
% 0.79/1.01 inference(quant_inst,[status(thm)],[])).
% 0.79/1.01 tff(2171,plain,
% 0.79/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a749) | c1_1(a749) | c3_1(a749) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2170, 2169])).
% 0.79/1.01 tff(2172,plain,
% 0.79/1.01 ($false),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2171, 104, 2014, 2012, 2165, 2164, 2163, 2011, 10, 2013])).
% 0.79/1.01 tff(2173,plain,(c3_1(a734) | hskp12 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.79/1.01 tff(2174,plain,
% 0.79/1.01 (hskp12),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2173, 1018, 33])).
% 0.79/1.01 tff(2175,plain,
% 0.79/1.01 (((~hskp12) | (~c3_1(a755))) <=> ((~hskp12) | (~c3_1(a755)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2176,plain,
% 0.79/1.01 (((~c3_1(a755)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a755)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2177,axiom,((~c3_1(a755)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 0.79/1.01 tff(2178,plain,
% 0.79/1.01 ((~hskp12) | (~c3_1(a755))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2177, 2176])).
% 0.79/1.01 tff(2179,plain,
% 0.79/1.01 ((~hskp12) | (~c3_1(a755))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2178, 2175])).
% 0.79/1.01 tff(2180,plain,
% 0.79/1.01 (~c3_1(a755)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2179, 2174])).
% 0.79/1.01 tff(2181,plain,
% 0.79/1.01 (((~hskp12) | c2_1(a755)) <=> ((~hskp12) | c2_1(a755))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2182,axiom,((~hskp12) | c2_1(a755)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 0.79/1.01 tff(2183,plain,
% 0.79/1.01 ((~hskp12) | c2_1(a755)),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2182, 2181])).
% 0.79/1.01 tff(2184,plain,
% 0.79/1.01 ((~hskp12) | c2_1(a755)),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2183, 2181])).
% 0.79/1.01 tff(2185,plain,
% 0.79/1.01 ((~hskp12) | c2_1(a755)),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2184, 2181])).
% 0.79/1.01 tff(2186,plain,
% 0.79/1.01 ((~hskp12) | c2_1(a755)),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2185, 2181])).
% 0.79/1.01 tff(2187,plain,
% 0.79/1.01 ((~hskp12) | c2_1(a755)),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2186, 2181])).
% 0.79/1.01 tff(2188,plain,
% 0.79/1.01 (c2_1(a755)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2187, 2174])).
% 0.79/1.01 tff(2189,plain,
% 0.79/1.01 (((~hskp12) | c1_1(a755)) <=> ((~hskp12) | c1_1(a755))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2190,axiom,((~hskp12) | c1_1(a755)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 0.79/1.01 tff(2191,plain,
% 0.79/1.01 ((~hskp12) | c1_1(a755)),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2190, 2189])).
% 0.79/1.01 tff(2192,plain,
% 0.79/1.01 ((~hskp12) | c1_1(a755)),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2191, 2189])).
% 0.79/1.01 tff(2193,plain,
% 0.79/1.01 ((~hskp12) | c1_1(a755)),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2192, 2189])).
% 0.79/1.01 tff(2194,plain,
% 0.79/1.01 ((~hskp12) | c1_1(a755)),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2193, 2189])).
% 0.79/1.01 tff(2195,plain,
% 0.79/1.01 ((~hskp12) | c1_1(a755)),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2194, 2189])).
% 0.79/1.01 tff(2196,plain,
% 0.79/1.01 (c1_1(a755)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2195, 2174])).
% 0.79/1.01 tff(2197,plain,
% 0.79/1.01 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp11 | c3_1(a755) | (~ndr1_0) | (~c1_1(a755)) | (~c2_1(a755)))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp11 | c3_1(a755) | (~ndr1_0) | (~c1_1(a755)) | (~c2_1(a755)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2198,plain,
% 0.79/1.01 ((hskp27 | hskp11 | (~ndr1_0) | c3_1(a755) | (~c2_1(a755)) | (~c1_1(a755))) <=> (hskp27 | hskp11 | c3_1(a755) | (~ndr1_0) | (~c1_1(a755)) | (~c2_1(a755)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2199,plain,
% 0.79/1.01 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp11 | (~ndr1_0) | c3_1(a755) | (~c2_1(a755)) | (~c1_1(a755)))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp11 | c3_1(a755) | (~ndr1_0) | (~c1_1(a755)) | (~c2_1(a755))))),
% 0.79/1.01 inference(monotonicity,[status(thm)],[2198])).
% 0.79/1.01 tff(2200,plain,
% 0.79/1.01 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp11 | (~ndr1_0) | c3_1(a755) | (~c2_1(a755)) | (~c1_1(a755)))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp11 | c3_1(a755) | (~ndr1_0) | (~c1_1(a755)) | (~c2_1(a755)))),
% 0.79/1.01 inference(transitivity,[status(thm)],[2199, 2197])).
% 0.79/1.01 tff(2201,plain,
% 0.79/1.01 ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp11 | (~ndr1_0) | c3_1(a755) | (~c2_1(a755)) | (~c1_1(a755)))),
% 0.79/1.01 inference(quant_inst,[status(thm)],[])).
% 0.79/1.01 tff(2202,plain,
% 0.79/1.01 ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp11 | c3_1(a755) | (~ndr1_0) | (~c1_1(a755)) | (~c2_1(a755))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2201, 2200])).
% 0.79/1.01 tff(2203,plain,
% 0.79/1.01 (hskp27),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2202, 104, 21, 2196, 2188, 2180, 559])).
% 0.79/1.01 tff(2204,plain,
% 0.79/1.01 (c0_1(a750)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[716, 2203])).
% 0.79/1.01 tff(2205,plain,
% 0.79/1.01 (c2_1(a750)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[724, 2203])).
% 0.79/1.01 tff(2206,plain,
% 0.79/1.01 (c1_1(a750)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[732, 2203])).
% 0.79/1.01 tff(2207,assumption,(~c3_1(a741)), introduced(assumption)).
% 0.79/1.01 tff(2208,plain,
% 0.79/1.01 (((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | c1_1(a741) | c0_1(a741) | (~ndr1_0) | c2_1(a741))) <=> ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | hskp1 | c1_1(a741) | c0_1(a741) | (~ndr1_0) | c2_1(a741))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2209,plain,
% 0.79/1.01 ((hskp0 | hskp1 | (~ndr1_0) | c2_1(a741) | c1_1(a741) | c0_1(a741)) <=> (hskp0 | hskp1 | c1_1(a741) | c0_1(a741) | (~ndr1_0) | c2_1(a741))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2210,plain,
% 0.79/1.01 (((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | (~ndr1_0) | c2_1(a741) | c1_1(a741) | c0_1(a741))) <=> ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | c1_1(a741) | c0_1(a741) | (~ndr1_0) | c2_1(a741)))),
% 0.79/1.01 inference(monotonicity,[status(thm)],[2209])).
% 0.79/1.01 tff(2211,plain,
% 0.79/1.01 (((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | (~ndr1_0) | c2_1(a741) | c1_1(a741) | c0_1(a741))) <=> ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | hskp1 | c1_1(a741) | c0_1(a741) | (~ndr1_0) | c2_1(a741))),
% 0.79/1.01 inference(transitivity,[status(thm)],[2210, 2208])).
% 0.79/1.01 tff(2212,plain,
% 0.79/1.01 ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | (~ndr1_0) | c2_1(a741) | c1_1(a741) | c0_1(a741))),
% 0.79/1.01 inference(quant_inst,[status(thm)],[])).
% 0.79/1.01 tff(2213,plain,
% 0.79/1.01 ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | hskp1 | c1_1(a741) | c0_1(a741) | (~ndr1_0) | c2_1(a741)),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2212, 2211])).
% 0.79/1.01 tff(2214,plain,
% 0.79/1.01 (hskp0 | hskp1 | c1_1(a741) | c2_1(a741)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2213, 104, 177, 236])).
% 0.79/1.01 tff(2215,plain,
% 0.79/1.01 (c2_1(a741)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2214, 217, 1017, 255])).
% 0.79/1.01 tff(2216,plain,
% 0.79/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a741) | c0_1(a746) | c2_1(a746) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | c1_1(a746))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a741) | c0_1(a746) | c2_1(a746) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | c1_1(a746))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2217,plain,
% 0.79/1.01 (((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a741) | c0_1(a741) | (~c2_1(a741)) | c2_1(a746) | c1_1(a746) | c0_1(a746)) <=> (c3_1(a741) | c0_1(a746) | c2_1(a746) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | c1_1(a746))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2218,plain,
% 0.79/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a741) | c0_1(a741) | (~c2_1(a741)) | c2_1(a746) | c1_1(a746) | c0_1(a746))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a741) | c0_1(a746) | c2_1(a746) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | c1_1(a746)))),
% 0.79/1.01 inference(monotonicity,[status(thm)],[2217])).
% 0.79/1.01 tff(2219,plain,
% 0.79/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a741) | c0_1(a741) | (~c2_1(a741)) | c2_1(a746) | c1_1(a746) | c0_1(a746))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a741) | c0_1(a746) | c2_1(a746) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | c1_1(a746))),
% 0.79/1.01 inference(transitivity,[status(thm)],[2218, 2216])).
% 0.79/1.01 tff(2220,plain,
% 0.79/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a741) | c0_1(a741) | (~c2_1(a741)) | c2_1(a746) | c1_1(a746) | c0_1(a746))),
% 0.79/1.01 inference(quant_inst,[status(thm)],[])).
% 0.79/1.01 tff(2221,plain,
% 0.79/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a741) | c0_1(a746) | c2_1(a746) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | c1_1(a746)),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2220, 2219])).
% 0.79/1.01 tff(2222,plain,
% 0.79/1.01 ($false),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2221, 104, 744, 802, 801, 2207, 1010, 1009, 177, 952, 2215, 1012])).
% 0.79/1.01 tff(2223,plain,(hskp0 | (~c0_1(a750)) | (~c1_1(a750)) | (~c2_1(a750)) | c3_1(a741) | c0_1(a741) | c1_1(a741) | hskp1 | (~c1_1(a734)) | c3_1(a734) | c0_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.79/1.01 tff(2224,plain,
% 0.79/1.01 (hskp0),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2223, 255, 802, 801, 2207, 177, 1017, 744, 1006, 33, 22])).
% 0.79/1.01 tff(2225,plain,
% 0.79/1.01 (~c1_1(a730)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[384, 2224])).
% 0.79/1.01 tff(2226,plain,
% 0.79/1.01 (c3_1(a730)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[435, 2224])).
% 0.79/1.01 tff(2227,plain,
% 0.79/1.01 (c0_1(a730)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[443, 2224])).
% 0.79/1.01 tff(2228,assumption,(~c3_1(a755)), introduced(assumption)).
% 0.79/1.01 tff(2229,assumption,(c1_1(a755)), introduced(assumption)).
% 0.79/1.01 tff(2230,plain,
% 0.79/1.01 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | c1_1(a741) | c0_1(a741) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a741))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c1_1(a741) | c0_1(a741) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a741))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2231,plain,
% 0.79/1.01 ((hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a741) | c0_1(a741) | c2_1(a741)) <=> (hskp25 | c1_1(a741) | c0_1(a741) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a741))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2232,plain,
% 0.79/1.01 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a741) | c0_1(a741) | c2_1(a741))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | c1_1(a741) | c0_1(a741) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a741)))),
% 0.79/1.01 inference(monotonicity,[status(thm)],[2231])).
% 0.79/1.01 tff(2233,plain,
% 0.79/1.01 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a741) | c0_1(a741) | c2_1(a741))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c1_1(a741) | c0_1(a741) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a741))),
% 0.79/1.01 inference(transitivity,[status(thm)],[2232, 2230])).
% 0.79/1.01 tff(2234,plain,
% 0.79/1.01 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a741) | c0_1(a741) | c2_1(a741))),
% 0.79/1.01 inference(quant_inst,[status(thm)],[])).
% 0.79/1.01 tff(2235,plain,
% 0.79/1.01 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c1_1(a741) | c0_1(a741) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a741)),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2234, 2233])).
% 0.79/1.01 tff(2236,plain,
% 0.79/1.01 (hskp25 | c2_1(a741)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2235, 104, 1017, 469, 468, 177, 456, 20])).
% 0.79/1.01 tff(2237,plain,
% 0.79/1.01 (hskp25),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2236, 165])).
% 0.79/1.01 tff(2238,plain,
% 0.79/1.01 (c3_1(a729)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[762, 2237])).
% 0.79/1.01 tff(2239,plain,
% 0.79/1.01 (c2_1(a729)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[770, 2237])).
% 0.79/1.01 tff(2240,plain,
% 0.79/1.01 (c0_1(a729)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[778, 2237])).
% 0.79/1.01 tff(2241,plain,
% 0.79/1.01 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | c3_1(a755) | (~ndr1_0) | (~c1_1(a755)) | (~c0_1(a755)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp1 | c3_1(a755) | (~ndr1_0) | (~c1_1(a755)) | (~c0_1(a755)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2242,plain,
% 0.79/1.01 ((hskp1 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c3_1(a755) | (~c1_1(a755)) | (~c0_1(a755))) <=> (hskp1 | c3_1(a755) | (~ndr1_0) | (~c1_1(a755)) | (~c0_1(a755)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2243,plain,
% 0.79/1.01 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c3_1(a755) | (~c1_1(a755)) | (~c0_1(a755)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | c3_1(a755) | (~ndr1_0) | (~c1_1(a755)) | (~c0_1(a755)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729))))),
% 0.79/1.01 inference(monotonicity,[status(thm)],[2242])).
% 0.79/1.01 tff(2244,plain,
% 0.79/1.01 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c3_1(a755) | (~c1_1(a755)) | (~c0_1(a755)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp1 | c3_1(a755) | (~ndr1_0) | (~c1_1(a755)) | (~c0_1(a755)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)))),
% 0.79/1.01 inference(transitivity,[status(thm)],[2243, 2241])).
% 0.79/1.01 tff(2245,plain,
% 0.79/1.01 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c3_1(a755) | (~c1_1(a755)) | (~c0_1(a755)))),
% 0.79/1.01 inference(quant_inst,[status(thm)],[])).
% 0.79/1.01 tff(2246,plain,
% 0.79/1.01 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp1 | c3_1(a755) | (~ndr1_0) | (~c1_1(a755)) | (~c0_1(a755)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2245, 2244])).
% 0.79/1.01 tff(2247,plain,
% 0.79/1.01 (~c0_1(a755)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2246, 104, 255, 2240, 2239, 2238, 2229, 2228, 743])).
% 0.79/1.01 tff(2248,assumption,(c2_1(a755)), introduced(assumption)).
% 0.79/1.01 tff(2249,plain,
% 0.79/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a741) | c3_1(a755) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a755)) | c0_1(a755))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a741) | c3_1(a755) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a755)) | c0_1(a755))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2250,plain,
% 0.79/1.01 (((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a755) | c0_1(a755) | (~c2_1(a755)) | c2_1(a741) | c1_1(a741) | c0_1(a741)) <=> (c1_1(a741) | c3_1(a755) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a755)) | c0_1(a755))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2251,plain,
% 0.79/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a755) | c0_1(a755) | (~c2_1(a755)) | c2_1(a741) | c1_1(a741) | c0_1(a741))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a741) | c3_1(a755) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a755)) | c0_1(a755)))),
% 0.79/1.01 inference(monotonicity,[status(thm)],[2250])).
% 0.79/1.01 tff(2252,plain,
% 0.79/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a755) | c0_1(a755) | (~c2_1(a755)) | c2_1(a741) | c1_1(a741) | c0_1(a741))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a741) | c3_1(a755) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a755)) | c0_1(a755))),
% 0.79/1.01 inference(transitivity,[status(thm)],[2251, 2249])).
% 0.79/1.01 tff(2253,plain,
% 0.79/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a755) | c0_1(a755) | (~c2_1(a755)) | c2_1(a741) | c1_1(a741) | c0_1(a741))),
% 0.79/1.02 inference(quant_inst,[status(thm)],[])).
% 0.79/1.02 tff(2254,plain,
% 0.79/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a741) | c3_1(a755) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a755)) | c0_1(a755)),
% 0.79/1.02 inference(modus_ponens,[status(thm)],[2253, 2252])).
% 0.79/1.02 tff(2255,plain,
% 0.79/1.02 ($false),
% 0.79/1.02 inference(unit_resolution,[status(thm)],[2254, 104, 744, 802, 801, 2248, 1017, 2228, 177, 952, 165, 2247])).
% 0.79/1.02 tff(2256,plain,(c2_1(a741) | (~c0_1(a750)) | (~c1_1(a750)) | (~c2_1(a750)) | (~c2_1(a755)) | c1_1(a741) | c3_1(a755) | c0_1(a741) | hskp1 | (~c1_1(a755)) | (~c0_1(a730)) | (~c3_1(a730)) | c1_1(a730)), inference(lemma,lemma(discharge,[]))).
% 0.79/1.02 tff(2257,plain,
% 0.79/1.02 (c2_1(a741)),
% 0.79/1.02 inference(unit_resolution,[status(thm)],[2256, 255, 802, 801, 2188, 1017, 2180, 177, 744, 2196, 2227, 2226, 2225])).
% 0.79/1.02 tff(2258,plain,
% 0.79/1.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a741) | c3_1(a741) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a741) | c3_1(a741) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)))),
% 0.79/1.02 inference(rewrite,[status(thm)],[])).
% 0.79/1.02 tff(2259,plain,
% 0.79/1.02 ((hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a741) | c1_1(a741) | (~c2_1(a741))) <=> (hskp5 | c1_1(a741) | c3_1(a741) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)))),
% 0.79/1.02 inference(rewrite,[status(thm)],[])).
% 0.79/1.02 tff(2260,plain,
% 0.79/1.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a741) | c1_1(a741) | (~c2_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a741) | c3_1(a741) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a741))))),
% 0.79/1.02 inference(monotonicity,[status(thm)],[2259])).
% 0.79/1.02 tff(2261,plain,
% 0.79/1.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a741) | c1_1(a741) | (~c2_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a741) | c3_1(a741) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)))),
% 0.79/1.02 inference(transitivity,[status(thm)],[2260, 2258])).
% 0.79/1.02 tff(2262,plain,
% 0.79/1.02 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a741) | c1_1(a741) | (~c2_1(a741)))),
% 0.79/1.02 inference(quant_inst,[status(thm)],[])).
% 0.79/1.02 tff(2263,plain,
% 0.79/1.02 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a741) | c3_1(a741) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a741))),
% 0.79/1.02 inference(modus_ponens,[status(thm)],[2262, 2261])).
% 0.79/1.02 tff(2264,plain,
% 0.79/1.02 (hskp5 | (~c2_1(a741))),
% 0.79/1.02 inference(unit_resolution,[status(thm)],[2263, 104, 1017, 2207, 469, 468, 456, 1456])).
% 0.79/1.02 tff(2265,plain,
% 0.79/1.02 (~c2_1(a741)),
% 0.79/1.02 inference(unit_resolution,[status(thm)],[2264, 396])).
% 0.79/1.02 tff(2266,plain,
% 0.79/1.02 (c2_1(a734)),
% 0.79/1.02 inference(unit_resolution,[status(thm)],[1177, 396, 33, 1006])).
% 0.79/1.02 tff(2267,plain,
% 0.79/1.02 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)))),
% 0.79/1.02 inference(rewrite,[status(thm)],[])).
% 0.79/1.02 tff(2268,plain,
% 0.79/1.02 ((hskp16 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c0_1(a734) | (~c2_1(a734)) | (~c1_1(a734))) <=> (hskp16 | c0_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)))),
% 0.79/1.02 inference(rewrite,[status(thm)],[])).
% 0.79/1.02 tff(2269,plain,
% 0.79/1.02 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c0_1(a734) | (~c2_1(a734)) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729))))),
% 0.79/1.02 inference(monotonicity,[status(thm)],[2268])).
% 0.79/1.02 tff(2270,plain,
% 0.79/1.02 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c0_1(a734) | (~c2_1(a734)) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)))),
% 0.79/1.02 inference(transitivity,[status(thm)],[2269, 2267])).
% 0.79/1.02 tff(2271,plain,
% 0.79/1.02 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729)) | c0_1(a734) | (~c2_1(a734)) | (~c1_1(a734)))),
% 0.79/1.02 inference(quant_inst,[status(thm)],[])).
% 0.79/1.02 tff(2272,plain,
% 0.79/1.02 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734)) | (~c2_1(a729)) | (~c3_1(a729)) | (~c0_1(a729))),
% 0.79/1.02 inference(modus_ponens,[status(thm)],[2271, 2270])).
% 0.79/1.02 tff(2273,plain,
% 0.79/1.02 (hskp16),
% 0.79/1.02 inference(unit_resolution,[status(thm)],[2272, 104, 779, 771, 763, 1006, 22, 754, 1533])).
% 0.79/1.02 tff(2274,plain,
% 0.79/1.02 (~c3_1(a764)),
% 0.79/1.02 inference(unit_resolution,[status(thm)],[791, 2273])).
% 0.79/1.02 tff(2275,plain,
% 0.79/1.02 (c0_1(a764)),
% 0.79/1.02 inference(unit_resolution,[status(thm)],[809, 2273])).
% 0.79/1.02 tff(2276,plain,
% 0.79/1.02 (~c1_1(a764)),
% 0.79/1.02 inference(unit_resolution,[status(thm)],[816, 104, 255, 779, 771, 763, 2275, 2274, 743])).
% 0.79/1.02 tff(2277,plain,
% 0.79/1.02 (c2_1(a764)),
% 0.79/1.02 inference(unit_resolution,[status(thm)],[799, 2273])).
% 0.79/1.02 tff(2278,plain,
% 0.79/1.02 ($false),
% 0.79/1.02 inference(unit_resolution,[status(thm)],[1611, 104, 396, 2277, 469, 468, 2274, 456, 1456, 2276])).
% 0.79/1.02 tff(2279,plain,((~hskp25) | hskp5 | (~c0_1(a730)) | (~c3_1(a730)) | c1_1(a730) | hskp1 | (~c1_1(a734)) | c0_1(a734) | (~c2_1(a734))), inference(lemma,lemma(discharge,[]))).
% 0.79/1.02 tff(2280,plain,
% 0.79/1.02 (~hskp25),
% 0.79/1.02 inference(unit_resolution,[status(thm)],[2279, 2266, 469, 468, 456, 255, 1006, 22, 396])).
% 0.79/1.02 tff(2281,plain,
% 0.79/1.02 ($false),
% 0.79/1.02 inference(unit_resolution,[status(thm)],[2236, 2280, 2265])).
% 0.79/1.02 tff(2282,plain,(hskp5 | c1_1(a741) | (~c0_1(a730)) | (~c3_1(a730)) | c0_1(a741) | c1_1(a730) | hskp1 | (~c1_1(a734)) | c0_1(a734) | c3_1(a741) | c3_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.79/1.02 tff(2283,plain,
% 0.79/1.02 (hskp5),
% 0.79/1.02 inference(unit_resolution,[status(thm)],[2282, 2227, 1017, 2226, 177, 2225, 255, 1006, 22, 2207, 33])).
% 0.79/1.02 tff(2284,plain,
% 0.79/1.02 (c3_1(a735)),
% 0.79/1.02 inference(unit_resolution,[status(thm)],[413, 2283])).
% 0.79/1.02 tff(2285,plain,
% 0.79/1.02 (c2_1(a735)),
% 0.79/1.02 inference(unit_resolution,[status(thm)],[421, 2283])).
% 0.79/1.02 tff(2286,plain,
% 0.79/1.02 (~c0_1(a735)),
% 0.79/1.02 inference(unit_resolution,[status(thm)],[427, 2283])).
% 0.79/1.02 tff(2287,plain,
% 0.79/1.02 (~c2_1(a730)),
% 0.79/1.02 inference(unit_resolution,[status(thm)],[509, 2284, 2227, 2226, 2286, 2225, 2285])).
% 0.79/1.02 tff(2288,plain,
% 0.79/1.02 (hskp2),
% 0.79/1.02 inference(unit_resolution,[status(thm)],[540, 2287, 2227, 2286, 2225, 2285, 255, 2284])).
% 0.85/1.02 tff(2289,plain,
% 0.85/1.02 (~c2_1(a732)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[282, 2288])).
% 0.85/1.02 tff(2290,plain,
% 0.85/1.02 (~c0_1(a732)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[288, 2288])).
% 0.85/1.02 tff(2291,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a741) | c0_1(a741) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c2_1(a741)) | c1_1(a732) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a741) | c0_1(a741) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c2_1(a741)) | c1_1(a732) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2292,plain,
% 0.85/1.02 (((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a741) | c0_1(a741) | (~c2_1(a741)) | c2_1(a732) | c1_1(a732) | c0_1(a732)) <=> (c3_1(a741) | c0_1(a741) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c2_1(a741)) | c1_1(a732) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2293,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a741) | c0_1(a741) | (~c2_1(a741)) | c2_1(a732) | c1_1(a732) | c0_1(a732))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a741) | c0_1(a741) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c2_1(a741)) | c1_1(a732) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[2292])).
% 0.85/1.02 tff(2294,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a741) | c0_1(a741) | (~c2_1(a741)) | c2_1(a732) | c1_1(a732) | c0_1(a732))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a741) | c0_1(a741) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c2_1(a741)) | c1_1(a732) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[2293, 2291])).
% 0.85/1.02 tff(2295,plain,
% 0.85/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a741) | c0_1(a741) | (~c2_1(a741)) | c2_1(a732) | c1_1(a732) | c0_1(a732))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(2296,plain,
% 0.85/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a741) | c0_1(a741) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c2_1(a741)) | c1_1(a732) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2295, 2294])).
% 0.85/1.02 tff(2297,plain,
% 0.85/1.02 ((~c2_1(a741)) | c1_1(a732)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2296, 104, 744, 802, 801, 2207, 177, 2290, 2289, 952])).
% 0.85/1.02 tff(2298,plain,
% 0.85/1.02 (c1_1(a732)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2297, 2257])).
% 0.85/1.02 tff(2299,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a735) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c3_1(a735)) | (~c2_1(a735)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a735) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c3_1(a735)) | (~c2_1(a735)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2300,plain,
% 0.85/1.02 ((hskp10 | (~ndr1_0) | c0_1(a735) | (~c2_1(a735)) | (~c3_1(a735)) | c0_1(a732) | c2_1(a732) | (~c1_1(a732))) <=> (hskp10 | c0_1(a735) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c3_1(a735)) | (~c2_1(a735)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2301,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a735) | (~c2_1(a735)) | (~c3_1(a735)) | c0_1(a732) | c2_1(a732) | (~c1_1(a732)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a735) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c3_1(a735)) | (~c2_1(a735))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[2300])).
% 0.85/1.02 tff(2302,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a735) | (~c2_1(a735)) | (~c3_1(a735)) | c0_1(a732) | c2_1(a732) | (~c1_1(a732)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a735) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c3_1(a735)) | (~c2_1(a735)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[2301, 2299])).
% 0.85/1.02 tff(2303,plain,
% 0.85/1.02 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a735) | (~c2_1(a735)) | (~c3_1(a735)) | c0_1(a732) | c2_1(a732) | (~c1_1(a732)))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(2304,plain,
% 0.85/1.02 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a735) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c3_1(a735)) | (~c2_1(a735))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2303, 2302])).
% 0.85/1.02 tff(2305,plain,
% 0.85/1.02 (hskp10 | (~c1_1(a732))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2304, 104, 2285, 2284, 2286, 2290, 2289, 970])).
% 0.85/1.02 tff(2306,plain,
% 0.85/1.02 (hskp10),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2305, 2298])).
% 0.85/1.02 tff(2307,plain,
% 0.85/1.02 (~c2_1(a748)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[983, 2306])).
% 0.85/1.02 tff(2308,plain,
% 0.85/1.02 (~c1_1(a748)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[989, 2306])).
% 0.85/1.02 tff(2309,plain,
% 0.85/1.02 (~c0_1(a748)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[995, 2306])).
% 0.85/1.02 tff(2310,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a741) | c0_1(a748) | c1_1(a748) | c2_1(a748) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a741) | c0_1(a748) | c1_1(a748) | c2_1(a748) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2311,plain,
% 0.85/1.02 (((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a741) | c0_1(a741) | (~c2_1(a741)) | c2_1(a748) | c1_1(a748) | c0_1(a748)) <=> (c3_1(a741) | c0_1(a748) | c1_1(a748) | c2_1(a748) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2312,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a741) | c0_1(a741) | (~c2_1(a741)) | c2_1(a748) | c1_1(a748) | c0_1(a748))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a741) | c0_1(a748) | c1_1(a748) | c2_1(a748) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[2311])).
% 0.85/1.02 tff(2313,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a741) | c0_1(a741) | (~c2_1(a741)) | c2_1(a748) | c1_1(a748) | c0_1(a748))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a741) | c0_1(a748) | c1_1(a748) | c2_1(a748) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[2312, 2310])).
% 0.85/1.02 tff(2314,plain,
% 0.85/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a741) | c0_1(a741) | (~c2_1(a741)) | c2_1(a748) | c1_1(a748) | c0_1(a748))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(2315,plain,
% 0.85/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a741) | c0_1(a748) | c1_1(a748) | c2_1(a748) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2314, 2313])).
% 0.85/1.02 tff(2316,plain,
% 0.85/1.02 ($false),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2315, 104, 744, 802, 801, 2207, 2309, 2308, 2307, 177, 952, 2257])).
% 0.85/1.02 tff(2317,plain,(hskp1 | (~c0_1(a750)) | (~c1_1(a750)) | (~c2_1(a750)) | c3_1(a741) | c0_1(a741) | c1_1(a741) | (~c1_1(a734)) | c0_1(a734) | c3_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.02 tff(2318,plain,
% 0.85/1.02 (hskp1),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2317, 2207, 802, 801, 744, 177, 1017, 1006, 22, 33])).
% 0.85/1.02 tff(2319,plain,
% 0.85/1.02 (~c2_1(a731)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[58, 2318])).
% 0.85/1.02 tff(2320,plain,
% 0.85/1.02 (c3_1(a731)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[66, 2318])).
% 0.85/1.02 tff(2321,plain,
% 0.85/1.02 (c1_1(a731)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[74, 2318])).
% 0.85/1.02 tff(2322,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a741) | c3_1(a741) | c0_1(a741) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a741) | c3_1(a741) | c0_1(a741) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2323,plain,
% 0.85/1.02 (((~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c1_1(a741) | c0_1(a741) | c3_1(a741)) <=> (c1_1(a741) | c3_1(a741) | c0_1(a741) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2324,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c1_1(a741) | c0_1(a741) | c3_1(a741))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a741) | c3_1(a741) | c0_1(a741) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[2323])).
