%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN504-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:23 AM UTC 2025
% Result : Unsatisfiable 0.77s 0.94s
% Output : Proof 0.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN504-1 : TPTP v9.0.0. Released v2.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:36:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.77/0.94 % SZS status Unsatisfiable
% 0.77/0.94 % SZS output start Proof
% 0.77/0.94 tff(c3_1_type, type, (
% 0.77/0.94 c3_1: $i > $o)).
% 0.77/0.94 tff(a360_type, type, (
% 0.77/0.94 a360: $i)).
% 0.77/0.94 tff(hskp6_type, type, (
% 0.77/0.94 hskp6: $o)).
% 0.77/0.94 tff(c1_1_type, type, (
% 0.77/0.94 c1_1: $i > $o)).
% 0.77/0.94 tff(a369_type, type, (
% 0.77/0.94 a369: $i)).
% 0.77/0.94 tff(a353_type, type, (
% 0.77/0.94 a353: $i)).
% 0.77/0.94 tff(c2_1_type, type, (
% 0.77/0.94 c2_1: $i > $o)).
% 0.77/0.94 tff(a359_type, type, (
% 0.77/0.94 a359: $i)).
% 0.77/0.94 tff(c0_1_type, type, (
% 0.77/0.94 c0_1: $i > $o)).
% 0.77/0.94 tff(ndr1_0_type, type, (
% 0.77/0.94 ndr1_0: $o)).
% 0.77/0.94 tff(hskp5_type, type, (
% 0.77/0.94 hskp5: $o)).
% 0.77/0.94 tff(a387_type, type, (
% 0.77/0.94 a387: $i)).
% 0.77/0.94 tff(hskp19_type, type, (
% 0.77/0.94 hskp19: $o)).
% 0.77/0.94 tff(hskp28_type, type, (
% 0.77/0.94 hskp28: $o)).
% 0.77/0.94 tff(a379_type, type, (
% 0.77/0.94 a379: $i)).
% 0.77/0.94 tff(a365_type, type, (
% 0.77/0.94 a365: $i)).
% 0.77/0.94 tff(a382_type, type, (
% 0.77/0.94 a382: $i)).
% 0.77/0.94 tff(hskp18_type, type, (
% 0.77/0.94 hskp18: $o)).
% 0.77/0.94 tff(hskp21_type, type, (
% 0.77/0.94 hskp21: $o)).
% 0.77/0.94 tff(a395_type, type, (
% 0.77/0.94 a395: $i)).
% 0.77/0.94 tff(hskp13_type, type, (
% 0.77/0.94 hskp13: $o)).
% 0.77/0.94 tff(hskp29_type, type, (
% 0.77/0.94 hskp29: $o)).
% 0.77/0.94 tff(hskp15_type, type, (
% 0.77/0.94 hskp15: $o)).
% 0.77/0.94 tff(a358_type, type, (
% 0.77/0.94 a358: $i)).
% 0.77/0.94 tff(hskp4_type, type, (
% 0.77/0.94 hskp4: $o)).
% 0.77/0.94 tff(a388_type, type, (
% 0.77/0.94 a388: $i)).
% 0.77/0.94 tff(hskp20_type, type, (
% 0.77/0.94 hskp20: $o)).
% 0.77/0.94 tff(a357_type, type, (
% 0.77/0.94 a357: $i)).
% 0.77/0.94 tff(hskp3_type, type, (
% 0.77/0.94 hskp3: $o)).
% 0.77/0.94 tff(a370_type, type, (
% 0.77/0.94 a370: $i)).
% 0.77/0.94 tff(hskp16_type, type, (
% 0.77/0.94 hskp16: $o)).
% 0.77/0.94 tff(hskp0_type, type, (
% 0.77/0.94 hskp0: $o)).
% 0.77/0.94 tff(hskp12_type, type, (
% 0.77/0.94 hskp12: $o)).
% 0.77/0.94 tff(a418_type, type, (
% 0.77/0.94 a418: $i)).
% 0.77/0.94 tff(hskp26_type, type, (
% 0.77/0.94 hskp26: $o)).
% 0.77/0.94 tff(a398_type, type, (
% 0.77/0.94 a398: $i)).
% 0.77/0.94 tff(a410_type, type, (
% 0.77/0.94 a410: $i)).
% 0.77/0.94 tff(hskp31_type, type, (
% 0.77/0.94 hskp31: $o)).
% 0.77/0.94 tff(a355_type, type, (
% 0.77/0.94 a355: $i)).
% 0.77/0.94 tff(hskp1_type, type, (
% 0.77/0.94 hskp1: $o)).
% 0.77/0.94 tff(hskp23_type, type, (
% 0.77/0.94 hskp23: $o)).
% 0.77/0.94 tff(a366_type, type, (
% 0.77/0.94 a366: $i)).
% 0.77/0.94 tff(hskp10_type, type, (
% 0.77/0.94 hskp10: $o)).
% 0.77/0.94 tff(1,plain,
% 0.77/0.94 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(2,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[1])).
% 0.77/0.94 tff(3,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(4,plain,
% 0.77/0.94 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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)) | 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)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c0_1(W))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c0_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(5,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[4])).
% 0.77/0.94 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause194')).
% 0.77/0.94 tff(7,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.77/0.94 tff(8,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.77/0.94 tff(9,plain,(
% 0.77/0.94 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.77/0.94 inference(skolemize,[status(sab)],[8])).
% 0.77/0.94 tff(10,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.77/0.94 tff(11,plain,
% 0.77/0.94 (^[U: $i] : refl((hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(12,plain,
% 0.77/0.94 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[11])).
% 0.77/0.94 tff(13,plain,
% 0.77/0.94 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(14,plain,
% 0.77/0.94 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp6) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp6))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp6) <=> (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp6) <=> (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(15,plain,
% 0.77/0.94 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp6) <=> ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[14])).
% 0.77/0.94 tff(16,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 0.77/0.94 tff(17,plain,
% 0.77/0.94 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.77/0.94 tff(18,plain,
% 0.77/0.94 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.77/0.94 tff(19,plain,(
% 0.77/0.94 ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.94 inference(skolemize,[status(sab)],[18])).
% 0.77/0.94 tff(20,plain,
% 0.77/0.94 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.77/0.94 tff(21,assumption,(~hskp6), introduced(assumption)).
% 0.77/0.94 tff(22,assumption,(hskp28), introduced(assumption)).
% 0.77/0.94 tff(23,plain,
% 0.77/0.94 (((~hskp28) | c1_1(a365)) <=> ((~hskp28) | c1_1(a365))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(24,axiom,((~hskp28) | c1_1(a365)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 0.77/0.94 tff(25,plain,
% 0.77/0.94 ((~hskp28) | c1_1(a365)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.77/0.94 tff(26,plain,
% 0.77/0.94 ((~hskp28) | c1_1(a365)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[25, 23])).
% 0.77/0.94 tff(27,plain,
% 0.77/0.94 ((~hskp28) | c1_1(a365)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.77/0.94 tff(28,plain,
% 0.77/0.94 ((~hskp28) | c1_1(a365)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.77/0.94 tff(29,plain,
% 0.77/0.94 ((~hskp28) | c1_1(a365)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.77/0.94 tff(30,plain,
% 0.77/0.94 (c1_1(a365)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[29, 22])).
% 0.77/0.94 tff(31,plain,
% 0.77/0.94 (((~hskp28) | c3_1(a365)) <=> ((~hskp28) | c3_1(a365))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(32,axiom,((~hskp28) | c3_1(a365)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 0.77/0.94 tff(33,plain,
% 0.77/0.94 ((~hskp28) | c3_1(a365)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.77/0.94 tff(34,plain,
% 0.77/0.94 ((~hskp28) | c3_1(a365)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[33, 31])).
% 0.77/0.94 tff(35,plain,
% 0.77/0.94 ((~hskp28) | c3_1(a365)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[34, 31])).
% 0.77/0.94 tff(36,plain,
% 0.77/0.94 ((~hskp28) | c3_1(a365)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.77/0.94 tff(37,plain,
% 0.77/0.94 ((~hskp28) | c3_1(a365)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[36, 31])).
% 0.77/0.94 tff(38,plain,
% 0.77/0.94 (c3_1(a365)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[37, 22])).
% 0.77/0.94 tff(39,plain,
% 0.77/0.94 (((~hskp28) | c2_1(a365)) <=> ((~hskp28) | c2_1(a365))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(40,axiom,((~hskp28) | c2_1(a365)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 0.77/0.94 tff(41,plain,
% 0.77/0.94 ((~hskp28) | c2_1(a365)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.77/0.94 tff(42,plain,
% 0.77/0.94 ((~hskp28) | c2_1(a365)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[41, 39])).
% 0.77/0.94 tff(43,plain,
% 0.77/0.94 ((~hskp28) | c2_1(a365)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[42, 39])).
% 0.77/0.94 tff(44,plain,
% 0.77/0.94 ((~hskp28) | c2_1(a365)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.77/0.94 tff(45,plain,
% 0.77/0.94 ((~hskp28) | c2_1(a365)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[44, 39])).
% 0.77/0.94 tff(46,plain,
% 0.77/0.94 (c2_1(a365)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[45, 22])).
% 0.77/0.94 tff(47,assumption,(c0_1(a365)), introduced(assumption)).
% 0.77/0.94 tff(48,plain,
% 0.77/0.94 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(49,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[48])).
% 0.77/0.94 tff(50,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(51,plain,
% 0.77/0.94 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | 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))) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | 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))) | (~c3_1(W))) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | 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))) | (~c3_1(W))) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(52,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[51])).
% 0.77/0.94 tff(53,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause207')).
% 0.77/0.94 tff(54,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.77/0.94 tff(55,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.77/0.94 tff(56,plain,(
% 0.77/0.94 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.95 inference(skolemize,[status(sab)],[55])).
% 0.77/0.95 tff(57,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.77/0.95 tff(58,assumption,(c1_1(a365)), introduced(assumption)).
% 0.77/0.95 tff(59,assumption,(c3_1(a365)), introduced(assumption)).
% 0.77/0.95 tff(60,assumption,(c2_1(a365)), introduced(assumption)).
% 0.77/0.95 tff(61,assumption,(hskp21), introduced(assumption)).
% 0.77/0.95 tff(62,plain,
% 0.77/0.95 (((~hskp21) | (~c2_1(a395))) <=> ((~hskp21) | (~c2_1(a395)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(63,plain,
% 0.77/0.95 (((~c2_1(a395)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a395)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(64,axiom,((~c2_1(a395)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 0.77/0.95 tff(65,plain,
% 0.77/0.95 ((~hskp21) | (~c2_1(a395))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.77/0.95 tff(66,plain,
% 0.77/0.95 ((~hskp21) | (~c2_1(a395))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[65, 62])).
% 0.77/0.95 tff(67,plain,
% 0.77/0.95 (~c2_1(a395)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[66, 61])).
% 0.77/0.95 tff(68,plain,
% 0.77/0.95 (((~hskp21) | (~c0_1(a395))) <=> ((~hskp21) | (~c0_1(a395)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(69,plain,
% 0.77/0.95 (((~c0_1(a395)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a395)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(70,axiom,((~c0_1(a395)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 0.77/0.95 tff(71,plain,
% 0.77/0.95 ((~hskp21) | (~c0_1(a395))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.77/0.95 tff(72,plain,
% 0.77/0.95 ((~hskp21) | (~c0_1(a395))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[71, 68])).
% 0.77/0.95 tff(73,plain,
% 0.77/0.95 (~c0_1(a395)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[72, 61])).
% 0.77/0.95 tff(74,assumption,(~ndr1_0), introduced(assumption)).
% 0.77/0.95 tff(75,plain,
% 0.77/0.95 ((ndr1_0 | (~hskp13)) <=> (ndr1_0 | (~hskp13))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(76,plain,
% 0.77/0.95 (((~hskp13) | ndr1_0) <=> (ndr1_0 | (~hskp13))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(77,axiom,((~hskp13) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause20')).
% 0.77/0.95 tff(78,plain,
% 0.77/0.95 (ndr1_0 | (~hskp13)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.77/0.95 tff(79,plain,
% 0.77/0.95 (ndr1_0 | (~hskp13)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[78, 75])).
% 0.77/0.95 tff(80,plain,
% 0.77/0.95 (~hskp13),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[79, 74])).
% 0.77/0.95 tff(81,plain,
% 0.77/0.95 ((ndr1_0 | (~hskp29)) <=> (ndr1_0 | (~hskp29))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(82,plain,
% 0.77/0.95 (((~hskp29) | ndr1_0) <=> (ndr1_0 | (~hskp29))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(83,axiom,((~hskp29) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause4')).
% 0.77/0.95 tff(84,plain,
% 0.77/0.95 (ndr1_0 | (~hskp29)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.77/0.95 tff(85,plain,
% 0.77/0.95 (ndr1_0 | (~hskp29)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[84, 81])).
% 0.77/0.95 tff(86,plain,
% 0.77/0.95 (~hskp29),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[85, 74])).
% 0.77/0.95 tff(87,plain,
% 0.77/0.95 ((ndr1_0 | (~hskp15)) <=> (ndr1_0 | (~hskp15))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(88,plain,
% 0.77/0.95 (((~hskp15) | ndr1_0) <=> (ndr1_0 | (~hskp15))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(89,axiom,((~hskp15) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause18')).
% 0.77/0.95 tff(90,plain,
% 0.77/0.95 (ndr1_0 | (~hskp15)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.77/0.95 tff(91,plain,
% 0.77/0.95 (ndr1_0 | (~hskp15)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[90, 87])).
% 0.77/0.95 tff(92,plain,
% 0.77/0.95 (~hskp15),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[91, 74])).
% 0.77/0.95 tff(93,plain,
% 0.77/0.95 ((hskp29 | hskp15 | hskp13) <=> (hskp29 | hskp15 | hskp13)),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(94,plain,
% 0.77/0.95 (((hskp29 | hskp13) | hskp15) <=> (hskp29 | hskp15 | hskp13)),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(95,plain,
% 0.77/0.95 ((hskp29 | hskp13) <=> (hskp29 | hskp13)),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(96,plain,
% 0.77/0.95 (((hskp29 | hskp13) | hskp15) <=> ((hskp29 | hskp13) | hskp15)),
% 0.77/0.95 inference(monotonicity,[status(thm)],[95])).
% 0.77/0.95 tff(97,plain,
% 0.77/0.95 (((hskp29 | hskp13) | hskp15) <=> (hskp29 | hskp15 | hskp13)),
% 0.77/0.95 inference(transitivity,[status(thm)],[96, 94])).
% 0.77/0.95 tff(98,axiom,((hskp29 | hskp13) | hskp15), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 0.77/0.95 tff(99,plain,
% 0.77/0.95 (hskp29 | hskp15 | hskp13),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.77/0.95 tff(100,plain,
% 0.77/0.95 (hskp29 | hskp15 | hskp13),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[99, 93])).
% 0.77/0.95 tff(101,plain,
% 0.77/0.95 (hskp29 | hskp15 | hskp13),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.77/0.95 tff(102,plain,
% 0.77/0.95 (hskp29 | hskp15 | hskp13),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[101, 93])).
% 0.77/0.95 tff(103,plain,
% 0.77/0.95 (hskp29 | hskp15 | hskp13),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[102, 93])).
% 0.77/0.95 tff(104,plain,
% 0.77/0.95 ($false),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[103, 92, 86, 80])).
% 0.77/0.95 tff(105,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.77/0.95 tff(106,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a395)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a395)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(107,plain,
% 0.77/0.95 (((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a395) | c0_1(a395) | (~c3_1(a395))) <=> (c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a395)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(108,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a395) | c0_1(a395) | (~c3_1(a395)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a395))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[107])).
% 0.77/0.95 tff(109,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a395) | c0_1(a395) | (~c3_1(a395)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a395)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[108, 106])).
% 0.77/0.95 tff(110,plain,
% 0.77/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a395) | c0_1(a395) | (~c3_1(a395)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(111,plain,
% 0.77/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a395))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.77/0.95 tff(112,plain,
% 0.77/0.95 (~c3_1(a395)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[111, 105, 58, 60, 59, 73, 67, 57, 47])).
% 0.77/0.95 tff(113,plain,
% 0.77/0.95 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(114,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[113])).
% 0.77/0.95 tff(115,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(116,plain,
% 0.77/0.95 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp13) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp13))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(117,plain,
% 0.77/0.95 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[116])).
% 0.77/0.95 tff(118,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 0.77/0.95 tff(119,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.77/0.95 tff(120,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.77/0.95 tff(121,plain,(
% 0.77/0.95 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.95 inference(skolemize,[status(sab)],[120])).
% 0.77/0.95 tff(122,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.77/0.95 tff(123,plain,
% 0.77/0.95 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(124,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[123])).
% 0.77/0.95 tff(125,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(126,plain,
% 0.77/0.95 (^[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))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(127,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[126])).
% 0.77/0.95 tff(128,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause206')).
% 0.77/0.95 tff(129,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.77/0.95 tff(130,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.77/0.95 tff(131,plain,(
% 0.77/0.95 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.77/0.95 inference(skolemize,[status(sab)],[130])).
% 0.77/0.95 tff(132,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.77/0.95 tff(133,assumption,(~hskp4), introduced(assumption)).
% 0.77/0.95 tff(134,assumption,(~c0_1(a388)), introduced(assumption)).
% 0.77/0.95 tff(135,plain,
% 0.77/0.95 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(136,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[135])).
% 0.77/0.95 tff(137,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(138,plain,
% 0.77/0.95 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp4))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(139,plain,
% 0.77/0.95 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[138])).
% 0.77/0.95 tff(140,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)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 0.77/0.95 tff(141,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.77/0.95 tff(142,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.77/0.95 tff(143,plain,(
% 0.77/0.95 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.77/0.95 inference(skolemize,[status(sab)],[142])).
% 0.77/0.95 tff(144,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[143, 136])).
% 0.77/0.95 tff(145,plain,
% 0.77/0.95 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(146,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[145])).
% 0.77/0.95 tff(147,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(148,plain,
% 0.77/0.95 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | 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))), (((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)))), ((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V))), ((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)))), (((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp20) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp20))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(149,plain,
% 0.77/0.95 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[148])).
% 0.77/0.95 tff(150,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 0.77/0.95 tff(151,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.77/0.95 tff(152,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.77/0.95 tff(153,plain,(
% 0.77/0.95 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.77/0.95 inference(skolemize,[status(sab)],[152])).
% 0.77/0.95 tff(154,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[153, 146])).
% 0.77/0.95 tff(155,plain,
% 0.77/0.95 (^[U: $i] : refl((hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(156,plain,
% 0.77/0.95 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[155])).
% 0.77/0.95 tff(157,plain,
% 0.77/0.95 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(158,plain,
% 0.77/0.95 (^[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)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) | hskp4) <=> ((hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp4))), rewrite(((hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(159,plain,
% 0.77/0.95 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) | hskp4) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[158])).
% 0.77/0.95 tff(160,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 0.77/0.95 tff(161,plain,
% 0.77/0.95 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.77/0.95 tff(162,plain,
% 0.77/0.95 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[161, 157])).
% 0.77/0.95 tff(163,plain,(
% 0.77/0.95 ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.95 inference(skolemize,[status(sab)],[162])).
% 0.77/0.95 tff(164,plain,
% 0.77/0.95 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[163, 156])).
% 0.77/0.95 tff(165,assumption,(~hskp3), introduced(assumption)).
% 0.77/0.95 tff(166,plain,
% 0.77/0.95 ((hskp4 | hskp6) <=> (hskp4 | hskp6)),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(167,axiom,(hskp4 | hskp6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 0.77/0.95 tff(168,plain,
% 0.77/0.95 (hskp4 | hskp6),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.77/0.95 tff(169,plain,
% 0.77/0.95 (hskp6),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[168, 133])).
% 0.77/0.95 tff(170,plain,
% 0.77/0.95 (((~hskp6) | (~c2_1(a360))) <=> ((~hskp6) | (~c2_1(a360)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(171,plain,
% 0.77/0.95 (((~c2_1(a360)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a360)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(172,axiom,((~c2_1(a360)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 0.77/0.95 tff(173,plain,
% 0.77/0.95 ((~hskp6) | (~c2_1(a360))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.77/0.95 tff(174,plain,
% 0.77/0.95 ((~hskp6) | (~c2_1(a360))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[173, 170])).
% 0.77/0.95 tff(175,plain,
% 0.77/0.95 (~c2_1(a360)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[174, 169])).
% 0.77/0.95 tff(176,plain,
% 0.77/0.95 (((~hskp6) | (~c1_1(a360))) <=> ((~hskp6) | (~c1_1(a360)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(177,plain,
% 0.77/0.95 (((~c1_1(a360)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a360)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(178,axiom,((~c1_1(a360)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 0.77/0.95 tff(179,plain,
% 0.77/0.95 ((~hskp6) | (~c1_1(a360))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.77/0.95 tff(180,plain,
% 0.77/0.95 ((~hskp6) | (~c1_1(a360))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[179, 176])).
% 0.77/0.95 tff(181,plain,
% 0.77/0.95 (~c1_1(a360)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[180, 169])).
% 0.77/0.95 tff(182,plain,
% 0.77/0.95 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(183,plain,
% 0.77/0.95 ((hskp4 | hskp3 | (~ndr1_0) | c2_1(a360) | c1_1(a360) | c0_1(a360)) <=> (hskp4 | hskp3 | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(184,plain,
% 0.77/0.95 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c2_1(a360) | c1_1(a360) | c0_1(a360))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360)))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[183])).
% 0.77/0.95 tff(185,plain,
% 0.77/0.95 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c2_1(a360) | c1_1(a360) | c0_1(a360))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360))),
% 0.77/0.95 inference(transitivity,[status(thm)],[184, 182])).
% 0.77/0.95 tff(186,plain,
% 0.77/0.95 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c2_1(a360) | c1_1(a360) | c0_1(a360))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(187,plain,
% 0.77/0.95 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.77/0.95 tff(188,plain,
% 0.77/0.95 (hskp3 | c0_1(a360)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[187, 133, 105, 181, 175, 164])).
% 0.77/0.95 tff(189,plain,
% 0.77/0.95 (c0_1(a360)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[188, 165])).
% 0.77/0.95 tff(190,plain,
% 0.77/0.95 (^[U: $i] : refl((hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(191,plain,
% 0.77/0.95 (![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[190])).
% 0.77/0.95 tff(192,plain,
% 0.77/0.95 (![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(193,plain,
% 0.77/0.95 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | 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) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp19) <=> ((hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp19))), rewrite(((hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp19) <=> (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp19) <=> (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(194,plain,
% 0.77/0.96 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp19) <=> ![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[193])).
% 0.77/0.96 tff(195,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause150')).
% 0.77/0.96 tff(196,plain,
% 0.77/0.96 (![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.77/0.96 tff(197,plain,
% 0.77/0.96 (![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[196, 192])).
% 0.77/0.96 tff(198,plain,(
% 0.77/0.96 ![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.77/0.96 inference(skolemize,[status(sab)],[197])).
% 0.77/0.96 tff(199,plain,
% 0.77/0.96 (![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[198, 191])).
% 0.77/0.96 tff(200,plain,
% 0.77/0.96 (((~hskp6) | (~c3_1(a360))) <=> ((~hskp6) | (~c3_1(a360)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(201,plain,
% 0.77/0.96 (((~c3_1(a360)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a360)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(202,axiom,((~c3_1(a360)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 0.77/0.96 tff(203,plain,
% 0.77/0.96 ((~hskp6) | (~c3_1(a360))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.77/0.96 tff(204,plain,
% 0.77/0.96 ((~hskp6) | (~c3_1(a360))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[203, 200])).
% 0.77/0.96 tff(205,plain,
% 0.77/0.96 (~c3_1(a360)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[204, 169])).
% 0.77/0.96 tff(206,plain,
% 0.77/0.96 (((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp3 | c1_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360)))) <=> ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp3 | c1_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(207,plain,
% 0.77/0.96 ((hskp19 | hskp3 | (~ndr1_0) | c1_1(a360) | c3_1(a360) | (~c0_1(a360))) <=> (hskp19 | hskp3 | c1_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(208,plain,
% 0.77/0.96 (((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp3 | (~ndr1_0) | c1_1(a360) | c3_1(a360) | (~c0_1(a360)))) <=> ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp3 | c1_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[207])).
% 0.77/0.96 tff(209,plain,
% 0.77/0.96 (((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp3 | (~ndr1_0) | c1_1(a360) | c3_1(a360) | (~c0_1(a360)))) <=> ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp3 | c1_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[208, 206])).
% 0.77/0.96 tff(210,plain,
% 0.77/0.96 ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp3 | (~ndr1_0) | c1_1(a360) | c3_1(a360) | (~c0_1(a360)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(211,plain,
% 0.77/0.96 ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp3 | c1_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.77/0.96 tff(212,plain,
% 0.77/0.96 (hskp19 | hskp3 | (~c0_1(a360))),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[211, 105, 181, 205, 199])).
% 0.77/0.96 tff(213,plain,
% 0.77/0.96 (hskp19),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[212, 189, 165])).
% 0.77/0.96 tff(214,plain,
% 0.77/0.96 (((~hskp19) | (~c2_1(a387))) <=> ((~hskp19) | (~c2_1(a387)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(215,plain,
% 0.77/0.96 (((~c2_1(a387)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a387)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(216,axiom,((~c2_1(a387)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 0.77/0.96 tff(217,plain,
% 0.77/0.96 ((~hskp19) | (~c2_1(a387))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.77/0.96 tff(218,plain,
% 0.77/0.96 ((~hskp19) | (~c2_1(a387))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[217, 214])).
% 0.77/0.96 tff(219,plain,
% 0.77/0.96 (~c2_1(a387)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[218, 213])).
% 0.77/0.96 tff(220,plain,
% 0.77/0.96 (((~hskp19) | (~c1_1(a387))) <=> ((~hskp19) | (~c1_1(a387)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(221,plain,
% 0.77/0.96 (((~c1_1(a387)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a387)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(222,axiom,((~c1_1(a387)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 0.77/0.96 tff(223,plain,
% 0.77/0.96 ((~hskp19) | (~c1_1(a387))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.77/0.96 tff(224,plain,
% 0.77/0.96 ((~hskp19) | (~c1_1(a387))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[223, 220])).
% 0.77/0.96 tff(225,plain,
% 0.77/0.96 (~c1_1(a387)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[224, 213])).
% 0.77/0.96 tff(226,plain,
% 0.77/0.96 (((~hskp19) | (~c0_1(a387))) <=> ((~hskp19) | (~c0_1(a387)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(227,plain,
% 0.77/0.96 (((~c0_1(a387)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a387)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(228,axiom,((~c0_1(a387)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 0.77/0.96 tff(229,plain,
% 0.77/0.96 ((~hskp19) | (~c0_1(a387))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.77/0.96 tff(230,plain,
% 0.77/0.96 ((~hskp19) | (~c0_1(a387))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[229, 226])).
% 0.77/0.96 tff(231,plain,
% 0.77/0.96 (~c0_1(a387)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[230, 213])).
% 0.77/0.96 tff(232,plain,
% 0.77/0.96 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(233,plain,
% 0.77/0.96 ((hskp4 | hskp3 | (~ndr1_0) | c2_1(a387) | c1_1(a387) | c0_1(a387)) <=> (hskp4 | hskp3 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(234,plain,
% 0.77/0.96 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0)))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[233])).
% 0.77/0.96 tff(235,plain,
% 0.77/0.96 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0))),
% 0.77/0.96 inference(transitivity,[status(thm)],[234, 232])).
% 0.77/0.96 tff(236,plain,
% 0.77/0.96 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c2_1(a387) | c1_1(a387) | c0_1(a387))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(237,plain,
% 0.77/0.96 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.77/0.96 tff(238,plain,
% 0.77/0.96 ($false),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[237, 133, 105, 165, 231, 225, 219, 164])).
% 0.77/0.96 tff(239,plain,(hskp3 | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.77/0.96 tff(240,plain,
% 0.77/0.96 (hskp3),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[239, 133])).
% 0.77/0.96 tff(241,plain,
% 0.77/0.96 (((~hskp3) | (~c0_1(a357))) <=> ((~hskp3) | (~c0_1(a357)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(242,plain,
% 0.77/0.96 (((~c0_1(a357)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a357)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(243,axiom,((~c0_1(a357)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 0.77/0.96 tff(244,plain,
% 0.77/0.96 ((~hskp3) | (~c0_1(a357))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.77/0.96 tff(245,plain,
% 0.77/0.96 ((~hskp3) | (~c0_1(a357))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[244, 241])).
% 0.77/0.96 tff(246,plain,
% 0.77/0.96 (~c0_1(a357)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[245, 240])).
% 0.77/0.96 tff(247,plain,
% 0.77/0.96 (((~hskp3) | c3_1(a357)) <=> ((~hskp3) | c3_1(a357))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(248,axiom,((~hskp3) | c3_1(a357)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 0.77/0.96 tff(249,plain,
% 0.77/0.96 ((~hskp3) | c3_1(a357)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.77/0.96 tff(250,plain,
% 0.77/0.96 ((~hskp3) | c3_1(a357)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[249, 247])).
% 0.77/0.96 tff(251,plain,
% 0.77/0.96 ((~hskp3) | c3_1(a357)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[250, 247])).
% 0.77/0.96 tff(252,plain,
% 0.77/0.96 ((~hskp3) | c3_1(a357)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[251, 247])).
% 0.77/0.96 tff(253,plain,
% 0.77/0.96 ((~hskp3) | c3_1(a357)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[252, 247])).
% 0.77/0.96 tff(254,plain,
% 0.77/0.96 (c3_1(a357)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[253, 240])).
% 0.77/0.96 tff(255,plain,
% 0.77/0.96 (((~hskp3) | c1_1(a357)) <=> ((~hskp3) | c1_1(a357))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(256,axiom,((~hskp3) | c1_1(a357)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 0.77/0.96 tff(257,plain,
% 0.77/0.96 ((~hskp3) | c1_1(a357)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.77/0.96 tff(258,plain,
% 0.77/0.96 ((~hskp3) | c1_1(a357)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[257, 255])).
% 0.77/0.96 tff(259,plain,
% 0.77/0.96 ((~hskp3) | c1_1(a357)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[258, 255])).
% 0.77/0.96 tff(260,plain,
% 0.77/0.96 ((~hskp3) | c1_1(a357)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[259, 255])).
% 0.77/0.96 tff(261,plain,
% 0.77/0.96 ((~hskp3) | c1_1(a357)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[260, 255])).
% 0.77/0.96 tff(262,plain,
% 0.77/0.96 (c1_1(a357)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[261, 240])).
% 0.77/0.96 tff(263,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp20 | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(264,plain,
% 0.77/0.96 ((hskp20 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a360) | c1_1(a360) | c3_1(a360)) <=> (hskp20 | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(265,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a360) | c1_1(a360) | c3_1(a360))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[264])).
% 0.77/0.96 tff(266,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a360) | c1_1(a360) | c3_1(a360))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp20 | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[265, 263])).
% 0.77/0.96 tff(267,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a360) | c1_1(a360) | c3_1(a360))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(268,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp20 | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.77/0.96 tff(269,plain,
% 0.77/0.96 (hskp20),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[268, 105, 262, 254, 181, 175, 205, 246, 154])).
% 0.77/0.96 tff(270,plain,
% 0.77/0.96 (((~hskp20) | (~c3_1(a388))) <=> ((~hskp20) | (~c3_1(a388)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(271,plain,
% 0.77/0.96 (((~c3_1(a388)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a388)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(272,axiom,((~c3_1(a388)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 0.77/0.96 tff(273,plain,
% 0.77/0.96 ((~hskp20) | (~c3_1(a388))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.77/0.96 tff(274,plain,
% 0.77/0.96 ((~hskp20) | (~c3_1(a388))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[273, 270])).
% 0.77/0.96 tff(275,plain,
% 0.77/0.96 (~c3_1(a388)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[274, 269])).
% 0.77/0.96 tff(276,plain,
% 0.77/0.96 (((~hskp20) | (~c2_1(a388))) <=> ((~hskp20) | (~c2_1(a388)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(277,plain,
% 0.77/0.96 (((~c2_1(a388)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a388)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(278,axiom,((~c2_1(a388)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 0.77/0.96 tff(279,plain,
% 0.77/0.96 ((~hskp20) | (~c2_1(a388))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.77/0.96 tff(280,plain,
% 0.77/0.96 ((~hskp20) | (~c2_1(a388))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[279, 276])).
% 0.77/0.96 tff(281,plain,
% 0.77/0.96 (~c2_1(a388)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[280, 269])).
% 0.77/0.96 tff(282,plain,
% 0.77/0.96 (((~hskp20) | c1_1(a388)) <=> ((~hskp20) | c1_1(a388))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(283,axiom,((~hskp20) | c1_1(a388)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 0.77/0.96 tff(284,plain,
% 0.77/0.96 ((~hskp20) | c1_1(a388)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.77/0.96 tff(285,plain,
% 0.77/0.96 ((~hskp20) | c1_1(a388)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[284, 282])).
% 0.77/0.96 tff(286,plain,
% 0.77/0.96 ((~hskp20) | c1_1(a388)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[285, 282])).
% 0.77/0.96 tff(287,plain,
% 0.77/0.96 ((~hskp20) | c1_1(a388)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[286, 282])).
% 0.77/0.96 tff(288,plain,
% 0.77/0.96 ((~hskp20) | c1_1(a388)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[287, 282])).
% 0.77/0.96 tff(289,plain,
% 0.77/0.96 (c1_1(a388)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[288, 269])).
% 0.77/0.96 tff(290,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | c0_1(a388))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | c0_1(a388))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(291,plain,
% 0.77/0.96 ((hskp4 | (~ndr1_0) | c0_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a388) | c0_1(a388) | (~c1_1(a388))) <=> (hskp4 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | c0_1(a388))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(292,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a388) | c0_1(a388) | (~c1_1(a388)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | c0_1(a388)))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[291])).
% 0.77/0.96 tff(293,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a388) | c0_1(a388) | (~c1_1(a388)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | c0_1(a388))),
% 0.77/0.96 inference(transitivity,[status(thm)],[292, 290])).
% 0.77/0.96 tff(294,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a388) | c0_1(a388) | (~c1_1(a388)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(295,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | c0_1(a388)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.77/0.96 tff(296,plain,
% 0.77/0.96 ($false),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[295, 133, 105, 289, 281, 275, 144, 134])).
% 0.77/0.96 tff(297,plain,(c0_1(a388) | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.77/0.96 tff(298,plain,
% 0.77/0.96 (c0_1(a388)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[297, 133])).
% 0.77/0.96 tff(299,plain,
% 0.77/0.96 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(300,plain,
% 0.77/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[299])).
% 0.77/0.96 tff(301,plain,
% 0.77/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(302,plain,
% 0.77/0.96 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(303,plain,
% 0.77/0.96 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[302])).
% 0.77/0.96 tff(304,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause205')).
% 0.77/0.96 tff(305,plain,
% 0.77/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.77/0.96 tff(306,plain,
% 0.77/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[305, 301])).
% 0.77/0.96 tff(307,plain,(
% 0.77/0.96 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.77/0.96 inference(skolemize,[status(sab)],[306])).
% 0.77/0.96 tff(308,plain,
% 0.77/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[307, 300])).
% 0.77/0.96 tff(309,assumption,(c0_1(a388)), introduced(assumption)).
% 0.77/0.96 tff(310,assumption,(~c2_1(a357)), introduced(assumption)).
% 0.77/0.96 tff(311,assumption,(~c3_1(a388)), introduced(assumption)).
% 0.77/0.96 tff(312,assumption,(~c2_1(a388)), introduced(assumption)).
% 0.77/0.96 tff(313,assumption,(c3_1(a357)), introduced(assumption)).
% 0.77/0.96 tff(314,assumption,(c1_1(a357)), introduced(assumption)).
% 0.77/0.96 tff(315,assumption,(c1_1(a388)), introduced(assumption)).
% 0.77/0.96 tff(316,plain,
% 0.77/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a357)) | c2_1(a357) | (~c3_1(a357)) | (~c1_1(a388)) | (~c0_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a357)) | c2_1(a357) | (~c3_1(a357)) | (~c1_1(a388)) | (~c0_1(a388)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(317,plain,
% 0.77/0.96 (((~ndr1_0) | c2_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a388) | (~c1_1(a388)) | (~c0_1(a388)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388))) <=> (c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a357)) | c2_1(a357) | (~c3_1(a357)) | (~c1_1(a388)) | (~c0_1(a388)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(318,plain,
% 0.77/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a388) | (~c1_1(a388)) | (~c0_1(a388)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a357)) | c2_1(a357) | (~c3_1(a357)) | (~c1_1(a388)) | (~c0_1(a388))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[317])).
% 0.77/0.96 tff(319,plain,
% 0.77/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a388) | (~c1_1(a388)) | (~c0_1(a388)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a357)) | c2_1(a357) | (~c3_1(a357)) | (~c1_1(a388)) | (~c0_1(a388)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[318, 316])).
% 0.77/0.96 tff(320,plain,
% 0.77/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a388) | (~c1_1(a388)) | (~c0_1(a388)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(321,plain,
% 0.77/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a357)) | c2_1(a357) | (~c3_1(a357)) | (~c1_1(a388)) | (~c0_1(a388))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.77/0.96 tff(322,plain,
% 0.77/0.96 ($false),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[321, 105, 315, 314, 313, 312, 311, 308, 310, 309])).
% 0.77/0.96 tff(323,plain,(c2_1(a357) | (~c1_1(a388)) | (~c1_1(a357)) | (~c3_1(a357)) | c2_1(a388) | c3_1(a388) | (~c0_1(a388))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.96 tff(324,plain,
% 0.77/0.96 (c2_1(a357)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[323, 289, 262, 254, 281, 275, 298])).
% 0.77/0.96 tff(325,plain,
% 0.77/0.96 (^[U: $i] : refl((hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(326,plain,
% 0.77/0.96 (![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[325])).
% 0.77/0.96 tff(327,plain,
% 0.77/0.96 (![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(328,plain,
% 0.77/0.96 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp21))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp4) <=> ((hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp4))), rewrite(((hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp4) <=> (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp4) <=> (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(329,plain,
% 0.77/0.96 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp4) <=> ![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[328])).
% 0.77/0.96 tff(330,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 0.77/0.96 tff(331,plain,
% 0.77/0.96 (![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[330, 329])).
% 0.77/0.96 tff(332,plain,
% 0.77/0.96 (![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[331, 327])).
% 0.77/0.96 tff(333,plain,(
% 0.77/0.96 ![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.77/0.96 inference(skolemize,[status(sab)],[332])).
% 0.77/0.96 tff(334,plain,
% 0.77/0.96 (![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[333, 326])).
% 0.77/0.96 tff(335,plain,
% 0.77/0.96 (((~![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp21 | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357)))) <=> ((~![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp4 | hskp21 | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(336,plain,
% 0.77/0.96 ((hskp4 | hskp21 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c2_1(a357))) <=> (hskp4 | hskp21 | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(337,plain,
% 0.77/0.96 (((~![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp21 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c2_1(a357)))) <=> ((~![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp21 | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[336])).
% 0.77/0.97 tff(338,plain,
% 0.77/0.97 (((~![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp21 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c2_1(a357)))) <=> ((~![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp4 | hskp21 | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357)))),
% 0.77/0.97 inference(transitivity,[status(thm)],[337, 335])).
% 0.77/0.97 tff(339,plain,
% 0.77/0.97 ((~![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp21 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c2_1(a357)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(340,plain,
% 0.77/0.97 ((~![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp4 | hskp21 | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.77/0.97 tff(341,plain,
% 0.77/0.97 (hskp21 | (~c2_1(a357))),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[340, 133, 105, 254, 246, 334])).
% 0.77/0.97 tff(342,plain,
% 0.77/0.97 (hskp21),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[341, 324])).
% 0.77/0.97 tff(343,plain,
% 0.77/0.97 (~c2_1(a395)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[66, 342])).
% 0.77/0.97 tff(344,plain,
% 0.77/0.97 (((~hskp21) | c1_1(a395)) <=> ((~hskp21) | c1_1(a395))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(345,axiom,((~hskp21) | c1_1(a395)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 0.77/0.97 tff(346,plain,
% 0.77/0.97 ((~hskp21) | c1_1(a395)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.77/0.97 tff(347,plain,
% 0.77/0.97 ((~hskp21) | c1_1(a395)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[346, 344])).
% 0.77/0.97 tff(348,plain,
% 0.77/0.97 ((~hskp21) | c1_1(a395)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[347, 344])).
% 0.77/0.97 tff(349,plain,
% 0.77/0.97 ((~hskp21) | c1_1(a395)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[348, 344])).
% 0.77/0.97 tff(350,plain,
% 0.77/0.97 ((~hskp21) | c1_1(a395)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[349, 344])).
% 0.77/0.97 tff(351,plain,
% 0.77/0.97 (c1_1(a395)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[350, 342])).
% 0.77/0.97 tff(352,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a395) | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | (~c0_1(a388)) | (~c3_1(a395)) | (~c1_1(a395)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a395) | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | (~c0_1(a388)) | (~c3_1(a395)) | (~c1_1(a395)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(353,plain,
% 0.77/0.97 (((~ndr1_0) | c2_1(a395) | (~c3_1(a395)) | (~c1_1(a395)) | c2_1(a388) | (~c1_1(a388)) | (~c0_1(a388)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388))) <=> (c2_1(a395) | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | (~c0_1(a388)) | (~c3_1(a395)) | (~c1_1(a395)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(354,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a395) | (~c3_1(a395)) | (~c1_1(a395)) | c2_1(a388) | (~c1_1(a388)) | (~c0_1(a388)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a395) | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | (~c0_1(a388)) | (~c3_1(a395)) | (~c1_1(a395))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[353])).