% 0.85/1.02 tff(2325,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c1_1(a741) | c0_1(a741) | c3_1(a741))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a741) | c3_1(a741) | c0_1(a741) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[2324, 2322])).
% 0.85/1.02 tff(2326,plain,
% 0.85/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731)) | c2_1(a731) | (~c1_1(a731)) | (~c0_1(a731)) | c1_1(a741) | c0_1(a741) | c3_1(a741))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(2327,plain,
% 0.85/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a741) | c3_1(a741) | c0_1(a741) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | (~c0_1(a731))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2326, 2325])).
% 0.85/1.02 tff(2328,plain,
% 0.85/1.02 (~c0_1(a731)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2327, 104, 1017, 2207, 2321, 2320, 177, 2319, 10])).
% 0.85/1.02 tff(2329,plain,
% 0.85/1.02 ($false),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[127, 104, 2321, 2320, 2319, 121, 2328])).
% 0.85/1.02 tff(2330,plain,(c3_1(a741) | c1_1(a741) | c0_1(a741) | (~c1_1(a750)) | (~c2_1(a750)) | (~c0_1(a750)) | (~c1_1(a734)) | c0_1(a734) | c3_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.02 tff(2331,plain,
% 0.85/1.02 (c3_1(a741)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2330, 1017, 177, 2206, 2205, 2204, 1005, 22, 33])).
% 0.85/1.02 tff(2332,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a741) | c0_1(a741) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c3_1(a741)) | (~c2_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a741) | c0_1(a741) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c3_1(a741)) | (~c2_1(a734)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2333,plain,
% 0.85/1.02 ((hskp7 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c1_1(a741) | c0_1(a741) | (~c3_1(a741))) <=> (hskp7 | c1_1(a741) | c0_1(a741) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c3_1(a741)) | (~c2_1(a734)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2334,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c1_1(a741) | c0_1(a741) | (~c3_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a741) | c0_1(a741) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c3_1(a741)) | (~c2_1(a734))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[2333])).
% 0.85/1.02 tff(2335,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c1_1(a741) | c0_1(a741) | (~c3_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a741) | c0_1(a741) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c3_1(a741)) | (~c2_1(a734)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[2334, 2332])).
% 0.85/1.02 tff(2336,plain,
% 0.85/1.02 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c1_1(a741) | c0_1(a741) | (~c3_1(a741)))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(2337,plain,
% 0.85/1.02 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a741) | c0_1(a741) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c3_1(a741)) | (~c2_1(a734))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2336, 2335])).
% 0.85/1.02 tff(2338,plain,
% 0.85/1.02 ((~c3_1(a741)) | (~c2_1(a734))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2337, 104, 1018, 1017, 177, 22, 33, 1263])).
% 0.85/1.02 tff(2339,plain,
% 0.85/1.02 (~c2_1(a734)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2338, 2331])).
% 0.85/1.02 tff(2340,plain,
% 0.85/1.02 (hskp5),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[1177, 2339, 33, 1005])).
% 0.85/1.02 tff(2341,plain,
% 0.85/1.02 (~c0_1(a735)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[427, 2340])).
% 0.85/1.02 tff(2342,plain,
% 0.85/1.02 (c3_1(a735)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[413, 2340])).
% 0.85/1.02 tff(2343,plain,
% 0.85/1.02 (c2_1(a735)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[421, 2340])).
% 0.85/1.02 tff(2344,plain,
% 0.85/1.02 (hskp10),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[1191, 104, 2343, 2342, 1005, 2341, 22, 970, 2339])).
% 0.85/1.02 tff(2345,plain,
% 0.85/1.02 (~c2_1(a748)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[983, 2344])).
% 0.85/1.02 tff(2346,plain,
% 0.85/1.02 (~c1_1(a748)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[989, 2344])).
% 0.85/1.02 tff(2347,plain,
% 0.85/1.02 (~c0_1(a748)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[995, 2344])).
% 0.85/1.02 tff(2348,plain,
% 0.85/1.02 (hskp0 | hskp1),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[1301, 104, 1294, 1293, 1295, 236])).
% 0.85/1.02 tff(2349,plain,
% 0.85/1.02 (hskp0),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2348, 255])).
% 0.85/1.02 tff(2350,plain,
% 0.85/1.02 (~c1_1(a730)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[384, 2349])).
% 0.85/1.02 tff(2351,plain,
% 0.85/1.02 (c3_1(a730)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[435, 2349])).
% 0.85/1.02 tff(2352,plain,
% 0.85/1.02 (c0_1(a730)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[443, 2349])).
% 0.85/1.02 tff(2353,plain,
% 0.85/1.02 (c2_1(a741)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2256, 2352, 802, 801, 2248, 1017, 2228, 177, 744, 2229, 255, 2351, 2350])).
% 0.85/1.02 tff(2354,plain,
% 0.85/1.02 (~c2_1(a730)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[509, 2352, 484, 2351, 457, 2350, 485])).
% 0.85/1.02 tff(2355,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a741) | c0_1(a741) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a741) | c0_1(a741) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2356,plain,
% 0.85/1.02 (((~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a741) | (~c2_1(a741)) | (~c3_1(a741)) | c0_1(a741) | (~c3_1(a741)) | (~c2_1(a741))) <=> (c1_1(a741) | c0_1(a741) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2357,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a741) | (~c2_1(a741)) | (~c3_1(a741)) | c0_1(a741) | (~c3_1(a741)) | (~c2_1(a741)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a741) | c0_1(a741) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[2356])).
% 0.85/1.02 tff(2358,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a741) | (~c2_1(a741)) | (~c3_1(a741)) | c0_1(a741) | (~c3_1(a741)) | (~c2_1(a741)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a741) | c0_1(a741) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[2357, 2355])).
% 0.85/1.02 tff(2359,plain,
% 0.85/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a741) | (~c2_1(a741)) | (~c3_1(a741)) | c0_1(a741) | (~c3_1(a741)) | (~c2_1(a741)))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(2360,plain,
% 0.85/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a741) | c0_1(a741) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[2359, 2358])).
% 0.85/1.03 tff(2361,plain,
% 0.85/1.03 ($false),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2360, 104, 1017, 178, 2352, 2351, 177, 455, 2354, 2353])).
% 0.85/1.03 tff(2362,plain,(hskp1 | c1_1(a741) | (~c3_1(a741)) | c0_1(a741) | (~c1_1(a750)) | (~c2_1(a750)) | (~c2_1(a755)) | c3_1(a755) | (~c0_1(a750)) | (~c1_1(a755)) | (~c3_1(a735)) | c0_1(a735) | (~c2_1(a735)) | c0_1(a748) | c1_1(a748) | c2_1(a748)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.03 tff(2363,plain,
% 0.85/1.03 (hskp1),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2362, 1017, 2331, 177, 2206, 2205, 2188, 2180, 2204, 2196, 2342, 2341, 2343, 2347, 2346, 2345])).
% 0.85/1.03 tff(2364,plain,
% 0.85/1.03 (~c2_1(a731)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[58, 2363])).
% 0.85/1.03 tff(2365,plain,
% 0.85/1.03 (c3_1(a731)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[66, 2363])).
% 0.85/1.03 tff(2366,plain,
% 0.85/1.03 (c1_1(a731)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[74, 2363])).
% 0.85/1.03 tff(2367,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a734) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | c2_1(a734) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a734) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | c2_1(a734) | (~c1_1(a734)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(2368,plain,
% 0.85/1.03 ((hskp11 | (~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a734) | c2_1(a734) | (~c1_1(a734))) <=> (hskp11 | c0_1(a734) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | c2_1(a734) | (~c1_1(a734)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(2369,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a734) | c2_1(a734) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a734) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | c2_1(a734) | (~c1_1(a734))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[2368])).
% 0.85/1.03 tff(2370,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a734) | c2_1(a734) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a734) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | c2_1(a734) | (~c1_1(a734)))),
% 0.85/1.03 inference(transitivity,[status(thm)],[2369, 2367])).
% 0.85/1.03 tff(2371,plain,
% 0.85/1.03 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a734) | c2_1(a734) | (~c1_1(a734)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(2372,plain,
% 0.85/1.03 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a734) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | c2_1(a734) | (~c1_1(a734))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[2371, 2370])).
% 0.85/1.03 tff(2373,plain,
% 0.85/1.03 ($false),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2372, 104, 21, 1005, 2366, 2365, 22, 2364, 43, 2339])).
% 0.85/1.03 tff(2374,plain,(c1_1(a741) | hskp11 | c0_1(a734) | c0_1(a741) | c3_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.03 tff(2375,plain,
% 0.85/1.03 (c1_1(a741)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2374, 177, 22, 21, 33])).
% 0.85/1.03 tff(2376,plain,
% 0.85/1.03 (c3_1(a730)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[435, 1015])).
% 0.85/1.03 tff(2377,plain,
% 0.85/1.03 (c0_1(a730)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[443, 1015])).
% 0.85/1.03 tff(2378,plain,
% 0.85/1.03 (~hskp7),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[157, 2207])).
% 0.85/1.03 tff(2379,plain,
% 0.85/1.03 (hskp12),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2173, 2378, 33])).
% 0.85/1.03 tff(2380,plain,
% 0.85/1.03 (c2_1(a755)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2187, 2379])).
% 0.85/1.03 tff(2381,plain,
% 0.85/1.03 (~c3_1(a755)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2179, 2379])).
% 0.85/1.03 tff(2382,plain,
% 0.85/1.03 (c1_1(a755)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2195, 2379])).
% 0.85/1.03 tff(2383,plain,
% 0.85/1.03 (hskp27),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2202, 104, 21, 2382, 2380, 2381, 559])).
% 0.85/1.03 tff(2384,plain,
% 0.85/1.03 (c2_1(a750)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[724, 2383])).
% 0.85/1.03 tff(2385,plain,
% 0.85/1.03 (c1_1(a750)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[732, 2383])).
% 0.85/1.03 tff(2386,plain,
% 0.85/1.03 (c0_1(a750)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[716, 2383])).
% 0.85/1.03 tff(2387,assumption,(hskp10), introduced(assumption)).
% 0.85/1.03 tff(2388,plain,
% 0.85/1.03 (~c2_1(a748)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[983, 2387])).
% 0.85/1.03 tff(2389,plain,
% 0.85/1.03 (~c1_1(a748)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[989, 2387])).
% 0.85/1.03 tff(2390,plain,
% 0.85/1.03 (~c0_1(a748)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[995, 2387])).
% 0.85/1.03 tff(2391,plain,
% 0.85/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a755) | c0_1(a748) | c1_1(a748) | c2_1(a748) | (~ndr1_0) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a755)) | c0_1(a755))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a755) | c0_1(a748) | c1_1(a748) | c2_1(a748) | (~ndr1_0) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a755)) | c0_1(a755))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(2392,plain,
% 0.85/1.03 (((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a755) | c0_1(a755) | (~c2_1(a755)) | c2_1(a748) | c1_1(a748) | c0_1(a748)) <=> (c3_1(a755) | c0_1(a748) | c1_1(a748) | c2_1(a748) | (~ndr1_0) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a755)) | c0_1(a755))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(2393,plain,
% 0.85/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a755) | c0_1(a755) | (~c2_1(a755)) | c2_1(a748) | c1_1(a748) | c0_1(a748))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a755) | c0_1(a748) | c1_1(a748) | c2_1(a748) | (~ndr1_0) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a755)) | c0_1(a755)))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[2392])).
% 0.85/1.03 tff(2394,plain,
% 0.85/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a755) | c0_1(a755) | (~c2_1(a755)) | c2_1(a748) | c1_1(a748) | c0_1(a748))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a755) | c0_1(a748) | c1_1(a748) | c2_1(a748) | (~ndr1_0) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a755)) | c0_1(a755))),
% 0.85/1.03 inference(transitivity,[status(thm)],[2393, 2391])).
% 0.85/1.03 tff(2395,plain,
% 0.85/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a755) | c0_1(a755) | (~c2_1(a755)) | c2_1(a748) | c1_1(a748) | c0_1(a748))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(2396,plain,
% 0.85/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a755) | c0_1(a748) | c1_1(a748) | c2_1(a748) | (~ndr1_0) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | (~c2_1(a755)) | c0_1(a755)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[2395, 2394])).
% 0.85/1.03 tff(2397,plain,
% 0.85/1.03 (c0_1(a755)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2396, 104, 744, 802, 801, 2248, 2228, 2390, 2389, 2388, 952])).
% 0.85/1.03 tff(2398,plain,
% 0.85/1.03 (hskp25),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1204, 104, 469, 468, 2390, 2389, 2388, 456, 20])).
% 0.85/1.03 tff(2399,plain,
% 0.85/1.03 (c3_1(a729)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[762, 2398])).
% 0.85/1.03 tff(2400,plain,
% 0.85/1.03 (c2_1(a729)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[770, 2398])).
% 0.85/1.03 tff(2401,plain,
% 0.85/1.03 (c0_1(a729)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[778, 2398])).
% 0.85/1.03 tff(2402,plain,
% 0.85/1.03 ($false),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2246, 104, 255, 2401, 2400, 2399, 2229, 2228, 743, 2397])).
% 0.85/1.03 tff(2403,plain,((~hskp10) | hskp1 | (~c1_1(a755)) | c3_1(a755) | (~c0_1(a730)) | (~c3_1(a730)) | c1_1(a730) | (~c0_1(a750)) | (~c1_1(a750)) | (~c2_1(a750)) | (~c2_1(a755))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.03 tff(2404,plain,
% 0.85/1.03 (~hskp10),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2403, 2382, 255, 2381, 469, 468, 456, 2386, 2385, 2384, 2380])).
% 0.85/1.03 tff(2405,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c3_1(a741) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c3_1(a741) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(2406,plain,
% 0.85/1.03 ((hskp5 | (~ndr1_0) | c0_1(a741) | c3_1(a741) | (~c1_1(a741)) | c0_1(a741) | c2_1(a741) | (~c1_1(a741))) <=> (hskp5 | c3_1(a741) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(2407,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a741) | c3_1(a741) | (~c1_1(a741)) | c0_1(a741) | c2_1(a741) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c3_1(a741) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[2406])).
% 0.85/1.03 tff(2408,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a741) | c3_1(a741) | (~c1_1(a741)) | c0_1(a741) | c2_1(a741) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c3_1(a741) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)))),
% 0.85/1.03 inference(transitivity,[status(thm)],[2407, 2405])).
% 0.85/1.03 tff(2409,plain,
% 0.85/1.03 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a741) | c3_1(a741) | (~c1_1(a741)) | c0_1(a741) | c2_1(a741) | (~c1_1(a741)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(2410,plain,
% 0.85/1.03 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c3_1(a741) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[2409, 2408])).
% 0.85/1.03 tff(2411,plain,
% 0.85/1.03 (hskp5 | c3_1(a741) | c2_1(a741) | (~c1_1(a741))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2410, 104, 177, 1170])).
% 0.85/1.03 tff(2412,plain,
% 0.85/1.03 (c2_1(a741)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2411, 396, 207, 2207])).
% 0.85/1.03 tff(2413,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(2414,plain,
% 0.85/1.03 ((hskp16 | (~ndr1_0) | (~c2_1(a750)) | (~c3_1(a750)) | (~c0_1(a750)) | c0_1(a741) | (~c2_1(a741)) | (~c1_1(a741))) <=> (hskp16 | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(2415,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a750)) | (~c3_1(a750)) | (~c0_1(a750)) | c0_1(a741) | (~c2_1(a741)) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[2414])).
% 0.85/1.03 tff(2416,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a750)) | (~c3_1(a750)) | (~c0_1(a750)) | c0_1(a741) | (~c2_1(a741)) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)))),
% 0.85/1.03 inference(transitivity,[status(thm)],[2415, 2413])).
% 0.85/1.03 tff(2417,plain,
% 0.85/1.03 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a750)) | (~c3_1(a750)) | (~c0_1(a750)) | c0_1(a741) | (~c2_1(a741)) | (~c1_1(a741)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(2418,plain,
% 0.85/1.03 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[2417, 2416])).
% 0.85/1.03 tff(2419,plain,
% 0.85/1.03 (hskp16 | (~c3_1(a750))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2418, 104, 744, 801, 207, 177, 754, 561])).
% 0.85/1.03 tff(2420,plain,
% 0.85/1.03 (hskp16),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2419, 1587])).
% 0.85/1.03 tff(2421,plain,
% 0.85/1.03 (~c3_1(a764)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[791, 2420])).
% 0.85/1.03 tff(2422,plain,
% 0.85/1.03 (c0_1(a764)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[809, 2420])).
% 0.85/1.03 tff(2423,plain,
% 0.85/1.03 (~c1_1(a764)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1603, 104, 255, 744, 801, 2422, 2421, 743, 1587])).
% 0.85/1.03 tff(2424,plain,
% 0.85/1.03 (~c1_1(a744)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[693, 1283])).
% 0.85/1.03 tff(2425,plain,
% 0.85/1.03 (~c0_1(a744)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[672, 1283])).
% 0.85/1.03 tff(2426,plain,
% 0.85/1.03 ((hskp0 | hskp19 | hskp5) <=> (hskp0 | hskp19 | hskp5)),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(2427,plain,
% 0.85/1.03 (((hskp0 | hskp5) | hskp19) <=> (hskp0 | hskp19 | hskp5)),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(2428,axiom,((hskp0 | hskp5) | hskp19), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 0.85/1.03 tff(2429,plain,
% 0.85/1.03 (hskp0 | hskp19 | hskp5),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[2428, 2427])).
% 0.85/1.03 tff(2430,plain,
% 0.85/1.03 (hskp0 | hskp19 | hskp5),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[2429, 2426])).
% 0.85/1.03 tff(2431,plain,
% 0.85/1.03 (hskp19),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2430, 217, 396])).
% 0.85/1.03 tff(2432,plain,
% 0.85/1.03 (~c0_1(a777)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[651, 2431])).
% 0.85/1.03 tff(2433,plain,
% 0.85/1.03 (c2_1(a777)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[659, 2431])).
% 0.85/1.03 tff(2434,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a777) | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c3_1(a744)) | (~c2_1(a777)) | (~c1_1(a777)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a777) | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c3_1(a744)) | (~c2_1(a777)) | (~c1_1(a777)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(2435,plain,
% 0.85/1.03 ((hskp5 | (~ndr1_0) | c0_1(a777) | (~c2_1(a777)) | (~c1_1(a777)) | c1_1(a744) | c0_1(a744) | (~c3_1(a744))) <=> (hskp5 | c0_1(a777) | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c3_1(a744)) | (~c2_1(a777)) | (~c1_1(a777)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(2436,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a777) | (~c2_1(a777)) | (~c1_1(a777)) | c1_1(a744) | c0_1(a744) | (~c3_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a777) | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c3_1(a744)) | (~c2_1(a777)) | (~c1_1(a777))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[2435])).
% 0.85/1.03 tff(2437,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a777) | (~c2_1(a777)) | (~c1_1(a777)) | c1_1(a744) | c0_1(a744) | (~c3_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a777) | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c3_1(a744)) | (~c2_1(a777)) | (~c1_1(a777)))),
% 0.85/1.03 inference(transitivity,[status(thm)],[2436, 2434])).
% 0.85/1.03 tff(2438,plain,
% 0.85/1.03 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a777) | (~c2_1(a777)) | (~c1_1(a777)) | c1_1(a744) | c0_1(a744) | (~c3_1(a744)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(2439,plain,
% 0.85/1.03 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a777) | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c3_1(a744)) | (~c2_1(a777)) | (~c1_1(a777))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[2438, 2437])).
% 0.85/1.03 tff(2440,plain,
% 0.85/1.03 (~c1_1(a777)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2439, 104, 396, 2433, 1290, 2432, 2425, 2424, 1805])).
% 0.85/1.03 tff(2441,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a744) | c1_1(a744) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a744) | c1_1(a744) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a744)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(2442,plain,
% 0.85/1.03 ((hskp5 | (~ndr1_0) | c0_1(a741) | (~c2_1(a741)) | (~c1_1(a741)) | c1_1(a744) | c0_1(a744) | (~c3_1(a744))) <=> (hskp5 | c0_1(a744) | c1_1(a744) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a744)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(2443,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a741) | (~c2_1(a741)) | (~c1_1(a741)) | c1_1(a744) | c0_1(a744) | (~c3_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a744) | c1_1(a744) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a744))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[2442])).
% 0.85/1.03 tff(2444,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a741) | (~c2_1(a741)) | (~c1_1(a741)) | c1_1(a744) | c0_1(a744) | (~c3_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a744) | c1_1(a744) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a744)))),
% 0.85/1.03 inference(transitivity,[status(thm)],[2443, 2441])).
% 0.85/1.03 tff(2445,plain,
% 0.85/1.03 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a741) | (~c2_1(a741)) | (~c1_1(a741)) | c1_1(a744) | c0_1(a744) | (~c3_1(a744)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(2446,plain,
% 0.85/1.03 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a744) | c1_1(a744) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a744))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[2445, 2444])).
% 0.85/1.03 tff(2447,plain,
% 0.85/1.03 (~c2_1(a741)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2446, 104, 396, 1290, 207, 2425, 2424, 177, 1805])).
% 0.85/1.03 tff(2448,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | c0_1(a777) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | c1_1(a777) | (~c2_1(a777)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a777) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | c1_1(a777) | (~c2_1(a777)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(2449,plain,
% 0.85/1.03 ((hskp0 | (~ndr1_0) | c2_1(a741) | c0_1(a741) | (~c1_1(a741)) | c1_1(a777) | c0_1(a777) | (~c2_1(a777))) <=> (hskp0 | c0_1(a777) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | c1_1(a777) | (~c2_1(a777)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(2450,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a741) | c0_1(a741) | (~c1_1(a741)) | c1_1(a777) | c0_1(a777) | (~c2_1(a777)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | c0_1(a777) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | c1_1(a777) | (~c2_1(a777))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[2449])).
% 0.85/1.03 tff(2451,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a741) | c0_1(a741) | (~c1_1(a741)) | c1_1(a777) | c0_1(a777) | (~c2_1(a777)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a777) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | c1_1(a777) | (~c2_1(a777)))),
% 0.85/1.03 inference(transitivity,[status(thm)],[2450, 2448])).
% 0.85/1.03 tff(2452,plain,
% 0.85/1.03 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a741) | c0_1(a741) | (~c1_1(a741)) | c1_1(a777) | c0_1(a777) | (~c2_1(a777)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(2453,plain,
% 0.85/1.03 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a777) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | c1_1(a777) | (~c2_1(a777))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[2452, 2451])).
% 0.85/1.03 tff(2454,plain,
% 0.85/1.03 ($false),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2453, 217, 104, 2433, 207, 2432, 177, 254, 2447, 2440])).
% 0.85/1.03 tff(2455,plain,(hskp0 | (~c1_1(a741)) | c0_1(a741) | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.85/1.03 tff(2456,plain,
% 0.85/1.03 (hskp0),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2455, 396, 177, 207])).
% 0.85/1.03 tff(2457,plain,
% 0.85/1.03 (~c1_1(a730)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[384, 2456])).
% 0.85/1.03 tff(2458,plain,
% 0.85/1.03 (c3_1(a730)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[435, 2456])).
% 0.85/1.03 tff(2459,plain,
% 0.85/1.03 (c0_1(a730)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[443, 2456])).
% 0.85/1.03 tff(2460,plain,
% 0.85/1.03 (c2_1(a764)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[799, 2420])).
% 0.85/1.03 tff(2461,plain,
% 0.85/1.03 ($false),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1611, 104, 396, 2460, 2459, 2458, 2421, 2457, 1456, 2423])).
% 0.85/1.03 tff(2462,plain,((~c3_1(a750)) | hskp5 | hskp1 | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a741)) | c0_1(a741) | (~c2_1(a741))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.03 tff(2463,plain,
% 0.85/1.03 (~c3_1(a750)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2462, 396, 255, 2412, 801, 207, 177, 744])).
% 0.85/1.03 tff(2464,plain,
% 0.85/1.03 (hskp18 | c3_1(a750)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1622, 104, 21, 744, 802, 1075])).
% 0.85/1.03 tff(2465,plain,
% 0.85/1.03 (hskp18),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2464, 2463])).
% 0.85/1.03 tff(2466,plain,
% 0.85/1.03 (~c3_1(a775)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1630, 2465])).
% 0.85/1.03 tff(2467,plain,
% 0.85/1.03 (~c2_1(a775)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1636, 2465])).
% 0.85/1.03 tff(2468,plain,
% 0.85/1.03 (c1_1(a775)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1829, 2465])).
% 0.85/1.03 tff(2469,assumption,(~c3_1(a775)), introduced(assumption)).
% 0.85/1.03 tff(2470,assumption,(~c2_1(a775)), introduced(assumption)).
% 0.85/1.03 tff(2471,plain,
% 0.85/1.03 (hskp9 | c0_1(a775)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2127, 104, 396, 2470, 2469, 1085])).
% 0.85/1.03 tff(2472,plain,
% 0.85/1.03 (c0_1(a775)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2471, 1655])).
% 0.85/1.03 tff(2473,assumption,(c1_1(a775)), introduced(assumption)).
% 0.85/1.03 tff(2474,plain,
% 0.85/1.03 (hskp25 | hskp9 | (~c0_1(a775))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1662, 104, 2470, 2469, 1654])).
% 0.85/1.03 tff(2475,plain,
% 0.85/1.03 (hskp25),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2474, 2472, 1655])).
% 0.85/1.03 tff(2476,plain,
% 0.85/1.03 (c3_1(a729)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[762, 2475])).
% 0.85/1.03 tff(2477,plain,
% 0.85/1.03 (c2_1(a729)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[770, 2475])).
% 0.85/1.03 tff(2478,plain,
% 0.85/1.03 (c0_1(a729)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[778, 2475])).
% 0.85/1.03 tff(2479,plain,
% 0.85/1.03 ($false),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1840, 104, 255, 2478, 2477, 2476, 2473, 2469, 743, 2472])).
% 0.85/1.03 tff(2480,plain,(hskp9 | hskp1 | (~c1_1(a775)) | c3_1(a775) | c2_1(a775) | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.85/1.03 tff(2481,plain,
% 0.85/1.03 (hskp9),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2480, 2468, 396, 255, 2467, 2466])).
% 0.85/1.03 tff(2482,plain,
% 0.85/1.03 (~c2_1(a746)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[328, 2481])).
% 0.85/1.03 tff(2483,plain,
% 0.85/1.03 (~c0_1(a746)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[334, 2481])).
% 0.85/1.03 tff(2484,plain,
% 0.85/1.03 (c3_1(a746)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[342, 2481])).
% 0.85/1.03 tff(2485,plain,
% 0.85/1.03 (~c1_1(a746)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[349, 104, 2484, 2483, 2482, 121])).
% 0.85/1.03 tff(2486,plain,
% 0.85/1.03 ($false),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2221, 104, 744, 802, 801, 2207, 2483, 2482, 177, 952, 2412, 2485])).
% 0.85/1.03 tff(2487,plain,(hskp5 | (~c0_1(a750)) | (~c1_1(a750)) | (~c2_1(a750)) | c3_1(a741) | c0_1(a741) | hskp1 | hskp11 | (~c1_1(a741))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.03 tff(2488,plain,
% 0.85/1.03 (hskp5),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2487, 2386, 2385, 2384, 2207, 177, 255, 21, 207])).
% 0.85/1.03 tff(2489,plain,
% 0.85/1.03 (~c0_1(a735)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[427, 2488])).
% 0.85/1.03 tff(2490,plain,
% 0.85/1.03 (c3_1(a735)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[413, 2488])).
% 0.85/1.03 tff(2491,plain,
% 0.85/1.03 (c2_1(a735)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[421, 2488])).
% 0.85/1.03 tff(2492,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a741) | c0_1(a735) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a735)) | (~c2_1(a735)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a741) | c0_1(a735) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a735)) | (~c2_1(a735)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(2493,plain,
% 0.85/1.03 ((hskp10 | (~ndr1_0) | c0_1(a735) | (~c2_1(a735)) | (~c3_1(a735)) | c0_1(a741) | c2_1(a741) | (~c1_1(a741))) <=> (hskp10 | c0_1(a741) | c0_1(a735) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a735)) | (~c2_1(a735)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(2494,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a735) | (~c2_1(a735)) | (~c3_1(a735)) | c0_1(a741) | c2_1(a741) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a741) | c0_1(a735) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a735)) | (~c2_1(a735))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[2493])).
% 0.85/1.03 tff(2495,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a735) | (~c2_1(a735)) | (~c3_1(a735)) | c0_1(a741) | c2_1(a741) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a741) | c0_1(a735) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a735)) | (~c2_1(a735)))),
% 0.85/1.03 inference(transitivity,[status(thm)],[2494, 2492])).
% 0.85/1.03 tff(2496,plain,
% 0.85/1.03 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a735) | (~c2_1(a735)) | (~c3_1(a735)) | c0_1(a741) | c2_1(a741) | (~c1_1(a741)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(2497,plain,
% 0.85/1.03 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a741) | c0_1(a735) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a735)) | (~c2_1(a735))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[2496, 2495])).
% 0.85/1.03 tff(2498,plain,
% 0.85/1.03 (hskp10 | c2_1(a741)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2497, 104, 207, 2491, 2490, 177, 2489, 970])).
% 0.85/1.03 tff(2499,plain,
% 0.85/1.03 (c2_1(a741)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2498, 2404])).
% 0.85/1.03 tff(2500,plain,
% 0.85/1.03 (~c2_1(a730)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[509, 2490, 469, 468, 2489, 456, 2491])).
% 0.85/1.03 tff(2501,plain,
% 0.85/1.03 (hskp2),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[540, 2500, 469, 2489, 456, 2491, 255, 2490])).
% 0.85/1.03 tff(2502,plain,
% 0.85/1.03 (~c2_1(a732)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[282, 2501])).
% 0.85/1.03 tff(2503,plain,
% 0.85/1.03 (~c0_1(a732)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[288, 2501])).
% 0.85/1.03 tff(2504,plain,
% 0.85/1.03 (hskp10 | (~c1_1(a732))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2304, 104, 2491, 2490, 2489, 2503, 2502, 970])).
% 0.85/1.03 tff(2505,plain,
% 0.85/1.03 (~c1_1(a732)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2504, 2404])).
% 0.85/1.03 tff(2506,plain,
% 0.85/1.03 ((~c2_1(a741)) | c1_1(a732)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2296, 104, 2386, 2385, 2384, 2207, 177, 2503, 2502, 952])).
% 0.85/1.03 tff(2507,plain,
% 0.85/1.03 ($false),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2506, 2505, 2499])).
% 0.85/1.03 tff(2508,plain,(c3_1(a741) | c0_1(a741) | (~c1_1(a741)) | hskp1 | (~c0_1(a730)) | (~c3_1(a730)) | c1_1(a730) | hskp11 | c3_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.03 tff(2509,plain,
% 0.85/1.03 (c3_1(a741)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2508, 255, 2375, 177, 2377, 2376, 1016, 21, 33])).
% 0.85/1.03 tff(2510,plain,
% 0.85/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a741)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a741)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(2511,plain,
% 0.85/1.03 (((~ndr1_0) | c2_1(a741) | (~c3_1(a741)) | (~c1_1(a741)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741)) | c2_1(a741) | c0_1(a741) | (~c3_1(a741))) <=> (c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a741)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(2512,plain,
% 0.85/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a741) | (~c3_1(a741)) | (~c1_1(a741)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741)) | c2_1(a741) | c0_1(a741) | (~c3_1(a741)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a741))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[2511])).
% 0.85/1.03 tff(2513,plain,
% 0.85/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a741) | (~c3_1(a741)) | (~c1_1(a741)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741)) | c2_1(a741) | c0_1(a741) | (~c3_1(a741)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a741)))),
% 0.85/1.04 inference(transitivity,[status(thm)],[2512, 2510])).
% 0.85/1.04 tff(2514,plain,
% 0.85/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a741) | (~c3_1(a741)) | (~c1_1(a741)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741)) | c2_1(a741) | c0_1(a741) | (~c3_1(a741)))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(2515,plain,
% 0.85/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a741))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[2514, 2513])).
% 0.85/1.04 tff(2516,plain,
% 0.85/1.04 ($false),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[2515, 104, 207, 178, 177, 121, 165])).
% 0.85/1.04 tff(2517,plain,(c2_1(a741) | (~c1_1(a741)) | (~c3_1(a741)) | c0_1(a741)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.04 tff(2518,plain,
% 0.85/1.04 (c2_1(a741)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[2517, 2509, 2375, 177])).
% 0.85/1.04 tff(2519,plain,
% 0.85/1.04 (c1_1(a734)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[405, 22, 396, 33])).
% 0.85/1.04 tff(2520,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a741) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a741) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c1_1(a734)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(2521,plain,
% 0.85/1.04 ((hskp5 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c1_1(a734)) | c0_1(a741) | c2_1(a741) | (~c1_1(a741))) <=> (hskp5 | c0_1(a741) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c1_1(a734)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(2522,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c1_1(a734)) | c0_1(a741) | c2_1(a741) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a741) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c1_1(a734))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[2521])).
% 0.85/1.04 tff(2523,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c1_1(a734)) | c0_1(a741) | c2_1(a741) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a741) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c1_1(a734)))),
% 0.85/1.04 inference(transitivity,[status(thm)],[2522, 2520])).
% 0.85/1.04 tff(2524,plain,
% 0.85/1.04 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c1_1(a734)) | c0_1(a741) | c2_1(a741) | (~c1_1(a741)))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(2525,plain,
% 0.85/1.04 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a741) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c1_1(a734))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[2524, 2523])).
% 0.85/1.04 tff(2526,plain,
% 0.85/1.04 (c2_1(a741) | (~c1_1(a734))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[2525, 104, 396, 207, 177, 22, 33, 1170])).
% 0.85/1.04 tff(2527,plain,
% 0.85/1.04 (c2_1(a741)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[2526, 2519])).
% 0.85/1.04 tff(2528,plain,
% 0.85/1.04 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.85/1.04 inference(bind,[status(th)],[])).
% 0.85/1.04 tff(2529,plain,
% 0.85/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.85/1.04 inference(quant_intro,[status(thm)],[2528])).
% 0.85/1.04 tff(2530,plain,
% 0.85/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(2531,plain,
% 0.85/1.04 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.85/1.04 inference(bind,[status(th)],[])).
% 0.85/1.04 tff(2532,plain,
% 0.85/1.04 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.85/1.04 inference(quant_intro,[status(thm)],[2531])).
% 0.85/1.04 tff(2533,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 0.85/1.04 tff(2534,plain,
% 0.85/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[2533, 2532])).
% 0.85/1.04 tff(2535,plain,
% 0.85/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[2534, 2530])).
% 0.85/1.04 tff(2536,plain,(
% 0.85/1.04 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.85/1.04 inference(skolemize,[status(sab)],[2535])).
% 0.85/1.04 tff(2537,plain,
% 0.85/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[2536, 2529])).
% 0.85/1.04 tff(2538,plain,
% 0.85/1.04 (c2_1(a734) | (~c1_1(a734))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1176, 104, 396, 22, 33, 1170])).
% 0.85/1.04 tff(2539,plain,
% 0.85/1.04 (c2_1(a734)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[2538, 2519])).
% 0.85/1.04 tff(2540,plain,
% 0.85/1.04 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.85/1.04 inference(bind,[status(th)],[])).
% 0.85/1.04 tff(2541,plain,
% 0.85/1.04 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.85/1.04 inference(quant_intro,[status(thm)],[2540])).
% 0.85/1.04 tff(2542,plain,
% 0.85/1.04 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(2543,plain,
% 0.85/1.04 (^[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))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_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))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_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))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.85/1.04 inference(bind,[status(th)],[])).
% 0.85/1.04 tff(2544,plain,
% 0.85/1.04 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.85/1.04 inference(quant_intro,[status(thm)],[2543])).
% 0.85/1.04 tff(2545,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 0.85/1.04 tff(2546,plain,
% 0.85/1.04 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[2545, 2544])).
% 0.85/1.04 tff(2547,plain,
% 0.85/1.04 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[2546, 2542])).
% 0.85/1.04 tff(2548,plain,(
% 0.85/1.04 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.85/1.04 inference(skolemize,[status(sab)],[2547])).
% 0.85/1.04 tff(2549,plain,
% 0.85/1.04 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[2548, 2541])).
% 0.85/1.04 tff(2550,plain,
% 0.85/1.04 (hskp27),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1583, 21, 2519, 2539])).
% 0.85/1.04 tff(2551,plain,
% 0.85/1.04 (c2_1(a750)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[724, 2550])).
% 0.85/1.04 tff(2552,plain,
% 0.85/1.04 (c0_1(a750)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[716, 2550])).
% 0.85/1.04 tff(2553,plain,
% 0.85/1.04 (~c3_1(a750)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[2462, 2552, 255, 396, 2551, 207, 177, 2527])).
% 0.85/1.04 tff(2554,plain,
% 0.85/1.04 (c1_1(a750)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[732, 2550])).
% 0.85/1.04 tff(2555,plain,
% 0.85/1.04 (hskp18 | c3_1(a750)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1622, 104, 21, 2552, 2554, 1075])).
% 0.85/1.04 tff(2556,plain,
% 0.85/1.04 (hskp18),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[2555, 2553])).
% 0.85/1.04 tff(2557,plain,
% 0.85/1.04 (~c3_1(a775)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1630, 2556])).
% 0.85/1.04 tff(2558,plain,
% 0.85/1.04 (~c2_1(a775)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1636, 2556])).
% 0.85/1.04 tff(2559,plain,
% 0.85/1.04 (c1_1(a775)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1829, 2556])).
% 0.85/1.04 tff(2560,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a775) | c3_1(a775) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a775)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a775) | c3_1(a775) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a775)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(2561,plain,
% 0.85/1.04 ((hskp14 | (~ndr1_0) | c2_1(a775) | c3_1(a775) | (~c1_1(a775)) | c3_1(a734) | c0_1(a734) | (~c2_1(a734))) <=> (hskp14 | c2_1(a775) | c3_1(a775) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a775)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(2562,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a775) | c3_1(a775) | (~c1_1(a775)) | c3_1(a734) | c0_1(a734) | (~c2_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a775) | c3_1(a775) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a775))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[2561])).
% 0.85/1.04 tff(2563,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a775) | c3_1(a775) | (~c1_1(a775)) | c3_1(a734) | c0_1(a734) | (~c2_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a775) | c3_1(a775) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a775)))),
% 0.85/1.04 inference(transitivity,[status(thm)],[2562, 2560])).
% 0.85/1.04 tff(2564,plain,
% 0.85/1.04 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a775) | c3_1(a775) | (~c1_1(a775)) | c3_1(a734) | c0_1(a734) | (~c2_1(a734)))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(2565,plain,
% 0.85/1.04 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a775) | c3_1(a775) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a775))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[2564, 2563])).
% 0.85/1.04 tff(2566,plain,
% 0.85/1.04 (hskp14),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[2565, 104, 2559, 2558, 2557, 22, 33, 2549, 2539])).
% 0.85/1.04 tff(2567,plain,
% 0.85/1.04 (((~hskp14) | (~c2_1(a762))) <=> ((~hskp14) | (~c2_1(a762)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(2568,plain,
% 0.85/1.04 (((~c2_1(a762)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a762)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(2569,axiom,((~c2_1(a762)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 0.85/1.04 tff(2570,plain,
% 0.85/1.04 ((~hskp14) | (~c2_1(a762))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[2569, 2568])).
% 0.85/1.04 tff(2571,plain,
% 0.85/1.04 ((~hskp14) | (~c2_1(a762))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[2570, 2567])).
% 0.85/1.04 tff(2572,plain,
% 0.85/1.04 (~c2_1(a762)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[2571, 2566])).
% 0.85/1.04 tff(2573,plain,
% 0.85/1.04 (((~hskp14) | (~c1_1(a762))) <=> ((~hskp14) | (~c1_1(a762)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(2574,plain,
% 0.85/1.04 (((~c1_1(a762)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a762)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(2575,axiom,((~c1_1(a762)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 0.85/1.04 tff(2576,plain,
% 0.85/1.04 ((~hskp14) | (~c1_1(a762))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[2575, 2574])).
% 0.85/1.04 tff(2577,plain,
% 0.85/1.04 ((~hskp14) | (~c1_1(a762))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[2576, 2573])).
% 0.85/1.04 tff(2578,plain,
% 0.85/1.04 (~c1_1(a762)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[2577, 2566])).
% 0.85/1.04 tff(2579,plain,
% 0.85/1.04 (((~hskp14) | c0_1(a762)) <=> ((~hskp14) | c0_1(a762))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(2580,axiom,((~hskp14) | c0_1(a762)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 0.85/1.04 tff(2581,plain,
% 0.85/1.04 ((~hskp14) | c0_1(a762)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[2580, 2579])).
% 0.85/1.04 tff(2582,plain,
% 0.85/1.04 ((~hskp14) | c0_1(a762)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[2581, 2579])).
% 0.85/1.04 tff(2583,plain,
% 0.85/1.04 ((~hskp14) | c0_1(a762)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[2582, 2579])).
% 0.85/1.04 tff(2584,plain,
% 0.85/1.04 ((~hskp14) | c0_1(a762)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[2583, 2579])).
% 0.85/1.04 tff(2585,plain,
% 0.85/1.04 ((~hskp14) | c0_1(a762)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[2584, 2579])).
% 0.85/1.04 tff(2586,plain,
% 0.85/1.04 (c0_1(a762)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[2585, 2566])).
% 0.85/1.04 tff(2587,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c1_1(a762) | c2_1(a762) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c0_1(a762)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c1_1(a762) | c2_1(a762) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c0_1(a762)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(2588,plain,
% 0.85/1.04 ((hskp2 | (~ndr1_0) | c2_1(a762) | c1_1(a762) | (~c0_1(a762)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741))) <=> (hskp2 | c1_1(a762) | c2_1(a762) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c0_1(a762)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(2589,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a762) | c1_1(a762) | (~c0_1(a762)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c1_1(a762) | c2_1(a762) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c0_1(a762))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[2588])).
% 0.85/1.04 tff(2590,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a762) | c1_1(a762) | (~c0_1(a762)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c1_1(a762) | c2_1(a762) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c0_1(a762)))),
% 0.85/1.04 inference(transitivity,[status(thm)],[2589, 2587])).
% 0.85/1.04 tff(2591,plain,
% 0.85/1.04 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a762) | c1_1(a762) | (~c0_1(a762)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741)))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(2592,plain,
% 0.85/1.04 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c1_1(a762) | c2_1(a762) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c0_1(a762))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[2591, 2590])).
% 0.85/1.04 tff(2593,plain,
% 0.85/1.04 (hskp2),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[2592, 104, 2586, 207, 178, 2578, 2572, 177, 530])).
% 0.85/1.04 tff(2594,plain,
% 0.85/1.04 (~c2_1(a732)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[282, 2593])).
% 0.85/1.04 tff(2595,plain,
% 0.85/1.04 (~c0_1(a732)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[288, 2593])).
% 0.85/1.04 tff(2596,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a734) | c3_1(a734) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a734) | c3_1(a734) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c1_1(a734)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(2597,plain,
% 0.85/1.04 ((hskp5 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c1_1(a734)) | c0_1(a732) | c2_1(a732) | (~c1_1(a732))) <=> (hskp5 | c0_1(a734) | c3_1(a734) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c1_1(a734)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(2598,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c1_1(a734)) | c0_1(a732) | c2_1(a732) | (~c1_1(a732)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a734) | c3_1(a734) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c1_1(a734))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[2597])).
% 0.85/1.04 tff(2599,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c1_1(a734)) | c0_1(a732) | c2_1(a732) | (~c1_1(a732)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a734) | c3_1(a734) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c1_1(a734)))),
% 0.85/1.04 inference(transitivity,[status(thm)],[2598, 2596])).
% 0.85/1.04 tff(2600,plain,
% 0.85/1.04 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c1_1(a734)) | c0_1(a732) | c2_1(a732) | (~c1_1(a732)))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(2601,plain,
% 0.85/1.04 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a734) | c3_1(a734) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c1_1(a734))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[2600, 2599])).
% 0.85/1.04 tff(2602,plain,
% 0.85/1.04 (~c1_1(a732)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[2601, 104, 396, 2519, 22, 33, 2595, 2594, 1170])).
% 0.85/1.04 tff(2603,plain,
% 0.85/1.04 ($false),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[958, 104, 2552, 2554, 2551, 22, 33, 2595, 2594, 952, 2539, 2602])).
% 0.85/1.04 tff(2604,plain,(hskp11 | c0_1(a734) | c3_1(a734) | hskp5 | (~c1_1(a741)) | (~c3_1(a741)) | c0_1(a741) | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.85/1.04 tff(2605,plain,
% 0.85/1.04 (hskp11),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[2604, 255, 33, 396, 207, 178, 177, 22])).
% 0.85/1.04 tff(2606,plain,
% 0.85/1.04 (~c1_1(a749)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1566, 2605])).
% 0.85/1.04 tff(2607,plain,
% 0.85/1.04 (~c0_1(a749)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1540, 2605])).
% 0.85/1.04 tff(2608,plain,
% 0.85/1.04 (~hskp25),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[2279, 255, 2459, 2458, 2457, 2539, 2519, 22, 396])).
% 0.85/1.04 tff(2609,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | c0_1(a749) | c1_1(a749) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a749))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c0_1(a749) | c1_1(a749) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a749))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(2610,plain,
% 0.85/1.04 ((hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a749) | c0_1(a749) | c2_1(a749)) <=> (hskp25 | c0_1(a749) | c1_1(a749) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a749))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(2611,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a749) | c0_1(a749) | c2_1(a749))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | c0_1(a749) | c1_1(a749) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a749)))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[2610])).
% 0.85/1.04 tff(2612,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a749) | c0_1(a749) | c2_1(a749))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c0_1(a749) | c1_1(a749) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a749))),
% 0.85/1.04 inference(transitivity,[status(thm)],[2611, 2609])).
% 0.85/1.04 tff(2613,plain,
% 0.85/1.04 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a749) | c0_1(a749) | c2_1(a749))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(2614,plain,
% 0.85/1.04 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c0_1(a749) | c1_1(a749) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a749)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[2613, 2612])).
% 0.85/1.04 tff(2615,plain,
% 0.85/1.04 (c2_1(a749)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[2614, 104, 2608, 2459, 2458, 2607, 2606, 2457, 20])).
% 0.85/1.04 tff(2616,plain,
% 0.85/1.04 (~c3_1(a749)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1863, 2605])).
% 0.85/1.04 tff(2617,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a749) | c3_1(a749) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a749)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a749) | c3_1(a749) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a749)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(2618,plain,
% 0.85/1.04 ((hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a749) | c1_1(a749) | (~c2_1(a749))) <=> (hskp5 | c1_1(a749) | c3_1(a749) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a749)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(2619,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a749) | c1_1(a749) | (~c2_1(a749)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a749) | c3_1(a749) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a749))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[2618])).
% 0.85/1.04 tff(2620,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a749) | c1_1(a749) | (~c2_1(a749)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a749) | c3_1(a749) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a749)))),
% 0.85/1.04 inference(transitivity,[status(thm)],[2619, 2617])).
% 0.85/1.04 tff(2621,plain,
% 0.85/1.04 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a749) | c1_1(a749) | (~c2_1(a749)))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(2622,plain,
% 0.85/1.04 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a749) | c3_1(a749) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a749))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[2621, 2620])).
% 0.85/1.05 tff(2623,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2622, 104, 396, 2459, 2458, 2606, 2616, 2457, 1456, 2615])).
% 0.85/1.05 tff(2624,plain,(hskp1 | hskp5 | c3_1(a734) | (~c1_1(a741)) | (~c3_1(a741)) | c0_1(a741) | c0_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(2625,plain,
% 0.85/1.05 (hskp1),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2624, 22, 33, 207, 178, 177, 396])).
% 0.85/1.05 tff(2626,plain,
% 0.85/1.05 (~c2_1(a731)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[58, 2625])).
% 0.85/1.05 tff(2627,plain,
% 0.85/1.05 (c3_1(a731)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[66, 2625])).
% 0.85/1.05 tff(2628,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a741) | c2_1(a731) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c3_1(a731)) | c0_1(a731))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a741) | c2_1(a731) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c3_1(a731)) | c0_1(a731))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2629,plain,
% 0.85/1.05 (((~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | (~c1_1(a741)) | c0_1(a741) | (~c2_1(a741)) | (~c3_1(a741)) | c2_1(a731) | c0_1(a731) | (~c3_1(a731))) <=> (c0_1(a741) | c2_1(a731) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c3_1(a731)) | c0_1(a731))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2630,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | (~c1_1(a741)) | c0_1(a741) | (~c2_1(a741)) | (~c3_1(a741)) | c2_1(a731) | c0_1(a731) | (~c3_1(a731)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a741) | c2_1(a731) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c3_1(a731)) | c0_1(a731)))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[2629])).
% 0.85/1.05 tff(2631,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | (~c1_1(a741)) | c0_1(a741) | (~c2_1(a741)) | (~c3_1(a741)) | c2_1(a731) | c0_1(a731) | (~c3_1(a731)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a741) | c2_1(a731) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c3_1(a731)) | c0_1(a731))),
% 0.85/1.05 inference(transitivity,[status(thm)],[2630, 2628])).
% 0.85/1.05 tff(2632,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | (~c1_1(a741)) | c0_1(a741) | (~c2_1(a741)) | (~c3_1(a741)) | c2_1(a731) | c0_1(a731) | (~c3_1(a731)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(2633,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a741) | c2_1(a731) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c3_1(a731)) | c0_1(a731)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[2632, 2631])).
% 0.85/1.05 tff(2634,plain,
% 0.85/1.05 (c0_1(a731)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2633, 104, 207, 178, 2627, 177, 2626, 2537, 2527])).
% 0.85/1.05 tff(2635,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a741) | c2_1(a731) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c3_1(a731)) | (~c0_1(a731)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a741) | c2_1(a731) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c3_1(a731)) | (~c0_1(a731)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2636,plain,
% 0.85/1.05 (((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c0_1(a731)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a741) | (~c3_1(a741)) | (~c2_1(a741))) <=> (c0_1(a741) | c2_1(a731) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c3_1(a731)) | (~c0_1(a731)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2637,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c0_1(a731)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a741) | (~c3_1(a741)) | (~c2_1(a741)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a741) | c2_1(a731) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c3_1(a731)) | (~c0_1(a731))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[2636])).
% 0.85/1.05 tff(2638,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c0_1(a731)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a741) | (~c3_1(a741)) | (~c2_1(a741)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a741) | c2_1(a731) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c3_1(a731)) | (~c0_1(a731)))),
% 0.85/1.05 inference(transitivity,[status(thm)],[2637, 2635])).
% 0.85/1.05 tff(2639,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c0_1(a731)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a741) | (~c3_1(a741)) | (~c2_1(a741)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(2640,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a741) | c2_1(a731) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c3_1(a731)) | (~c0_1(a731))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[2639, 2638])).
% 0.85/1.05 tff(2641,plain,
% 0.85/1.05 ((~c2_1(a730)) | (~c0_1(a731))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2640, 104, 178, 2627, 2458, 177, 2626, 2457, 455, 2527])).
% 0.85/1.05 tff(2642,plain,
% 0.85/1.05 (~c2_1(a730)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2641, 2634])).
% 0.85/1.05 tff(2643,plain,
% 0.85/1.05 (c1_1(a731)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[74, 2625])).
% 0.85/1.05 tff(2644,plain,
% 0.85/1.05 (hskp13),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1883, 104, 2519, 2643, 22, 33, 2626, 32, 2634])).
% 0.85/1.05 tff(2645,plain,
% 0.85/1.05 (~c1_1(a759)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[873, 2644])).
% 0.85/1.05 tff(2646,plain,
% 0.85/1.05 (c3_1(a759)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[882, 2644])).
% 0.85/1.05 tff(2647,plain,
% 0.85/1.05 (c2_1(a759)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[890, 2644])).
% 0.85/1.05 tff(2648,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a759) | c0_1(a741) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c2_1(a759)) | (~c3_1(a759)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a759) | c0_1(a741) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c2_1(a759)) | (~c3_1(a759)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2649,plain,
% 0.85/1.05 (((~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a759) | (~c2_1(a759)) | (~c3_1(a759)) | c0_1(a741) | (~c3_1(a741)) | (~c2_1(a741))) <=> (c1_1(a759) | c0_1(a741) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c2_1(a759)) | (~c3_1(a759)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2650,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a759) | (~c2_1(a759)) | (~c3_1(a759)) | c0_1(a741) | (~c3_1(a741)) | (~c2_1(a741)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a759) | c0_1(a741) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c2_1(a759)) | (~c3_1(a759))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[2649])).
% 0.85/1.05 tff(2651,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a759) | (~c2_1(a759)) | (~c3_1(a759)) | c0_1(a741) | (~c3_1(a741)) | (~c2_1(a741)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a759) | c0_1(a741) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c2_1(a759)) | (~c3_1(a759)))),
% 0.85/1.05 inference(transitivity,[status(thm)],[2650, 2648])).
% 0.85/1.05 tff(2652,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a759) | (~c2_1(a759)) | (~c3_1(a759)) | c0_1(a741) | (~c3_1(a741)) | (~c2_1(a741)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(2653,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a759) | c0_1(a741) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c2_1(a759)) | (~c3_1(a759))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[2652, 2651])).
% 0.85/1.05 tff(2654,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2653, 104, 2647, 2646, 178, 2459, 2458, 2645, 177, 455, 2642, 2527])).
% 0.85/1.05 tff(2655,plain,(c0_1(a734) | (~c3_1(a741)) | c0_1(a741) | c3_1(a734) | (~c1_1(a741)) | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(2656,plain,
% 0.85/1.05 (c0_1(a734)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2655, 33, 177, 178, 207, 396])).
% 0.85/1.05 tff(2657,plain,
% 0.85/1.05 (~hskp4),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2008, 2656])).
% 0.85/1.05 tff(2658,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2154, 104, 396, 166, 1541, 1567, 1944, 395])).
% 0.85/1.05 tff(2659,plain,((~hskp11) | hskp5 | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(2660,plain,
% 0.85/1.05 (~hskp11),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2659, 2657, 396])).
% 0.85/1.05 tff(2661,plain,
% 0.85/1.05 (c1_1(a734) | (~c2_1(a734))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2106, 104, 396, 2459, 2458, 33, 2457, 1456])).
% 0.85/1.05 tff(2662,plain,
% 0.85/1.05 (~c2_1(a734)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2661, 44])).
% 0.85/1.05 tff(2663,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c1_1(a732)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c1_1(a732)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2664,plain,
% 0.85/1.05 ((hskp5 | (~ndr1_0) | c0_1(a732) | c3_1(a732) | (~c1_1(a732)) | c0_1(a732) | c2_1(a732) | (~c1_1(a732))) <=> (hskp5 | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c1_1(a732)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2665,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a732) | c3_1(a732) | (~c1_1(a732)) | c0_1(a732) | c2_1(a732) | (~c1_1(a732)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c1_1(a732))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[2664])).
% 0.85/1.05 tff(2666,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a732) | c3_1(a732) | (~c1_1(a732)) | c0_1(a732) | c2_1(a732) | (~c1_1(a732)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c1_1(a732)))),
% 0.85/1.05 inference(transitivity,[status(thm)],[2665, 2663])).
% 0.85/1.05 tff(2667,plain,
% 0.85/1.05 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a732) | c3_1(a732) | (~c1_1(a732)) | c0_1(a732) | c2_1(a732) | (~c1_1(a732)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(2668,plain,
% 0.85/1.05 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a732) | c2_1(a732) | c3_1(a732) | (~ndr1_0) | (~c1_1(a732))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[2667, 2666])).
% 0.85/1.05 tff(2669,plain,
% 0.85/1.05 (~c1_1(a732)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2668, 104, 396, 1126, 1127, 1125, 1170])).
% 0.85/1.05 tff(2670,plain,
% 0.85/1.05 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | c0_1(a732) | c3_1(a732) | (~ndr1_0) | c1_1(a732))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp5 | hskp4 | c0_1(a732) | c3_1(a732) | (~ndr1_0) | c1_1(a732))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2671,plain,
% 0.85/1.05 ((hskp5 | hskp4 | (~ndr1_0) | c1_1(a732) | c0_1(a732) | c3_1(a732)) <=> (hskp5 | hskp4 | c0_1(a732) | c3_1(a732) | (~ndr1_0) | c1_1(a732))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2672,plain,
% 0.85/1.05 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c1_1(a732) | c0_1(a732) | c3_1(a732))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | c0_1(a732) | c3_1(a732) | (~ndr1_0) | c1_1(a732)))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[2671])).
% 0.85/1.05 tff(2673,plain,
% 0.85/1.05 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c1_1(a732) | c0_1(a732) | c3_1(a732))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp5 | hskp4 | c0_1(a732) | c3_1(a732) | (~ndr1_0) | c1_1(a732))),
% 0.85/1.05 inference(transitivity,[status(thm)],[2672, 2670])).
% 0.85/1.05 tff(2674,plain,
% 0.85/1.05 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c1_1(a732) | c0_1(a732) | c3_1(a732))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(2675,plain,
% 0.85/1.05 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp5 | hskp4 | c0_1(a732) | c3_1(a732) | (~ndr1_0) | c1_1(a732)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[2674, 2673])).
% 0.85/1.05 tff(2676,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2675, 104, 396, 166, 1126, 1125, 395, 2669])).
% 0.85/1.05 tff(2677,plain,((~hskp2) | hskp5 | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(2678,plain,
% 0.85/1.05 (~hskp2),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2677, 2657, 396])).
% 0.85/1.05 tff(2679,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c1_1(a734) | c0_1(a741) | (~c0_1(a734)) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | c2_1(a734))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c1_1(a734) | c0_1(a741) | (~c0_1(a734)) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | c2_1(a734))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2680,plain,
% 0.85/1.05 ((hskp2 | (~ndr1_0) | c2_1(a734) | c1_1(a734) | (~c0_1(a734)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741))) <=> (hskp2 | c1_1(a734) | c0_1(a741) | (~c0_1(a734)) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | c2_1(a734))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2681,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a734) | c1_1(a734) | (~c0_1(a734)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c1_1(a734) | c0_1(a741) | (~c0_1(a734)) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | c2_1(a734)))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[2680])).
% 0.85/1.05 tff(2682,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a734) | c1_1(a734) | (~c0_1(a734)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c1_1(a734) | c0_1(a741) | (~c0_1(a734)) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | c2_1(a734))),
% 0.85/1.05 inference(transitivity,[status(thm)],[2681, 2679])).
% 0.85/1.05 tff(2683,plain,
% 0.85/1.05 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a734) | c1_1(a734) | (~c0_1(a734)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(2684,plain,
% 0.85/1.05 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c1_1(a734) | c0_1(a741) | (~c0_1(a734)) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | c2_1(a734)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[2683, 2682])).
% 0.85/1.05 tff(2685,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2684, 104, 2678, 207, 178, 44, 177, 2656, 530, 2662])).
% 0.85/1.05 tff(2686,plain,(c1_1(a734) | (~c1_1(a741)) | (~c3_1(a741)) | c0_1(a741) | hskp5 | c3_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(2687,plain,
% 0.85/1.05 (c1_1(a734)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2686, 33, 178, 177, 396, 207])).
% 0.85/1.05 tff(2688,plain,
% 0.85/1.05 (hskp18),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2118, 2687, 2656, 2660])).
% 0.85/1.05 tff(2689,plain,
% 0.85/1.05 (~c2_1(a775)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1636, 2688])).
% 0.85/1.05 tff(2690,plain,
% 0.85/1.05 (~c3_1(a775)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1630, 2688])).
% 0.85/1.05 tff(2691,plain,
% 0.85/1.05 (c1_1(a775)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1829, 2688])).
% 0.85/1.05 tff(2692,plain,
% 0.85/1.05 (~c1_1(a746)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[349, 104, 1052, 1051, 1050, 121])).
% 0.85/1.05 tff(2693,plain,
% 0.85/1.05 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp6 | hskp4 | c0_1(a746) | c2_1(a746) | (~ndr1_0) | (~c3_1(a746)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp6 | hskp4 | c0_1(a746) | c2_1(a746) | (~ndr1_0) | (~c3_1(a746)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2694,plain,
% 0.85/1.05 ((hskp6 | hskp4 | (~ndr1_0) | c2_1(a746) | c0_1(a746) | (~c3_1(a746))) <=> (hskp6 | hskp4 | c0_1(a746) | c2_1(a746) | (~ndr1_0) | (~c3_1(a746)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2695,plain,
% 0.85/1.05 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c2_1(a746) | c0_1(a746) | (~c3_1(a746)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp6 | hskp4 | c0_1(a746) | c2_1(a746) | (~ndr1_0) | (~c3_1(a746))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[2694])).