% 0.77/0.97 tff(355,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a395) | (~c3_1(a395)) | (~c1_1(a395)) | c2_1(a388) | (~c1_1(a388)) | (~c0_1(a388)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a395) | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | (~c0_1(a388)) | (~c3_1(a395)) | (~c1_1(a395)))),
% 0.77/0.97 inference(transitivity,[status(thm)],[354, 352])).
% 0.77/0.97 tff(356,plain,
% 0.77/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a395) | (~c3_1(a395)) | (~c1_1(a395)) | c2_1(a388) | (~c1_1(a388)) | (~c0_1(a388)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(357,plain,
% 0.77/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a395) | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | (~c0_1(a388)) | (~c3_1(a395)) | (~c1_1(a395))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[356, 355])).
% 0.77/0.97 tff(358,plain,
% 0.77/0.97 (~c3_1(a395)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[357, 105, 351, 289, 343, 281, 275, 308, 298])).
% 0.77/0.97 tff(359,plain,
% 0.77/0.97 (~c0_1(a395)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[72, 342])).
% 0.77/0.97 tff(360,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | c3_1(a395) | (~c1_1(a395)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | c3_1(a395) | (~c1_1(a395)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(361,plain,
% 0.77/0.97 ((hskp4 | (~ndr1_0) | c0_1(a395) | c3_1(a395) | (~c1_1(a395)) | c2_1(a395) | c0_1(a395) | (~c1_1(a395))) <=> (hskp4 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | c3_1(a395) | (~c1_1(a395)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(362,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a395) | c3_1(a395) | (~c1_1(a395)) | c2_1(a395) | c0_1(a395) | (~c1_1(a395)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | c3_1(a395) | (~c1_1(a395))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[361])).
% 0.77/0.97 tff(363,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a395) | c3_1(a395) | (~c1_1(a395)) | c2_1(a395) | c0_1(a395) | (~c1_1(a395)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | c3_1(a395) | (~c1_1(a395)))),
% 0.77/0.97 inference(transitivity,[status(thm)],[362, 360])).
% 0.77/0.97 tff(364,plain,
% 0.77/0.97 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a395) | c3_1(a395) | (~c1_1(a395)) | c2_1(a395) | c0_1(a395) | (~c1_1(a395)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(365,plain,
% 0.77/0.97 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | c3_1(a395) | (~c1_1(a395))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.77/0.97 tff(366,plain,
% 0.77/0.97 ($false),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[365, 133, 105, 351, 359, 343, 144, 358])).
% 0.77/0.97 tff(367,plain,(hskp4), inference(lemma,lemma(discharge,[]))).
% 0.77/0.97 tff(368,plain,
% 0.77/0.97 (((~hskp4) | (~c3_1(a358))) <=> ((~hskp4) | (~c3_1(a358)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(369,plain,
% 0.77/0.97 (((~c3_1(a358)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a358)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(370,axiom,((~c3_1(a358)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 0.77/0.97 tff(371,plain,
% 0.77/0.97 ((~hskp4) | (~c3_1(a358))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.77/0.97 tff(372,plain,
% 0.77/0.97 ((~hskp4) | (~c3_1(a358))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[371, 368])).
% 0.77/0.97 tff(373,plain,
% 0.77/0.97 (~c3_1(a358)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[372, 367])).
% 0.77/0.97 tff(374,plain,
% 0.77/0.97 (((~hskp4) | (~c0_1(a358))) <=> ((~hskp4) | (~c0_1(a358)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(375,plain,
% 0.77/0.97 (((~c0_1(a358)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a358)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(376,axiom,((~c0_1(a358)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 0.77/0.97 tff(377,plain,
% 0.77/0.97 ((~hskp4) | (~c0_1(a358))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[376, 375])).
% 0.77/0.97 tff(378,plain,
% 0.77/0.97 ((~hskp4) | (~c0_1(a358))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[377, 374])).
% 0.77/0.97 tff(379,plain,
% 0.77/0.97 (~c0_1(a358)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[378, 367])).
% 0.77/0.97 tff(380,assumption,(hskp13), introduced(assumption)).
% 0.77/0.97 tff(381,plain,
% 0.77/0.97 (((~hskp13) | (~c3_1(a370))) <=> ((~hskp13) | (~c3_1(a370)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(382,plain,
% 0.77/0.97 (((~c3_1(a370)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a370)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(383,axiom,((~c3_1(a370)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 0.77/0.97 tff(384,plain,
% 0.77/0.97 ((~hskp13) | (~c3_1(a370))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.77/0.97 tff(385,plain,
% 0.77/0.97 ((~hskp13) | (~c3_1(a370))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[384, 381])).
% 0.77/0.97 tff(386,plain,
% 0.77/0.97 (~c3_1(a370)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[385, 380])).
% 0.77/0.97 tff(387,plain,
% 0.77/0.97 (((~hskp4) | c2_1(a358)) <=> ((~hskp4) | c2_1(a358))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(388,axiom,((~hskp4) | c2_1(a358)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 0.77/0.97 tff(389,plain,
% 0.77/0.97 ((~hskp4) | c2_1(a358)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.77/0.97 tff(390,plain,
% 0.77/0.97 ((~hskp4) | c2_1(a358)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[389, 387])).
% 0.77/0.97 tff(391,plain,
% 0.77/0.97 ((~hskp4) | c2_1(a358)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[390, 387])).
% 0.77/0.97 tff(392,plain,
% 0.77/0.97 ((~hskp4) | c2_1(a358)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[391, 387])).
% 0.77/0.97 tff(393,plain,
% 0.77/0.97 ((~hskp4) | c2_1(a358)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[392, 387])).
% 0.77/0.97 tff(394,plain,
% 0.77/0.97 (c2_1(a358)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[393, 367])).
% 0.77/0.97 tff(395,plain,
% 0.77/0.97 (((~hskp13) | c2_1(a370)) <=> ((~hskp13) | c2_1(a370))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(396,axiom,((~hskp13) | c2_1(a370)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 0.77/0.97 tff(397,plain,
% 0.77/0.97 ((~hskp13) | c2_1(a370)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[396, 395])).
% 0.77/0.97 tff(398,plain,
% 0.77/0.97 ((~hskp13) | c2_1(a370)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[397, 395])).
% 0.77/0.97 tff(399,plain,
% 0.77/0.97 ((~hskp13) | c2_1(a370)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[398, 395])).
% 0.77/0.97 tff(400,plain,
% 0.77/0.97 ((~hskp13) | c2_1(a370)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[399, 395])).
% 0.77/0.97 tff(401,plain,
% 0.77/0.97 ((~hskp13) | c2_1(a370)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[400, 395])).
% 0.77/0.97 tff(402,plain,
% 0.77/0.97 (c2_1(a370)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[401, 380])).
% 0.77/0.97 tff(403,plain,
% 0.77/0.97 (((~hskp13) | c0_1(a370)) <=> ((~hskp13) | c0_1(a370))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(404,axiom,((~hskp13) | c0_1(a370)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 0.77/0.97 tff(405,plain,
% 0.77/0.97 ((~hskp13) | c0_1(a370)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.77/0.97 tff(406,plain,
% 0.77/0.97 ((~hskp13) | c0_1(a370)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[405, 403])).
% 0.77/0.97 tff(407,plain,
% 0.77/0.97 ((~hskp13) | c0_1(a370)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[406, 403])).
% 0.77/0.97 tff(408,plain,
% 0.77/0.97 ((~hskp13) | c0_1(a370)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[407, 403])).
% 0.77/0.97 tff(409,plain,
% 0.77/0.97 ((~hskp13) | c0_1(a370)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[408, 403])).
% 0.77/0.97 tff(410,plain,
% 0.77/0.97 (c0_1(a370)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[409, 380])).
% 0.77/0.97 tff(411,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a370) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a370)) | (~c0_1(a370)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a370) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a370)) | (~c0_1(a370)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(412,plain,
% 0.77/0.97 (((~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c3_1(a370) | (~c2_1(a370)) | (~c0_1(a370)) | c0_1(a358) | c3_1(a358) | (~c2_1(a358))) <=> (c3_1(a370) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a370)) | (~c0_1(a370)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(413,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c3_1(a370) | (~c2_1(a370)) | (~c0_1(a370)) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a370) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a370)) | (~c0_1(a370))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[412])).
% 0.77/0.97 tff(414,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c3_1(a370) | (~c2_1(a370)) | (~c0_1(a370)) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a370) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a370)) | (~c0_1(a370)))),
% 0.77/0.97 inference(transitivity,[status(thm)],[413, 411])).
% 0.77/0.97 tff(415,plain,
% 0.77/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c3_1(a370) | (~c2_1(a370)) | (~c0_1(a370)) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(416,plain,
% 0.77/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a370) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a370)) | (~c0_1(a370))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[415, 414])).
% 0.77/0.97 tff(417,plain,
% 0.77/0.97 ($false),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[416, 105, 58, 60, 59, 410, 402, 394, 386, 379, 373, 132])).
% 0.77/0.97 tff(418,plain,((~hskp13) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.97 tff(419,plain,
% 0.77/0.97 (~hskp13),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[418, 58, 60, 59])).
% 0.77/0.97 tff(420,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a395))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a395))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(421,plain,
% 0.77/0.97 ((hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a395) | c0_1(a395) | c3_1(a395)) <=> (hskp13 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a395))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(422,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a395) | c0_1(a395) | c3_1(a395))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a395)))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[421])).
% 0.77/0.97 tff(423,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a395) | c0_1(a395) | c3_1(a395))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a395))),
% 0.77/0.97 inference(transitivity,[status(thm)],[422, 420])).
% 0.77/0.97 tff(424,plain,
% 0.77/0.97 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a395) | c0_1(a395) | c3_1(a395))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(425,plain,
% 0.77/0.97 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a395)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[424, 423])).
% 0.77/0.97 tff(426,plain,
% 0.77/0.97 ($false),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[425, 105, 419, 58, 60, 59, 73, 67, 122, 112])).
% 0.77/0.97 tff(427,plain,((~hskp21) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.97 tff(428,plain,
% 0.77/0.97 (~hskp21),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[427, 47, 60, 59, 58])).
% 0.77/0.97 tff(429,plain,
% 0.77/0.97 ((hskp6 | hskp21 | hskp18) <=> (hskp6 | hskp21 | hskp18)),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(430,plain,
% 0.77/0.97 (((hskp21 | hskp18) | hskp6) <=> (hskp6 | hskp21 | hskp18)),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(431,plain,
% 0.77/0.97 ((hskp21 | hskp18) <=> (hskp21 | hskp18)),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(432,plain,
% 0.77/0.97 (((hskp21 | hskp18) | hskp6) <=> ((hskp21 | hskp18) | hskp6)),
% 0.77/0.97 inference(monotonicity,[status(thm)],[431])).
% 0.77/0.97 tff(433,plain,
% 0.77/0.97 (((hskp21 | hskp18) | hskp6) <=> (hskp6 | hskp21 | hskp18)),
% 0.77/0.97 inference(transitivity,[status(thm)],[432, 430])).
% 0.77/0.97 tff(434,axiom,((hskp21 | hskp18) | hskp6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 0.77/0.97 tff(435,plain,
% 0.77/0.97 (hskp6 | hskp21 | hskp18),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[434, 433])).
% 0.77/0.97 tff(436,plain,
% 0.77/0.97 (hskp6 | hskp21 | hskp18),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[435, 429])).
% 0.77/0.97 tff(437,plain,
% 0.77/0.97 (hskp6 | hskp21 | hskp18),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[436, 429])).
% 0.77/0.97 tff(438,plain,
% 0.77/0.97 (hskp6 | hskp21 | hskp18),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[437, 429])).
% 0.77/0.97 tff(439,plain,
% 0.77/0.97 (hskp6 | hskp21 | hskp18),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[438, 429])).
% 0.77/0.97 tff(440,plain,
% 0.77/0.97 (hskp18),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[439, 428, 21])).
% 0.77/0.97 tff(441,plain,
% 0.77/0.97 (((~hskp18) | (~c2_1(a382))) <=> ((~hskp18) | (~c2_1(a382)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(442,plain,
% 0.77/0.97 (((~c2_1(a382)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a382)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(443,axiom,((~c2_1(a382)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 0.77/0.97 tff(444,plain,
% 0.77/0.97 ((~hskp18) | (~c2_1(a382))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[443, 442])).
% 0.77/0.97 tff(445,plain,
% 0.77/0.97 ((~hskp18) | (~c2_1(a382))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[444, 441])).
% 0.77/0.97 tff(446,plain,
% 0.77/0.97 (~c2_1(a382)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[445, 440])).
% 0.77/0.97 tff(447,plain,
% 0.77/0.97 (((~hskp18) | (~c0_1(a382))) <=> ((~hskp18) | (~c0_1(a382)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(448,plain,
% 0.77/0.97 (((~c0_1(a382)) | (~hskp18)) <=> ((~hskp18) | (~c0_1(a382)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(449,axiom,((~c0_1(a382)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 0.77/0.97 tff(450,plain,
% 0.77/0.97 ((~hskp18) | (~c0_1(a382))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[449, 448])).
% 0.77/0.97 tff(451,plain,
% 0.77/0.97 ((~hskp18) | (~c0_1(a382))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[450, 447])).
% 0.77/0.97 tff(452,plain,
% 0.77/0.97 (~c0_1(a382)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[451, 440])).
% 0.77/0.97 tff(453,plain,
% 0.77/0.97 (((~hskp18) | c3_1(a382)) <=> ((~hskp18) | c3_1(a382))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(454,axiom,((~hskp18) | c3_1(a382)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 0.77/0.97 tff(455,plain,
% 0.77/0.97 ((~hskp18) | c3_1(a382)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[454, 453])).
% 0.77/0.97 tff(456,plain,
% 0.77/0.97 ((~hskp18) | c3_1(a382)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[455, 453])).
% 0.77/0.97 tff(457,plain,
% 0.77/0.97 ((~hskp18) | c3_1(a382)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[456, 453])).
% 0.77/0.97 tff(458,plain,
% 0.77/0.97 ((~hskp18) | c3_1(a382)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[457, 453])).
% 0.77/0.97 tff(459,plain,
% 0.77/0.97 ((~hskp18) | c3_1(a382)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[458, 453])).
% 0.77/0.97 tff(460,plain,
% 0.77/0.97 (c3_1(a382)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[459, 440])).
% 0.77/0.97 tff(461,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a382) | c2_1(a382) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a382)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a382) | c2_1(a382) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a382)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(462,plain,
% 0.77/0.97 (((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a382) | c0_1(a382) | (~c3_1(a382))) <=> (c0_1(a382) | c2_1(a382) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a382)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(463,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a382) | c0_1(a382) | (~c3_1(a382)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a382) | c2_1(a382) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a382))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[462])).
% 0.77/0.97 tff(464,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a382) | c0_1(a382) | (~c3_1(a382)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a382) | c2_1(a382) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a382)))),
% 0.77/0.97 inference(transitivity,[status(thm)],[463, 461])).
% 0.77/0.97 tff(465,plain,
% 0.77/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a382) | c0_1(a382) | (~c3_1(a382)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(466,plain,
% 0.77/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a382) | c2_1(a382) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a382))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[465, 464])).
% 0.77/0.97 tff(467,plain,
% 0.77/0.97 ($false),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[466, 105, 58, 60, 59, 460, 452, 446, 57, 47])).
% 0.77/0.97 tff(468,plain,((~c0_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | hskp6), inference(lemma,lemma(discharge,[]))).
% 0.77/0.97 tff(469,plain,
% 0.77/0.97 (~c0_1(a365)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[468, 46, 21, 38, 30])).
% 0.77/0.97 tff(470,plain,
% 0.77/0.97 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.77/0.97 inference(bind,[status(th)],[])).
% 0.77/0.97 tff(471,plain,
% 0.77/0.97 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.77/0.97 inference(quant_intro,[status(thm)],[470])).
% 0.77/0.97 tff(472,plain,
% 0.77/0.97 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(473,plain,
% 0.77/0.97 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_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) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp6) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp6))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.77/0.97 inference(bind,[status(th)],[])).
% 0.77/0.97 tff(474,plain,
% 0.77/0.97 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.77/0.97 inference(quant_intro,[status(thm)],[473])).
% 0.77/0.97 tff(475,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 0.77/0.97 tff(476,plain,
% 0.77/0.97 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[475, 474])).
% 0.77/0.97 tff(477,plain,
% 0.77/0.97 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[476, 472])).
% 0.77/0.97 tff(478,plain,(
% 0.77/0.97 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.77/0.97 inference(skolemize,[status(sab)],[477])).
% 0.77/0.97 tff(479,plain,
% 0.77/0.97 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[478, 471])).
% 0.77/0.97 tff(480,plain,
% 0.77/0.97 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.77/0.97 inference(bind,[status(th)],[])).
% 0.77/0.97 tff(481,plain,
% 0.77/0.97 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.77/0.97 inference(quant_intro,[status(thm)],[480])).
% 0.77/0.97 tff(482,plain,
% 0.77/0.97 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(483,plain,
% 0.77/0.97 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp16))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.82/0.98 inference(bind,[status(th)],[])).
% 0.82/0.98 tff(484,plain,
% 0.82/0.98 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.82/0.98 inference(quant_intro,[status(thm)],[483])).
% 0.82/0.98 tff(485,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause196')).
% 0.82/0.98 tff(486,plain,
% 0.82/0.98 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[485, 484])).
% 0.82/0.98 tff(487,plain,
% 0.82/0.98 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[486, 482])).
% 0.82/0.98 tff(488,plain,(
% 0.82/0.98 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.82/0.98 inference(skolemize,[status(sab)],[487])).
% 0.82/0.98 tff(489,plain,
% 0.82/0.98 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[488, 481])).
% 0.82/0.98 tff(490,plain,
% 0.82/0.98 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(491,plain,
% 0.82/0.98 ((hskp16 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c0_1(a365) | (~c3_1(a365)) | (~c2_1(a365))) <=> (hskp16 | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(492,plain,
% 0.82/0.98 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c0_1(a365) | (~c3_1(a365)) | (~c2_1(a365)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365)))),
% 0.82/0.98 inference(monotonicity,[status(thm)],[491])).
% 0.82/0.98 tff(493,plain,
% 0.82/0.98 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c0_1(a365) | (~c3_1(a365)) | (~c2_1(a365)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365))),
% 0.82/0.98 inference(transitivity,[status(thm)],[492, 490])).
% 0.82/0.98 tff(494,plain,
% 0.82/0.98 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c0_1(a365) | (~c3_1(a365)) | (~c2_1(a365)))),
% 0.82/0.98 inference(quant_inst,[status(thm)],[])).
% 0.82/0.98 tff(495,plain,
% 0.82/0.98 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365)),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[494, 493])).
% 0.82/0.98 tff(496,plain,
% 0.82/0.98 (hskp16),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[495, 105, 30, 46, 38, 489, 469])).
% 0.82/0.98 tff(497,plain,
% 0.82/0.98 (((~hskp16) | (~c1_1(a379))) <=> ((~hskp16) | (~c1_1(a379)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(498,plain,
% 0.82/0.98 (((~c1_1(a379)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a379)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(499,axiom,((~c1_1(a379)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 0.82/0.98 tff(500,plain,
% 0.82/0.98 ((~hskp16) | (~c1_1(a379))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[499, 498])).
% 0.82/0.98 tff(501,plain,
% 0.82/0.98 ((~hskp16) | (~c1_1(a379))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[500, 497])).
% 0.82/0.98 tff(502,plain,
% 0.82/0.98 (~c1_1(a379)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[501, 496])).
% 0.82/0.98 tff(503,plain,
% 0.82/0.98 (((~hskp16) | c2_1(a379)) <=> ((~hskp16) | c2_1(a379))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(504,axiom,((~hskp16) | c2_1(a379)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 0.82/0.98 tff(505,plain,
% 0.82/0.98 ((~hskp16) | c2_1(a379)),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[504, 503])).
% 0.82/0.98 tff(506,plain,
% 0.82/0.98 ((~hskp16) | c2_1(a379)),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[505, 503])).
% 0.82/0.98 tff(507,plain,
% 0.82/0.98 ((~hskp16) | c2_1(a379)),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[506, 503])).
% 0.82/0.98 tff(508,plain,
% 0.82/0.98 ((~hskp16) | c2_1(a379)),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[507, 503])).
% 0.82/0.98 tff(509,plain,
% 0.82/0.98 ((~hskp16) | c2_1(a379)),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[508, 503])).