% 0.85/1.05 tff(2696,plain,
% 0.85/1.05 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c2_1(a746) | c0_1(a746) | (~c3_1(a746)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp6 | hskp4 | c0_1(a746) | c2_1(a746) | (~ndr1_0) | (~c3_1(a746)))),
% 0.85/1.05 inference(transitivity,[status(thm)],[2695, 2693])).
% 0.85/1.05 tff(2697,plain,
% 0.85/1.05 ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c2_1(a746) | c0_1(a746) | (~c3_1(a746)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(2698,plain,
% 0.85/1.05 ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp6 | hskp4 | c0_1(a746) | c2_1(a746) | (~ndr1_0) | (~c3_1(a746))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[2697, 2696])).
% 0.85/1.05 tff(2699,plain,
% 0.85/1.05 (hskp6),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2698, 104, 166, 1052, 1051, 1050, 176])).
% 0.85/1.05 tff(2700,plain,
% 0.85/1.05 (~c2_1(a738)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[191, 2699])).
% 0.85/1.05 tff(2701,plain,
% 0.85/1.05 (c1_1(a738)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[205, 2699])).
% 0.85/1.05 tff(2702,plain,
% 0.85/1.05 (~hskp11),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2659, 166, 396])).
% 0.85/1.05 tff(2703,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a746) | c2_1(a738) | (~ndr1_0) | (~c3_1(a738)) | (~c1_1(a738)) | (~c3_1(a746)) | c1_1(a746))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a746) | c2_1(a738) | (~ndr1_0) | (~c3_1(a738)) | (~c1_1(a738)) | (~c3_1(a746)) | c1_1(a746))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2704,plain,
% 0.85/1.05 ((hskp11 | (~ndr1_0) | c2_1(a738) | (~c3_1(a738)) | (~c1_1(a738)) | c1_1(a746) | c2_1(a746) | (~c3_1(a746))) <=> (hskp11 | c2_1(a746) | c2_1(a738) | (~ndr1_0) | (~c3_1(a738)) | (~c1_1(a738)) | (~c3_1(a746)) | c1_1(a746))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2705,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a738) | (~c3_1(a738)) | (~c1_1(a738)) | c1_1(a746) | c2_1(a746) | (~c3_1(a746)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a746) | c2_1(a738) | (~ndr1_0) | (~c3_1(a738)) | (~c1_1(a738)) | (~c3_1(a746)) | c1_1(a746)))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[2704])).
% 0.85/1.05 tff(2706,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a738) | (~c3_1(a738)) | (~c1_1(a738)) | c1_1(a746) | c2_1(a746) | (~c3_1(a746)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a746) | c2_1(a738) | (~ndr1_0) | (~c3_1(a738)) | (~c1_1(a738)) | (~c3_1(a746)) | c1_1(a746))),
% 0.85/1.05 inference(transitivity,[status(thm)],[2705, 2703])).
% 0.85/1.05 tff(2707,plain,
% 0.85/1.05 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a738) | (~c3_1(a738)) | (~c1_1(a738)) | c1_1(a746) | c2_1(a746) | (~c3_1(a746)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(2708,plain,
% 0.85/1.05 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a746) | c2_1(a738) | (~ndr1_0) | (~c3_1(a738)) | (~c1_1(a738)) | (~c3_1(a746)) | c1_1(a746)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[2707, 2706])).
% 0.85/1.05 tff(2709,plain,
% 0.85/1.05 (~c3_1(a738)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2708, 104, 2702, 1052, 2701, 1050, 2700, 360, 2692])).
% 0.85/1.05 tff(2710,plain,
% 0.85/1.05 (~c0_1(a738)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[197, 2699])).
% 0.85/1.05 tff(2711,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a738) | c2_1(a738) | (~ndr1_0) | c3_1(a738) | (~c1_1(a738)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a738) | c2_1(a738) | (~ndr1_0) | c3_1(a738) | (~c1_1(a738)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2712,plain,
% 0.85/1.05 ((hskp5 | (~ndr1_0) | c0_1(a738) | c3_1(a738) | (~c1_1(a738)) | c0_1(a738) | c2_1(a738) | (~c1_1(a738))) <=> (hskp5 | c0_1(a738) | c2_1(a738) | (~ndr1_0) | c3_1(a738) | (~c1_1(a738)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2713,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a738) | c3_1(a738) | (~c1_1(a738)) | c0_1(a738) | c2_1(a738) | (~c1_1(a738)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a738) | c2_1(a738) | (~ndr1_0) | c3_1(a738) | (~c1_1(a738))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[2712])).
% 0.85/1.05 tff(2714,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a738) | c3_1(a738) | (~c1_1(a738)) | c0_1(a738) | c2_1(a738) | (~c1_1(a738)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a738) | c2_1(a738) | (~ndr1_0) | c3_1(a738) | (~c1_1(a738)))),
% 0.85/1.05 inference(transitivity,[status(thm)],[2713, 2711])).
% 0.85/1.05 tff(2715,plain,
% 0.85/1.05 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a738) | c3_1(a738) | (~c1_1(a738)) | c0_1(a738) | c2_1(a738) | (~c1_1(a738)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(2716,plain,
% 0.85/1.05 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a738) | c2_1(a738) | (~ndr1_0) | c3_1(a738) | (~c1_1(a738))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[2715, 2714])).
% 0.85/1.05 tff(2717,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2716, 104, 396, 2701, 2710, 2700, 1170, 2709])).
% 0.85/1.05 tff(2718,plain,((~hskp9) | hskp5 | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(2719,plain,
% 0.85/1.05 (~hskp9),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2718, 2657, 396])).
% 0.85/1.05 tff(2720,plain,
% 0.85/1.05 (hskp1),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2480, 2719, 2691, 2690, 2689, 396])).
% 0.85/1.05 tff(2721,plain,
% 0.85/1.05 (~c2_1(a731)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[58, 2720])).
% 0.85/1.05 tff(2722,plain,
% 0.85/1.05 (c1_1(a731)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[74, 2720])).
% 0.85/1.05 tff(2723,plain,
% 0.85/1.05 (c3_1(a731)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[66, 2720])).
% 0.85/1.05 tff(2724,plain,
% 0.85/1.05 (~hskp11),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2659, 396, 166])).
% 0.85/1.05 tff(2725,plain,
% 0.85/1.05 (c2_1(a730)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2130, 2724])).
% 0.85/1.05 tff(2726,plain,
% 0.85/1.05 (hskp20),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2132, 2725, 396])).
% 0.85/1.05 tff(2727,plain,
% 0.85/1.05 (~c3_1(a779)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1737, 2726])).
% 0.85/1.05 tff(2728,plain,
% 0.85/1.05 (~c1_1(a779)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1743, 2726])).
% 0.85/1.05 tff(2729,plain,
% 0.85/1.05 (c2_1(a779)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1751, 2726])).
% 0.85/1.05 tff(2730,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a779) | c3_1(a779) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a779)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a779) | c3_1(a779) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a779)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2731,plain,
% 0.85/1.05 ((hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a779) | c1_1(a779) | (~c2_1(a779))) <=> (hskp5 | c1_1(a779) | c3_1(a779) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a779)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2732,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a779) | c1_1(a779) | (~c2_1(a779)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a779) | c3_1(a779) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a779))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[2731])).
% 0.85/1.05 tff(2733,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a779) | c1_1(a779) | (~c2_1(a779)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a779) | c3_1(a779) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a779)))),
% 0.85/1.05 inference(transitivity,[status(thm)],[2732, 2730])).
% 0.85/1.05 tff(2734,plain,
% 0.85/1.05 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c3_1(a779) | c1_1(a779) | (~c2_1(a779)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(2735,plain,
% 0.85/1.05 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a779) | c3_1(a779) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a779))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[2734, 2733])).
% 0.85/1.05 tff(2736,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2735, 104, 396, 2729, 469, 468, 2728, 2727, 456, 1456])).
% 0.85/1.05 tff(2737,plain,(hskp5 | (~c0_1(a730)) | (~c3_1(a730)) | c1_1(a730) | (~c1_1(a731)) | (~c3_1(a731)) | c2_1(a731) | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(2738,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2737, 2723, 2722, 396, 2457, 2459, 2458, 2657, 2721])).
% 0.85/1.05 tff(2739,plain,(c3_1(a734) | hskp5 | (~c3_1(a741)) | c0_1(a741) | (~c1_1(a741))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(2740,plain,
% 0.85/1.05 (c3_1(a734)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2739, 396, 178, 177, 207])).
% 0.85/1.05 tff(2741,plain,
% 0.85/1.05 (((~hskp4) | (~c3_1(a734))) <=> ((~hskp4) | (~c3_1(a734)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2742,plain,
% 0.85/1.05 (((~c3_1(a734)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a734)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2743,axiom,((~c3_1(a734)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 0.85/1.05 tff(2744,plain,
% 0.85/1.05 ((~hskp4) | (~c3_1(a734))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[2743, 2742])).
% 0.85/1.05 tff(2745,plain,
% 0.85/1.05 ((~hskp4) | (~c3_1(a734))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[2744, 2741])).
% 0.85/1.05 tff(2746,plain,
% 0.85/1.05 (~hskp4),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2745, 2740])).
% 0.85/1.05 tff(2747,plain,
% 0.85/1.05 (~hskp2),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2677, 2746, 396])).
% 0.85/1.05 tff(2748,plain,
% 0.85/1.05 (~hskp11),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[2659, 2746, 396])).
% 0.85/1.05 tff(2749,assumption,(hskp21), introduced(assumption)).
% 0.85/1.05 tff(2750,plain,
% 0.85/1.05 (~c2_1(a793)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[482, 2749])).
% 0.85/1.05 tff(2751,plain,
% 0.85/1.05 (c0_1(a793)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[500, 2749])).
% 0.85/1.05 tff(2752,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a793) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c0_1(a793)) | c1_1(a793))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a793) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c0_1(a793)) | c1_1(a793))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2753,plain,
% 0.85/1.05 ((hskp2 | (~ndr1_0) | c2_1(a793) | c1_1(a793) | (~c0_1(a793)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741))) <=> (hskp2 | c2_1(a793) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c0_1(a793)) | c1_1(a793))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(2754,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a793) | c1_1(a793) | (~c0_1(a793)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a793) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c0_1(a793)) | c1_1(a793)))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[2753])).
% 0.85/1.06 tff(2755,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a793) | c1_1(a793) | (~c0_1(a793)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a793) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c0_1(a793)) | c1_1(a793))),
% 0.85/1.06 inference(transitivity,[status(thm)],[2754, 2752])).
% 0.85/1.06 tff(2756,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a793) | c1_1(a793) | (~c0_1(a793)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(2757,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a793) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c0_1(a793)) | c1_1(a793)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[2756, 2755])).
% 0.85/1.06 tff(2758,plain,
% 0.85/1.06 (c1_1(a793)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2757, 104, 256, 2751, 207, 178, 2750, 177, 530])).
% 0.85/1.06 tff(2759,plain,
% 0.85/1.06 (c3_1(a793)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[492, 2749])).
% 0.85/1.06 tff(2760,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | c2_1(a793) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a793)) | (~c1_1(a793)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a793) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a793)) | (~c1_1(a793)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(2761,plain,
% 0.85/1.06 ((hskp11 | (~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c1_1(a793)) | c0_1(a741) | c2_1(a741) | (~c1_1(a741))) <=> (hskp11 | c2_1(a793) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a793)) | (~c1_1(a793)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(2762,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c1_1(a793)) | c0_1(a741) | c2_1(a741) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | c2_1(a793) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a793)) | (~c1_1(a793))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[2761])).
% 0.85/1.06 tff(2763,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c1_1(a793)) | c0_1(a741) | c2_1(a741) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a793) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a793)) | (~c1_1(a793)))),
% 0.85/1.06 inference(transitivity,[status(thm)],[2762, 2760])).
% 0.85/1.06 tff(2764,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c1_1(a793)) | c0_1(a741) | c2_1(a741) | (~c1_1(a741)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(2765,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a793) | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a793)) | (~c1_1(a793))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[2764, 2763])).
% 0.85/1.06 tff(2766,plain,
% 0.85/1.06 (c2_1(a741)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2765, 104, 21, 2759, 207, 2750, 177, 43, 2758])).
% 0.85/1.06 tff(2767,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a793) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c3_1(a793)) | (~c1_1(a793)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a793) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c3_1(a793)) | (~c1_1(a793)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(2768,plain,
% 0.85/1.06 ((hskp11 | (~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c1_1(a793)) | c1_1(a730) | c2_1(a730) | (~c3_1(a730))) <=> (hskp11 | c2_1(a793) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c3_1(a793)) | (~c1_1(a793)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(2769,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c1_1(a793)) | c1_1(a730) | c2_1(a730) | (~c3_1(a730)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a793) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c3_1(a793)) | (~c1_1(a793))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[2768])).
% 0.85/1.06 tff(2770,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c1_1(a793)) | c1_1(a730) | c2_1(a730) | (~c3_1(a730)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a793) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c3_1(a793)) | (~c1_1(a793)))),
% 0.85/1.06 inference(transitivity,[status(thm)],[2769, 2767])).
% 0.85/1.06 tff(2771,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c1_1(a793)) | c1_1(a730) | c2_1(a730) | (~c3_1(a730)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(2772,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a793) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c3_1(a793)) | (~c1_1(a793))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[2771, 2770])).
% 0.85/1.06 tff(2773,plain,
% 0.85/1.06 (c2_1(a730) | (~c1_1(a793))),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2772, 104, 21, 2759, 468, 2750, 456, 360])).
% 0.85/1.06 tff(2774,plain,
% 0.85/1.06 (c2_1(a730)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2773, 2758])).
% 0.85/1.06 tff(2775,plain,
% 0.85/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a793) | c0_1(a741) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c3_1(a793)) | (~c0_1(a793)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a793) | c0_1(a741) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c3_1(a793)) | (~c0_1(a793)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(2776,plain,
% 0.85/1.06 (((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a741) | (~c3_1(a741)) | (~c2_1(a741))) <=> (c2_1(a793) | c0_1(a741) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c3_1(a793)) | (~c0_1(a793)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(2777,plain,
% 0.85/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a741) | (~c3_1(a741)) | (~c2_1(a741)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a793) | c0_1(a741) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c3_1(a793)) | (~c0_1(a793))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[2776])).
% 0.85/1.06 tff(2778,plain,
% 0.85/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a741) | (~c3_1(a741)) | (~c2_1(a741)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a793) | c0_1(a741) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c3_1(a793)) | (~c0_1(a793)))),
% 0.85/1.06 inference(transitivity,[status(thm)],[2777, 2775])).
% 0.85/1.06 tff(2779,plain,
% 0.85/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a741) | (~c3_1(a741)) | (~c2_1(a741)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(2780,plain,
% 0.85/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a793) | c0_1(a741) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a741)) | (~c3_1(a741)) | (~c3_1(a793)) | (~c0_1(a793))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[2779, 2778])).
% 0.85/1.06 tff(2781,plain,
% 0.85/1.06 ((~c2_1(a730)) | (~c2_1(a741))),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2780, 104, 2751, 2759, 178, 468, 2750, 177, 456, 455])).
% 0.85/1.06 tff(2782,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2781, 2774, 2766])).
% 0.85/1.06 tff(2783,plain,((~hskp21) | (~c3_1(a741)) | (~c3_1(a730)) | c0_1(a741) | c1_1(a730) | hskp11 | (~c1_1(a741)) | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(2784,plain,
% 0.85/1.06 (~hskp21),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2783, 2458, 178, 177, 2457, 2748, 207, 2747])).
% 0.85/1.06 tff(2785,plain,
% 0.85/1.06 (hskp21 | (~c2_1(a730))),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[475, 104, 2459, 2458, 467])).
% 0.85/1.06 tff(2786,plain,
% 0.85/1.06 (~c2_1(a730)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2785, 2784])).
% 0.85/1.06 tff(2787,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c0_1(a741) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c1_1(a741)) | (~c3_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c0_1(a741) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c1_1(a741)) | (~c3_1(a741)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(2788,plain,
% 0.85/1.06 ((hskp2 | (~ndr1_0) | c2_1(a730) | c1_1(a730) | (~c0_1(a730)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741))) <=> (hskp2 | c0_1(a741) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c1_1(a741)) | (~c3_1(a741)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(2789,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a730) | c1_1(a730) | (~c0_1(a730)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c0_1(a741) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c1_1(a741)) | (~c3_1(a741))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[2788])).
% 0.85/1.06 tff(2790,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a730) | c1_1(a730) | (~c0_1(a730)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c0_1(a741) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c1_1(a741)) | (~c3_1(a741)))),
% 0.85/1.06 inference(transitivity,[status(thm)],[2789, 2787])).
% 0.85/1.06 tff(2791,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a730) | c1_1(a730) | (~c0_1(a730)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(2792,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c0_1(a741) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c1_1(a741)) | (~c3_1(a741))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[2791, 2790])).
% 0.85/1.06 tff(2793,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2792, 104, 2747, 207, 178, 2459, 177, 2457, 530, 2786])).
% 0.85/1.06 tff(2794,plain,(hskp5 | (~c1_1(a741)) | (~c3_1(a741)) | c0_1(a741)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(2795,plain,
% 0.85/1.06 (hskp5),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2794, 2509, 2375, 177])).
% 0.85/1.06 tff(2796,plain,
% 0.85/1.06 (~c0_1(a735)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[427, 2795])).
% 0.85/1.06 tff(2797,plain,
% 0.85/1.06 (c3_1(a735)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[413, 2795])).
% 0.85/1.06 tff(2798,plain,
% 0.85/1.06 (c2_1(a735)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[421, 2795])).
% 0.85/1.06 tff(2799,plain,
% 0.85/1.06 (~c2_1(a730)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[509, 2797, 2377, 2376, 2796, 1016, 2798])).
% 0.85/1.06 tff(2800,plain,
% 0.85/1.06 (hskp2),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[540, 2799, 2377, 2796, 1016, 2798, 255, 2797])).
% 0.85/1.06 tff(2801,plain,
% 0.85/1.06 (~c2_1(a732)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[282, 2800])).
% 0.85/1.06 tff(2802,plain,
% 0.85/1.06 (~c0_1(a732)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[288, 2800])).
% 0.85/1.06 tff(2803,plain,
% 0.85/1.06 (~c3_1(a732)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[546, 2800])).
% 0.85/1.06 tff(2804,plain,
% 0.85/1.06 (hskp5),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2794, 178, 207, 177])).
% 0.85/1.06 tff(2805,plain,
% 0.85/1.06 (c2_1(a735)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[421, 2804])).
% 0.85/1.06 tff(2806,plain,
% 0.85/1.06 (~c0_1(a735)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[427, 2804])).
% 0.85/1.06 tff(2807,plain,
% 0.85/1.06 (c3_1(a735)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[413, 2804])).
% 0.85/1.06 tff(2808,plain,
% 0.85/1.06 (~c2_1(a730)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[509, 2807, 469, 468, 2806, 456, 2805])).
% 0.85/1.06 tff(2809,plain,
% 0.85/1.06 (~c2_1(a741)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[708, 560, 468, 469, 21, 2808, 621, 620, 456, 207, 177, 622])).
% 0.85/1.06 tff(2810,plain,
% 0.85/1.06 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp27 | hskp11 | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c3_1(a741)))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp27 | hskp11 | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c3_1(a741)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(2811,plain,
% 0.85/1.06 ((hskp27 | hskp11 | (~ndr1_0) | c2_1(a741) | c0_1(a741) | (~c3_1(a741))) <=> (hskp27 | hskp11 | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c3_1(a741)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(2812,plain,
% 0.85/1.06 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp27 | hskp11 | (~ndr1_0) | c2_1(a741) | c0_1(a741) | (~c3_1(a741)))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp27 | hskp11 | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c3_1(a741))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[2811])).
% 0.85/1.06 tff(2813,plain,
% 0.85/1.06 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp27 | hskp11 | (~ndr1_0) | c2_1(a741) | c0_1(a741) | (~c3_1(a741)))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp27 | hskp11 | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c3_1(a741)))),
% 0.85/1.06 inference(transitivity,[status(thm)],[2812, 2810])).
% 0.85/1.06 tff(2814,plain,
% 0.85/1.06 ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp27 | hskp11 | (~ndr1_0) | c2_1(a741) | c0_1(a741) | (~c3_1(a741)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(2815,plain,
% 0.85/1.06 ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp27 | hskp11 | c0_1(a741) | (~ndr1_0) | c2_1(a741) | (~c3_1(a741))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[2814, 2813])).
% 0.85/1.06 tff(2816,plain,
% 0.85/1.06 (hskp27 | c2_1(a741) | (~c3_1(a741))),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2815, 104, 21, 177, 609])).
% 0.85/1.06 tff(2817,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2816, 2809, 560, 178])).
% 0.85/1.06 tff(2818,plain,(hskp27 | (~c3_1(a741)) | hskp11 | c0_1(a741) | (~c3_1(a730)) | (~c0_1(a730)) | c2_1(a732) | c3_1(a732) | c1_1(a730) | (~c1_1(a741)) | c0_1(a732)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(2819,plain,
% 0.85/1.06 (hskp27),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2818, 2509, 21, 177, 2376, 2377, 2801, 2803, 1016, 2375, 2802])).
% 0.85/1.06 tff(2820,plain,
% 0.85/1.06 (c2_1(a750)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[724, 2819])).
% 0.85/1.06 tff(2821,plain,
% 0.85/1.06 (c1_1(a750)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[732, 2819])).
% 0.85/1.06 tff(2822,plain,
% 0.85/1.06 (c0_1(a750)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[716, 2819])).
% 0.85/1.06 tff(2823,assumption,(~hskp10), introduced(assumption)).
% 0.85/1.06 tff(2824,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a741) | c0_1(a734) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | c2_1(a734) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a741) | c0_1(a734) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | c2_1(a734) | (~c1_1(a734)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(2825,plain,
% 0.85/1.06 ((hskp10 | (~ndr1_0) | c0_1(a741) | (~c2_1(a741)) | (~c3_1(a741)) | c0_1(a734) | c2_1(a734) | (~c1_1(a734))) <=> (hskp10 | c0_1(a741) | c0_1(a734) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | c2_1(a734) | (~c1_1(a734)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(2826,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a741) | (~c2_1(a741)) | (~c3_1(a741)) | c0_1(a734) | c2_1(a734) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a741) | c0_1(a734) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | c2_1(a734) | (~c1_1(a734))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[2825])).
% 0.85/1.06 tff(2827,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a741) | (~c2_1(a741)) | (~c3_1(a741)) | c0_1(a734) | c2_1(a734) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a741) | c0_1(a734) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | c2_1(a734) | (~c1_1(a734)))),
% 0.85/1.06 inference(transitivity,[status(thm)],[2826, 2824])).
% 0.85/1.06 tff(2828,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a741) | (~c2_1(a741)) | (~c3_1(a741)) | c0_1(a734) | c2_1(a734) | (~c1_1(a734)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(2829,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a741) | c0_1(a734) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | c2_1(a734) | (~c1_1(a734))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[2828, 2827])).
% 0.85/1.06 tff(2830,plain,
% 0.85/1.06 (hskp10 | (~c2_1(a741)) | (~c3_1(a741)) | c2_1(a734)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2829, 104, 1006, 177, 22, 970])).
% 0.85/1.06 tff(2831,plain,
% 0.85/1.06 (c2_1(a734)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2830, 2823, 178, 561])).
% 0.85/1.06 tff(2832,plain,
% 0.85/1.06 (hskp10 | (~c1_1(a732))),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2304, 104, 485, 484, 457, 622, 621, 970])).
% 0.85/1.06 tff(2833,plain,
% 0.85/1.06 (~c1_1(a732)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2832, 2823])).
% 0.85/1.06 tff(2834,plain,
% 0.85/1.06 (c1_1(a732) | (~c2_1(a734))),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[958, 104, 744, 802, 801, 22, 33, 622, 621, 952])).
% 0.85/1.06 tff(2835,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2834, 2833, 2831])).
% 0.85/1.06 tff(2836,plain,(hskp10 | (~c0_1(a750)) | (~c1_1(a750)) | (~c2_1(a750)) | c0_1(a734) | c3_1(a734) | c0_1(a732) | c2_1(a732) | (~c2_1(a735)) | (~c3_1(a735)) | c0_1(a735) | (~c3_1(a741)) | (~c2_1(a741)) | (~c1_1(a734)) | c0_1(a741)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(2837,plain,
% 0.85/1.06 (hskp10),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2836, 2822, 2821, 2820, 22, 33, 2802, 2801, 2798, 2797, 2796, 2509, 2518, 1005, 177])).
% 0.85/1.06 tff(2838,plain,
% 0.85/1.06 (~c2_1(a748)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[983, 2837])).
% 0.85/1.06 tff(2839,plain,
% 0.85/1.06 (~c1_1(a748)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[989, 2837])).
% 0.85/1.06 tff(2840,plain,
% 0.85/1.06 (~c0_1(a748)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[995, 2837])).
% 0.85/1.06 tff(2841,plain,
% 0.85/1.06 (~hskp25),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[933, 2518, 2375, 177, 255, 2509, 2820, 2822, 2821])).
% 0.85/1.06 tff(2842,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1204, 104, 2841, 2377, 2376, 2840, 2839, 2838, 1016, 20])).
% 0.85/1.06 tff(2843,plain,(hskp1 | c0_1(a734) | c3_1(a734) | c0_1(a741) | hskp11), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(2844,plain,
% 0.85/1.06 (hskp1),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2843, 177, 33, 22, 21])).
% 0.85/1.06 tff(2845,plain,
% 0.85/1.06 (~c2_1(a731)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[58, 2844])).
% 0.85/1.06 tff(2846,plain,
% 0.85/1.06 (c3_1(a731)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[66, 2844])).
% 0.85/1.06 tff(2847,plain,
% 0.85/1.06 (c1_1(a731)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[74, 2844])).
% 0.85/1.06 tff(2848,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a741) | c2_1(a731) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a731)) | (~c1_1(a731)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a741) | c2_1(a731) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a731)) | (~c1_1(a731)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(2849,plain,
% 0.85/1.06 ((hskp11 | (~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a741) | c2_1(a741) | (~c1_1(a741))) <=> (hskp11 | c0_1(a741) | c2_1(a731) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a731)) | (~c1_1(a731)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(2850,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a741) | c2_1(a741) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a741) | c2_1(a731) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a731)) | (~c1_1(a731))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[2849])).
% 0.85/1.06 tff(2851,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a741) | c2_1(a741) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a741) | c2_1(a731) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a731)) | (~c1_1(a731)))),
% 0.85/1.06 inference(transitivity,[status(thm)],[2850, 2848])).
% 0.85/1.06 tff(2852,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c0_1(a741) | c2_1(a741) | (~c1_1(a741)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(2853,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a741) | c2_1(a731) | (~ndr1_0) | c2_1(a741) | (~c1_1(a741)) | (~c3_1(a731)) | (~c1_1(a731))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[2852, 2851])).
% 0.85/1.06 tff(2854,plain,
% 0.85/1.06 (c2_1(a741)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2853, 104, 21, 2375, 2847, 2846, 177, 2845, 43])).
% 0.85/1.06 tff(2855,plain,
% 0.85/1.06 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.85/1.06 inference(bind,[status(th)],[])).
% 0.85/1.06 tff(2856,plain,
% 0.85/1.06 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.85/1.06 inference(quant_intro,[status(thm)],[2855])).
% 0.85/1.06 tff(2857,plain,
% 0.85/1.06 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(2858,plain,
% 0.85/1.06 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp15) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp15))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.85/1.06 inference(bind,[status(th)],[])).
% 0.85/1.06 tff(2859,plain,
% 0.85/1.06 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.85/1.06 inference(quant_intro,[status(thm)],[2858])).
% 0.85/1.06 tff(2860,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 0.85/1.06 tff(2861,plain,
% 0.85/1.06 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[2860, 2859])).
% 0.85/1.06 tff(2862,plain,
% 0.85/1.06 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[2861, 2857])).
% 0.85/1.06 tff(2863,plain,(
% 0.85/1.06 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.85/1.06 inference(skolemize,[status(sab)],[2862])).
% 0.85/1.06 tff(2864,plain,
% 0.85/1.06 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[2863, 2856])).
% 0.85/1.06 tff(2865,plain,
% 0.85/1.06 (c2_1(a734)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2372, 104, 21, 1005, 2847, 2846, 22, 2845, 43])).
% 0.85/1.06 tff(2866,plain,
% 0.85/1.06 (hskp27 | (~c2_1(a734)) | (~c1_1(a734))),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1582, 104, 21, 33, 559])).
% 0.85/1.06 tff(2867,plain,
% 0.85/1.06 (hskp27),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2866, 2865, 1005])).
% 0.85/1.06 tff(2868,plain,
% 0.85/1.06 (c0_1(a750)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[716, 2867])).
% 0.85/1.06 tff(2869,plain,
% 0.85/1.06 (c2_1(a750)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[724, 2867])).
% 0.85/1.06 tff(2870,plain,
% 0.85/1.06 (c1_1(a750)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[732, 2867])).
% 0.85/1.06 tff(2871,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[2221, 104, 744, 802, 801, 2207, 1051, 1050, 177, 952, 561, 2692])).
% 0.85/1.06 tff(2872,plain,((~hskp9) | (~c0_1(a750)) | (~c1_1(a750)) | (~c2_1(a750)) | c3_1(a741) | c0_1(a741) | (~c2_1(a741))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.07 tff(2873,plain,
% 0.85/1.07 (~hskp9),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2872, 2207, 2870, 2869, 2868, 177, 2854])).
% 0.85/1.07 tff(2874,plain,
% 0.85/1.07 (hskp0),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1007, 2873, 1005, 33])).
% 0.85/1.07 tff(2875,plain,
% 0.85/1.07 (~c1_1(a730)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[384, 2874])).
% 0.85/1.07 tff(2876,plain,
% 0.85/1.07 (c3_1(a730)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[435, 2874])).
% 0.85/1.07 tff(2877,plain,
% 0.85/1.07 (c2_1(a730)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1901, 104, 21, 2847, 2846, 2876, 2845, 2875, 360])).
% 0.85/1.07 tff(2878,plain,
% 0.85/1.07 (^[U: $i] : refl((hskp28 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))),
% 0.85/1.07 inference(bind,[status(th)],[])).
% 0.85/1.07 tff(2879,plain,
% 0.85/1.07 (![U: $i] : (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.07 inference(quant_intro,[status(thm)],[2878])).
% 0.85/1.07 tff(2880,plain,
% 0.85/1.07 (![U: $i] : (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(2881,plain,
% 0.85/1.07 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp28) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp28))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp28) | hskp11) <=> ((hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp11))), rewrite(((hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp11) <=> (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp28) | hskp11) <=> (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.85/1.07 inference(bind,[status(th)],[])).
% 0.85/1.07 tff(2882,plain,
% 0.85/1.07 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp28) | hskp11) <=> ![U: $i] : (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.07 inference(quant_intro,[status(thm)],[2881])).
% 0.85/1.07 tff(2883,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp28) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 0.85/1.07 tff(2884,plain,
% 0.85/1.07 (![U: $i] : (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2883, 2882])).
% 0.85/1.07 tff(2885,plain,
% 0.85/1.07 (![U: $i] : (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2884, 2880])).
% 0.85/1.07 tff(2886,plain,(
% 0.85/1.07 ![U: $i] : (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.07 inference(skolemize,[status(sab)],[2885])).
% 0.85/1.07 tff(2887,plain,
% 0.85/1.07 (![U: $i] : (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2886, 2879])).
% 0.85/1.07 tff(2888,plain,
% 0.85/1.07 (c0_1(a730)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[443, 2874])).
% 0.85/1.07 tff(2889,plain,
% 0.85/1.07 (((~![U: $i] : (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(a730)) | (~c0_1(a730)) | (~c3_1(a730)))) <=> ((~![U: $i] : (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp11 | (~ndr1_0) | (~c2_1(a730)) | (~c0_1(a730)) | (~c3_1(a730)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(2890,plain,
% 0.85/1.07 ((hskp28 | hskp11 | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c0_1(a730))) <=> (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(a730)) | (~c0_1(a730)) | (~c3_1(a730)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(2891,plain,
% 0.85/1.07 (((~![U: $i] : (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c0_1(a730)))) <=> ((~![U: $i] : (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(a730)) | (~c0_1(a730)) | (~c3_1(a730))))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[2890])).
% 0.85/1.07 tff(2892,plain,
% 0.85/1.07 (((~![U: $i] : (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c0_1(a730)))) <=> ((~![U: $i] : (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp11 | (~ndr1_0) | (~c2_1(a730)) | (~c0_1(a730)) | (~c3_1(a730)))),
% 0.85/1.07 inference(transitivity,[status(thm)],[2891, 2889])).
% 0.85/1.07 tff(2893,plain,
% 0.85/1.07 ((~![U: $i] : (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c0_1(a730)))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(2894,plain,
% 0.85/1.07 ((~![U: $i] : (hskp28 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp11 | (~ndr1_0) | (~c2_1(a730)) | (~c0_1(a730)) | (~c3_1(a730))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2893, 2892])).
% 0.85/1.07 tff(2895,plain,
% 0.85/1.07 (hskp28 | (~c2_1(a730))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2894, 104, 21, 2888, 2876, 2887])).
% 0.85/1.07 tff(2896,plain,
% 0.85/1.07 (hskp28),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2895, 2877])).
% 0.85/1.07 tff(2897,plain,
% 0.85/1.07 (((~hskp28) | c3_1(a784)) <=> ((~hskp28) | c3_1(a784))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(2898,axiom,((~hskp28) | c3_1(a784)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 0.85/1.07 tff(2899,plain,
% 0.85/1.07 ((~hskp28) | c3_1(a784)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2898, 2897])).
% 0.85/1.07 tff(2900,plain,
% 0.85/1.07 ((~hskp28) | c3_1(a784)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2899, 2897])).
% 0.85/1.07 tff(2901,plain,
% 0.85/1.07 ((~hskp28) | c3_1(a784)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2900, 2897])).
% 0.85/1.07 tff(2902,plain,
% 0.85/1.07 ((~hskp28) | c3_1(a784)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2901, 2897])).
% 0.85/1.07 tff(2903,plain,
% 0.85/1.07 ((~hskp28) | c3_1(a784)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2902, 2897])).
% 0.85/1.07 tff(2904,plain,
% 0.85/1.07 (c3_1(a784)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2903, 2896])).
% 0.85/1.07 tff(2905,plain,
% 0.85/1.07 (((~hskp28) | c1_1(a784)) <=> ((~hskp28) | c1_1(a784))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(2906,axiom,((~hskp28) | c1_1(a784)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 0.85/1.07 tff(2907,plain,
% 0.85/1.07 ((~hskp28) | c1_1(a784)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2906, 2905])).
% 0.85/1.07 tff(2908,plain,
% 0.85/1.07 ((~hskp28) | c1_1(a784)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2907, 2905])).
% 0.85/1.07 tff(2909,plain,
% 0.85/1.07 ((~hskp28) | c1_1(a784)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2908, 2905])).
% 0.85/1.07 tff(2910,plain,
% 0.85/1.07 ((~hskp28) | c1_1(a784)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2909, 2905])).
% 0.85/1.07 tff(2911,plain,
% 0.85/1.07 ((~hskp28) | c1_1(a784)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2910, 2905])).
% 0.85/1.07 tff(2912,plain,
% 0.85/1.07 (c1_1(a784)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2911, 2896])).
% 0.85/1.07 tff(2913,plain,
% 0.85/1.07 (((~hskp28) | c0_1(a784)) <=> ((~hskp28) | c0_1(a784))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(2914,axiom,((~hskp28) | c0_1(a784)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 0.85/1.07 tff(2915,plain,
% 0.85/1.07 ((~hskp28) | c0_1(a784)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2914, 2913])).
% 0.85/1.07 tff(2916,plain,
% 0.85/1.07 ((~hskp28) | c0_1(a784)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2915, 2913])).
% 0.85/1.07 tff(2917,plain,
% 0.85/1.07 ((~hskp28) | c0_1(a784)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2916, 2913])).
% 0.85/1.07 tff(2918,plain,
% 0.85/1.07 ((~hskp28) | c0_1(a784)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2917, 2913])).
% 0.85/1.07 tff(2919,plain,
% 0.85/1.07 ((~hskp28) | c0_1(a784)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2918, 2913])).
% 0.85/1.07 tff(2920,plain,
% 0.85/1.07 (c0_1(a784)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2919, 2896])).
% 0.85/1.07 tff(2921,plain,
% 0.85/1.07 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c3_1(a741) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c1_1(a784)) | (~c3_1(a784)) | (~c0_1(a784)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c3_1(a741) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c1_1(a784)) | (~c3_1(a784)) | (~c0_1(a784)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(2922,plain,
% 0.85/1.07 ((hskp15 | (~ndr1_0) | (~c3_1(a784)) | (~c1_1(a784)) | (~c0_1(a784)) | c3_1(a741) | c0_1(a741) | (~c2_1(a741))) <=> (hskp15 | c3_1(a741) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c1_1(a784)) | (~c3_1(a784)) | (~c0_1(a784)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(2923,plain,
% 0.85/1.07 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a784)) | (~c1_1(a784)) | (~c0_1(a784)) | c3_1(a741) | c0_1(a741) | (~c2_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c3_1(a741) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c1_1(a784)) | (~c3_1(a784)) | (~c0_1(a784))))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[2922])).
% 0.85/1.07 tff(2924,plain,
% 0.85/1.07 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a784)) | (~c1_1(a784)) | (~c0_1(a784)) | c3_1(a741) | c0_1(a741) | (~c2_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c3_1(a741) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c1_1(a784)) | (~c3_1(a784)) | (~c0_1(a784)))),
% 0.85/1.07 inference(transitivity,[status(thm)],[2923, 2921])).
% 0.85/1.07 tff(2925,plain,
% 0.85/1.07 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a784)) | (~c1_1(a784)) | (~c0_1(a784)) | c3_1(a741) | c0_1(a741) | (~c2_1(a741)))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(2926,plain,
% 0.85/1.07 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c3_1(a741) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c1_1(a784)) | (~c3_1(a784)) | (~c0_1(a784))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2925, 2924])).
% 0.85/1.07 tff(2927,plain,
% 0.85/1.07 (hskp15),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2926, 104, 2920, 2912, 2904, 2207, 177, 2864, 2854])).
% 0.85/1.07 tff(2928,plain,
% 0.85/1.07 (((~hskp15) | (~c2_1(a763))) <=> ((~hskp15) | (~c2_1(a763)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(2929,plain,
% 0.85/1.07 (((~c2_1(a763)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a763)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(2930,axiom,((~c2_1(a763)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 0.85/1.07 tff(2931,plain,
% 0.85/1.07 ((~hskp15) | (~c2_1(a763))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2930, 2929])).
% 0.85/1.07 tff(2932,plain,
% 0.85/1.07 ((~hskp15) | (~c2_1(a763))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2931, 2928])).
% 0.85/1.07 tff(2933,plain,
% 0.85/1.07 (~c2_1(a763)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2932, 2927])).
% 0.85/1.07 tff(2934,plain,
% 0.85/1.07 (((~hskp15) | c1_1(a763)) <=> ((~hskp15) | c1_1(a763))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(2935,axiom,((~hskp15) | c1_1(a763)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 0.85/1.07 tff(2936,plain,
% 0.85/1.07 ((~hskp15) | c1_1(a763)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2935, 2934])).
% 0.85/1.07 tff(2937,plain,
% 0.85/1.07 ((~hskp15) | c1_1(a763)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2936, 2934])).
% 0.85/1.07 tff(2938,plain,
% 0.85/1.07 ((~hskp15) | c1_1(a763)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2937, 2934])).
% 0.85/1.07 tff(2939,plain,
% 0.85/1.07 ((~hskp15) | c1_1(a763)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2938, 2934])).
% 0.85/1.07 tff(2940,plain,
% 0.85/1.07 ((~hskp15) | c1_1(a763)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2939, 2934])).
% 0.85/1.07 tff(2941,plain,
% 0.85/1.07 (c1_1(a763)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2940, 2927])).
% 0.85/1.07 tff(2942,plain,
% 0.85/1.07 (((~hskp15) | c0_1(a763)) <=> ((~hskp15) | c0_1(a763))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(2943,axiom,((~hskp15) | c0_1(a763)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 0.85/1.07 tff(2944,plain,
% 0.85/1.07 ((~hskp15) | c0_1(a763)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2943, 2942])).
% 0.85/1.07 tff(2945,plain,
% 0.85/1.07 ((~hskp15) | c0_1(a763)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2944, 2942])).
% 0.85/1.07 tff(2946,plain,
% 0.85/1.07 ((~hskp15) | c0_1(a763)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2945, 2942])).
% 0.85/1.07 tff(2947,plain,
% 0.85/1.07 ((~hskp15) | c0_1(a763)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2946, 2942])).
% 0.85/1.07 tff(2948,plain,
% 0.85/1.07 ((~hskp15) | c0_1(a763)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2947, 2942])).
% 0.85/1.07 tff(2949,plain,
% 0.85/1.07 (c0_1(a763)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2948, 2927])).
% 0.85/1.07 tff(2950,plain,
% 0.85/1.07 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | c3_1(a741) | c2_1(a763) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c0_1(a763)) | (~c1_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp13 | c3_1(a741) | c2_1(a763) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c0_1(a763)) | (~c1_1(a763)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(2951,plain,
% 0.85/1.07 ((hskp13 | (~ndr1_0) | c2_1(a763) | (~c1_1(a763)) | (~c0_1(a763)) | c3_1(a741) | c0_1(a741) | (~c1_1(a741))) <=> (hskp13 | c3_1(a741) | c2_1(a763) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c0_1(a763)) | (~c1_1(a763)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(2952,plain,
% 0.85/1.07 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a763) | (~c1_1(a763)) | (~c0_1(a763)) | c3_1(a741) | c0_1(a741) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | c3_1(a741) | c2_1(a763) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c0_1(a763)) | (~c1_1(a763))))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[2951])).
% 0.85/1.07 tff(2953,plain,
% 0.85/1.07 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a763) | (~c1_1(a763)) | (~c0_1(a763)) | c3_1(a741) | c0_1(a741) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp13 | c3_1(a741) | c2_1(a763) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c0_1(a763)) | (~c1_1(a763)))),
% 0.85/1.07 inference(transitivity,[status(thm)],[2952, 2950])).
% 0.85/1.07 tff(2954,plain,
% 0.85/1.07 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a763) | (~c1_1(a763)) | (~c0_1(a763)) | c3_1(a741) | c0_1(a741) | (~c1_1(a741)))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(2955,plain,
% 0.85/1.07 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp13 | c3_1(a741) | c2_1(a763) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c0_1(a763)) | (~c1_1(a763))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2954, 2953])).
% 0.85/1.07 tff(2956,plain,
% 0.85/1.07 (hskp13),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2955, 104, 2949, 2941, 2375, 2207, 2933, 177, 32])).
% 0.85/1.07 tff(2957,plain,
% 0.85/1.07 (c3_1(a759)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[882, 2956])).
% 0.85/1.07 tff(2958,plain,
% 0.85/1.07 (~c1_1(a759)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[873, 2956])).
% 0.85/1.07 tff(2959,plain,
% 0.85/1.07 (c2_1(a759)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[890, 2956])).
% 0.85/1.07 tff(2960,plain,
% 0.85/1.07 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c3_1(a741) | c1_1(a759) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a759)) | c0_1(a759))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c3_1(a741) | c1_1(a759) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a759)) | c0_1(a759))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(2961,plain,
% 0.85/1.07 ((hskp7 | (~ndr1_0) | c0_1(a741) | c3_1(a741) | (~c2_1(a741)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759))) <=> (hskp7 | c3_1(a741) | c1_1(a759) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a759)) | c0_1(a759))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(2962,plain,
% 0.85/1.07 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a741) | c3_1(a741) | (~c2_1(a741)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c3_1(a741) | c1_1(a759) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a759)) | c0_1(a759)))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[2961])).
% 0.85/1.07 tff(2963,plain,
% 0.85/1.07 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a741) | c3_1(a741) | (~c2_1(a741)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c3_1(a741) | c1_1(a759) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a759)) | c0_1(a759))),
% 0.85/1.07 inference(transitivity,[status(thm)],[2962, 2960])).
% 0.85/1.07 tff(2964,plain,
% 0.85/1.07 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a741) | c3_1(a741) | (~c2_1(a741)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759)))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(2965,plain,
% 0.85/1.07 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c3_1(a741) | c1_1(a759) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | (~c3_1(a759)) | c0_1(a759)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[2964, 2963])).
% 0.85/1.07 tff(2966,plain,
% 0.85/1.07 (c0_1(a759)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2965, 104, 2378, 2957, 2207, 2958, 177, 1263, 2854])).
% 0.85/1.07 tff(2967,plain,
% 0.85/1.07 (hskp5),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1760, 2966, 2959, 2958, 2957])).
% 0.85/1.07 tff(2968,plain,
% 0.85/1.07 (c2_1(a735)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[421, 2967])).
% 0.85/1.07 tff(2969,plain,
% 0.85/1.07 (c3_1(a735)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[413, 2967])).
% 0.85/1.07 tff(2970,plain,
% 0.85/1.07 (~c0_1(a735)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[427, 2967])).
% 0.85/1.07 tff(2971,plain,
% 0.85/1.07 ($false),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[509, 2970, 2969, 2888, 2876, 2877, 2875, 2968])).
% 0.85/1.07 tff(2972,plain,(c3_1(a741) | c0_1(a741) | hskp11 | c3_1(a734) | c0_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.07 tff(2973,plain,
% 0.85/1.07 (c3_1(a741)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2972, 177, 21, 33, 22])).
% 0.85/1.07 tff(2974,plain,
% 0.85/1.07 ((~c3_1(a741)) | c0_1(a731)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[223, 104, 2375, 2847, 2846, 177, 2845, 121])).
% 0.85/1.07 tff(2975,plain,
% 0.85/1.07 (c0_1(a731)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2974, 2973])).
% 0.85/1.07 tff(2976,plain,
% 0.85/1.07 (hskp5),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2794, 2973, 2375, 177])).
% 0.85/1.07 tff(2977,plain,
% 0.85/1.07 (~c0_1(a735)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[427, 2976])).
% 0.85/1.07 tff(2978,plain,
% 0.85/1.07 (hskp13 | (~c0_1(a731))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1883, 104, 1005, 2847, 22, 33, 2845, 32])).
% 0.85/1.07 tff(2979,plain,
% 0.85/1.07 (hskp13),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2978, 2975])).
% 0.85/1.07 tff(2980,plain,
% 0.85/1.07 (~c1_1(a759)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[873, 2979])).
% 0.85/1.07 tff(2981,plain,
% 0.85/1.07 (c3_1(a735)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[413, 2976])).
% 0.85/1.07 tff(2982,plain,
% 0.85/1.07 (c2_1(a735)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[421, 2976])).
% 0.85/1.07 tff(2983,plain,
% 0.85/1.07 (c3_1(a759)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[882, 2979])).
% 0.85/1.07 tff(2984,plain,
% 0.85/1.07 (c2_1(a759)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[890, 2979])).
% 0.85/1.07 tff(2985,plain,
% 0.85/1.07 ($false),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1769, 104, 2984, 2983, 2982, 2981, 2846, 2980, 2977, 2845, 455, 2975])).
% 0.85/1.07 tff(2986,plain,(c0_1(a741) | c0_1(a734) | c3_1(a734) | hskp11), inference(lemma,lemma(discharge,[]))).
% 0.85/1.07 tff(2987,plain,
% 0.85/1.07 (c0_1(a741)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2986, 33, 22, 21])).
% 0.85/1.07 tff(2988,plain,
% 0.85/1.07 (~hskp7),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[163, 2987])).
% 0.85/1.07 tff(2989,plain,
% 0.85/1.07 (hskp12),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2173, 2988, 33])).
% 0.85/1.07 tff(2990,plain,
% 0.85/1.07 (~c3_1(a755)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2179, 2989])).
% 0.85/1.07 tff(2991,plain,
% 0.85/1.07 (c2_1(a755)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2187, 2989])).
% 0.85/1.07 tff(2992,plain,
% 0.85/1.07 (c1_1(a755)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2195, 2989])).
% 0.85/1.07 tff(2993,plain,
% 0.85/1.07 (hskp27),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2202, 104, 21, 2992, 2991, 2990, 559])).
% 0.85/1.07 tff(2994,plain,
% 0.85/1.07 (c0_1(a750)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[716, 2993])).
% 0.85/1.07 tff(2995,plain,
% 0.85/1.07 (c2_1(a750)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[724, 2993])).
% 0.85/1.07 tff(2996,plain,
% 0.85/1.07 (c1_1(a750)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[732, 2993])).
% 0.85/1.07 tff(2997,plain,
% 0.85/1.07 (~hskp10),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2403, 2377, 2992, 2990, 255, 2376, 1016, 2994, 2996, 2995, 2991])).
% 0.85/1.07 tff(2998,assumption,(hskp5), introduced(assumption)).
% 0.85/1.07 tff(2999,plain,
% 0.85/1.07 (~c0_1(a735)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[427, 2998])).
% 0.85/1.07 tff(3000,plain,
% 0.85/1.07 (c3_1(a735)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[413, 2998])).
% 0.85/1.07 tff(3001,plain,
% 0.85/1.07 (c2_1(a735)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[421, 2998])).
% 0.85/1.07 tff(3002,plain,
% 0.85/1.07 (c2_1(a734)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1191, 104, 2823, 3001, 3000, 1006, 2999, 22, 970])).
% 0.85/1.07 tff(3003,plain,
% 0.85/1.07 (hskp0),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1014, 255, 1006, 33, 22])).
% 0.85/1.07 tff(3004,plain,
% 0.85/1.07 (~c1_1(a730)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[384, 3003])).
% 0.85/1.07 tff(3005,plain,
% 0.85/1.07 (c3_1(a730)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[435, 3003])).
% 0.85/1.07 tff(3006,plain,
% 0.85/1.07 (c0_1(a730)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[443, 3003])).
% 0.85/1.07 tff(3007,plain,
% 0.85/1.07 (~c2_1(a730)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[509, 2999, 3006, 3005, 3000, 3004, 3001])).
% 0.85/1.07 tff(3008,plain,
% 0.85/1.07 (hskp2),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[540, 2999, 255, 3006, 3004, 3001, 3007, 3000])).
% 0.85/1.07 tff(3009,plain,
% 0.85/1.07 (~c2_1(a732)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[282, 3008])).
% 0.85/1.07 tff(3010,plain,
% 0.85/1.07 (~c0_1(a732)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[288, 3008])).
% 0.85/1.07 tff(3011,plain,
% 0.85/1.07 (~c1_1(a732)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2304, 104, 2823, 3001, 3000, 2999, 3010, 3009, 970])).
% 0.85/1.07 tff(3012,plain,
% 0.85/1.07 (c1_1(a732) | (~c2_1(a734))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[958, 104, 744, 802, 801, 22, 33, 3010, 3009, 952])).
% 0.85/1.07 tff(3013,plain,
% 0.85/1.07 ($false),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[3012, 3011, 3002])).
% 0.85/1.07 tff(3014,plain,((~hskp5) | (~c0_1(a750)) | (~c1_1(a750)) | (~c2_1(a750)) | c0_1(a734) | c3_1(a734) | hskp10 | (~c1_1(a734)) | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.85/1.07 tff(3015,plain,
% 0.85/1.07 (~hskp5),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[3014, 2997, 2996, 2995, 22, 33, 2994, 1005, 255])).
% 0.85/1.07 tff(3016,plain,
% 0.85/1.07 (c2_1(a734)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1177, 3015, 33, 1005])).
% 0.85/1.07 tff(3017,plain,
% 0.85/1.07 (c3_1(a744)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[680, 2048])).
% 0.85/1.07 tff(3018,plain,
% 0.85/1.07 ($false),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1269, 104, 1029, 3017, 2049, 2050, 22, 33, 1263, 1533])).
% 0.85/1.07 tff(3019,plain,((~hskp8) | hskp7 | c0_1(a734) | c3_1(a734) | (~c2_1(a734))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.07 tff(3020,plain,
% 0.85/1.07 (~hskp8),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[3019, 3016, 22, 33, 2988])).
% 0.85/1.07 tff(3021,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a746) | c2_1(a746) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | c1_1(a746))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a746) | c2_1(a746) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | c1_1(a746))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(3022,plain,
% 0.85/1.07 (((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a734) | c0_1(a734) | (~c2_1(a734)) | c2_1(a746) | c1_1(a746) | c0_1(a746)) <=> (c0_1(a746) | c2_1(a746) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | c1_1(a746))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(3023,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a734) | c0_1(a734) | (~c2_1(a734)) | c2_1(a746) | c1_1(a746) | c0_1(a746))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a746) | c2_1(a746) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | c1_1(a746)))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[3022])).
% 0.85/1.07 tff(3024,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a734) | c0_1(a734) | (~c2_1(a734)) | c2_1(a746) | c1_1(a746) | c0_1(a746))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a746) | c2_1(a746) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | c1_1(a746))),
% 0.85/1.07 inference(transitivity,[status(thm)],[3023, 3021])).
% 0.85/1.07 tff(3025,plain,
% 0.85/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a750)) | (~c1_1(a750)) | (~c0_1(a750)) | c3_1(a734) | c0_1(a734) | (~c2_1(a734)) | c2_1(a746) | c1_1(a746) | c0_1(a746))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(3026,plain,
% 0.85/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a746) | c2_1(a746) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c0_1(a750)) | (~c2_1(a750)) | (~c1_1(a750)) | c1_1(a746)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[3025, 3024])).
% 0.85/1.07 tff(3027,plain,
% 0.85/1.07 ($false),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[3026, 104, 744, 802, 801, 1051, 1050, 22, 33, 952, 1533, 2692])).
% 0.85/1.07 tff(3028,plain,((~hskp9) | (~c0_1(a750)) | (~c1_1(a750)) | (~c2_1(a750)) | c0_1(a734) | c3_1(a734) | (~c2_1(a734))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.07 tff(3029,plain,
% 0.85/1.07 (~hskp9),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[3028, 3016, 2996, 2995, 22, 33, 2994])).
% 0.85/1.07 tff(3030,plain,
% 0.85/1.07 (~hskp18),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1842, 3029, 255, 3020, 22, 33, 3016])).
% 0.85/1.07 tff(3031,plain,
% 0.85/1.07 (hskp18 | c3_1(a750)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1622, 104, 21, 2994, 2996, 1075])).
% 0.85/1.07 tff(3032,plain,
% 0.85/1.07 (c3_1(a750)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[3031, 3030])).
% 0.85/1.07 tff(3033,plain,
% 0.85/1.07 (hskp16 | (~c2_1(a734)) | (~c3_1(a750))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1959, 104, 2994, 2995, 1005, 22, 754])).
% 0.85/1.07 tff(3034,plain,
% 0.85/1.07 (hskp16),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[3033, 3032, 3016])).
% 0.85/1.07 tff(3035,plain,
% 0.85/1.07 (~c3_1(a764)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[791, 3034])).
% 0.85/1.07 tff(3036,plain,
% 0.85/1.07 (c0_1(a764)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[809, 3034])).
% 0.85/1.07 tff(3037,plain,
% 0.85/1.07 (~c1_1(a764)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1603, 104, 255, 2994, 2995, 3036, 3035, 743, 3032])).
% 0.85/1.07 tff(3038,plain,
% 0.85/1.07 (c2_1(a764)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[799, 3034])).
% 0.85/1.07 tff(3039,plain,
% 0.85/1.07 ($false),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1611, 104, 3015, 3038, 2377, 2376, 3035, 1016, 1456, 3037])).
% 0.85/1.07 tff(3040,plain,(hskp1 | c0_1(a734) | hskp11 | c3_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.07 tff(3041,plain,
% 0.85/1.07 (hskp1),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[3040, 33, 21, 22])).
% 0.85/1.07 tff(3042,plain,
% 0.85/1.07 (~c2_1(a731)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[58, 3041])).
% 0.85/1.07 tff(3043,plain,
% 0.85/1.07 (c3_1(a731)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[66, 3041])).
% 0.85/1.07 tff(3044,plain,
% 0.85/1.07 (c1_1(a731)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[74, 3041])).
% 0.85/1.07 tff(3045,plain,
% 0.85/1.07 (c2_1(a734)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2372, 104, 21, 1005, 3044, 3043, 22, 3042, 43])).
% 0.85/1.07 tff(3046,plain,
% 0.85/1.07 (~hskp8),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[3019, 3045, 22, 33, 2988])).
% 0.85/1.07 tff(3047,plain,
% 0.85/1.07 (hskp0),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1182, 3046])).
% 0.85/1.07 tff(3048,plain,
% 0.85/1.07 (~c1_1(a730)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[384, 3047])).
% 0.85/1.07 tff(3049,plain,
% 0.85/1.07 (c3_1(a730)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[435, 3047])).
% 0.85/1.07 tff(3050,plain,
% 0.85/1.07 (c2_1(a730)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1901, 104, 21, 3044, 3043, 3049, 3042, 3048, 360])).
% 0.85/1.07 tff(3051,plain,
% 0.85/1.07 (c0_1(a730)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[443, 3047])).
% 0.85/1.07 tff(3052,plain,
% 0.85/1.07 (hskp28 | (~c2_1(a730))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2894, 104, 21, 3051, 3049, 2887])).
% 0.85/1.07 tff(3053,plain,
% 0.85/1.07 (hskp28),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[3052, 3050])).
% 0.85/1.07 tff(3054,plain,
% 0.85/1.07 (c3_1(a784)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2903, 3053])).
% 0.85/1.07 tff(3055,plain,
% 0.85/1.07 (c1_1(a784)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2911, 3053])).
% 0.85/1.07 tff(3056,plain,
% 0.85/1.07 (c0_1(a784)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2919, 3053])).
% 0.85/1.07 tff(3057,plain,
% 0.85/1.07 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a784)) | (~c3_1(a784)) | (~c0_1(a784)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a784)) | (~c3_1(a784)) | (~c0_1(a784)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(3058,plain,
% 0.85/1.07 ((hskp15 | (~ndr1_0) | (~c3_1(a784)) | (~c1_1(a784)) | (~c0_1(a784)) | c3_1(a734) | c0_1(a734) | (~c2_1(a734))) <=> (hskp15 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a784)) | (~c3_1(a784)) | (~c0_1(a784)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(3059,plain,
% 0.85/1.07 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a784)) | (~c1_1(a784)) | (~c0_1(a784)) | c3_1(a734) | c0_1(a734) | (~c2_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a784)) | (~c3_1(a784)) | (~c0_1(a784))))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[3058])).
% 0.85/1.07 tff(3060,plain,
% 0.85/1.07 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a784)) | (~c1_1(a784)) | (~c0_1(a784)) | c3_1(a734) | c0_1(a734) | (~c2_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a784)) | (~c3_1(a784)) | (~c0_1(a784)))),
% 0.85/1.07 inference(transitivity,[status(thm)],[3059, 3057])).
% 0.85/1.07 tff(3061,plain,
% 0.85/1.07 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a784)) | (~c1_1(a784)) | (~c0_1(a784)) | c3_1(a734) | c0_1(a734) | (~c2_1(a734)))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(3062,plain,
% 0.85/1.07 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a784)) | (~c3_1(a784)) | (~c0_1(a784))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[3061, 3060])).
% 0.85/1.07 tff(3063,plain,
% 0.85/1.07 (hskp15),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[3062, 104, 3056, 3055, 3054, 22, 33, 2864, 3045])).
% 0.85/1.07 tff(3064,plain,
% 0.85/1.07 (~c2_1(a763)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2932, 3063])).
% 0.85/1.07 tff(3065,plain,
% 0.85/1.07 (c1_1(a763)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2940, 3063])).
% 0.85/1.07 tff(3066,plain,
% 0.85/1.07 (c0_1(a763)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[2948, 3063])).
% 0.85/1.07 tff(3067,plain,
% 0.85/1.07 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | c2_1(a763) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c1_1(a734)) | (~c0_1(a763)) | (~c1_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp13 | c2_1(a763) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c1_1(a734)) | (~c0_1(a763)) | (~c1_1(a763)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(3068,plain,
% 0.85/1.07 ((hskp13 | (~ndr1_0) | c2_1(a763) | (~c1_1(a763)) | (~c0_1(a763)) | c3_1(a734) | c0_1(a734) | (~c1_1(a734))) <=> (hskp13 | c2_1(a763) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c1_1(a734)) | (~c0_1(a763)) | (~c1_1(a763)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(3069,plain,
% 0.85/1.07 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a763) | (~c1_1(a763)) | (~c0_1(a763)) | c3_1(a734) | c0_1(a734) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | c2_1(a763) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c1_1(a734)) | (~c0_1(a763)) | (~c1_1(a763))))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[3068])).
% 0.91/1.08 tff(3070,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a763) | (~c1_1(a763)) | (~c0_1(a763)) | c3_1(a734) | c0_1(a734) | (~c1_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp13 | c2_1(a763) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c1_1(a734)) | (~c0_1(a763)) | (~c1_1(a763)))),
% 0.91/1.08 inference(transitivity,[status(thm)],[3069, 3067])).