% 0.82/0.98 tff(510,plain,
% 0.82/0.98 (c2_1(a379)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[509, 496])).
% 0.82/0.98 tff(511,plain,
% 0.82/0.98 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c1_1(a379) | (~ndr1_0) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365) | (~c2_1(a379)) | c0_1(a379))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c1_1(a379) | (~ndr1_0) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365) | (~c2_1(a379)) | c0_1(a379))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(512,plain,
% 0.82/0.98 ((hskp6 | (~ndr1_0) | c0_1(a365) | (~c3_1(a365)) | (~c2_1(a365)) | c1_1(a379) | c0_1(a379) | (~c2_1(a379))) <=> (hskp6 | c1_1(a379) | (~ndr1_0) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365) | (~c2_1(a379)) | c0_1(a379))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(513,plain,
% 0.82/0.98 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a365) | (~c3_1(a365)) | (~c2_1(a365)) | c1_1(a379) | c0_1(a379) | (~c2_1(a379)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c1_1(a379) | (~ndr1_0) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365) | (~c2_1(a379)) | c0_1(a379)))),
% 0.82/0.98 inference(monotonicity,[status(thm)],[512])).
% 0.82/0.98 tff(514,plain,
% 0.82/0.98 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a365) | (~c3_1(a365)) | (~c2_1(a365)) | c1_1(a379) | c0_1(a379) | (~c2_1(a379)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c1_1(a379) | (~ndr1_0) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365) | (~c2_1(a379)) | c0_1(a379))),
% 0.82/0.98 inference(transitivity,[status(thm)],[513, 511])).
% 0.82/0.98 tff(515,plain,
% 0.82/0.98 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a365) | (~c3_1(a365)) | (~c2_1(a365)) | c1_1(a379) | c0_1(a379) | (~c2_1(a379)))),
% 0.82/0.98 inference(quant_inst,[status(thm)],[])).
% 0.82/0.98 tff(516,plain,
% 0.82/0.98 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c1_1(a379) | (~ndr1_0) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365) | (~c2_1(a379)) | c0_1(a379)),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[515, 514])).
% 0.82/0.98 tff(517,plain,
% 0.82/0.98 (c0_1(a379)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[516, 21, 105, 46, 38, 510, 502, 479, 469])).
% 0.82/0.98 tff(518,plain,
% 0.82/0.98 (((~hskp16) | (~c3_1(a379))) <=> ((~hskp16) | (~c3_1(a379)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(519,plain,
% 0.82/0.98 (((~c3_1(a379)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a379)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(520,axiom,((~c3_1(a379)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 0.82/0.98 tff(521,plain,
% 0.82/0.98 ((~hskp16) | (~c3_1(a379))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[520, 519])).
% 0.82/0.98 tff(522,plain,
% 0.82/0.98 ((~hskp16) | (~c3_1(a379))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[521, 518])).
% 0.82/0.98 tff(523,plain,
% 0.82/0.98 (~c3_1(a379)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[522, 496])).
% 0.82/0.98 tff(524,plain,
% 0.82/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a379) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a379)) | (~c0_1(a379)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a379) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a379)) | (~c0_1(a379)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(525,plain,
% 0.82/0.98 (((~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c3_1(a379) | (~c2_1(a379)) | (~c0_1(a379)) | c0_1(a358) | c3_1(a358) | (~c2_1(a358))) <=> (c3_1(a379) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a379)) | (~c0_1(a379)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(526,plain,
% 0.82/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c3_1(a379) | (~c2_1(a379)) | (~c0_1(a379)) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a379) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a379)) | (~c0_1(a379))))),
% 0.82/0.98 inference(monotonicity,[status(thm)],[525])).
% 0.82/0.98 tff(527,plain,
% 0.82/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c3_1(a379) | (~c2_1(a379)) | (~c0_1(a379)) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a379) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a379)) | (~c0_1(a379)))),
% 0.82/0.98 inference(transitivity,[status(thm)],[526, 524])).
% 0.82/0.98 tff(528,plain,
% 0.82/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c3_1(a379) | (~c2_1(a379)) | (~c0_1(a379)) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)))),
% 0.82/0.98 inference(quant_inst,[status(thm)],[])).
% 0.82/0.98 tff(529,plain,
% 0.82/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a379) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a379)) | (~c0_1(a379))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[528, 527])).
% 0.82/0.98 tff(530,plain,
% 0.82/0.98 ($false),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[529, 105, 30, 46, 38, 510, 394, 523, 379, 373, 132, 517])).
% 0.82/0.98 tff(531,plain,((~hskp28) | hskp6), inference(lemma,lemma(discharge,[]))).
% 0.82/0.98 tff(532,plain,
% 0.82/0.98 (~hskp28),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[531, 21])).
% 0.82/0.98 tff(533,plain,
% 0.82/0.98 (^[U: $i] : refl((hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 0.82/0.98 inference(bind,[status(th)],[])).
% 0.82/0.98 tff(534,plain,
% 0.82/0.98 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.82/0.98 inference(quant_intro,[status(thm)],[533])).
% 0.82/0.98 tff(535,plain,
% 0.82/0.98 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(536,plain,
% 0.82/0.98 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp28))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) | hskp19) <=> ((hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp19))), rewrite(((hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp19) <=> (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) | hskp19) <=> (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 0.82/0.98 inference(bind,[status(th)],[])).
% 0.82/0.98 tff(537,plain,
% 0.82/0.98 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) | hskp19) <=> ![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.82/0.98 inference(quant_intro,[status(thm)],[536])).
% 0.82/0.98 tff(538,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 0.82/0.98 tff(539,plain,
% 0.82/0.98 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[538, 537])).
% 0.82/0.98 tff(540,plain,
% 0.82/0.98 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[539, 535])).
% 0.82/0.98 tff(541,plain,(
% 0.82/0.98 ![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.82/0.98 inference(skolemize,[status(sab)],[540])).
% 0.82/0.98 tff(542,plain,
% 0.82/0.98 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[541, 534])).
% 0.82/0.98 tff(543,plain,
% 0.82/0.98 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp19 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp19 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(544,plain,
% 0.82/0.98 ((hskp28 | hskp19 | (~ndr1_0) | c0_1(a358) | c3_1(a358) | (~c2_1(a358))) <=> (hskp28 | hskp19 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(545,plain,
% 0.82/0.98 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp19 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358))))),
% 0.82/0.98 inference(monotonicity,[status(thm)],[544])).
% 0.82/0.98 tff(546,plain,
% 0.82/0.98 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp19 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)))),
% 0.82/0.98 inference(transitivity,[status(thm)],[545, 543])).
% 0.82/0.98 tff(547,plain,
% 0.82/0.98 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)))),
% 0.82/0.98 inference(quant_inst,[status(thm)],[])).
% 0.82/0.98 tff(548,plain,
% 0.82/0.98 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp19 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[547, 546])).
% 0.82/0.98 tff(549,plain,
% 0.82/0.98 (hskp28 | hskp19),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[548, 105, 394, 379, 373, 542])).
% 0.82/0.98 tff(550,plain,
% 0.82/0.98 (hskp19),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[549, 532])).
% 0.82/0.98 tff(551,plain,
% 0.82/0.98 (~c2_1(a387)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[218, 550])).
% 0.82/0.98 tff(552,plain,
% 0.82/0.98 (~c1_1(a387)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[224, 550])).
% 0.82/0.98 tff(553,plain,
% 0.82/0.98 (~c0_1(a387)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[230, 550])).
% 0.82/0.98 tff(554,plain,
% 0.82/0.98 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp6 | hskp5 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp6 | hskp5 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(555,plain,
% 0.82/0.98 ((hskp6 | hskp5 | (~ndr1_0) | c2_1(a387) | c1_1(a387) | c0_1(a387)) <=> (hskp6 | hskp5 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(556,plain,
% 0.82/0.98 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp6 | hskp5 | (~ndr1_0) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp6 | hskp5 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0)))),
% 0.82/0.98 inference(monotonicity,[status(thm)],[555])).
% 0.82/0.98 tff(557,plain,
% 0.82/0.98 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp6 | hskp5 | (~ndr1_0) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp6 | hskp5 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0))),
% 0.82/0.98 inference(transitivity,[status(thm)],[556, 554])).
% 0.82/0.98 tff(558,plain,
% 0.82/0.98 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp6 | hskp5 | (~ndr1_0) | c2_1(a387) | c1_1(a387) | c0_1(a387))),
% 0.82/0.98 inference(quant_inst,[status(thm)],[])).
% 0.82/0.98 tff(559,plain,
% 0.82/0.98 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp6 | hskp5 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0)),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[558, 557])).
% 0.82/0.98 tff(560,plain,
% 0.82/0.98 (hskp5),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[559, 21, 105, 553, 552, 551, 20])).
% 0.82/0.98 tff(561,plain,
% 0.82/0.98 (((~hskp5) | (~c3_1(a359))) <=> ((~hskp5) | (~c3_1(a359)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(562,plain,
% 0.82/0.98 (((~c3_1(a359)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a359)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(563,axiom,((~c3_1(a359)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 0.82/0.98 tff(564,plain,
% 0.82/0.98 ((~hskp5) | (~c3_1(a359))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[563, 562])).
% 0.82/0.98 tff(565,plain,
% 0.82/0.98 ((~hskp5) | (~c3_1(a359))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[564, 561])).
% 0.82/0.98 tff(566,plain,
% 0.82/0.98 (~c3_1(a359)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[565, 560])).
% 0.82/0.98 tff(567,plain,
% 0.82/0.98 (((~hskp5) | (~c1_1(a359))) <=> ((~hskp5) | (~c1_1(a359)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(568,plain,
% 0.82/0.98 (((~c1_1(a359)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a359)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(569,axiom,((~c1_1(a359)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 0.82/0.98 tff(570,plain,
% 0.82/0.98 ((~hskp5) | (~c1_1(a359))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[569, 568])).
% 0.82/0.98 tff(571,plain,
% 0.82/0.98 ((~hskp5) | (~c1_1(a359))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[570, 567])).
% 0.82/0.98 tff(572,plain,
% 0.82/0.98 (~c1_1(a359)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[571, 560])).
% 0.82/0.98 tff(573,plain,
% 0.82/0.98 (((~hskp5) | (~c0_1(a359))) <=> ((~hskp5) | (~c0_1(a359)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(574,plain,
% 0.82/0.98 (((~c0_1(a359)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a359)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(575,axiom,((~c0_1(a359)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 0.82/0.98 tff(576,plain,
% 0.82/0.98 ((~hskp5) | (~c0_1(a359))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[575, 574])).
% 0.82/0.98 tff(577,plain,
% 0.82/0.98 ((~hskp5) | (~c0_1(a359))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[576, 573])).
% 0.82/0.98 tff(578,plain,
% 0.82/0.98 (~c0_1(a359)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[577, 560])).
% 0.82/0.98 tff(579,plain,
% 0.82/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0) | (~c2_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0) | (~c2_1(a359)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(580,plain,
% 0.82/0.98 (((~ndr1_0) | c1_1(a359) | c0_1(a359) | (~c2_1(a359)) | c1_1(a359) | c0_1(a359) | c3_1(a359) | c2_1(a387) | c1_1(a387) | c0_1(a387)) <=> (c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0) | (~c2_1(a359)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(581,plain,
% 0.82/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a359) | c0_1(a359) | (~c2_1(a359)) | c1_1(a359) | c0_1(a359) | c3_1(a359) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0) | (~c2_1(a359))))),
% 0.82/0.98 inference(monotonicity,[status(thm)],[580])).
% 0.82/0.98 tff(582,plain,
% 0.82/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a359) | c0_1(a359) | (~c2_1(a359)) | c1_1(a359) | c0_1(a359) | c3_1(a359) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0) | (~c2_1(a359)))),
% 0.82/0.98 inference(transitivity,[status(thm)],[581, 579])).
% 0.82/0.98 tff(583,plain,
% 0.82/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a359) | c0_1(a359) | (~c2_1(a359)) | c1_1(a359) | c0_1(a359) | c3_1(a359) | c2_1(a387) | c1_1(a387) | c0_1(a387))),
% 0.82/0.98 inference(quant_inst,[status(thm)],[])).
% 0.82/0.98 tff(584,plain,
% 0.82/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0) | (~c2_1(a359))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[583, 582])).
% 0.82/0.98 tff(585,plain,
% 0.82/0.98 (~c2_1(a359)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[584, 105, 553, 552, 551, 578, 572, 566, 10])).
% 0.82/0.98 tff(586,plain,
% 0.82/0.98 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W)))),
% 0.82/0.98 inference(bind,[status(th)],[])).
% 0.82/0.98 tff(587,plain,
% 0.82/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_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)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.82/0.98 inference(quant_intro,[status(thm)],[586])).
% 0.82/0.98 tff(588,plain,
% 0.82/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_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)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(589,plain,
% 0.82/0.98 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))))),
% 0.82/0.98 inference(bind,[status(th)],[])).
% 0.82/0.98 tff(590,plain,
% 0.82/0.98 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.82/0.98 inference(quant_intro,[status(thm)],[589])).
% 0.82/0.98 tff(591,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause200')).
% 0.82/0.98 tff(592,plain,
% 0.82/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[591, 590])).
% 0.82/0.98 tff(593,plain,
% 0.82/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[592, 588])).
% 0.82/0.98 tff(594,plain,(
% 0.82/0.98 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.82/0.98 inference(skolemize,[status(sab)],[593])).
% 0.82/0.98 tff(595,plain,
% 0.82/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[594, 587])).
% 0.82/0.98 tff(596,assumption,(~c1_1(a387)), introduced(assumption)).
% 0.82/0.98 tff(597,assumption,(~c2_1(a387)), introduced(assumption)).
% 0.82/0.98 tff(598,assumption,(~c0_1(a387)), introduced(assumption)).
% 0.82/0.98 tff(599,plain,
% 0.82/0.98 (hskp5 | c1_1(a387) | c2_1(a387)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[559, 21, 105, 598, 20])).
% 0.82/0.98 tff(600,plain,
% 0.82/0.98 (hskp5),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[599, 597, 596])).
% 0.82/0.98 tff(601,plain,
% 0.82/0.98 (~c3_1(a359)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[565, 600])).
% 0.82/0.98 tff(602,plain,
% 0.82/0.98 (~c1_1(a359)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[571, 600])).
% 0.82/0.98 tff(603,plain,
% 0.82/0.98 (~c0_1(a359)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[577, 600])).
% 0.82/0.98 tff(604,plain,
% 0.82/0.98 (~c2_1(a359)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[584, 105, 598, 596, 597, 603, 602, 601, 10])).
% 0.82/0.98 tff(605,plain,
% 0.82/0.98 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.82/0.98 inference(bind,[status(th)],[])).
% 0.82/0.98 tff(606,plain,
% 0.82/0.98 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.82/0.98 inference(quant_intro,[status(thm)],[605])).
% 0.82/0.98 tff(607,plain,
% 0.82/0.98 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(608,plain,
% 0.82/0.98 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(609,plain,
% 0.82/0.99 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[608])).
% 0.82/0.99 tff(610,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 0.82/0.99 tff(611,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[610, 609])).
% 0.82/0.99 tff(612,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[611, 607])).
% 0.82/0.99 tff(613,plain,(
% 0.82/0.99 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.82/0.99 inference(skolemize,[status(sab)],[612])).
% 0.82/0.99 tff(614,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[613, 606])).
% 0.82/0.99 tff(615,assumption,(~hskp0), introduced(assumption)).
% 0.82/0.99 tff(616,plain,
% 0.82/0.99 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c3_1(a387)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c3_1(a387)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(617,plain,
% 0.82/0.99 ((hskp0 | (~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c3_1(a387)) | c2_1(a387) | c1_1(a387) | c0_1(a387)) <=> (hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c3_1(a387)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(618,plain,
% 0.82/0.99 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c3_1(a387)) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c3_1(a387))))),
% 0.82/0.99 inference(monotonicity,[status(thm)],[617])).
% 0.82/0.99 tff(619,plain,
% 0.82/0.99 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c3_1(a387)) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c3_1(a387)))),
% 0.82/0.99 inference(transitivity,[status(thm)],[618, 616])).
% 0.82/0.99 tff(620,plain,
% 0.82/0.99 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c3_1(a387)) | c2_1(a387) | c1_1(a387) | c0_1(a387))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(621,plain,
% 0.82/0.99 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c3_1(a387))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[620, 619])).
% 0.82/0.99 tff(622,plain,
% 0.82/0.99 (~c3_1(a387)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[621, 105, 615, 598, 596, 597, 614])).
% 0.82/0.99 tff(623,plain,
% 0.82/0.99 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(624,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[623])).
% 0.82/0.99 tff(625,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(626,plain,
% 0.82/0.99 (^[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) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(627,plain,
% 0.82/0.99 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[626])).
% 0.82/0.99 tff(628,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 0.82/0.99 tff(629,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[628, 627])).
% 0.82/0.99 tff(630,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[629, 625])).
% 0.82/0.99 tff(631,plain,(
% 0.82/0.99 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.82/0.99 inference(skolemize,[status(sab)],[630])).
% 0.82/0.99 tff(632,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[631, 624])).
% 0.82/0.99 tff(633,plain,
% 0.82/0.99 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(634,plain,
% 0.82/0.99 ((hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a387) | c1_1(a387) | c0_1(a387)) <=> (hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(635,plain,
% 0.82/0.99 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358))))),
% 0.82/0.99 inference(monotonicity,[status(thm)],[634])).
% 0.82/0.99 tff(636,plain,
% 0.82/0.99 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)))),
% 0.82/0.99 inference(transitivity,[status(thm)],[635, 633])).
% 0.82/0.99 tff(637,plain,
% 0.82/0.99 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a387) | c1_1(a387) | c0_1(a387))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(638,plain,
% 0.82/0.99 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[637, 636])).
% 0.82/0.99 tff(639,plain,
% 0.82/0.99 (~c1_1(a358)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[638, 105, 615, 394, 598, 596, 597, 379, 632])).
% 0.82/0.99 tff(640,plain,
% 0.82/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a387) | c1_1(a387) | c0_1(a359) | c1_1(a359) | c0_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c2_1(a359) | c3_1(a387))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | c0_1(a359) | c1_1(a359) | c0_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c2_1(a359) | c3_1(a387))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(641,plain,
% 0.82/0.99 (((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a359) | c1_1(a359) | c0_1(a359)) <=> (c0_1(a387) | c1_1(a387) | c0_1(a359) | c1_1(a359) | c0_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c2_1(a359) | c3_1(a387))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(642,plain,
% 0.82/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a359) | c1_1(a359) | c0_1(a359))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a387) | c1_1(a387) | c0_1(a359) | c1_1(a359) | c0_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c2_1(a359) | c3_1(a387)))),
% 0.82/0.99 inference(monotonicity,[status(thm)],[641])).
% 0.82/0.99 tff(643,plain,
% 0.82/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a359) | c1_1(a359) | c0_1(a359))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | c0_1(a359) | c1_1(a359) | c0_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c2_1(a359) | c3_1(a387))),
% 0.82/0.99 inference(transitivity,[status(thm)],[642, 640])).
% 0.82/0.99 tff(644,plain,
% 0.82/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a359) | c1_1(a359) | c0_1(a359))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(645,plain,
% 0.82/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | c0_1(a359) | c1_1(a359) | c0_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c2_1(a359) | c3_1(a387)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[644, 643])).
% 0.82/0.99 tff(646,plain,
% 0.82/0.99 ($false),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[645, 105, 394, 598, 596, 603, 602, 379, 10, 639, 622, 604])).
% 0.82/0.99 tff(647,plain,(c2_1(a387) | c0_1(a387) | c1_1(a387) | hskp0 | hskp6), inference(lemma,lemma(discharge,[]))).
% 0.82/0.99 tff(648,plain,
% 0.82/0.99 (hskp0),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[647, 553, 21, 552, 551])).
% 0.82/0.99 tff(649,plain,
% 0.82/0.99 (((~hskp0) | (~c2_1(a353))) <=> ((~hskp0) | (~c2_1(a353)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(650,plain,
% 0.82/0.99 (((~c2_1(a353)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a353)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(651,axiom,((~c2_1(a353)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 0.82/0.99 tff(652,plain,
% 0.82/0.99 ((~hskp0) | (~c2_1(a353))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[651, 650])).
% 0.82/0.99 tff(653,plain,
% 0.82/0.99 ((~hskp0) | (~c2_1(a353))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[652, 649])).
% 0.82/0.99 tff(654,plain,
% 0.82/0.99 (~c2_1(a353)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[653, 648])).
% 0.82/0.99 tff(655,plain,
% 0.82/0.99 (((~hskp0) | c1_1(a353)) <=> ((~hskp0) | c1_1(a353))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(656,axiom,((~hskp0) | c1_1(a353)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 0.82/0.99 tff(657,plain,
% 0.82/0.99 ((~hskp0) | c1_1(a353)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[656, 655])).