% 0.91/1.08 tff(3071,plain,
% 0.91/1.08 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a763) | (~c1_1(a763)) | (~c0_1(a763)) | c3_1(a734) | c0_1(a734) | (~c1_1(a734)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3072,plain,
% 0.91/1.08 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp13 | c2_1(a763) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c1_1(a734)) | (~c0_1(a763)) | (~c1_1(a763))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3071, 3070])).
% 0.91/1.08 tff(3073,plain,
% 0.91/1.08 (hskp13),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3072, 104, 3066, 3065, 1005, 3064, 22, 33, 32])).
% 0.91/1.08 tff(3074,plain,
% 0.91/1.08 (c3_1(a759)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[882, 3073])).
% 0.91/1.08 tff(3075,plain,
% 0.91/1.08 (~c1_1(a759)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[873, 3073])).
% 0.91/1.08 tff(3076,plain,
% 0.91/1.08 (c2_1(a759)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[890, 3073])).
% 0.91/1.08 tff(3077,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a759) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c3_1(a759)) | c0_1(a759))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a759) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c3_1(a759)) | c0_1(a759))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3078,plain,
% 0.91/1.08 ((hskp7 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759))) <=> (hskp7 | c1_1(a759) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c3_1(a759)) | c0_1(a759))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3079,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a759) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c3_1(a759)) | c0_1(a759)))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[3078])).
% 0.91/1.08 tff(3080,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a759) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c3_1(a759)) | c0_1(a759))),
% 0.91/1.08 inference(transitivity,[status(thm)],[3079, 3077])).
% 0.91/1.08 tff(3081,plain,
% 0.91/1.08 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c1_1(a759) | c0_1(a759) | (~c3_1(a759)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3082,plain,
% 0.91/1.08 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a759) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | (~c3_1(a759)) | c0_1(a759)),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3081, 3080])).
% 0.91/1.08 tff(3083,plain,
% 0.91/1.08 (c0_1(a759)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3082, 104, 2988, 3074, 3075, 22, 33, 1263, 3045])).
% 0.91/1.08 tff(3084,plain,
% 0.91/1.08 (hskp5),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1760, 3083, 3076, 3075, 3074])).
% 0.91/1.08 tff(3085,plain,
% 0.91/1.08 (c2_1(a735)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[421, 3084])).
% 0.91/1.08 tff(3086,plain,
% 0.91/1.08 (c3_1(a735)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[413, 3084])).
% 0.91/1.08 tff(3087,plain,
% 0.91/1.08 (~c0_1(a735)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[427, 3084])).
% 0.91/1.08 tff(3088,plain,
% 0.91/1.08 ($false),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[509, 3087, 3086, 3051, 3049, 3050, 3048, 3085])).
% 0.91/1.08 tff(3089,plain,(c3_1(a734) | c0_1(a734) | hskp11), inference(lemma,lemma(discharge,[]))).
% 0.91/1.08 tff(3090,plain,
% 0.91/1.08 (c3_1(a734)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3089, 22, 21])).
% 0.91/1.08 tff(3091,plain,
% 0.91/1.08 (~hskp4),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2745, 3090])).
% 0.91/1.08 tff(3092,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | c2_1(a744) | (~c3_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | c2_1(a744) | (~c3_1(a744)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3093,plain,
% 0.91/1.08 ((hskp11 | (~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c1_1(a744) | c2_1(a744) | (~c3_1(a744))) <=> (hskp11 | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | c2_1(a744) | (~c3_1(a744)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3094,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c1_1(a744) | c2_1(a744) | (~c3_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | c2_1(a744) | (~c3_1(a744))))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[3093])).
% 0.91/1.08 tff(3095,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c1_1(a744) | c2_1(a744) | (~c3_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | c2_1(a744) | (~c3_1(a744)))),
% 0.91/1.08 inference(transitivity,[status(thm)],[3094, 3092])).
% 0.91/1.08 tff(3096,plain,
% 0.91/1.08 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a731) | (~c3_1(a731)) | (~c1_1(a731)) | c1_1(a744) | c2_1(a744) | (~c3_1(a744)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3097,plain,
% 0.91/1.08 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a744) | c2_1(a731) | (~ndr1_0) | (~c3_1(a731)) | (~c1_1(a731)) | c2_1(a744) | (~c3_1(a744))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3096, 3095])).
% 0.91/1.08 tff(3098,plain,
% 0.91/1.08 (c2_1(a744)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3097, 104, 21, 1290, 2026, 2129, 2424, 1033, 360])).
% 0.91/1.08 tff(3099,plain,
% 0.91/1.08 (c0_1(a731)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1311, 217, 104, 2026, 2425, 2424, 1033, 254, 3098])).
% 0.91/1.08 tff(3100,plain,
% 0.91/1.08 ((~c0_1(a731)) | (~c2_1(a744))),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1119, 104, 1290, 2129, 2425, 2424, 1033, 455])).
% 0.91/1.08 tff(3101,plain,
% 0.91/1.08 ($false),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3100, 3099, 3098])).
% 0.91/1.08 tff(3102,plain,(hskp0 | (~c3_1(a731)) | c2_1(a731) | (~c1_1(a731)) | hskp11), inference(lemma,lemma(discharge,[]))).
% 0.91/1.08 tff(3103,plain,
% 0.91/1.08 (hskp0),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3102, 67, 59, 75, 21])).
% 0.91/1.08 tff(3104,plain,
% 0.91/1.08 (c0_1(a730)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[443, 3103])).
% 0.91/1.08 tff(3105,plain,
% 0.91/1.08 (c3_1(a730)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[435, 3103])).
% 0.91/1.08 tff(3106,plain,
% 0.91/1.08 (~c1_1(a730)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[384, 3103])).
% 0.91/1.08 tff(3107,plain,
% 0.91/1.08 (hskp5),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2737, 3106, 166, 67, 75, 3105, 3104, 59])).
% 0.91/1.08 tff(3108,plain,
% 0.91/1.08 (c2_1(a735)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[421, 3107])).
% 0.91/1.08 tff(3109,plain,
% 0.91/1.08 (~c0_1(a735)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[427, 3107])).
% 0.91/1.08 tff(3110,plain,
% 0.91/1.08 (c3_1(a735)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[413, 3107])).
% 0.91/1.08 tff(3111,plain,
% 0.91/1.08 (~c2_1(a730)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[509, 3110, 3105, 3109, 3104, 3106, 3108])).
% 0.91/1.08 tff(3112,plain,
% 0.91/1.08 ($false),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1901, 104, 21, 75, 67, 3105, 59, 3106, 360, 3111])).
% 0.91/1.08 tff(3113,plain,((~hskp1) | hskp11 | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.91/1.08 tff(3114,plain,
% 0.91/1.08 (~hskp1),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3113, 3091, 21])).
% 0.91/1.08 tff(3115,plain,
% 0.91/1.08 (hskp7),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[141, 3114, 3091])).
% 0.91/1.08 tff(3116,plain,
% 0.91/1.08 (((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | c0_1(a744) | c1_1(a744) | (~ndr1_0) | c2_1(a744))) <=> ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | hskp1 | c0_1(a744) | c1_1(a744) | (~ndr1_0) | c2_1(a744))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3117,plain,
% 0.91/1.08 ((hskp0 | hskp1 | (~ndr1_0) | c2_1(a744) | c1_1(a744) | c0_1(a744)) <=> (hskp0 | hskp1 | c0_1(a744) | c1_1(a744) | (~ndr1_0) | c2_1(a744))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3118,plain,
% 0.91/1.08 (((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | (~ndr1_0) | c2_1(a744) | c1_1(a744) | c0_1(a744))) <=> ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | c0_1(a744) | c1_1(a744) | (~ndr1_0) | c2_1(a744)))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[3117])).
% 0.91/1.08 tff(3119,plain,
% 0.91/1.08 (((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | (~ndr1_0) | c2_1(a744) | c1_1(a744) | c0_1(a744))) <=> ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | hskp1 | c0_1(a744) | c1_1(a744) | (~ndr1_0) | c2_1(a744))),
% 0.91/1.08 inference(transitivity,[status(thm)],[3118, 3116])).
% 0.91/1.08 tff(3120,plain,
% 0.91/1.08 ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | hskp1 | (~ndr1_0) | c2_1(a744) | c1_1(a744) | c0_1(a744))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3121,plain,
% 0.91/1.08 ((~![U: $i] : (hskp0 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | hskp1 | c0_1(a744) | c1_1(a744) | (~ndr1_0) | c2_1(a744)),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3120, 3119])).
% 0.91/1.08 tff(3122,plain,
% 0.91/1.08 (c2_1(a744)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3121, 217, 104, 255, 2425, 2424, 236])).
% 0.91/1.08 tff(3123,plain,
% 0.91/1.08 (hskp2 | (~c2_1(a744))),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1433, 104, 255, 2425, 2424, 266])).
% 0.91/1.08 tff(3124,plain,
% 0.91/1.08 (hskp2),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3123, 3122])).
% 0.91/1.08 tff(3125,plain,
% 0.91/1.08 (~c2_1(a732)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[282, 3124])).
% 0.91/1.08 tff(3126,plain,
% 0.91/1.08 (~c0_1(a732)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[288, 3124])).
% 0.91/1.08 tff(3127,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | c0_1(a744) | c1_1(a744) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c2_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a744) | c1_1(a744) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c2_1(a744)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3128,plain,
% 0.91/1.08 ((hskp0 | (~ndr1_0) | c2_1(a732) | c0_1(a732) | (~c1_1(a732)) | c1_1(a744) | c0_1(a744) | (~c2_1(a744))) <=> (hskp0 | c0_1(a744) | c1_1(a744) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c2_1(a744)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3129,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a732) | c0_1(a732) | (~c1_1(a732)) | c1_1(a744) | c0_1(a744) | (~c2_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | c0_1(a744) | c1_1(a744) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c2_1(a744))))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[3128])).
% 0.91/1.08 tff(3130,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a732) | c0_1(a732) | (~c1_1(a732)) | c1_1(a744) | c0_1(a744) | (~c2_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a744) | c1_1(a744) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c2_1(a744)))),
% 0.91/1.08 inference(transitivity,[status(thm)],[3129, 3127])).
% 0.91/1.08 tff(3131,plain,
% 0.91/1.08 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a732) | c0_1(a732) | (~c1_1(a732)) | c1_1(a744) | c0_1(a744) | (~c2_1(a744)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3132,plain,
% 0.91/1.08 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp0 | c0_1(a744) | c1_1(a744) | c0_1(a732) | c2_1(a732) | (~ndr1_0) | (~c1_1(a732)) | (~c2_1(a744))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3131, 3130])).
% 0.91/1.08 tff(3133,plain,
% 0.91/1.08 (~c1_1(a732)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3132, 217, 104, 2425, 2424, 3126, 3125, 254, 3122])).
% 0.91/1.08 tff(3134,plain,
% 0.91/1.08 ($false),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[302, 217, 104, 255, 3126, 3125, 236, 3133])).
% 0.91/1.08 tff(3135,plain,(hskp0 | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.91/1.08 tff(3136,plain,
% 0.91/1.08 (hskp0),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3135, 255])).
% 0.91/1.08 tff(3137,plain,
% 0.91/1.08 (~c1_1(a730)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[384, 3136])).
% 0.91/1.08 tff(3138,plain,
% 0.91/1.08 (hskp7),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[141, 255, 3091])).
% 0.91/1.08 tff(3139,plain,
% 0.91/1.08 (c1_1(a741)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[149, 3138])).
% 0.91/1.08 tff(3140,plain,
% 0.91/1.08 (c3_1(a741)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[157, 3138])).
% 0.91/1.08 tff(3141,assumption,(c3_1(a734)), introduced(assumption)).
% 0.91/1.08 tff(3142,plain,
% 0.91/1.08 (~hskp4),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2745, 3141])).
% 0.91/1.08 tff(3143,plain,
% 0.91/1.08 (~hskp2),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2677, 3142, 396])).
% 0.91/1.08 tff(3144,plain,
% 0.91/1.08 (c1_1(a734) | (~c2_1(a734))),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[272, 104, 3143, 255, 22, 266])).
% 0.91/1.08 tff(3145,plain,
% 0.91/1.08 (~c2_1(a734)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3144, 44])).
% 0.91/1.08 tff(3146,plain,
% 0.91/1.08 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp6 | hskp4 | c0_1(a734) | (~c3_1(a734)) | (~ndr1_0) | c2_1(a734))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp6 | hskp4 | c0_1(a734) | (~c3_1(a734)) | (~ndr1_0) | c2_1(a734))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3147,plain,
% 0.91/1.08 ((hskp6 | hskp4 | (~ndr1_0) | c2_1(a734) | c0_1(a734) | (~c3_1(a734))) <=> (hskp6 | hskp4 | c0_1(a734) | (~c3_1(a734)) | (~ndr1_0) | c2_1(a734))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3148,plain,
% 0.91/1.08 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c2_1(a734) | c0_1(a734) | (~c3_1(a734)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp6 | hskp4 | c0_1(a734) | (~c3_1(a734)) | (~ndr1_0) | c2_1(a734)))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[3147])).
% 0.91/1.08 tff(3149,plain,
% 0.91/1.08 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c2_1(a734) | c0_1(a734) | (~c3_1(a734)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp6 | hskp4 | c0_1(a734) | (~c3_1(a734)) | (~ndr1_0) | c2_1(a734))),
% 0.91/1.08 inference(transitivity,[status(thm)],[3148, 3146])).
% 0.91/1.08 tff(3150,plain,
% 0.91/1.08 ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c2_1(a734) | c0_1(a734) | (~c3_1(a734)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3151,plain,
% 0.91/1.08 ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp6 | hskp4 | c0_1(a734) | (~c3_1(a734)) | (~ndr1_0) | c2_1(a734)),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3150, 3149])).
% 0.91/1.08 tff(3152,plain,
% 0.91/1.08 (hskp6 | c0_1(a734) | c2_1(a734)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3151, 104, 3142, 3141, 176])).
% 0.91/1.08 tff(3153,plain,
% 0.91/1.08 (hskp6),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3152, 3145, 22])).
% 0.91/1.08 tff(3154,plain,
% 0.91/1.08 (~c2_1(a738)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[191, 3153])).
% 0.91/1.08 tff(3155,plain,
% 0.91/1.08 (c1_1(a738)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[205, 3153])).
% 0.91/1.08 tff(3156,plain,
% 0.91/1.08 (~hskp11),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2659, 3142, 396])).
% 0.91/1.08 tff(3157,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c1_1(a734) | c2_1(a738) | (~c3_1(a734)) | (~ndr1_0) | c2_1(a734) | (~c3_1(a738)) | (~c1_1(a738)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a734) | c2_1(a738) | (~c3_1(a734)) | (~ndr1_0) | c2_1(a734) | (~c3_1(a738)) | (~c1_1(a738)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3158,plain,
% 0.91/1.08 ((hskp11 | (~ndr1_0) | c2_1(a738) | (~c3_1(a738)) | (~c1_1(a738)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734))) <=> (hskp11 | c1_1(a734) | c2_1(a738) | (~c3_1(a734)) | (~ndr1_0) | c2_1(a734) | (~c3_1(a738)) | (~c1_1(a738)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3159,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a738) | (~c3_1(a738)) | (~c1_1(a738)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c1_1(a734) | c2_1(a738) | (~c3_1(a734)) | (~ndr1_0) | c2_1(a734) | (~c3_1(a738)) | (~c1_1(a738))))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[3158])).
% 0.91/1.08 tff(3160,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a738) | (~c3_1(a738)) | (~c1_1(a738)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a734) | c2_1(a738) | (~c3_1(a734)) | (~ndr1_0) | c2_1(a734) | (~c3_1(a738)) | (~c1_1(a738)))),
% 0.91/1.08 inference(transitivity,[status(thm)],[3159, 3157])).
% 0.91/1.08 tff(3161,plain,
% 0.91/1.08 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a738) | (~c3_1(a738)) | (~c1_1(a738)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3162,plain,
% 0.91/1.08 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a734) | c2_1(a738) | (~c3_1(a734)) | (~ndr1_0) | c2_1(a734) | (~c3_1(a738)) | (~c1_1(a738))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3161, 3160])).
% 0.91/1.08 tff(3163,plain,
% 0.91/1.08 (~c3_1(a738)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3162, 104, 3156, 3155, 44, 3154, 3141, 360, 3145])).
% 0.91/1.08 tff(3164,plain,
% 0.91/1.08 (~c0_1(a738)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[197, 3153])).
% 0.91/1.08 tff(3165,plain,
% 0.91/1.08 (~hskp9),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2718, 3142, 396])).
% 0.91/1.08 tff(3166,plain,
% 0.91/1.08 (((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | c0_1(a738) | c2_1(a738) | (~ndr1_0) | c3_1(a738))) <=> ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp5 | c0_1(a738) | c2_1(a738) | (~ndr1_0) | c3_1(a738))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3167,plain,
% 0.91/1.08 ((hskp9 | hskp5 | (~ndr1_0) | c2_1(a738) | c0_1(a738) | c3_1(a738)) <=> (hskp9 | hskp5 | c0_1(a738) | c2_1(a738) | (~ndr1_0) | c3_1(a738))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3168,plain,
% 0.91/1.08 (((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | (~ndr1_0) | c2_1(a738) | c0_1(a738) | c3_1(a738))) <=> ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | c0_1(a738) | c2_1(a738) | (~ndr1_0) | c3_1(a738)))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[3167])).
% 0.91/1.08 tff(3169,plain,
% 0.91/1.08 (((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | (~ndr1_0) | c2_1(a738) | c0_1(a738) | c3_1(a738))) <=> ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp5 | c0_1(a738) | c2_1(a738) | (~ndr1_0) | c3_1(a738))),
% 0.91/1.08 inference(transitivity,[status(thm)],[3168, 3166])).
% 0.91/1.08 tff(3170,plain,
% 0.91/1.08 ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp5 | (~ndr1_0) | c2_1(a738) | c0_1(a738) | c3_1(a738))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3171,plain,
% 0.91/1.08 ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp5 | c0_1(a738) | c2_1(a738) | (~ndr1_0) | c3_1(a738)),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3170, 3169])).
% 0.91/1.08 tff(3172,plain,
% 0.91/1.08 ($false),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3171, 104, 3165, 396, 3164, 3154, 1085, 3163])).
% 0.91/1.08 tff(3173,plain,(c1_1(a734) | hskp5 | (~c3_1(a734)) | c0_1(a734) | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.91/1.08 tff(3174,plain,
% 0.91/1.08 (c1_1(a734)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3173, 22, 2740, 396, 255])).
% 0.91/1.08 tff(3175,plain,
% 0.91/1.08 (hskp6),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3152, 1478, 22])).
% 0.91/1.08 tff(3176,plain,
% 0.91/1.08 (~c2_1(a738)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[191, 3175])).
% 0.91/1.08 tff(3177,plain,
% 0.91/1.08 (~c0_1(a738)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[197, 3175])).
% 0.91/1.08 tff(3178,plain,
% 0.91/1.08 (c1_1(a738)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[205, 3175])).
% 0.91/1.08 tff(3179,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a738) | c2_1(a738) | (~c3_1(a734)) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c1_1(a738)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a738) | c2_1(a738) | (~c3_1(a734)) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c1_1(a738)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3180,plain,
% 0.91/1.08 ((hskp11 | (~ndr1_0) | c2_1(a734) | (~c3_1(a734)) | (~c1_1(a734)) | c0_1(a738) | c2_1(a738) | (~c1_1(a738))) <=> (hskp11 | c0_1(a738) | c2_1(a738) | (~c3_1(a734)) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c1_1(a738)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3181,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a734) | (~c3_1(a734)) | (~c1_1(a734)) | c0_1(a738) | c2_1(a738) | (~c1_1(a738)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a738) | c2_1(a738) | (~c3_1(a734)) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c1_1(a738))))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[3180])).
% 0.91/1.08 tff(3182,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a734) | (~c3_1(a734)) | (~c1_1(a734)) | c0_1(a738) | c2_1(a738) | (~c1_1(a738)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a738) | c2_1(a738) | (~c3_1(a734)) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c1_1(a738)))),
% 0.91/1.08 inference(transitivity,[status(thm)],[3181, 3179])).
% 0.91/1.08 tff(3183,plain,
% 0.91/1.08 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a734) | (~c3_1(a734)) | (~c1_1(a734)) | c0_1(a738) | c2_1(a738) | (~c1_1(a738)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3184,plain,
% 0.91/1.08 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a738) | c2_1(a738) | (~c3_1(a734)) | (~ndr1_0) | c2_1(a734) | (~c1_1(a734)) | (~c1_1(a738))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3183, 3182])).
% 0.91/1.08 tff(3185,plain,
% 0.91/1.08 ($false),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3184, 104, 21, 3178, 1006, 3177, 3176, 3141, 43, 1478])).
% 0.91/1.08 tff(3186,plain,(c2_1(a734) | hskp11 | (~c1_1(a734)) | (~c3_1(a734)) | c0_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.08 tff(3187,plain,
% 0.91/1.08 (c2_1(a734)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3186, 3174, 2748, 2740, 22])).
% 0.91/1.08 tff(3188,plain,
% 0.91/1.08 (~hskp25),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2279, 3187, 2459, 2458, 2457, 255, 22, 3174, 396])).
% 0.91/1.08 tff(3189,plain,
% 0.91/1.08 (~hskp9),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2718, 2746, 396])).
% 0.91/1.08 tff(3190,plain,
% 0.91/1.08 (c3_1(a775) | (~c0_1(a775))),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1662, 104, 1656, 1655, 2470, 1654])).
% 0.91/1.08 tff(3191,plain,
% 0.91/1.08 (~c0_1(a775)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3190, 2469])).
% 0.91/1.08 tff(3192,plain,
% 0.91/1.08 (c3_1(a775) | c0_1(a775)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2127, 104, 1655, 396, 2470, 1085])).
% 0.91/1.08 tff(3193,plain,
% 0.91/1.08 ($false),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3192, 3191, 2469])).
% 0.91/1.08 tff(3194,plain,(c3_1(a775) | hskp9 | hskp5 | c2_1(a775) | hskp25), inference(lemma,lemma(discharge,[]))).
% 0.91/1.08 tff(3195,plain,
% 0.91/1.08 (c3_1(a775)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3194, 2470, 396, 3189, 1656])).
% 0.91/1.08 tff(3196,plain,
% 0.91/1.08 (c2_1(a734)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3186, 1006, 2748, 2740, 22])).
% 0.91/1.08 tff(3197,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a775) | (~c3_1(a775)) | c0_1(a734) | (~c3_1(a734)) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734)) | c0_1(a775))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a775) | (~c3_1(a775)) | c0_1(a734) | (~c3_1(a734)) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734)) | c0_1(a775))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3198,plain,
% 0.91/1.08 (((~ndr1_0) | (~c2_1(a734)) | (~c3_1(a734)) | (~c1_1(a734)) | c0_1(a734) | (~c2_1(a734)) | (~c3_1(a734)) | c2_1(a775) | c0_1(a775) | (~c3_1(a775))) <=> (c2_1(a775) | (~c3_1(a775)) | c0_1(a734) | (~c3_1(a734)) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734)) | c0_1(a775))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3199,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a734)) | (~c3_1(a734)) | (~c1_1(a734)) | c0_1(a734) | (~c2_1(a734)) | (~c3_1(a734)) | c2_1(a775) | c0_1(a775) | (~c3_1(a775)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a775) | (~c3_1(a775)) | c0_1(a734) | (~c3_1(a734)) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734)) | c0_1(a775)))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[3198])).
% 0.91/1.08 tff(3200,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a734)) | (~c3_1(a734)) | (~c1_1(a734)) | c0_1(a734) | (~c2_1(a734)) | (~c3_1(a734)) | c2_1(a775) | c0_1(a775) | (~c3_1(a775)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a775) | (~c3_1(a775)) | c0_1(a734) | (~c3_1(a734)) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734)) | c0_1(a775))),
% 0.91/1.09 inference(transitivity,[status(thm)],[3199, 3197])).
% 0.91/1.09 tff(3201,plain,
% 0.91/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a734)) | (~c3_1(a734)) | (~c1_1(a734)) | c0_1(a734) | (~c2_1(a734)) | (~c3_1(a734)) | c2_1(a775) | c0_1(a775) | (~c3_1(a775)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3202,plain,
% 0.91/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a775) | (~c3_1(a775)) | c0_1(a734) | (~c3_1(a734)) | (~ndr1_0) | (~c2_1(a734)) | (~c1_1(a734)) | c0_1(a775)),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3201, 3200])).
% 0.91/1.09 tff(3203,plain,
% 0.91/1.09 ((~c3_1(a775)) | c0_1(a775)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3202, 104, 1006, 2470, 22, 2740, 2537, 3196])).
% 0.91/1.09 tff(3204,plain,
% 0.91/1.09 (c0_1(a775)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3203, 3195])).
% 0.91/1.09 tff(3205,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c1_1(a775) | c2_1(a775) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c0_1(a775)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c1_1(a775) | c2_1(a775) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c0_1(a775)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3206,plain,
% 0.91/1.09 ((hskp2 | (~ndr1_0) | c2_1(a775) | c1_1(a775) | (~c0_1(a775)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741))) <=> (hskp2 | c1_1(a775) | c2_1(a775) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c0_1(a775)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3207,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a775) | c1_1(a775) | (~c0_1(a775)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c1_1(a775) | c2_1(a775) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c0_1(a775))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[3206])).
% 0.91/1.09 tff(3208,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a775) | c1_1(a775) | (~c0_1(a775)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c1_1(a775) | c2_1(a775) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c0_1(a775)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[3207, 3205])).
% 0.91/1.09 tff(3209,plain,
% 0.91/1.09 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a775) | c1_1(a775) | (~c0_1(a775)) | c0_1(a741) | (~c3_1(a741)) | (~c1_1(a741)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3210,plain,
% 0.91/1.09 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c1_1(a775) | c2_1(a775) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c3_1(a741)) | (~c0_1(a775))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3209, 3208])).
% 0.91/1.09 tff(3211,plain,
% 0.91/1.09 (c1_1(a775) | (~c0_1(a775))),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3210, 104, 2747, 207, 178, 2470, 177, 530])).
% 0.91/1.09 tff(3212,plain,
% 0.91/1.09 (c1_1(a775)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3211, 3204])).
% 0.91/1.09 tff(3213,plain,
% 0.91/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a775) | (~c3_1(a775)) | c0_1(a734) | (~c3_1(a734)) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a734)) | (~c0_1(a775)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a775) | (~c3_1(a775)) | c0_1(a734) | (~c3_1(a734)) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a734)) | (~c0_1(a775)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3214,plain,
% 0.91/1.09 (((~ndr1_0) | c2_1(a775) | (~c3_1(a775)) | (~c0_1(a775)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a734) | (~c3_1(a734)) | (~c2_1(a734))) <=> (c2_1(a775) | (~c3_1(a775)) | c0_1(a734) | (~c3_1(a734)) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a734)) | (~c0_1(a775)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3215,plain,
% 0.91/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a775) | (~c3_1(a775)) | (~c0_1(a775)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a734) | (~c3_1(a734)) | (~c2_1(a734)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a775) | (~c3_1(a775)) | c0_1(a734) | (~c3_1(a734)) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a734)) | (~c0_1(a775))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[3214])).
% 0.91/1.09 tff(3216,plain,
% 0.91/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a775) | (~c3_1(a775)) | (~c0_1(a775)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a734) | (~c3_1(a734)) | (~c2_1(a734)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a775) | (~c3_1(a775)) | c0_1(a734) | (~c3_1(a734)) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a734)) | (~c0_1(a775)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[3215, 3213])).
% 0.91/1.09 tff(3217,plain,
% 0.91/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a775) | (~c3_1(a775)) | (~c0_1(a775)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a734) | (~c3_1(a734)) | (~c2_1(a734)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3218,plain,
% 0.91/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a775) | (~c3_1(a775)) | c0_1(a734) | (~c3_1(a734)) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a734)) | (~c0_1(a775))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3217, 3216])).
% 0.91/1.09 tff(3219,plain,
% 0.91/1.09 ((~c3_1(a775)) | (~c2_1(a730)) | (~c0_1(a775))),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3218, 104, 2458, 2470, 22, 2740, 2457, 455, 3196])).
% 0.91/1.09 tff(3220,plain,
% 0.91/1.09 (~c2_1(a730)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3219, 3204, 3195])).
% 0.91/1.09 tff(3221,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a775) | (~c3_1(a775)) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c1_1(a775)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a775) | (~c3_1(a775)) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c1_1(a775)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3222,plain,
% 0.91/1.09 ((hskp11 | (~ndr1_0) | c2_1(a775) | (~c3_1(a775)) | (~c1_1(a775)) | c1_1(a730) | c2_1(a730) | (~c3_1(a730))) <=> (hskp11 | c2_1(a775) | (~c3_1(a775)) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c1_1(a775)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3223,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a775) | (~c3_1(a775)) | (~c1_1(a775)) | c1_1(a730) | c2_1(a730) | (~c3_1(a730)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a775) | (~c3_1(a775)) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c1_1(a775))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[3222])).
% 0.91/1.09 tff(3224,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a775) | (~c3_1(a775)) | (~c1_1(a775)) | c1_1(a730) | c2_1(a730) | (~c3_1(a730)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a775) | (~c3_1(a775)) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c1_1(a775)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[3223, 3221])).
% 0.91/1.09 tff(3225,plain,
% 0.91/1.09 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a775) | (~c3_1(a775)) | (~c1_1(a775)) | c1_1(a730) | c2_1(a730) | (~c3_1(a730)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3226,plain,
% 0.91/1.09 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a775) | (~c3_1(a775)) | c1_1(a730) | (~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c1_1(a775))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3225, 3224])).
% 0.91/1.09 tff(3227,plain,
% 0.91/1.09 ((~c3_1(a775)) | c2_1(a730) | (~c1_1(a775))),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3226, 104, 2748, 2458, 2470, 2457, 360])).
% 0.91/1.09 tff(3228,plain,
% 0.91/1.09 ($false),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3227, 3220, 3212, 3195])).
% 0.91/1.09 tff(3229,plain,(c2_1(a775) | c0_1(a734) | (~c1_1(a741)) | (~c3_1(a741)) | c0_1(a741) | (~c1_1(a734)) | hskp5 | hskp25), inference(lemma,lemma(discharge,[]))).
% 0.91/1.09 tff(3230,plain,
% 0.91/1.09 (c2_1(a775)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3229, 22, 207, 178, 177, 3174, 396, 3188])).
% 0.91/1.09 tff(3231,plain,
% 0.91/1.09 (~hskp18),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1636, 3230])).