% 0.82/0.99 tff(658,plain,
% 0.82/0.99 ((~hskp0) | c1_1(a353)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[657, 655])).
% 0.82/0.99 tff(659,plain,
% 0.82/0.99 ((~hskp0) | c1_1(a353)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[658, 655])).
% 0.82/0.99 tff(660,plain,
% 0.82/0.99 ((~hskp0) | c1_1(a353)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[659, 655])).
% 0.82/0.99 tff(661,plain,
% 0.82/0.99 ((~hskp0) | c1_1(a353)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[660, 655])).
% 0.82/0.99 tff(662,plain,
% 0.82/0.99 (c1_1(a353)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[661, 648])).
% 0.82/0.99 tff(663,plain,
% 0.82/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a359))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a359))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(664,plain,
% 0.82/0.99 (((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a359) | c1_1(a359) | c3_1(a359) | c1_1(a359) | c0_1(a359) | c3_1(a359)) <=> (c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a359))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(665,plain,
% 0.82/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a359) | c1_1(a359) | c3_1(a359) | c1_1(a359) | c0_1(a359) | c3_1(a359))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a359)))),
% 0.82/0.99 inference(monotonicity,[status(thm)],[664])).
% 0.82/0.99 tff(666,plain,
% 0.82/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a359) | c1_1(a359) | c3_1(a359) | c1_1(a359) | c0_1(a359) | c3_1(a359))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a359))),
% 0.82/0.99 inference(transitivity,[status(thm)],[665, 663])).
% 0.82/0.99 tff(667,plain,
% 0.82/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a359) | c1_1(a359) | c3_1(a359) | c1_1(a359) | c0_1(a359) | c3_1(a359))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(668,plain,
% 0.82/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a359)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[667, 666])).
% 0.82/0.99 tff(669,plain,
% 0.82/0.99 (~c3_1(a353)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[668, 105, 662, 578, 572, 566, 654, 595, 585])).
% 0.82/0.99 tff(670,plain,
% 0.82/0.99 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(671,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[670])).
% 0.82/0.99 tff(672,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(673,plain,
% 0.82/0.99 (^[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)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(674,plain,
% 0.82/0.99 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[673])).
% 0.82/0.99 tff(675,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 0.82/0.99 tff(676,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[675, 674])).
% 0.82/0.99 tff(677,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[676, 672])).
% 0.82/0.99 tff(678,plain,(
% 0.82/0.99 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.82/0.99 inference(skolemize,[status(sab)],[677])).
% 0.82/0.99 tff(679,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[678, 671])).
% 0.82/0.99 tff(680,plain,
% 0.82/0.99 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | c0_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c2_1(a359))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c0_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c2_1(a359))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(681,plain,
% 0.82/0.99 ((hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a359) | c0_1(a359) | c3_1(a359)) <=> (hskp12 | c0_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c2_1(a359))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(682,plain,
% 0.82/0.99 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a359) | c0_1(a359) | c3_1(a359))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | c0_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c2_1(a359)))),
% 0.82/0.99 inference(monotonicity,[status(thm)],[681])).
% 0.82/0.99 tff(683,plain,
% 0.82/0.99 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a359) | c0_1(a359) | c3_1(a359))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c0_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c2_1(a359))),
% 0.82/0.99 inference(transitivity,[status(thm)],[682, 680])).
% 0.82/0.99 tff(684,plain,
% 0.82/0.99 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a359) | c0_1(a359) | c3_1(a359))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(685,plain,
% 0.82/0.99 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c0_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c2_1(a359)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[684, 683])).
% 0.82/0.99 tff(686,plain,
% 0.82/0.99 (hskp12),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[685, 105, 662, 578, 566, 654, 679, 669, 585])).
% 0.82/0.99 tff(687,plain,
% 0.82/0.99 (((~hskp12) | (~c2_1(a369))) <=> ((~hskp12) | (~c2_1(a369)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(688,plain,
% 0.82/0.99 (((~c2_1(a369)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a369)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(689,axiom,((~c2_1(a369)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 0.82/0.99 tff(690,plain,
% 0.82/0.99 ((~hskp12) | (~c2_1(a369))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[689, 688])).
% 0.82/0.99 tff(691,plain,
% 0.82/0.99 ((~hskp12) | (~c2_1(a369))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[690, 687])).
% 0.82/0.99 tff(692,plain,
% 0.82/0.99 (~c2_1(a369)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[691, 686])).
% 0.82/0.99 tff(693,plain,
% 0.82/0.99 (((~hskp12) | c3_1(a369)) <=> ((~hskp12) | c3_1(a369))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(694,axiom,((~hskp12) | c3_1(a369)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 0.82/0.99 tff(695,plain,
% 0.82/0.99 ((~hskp12) | c3_1(a369)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[694, 693])).
% 0.82/1.00 tff(696,plain,
% 0.82/1.00 ((~hskp12) | c3_1(a369)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[695, 693])).
% 0.82/1.00 tff(697,plain,
% 0.82/1.00 ((~hskp12) | c3_1(a369)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[696, 693])).
% 0.82/1.00 tff(698,plain,
% 0.82/1.00 ((~hskp12) | c3_1(a369)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[697, 693])).
% 0.82/1.00 tff(699,plain,
% 0.82/1.00 ((~hskp12) | c3_1(a369)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[698, 693])).
% 0.82/1.00 tff(700,plain,
% 0.82/1.00 (c3_1(a369)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[699, 686])).
% 0.82/1.00 tff(701,plain,
% 0.82/1.00 (((~hskp12) | c0_1(a369)) <=> ((~hskp12) | c0_1(a369))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(702,axiom,((~hskp12) | c0_1(a369)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 0.82/1.00 tff(703,plain,
% 0.82/1.00 ((~hskp12) | c0_1(a369)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[702, 701])).
% 0.82/1.00 tff(704,plain,
% 0.82/1.00 ((~hskp12) | c0_1(a369)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[703, 701])).
% 0.82/1.00 tff(705,plain,
% 0.82/1.00 ((~hskp12) | c0_1(a369)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[704, 701])).
% 0.82/1.00 tff(706,plain,
% 0.82/1.00 ((~hskp12) | c0_1(a369)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[705, 701])).
% 0.82/1.00 tff(707,plain,
% 0.82/1.00 ((~hskp12) | c0_1(a369)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[706, 701])).
% 0.82/1.00 tff(708,plain,
% 0.82/1.00 (c0_1(a369)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[707, 686])).
% 0.82/1.00 tff(709,plain,
% 0.82/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | (~c3_1(a369)) | (~c1_1(a369)) | (~c0_1(a369)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | (~c3_1(a369)) | (~c1_1(a369)) | (~c0_1(a369)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(710,plain,
% 0.82/1.00 (((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a369) | (~c1_1(a369)) | (~c0_1(a369)) | c2_1(a353) | c3_1(a353) | (~c1_1(a353))) <=> (c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | (~c3_1(a369)) | (~c1_1(a369)) | (~c0_1(a369)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(711,plain,
% 0.82/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a369) | (~c1_1(a369)) | (~c0_1(a369)) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | (~c3_1(a369)) | (~c1_1(a369)) | (~c0_1(a369))))),
% 0.82/1.00 inference(monotonicity,[status(thm)],[710])).
% 0.82/1.00 tff(712,plain,
% 0.82/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a369) | (~c1_1(a369)) | (~c0_1(a369)) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | (~c3_1(a369)) | (~c1_1(a369)) | (~c0_1(a369)))),
% 0.82/1.00 inference(transitivity,[status(thm)],[711, 709])).
% 0.82/1.00 tff(713,plain,
% 0.82/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a369) | (~c1_1(a369)) | (~c0_1(a369)) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(714,plain,
% 0.82/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | (~c3_1(a369)) | (~c1_1(a369)) | (~c0_1(a369))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[713, 712])).
% 0.82/1.00 tff(715,plain,
% 0.82/1.00 (~c1_1(a369)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[714, 105, 708, 700, 662, 692, 654, 308, 669])).
% 0.82/1.00 tff(716,plain,
% 0.82/1.00 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)))),
% 0.82/1.00 inference(bind,[status(th)],[])).
% 0.82/1.00 tff(717,plain,
% 0.82/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_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)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[716])).
% 0.82/1.00 tff(718,plain,
% 0.82/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_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)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(719,plain,
% 0.82/1.00 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))))),
% 0.82/1.00 inference(bind,[status(th)],[])).
% 0.82/1.00 tff(720,plain,
% 0.82/1.00 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[719])).
% 0.82/1.00 tff(721,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause201')).
% 0.82/1.00 tff(722,plain,
% 0.82/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[721, 720])).
% 0.82/1.00 tff(723,plain,
% 0.82/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[722, 718])).
% 0.82/1.00 tff(724,plain,(
% 0.82/1.00 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.82/1.00 inference(skolemize,[status(sab)],[723])).
% 0.82/1.00 tff(725,plain,
% 0.82/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[724, 717])).
% 0.82/1.00 tff(726,plain,
% 0.82/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a369) | c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a369) | c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(727,plain,
% 0.82/1.00 (((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a359) | c0_1(a359) | c3_1(a359)) <=> (c2_1(a369) | c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(728,plain,
% 0.82/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a359) | c0_1(a359) | c3_1(a359))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a369) | c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369))))),
% 0.82/1.00 inference(monotonicity,[status(thm)],[727])).
% 0.82/1.00 tff(729,plain,
% 0.82/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a359) | c0_1(a359) | c3_1(a359))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a369) | c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369)))),
% 0.82/1.00 inference(transitivity,[status(thm)],[728, 726])).
% 0.82/1.00 tff(730,plain,
% 0.82/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a359) | c0_1(a359) | c3_1(a359))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(731,plain,
% 0.82/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a369) | c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[730, 729])).
% 0.82/1.00 tff(732,plain,
% 0.82/1.00 ($false),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[731, 105, 708, 662, 692, 578, 572, 566, 654, 725, 669, 715])).
% 0.82/1.00 tff(733,plain,(hskp6), inference(lemma,lemma(discharge,[]))).
% 0.82/1.00 tff(734,plain,
% 0.82/1.00 (~c3_1(a360)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[204, 733])).
% 0.82/1.00 tff(735,plain,
% 0.82/1.00 (~c1_1(a360)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[180, 733])).
% 0.82/1.00 tff(736,plain,
% 0.82/1.00 (~c2_1(a360)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[174, 733])).
% 0.82/1.00 tff(737,assumption,(~c2_1(a360)), introduced(assumption)).
% 0.82/1.00 tff(738,assumption,(~c3_1(a360)), introduced(assumption)).
% 0.82/1.00 tff(739,assumption,(~c1_1(a360)), introduced(assumption)).
% 0.82/1.00 tff(740,assumption,(~c0_1(a360)), introduced(assumption)).
% 0.82/1.00 tff(741,plain,
% 0.82/1.00 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a360) | c2_1(a360) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a360))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a360) | c2_1(a360) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a360))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(742,plain,
% 0.82/1.00 ((hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a360) | c1_1(a360) | c0_1(a360)) <=> (hskp0 | c1_1(a360) | c2_1(a360) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a360))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(743,plain,
% 0.82/1.00 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a360) | c1_1(a360) | c0_1(a360))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a360) | c2_1(a360) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a360)))),
% 0.82/1.00 inference(monotonicity,[status(thm)],[742])).
% 0.82/1.00 tff(744,plain,
% 0.82/1.00 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a360) | c1_1(a360) | c0_1(a360))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a360) | c2_1(a360) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a360))),
% 0.82/1.00 inference(transitivity,[status(thm)],[743, 741])).
% 0.82/1.00 tff(745,plain,
% 0.82/1.00 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a360) | c1_1(a360) | c0_1(a360))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(746,plain,
% 0.82/1.00 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a360) | c2_1(a360) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a360)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[745, 744])).
% 0.82/1.00 tff(747,plain,
% 0.82/1.00 (hskp0 | c1_1(a360) | (~c1_1(a358)) | c0_1(a360)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[746, 105, 394, 737, 379, 632])).
% 0.82/1.00 tff(748,plain,
% 0.82/1.00 (~c1_1(a358)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[747, 740, 739, 615])).
% 0.82/1.00 tff(749,assumption,(~c1_1(a388)), introduced(assumption)).
% 0.82/1.00 tff(750,assumption,(hskp3), introduced(assumption)).
% 0.82/1.00 tff(751,plain,
% 0.82/1.00 (~c0_1(a357)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[245, 750])).
% 0.82/1.00 tff(752,plain,
% 0.82/1.00 (c3_1(a357)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[253, 750])).
% 0.82/1.00 tff(753,plain,
% 0.82/1.00 (c1_1(a357)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[261, 750])).
% 0.82/1.00 tff(754,plain,
% 0.82/1.00 (~hskp20),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[288, 749])).
% 0.82/1.00 tff(755,plain,
% 0.82/1.00 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | c1_1(a388) | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp20 | c1_1(a388) | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(756,plain,
% 0.82/1.00 ((hskp20 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a388) | c1_1(a388) | c3_1(a388)) <=> (hskp20 | c1_1(a388) | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(757,plain,
% 0.82/1.00 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a388) | c1_1(a388) | c3_1(a388))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | c1_1(a388) | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357))))),
% 0.82/1.00 inference(monotonicity,[status(thm)],[756])).
% 0.82/1.00 tff(758,plain,
% 0.82/1.00 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a388) | c1_1(a388) | c3_1(a388))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp20 | c1_1(a388) | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357)))),
% 0.82/1.00 inference(transitivity,[status(thm)],[757, 755])).
% 0.82/1.00 tff(759,plain,
% 0.82/1.00 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a388) | c1_1(a388) | c3_1(a388))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(760,plain,
% 0.82/1.00 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp20 | c1_1(a388) | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[759, 758])).
% 0.82/1.00 tff(761,plain,
% 0.82/1.00 ($false),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[760, 105, 754, 749, 753, 752, 312, 311, 751, 154])).
% 0.82/1.00 tff(762,plain,((~hskp3) | c1_1(a388) | c2_1(a388) | c3_1(a388)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.00 tff(763,plain,
% 0.82/1.00 (~hskp3),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[762, 749, 312, 311])).
% 0.82/1.00 tff(764,plain,
% 0.82/1.00 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 0.82/1.00 inference(bind,[status(th)],[])).
% 0.82/1.00 tff(765,plain,
% 0.82/1.00 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[764])).
% 0.82/1.00 tff(766,plain,
% 0.82/1.00 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(767,plain,
% 0.82/1.00 (^[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))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 0.82/1.00 inference(bind,[status(th)],[])).
% 0.82/1.00 tff(768,plain,
% 0.82/1.00 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[767])).
% 0.82/1.00 tff(769,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 0.82/1.00 tff(770,plain,
% 0.82/1.00 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[769, 768])).
% 0.82/1.00 tff(771,plain,
% 0.82/1.00 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[770, 766])).
% 0.82/1.00 tff(772,plain,(
% 0.82/1.00 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.82/1.00 inference(skolemize,[status(sab)],[771])).
% 0.82/1.00 tff(773,plain,
% 0.82/1.00 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[772, 765])).
% 0.82/1.00 tff(774,plain,
% 0.82/1.00 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c1_1(a388) | c3_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a388)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c1_1(a388) | c3_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a388)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(775,plain,
% 0.82/1.00 ((hskp3 | (~ndr1_0) | c1_1(a388) | c3_1(a388) | (~c0_1(a388)) | c0_1(a358) | c3_1(a358) | (~c1_1(a358))) <=> (hskp3 | c1_1(a388) | c3_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a388)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(776,plain,
% 0.82/1.00 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a388) | c3_1(a388) | (~c0_1(a388)) | c0_1(a358) | c3_1(a358) | (~c1_1(a358)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c1_1(a388) | c3_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a388))))),
% 0.82/1.00 inference(monotonicity,[status(thm)],[775])).
% 0.82/1.00 tff(777,plain,
% 0.82/1.00 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a388) | c3_1(a388) | (~c0_1(a388)) | c0_1(a358) | c3_1(a358) | (~c1_1(a358)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c1_1(a388) | c3_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a388)))),
% 0.82/1.00 inference(transitivity,[status(thm)],[776, 774])).
% 0.82/1.00 tff(778,plain,
% 0.82/1.00 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a388) | c3_1(a388) | (~c0_1(a388)) | c0_1(a358) | c3_1(a358) | (~c1_1(a358)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(779,plain,
% 0.82/1.00 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c1_1(a388) | c3_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a388))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[778, 777])).
% 0.82/1.00 tff(780,plain,
% 0.82/1.00 (hskp3 | (~c1_1(a358)) | (~c0_1(a388))),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[779, 105, 749, 311, 379, 373, 773])).
% 0.82/1.00 tff(781,plain,
% 0.82/1.00 (~c1_1(a358)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[780, 165, 309])).
% 0.82/1.00 tff(782,plain,
% 0.82/1.00 (((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp3 | c1_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a388)))) <=> ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp3 | c1_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a388)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(783,plain,
% 0.82/1.00 ((hskp19 | hskp3 | (~ndr1_0) | c1_1(a388) | c3_1(a388) | (~c0_1(a388))) <=> (hskp19 | hskp3 | c1_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a388)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(784,plain,
% 0.82/1.00 (((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp3 | (~ndr1_0) | c1_1(a388) | c3_1(a388) | (~c0_1(a388)))) <=> ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp3 | c1_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a388))))),
% 0.82/1.00 inference(monotonicity,[status(thm)],[783])).
% 0.82/1.00 tff(785,plain,
% 0.82/1.00 (((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp3 | (~ndr1_0) | c1_1(a388) | c3_1(a388) | (~c0_1(a388)))) <=> ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp3 | c1_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a388)))),
% 0.82/1.00 inference(transitivity,[status(thm)],[784, 782])).
% 0.82/1.00 tff(786,plain,
% 0.82/1.00 ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp3 | (~ndr1_0) | c1_1(a388) | c3_1(a388) | (~c0_1(a388)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(787,plain,
% 0.82/1.00 ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp3 | c1_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a388))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[786, 785])).
% 0.82/1.00 tff(788,plain,
% 0.82/1.00 (hskp19 | hskp3 | c1_1(a388) | (~c0_1(a388))),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[787, 105, 311, 199])).
% 0.82/1.00 tff(789,plain,
% 0.82/1.00 (hskp19),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[788, 165, 749, 309])).
% 0.82/1.00 tff(790,plain,
% 0.82/1.00 (~c2_1(a387)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[218, 789])).
% 0.82/1.00 tff(791,plain,
% 0.82/1.00 (~c1_1(a387)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[224, 789])).
% 0.82/1.00 tff(792,plain,
% 0.82/1.00 (~c0_1(a387)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[230, 789])).
% 0.82/1.00 tff(793,plain,
% 0.82/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(794,plain,
% 0.82/1.00 (((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a358) | c0_1(a358) | c3_1(a358) | c2_1(a387) | c1_1(a387) | c0_1(a387)) <=> (c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(795,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a358) | c0_1(a358) | c3_1(a358) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358))))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[794])).
% 0.82/1.01 tff(796,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a358) | c0_1(a358) | c3_1(a358) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)))),
% 0.82/1.01 inference(transitivity,[status(thm)],[795, 793])).
% 0.82/1.01 tff(797,plain,
% 0.82/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a358) | c0_1(a358) | c3_1(a358) | c2_1(a387) | c1_1(a387) | c0_1(a387))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(798,plain,
% 0.82/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[797, 796])).
% 0.82/1.01 tff(799,plain,
% 0.82/1.01 ($false),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[798, 105, 394, 792, 791, 790, 379, 373, 10, 781])).
% 0.82/1.01 tff(800,plain,(hskp3 | c1_1(a388) | (~c0_1(a388)) | c3_1(a388)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.01 tff(801,plain,
% 0.82/1.01 (~c0_1(a388)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[800, 763, 749, 311])).
% 0.82/1.01 tff(802,plain,
% 0.82/1.01 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a388) | c2_1(a388) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a388))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a388) | c2_1(a388) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a388))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(803,plain,
% 0.82/1.01 ((hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a388) | c1_1(a388) | c0_1(a388)) <=> (hskp0 | c1_1(a388) | c2_1(a388) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a388))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(804,plain,
% 0.82/1.01 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a388) | c1_1(a388) | c0_1(a388))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a388) | c2_1(a388) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a388)))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[803])).
% 0.82/1.01 tff(805,plain,
% 0.82/1.01 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a388) | c1_1(a388) | c0_1(a388))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a388) | c2_1(a388) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a388))),
% 0.82/1.01 inference(transitivity,[status(thm)],[804, 802])).
% 0.82/1.01 tff(806,plain,
% 0.82/1.01 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a388) | c1_1(a388) | c0_1(a388))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(807,plain,
% 0.82/1.01 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a388) | c2_1(a388) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a388)),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[806, 805])).
% 0.82/1.01 tff(808,plain,
% 0.82/1.01 (hskp0 | c1_1(a388) | (~c1_1(a358)) | c0_1(a388)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[807, 105, 394, 312, 379, 632])).
% 0.82/1.01 tff(809,plain,
% 0.82/1.01 (~c1_1(a358)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[808, 134, 749, 615])).
% 0.82/1.01 tff(810,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a388) | c2_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c0_1(a388))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a388) | c2_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c0_1(a388))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(811,plain,
% 0.82/1.01 (((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a358) | c0_1(a358) | c3_1(a358) | c2_1(a388) | c1_1(a388) | c0_1(a388)) <=> (c1_1(a388) | c2_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c0_1(a388))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(812,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a358) | c0_1(a358) | c3_1(a358) | c2_1(a388) | c1_1(a388) | c0_1(a388))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a388) | c2_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c0_1(a388)))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[811])).
% 0.82/1.01 tff(813,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a358) | c0_1(a358) | c3_1(a358) | c2_1(a388) | c1_1(a388) | c0_1(a388))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a388) | c2_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c0_1(a388))),
% 0.82/1.01 inference(transitivity,[status(thm)],[812, 810])).
% 0.82/1.01 tff(814,plain,
% 0.82/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a358) | c0_1(a358) | c3_1(a358) | c2_1(a388) | c1_1(a388) | c0_1(a388))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(815,plain,
% 0.82/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a388) | c2_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c0_1(a388)),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[814, 813])).
% 0.82/1.01 tff(816,plain,
% 0.82/1.01 ($false),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[815, 105, 749, 394, 312, 379, 373, 10, 134, 809])).
% 0.82/1.01 tff(817,plain,(c0_1(a388) | c1_1(a388) | c2_1(a388) | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.82/1.01 tff(818,plain,
% 0.82/1.01 (hskp0),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[817, 801, 312, 749])).
% 0.82/1.01 tff(819,plain,
% 0.82/1.01 (~c2_1(a353)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[653, 818])).
% 0.82/1.01 tff(820,plain,
% 0.82/1.01 (c1_1(a353)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[661, 818])).
% 0.82/1.01 tff(821,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a388) | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a388))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a388) | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a388))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(822,plain,
% 0.82/1.01 (((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a388) | c1_1(a388) | c3_1(a388) | c1_1(a388) | c0_1(a388) | c3_1(a388)) <=> (c1_1(a388) | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a388))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(823,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a388) | c1_1(a388) | c3_1(a388) | c1_1(a388) | c0_1(a388) | c3_1(a388))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a388) | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a388)))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[822])).
% 0.82/1.01 tff(824,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a388) | c1_1(a388) | c3_1(a388) | c1_1(a388) | c0_1(a388) | c3_1(a388))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a388) | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a388))),
% 0.82/1.01 inference(transitivity,[status(thm)],[823, 821])).
% 0.82/1.01 tff(825,plain,
% 0.82/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a388) | c1_1(a388) | c3_1(a388) | c1_1(a388) | c0_1(a388) | c3_1(a388))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(826,plain,
% 0.82/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a388) | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a388)),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[825, 824])).
% 0.82/1.01 tff(827,plain,
% 0.82/1.01 (~c3_1(a353)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[826, 105, 749, 820, 312, 311, 819, 595, 801])).
% 0.82/1.01 tff(828,plain,
% 0.82/1.01 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a388))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a388))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(829,plain,
% 0.82/1.01 ((hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a388) | c0_1(a388) | c3_1(a388)) <=> (hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a388))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(830,plain,
% 0.82/1.01 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a388) | c0_1(a388) | c3_1(a388))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a388)))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[829])).
% 0.82/1.01 tff(831,plain,
% 0.82/1.01 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a388) | c0_1(a388) | c3_1(a388))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a388))),
% 0.82/1.01 inference(transitivity,[status(thm)],[830, 828])).
% 0.82/1.01 tff(832,plain,
% 0.82/1.01 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a388) | c0_1(a388) | c3_1(a388))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(833,plain,
% 0.82/1.01 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a388)),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[832, 831])).
% 0.82/1.01 tff(834,plain,
% 0.82/1.01 (hskp12),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[833, 105, 820, 312, 311, 819, 679, 801, 827])).
% 0.82/1.01 tff(835,plain,
% 0.82/1.01 (~c2_1(a369)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[691, 834])).
% 0.82/1.01 tff(836,plain,
% 0.82/1.01 (c3_1(a369)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[699, 834])).
% 0.82/1.01 tff(837,plain,
% 0.82/1.01 (c0_1(a369)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[707, 834])).
% 0.82/1.01 tff(838,plain,
% 0.82/1.01 (~c1_1(a369)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[714, 105, 837, 836, 820, 835, 819, 308, 827])).
% 0.82/1.01 tff(839,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a388) | c3_1(a388) | c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369)) | c0_1(a388))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a388) | c3_1(a388) | c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369)) | c0_1(a388))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(840,plain,
% 0.82/1.01 (((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a388) | c0_1(a388) | c3_1(a388)) <=> (c1_1(a388) | c3_1(a388) | c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369)) | c0_1(a388))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(841,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a388) | c0_1(a388) | c3_1(a388))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a388) | c3_1(a388) | c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369)) | c0_1(a388)))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[840])).
% 0.82/1.01 tff(842,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a388) | c0_1(a388) | c3_1(a388))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a388) | c3_1(a388) | c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369)) | c0_1(a388))),
% 0.82/1.01 inference(transitivity,[status(thm)],[841, 839])).
% 0.82/1.01 tff(843,plain,
% 0.82/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a388) | c0_1(a388) | c3_1(a388))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(844,plain,
% 0.82/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a388) | c3_1(a388) | c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369)) | c0_1(a388)),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[843, 842])).
% 0.82/1.01 tff(845,plain,
% 0.82/1.01 ($false),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[844, 105, 749, 837, 820, 311, 835, 819, 725, 801, 827, 838])).
% 0.82/1.01 tff(846,plain,(c1_1(a388) | c3_1(a388) | c2_1(a388)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.01 tff(847,plain,
% 0.82/1.01 (c1_1(a388)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[846, 311, 312])).
% 0.82/1.01 tff(848,plain,
% 0.82/1.01 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(849,plain,
% 0.82/1.01 ((hskp12 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a360) | c0_1(a360) | c3_1(a360)) <=> (hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(850,plain,
% 0.82/1.01 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388))))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[849])).
% 0.82/1.01 tff(851,plain,
% 0.82/1.01 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388)))),
% 0.82/1.01 inference(transitivity,[status(thm)],[850, 848])).
% 0.82/1.01 tff(852,plain,
% 0.82/1.01 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a360) | c0_1(a360) | c3_1(a360))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(853,plain,
% 0.82/1.01 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[852, 851])).
% 0.82/1.01 tff(854,plain,
% 0.82/1.01 (hskp12 | c3_1(a388) | c0_1(a360) | (~c1_1(a388))),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[853, 105, 312, 737, 738, 679])).
% 0.82/1.01 tff(855,plain,
% 0.82/1.01 (hskp12),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[854, 740, 311, 847])).
% 0.82/1.01 tff(856,plain,
% 0.82/1.01 (~c2_1(a369)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[691, 855])).
% 0.82/1.01 tff(857,plain,
% 0.82/1.01 (c0_1(a369)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[707, 855])).
% 0.82/1.01 tff(858,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a388) | c3_1(a388) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | c1_1(a369) | (~c0_1(a369)) | (~c1_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a388) | c3_1(a388) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | c1_1(a369) | (~c0_1(a369)) | (~c1_1(a388)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(859,plain,
% 0.82/1.01 (((~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a358) | c0_1(a358) | c3_1(a358)) <=> (c2_1(a388) | c3_1(a388) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | c1_1(a369) | (~c0_1(a369)) | (~c1_1(a388)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(860,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a388) | c3_1(a388) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | c1_1(a369) | (~c0_1(a369)) | (~c1_1(a388))))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[859])).
% 0.82/1.01 tff(861,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a388) | c3_1(a388) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | c1_1(a369) | (~c0_1(a369)) | (~c1_1(a388)))),
% 0.82/1.01 inference(transitivity,[status(thm)],[860, 858])).
% 0.82/1.01 tff(862,plain,
% 0.82/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a358) | c0_1(a358) | c3_1(a358))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(863,plain,
% 0.82/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a388) | c3_1(a388) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | c1_1(a369) | (~c0_1(a369)) | (~c1_1(a388))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[862, 861])).
% 0.82/1.01 tff(864,plain,
% 0.82/1.01 (c1_1(a369)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[863, 105, 847, 857, 312, 311, 856, 379, 373, 725, 748])).
% 0.82/1.01 tff(865,plain,
% 0.82/1.01 (c3_1(a369)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[699, 855])).
% 0.82/1.01 tff(866,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a369) | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a369) | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(867,plain,
% 0.82/1.01 (((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a358) | c0_1(a358) | c3_1(a358)) <=> (c2_1(a369) | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(868,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a369) | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369))))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[867])).
% 0.82/1.01 tff(869,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a369) | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369)))),
% 0.82/1.01 inference(transitivity,[status(thm)],[868, 866])).
% 0.82/1.01 tff(870,plain,
% 0.82/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a358) | c0_1(a358) | c3_1(a358))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(871,plain,
% 0.82/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a369) | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[870, 869])).
% 0.82/1.01 tff(872,plain,
% 0.82/1.01 ($false),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[871, 105, 865, 856, 739, 737, 738, 379, 373, 595, 748, 864])).
% 0.82/1.01 tff(873,plain,(c0_1(a360) | c1_1(a360) | c2_1(a360) | c3_1(a360) | c2_1(a388) | c3_1(a388) | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.82/1.01 tff(874,plain,
% 0.82/1.01 (c0_1(a360)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[873, 615, 737, 738, 312, 311, 739])).
% 0.82/1.01 tff(875,plain,
% 0.82/1.01 (hskp19 | hskp3 | c1_1(a360) | (~c0_1(a360))),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[211, 105, 738, 199])).
% 0.82/1.01 tff(876,plain,
% 0.82/1.01 (hskp19),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[875, 874, 739, 165])).
% 0.82/1.01 tff(877,plain,
% 0.82/1.01 (~c0_1(a387)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[230, 876])).
% 0.82/1.02 tff(878,plain,
% 0.82/1.02 (~c1_1(a387)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[224, 876])).
% 0.82/1.02 tff(879,plain,
% 0.82/1.02 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | c2_1(a388) | c3_1(a388) | c0_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c1_1(a388)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a388) | c3_1(a388) | c0_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c1_1(a388)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(880,plain,
% 0.82/1.02 ((hskp12 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a387) | c0_1(a387) | c3_1(a387)) <=> (hskp12 | c2_1(a388) | c3_1(a388) | c0_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c1_1(a388)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(881,plain,
% 0.82/1.02 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a387) | c0_1(a387) | c3_1(a387))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | c2_1(a388) | c3_1(a388) | c0_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c1_1(a388))))),
% 0.82/1.02 inference(monotonicity,[status(thm)],[880])).
% 0.82/1.02 tff(882,plain,
% 0.82/1.02 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a387) | c0_1(a387) | c3_1(a387))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a388) | c3_1(a388) | c0_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c1_1(a388)))),
% 0.82/1.02 inference(transitivity,[status(thm)],[881, 879])).
% 0.82/1.02 tff(883,plain,
% 0.82/1.02 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a387) | c0_1(a387) | c3_1(a387))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(884,plain,
% 0.82/1.02 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a388) | c3_1(a388) | c0_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c1_1(a388))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[883, 882])).
% 0.82/1.02 tff(885,plain,
% 0.82/1.02 (hskp12 | c3_1(a387)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[884, 105, 847, 312, 311, 598, 597, 679])).
% 0.82/1.02 tff(886,plain,
% 0.82/1.02 (hskp12),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[885, 622])).
% 0.82/1.02 tff(887,plain,
% 0.82/1.02 (~c2_1(a369)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[691, 886])).
% 0.82/1.02 tff(888,plain,
% 0.82/1.02 (c0_1(a369)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[707, 886])).
% 0.82/1.02 tff(889,plain,
% 0.82/1.02 (c1_1(a369)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[863, 105, 847, 888, 312, 311, 887, 379, 373, 725, 639])).
% 0.82/1.02 tff(890,plain,
% 0.82/1.02 (c3_1(a369)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[699, 886])).
% 0.82/1.02 tff(891,plain,
% 0.82/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a387) | c2_1(a387) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369)) | c3_1(a387))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a387) | c2_1(a387) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369)) | c3_1(a387))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(892,plain,
% 0.82/1.02 (((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a387) | c1_1(a387) | c3_1(a387) | c1_1(a358) | c0_1(a358) | c3_1(a358)) <=> (c1_1(a387) | c2_1(a387) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369)) | c3_1(a387))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(893,plain,
% 0.82/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a387) | c1_1(a387) | c3_1(a387) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a387) | c2_1(a387) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369)) | c3_1(a387)))),
% 0.82/1.02 inference(monotonicity,[status(thm)],[892])).
% 0.82/1.02 tff(894,plain,
% 0.82/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a387) | c1_1(a387) | c3_1(a387) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a387) | c2_1(a387) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369)) | c3_1(a387))),
% 0.82/1.02 inference(transitivity,[status(thm)],[893, 891])).
% 0.82/1.02 tff(895,plain,
% 0.82/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a387) | c1_1(a387) | c3_1(a387) | c1_1(a358) | c0_1(a358) | c3_1(a358))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(896,plain,
% 0.82/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a387) | c2_1(a387) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369)) | c3_1(a387)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[895, 894])).
% 0.82/1.02 tff(897,plain,
% 0.82/1.02 ($false),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[896, 105, 890, 596, 597, 887, 379, 373, 595, 639, 622, 889])).
% 0.82/1.02 tff(898,plain,(c2_1(a387) | c1_1(a387) | c2_1(a388) | c3_1(a388) | c0_1(a387) | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.82/1.02 tff(899,plain,
% 0.82/1.02 (c2_1(a387)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[898, 596, 312, 311, 598, 615])).
% 0.82/1.02 tff(900,plain,
% 0.82/1.02 (~hskp19),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[218, 899])).
% 0.82/1.02 tff(901,plain,
% 0.82/1.02 (^[U: $i] : refl((hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 0.82/1.02 inference(bind,[status(th)],[])).
% 0.82/1.02 tff(902,plain,
% 0.82/1.02 (![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.82/1.02 inference(quant_intro,[status(thm)],[901])).
% 0.82/1.02 tff(903,plain,
% 0.82/1.02 (![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(904,plain,
% 0.82/1.02 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp0))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.82/1.02 inference(bind,[status(th)],[])).
% 0.82/1.02 tff(905,plain,
% 0.82/1.02 (![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.82/1.02 inference(quant_intro,[status(thm)],[904])).
% 0.82/1.02 tff(906,axiom,(![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 0.82/1.02 tff(907,plain,
% 0.82/1.02 (![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[906, 905])).
% 0.82/1.02 tff(908,plain,
% 0.82/1.02 (![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[907, 903])).
% 0.82/1.02 tff(909,plain,(
% 0.82/1.02 ![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.82/1.02 inference(skolemize,[status(sab)],[908])).
% 0.82/1.02 tff(910,plain,
% 0.82/1.02 (![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[909, 902])).
% 0.82/1.02 tff(911,plain,
% 0.82/1.02 (((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp0 | c0_1(a387) | (~c2_1(a387)) | (~ndr1_0) | (~c3_1(a387)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp0 | c0_1(a387) | (~c2_1(a387)) | (~ndr1_0) | (~c3_1(a387)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(912,plain,
% 0.82/1.02 ((hskp0 | (~ndr1_0) | c0_1(a387) | (~c3_1(a387)) | (~c2_1(a387))) <=> (hskp0 | c0_1(a387) | (~c2_1(a387)) | (~ndr1_0) | (~c3_1(a387)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(913,plain,
% 0.82/1.02 (((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | c0_1(a387) | (~c3_1(a387)) | (~c2_1(a387)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp0 | c0_1(a387) | (~c2_1(a387)) | (~ndr1_0) | (~c3_1(a387))))),
% 0.82/1.02 inference(monotonicity,[status(thm)],[912])).
% 0.82/1.02 tff(914,plain,
% 0.82/1.02 (((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | c0_1(a387) | (~c3_1(a387)) | (~c2_1(a387)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp0 | c0_1(a387) | (~c2_1(a387)) | (~ndr1_0) | (~c3_1(a387)))),
% 0.82/1.02 inference(transitivity,[status(thm)],[913, 911])).
% 0.82/1.02 tff(915,plain,
% 0.82/1.02 ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | c0_1(a387) | (~c3_1(a387)) | (~c2_1(a387)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(916,plain,
% 0.82/1.02 ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp0 | c0_1(a387) | (~c2_1(a387)) | (~ndr1_0) | (~c3_1(a387))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[915, 914])).
% 0.82/1.02 tff(917,plain,
% 0.82/1.02 ((~c2_1(a387)) | (~c3_1(a387))),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[916, 105, 615, 598, 910])).
% 0.82/1.02 tff(918,plain,
% 0.82/1.02 (~c3_1(a387)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[917, 899])).
% 0.82/1.02 tff(919,plain,
% 0.82/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360) | c3_1(a387))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360) | c3_1(a387))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(920,plain,
% 0.82/1.02 (((~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c2_1(a387)) | c1_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a360) | c1_1(a360) | c0_1(a360)) <=> (c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360) | c3_1(a387))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(921,plain,
% 0.82/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c2_1(a387)) | c1_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a360) | c1_1(a360) | c0_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360) | c3_1(a387)))),
% 0.82/1.02 inference(monotonicity,[status(thm)],[920])).
% 0.82/1.02 tff(922,plain,
% 0.82/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c2_1(a387)) | c1_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a360) | c1_1(a360) | c0_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360) | c3_1(a387))),
% 0.82/1.02 inference(transitivity,[status(thm)],[921, 919])).
% 0.82/1.02 tff(923,plain,
% 0.82/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c2_1(a387)) | c1_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a360) | c1_1(a360) | c0_1(a360))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(924,plain,
% 0.82/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360) | c3_1(a387)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[923, 922])).
% 0.82/1.02 tff(925,plain,
% 0.82/1.02 ((~c2_1(a387)) | c0_1(a360) | c3_1(a387)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[924, 105, 598, 596, 739, 737, 10])).
% 0.82/1.02 tff(926,plain,
% 0.82/1.02 (c0_1(a360)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[925, 899, 918])).
% 0.82/1.02 tff(927,plain,
% 0.82/1.02 ($false),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[875, 926, 900, 739, 165])).
% 0.82/1.02 tff(928,plain,(c1_1(a387) | c1_1(a360) | hskp3 | c3_1(a360) | c0_1(a387) | c2_1(a360) | hskp0 | c2_1(a388) | c3_1(a388)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.02 tff(929,plain,
% 0.82/1.02 ($false),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[928, 878, 877, 165, 738, 739, 737, 615, 312, 311])).
% 0.82/1.02 tff(930,plain,(hskp0 | hskp3 | c3_1(a360) | c1_1(a360) | c2_1(a360) | c2_1(a388) | c3_1(a388)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.02 tff(931,plain,
% 0.82/1.02 (hskp0),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[930, 165, 738, 739, 737, 312, 311])).
% 0.82/1.02 tff(932,plain,
% 0.82/1.02 (~c2_1(a353)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[653, 931])).
% 0.82/1.02 tff(933,plain,
% 0.82/1.02 (c1_1(a353)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[661, 931])).
% 0.82/1.02 tff(934,plain,
% 0.82/1.02 (((~hskp0) | c0_1(a353)) <=> ((~hskp0) | c0_1(a353))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(935,axiom,((~hskp0) | c0_1(a353)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 0.82/1.02 tff(936,plain,
% 0.82/1.02 ((~hskp0) | c0_1(a353)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[935, 934])).
% 0.82/1.02 tff(937,plain,
% 0.82/1.02 ((~hskp0) | c0_1(a353)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[936, 934])).
% 0.82/1.02 tff(938,plain,
% 0.82/1.02 ((~hskp0) | c0_1(a353)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[937, 934])).
% 0.82/1.02 tff(939,plain,
% 0.82/1.02 ((~hskp0) | c0_1(a353)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[938, 934])).
% 0.82/1.02 tff(940,plain,
% 0.82/1.02 ((~hskp0) | c0_1(a353)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[939, 934])).
% 0.82/1.02 tff(941,plain,
% 0.82/1.02 (c0_1(a353)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[940, 931])).