% 0.91/1.09 tff(3232,plain,
% 0.91/1.09 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp11 | c3_1(a777) | (~ndr1_0) | (~c2_1(a777)) | (~c1_1(a777)))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp11 | c3_1(a777) | (~ndr1_0) | (~c2_1(a777)) | (~c1_1(a777)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3233,plain,
% 0.91/1.09 ((hskp27 | hskp11 | (~ndr1_0) | c3_1(a777) | (~c2_1(a777)) | (~c1_1(a777))) <=> (hskp27 | hskp11 | c3_1(a777) | (~ndr1_0) | (~c2_1(a777)) | (~c1_1(a777)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3234,plain,
% 0.91/1.09 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp11 | (~ndr1_0) | c3_1(a777) | (~c2_1(a777)) | (~c1_1(a777)))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp11 | c3_1(a777) | (~ndr1_0) | (~c2_1(a777)) | (~c1_1(a777))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[3233])).
% 0.91/1.09 tff(3235,plain,
% 0.91/1.09 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp11 | (~ndr1_0) | c3_1(a777) | (~c2_1(a777)) | (~c1_1(a777)))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp11 | c3_1(a777) | (~ndr1_0) | (~c2_1(a777)) | (~c1_1(a777)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[3234, 3232])).
% 0.91/1.09 tff(3236,plain,
% 0.91/1.09 ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp11 | (~ndr1_0) | c3_1(a777) | (~c2_1(a777)) | (~c1_1(a777)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3237,plain,
% 0.91/1.09 ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp11 | c3_1(a777) | (~ndr1_0) | (~c2_1(a777)) | (~c1_1(a777))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3236, 3235])).
% 0.91/1.09 tff(3238,plain,
% 0.91/1.09 (~c1_1(a777)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3237, 104, 560, 21, 660, 646, 559])).
% 0.91/1.09 tff(3239,plain,
% 0.91/1.09 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c0_1(a777) | (~ndr1_0) | c1_1(a777) | (~c2_1(a777)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a777) | (~ndr1_0) | c1_1(a777) | (~c2_1(a777)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3240,plain,
% 0.91/1.09 ((hskp2 | hskp1 | (~ndr1_0) | c1_1(a777) | c0_1(a777) | (~c2_1(a777))) <=> (hskp2 | hskp1 | c0_1(a777) | (~ndr1_0) | c1_1(a777) | (~c2_1(a777)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3241,plain,
% 0.91/1.09 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c1_1(a777) | c0_1(a777) | (~c2_1(a777)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | c0_1(a777) | (~ndr1_0) | c1_1(a777) | (~c2_1(a777))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[3240])).
% 0.91/1.09 tff(3242,plain,
% 0.91/1.09 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c1_1(a777) | c0_1(a777) | (~c2_1(a777)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a777) | (~ndr1_0) | c1_1(a777) | (~c2_1(a777)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[3241, 3239])).
% 0.91/1.09 tff(3243,plain,
% 0.91/1.09 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | c1_1(a777) | c0_1(a777) | (~c2_1(a777)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3244,plain,
% 0.91/1.09 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp2 | hskp1 | c0_1(a777) | (~ndr1_0) | c1_1(a777) | (~c2_1(a777))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3243, 3242])).
% 0.91/1.09 tff(3245,plain,
% 0.91/1.09 ($false),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3244, 104, 256, 255, 660, 652, 266, 3238])).
% 0.91/1.09 tff(3246,plain,(hskp27 | hskp2 | hskp1 | hskp11 | (~c0_1(a730)) | (~c3_1(a730)) | c1_1(a730)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.09 tff(3247,plain,
% 0.91/1.09 (hskp27),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3246, 255, 2747, 2748, 2459, 2458, 2457])).
% 0.91/1.09 tff(3248,plain,
% 0.91/1.09 (c1_1(a750)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[732, 3247])).
% 0.91/1.09 tff(3249,plain,
% 0.91/1.09 (c0_1(a750)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[716, 3247])).
% 0.91/1.09 tff(3250,plain,
% 0.91/1.09 (hskp18 | c3_1(a750)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1622, 104, 2748, 3249, 3248, 1075])).
% 0.91/1.09 tff(3251,plain,
% 0.91/1.09 (c3_1(a750)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3250, 3231])).
% 0.91/1.09 tff(3252,plain,
% 0.91/1.09 (c2_1(a750)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[724, 3247])).
% 0.91/1.09 tff(3253,plain,
% 0.91/1.09 (((~![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | (~ndr1_0) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | (~ndr1_0) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3254,plain,
% 0.91/1.09 ((hskp21 | (~ndr1_0) | (~c2_1(a750)) | (~c3_1(a750)) | (~c0_1(a750))) <=> (hskp21 | (~ndr1_0) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3255,plain,
% 0.91/1.09 (((~![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | (~ndr1_0) | (~c2_1(a750)) | (~c3_1(a750)) | (~c0_1(a750)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | (~ndr1_0) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[3254])).
% 0.91/1.09 tff(3256,plain,
% 0.91/1.09 (((~![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | (~ndr1_0) | (~c2_1(a750)) | (~c3_1(a750)) | (~c0_1(a750)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | (~ndr1_0) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[3255, 3253])).
% 0.91/1.09 tff(3257,plain,
% 0.91/1.09 ((~![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | (~ndr1_0) | (~c2_1(a750)) | (~c3_1(a750)) | (~c0_1(a750)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3258,plain,
% 0.91/1.09 ((~![U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | (~ndr1_0) | (~c3_1(a750)) | (~c0_1(a750)) | (~c2_1(a750))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3257, 3256])).
% 0.91/1.09 tff(3259,plain,
% 0.91/1.09 (hskp21 | (~c3_1(a750))),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3258, 104, 3249, 3252, 467])).
% 0.91/1.09 tff(3260,plain,
% 0.91/1.09 (hskp21),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3259, 3251])).
% 0.91/1.09 tff(3261,plain,
% 0.91/1.09 (~c2_1(a793)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[482, 3260])).
% 0.91/1.09 tff(3262,plain,
% 0.91/1.09 (c3_1(a793)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[492, 3260])).
% 0.91/1.09 tff(3263,plain,
% 0.91/1.09 (c0_1(a793)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[500, 3260])).
% 0.91/1.09 tff(3264,plain,
% 0.91/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a793) | c0_1(a734) | (~c3_1(a734)) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a734)) | (~c3_1(a793)) | (~c0_1(a793)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a793) | c0_1(a734) | (~c3_1(a734)) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a734)) | (~c3_1(a793)) | (~c0_1(a793)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3265,plain,
% 0.91/1.09 (((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a734) | (~c3_1(a734)) | (~c2_1(a734))) <=> (c2_1(a793) | c0_1(a734) | (~c3_1(a734)) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a734)) | (~c3_1(a793)) | (~c0_1(a793)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3266,plain,
% 0.91/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a734) | (~c3_1(a734)) | (~c2_1(a734)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a793) | c0_1(a734) | (~c3_1(a734)) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a734)) | (~c3_1(a793)) | (~c0_1(a793))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[3265])).
% 0.91/1.09 tff(3267,plain,
% 0.91/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a734) | (~c3_1(a734)) | (~c2_1(a734)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a793) | c0_1(a734) | (~c3_1(a734)) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a734)) | (~c3_1(a793)) | (~c0_1(a793)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[3266, 3264])).
% 0.91/1.09 tff(3268,plain,
% 0.91/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a793) | (~c3_1(a793)) | (~c0_1(a793)) | c1_1(a730) | (~c2_1(a730)) | (~c3_1(a730)) | c0_1(a734) | (~c3_1(a734)) | (~c2_1(a734)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3269,plain,
% 0.91/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a793) | c0_1(a734) | (~c3_1(a734)) | c1_1(a730) | (~ndr1_0) | (~c2_1(a730)) | (~c3_1(a730)) | (~c2_1(a734)) | (~c3_1(a793)) | (~c0_1(a793))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3268, 3267])).
% 0.91/1.09 tff(3270,plain,
% 0.91/1.09 (~c2_1(a730)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3269, 104, 3263, 3262, 2458, 3261, 22, 2740, 2457, 455, 3187])).
% 0.91/1.09 tff(3271,plain,
% 0.91/1.09 (~c1_1(a793)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[2772, 104, 2748, 3262, 2458, 3261, 2457, 360, 3270])).
% 0.91/1.09 tff(3272,plain,
% 0.91/1.09 ($false),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[2757, 104, 2747, 3263, 207, 178, 3261, 177, 530, 3271])).
% 0.91/1.09 tff(3273,plain,(c0_1(a734) | (~c1_1(a741)) | (~c3_1(a741)) | c0_1(a741) | hskp5 | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.91/1.09 tff(3274,plain,
% 0.91/1.09 (hskp5),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3273, 3140, 177, 255, 22, 3139])).
% 0.91/1.09 tff(3275,plain,
% 0.91/1.09 (c3_1(a735)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[413, 3274])).
% 0.91/1.09 tff(3276,plain,
% 0.91/1.09 (~c0_1(a735)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[427, 3274])).
% 0.91/1.09 tff(3277,plain,
% 0.91/1.09 (c0_1(a730)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[443, 3136])).
% 0.91/1.09 tff(3278,plain,
% 0.91/1.09 (c2_1(a735)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[421, 3274])).
% 0.91/1.09 tff(3279,plain,
% 0.91/1.09 (c3_1(a730)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[435, 3136])).
% 0.91/1.09 tff(3280,plain,
% 0.91/1.09 (~c2_1(a730)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[509, 3279, 3275, 3276, 3277, 3137, 3278])).
% 0.91/1.09 tff(3281,plain,
% 0.91/1.09 (hskp2),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[540, 3280, 255, 3278, 3137, 3277, 3276, 3275])).
% 0.91/1.09 tff(3282,plain,
% 0.91/1.09 (~c2_1(a732)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[282, 3281])).
% 0.91/1.09 tff(3283,plain,
% 0.91/1.09 (~c0_1(a732)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[288, 3281])).
% 0.91/1.09 tff(3284,plain,
% 0.91/1.09 (c2_1(a741)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[215, 3139, 3091, 177, 3140, 21])).
% 0.91/1.09 tff(3285,plain,
% 0.91/1.09 (c2_1(a744)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[687, 104, 560, 21, 1290, 2425, 609])).
% 0.91/1.09 tff(3286,plain,
% 0.91/1.09 (hskp2),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1433, 104, 255, 2425, 2424, 266, 3285])).
% 0.91/1.09 tff(3287,plain,
% 0.91/1.09 (~c2_1(a732)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[282, 3286])).
% 0.91/1.09 tff(3288,plain,
% 0.91/1.09 (~c0_1(a732)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[288, 3286])).
% 0.91/1.09 tff(3289,plain,
% 0.91/1.09 (~c1_1(a732)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3132, 217, 104, 2425, 2424, 3288, 3287, 254, 3285])).
% 0.91/1.09 tff(3290,plain,
% 0.91/1.09 (^[U: $i] : refl((hskp0 | hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> (hskp0 | hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))),
% 0.91/1.09 inference(bind,[status(th)],[])).
% 0.91/1.09 tff(3291,plain,
% 0.91/1.09 (![U: $i] : (hskp0 | hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp0 | hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.91/1.09 inference(quant_intro,[status(thm)],[3290])).
% 0.91/1.09 tff(3292,plain,
% 0.91/1.09 (![U: $i] : (hskp0 | hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp0 | hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3293,plain,
% 0.91/1.09 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp0) <=> ((hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp0))), rewrite(((hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp0) <=> (hskp0 | hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp0) <=> (hskp0 | hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))))),
% 0.91/1.09 inference(bind,[status(th)],[])).
% 0.91/1.09 tff(3294,plain,
% 0.91/1.09 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp0) <=> ![U: $i] : (hskp0 | hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.91/1.09 inference(quant_intro,[status(thm)],[3293])).
% 0.91/1.09 tff(3295,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 0.91/1.09 tff(3296,plain,
% 0.91/1.09 (![U: $i] : (hskp0 | hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3295, 3294])).
% 0.91/1.09 tff(3297,plain,
% 0.91/1.09 (![U: $i] : (hskp0 | hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3296, 3292])).
% 0.91/1.09 tff(3298,plain,(
% 0.91/1.09 ![U: $i] : (hskp0 | hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.91/1.09 inference(skolemize,[status(sab)],[3297])).
% 0.91/1.09 tff(3299,plain,
% 0.91/1.09 (![U: $i] : (hskp0 | hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3298, 3291])).
% 0.91/1.09 tff(3300,plain,
% 0.91/1.09 (~c3_1(a732)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[546, 3286])).
% 0.91/1.09 tff(3301,plain,
% 0.91/1.09 (((~![U: $i] : (hskp0 | hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp0 | hskp27 | c2_1(a732) | c3_1(a732) | (~ndr1_0) | c1_1(a732))) <=> ((~![U: $i] : (hskp0 | hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp0 | hskp27 | c2_1(a732) | c3_1(a732) | (~ndr1_0) | c1_1(a732))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3302,plain,
% 0.91/1.09 ((hskp0 | hskp27 | (~ndr1_0) | c2_1(a732) | c1_1(a732) | c3_1(a732)) <=> (hskp0 | hskp27 | c2_1(a732) | c3_1(a732) | (~ndr1_0) | c1_1(a732))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3303,plain,
% 0.91/1.09 (((~![U: $i] : (hskp0 | hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp0 | hskp27 | (~ndr1_0) | c2_1(a732) | c1_1(a732) | c3_1(a732))) <=> ((~![U: $i] : (hskp0 | hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp0 | hskp27 | c2_1(a732) | c3_1(a732) | (~ndr1_0) | c1_1(a732)))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[3302])).
% 0.91/1.09 tff(3304,plain,
% 0.91/1.09 (((~![U: $i] : (hskp0 | hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp0 | hskp27 | (~ndr1_0) | c2_1(a732) | c1_1(a732) | c3_1(a732))) <=> ((~![U: $i] : (hskp0 | hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp0 | hskp27 | c2_1(a732) | c3_1(a732) | (~ndr1_0) | c1_1(a732))),
% 0.91/1.09 inference(transitivity,[status(thm)],[3303, 3301])).
% 0.91/1.09 tff(3305,plain,
% 0.91/1.09 ((~![U: $i] : (hskp0 | hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp0 | hskp27 | (~ndr1_0) | c2_1(a732) | c1_1(a732) | c3_1(a732))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3306,plain,
% 0.91/1.09 ((~![U: $i] : (hskp0 | hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp0 | hskp27 | c2_1(a732) | c3_1(a732) | (~ndr1_0) | c1_1(a732)),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3305, 3304])).
% 0.91/1.09 tff(3307,plain,
% 0.91/1.09 ($false),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3306, 217, 104, 560, 3287, 3300, 3299, 3289])).
% 0.91/1.09 tff(3308,plain,(hskp0 | hskp27 | hskp1 | hskp11), inference(lemma,lemma(discharge,[]))).
% 0.91/1.09 tff(3309,plain,
% 0.91/1.09 (hskp0),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3308, 560, 255, 21])).
% 0.91/1.09 tff(3310,plain,
% 0.91/1.09 (~c1_1(a730)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[384, 3309])).
% 0.91/1.09 tff(3311,plain,
% 0.91/1.09 (c3_1(a730)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[435, 3309])).
% 0.91/1.09 tff(3312,plain,
% 0.91/1.09 (c0_1(a730)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[443, 3309])).
% 0.91/1.09 tff(3313,plain,
% 0.91/1.09 (hskp2),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3246, 3312, 560, 21, 255, 3311, 3310])).
% 0.91/1.09 tff(3314,plain,
% 0.91/1.09 (~c0_1(a732)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[288, 3313])).
% 0.91/1.09 tff(3315,plain,
% 0.91/1.09 (~c3_1(a732)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[546, 3313])).
% 0.91/1.09 tff(3316,plain,
% 0.91/1.09 (~c2_1(a730)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[509, 3311, 484, 457, 3312, 3310, 485])).
% 0.91/1.09 tff(3317,plain,
% 0.91/1.09 (~c2_1(a732)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[282, 3313])).
% 0.91/1.09 tff(3318,plain,
% 0.91/1.09 ($false),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[708, 3317, 3316, 561, 560, 21, 3312, 3311, 3315, 3310, 207, 177, 3314])).
% 0.91/1.09 tff(3319,plain,(hskp27 | (~c2_1(a741)) | hskp11 | (~c1_1(a741)) | c0_1(a741) | (~c3_1(a735)) | c0_1(a735) | (~c2_1(a735)) | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.91/1.09 tff(3320,plain,
% 0.91/1.09 (hskp27),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3319, 3284, 21, 3139, 177, 3275, 3276, 3278, 255])).
% 0.91/1.09 tff(3321,plain,
% 0.91/1.09 (c1_1(a750)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[732, 3320])).
% 0.91/1.09 tff(3322,plain,
% 0.91/1.09 (c0_1(a750)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[716, 3320])).
% 0.91/1.09 tff(3323,plain,
% 0.91/1.09 (c2_1(a750)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[724, 3320])).
% 0.91/1.09 tff(3324,plain,
% 0.91/1.09 (~hskp25),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[933, 3323, 177, 255, 3139, 3140, 3284, 3322, 3321])).
% 0.91/1.09 tff(3325,assumption,(~c1_1(a732)), introduced(assumption)).
% 0.91/1.09 tff(3326,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | c0_1(a732) | c2_1(a732) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c1_1(a732))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c0_1(a732) | c2_1(a732) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c1_1(a732))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3327,plain,
% 0.91/1.09 ((hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a732) | c0_1(a732) | c2_1(a732)) <=> (hskp25 | c0_1(a732) | c2_1(a732) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c1_1(a732))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3328,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a732) | c0_1(a732) | c2_1(a732))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | c0_1(a732) | c2_1(a732) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c1_1(a732)))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[3327])).
% 0.91/1.09 tff(3329,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a732) | c0_1(a732) | c2_1(a732))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c0_1(a732) | c2_1(a732) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c1_1(a732))),
% 0.91/1.09 inference(transitivity,[status(thm)],[3328, 3326])).
% 0.91/1.09 tff(3330,plain,
% 0.91/1.09 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a732) | c0_1(a732) | c2_1(a732))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3331,plain,
% 0.91/1.09 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c0_1(a732) | c2_1(a732) | c1_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c3_1(a730)) | c1_1(a732)),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3330, 3329])).
% 0.91/1.09 tff(3332,plain,
% 0.91/1.09 ($false),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3331, 104, 1656, 469, 468, 622, 621, 456, 20, 3325])).
% 0.91/1.09 tff(3333,plain,(c1_1(a732) | hskp25 | (~c0_1(a730)) | (~c3_1(a730)) | c0_1(a732) | c2_1(a732) | c1_1(a730)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.09 tff(3334,plain,
% 0.91/1.09 (c1_1(a732)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3333, 3324, 3277, 3279, 3283, 3282, 3137])).
% 0.91/1.09 tff(3335,plain,
% 0.91/1.09 (hskp10 | (~c1_1(a732))),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[976, 104, 3140, 177, 3283, 3282, 970, 3284])).
% 0.91/1.09 tff(3336,plain,
% 0.91/1.09 (hskp10),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3335, 3334])).
% 0.91/1.09 tff(3337,plain,
% 0.91/1.09 (~c2_1(a748)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[983, 3336])).
% 0.91/1.09 tff(3338,plain,
% 0.91/1.09 (~c1_1(a748)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[989, 3336])).
% 0.91/1.09 tff(3339,plain,
% 0.91/1.09 (~c0_1(a748)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[995, 3336])).
% 0.91/1.09 tff(3340,plain,
% 0.91/1.09 ($false),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1204, 104, 3324, 3277, 3279, 3339, 3338, 3337, 3137, 20])).
% 0.91/1.09 tff(3341,plain,(hskp1 | c0_1(a741) | hskp11 | c0_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.09 tff(3342,plain,
% 0.91/1.09 (c0_1(a741)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3341, 3114, 21, 22])).
% 0.91/1.09 tff(3343,plain,
% 0.91/1.09 ($false),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[163, 3342, 3115])).
% 0.91/1.09 tff(3344,plain,(c0_1(a734) | hskp11), inference(lemma,lemma(discharge,[]))).
% 0.91/1.09 tff(3345,plain,
% 0.91/1.09 (c0_1(a734)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3344, 21])).
% 0.91/1.09 tff(3346,plain,
% 0.91/1.09 (~hskp4),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[2008, 3345])).
% 0.91/1.09 tff(3347,plain,
% 0.91/1.09 (~hskp1),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3113, 3346, 21])).
% 0.91/1.09 tff(3348,plain,
% 0.91/1.09 (hskp0),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3135, 3347])).
% 0.91/1.09 tff(3349,plain,
% 0.91/1.09 (~c1_1(a730)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[384, 3348])).
% 0.91/1.09 tff(3350,plain,
% 0.91/1.09 (hskp7),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[141, 3347, 3346])).
% 0.91/1.09 tff(3351,plain,
% 0.91/1.09 (c1_1(a741)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[149, 3350])).
% 0.91/1.09 tff(3352,plain,
% 0.91/1.09 (~c0_1(a741)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[163, 3350])).
% 0.91/1.09 tff(3353,plain,
% 0.91/1.09 (c3_1(a741)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[157, 3350])).
% 0.91/1.09 tff(3354,plain,
% 0.91/1.09 (hskp5),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[2794, 3353, 3352, 3351])).
% 0.91/1.09 tff(3355,plain,
% 0.91/1.09 (c2_1(a735)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[421, 3354])).
% 0.91/1.09 tff(3356,plain,
% 0.91/1.09 (~c0_1(a735)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[427, 3354])).
% 0.91/1.09 tff(3357,plain,
% 0.91/1.09 (c2_1(a741)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[215, 3351, 3346, 3352, 3353, 21])).
% 0.91/1.09 tff(3358,plain,
% 0.91/1.09 (c3_1(a735)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[413, 3354])).
% 0.91/1.09 tff(3359,plain,
% 0.91/1.09 (hskp27),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3319, 3358, 21, 3351, 3352, 3357, 3356, 3355, 3347])).
% 0.91/1.09 tff(3360,plain,
% 0.91/1.09 (c1_1(a750)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[732, 3359])).
% 0.91/1.09 tff(3361,plain,
% 0.91/1.09 (c0_1(a750)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[716, 3359])).
% 0.91/1.09 tff(3362,plain,
% 0.91/1.09 (c2_1(a750)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[724, 3359])).
% 0.91/1.09 tff(3363,plain,
% 0.91/1.09 (~hskp25),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[933, 3362, 3352, 3347, 3351, 3353, 3357, 3361, 3360])).
% 0.91/1.09 tff(3364,plain,
% 0.91/1.09 (c0_1(a730)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[443, 3348])).
% 0.91/1.09 tff(3365,plain,
% 0.91/1.09 (c3_1(a730)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[435, 3348])).
% 0.91/1.09 tff(3366,plain,
% 0.91/1.09 (~c2_1(a730)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[509, 3358, 3365, 3356, 3364, 3349, 3355])).
% 0.91/1.09 tff(3367,plain,
% 0.91/1.09 (hskp2),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[540, 3366, 3347, 3355, 3349, 3364, 3356, 3358])).
% 0.91/1.09 tff(3368,plain,
% 0.91/1.09 (~c2_1(a732)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[282, 3367])).
% 0.91/1.09 tff(3369,plain,
% 0.91/1.09 (~c0_1(a732)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[288, 3367])).
% 0.91/1.09 tff(3370,plain,
% 0.91/1.09 (c1_1(a732)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3333, 3369, 3364, 3365, 3349, 3368, 3363])).
% 0.91/1.09 tff(3371,plain,
% 0.91/1.09 (hskp10),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[976, 104, 3353, 3352, 3369, 3368, 970, 3357, 3370])).
% 0.91/1.10 tff(3372,plain,
% 0.91/1.10 (~c2_1(a748)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[983, 3371])).
% 0.91/1.10 tff(3373,plain,
% 0.91/1.10 (~c1_1(a748)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[989, 3371])).
% 0.91/1.10 tff(3374,plain,
% 0.91/1.10 (~c0_1(a748)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[995, 3371])).
% 0.91/1.10 tff(3375,plain,
% 0.91/1.10 ($false),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1204, 104, 3363, 3364, 3365, 3374, 3373, 3372, 3349, 20])).
% 0.91/1.10 tff(3376,plain,(hskp11), inference(lemma,lemma(discharge,[]))).
% 0.91/1.10 tff(3377,plain,
% 0.91/1.10 (hskp4),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[141, 1018, 255])).
% 0.91/1.10 tff(3378,plain,
% 0.91/1.10 (c1_1(a734)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[51, 3377])).
% 0.91/1.10 tff(3379,plain,
% 0.91/1.10 (~c3_1(a734)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2745, 3377])).
% 0.91/1.10 tff(3380,plain,
% 0.91/1.10 (hskp5),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2282, 2207, 177, 3279, 3277, 3137, 255, 1017, 22, 3378, 3379])).
% 0.91/1.10 tff(3381,plain,
% 0.91/1.10 (c3_1(a735)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[413, 3380])).
% 0.91/1.10 tff(3382,plain,
% 0.91/1.10 (~c0_1(a735)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[427, 3380])).
% 0.91/1.10 tff(3383,plain,
% 0.91/1.10 (c2_1(a735)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[421, 3380])).
% 0.91/1.10 tff(3384,plain,
% 0.91/1.10 (~c2_1(a730)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[509, 3381, 3279, 3382, 3277, 3137, 3383])).
% 0.91/1.10 tff(3385,plain,
% 0.91/1.10 (hskp2),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[540, 3384, 255, 3383, 3137, 3277, 3382, 3381])).
% 0.91/1.10 tff(3386,plain,
% 0.91/1.10 (~c3_1(a732)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[546, 3385])).
% 0.91/1.10 tff(3387,plain,
% 0.91/1.10 (~c2_1(a732)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[282, 3385])).
% 0.91/1.10 tff(3388,plain,
% 0.91/1.10 (~c0_1(a732)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[288, 3385])).
% 0.91/1.10 tff(3389,plain,
% 0.91/1.10 (hskp8),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[666, 104, 2038, 2017, 2016, 622, 621, 620, 619])).
% 0.91/1.10 tff(3390,plain,
% 0.91/1.10 (~c1_1(a744)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[693, 3389])).
% 0.91/1.10 tff(3391,plain,
% 0.91/1.10 (~c0_1(a744)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[672, 3389])).
% 0.91/1.10 tff(3392,plain,
% 0.91/1.10 (c3_1(a744)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[680, 3389])).
% 0.91/1.10 tff(3393,plain,
% 0.91/1.10 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a777) | c3_1(a777) | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c3_1(a744)) | (~c2_1(a777)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a777) | c3_1(a777) | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c3_1(a744)) | (~c2_1(a777)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3394,plain,
% 0.91/1.10 ((hskp7 | (~ndr1_0) | c0_1(a777) | c3_1(a777) | (~c2_1(a777)) | c1_1(a744) | c0_1(a744) | (~c3_1(a744))) <=> (hskp7 | c0_1(a777) | c3_1(a777) | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c3_1(a744)) | (~c2_1(a777)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3395,plain,
% 0.91/1.10 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a777) | c3_1(a777) | (~c2_1(a777)) | c1_1(a744) | c0_1(a744) | (~c3_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a777) | c3_1(a777) | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c3_1(a744)) | (~c2_1(a777))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[3394])).
% 0.91/1.10 tff(3396,plain,
% 0.91/1.10 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a777) | c3_1(a777) | (~c2_1(a777)) | c1_1(a744) | c0_1(a744) | (~c3_1(a744)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a777) | c3_1(a777) | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c3_1(a744)) | (~c2_1(a777)))),
% 0.91/1.10 inference(transitivity,[status(thm)],[3395, 3393])).
% 0.91/1.10 tff(3397,plain,
% 0.91/1.10 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a777) | c3_1(a777) | (~c2_1(a777)) | c1_1(a744) | c0_1(a744) | (~c3_1(a744)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(3398,plain,
% 0.91/1.10 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a777) | c3_1(a777) | c0_1(a744) | c1_1(a744) | (~ndr1_0) | (~c3_1(a744)) | (~c2_1(a777))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3397, 3396])).
% 0.91/1.10 tff(3399,plain,
% 0.91/1.10 ($false),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3398, 104, 1029, 2038, 3392, 2017, 2016, 3391, 3390, 1263])).
% 0.91/1.10 tff(3400,plain,((~hskp19) | hskp7 | c0_1(a732) | c2_1(a732) | c3_1(a732)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.10 tff(3401,plain,
% 0.91/1.10 (~hskp19),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3400, 3388, 1018, 3387, 3386])).
% 0.91/1.10 tff(3402,plain,
% 0.91/1.10 (hskp27 | hskp19),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[638, 104, 3277, 3279, 3137, 632])).
% 0.91/1.10 tff(3403,plain,
% 0.91/1.10 (hskp27),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3402, 3401])).
% 0.91/1.10 tff(3404,plain,
% 0.91/1.10 (c1_1(a750)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[732, 3403])).
% 0.91/1.10 tff(3405,plain,
% 0.91/1.10 (c0_1(a750)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[716, 3403])).
% 0.91/1.10 tff(3406,plain,
% 0.91/1.10 (c2_1(a750)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[724, 3403])).
% 0.91/1.10 tff(3407,plain,
% 0.91/1.10 ($false),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2317, 3406, 3405, 177, 255, 2207, 1017, 3404, 3378, 22, 3379])).
% 0.91/1.10 tff(3408,plain,(c3_1(a741) | c0_1(a741) | hskp1 | c1_1(a741) | c0_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.10 tff(3409,plain,
% 0.91/1.10 (c3_1(a741)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3408, 1017, 255, 177, 22])).
% 0.91/1.10 tff(3410,plain,
% 0.91/1.10 ((~c3_1(a741)) | (~c2_1(a734))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2337, 104, 1018, 1017, 177, 22, 3379, 1263])).
% 0.91/1.10 tff(3411,plain,
% 0.91/1.10 (~c2_1(a734)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3410, 3409])).
% 0.91/1.10 tff(3412,plain,
% 0.91/1.10 (hskp5),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1177, 3411, 3379, 3378])).
% 0.91/1.10 tff(3413,plain,
% 0.91/1.10 (c3_1(a735)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[413, 3412])).
% 0.91/1.10 tff(3414,plain,
% 0.91/1.10 (~c0_1(a735)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[427, 3412])).
% 0.91/1.10 tff(3415,plain,
% 0.91/1.10 (c2_1(a735)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[421, 3412])).
% 0.91/1.10 tff(3416,plain,
% 0.91/1.10 (~c2_1(a730)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[509, 3413, 3279, 3414, 3277, 3137, 3415])).