% 0.82/1.02 tff(942,plain,
% 0.82/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | (~c0_1(a353)) | (~c1_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | (~c0_1(a353)) | (~c1_1(a388)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(943,plain,
% 0.82/1.02 (((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a353) | (~c1_1(a353)) | (~c0_1(a353)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388))) <=> (c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | (~c0_1(a353)) | (~c1_1(a388)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(944,plain,
% 0.82/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a353) | (~c1_1(a353)) | (~c0_1(a353)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | (~c0_1(a353)) | (~c1_1(a388))))),
% 0.82/1.02 inference(monotonicity,[status(thm)],[943])).
% 0.82/1.02 tff(945,plain,
% 0.82/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a353) | (~c1_1(a353)) | (~c0_1(a353)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | (~c0_1(a353)) | (~c1_1(a388)))),
% 0.82/1.02 inference(transitivity,[status(thm)],[944, 942])).
% 0.82/1.02 tff(946,plain,
% 0.82/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a353) | (~c1_1(a353)) | (~c0_1(a353)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(947,plain,
% 0.82/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | (~c0_1(a353)) | (~c1_1(a388))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[946, 945])).
% 0.82/1.02 tff(948,plain,
% 0.82/1.02 (~c3_1(a353)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[947, 105, 847, 941, 933, 312, 311, 932, 308])).
% 0.82/1.02 tff(949,plain,
% 0.82/1.02 (^[U: $i] : refl((hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 0.82/1.02 inference(bind,[status(th)],[])).
% 0.82/1.02 tff(950,plain,
% 0.82/1.02 (![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.82/1.02 inference(quant_intro,[status(thm)],[949])).
% 0.82/1.02 tff(951,plain,
% 0.82/1.02 (![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(952,plain,
% 0.82/1.02 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp26))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 0.82/1.02 inference(bind,[status(th)],[])).
% 0.82/1.02 tff(953,plain,
% 0.82/1.02 (![U: $i] : (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) <=> ![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.82/1.02 inference(quant_intro,[status(thm)],[952])).
% 0.82/1.02 tff(954,axiom,(![U: $i] : (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 0.82/1.02 tff(955,plain,
% 0.82/1.02 (![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[954, 953])).
% 0.82/1.02 tff(956,plain,
% 0.82/1.02 (![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[955, 951])).
% 0.82/1.02 tff(957,plain,(
% 0.82/1.02 ![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.82/1.02 inference(skolemize,[status(sab)],[956])).
% 0.82/1.02 tff(958,plain,
% 0.82/1.02 (![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[957, 950])).
% 0.82/1.02 tff(959,plain,
% 0.82/1.02 (((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp26 | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c0_1(a353)))) <=> ((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp26 | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c0_1(a353)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(960,plain,
% 0.82/1.02 ((hskp26 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c0_1(a353))) <=> (hskp26 | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c0_1(a353)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(961,plain,
% 0.82/1.02 (((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp26 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c0_1(a353)))) <=> ((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp26 | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c0_1(a353))))),
% 0.82/1.02 inference(monotonicity,[status(thm)],[960])).
% 0.82/1.02 tff(962,plain,
% 0.82/1.02 (((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp26 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c0_1(a353)))) <=> ((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp26 | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c0_1(a353)))),
% 0.82/1.02 inference(transitivity,[status(thm)],[961, 959])).
% 0.82/1.02 tff(963,plain,
% 0.82/1.02 ((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp26 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c0_1(a353)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(964,plain,
% 0.82/1.02 ((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp26 | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c0_1(a353))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[963, 962])).
% 0.82/1.02 tff(965,plain,
% 0.82/1.02 (hskp26 | c3_1(a353)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[964, 105, 941, 932, 958])).
% 0.82/1.02 tff(966,plain,
% 0.82/1.02 (hskp26),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[965, 948])).
% 0.82/1.02 tff(967,plain,
% 0.82/1.02 (((~hskp26) | (~c3_1(a418))) <=> ((~hskp26) | (~c3_1(a418)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(968,plain,
% 0.82/1.02 (((~c3_1(a418)) | (~hskp26)) <=> ((~hskp26) | (~c3_1(a418)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(969,axiom,((~c3_1(a418)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 0.82/1.02 tff(970,plain,
% 0.82/1.02 ((~hskp26) | (~c3_1(a418))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[969, 968])).
% 0.82/1.02 tff(971,plain,
% 0.82/1.02 ((~hskp26) | (~c3_1(a418))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[970, 967])).
% 0.82/1.02 tff(972,plain,
% 0.82/1.02 (~c3_1(a418)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[971, 966])).
% 0.82/1.02 tff(973,plain,
% 0.82/1.02 (((~hskp26) | (~c2_1(a418))) <=> ((~hskp26) | (~c2_1(a418)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(974,plain,
% 0.82/1.02 (((~c2_1(a418)) | (~hskp26)) <=> ((~hskp26) | (~c2_1(a418)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(975,axiom,((~c2_1(a418)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 0.82/1.02 tff(976,plain,
% 0.82/1.02 ((~hskp26) | (~c2_1(a418))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[975, 974])).
% 0.82/1.02 tff(977,plain,
% 0.82/1.02 ((~hskp26) | (~c2_1(a418))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[976, 973])).
% 0.82/1.02 tff(978,plain,
% 0.82/1.02 (~c2_1(a418)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[977, 966])).
% 0.82/1.02 tff(979,plain,
% 0.82/1.02 (((~hskp26) | c0_1(a418)) <=> ((~hskp26) | c0_1(a418))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(980,axiom,((~hskp26) | c0_1(a418)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 0.82/1.02 tff(981,plain,
% 0.82/1.02 ((~hskp26) | c0_1(a418)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[980, 979])).
% 0.82/1.02 tff(982,plain,
% 0.82/1.02 ((~hskp26) | c0_1(a418)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[981, 979])).
% 0.82/1.02 tff(983,plain,
% 0.82/1.02 ((~hskp26) | c0_1(a418)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[982, 979])).
% 0.82/1.02 tff(984,plain,
% 0.82/1.02 ((~hskp26) | c0_1(a418)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[983, 979])).
% 0.82/1.02 tff(985,plain,
% 0.82/1.02 ((~hskp26) | c0_1(a418)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[984, 979])).
% 0.82/1.02 tff(986,plain,
% 0.82/1.02 (c0_1(a418)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[985, 966])).
% 0.82/1.02 tff(987,assumption,(~hskp19), introduced(assumption)).
% 0.82/1.02 tff(988,plain,
% 0.82/1.02 (~c0_1(a360)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[875, 987, 739, 165])).
% 0.82/1.02 tff(989,plain,
% 0.82/1.02 (hskp28),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[549, 987])).
% 0.82/1.02 tff(990,plain,
% 0.82/1.02 (c3_1(a365)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[37, 989])).
% 0.82/1.02 tff(991,plain,
% 0.82/1.02 (c2_1(a365)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[45, 989])).
% 0.82/1.02 tff(992,plain,
% 0.82/1.02 (c1_1(a365)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[29, 989])).
% 0.82/1.02 tff(993,plain,
% 0.82/1.02 (~hskp13),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[418, 992, 991, 990])).
% 0.82/1.02 tff(994,plain,
% 0.82/1.02 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a360))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a360))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(995,plain,
% 0.82/1.02 ((hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a360) | c0_1(a360) | c3_1(a360)) <=> (hskp13 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a360))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(996,plain,
% 0.82/1.02 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a360)))),
% 0.82/1.02 inference(monotonicity,[status(thm)],[995])).
% 0.82/1.02 tff(997,plain,
% 0.82/1.02 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a360))),
% 0.82/1.02 inference(transitivity,[status(thm)],[996, 994])).
% 0.82/1.02 tff(998,plain,
% 0.82/1.02 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a360) | c0_1(a360) | c3_1(a360))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(999,plain,
% 0.82/1.02 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a360)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[998, 997])).
% 0.82/1.02 tff(1000,plain,
% 0.82/1.02 ($false),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[999, 105, 993, 992, 991, 990, 737, 738, 122, 988])).
% 0.82/1.02 tff(1001,plain,(hskp19 | c2_1(a360) | c3_1(a360) | c1_1(a360) | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.82/1.02 tff(1002,plain,
% 0.82/1.02 (hskp19),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1001, 165, 738, 739, 737])).
% 0.82/1.02 tff(1003,plain,
% 0.82/1.02 (~c1_1(a387)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[224, 1002])).
% 0.82/1.02 tff(1004,plain,
% 0.82/1.02 (~c0_1(a387)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[230, 1002])).
% 0.82/1.02 tff(1005,plain,
% 0.82/1.02 (~c2_1(a387)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[218, 1002])).
% 0.82/1.02 tff(1006,plain,
% 0.82/1.02 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))))),
% 0.82/1.03 inference(bind,[status(th)],[])).
% 0.82/1.03 tff(1007,plain,
% 0.82/1.03 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.82/1.03 inference(quant_intro,[status(thm)],[1006])).
% 0.82/1.03 tff(1008,plain,
% 0.82/1.03 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(1009,plain,
% 0.82/1.03 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_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) | (~c3_1(U)) | (~c0_1(U)) | (~c2_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)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp28) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | hskp28))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))))),
% 0.82/1.03 inference(bind,[status(th)],[])).
% 0.82/1.03 tff(1010,plain,
% 0.82/1.03 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.82/1.03 inference(quant_intro,[status(thm)],[1009])).
% 0.82/1.03 tff(1011,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 0.82/1.03 tff(1012,plain,
% 0.82/1.03 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1011, 1010])).
% 0.82/1.03 tff(1013,plain,
% 0.82/1.03 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1012, 1008])).
% 0.82/1.03 tff(1014,plain,(
% 0.82/1.03 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.82/1.03 inference(skolemize,[status(sab)],[1013])).
% 0.82/1.03 tff(1015,plain,
% 0.82/1.03 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1014, 1007])).
% 0.82/1.03 tff(1016,plain,
% 0.82/1.03 (^[V: $i, U: $i] : refl((hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 0.82/1.03 inference(bind,[status(th)],[])).
% 0.82/1.03 tff(1017,plain,
% 0.82/1.03 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.82/1.03 inference(quant_intro,[status(thm)],[1016])).
% 0.82/1.03 tff(1018,plain,
% 0.82/1.03 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(1019,plain,
% 0.82/1.03 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp31) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp31))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp31) <=> (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp31) <=> (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.82/1.03 inference(bind,[status(th)],[])).
% 0.82/1.03 tff(1020,plain,
% 0.82/1.03 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp31) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.82/1.03 inference(quant_intro,[status(thm)],[1019])).
% 0.82/1.03 tff(1021,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause186')).
% 0.82/1.03 tff(1022,plain,
% 0.82/1.03 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1021, 1020])).
% 0.82/1.03 tff(1023,plain,
% 0.82/1.03 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1022, 1018])).
% 0.82/1.03 tff(1024,plain,(
% 0.82/1.03 ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.82/1.03 inference(skolemize,[status(sab)],[1023])).
% 0.82/1.03 tff(1025,plain,
% 0.82/1.03 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1024, 1017])).
% 0.82/1.03 tff(1026,plain,
% 0.82/1.03 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.82/1.03 inference(bind,[status(th)],[])).
% 0.82/1.03 tff(1027,plain,
% 0.82/1.03 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.82/1.03 inference(quant_intro,[status(thm)],[1026])).
% 0.82/1.03 tff(1028,plain,
% 0.82/1.03 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(1029,plain,
% 0.82/1.03 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.82/1.03 inference(bind,[status(th)],[])).
% 0.82/1.03 tff(1030,plain,
% 0.82/1.03 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.82/1.03 inference(quant_intro,[status(thm)],[1029])).
% 0.82/1.03 tff(1031,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 0.82/1.03 tff(1032,plain,
% 0.82/1.03 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1031, 1030])).
% 0.82/1.03 tff(1033,plain,
% 0.82/1.03 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1032, 1028])).
% 0.82/1.03 tff(1034,plain,(
% 0.82/1.03 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.82/1.03 inference(skolemize,[status(sab)],[1033])).
% 0.82/1.03 tff(1035,plain,
% 0.82/1.03 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1034, 1027])).
% 0.82/1.03 tff(1036,assumption,(~c3_1(a418)), introduced(assumption)).
% 0.82/1.03 tff(1037,assumption,(~c2_1(a418)), introduced(assumption)).
% 0.82/1.03 tff(1038,assumption,(c0_1(a418)), introduced(assumption)).
% 0.82/1.03 tff(1039,plain,
% 0.82/1.03 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c2_1(a418) | c3_1(a418) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c0_1(a418)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c2_1(a418) | c3_1(a418) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c0_1(a418)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(1040,plain,
% 0.82/1.03 ((hskp1 | (~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c0_1(a418)) | c2_1(a387) | c1_1(a387) | c0_1(a387)) <=> (hskp1 | c2_1(a418) | c3_1(a418) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c0_1(a418)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(1041,plain,
% 0.82/1.03 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c0_1(a418)) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c2_1(a418) | c3_1(a418) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c0_1(a418))))),
% 0.82/1.03 inference(monotonicity,[status(thm)],[1040])).
% 0.82/1.03 tff(1042,plain,
% 0.82/1.03 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c0_1(a418)) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c2_1(a418) | c3_1(a418) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c0_1(a418)))),
% 0.82/1.03 inference(transitivity,[status(thm)],[1041, 1039])).
% 0.82/1.03 tff(1043,plain,
% 0.82/1.03 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c0_1(a418)) | c2_1(a387) | c1_1(a387) | c0_1(a387))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(1044,plain,
% 0.82/1.03 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c2_1(a418) | c3_1(a418) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c0_1(a418))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1043, 1042])).
% 0.82/1.03 tff(1045,plain,
% 0.82/1.03 (hskp1),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[1044, 105, 1038, 1037, 1036, 598, 596, 597, 1035])).
% 0.82/1.03 tff(1046,plain,
% 0.82/1.03 (((~hskp1) | (~c1_1(a355))) <=> ((~hskp1) | (~c1_1(a355)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(1047,plain,
% 0.82/1.03 (((~c1_1(a355)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a355)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(1048,axiom,((~c1_1(a355)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 0.82/1.03 tff(1049,plain,
% 0.82/1.03 ((~hskp1) | (~c1_1(a355))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1048, 1047])).
% 0.82/1.03 tff(1050,plain,
% 0.82/1.03 ((~hskp1) | (~c1_1(a355))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1049, 1046])).
% 0.82/1.03 tff(1051,plain,
% 0.82/1.03 (~c1_1(a355)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[1050, 1045])).
% 0.82/1.03 tff(1052,plain,
% 0.82/1.03 (((~hskp1) | c3_1(a355)) <=> ((~hskp1) | c3_1(a355))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(1053,axiom,((~hskp1) | c3_1(a355)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 0.82/1.03 tff(1054,plain,
% 0.82/1.03 ((~hskp1) | c3_1(a355)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 0.82/1.03 tff(1055,plain,
% 0.82/1.03 ((~hskp1) | c3_1(a355)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1054, 1052])).
% 0.82/1.03 tff(1056,plain,
% 0.82/1.03 ((~hskp1) | c3_1(a355)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1055, 1052])).
% 0.82/1.03 tff(1057,plain,
% 0.82/1.03 ((~hskp1) | c3_1(a355)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1056, 1052])).
% 0.82/1.03 tff(1058,plain,
% 0.82/1.03 ((~hskp1) | c3_1(a355)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1057, 1052])).
% 0.82/1.03 tff(1059,plain,
% 0.82/1.03 (c3_1(a355)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[1058, 1045])).
% 0.82/1.03 tff(1060,plain,
% 0.82/1.03 (((~hskp1) | c0_1(a355)) <=> ((~hskp1) | c0_1(a355))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(1061,axiom,((~hskp1) | c0_1(a355)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 0.82/1.03 tff(1062,plain,
% 0.82/1.03 ((~hskp1) | c0_1(a355)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1061, 1060])).
% 0.82/1.03 tff(1063,plain,
% 0.82/1.03 ((~hskp1) | c0_1(a355)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1062, 1060])).
% 0.82/1.03 tff(1064,plain,
% 0.82/1.03 ((~hskp1) | c0_1(a355)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1063, 1060])).
% 0.82/1.03 tff(1065,plain,
% 0.82/1.03 ((~hskp1) | c0_1(a355)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1064, 1060])).
% 0.82/1.03 tff(1066,plain,
% 0.82/1.03 ((~hskp1) | c0_1(a355)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1065, 1060])).
% 0.82/1.03 tff(1067,plain,
% 0.82/1.03 (c0_1(a355)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[1066, 1045])).
% 0.82/1.03 tff(1068,plain,
% 0.82/1.03 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp31 | c2_1(a418) | c3_1(a418) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c0_1(a418)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp31 | c2_1(a418) | c3_1(a418) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c0_1(a418)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(1069,plain,
% 0.82/1.03 ((hskp31 | (~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c0_1(a418)) | c1_1(a355) | (~c3_1(a355)) | (~c0_1(a355))) <=> (hskp31 | c2_1(a418) | c3_1(a418) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c0_1(a418)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(1070,plain,
% 0.82/1.03 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c0_1(a418)) | c1_1(a355) | (~c3_1(a355)) | (~c0_1(a355)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp31 | c2_1(a418) | c3_1(a418) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c0_1(a418))))),
% 0.82/1.03 inference(monotonicity,[status(thm)],[1069])).
% 0.82/1.03 tff(1071,plain,
% 0.82/1.03 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c0_1(a418)) | c1_1(a355) | (~c3_1(a355)) | (~c0_1(a355)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp31 | c2_1(a418) | c3_1(a418) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c0_1(a418)))),
% 0.82/1.03 inference(transitivity,[status(thm)],[1070, 1068])).
% 0.82/1.03 tff(1072,plain,
% 0.82/1.03 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c0_1(a418)) | c1_1(a355) | (~c3_1(a355)) | (~c0_1(a355)))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(1073,plain,
% 0.82/1.03 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp31 | c2_1(a418) | c3_1(a418) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c0_1(a418))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 0.82/1.03 tff(1074,plain,
% 0.82/1.03 (hskp31),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[1073, 105, 1038, 1067, 1059, 1037, 1036, 1051, 1025])).
% 0.82/1.03 tff(1075,plain,
% 0.82/1.03 (((~hskp31) | c3_1(a410)) <=> ((~hskp31) | c3_1(a410))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(1076,axiom,((~hskp31) | c3_1(a410)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 0.82/1.03 tff(1077,plain,
% 0.82/1.03 ((~hskp31) | c3_1(a410)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1076, 1075])).
% 0.82/1.03 tff(1078,plain,
% 0.82/1.03 ((~hskp31) | c3_1(a410)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1077, 1075])).
% 0.82/1.03 tff(1079,plain,
% 0.82/1.03 ((~hskp31) | c3_1(a410)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1078, 1075])).
% 0.82/1.03 tff(1080,plain,
% 0.82/1.03 ((~hskp31) | c3_1(a410)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1079, 1075])).
% 0.82/1.03 tff(1081,plain,
% 0.82/1.03 ((~hskp31) | c3_1(a410)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1080, 1075])).
% 0.82/1.03 tff(1082,plain,
% 0.82/1.03 (c3_1(a410)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[1081, 1074])).
% 0.82/1.03 tff(1083,plain,
% 0.82/1.03 (((~hskp31) | c2_1(a410)) <=> ((~hskp31) | c2_1(a410))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(1084,axiom,((~hskp31) | c2_1(a410)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 0.82/1.03 tff(1085,plain,
% 0.82/1.03 ((~hskp31) | c2_1(a410)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1084, 1083])).
% 0.82/1.03 tff(1086,plain,
% 0.82/1.03 ((~hskp31) | c2_1(a410)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1085, 1083])).
% 0.82/1.03 tff(1087,plain,
% 0.82/1.03 ((~hskp31) | c2_1(a410)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1086, 1083])).
% 0.82/1.03 tff(1088,plain,
% 0.82/1.03 ((~hskp31) | c2_1(a410)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1087, 1083])).
% 0.82/1.03 tff(1089,plain,
% 0.82/1.03 ((~hskp31) | c2_1(a410)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1088, 1083])).
% 0.82/1.03 tff(1090,plain,
% 0.82/1.03 (c2_1(a410)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[1089, 1074])).
% 0.82/1.03 tff(1091,plain,
% 0.82/1.03 (((~hskp31) | c0_1(a410)) <=> ((~hskp31) | c0_1(a410))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(1092,axiom,((~hskp31) | c0_1(a410)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 0.82/1.03 tff(1093,plain,
% 0.82/1.03 ((~hskp31) | c0_1(a410)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1092, 1091])).
% 0.82/1.03 tff(1094,plain,
% 0.82/1.03 ((~hskp31) | c0_1(a410)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1093, 1091])).
% 0.82/1.03 tff(1095,plain,
% 0.82/1.03 ((~hskp31) | c0_1(a410)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1094, 1091])).
% 0.82/1.03 tff(1096,plain,
% 0.82/1.03 ((~hskp31) | c0_1(a410)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1095, 1091])).
% 0.82/1.03 tff(1097,plain,
% 0.82/1.03 ((~hskp31) | c0_1(a410)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1096, 1091])).