% 0.91/1.10 tff(3417,plain,
% 0.91/1.10 (hskp2),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[540, 3416, 255, 3415, 3137, 3277, 3414, 3413])).
% 0.91/1.10 tff(3418,plain,
% 0.91/1.10 (~c3_1(a732)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[546, 3417])).
% 0.91/1.10 tff(3419,plain,
% 0.91/1.10 (~c2_1(a732)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[282, 3417])).
% 0.91/1.10 tff(3420,plain,
% 0.91/1.10 (~c0_1(a732)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[288, 3417])).
% 0.91/1.10 tff(3421,plain,
% 0.91/1.10 (~hskp19),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3400, 3420, 1018, 3419, 3418])).
% 0.91/1.10 tff(3422,plain,
% 0.91/1.10 (hskp27),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3402, 3421])).
% 0.91/1.10 tff(3423,plain,
% 0.91/1.10 (c0_1(a750)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[716, 3422])).
% 0.91/1.10 tff(3424,plain,
% 0.91/1.10 (c1_1(a750)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[732, 3422])).
% 0.91/1.10 tff(3425,plain,
% 0.91/1.10 (c2_1(a750)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[724, 3422])).
% 0.91/1.10 tff(3426,plain,
% 0.91/1.10 (c3_1(a734)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2173, 1029, 1030])).
% 0.91/1.10 tff(3427,plain,
% 0.91/1.10 (~hskp4),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2745, 3426])).
% 0.91/1.10 tff(3428,plain,
% 0.91/1.10 (hskp1),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[141, 3427, 1029])).
% 0.91/1.10 tff(3429,plain,
% 0.91/1.10 (~c2_1(a731)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[58, 3428])).
% 0.91/1.10 tff(3430,plain,
% 0.91/1.10 (c3_1(a731)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[66, 3428])).
% 0.91/1.10 tff(3431,plain,
% 0.91/1.10 (c0_1(a731)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1039, 104, 1030, 1029, 3430, 3429, 1028])).
% 0.91/1.10 tff(3432,plain,
% 0.91/1.10 (c1_1(a731)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[74, 3428])).
% 0.91/1.10 tff(3433,plain,
% 0.91/1.10 (~hskp8),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2052, 3428, 1030, 1029])).
% 0.91/1.10 tff(3434,plain,
% 0.91/1.10 (hskp0),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1182, 3433])).
% 0.91/1.10 tff(3435,plain,
% 0.91/1.10 (~c1_1(a730)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[384, 3434])).
% 0.91/1.10 tff(3436,plain,
% 0.91/1.10 (c3_1(a730)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[435, 3434])).
% 0.91/1.10 tff(3437,plain,
% 0.91/1.10 (c0_1(a730)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[443, 3434])).
% 0.91/1.10 tff(3438,plain,
% 0.91/1.10 (hskp5),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2737, 3437, 3436, 3435, 3432, 3430, 3429, 3427])).
% 0.91/1.10 tff(3439,plain,
% 0.91/1.10 (c2_1(a735)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[421, 3438])).
% 0.91/1.10 tff(3440,plain,
% 0.91/1.10 (c3_1(a735)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[413, 3438])).
% 0.91/1.10 tff(3441,plain,
% 0.91/1.10 (~c0_1(a735)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[427, 3438])).
% 0.91/1.10 tff(3442,plain,
% 0.91/1.10 (~c2_1(a730)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[509, 3441, 3437, 3436, 3440, 3435, 3439])).
% 0.91/1.10 tff(3443,plain,
% 0.91/1.10 (hskp11 | c2_1(a730)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1901, 104, 3432, 3430, 3436, 3429, 3435, 360])).
% 0.91/1.10 tff(3444,plain,
% 0.91/1.10 (hskp11),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3443, 3442])).
% 0.91/1.10 tff(3445,plain,
% 0.91/1.10 (~c3_1(a749)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1863, 3444])).
% 0.91/1.10 tff(3446,plain,
% 0.91/1.10 (~c1_1(a749)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1566, 3444])).
% 0.91/1.10 tff(3447,plain,
% 0.91/1.10 (~c0_1(a749)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1540, 3444])).
% 0.91/1.10 tff(3448,plain,
% 0.91/1.10 ($false),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2171, 104, 3432, 3430, 3447, 3446, 3445, 3429, 10, 3431])).
% 0.91/1.10 tff(3449,plain,(hskp7 | hskp12), inference(lemma,lemma(discharge,[]))).
% 0.91/1.10 tff(3450,plain,
% 0.91/1.10 (hskp12),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3449, 1018])).
% 0.91/1.10 tff(3451,plain,
% 0.91/1.10 (c2_1(a755)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2187, 3450])).
% 0.91/1.10 tff(3452,plain,
% 0.91/1.10 (~c3_1(a755)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2179, 3450])).
% 0.91/1.10 tff(3453,plain,
% 0.91/1.10 (c1_1(a755)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2195, 3450])).
% 0.91/1.10 tff(3454,plain,
% 0.91/1.10 (~hskp10),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2403, 3424, 255, 3453, 3277, 3279, 3137, 3452, 3423, 3425, 3451])).
% 0.91/1.10 tff(3455,plain,
% 0.91/1.10 ($false),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3014, 3454, 3425, 255, 3379, 22, 3424, 3423, 3378, 3412])).
% 0.91/1.10 tff(3456,plain,(c1_1(a741) | hskp1 | c0_1(a734) | c0_1(a741)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.10 tff(3457,plain,
% 0.91/1.10 (c1_1(a741)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3456, 177, 22, 255])).
% 0.91/1.10 tff(3458,plain,
% 0.91/1.10 (hskp4),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[141, 2378, 255])).
% 0.91/1.10 tff(3459,plain,
% 0.91/1.10 (c1_1(a734)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[51, 3458])).
% 0.91/1.10 tff(3460,plain,
% 0.91/1.10 (~c3_1(a734)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2745, 3458])).
% 0.91/1.10 tff(3461,plain,
% 0.91/1.10 (~c3_1(a749)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1863, 3376])).
% 0.91/1.10 tff(3462,plain,
% 0.91/1.10 (~c1_1(a749)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1566, 3376])).
% 0.91/1.10 tff(3463,plain,
% 0.91/1.10 (hskp5 | (~c2_1(a749))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2622, 104, 469, 468, 3462, 3461, 456, 1456])).
% 0.91/1.10 tff(3464,plain,
% 0.91/1.10 (~c2_1(a749)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3463, 396])).
% 0.91/1.10 tff(3465,plain,
% 0.91/1.10 (~c0_1(a749)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1540, 3376])).
% 0.91/1.10 tff(3466,plain,
% 0.91/1.10 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c3_1(a741) | c0_1(a749) | c3_1(a749) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | c2_1(a749))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c3_1(a741) | c0_1(a749) | c3_1(a749) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | c2_1(a749))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3467,plain,
% 0.91/1.10 ((hskp8 | (~ndr1_0) | c0_1(a741) | c3_1(a741) | (~c2_1(a741)) | c3_1(a749) | c0_1(a749) | c2_1(a749)) <=> (hskp8 | c3_1(a741) | c0_1(a749) | c3_1(a749) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | c2_1(a749))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3468,plain,
% 0.91/1.10 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a741) | c3_1(a741) | (~c2_1(a741)) | c3_1(a749) | c0_1(a749) | c2_1(a749))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c3_1(a741) | c0_1(a749) | c3_1(a749) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | c2_1(a749)))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[3467])).
% 0.91/1.10 tff(3469,plain,
% 0.91/1.10 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a741) | c3_1(a741) | (~c2_1(a741)) | c3_1(a749) | c0_1(a749) | c2_1(a749))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c3_1(a741) | c0_1(a749) | c3_1(a749) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | c2_1(a749))),
% 0.91/1.10 inference(transitivity,[status(thm)],[3468, 3466])).
% 0.91/1.10 tff(3470,plain,
% 0.91/1.10 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a741) | c3_1(a741) | (~c2_1(a741)) | c3_1(a749) | c0_1(a749) | c2_1(a749))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(3471,plain,
% 0.91/1.10 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c3_1(a741) | c0_1(a749) | c3_1(a749) | c0_1(a741) | (~ndr1_0) | (~c2_1(a741)) | c2_1(a749)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3470, 3469])).
% 0.91/1.10 tff(3472,plain,
% 0.91/1.10 (hskp8 | c3_1(a741) | (~c2_1(a741)) | c2_1(a749)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3471, 104, 3465, 3461, 177, 619])).
% 0.91/1.10 tff(3473,plain,
% 0.91/1.10 (hskp8),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3472, 3464, 2207, 2412])).
% 0.91/1.10 tff(3474,plain,
% 0.91/1.10 ($false),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3019, 3473, 2266, 22, 33, 2378])).
% 0.91/1.10 tff(3475,plain,(hskp5 | c0_1(a734) | c3_1(a734) | c3_1(a741) | c0_1(a741) | (~c1_1(a741)) | (~c1_1(a734)) | (~c0_1(a730)) | (~c3_1(a730)) | c1_1(a730)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.10 tff(3476,plain,
% 0.91/1.10 (hskp5),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3475, 3460, 22, 2207, 177, 3457, 3459, 3277, 3279, 3137])).
% 0.91/1.10 tff(3477,plain,
% 0.91/1.10 (c3_1(a735)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[413, 3476])).
% 0.91/1.10 tff(3478,plain,
% 0.91/1.10 (~c0_1(a735)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[427, 3476])).
% 0.91/1.10 tff(3479,plain,
% 0.91/1.10 (c2_1(a735)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[421, 3476])).
% 0.91/1.10 tff(3480,plain,
% 0.91/1.10 (~c2_1(a730)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[509, 3477, 3279, 3478, 3277, 3137, 3479])).
% 0.91/1.10 tff(3481,plain,
% 0.91/1.10 (hskp2),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[540, 3480, 255, 3479, 3137, 3277, 3478, 3477])).
% 0.91/1.10 tff(3482,plain,
% 0.91/1.10 (~c2_1(a732)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[282, 3481])).
% 0.91/1.10 tff(3483,plain,
% 0.91/1.10 (~c0_1(a732)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[288, 3481])).
% 0.91/1.10 tff(3484,plain,
% 0.91/1.10 (~c3_1(a732)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[546, 3481])).
% 0.91/1.10 tff(3485,plain,
% 0.91/1.10 (~hskp19),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3400, 3484, 2378, 3483, 3482])).
% 0.91/1.10 tff(3486,plain,
% 0.91/1.10 (hskp27),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3402, 3485])).
% 0.91/1.10 tff(3487,plain,
% 0.91/1.10 (c2_1(a750)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[724, 3486])).
% 0.91/1.10 tff(3488,plain,
% 0.91/1.10 (c0_1(a750)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[716, 3486])).
% 0.91/1.10 tff(3489,plain,
% 0.91/1.10 (c1_1(a750)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[732, 3486])).
% 0.91/1.10 tff(3490,plain,
% 0.91/1.10 (hskp12),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3449, 2378])).
% 0.91/1.10 tff(3491,plain,
% 0.91/1.10 (c2_1(a755)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2187, 3490])).
% 0.91/1.10 tff(3492,plain,
% 0.91/1.10 (~c3_1(a755)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2179, 3490])).
% 0.91/1.10 tff(3493,plain,
% 0.91/1.10 (c1_1(a755)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2195, 3490])).
% 0.91/1.10 tff(3494,plain,
% 0.91/1.10 (~hskp10),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2403, 3489, 255, 3493, 3277, 3279, 3137, 3492, 3488, 3487, 3491])).
% 0.91/1.10 tff(3495,plain,
% 0.91/1.10 ($false),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3014, 3494, 3489, 255, 3460, 22, 3476, 3488, 3459, 3487])).
% 0.91/1.10 tff(3496,plain,(c3_1(a741) | hskp1 | c0_1(a734) | c0_1(a741)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.10 tff(3497,plain,
% 0.91/1.10 (c3_1(a741)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3496, 177, 22, 255])).
% 0.91/1.10 tff(3498,plain,
% 0.91/1.10 (hskp5),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2794, 3497, 177, 3457])).
% 0.91/1.10 tff(3499,plain,
% 0.91/1.10 (c2_1(a735)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[421, 3498])).
% 0.91/1.10 tff(3500,plain,
% 0.91/1.10 (~c0_1(a735)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[427, 3498])).
% 0.91/1.10 tff(3501,plain,
% 0.91/1.10 (c3_1(a735)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[413, 3498])).
% 0.91/1.10 tff(3502,plain,
% 0.91/1.10 (~c2_1(a730)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[509, 3501, 3279, 3500, 3277, 3137, 3499])).
% 0.91/1.10 tff(3503,plain,
% 0.91/1.10 (c2_1(a741)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2517, 178, 177, 207])).
% 0.91/1.10 tff(3504,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a744) | c1_1(a744) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a744)) | (~c3_1(a744)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a744) | c1_1(a744) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a744)) | (~c3_1(a744)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3505,plain,
% 0.91/1.10 (((~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a744) | (~c2_1(a744)) | (~c3_1(a744)) | c0_1(a744) | (~c3_1(a744)) | (~c2_1(a744))) <=> (c0_1(a744) | c1_1(a744) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a744)) | (~c3_1(a744)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3506,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a744) | (~c2_1(a744)) | (~c3_1(a744)) | c0_1(a744) | (~c3_1(a744)) | (~c2_1(a744)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a744) | c1_1(a744) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a744)) | (~c3_1(a744))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[3505])).
% 0.91/1.10 tff(3507,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a744) | (~c2_1(a744)) | (~c3_1(a744)) | c0_1(a744) | (~c3_1(a744)) | (~c2_1(a744)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a744) | c1_1(a744) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a744)) | (~c3_1(a744)))),
% 0.91/1.10 inference(transitivity,[status(thm)],[3506, 3504])).
% 0.91/1.10 tff(3508,plain,
% 0.91/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a730) | (~c3_1(a730)) | (~c0_1(a730)) | c1_1(a744) | (~c2_1(a744)) | (~c3_1(a744)) | c0_1(a744) | (~c3_1(a744)) | (~c2_1(a744)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(3509,plain,
% 0.91/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a744) | c1_1(a744) | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c3_1(a730)) | (~c2_1(a744)) | (~c3_1(a744))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3508, 3507])).
% 0.91/1.10 tff(3510,plain,
% 0.91/1.10 (~c2_1(a744)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3509, 104, 3017, 469, 468, 2049, 2050, 455, 511])).
% 0.91/1.10 tff(3511,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a744) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a741)) | c2_1(a744) | (~c3_1(a744)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a744) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a741)) | c2_1(a744) | (~c3_1(a744)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3512,plain,
% 0.91/1.10 (((~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | (~c1_1(a741)) | c0_1(a741) | (~c2_1(a741)) | (~c3_1(a741)) | c2_1(a744) | c0_1(a744) | (~c3_1(a744))) <=> (c0_1(a744) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a741)) | c2_1(a744) | (~c3_1(a744)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3513,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | (~c1_1(a741)) | c0_1(a741) | (~c2_1(a741)) | (~c3_1(a741)) | c2_1(a744) | c0_1(a744) | (~c3_1(a744)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a744) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a741)) | c2_1(a744) | (~c3_1(a744))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[3512])).
% 0.91/1.10 tff(3514,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | (~c1_1(a741)) | c0_1(a741) | (~c2_1(a741)) | (~c3_1(a741)) | c2_1(a744) | c0_1(a744) | (~c3_1(a744)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a744) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a741)) | c2_1(a744) | (~c3_1(a744)))),
% 0.91/1.10 inference(transitivity,[status(thm)],[3513, 3511])).
% 0.91/1.10 tff(3515,plain,
% 0.91/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a741)) | (~c3_1(a741)) | (~c1_1(a741)) | c0_1(a741) | (~c2_1(a741)) | (~c3_1(a741)) | c2_1(a744) | c0_1(a744) | (~c3_1(a744)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(3516,plain,
% 0.91/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a744) | c0_1(a741) | (~ndr1_0) | (~c1_1(a741)) | (~c2_1(a741)) | (~c3_1(a741)) | c2_1(a744) | (~c3_1(a744))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3515, 3514])).
% 0.91/1.10 tff(3517,plain,
% 0.91/1.10 ($false),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3516, 104, 3017, 207, 178, 2049, 177, 2537, 3510, 3503])).
% 0.91/1.10 tff(3518,plain,((~hskp8) | (~c1_1(a741)) | (~c3_1(a741)) | c0_1(a741) | (~c0_1(a730)) | (~c3_1(a730)) | c2_1(a730)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.10 tff(3519,plain,
% 0.91/1.10 (~hskp8),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3518, 3457, 3497, 177, 3277, 3279, 3502])).
% 0.91/1.10 tff(3520,plain,
% 0.91/1.10 (hskp2),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[540, 3502, 255, 3499, 3137, 3277, 3500, 3501])).
% 0.91/1.10 tff(3521,plain,
% 0.91/1.10 (~c3_1(a732)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[546, 3520])).
% 0.91/1.10 tff(3522,plain,
% 0.91/1.10 (~c2_1(a732)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[282, 3520])).
% 0.91/1.10 tff(3523,plain,
% 0.91/1.10 (~c0_1(a732)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[288, 3520])).
% 0.91/1.10 tff(3524,plain,
% 0.91/1.10 (hskp8 | (~c2_1(a749))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1870, 104, 3465, 3461, 3523, 3522, 3521, 619])).
% 0.91/1.10 tff(3525,plain,
% 0.91/1.10 (~c2_1(a749)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3524, 3519])).
% 0.91/1.10 tff(3526,plain,
% 0.91/1.10 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c0_1(a777) | c3_1(a777) | c0_1(a749) | c3_1(a749) | (~ndr1_0) | c2_1(a749) | (~c2_1(a777)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a777) | c3_1(a777) | c0_1(a749) | c3_1(a749) | (~ndr1_0) | c2_1(a749) | (~c2_1(a777)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3527,plain,
% 0.91/1.10 ((hskp8 | (~ndr1_0) | c0_1(a777) | c3_1(a777) | (~c2_1(a777)) | c3_1(a749) | c0_1(a749) | c2_1(a749)) <=> (hskp8 | c0_1(a777) | c3_1(a777) | c0_1(a749) | c3_1(a749) | (~ndr1_0) | c2_1(a749) | (~c2_1(a777)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3528,plain,
% 0.91/1.10 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a777) | c3_1(a777) | (~c2_1(a777)) | c3_1(a749) | c0_1(a749) | c2_1(a749))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c0_1(a777) | c3_1(a777) | c0_1(a749) | c3_1(a749) | (~ndr1_0) | c2_1(a749) | (~c2_1(a777))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[3527])).
% 0.91/1.10 tff(3529,plain,
% 0.91/1.10 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a777) | c3_1(a777) | (~c2_1(a777)) | c3_1(a749) | c0_1(a749) | c2_1(a749))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a777) | c3_1(a777) | c0_1(a749) | c3_1(a749) | (~ndr1_0) | c2_1(a749) | (~c2_1(a777)))),
% 0.91/1.10 inference(transitivity,[status(thm)],[3528, 3526])).
% 0.91/1.10 tff(3530,plain,
% 0.91/1.10 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a777) | c3_1(a777) | (~c2_1(a777)) | c3_1(a749) | c0_1(a749) | c2_1(a749))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(3531,plain,
% 0.91/1.10 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a777) | c3_1(a777) | c0_1(a749) | c3_1(a749) | (~ndr1_0) | c2_1(a749) | (~c2_1(a777))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3530, 3529])).
% 0.91/1.10 tff(3532,plain,
% 0.91/1.10 ($false),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3531, 1496, 104, 2038, 2017, 2016, 3465, 3461, 619, 1542])).
% 0.91/1.10 tff(3533,plain,((~hskp19) | hskp8 | c2_1(a749)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.10 tff(3534,plain,
% 0.91/1.10 (~hskp19),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3533, 3519, 3525])).
% 0.91/1.10 tff(3535,plain,
% 0.91/1.10 (hskp27),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3402, 3534])).
% 0.91/1.10 tff(3536,plain,
% 0.91/1.10 (c1_1(a750)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[732, 3535])).
% 0.91/1.10 tff(3537,plain,
% 0.91/1.10 (hskp25 | c2_1(a749)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2614, 104, 3277, 3279, 3465, 3462, 3137, 20])).
% 0.91/1.10 tff(3538,plain,
% 0.91/1.10 (hskp25),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3537, 3525])).
% 0.91/1.10 tff(3539,plain,
% 0.91/1.10 (c2_1(a741)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2517, 3497, 177, 3457])).
% 0.91/1.10 tff(3540,plain,
% 0.91/1.10 (c0_1(a750)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[716, 3535])).
% 0.91/1.10 tff(3541,plain,
% 0.91/1.10 (c2_1(a750)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[724, 3535])).
% 0.91/1.10 tff(3542,plain,
% 0.91/1.10 ($false),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[933, 3541, 3540, 177, 255, 3457, 3497, 3539, 3538, 3536])).
% 0.91/1.10 tff(3543,plain,(c0_1(a741) | hskp1 | c0_1(a734)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.10 tff(3544,plain,
% 0.91/1.10 (c0_1(a741)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3543, 22, 255])).
% 0.91/1.10 tff(3545,plain,
% 0.91/1.10 (~hskp7),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[163, 3544])).
% 0.91/1.10 tff(3546,plain,
% 0.91/1.10 (hskp4),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[141, 3545, 255])).
% 0.91/1.10 tff(3547,plain,
% 0.91/1.10 (c1_1(a734)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[51, 3546])).
% 0.91/1.10 tff(3548,plain,
% 0.91/1.10 (~c3_1(a734)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2745, 3546])).
% 0.91/1.10 tff(3549,plain,
% 0.91/1.10 (~hskp8),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3019, 2266, 22, 1029, 33])).
% 0.91/1.10 tff(3550,plain,
% 0.91/1.10 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c0_1(a749) | c3_1(a749) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | c2_1(a749))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a749) | c3_1(a749) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | c2_1(a749))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3551,plain,
% 0.91/1.10 ((hskp8 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c3_1(a749) | c0_1(a749) | c2_1(a749)) <=> (hskp8 | c0_1(a749) | c3_1(a749) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | c2_1(a749))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3552,plain,
% 0.91/1.10 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c3_1(a749) | c0_1(a749) | c2_1(a749))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c0_1(a749) | c3_1(a749) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | c2_1(a749)))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[3551])).
% 0.91/1.10 tff(3553,plain,
% 0.91/1.10 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c3_1(a749) | c0_1(a749) | c2_1(a749))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a749) | c3_1(a749) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | c2_1(a749))),
% 0.91/1.10 inference(transitivity,[status(thm)],[3552, 3550])).
% 0.91/1.10 tff(3554,plain,
% 0.91/1.10 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a734) | c3_1(a734) | (~c2_1(a734)) | c3_1(a749) | c0_1(a749) | c2_1(a749))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(3555,plain,
% 0.91/1.10 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c0_1(a749) | c3_1(a749) | c0_1(a734) | c3_1(a734) | (~ndr1_0) | (~c2_1(a734)) | c2_1(a749)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3554, 3553])).
% 0.91/1.10 tff(3556,plain,
% 0.91/1.10 (hskp8 | c3_1(a734) | (~c2_1(a734)) | c2_1(a749)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3555, 104, 3465, 3461, 22, 619])).
% 0.91/1.10 tff(3557,plain,
% 0.91/1.10 ($false),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3556, 3549, 2266, 33, 3464])).
% 0.91/1.10 tff(3558,plain,(hskp5 | c3_1(a734) | c0_1(a734) | hskp7 | (~c1_1(a734)) | (~c0_1(a730)) | (~c3_1(a730)) | c1_1(a730)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.10 tff(3559,plain,
% 0.91/1.10 (hskp5),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3558, 3548, 22, 3545, 3547, 3277, 3279, 3137])).
% 0.91/1.10 tff(3560,plain,
% 0.91/1.10 (c3_1(a735)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[413, 3559])).
% 0.91/1.10 tff(3561,plain,
% 0.91/1.10 (~c0_1(a735)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[427, 3559])).
% 0.91/1.10 tff(3562,plain,
% 0.91/1.10 (c2_1(a735)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[421, 3559])).
% 0.91/1.10 tff(3563,plain,
% 0.91/1.10 (~c2_1(a730)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[509, 3560, 3279, 3561, 3277, 3137, 3562])).
% 0.91/1.10 tff(3564,plain,
% 0.91/1.10 (hskp2),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[540, 3563, 255, 3562, 3137, 3277, 3561, 3560])).
% 0.91/1.10 tff(3565,plain,
% 0.91/1.10 (~c2_1(a732)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[282, 3564])).
% 0.91/1.10 tff(3566,plain,
% 0.91/1.10 (~c0_1(a732)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[288, 3564])).
% 0.91/1.10 tff(3567,plain,
% 0.91/1.10 (~c3_1(a732)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[546, 3564])).
% 0.91/1.10 tff(3568,plain,
% 0.91/1.10 (~hskp19),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3400, 3567, 3545, 3566, 3565])).
% 0.91/1.10 tff(3569,plain,
% 0.91/1.10 (hskp27),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3402, 3568])).
% 0.91/1.10 tff(3570,plain,
% 0.91/1.10 (c2_1(a750)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[724, 3569])).
% 0.91/1.10 tff(3571,plain,
% 0.91/1.10 (c0_1(a750)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[716, 3569])).
% 0.91/1.10 tff(3572,plain,
% 0.91/1.10 (c1_1(a750)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[732, 3569])).
% 0.91/1.10 tff(3573,plain,
% 0.91/1.10 (hskp12),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3449, 3545])).
% 0.91/1.10 tff(3574,plain,
% 0.91/1.10 (c2_1(a755)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2187, 3573])).
% 0.91/1.10 tff(3575,plain,
% 0.91/1.10 (~c3_1(a755)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2179, 3573])).
% 0.91/1.10 tff(3576,plain,
% 0.91/1.10 (c1_1(a755)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2195, 3573])).
% 0.91/1.10 tff(3577,plain,
% 0.91/1.10 (~hskp10),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2403, 3572, 255, 3576, 3277, 3279, 3137, 3575, 3571, 3570, 3574])).
% 0.91/1.10 tff(3578,plain,
% 0.91/1.10 ($false),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3014, 3577, 3572, 255, 3548, 22, 3559, 3571, 3547, 3570])).
% 0.91/1.10 tff(3579,plain,(c0_1(a734) | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.91/1.10 tff(3580,plain,
% 0.91/1.10 (c0_1(a734)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3579, 255])).
% 0.91/1.10 tff(3581,plain,
% 0.91/1.10 (~hskp4),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2008, 3580])).
% 0.91/1.10 tff(3582,plain,
% 0.91/1.10 (hskp5),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[2659, 3581, 3376])).
% 0.91/1.10 tff(3583,plain,
% 0.91/1.10 (c2_1(a735)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[421, 3582])).
% 0.91/1.10 tff(3584,plain,
% 0.91/1.10 (~c0_1(a735)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[427, 3582])).
% 0.91/1.10 tff(3585,plain,
% 0.91/1.10 (c3_1(a735)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[413, 3582])).
% 0.91/1.10 tff(3586,plain,
% 0.91/1.10 (~c2_1(a730)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[509, 3585, 3279, 3584, 3277, 3137, 3583])).
% 0.91/1.11 tff(3587,plain,
% 0.91/1.11 (hskp7),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[141, 3581, 255])).
% 0.91/1.11 tff(3588,plain,
% 0.91/1.11 (~c0_1(a741)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[163, 3587])).
% 0.91/1.11 tff(3589,plain,
% 0.91/1.11 (c3_1(a741)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[157, 3587])).
% 0.91/1.11 tff(3590,plain,
% 0.91/1.11 (c1_1(a741)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[149, 3587])).
% 0.91/1.11 tff(3591,plain,
% 0.91/1.11 (~hskp8),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[3518, 3590, 3589, 3588, 3277, 3279, 3586])).
% 0.91/1.11 tff(3592,plain,
% 0.91/1.11 (hskp2),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[540, 3586, 255, 3583, 3137, 3277, 3584, 3585])).
% 0.91/1.11 tff(3593,plain,
% 0.91/1.11 (~c3_1(a732)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[546, 3592])).
% 0.91/1.11 tff(3594,plain,
% 0.91/1.11 (~c2_1(a732)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[282, 3592])).
% 0.91/1.11 tff(3595,plain,
% 0.91/1.11 (~c0_1(a732)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[288, 3592])).
% 0.91/1.11 tff(3596,plain,
% 0.91/1.11 (~c2_1(a749)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1870, 3591, 104, 3465, 3461, 3595, 3594, 3593, 619])).
% 0.91/1.11 tff(3597,plain,
% 0.91/1.11 (~hskp19),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[3533, 3596, 3591])).
% 0.91/1.11 tff(3598,plain,
% 0.91/1.11 (hskp27),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[3402, 3597])).
% 0.91/1.11 tff(3599,plain,
% 0.91/1.11 (c1_1(a750)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[732, 3598])).
% 0.91/1.11 tff(3600,plain,
% 0.91/1.11 (hskp25),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[3537, 3596])).
% 0.91/1.11 tff(3601,plain,
% 0.91/1.11 (c2_1(a741)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[2517, 3588, 3589, 3590])).
% 0.91/1.11 tff(3602,plain,
% 0.91/1.11 (c0_1(a750)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[716, 3598])).
% 0.91/1.11 tff(3603,plain,
% 0.91/1.11 (c2_1(a750)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[724, 3598])).
% 0.91/1.11 tff(3604,plain,
% 0.91/1.11 ($false),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[933, 3603, 3602, 3588, 255, 3590, 3589, 3601, 3600, 3599])).
% 0.91/1.11 tff(3605,plain,(hskp1), inference(lemma,lemma(discharge,[]))).
% 0.91/1.11 tff(3606,plain,
% 0.91/1.11 (~c2_1(a731)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[58, 3605])).
% 0.91/1.11 tff(3607,plain,
% 0.91/1.11 (c3_1(a731)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[66, 3605])).
% 0.91/1.11 tff(3608,plain,
% 0.91/1.11 (c1_1(a731)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[74, 3605])).
% 0.91/1.11 tff(3609,plain,
% 0.91/1.11 (~c0_1(a731)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[2171, 104, 3608, 3607, 3465, 3462, 3461, 3606, 10])).
% 0.91/1.11 tff(3610,plain,
% 0.91/1.11 ($false),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[127, 104, 3608, 3607, 3606, 121, 3609])).
% 0.91/1.11 % SZS output end Proof
% 0.91/1.11 % E exiting
%------------------------------------------------------------------------------