% 0.82/1.03 tff(1098,plain,
% 0.82/1.03 (c0_1(a410)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[1097, 1074])).
% 0.82/1.03 tff(1099,plain,
% 0.82/1.03 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c1_1(a388)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c1_1(a388)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(1100,plain,
% 0.82/1.03 ((hskp28 | (~ndr1_0) | (~c3_1(a410)) | (~c0_1(a410)) | (~c2_1(a410)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388))) <=> (hskp28 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c1_1(a388)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(1101,plain,
% 0.82/1.03 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a410)) | (~c0_1(a410)) | (~c2_1(a410)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c1_1(a388))))),
% 0.82/1.03 inference(monotonicity,[status(thm)],[1100])).
% 0.82/1.03 tff(1102,plain,
% 0.82/1.03 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a410)) | (~c0_1(a410)) | (~c2_1(a410)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c1_1(a388)))),
% 0.82/1.03 inference(transitivity,[status(thm)],[1101, 1099])).
% 0.82/1.03 tff(1103,plain,
% 0.82/1.03 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a410)) | (~c0_1(a410)) | (~c2_1(a410)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(1104,plain,
% 0.82/1.03 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c1_1(a388))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1103, 1102])).
% 0.82/1.03 tff(1105,plain,
% 0.82/1.03 (hskp28),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[1104, 105, 1098, 1090, 1082, 847, 312, 311, 1015])).
% 0.82/1.03 tff(1106,plain,
% 0.82/1.03 (c3_1(a365)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[37, 1105])).
% 0.82/1.03 tff(1107,plain,
% 0.82/1.03 (c2_1(a365)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[45, 1105])).
% 0.82/1.03 tff(1108,plain,
% 0.82/1.03 (c1_1(a365)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[29, 1105])).
% 0.82/1.03 tff(1109,plain,
% 0.82/1.03 (~hskp13),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[418, 1108, 1107, 1106])).
% 0.82/1.03 tff(1110,plain,
% 0.82/1.03 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a387))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a387))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(1111,plain,
% 0.82/1.03 ((hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a387) | c0_1(a387) | c3_1(a387)) <=> (hskp13 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a387))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(1112,plain,
% 0.82/1.03 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a387) | c0_1(a387) | c3_1(a387))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a387)))),
% 0.82/1.03 inference(monotonicity,[status(thm)],[1111])).
% 0.82/1.03 tff(1113,plain,
% 0.82/1.03 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a387) | c0_1(a387) | c3_1(a387))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a387))),
% 0.82/1.03 inference(transitivity,[status(thm)],[1112, 1110])).
% 0.82/1.03 tff(1114,plain,
% 0.82/1.03 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a387) | c0_1(a387) | c3_1(a387))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(1115,plain,
% 0.82/1.03 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a387)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[1114, 1113])).
% 0.82/1.03 tff(1116,plain,
% 0.82/1.03 (hskp13 | c3_1(a387)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[1115, 105, 1108, 1107, 1106, 598, 597, 122])).
% 0.82/1.03 tff(1117,plain,
% 0.82/1.03 (c3_1(a387)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[1116, 1109])).
% 0.82/1.03 tff(1118,plain,
% 0.82/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a387)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a387)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(1119,plain,
% 0.82/1.03 (((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a387) | c0_1(a387) | (~c3_1(a387))) <=> (c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a387)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(1120,plain,
% 0.82/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a387) | c0_1(a387) | (~c3_1(a387)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a387))))),
% 0.82/1.03 inference(monotonicity,[status(thm)],[1119])).
% 0.82/1.03 tff(1121,plain,
% 0.82/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a387) | c0_1(a387) | (~c3_1(a387)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a387)))),
% 0.82/1.03 inference(transitivity,[status(thm)],[1120, 1118])).
% 0.82/1.03 tff(1122,plain,
% 0.82/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a387) | c0_1(a387) | (~c3_1(a387)))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(1123,plain,
% 0.82/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a387))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 0.82/1.04 tff(1124,plain,
% 0.82/1.04 ((~c0_1(a365)) | (~c3_1(a387))),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[1123, 105, 1108, 1107, 1106, 598, 597, 57])).
% 0.82/1.04 tff(1125,plain,
% 0.82/1.04 (~c0_1(a365)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[1124, 1117])).
% 0.82/1.04 tff(1126,plain,
% 0.82/1.04 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 0.82/1.04 inference(bind,[status(th)],[])).
% 0.82/1.04 tff(1127,plain,
% 0.82/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.82/1.04 inference(quant_intro,[status(thm)],[1126])).
% 0.82/1.04 tff(1128,plain,
% 0.82/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(1129,plain,
% 0.82/1.04 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~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(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_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) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_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) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_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) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_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) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 0.82/1.04 inference(bind,[status(th)],[])).
% 0.82/1.04 tff(1130,plain,
% 0.82/1.04 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_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) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.82/1.04 inference(quant_intro,[status(thm)],[1129])).
% 0.82/1.04 tff(1131,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause202')).
% 0.82/1.04 tff(1132,plain,
% 0.82/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 0.82/1.04 tff(1133,plain,
% 0.82/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1132, 1128])).
% 0.82/1.04 tff(1134,plain,(
% 0.82/1.04 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.82/1.04 inference(skolemize,[status(sab)],[1133])).
% 0.82/1.04 tff(1135,plain,
% 0.82/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1134, 1127])).
% 0.82/1.04 tff(1136,plain,
% 0.82/1.04 (^[V: $i, U: $i] : refl((hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.82/1.04 inference(bind,[status(th)],[])).
% 0.82/1.04 tff(1137,plain,
% 0.82/1.04 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.82/1.04 inference(quant_intro,[status(thm)],[1136])).
% 0.82/1.04 tff(1138,plain,
% 0.82/1.04 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(1139,plain,
% 0.82/1.04 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp23))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp23) <=> (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.82/1.04 inference(bind,[status(th)],[])).
% 0.82/1.04 tff(1140,plain,
% 0.82/1.04 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.82/1.04 inference(quant_intro,[status(thm)],[1139])).
% 0.82/1.04 tff(1141,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 0.82/1.04 tff(1142,plain,
% 0.82/1.04 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1141, 1140])).
% 0.82/1.04 tff(1143,plain,
% 0.82/1.04 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1142, 1138])).
% 0.82/1.04 tff(1144,plain,(
% 0.82/1.04 ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.82/1.04 inference(skolemize,[status(sab)],[1143])).
% 0.82/1.04 tff(1145,plain,
% 0.82/1.04 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1144, 1137])).
% 0.82/1.04 tff(1146,plain,
% 0.82/1.04 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c1_1(a387) | c2_1(a387) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c3_1(a387)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a387) | c2_1(a387) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c3_1(a387)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(1147,plain,
% 0.82/1.04 ((hskp23 | (~ndr1_0) | c1_1(a355) | (~c3_1(a355)) | (~c0_1(a355)) | c2_1(a387) | c1_1(a387) | (~c3_1(a387))) <=> (hskp23 | c1_1(a387) | c2_1(a387) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c3_1(a387)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(1148,plain,
% 0.82/1.04 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c1_1(a355) | (~c3_1(a355)) | (~c0_1(a355)) | c2_1(a387) | c1_1(a387) | (~c3_1(a387)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c1_1(a387) | c2_1(a387) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c3_1(a387))))),
% 0.82/1.04 inference(monotonicity,[status(thm)],[1147])).
% 0.82/1.04 tff(1149,plain,
% 0.82/1.04 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c1_1(a355) | (~c3_1(a355)) | (~c0_1(a355)) | c2_1(a387) | c1_1(a387) | (~c3_1(a387)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a387) | c2_1(a387) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c3_1(a387)))),
% 0.82/1.04 inference(transitivity,[status(thm)],[1148, 1146])).
% 0.82/1.04 tff(1150,plain,
% 0.82/1.04 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c1_1(a355) | (~c3_1(a355)) | (~c0_1(a355)) | c2_1(a387) | c1_1(a387) | (~c3_1(a387)))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(1151,plain,
% 0.82/1.04 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a387) | c2_1(a387) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c3_1(a387))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1150, 1149])).
% 0.82/1.04 tff(1152,plain,
% 0.82/1.04 (hskp23 | (~c3_1(a387))),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[1151, 105, 1067, 1059, 596, 597, 1051, 1145])).
% 0.82/1.04 tff(1153,plain,
% 0.82/1.04 (hskp23),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[1152, 1117])).
% 0.82/1.04 tff(1154,plain,
% 0.82/1.04 (((~hskp23) | (~c2_1(a398))) <=> ((~hskp23) | (~c2_1(a398)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(1155,plain,
% 0.82/1.04 (((~c2_1(a398)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a398)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(1156,axiom,((~c2_1(a398)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 0.82/1.04 tff(1157,plain,
% 0.82/1.04 ((~hskp23) | (~c2_1(a398))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1156, 1155])).
% 0.82/1.04 tff(1158,plain,
% 0.82/1.04 ((~hskp23) | (~c2_1(a398))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1157, 1154])).
% 0.82/1.04 tff(1159,plain,
% 0.82/1.04 (~c2_1(a398)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[1158, 1153])).
% 0.82/1.04 tff(1160,plain,
% 0.82/1.04 (((~hskp23) | c3_1(a398)) <=> ((~hskp23) | c3_1(a398))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(1161,axiom,((~hskp23) | c3_1(a398)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 0.82/1.04 tff(1162,plain,
% 0.82/1.04 ((~hskp23) | c3_1(a398)),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1161, 1160])).
% 0.82/1.04 tff(1163,plain,
% 0.82/1.04 ((~hskp23) | c3_1(a398)),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1162, 1160])).
% 0.82/1.04 tff(1164,plain,
% 0.82/1.04 ((~hskp23) | c3_1(a398)),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1163, 1160])).
% 0.82/1.04 tff(1165,plain,
% 0.82/1.04 ((~hskp23) | c3_1(a398)),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1164, 1160])).
% 0.82/1.04 tff(1166,plain,
% 0.82/1.04 ((~hskp23) | c3_1(a398)),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1165, 1160])).
% 0.82/1.04 tff(1167,plain,
% 0.82/1.04 (c3_1(a398)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[1166, 1153])).
% 0.82/1.04 tff(1168,plain,
% 0.82/1.04 (((~hskp23) | c1_1(a398)) <=> ((~hskp23) | c1_1(a398))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(1169,axiom,((~hskp23) | c1_1(a398)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 0.82/1.04 tff(1170,plain,
% 0.82/1.04 ((~hskp23) | c1_1(a398)),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1169, 1168])).
% 0.82/1.04 tff(1171,plain,
% 0.82/1.04 ((~hskp23) | c1_1(a398)),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1170, 1168])).
% 0.82/1.04 tff(1172,plain,
% 0.82/1.04 ((~hskp23) | c1_1(a398)),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1171, 1168])).
% 0.82/1.04 tff(1173,plain,
% 0.82/1.04 ((~hskp23) | c1_1(a398)),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1172, 1168])).
% 0.82/1.04 tff(1174,plain,
% 0.82/1.04 ((~hskp23) | c1_1(a398)),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1173, 1168])).
% 0.82/1.04 tff(1175,plain,
% 0.82/1.04 (c1_1(a398)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[1174, 1153])).
% 0.82/1.04 tff(1176,plain,
% 0.82/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a398) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | c0_1(a365) | (~c3_1(a398)) | (~c1_1(a398)) | c0_1(a398))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a398) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | c0_1(a365) | (~c3_1(a398)) | (~c1_1(a398)) | c0_1(a398))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(1177,plain,
% 0.82/1.04 (((~ndr1_0) | c2_1(a398) | (~c3_1(a398)) | (~c1_1(a398)) | c0_1(a365) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a398) | c0_1(a398) | (~c1_1(a398))) <=> (c2_1(a398) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | c0_1(a365) | (~c3_1(a398)) | (~c1_1(a398)) | c0_1(a398))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(1178,plain,
% 0.82/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a398) | (~c3_1(a398)) | (~c1_1(a398)) | c0_1(a365) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a398) | c0_1(a398) | (~c1_1(a398)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a398) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | c0_1(a365) | (~c3_1(a398)) | (~c1_1(a398)) | c0_1(a398)))),
% 0.82/1.04 inference(monotonicity,[status(thm)],[1177])).
% 0.82/1.04 tff(1179,plain,
% 0.82/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a398) | (~c3_1(a398)) | (~c1_1(a398)) | c0_1(a365) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a398) | c0_1(a398) | (~c1_1(a398)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a398) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | c0_1(a365) | (~c3_1(a398)) | (~c1_1(a398)) | c0_1(a398))),
% 0.82/1.04 inference(transitivity,[status(thm)],[1178, 1176])).
% 0.82/1.04 tff(1180,plain,
% 0.82/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a398) | (~c3_1(a398)) | (~c1_1(a398)) | c0_1(a365) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a398) | c0_1(a398) | (~c1_1(a398)))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(1181,plain,
% 0.82/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a398) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | c0_1(a365) | (~c3_1(a398)) | (~c1_1(a398)) | c0_1(a398)),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1180, 1179])).
% 0.82/1.04 tff(1182,plain,
% 0.82/1.04 (c0_1(a398)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[1181, 105, 1108, 1107, 1175, 1167, 1159, 1135, 1125])).
% 0.82/1.04 tff(1183,plain,
% 0.82/1.04 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))))),
% 0.82/1.04 inference(bind,[status(th)],[])).
% 0.82/1.04 tff(1184,plain,
% 0.82/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.82/1.04 inference(quant_intro,[status(thm)],[1183])).
% 0.82/1.04 tff(1185,plain,
% 0.82/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(1186,plain,
% 0.82/1.04 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_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) | (~c3_1(U)) | (~c0_1(U)) | (~c2_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) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_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) | (~c3_1(U)) | (~c0_1(U)) | (~c2_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))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))))),
% 0.82/1.04 inference(bind,[status(th)],[])).
% 0.82/1.04 tff(1187,plain,
% 0.82/1.04 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.82/1.04 inference(quant_intro,[status(thm)],[1186])).
% 0.82/1.04 tff(1188,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause208')).
% 0.82/1.04 tff(1189,plain,
% 0.82/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1188, 1187])).
% 0.82/1.04 tff(1190,plain,
% 0.82/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1189, 1185])).
% 0.82/1.04 tff(1191,plain,(
% 0.82/1.04 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.82/1.04 inference(skolemize,[status(sab)],[1190])).
% 0.82/1.04 tff(1192,plain,
% 0.82/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1191, 1184])).
% 0.82/1.04 tff(1193,plain,
% 0.82/1.04 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.82/1.04 inference(bind,[status(th)],[])).
% 0.82/1.04 tff(1194,plain,
% 0.82/1.04 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.82/1.04 inference(quant_intro,[status(thm)],[1193])).
% 0.82/1.04 tff(1195,plain,
% 0.82/1.04 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(1196,plain,
% 0.82/1.04 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp16) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp16))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.82/1.04 inference(bind,[status(th)],[])).
% 0.82/1.04 tff(1197,plain,
% 0.82/1.04 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.82/1.04 inference(quant_intro,[status(thm)],[1196])).
% 0.82/1.04 tff(1198,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause191')).
% 0.82/1.04 tff(1199,plain,
% 0.82/1.04 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1198, 1197])).
% 0.82/1.04 tff(1200,plain,
% 0.82/1.04 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1199, 1195])).
% 0.82/1.04 tff(1201,plain,(
% 0.82/1.04 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.82/1.04 inference(skolemize,[status(sab)],[1200])).
% 0.82/1.04 tff(1202,plain,
% 0.82/1.04 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[1201, 1194])).
% 0.82/1.04 tff(1203,plain,
% 0.82/1.04 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp16 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c3_1(a387)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c3_1(a387)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(1204,plain,
% 0.82/1.04 ((hskp16 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a387) | c0_1(a387) | (~c3_1(a387))) <=> (hskp16 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c3_1(a387)))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(1205,plain,
% 0.88/1.04 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a387) | c0_1(a387) | (~c3_1(a387)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp16 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c3_1(a387))))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[1204])).
% 0.88/1.04 tff(1206,plain,
% 0.88/1.04 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a387) | c0_1(a387) | (~c3_1(a387)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c3_1(a387)))),
% 0.88/1.04 inference(transitivity,[status(thm)],[1205, 1203])).
% 0.88/1.04 tff(1207,plain,
% 0.88/1.04 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a387) | c0_1(a387) | (~c3_1(a387)))),
% 0.88/1.04 inference(quant_inst,[status(thm)],[])).
% 0.88/1.04 tff(1208,plain,
% 0.88/1.04 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c3_1(a387))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[1207, 1206])).
% 0.88/1.04 tff(1209,plain,
% 0.88/1.04 (hskp16 | (~c3_1(a387))),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1208, 105, 1108, 1107, 1106, 598, 597, 1202])).
% 0.88/1.04 tff(1210,plain,
% 0.88/1.04 (hskp16),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1209, 1117])).
% 0.88/1.04 tff(1211,plain,
% 0.88/1.04 (~c3_1(a379)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[522, 1210])).
% 0.88/1.04 tff(1212,plain,
% 0.88/1.04 (~c1_1(a379)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[501, 1210])).
% 0.88/1.04 tff(1213,plain,
% 0.88/1.04 (c2_1(a379)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[509, 1210])).
% 0.88/1.04 tff(1214,plain,
% 0.88/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a379) | c3_1(a379) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c2_1(a379)) | (~c3_1(a398)) | (~c1_1(a398)) | (~c0_1(a398)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a379) | c3_1(a379) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c2_1(a379)) | (~c3_1(a398)) | (~c1_1(a398)) | (~c0_1(a398)))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(1215,plain,
% 0.88/1.04 (((~ndr1_0) | (~c3_1(a410)) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a398)) | (~c1_1(a398)) | (~c0_1(a398)) | c1_1(a379) | c3_1(a379) | (~c2_1(a379))) <=> (c1_1(a379) | c3_1(a379) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c2_1(a379)) | (~c3_1(a398)) | (~c1_1(a398)) | (~c0_1(a398)))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(1216,plain,
% 0.88/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a410)) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a398)) | (~c1_1(a398)) | (~c0_1(a398)) | c1_1(a379) | c3_1(a379) | (~c2_1(a379)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a379) | c3_1(a379) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c2_1(a379)) | (~c3_1(a398)) | (~c1_1(a398)) | (~c0_1(a398))))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[1215])).
% 0.88/1.05 tff(1217,plain,
% 0.88/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a410)) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a398)) | (~c1_1(a398)) | (~c0_1(a398)) | c1_1(a379) | c3_1(a379) | (~c2_1(a379)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a379) | c3_1(a379) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c2_1(a379)) | (~c3_1(a398)) | (~c1_1(a398)) | (~c0_1(a398)))),
% 0.88/1.05 inference(transitivity,[status(thm)],[1216, 1214])).
% 0.88/1.05 tff(1218,plain,
% 0.88/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a410)) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a398)) | (~c1_1(a398)) | (~c0_1(a398)) | c1_1(a379) | c3_1(a379) | (~c2_1(a379)))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(1219,plain,
% 0.88/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a379) | c3_1(a379) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c2_1(a379)) | (~c3_1(a398)) | (~c1_1(a398)) | (~c0_1(a398))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1218, 1217])).
% 0.88/1.05 tff(1220,plain,
% 0.88/1.05 ($false),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1219, 105, 1098, 1090, 1082, 1175, 1167, 1213, 1212, 1211, 1192, 1182])).
% 0.88/1.05 tff(1221,plain,(c2_1(a387) | c0_1(a387) | c1_1(a387) | c2_1(a388) | c3_1(a388) | (~c0_1(a418)) | c2_1(a418) | c3_1(a418)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.05 tff(1222,plain,
% 0.88/1.05 ($false),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1221, 1005, 1004, 1003, 312, 311, 986, 978, 972])).
% 0.88/1.05 tff(1223,plain,(hskp3 | c2_1(a388) | c3_1(a388) | c3_1(a360) | c1_1(a360) | c2_1(a360)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.05 tff(1224,plain,
% 0.88/1.05 (hskp3),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1223, 311, 312, 738, 739, 737])).
% 0.88/1.05 tff(1225,plain,
% 0.88/1.05 (c1_1(a357)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[261, 1224])).
% 0.88/1.05 tff(1226,plain,
% 0.88/1.05 (~c0_1(a357)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[245, 1224])).
% 0.88/1.05 tff(1227,plain,
% 0.88/1.05 (c3_1(a357)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[253, 1224])).
% 0.88/1.05 tff(1228,plain,
% 0.88/1.05 (~hskp13),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[418, 30, 46, 38])).
% 0.88/1.05 tff(1229,plain,
% 0.88/1.05 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a388))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a388))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1230,plain,
% 0.88/1.05 ((hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a388) | c0_1(a388) | c3_1(a388)) <=> (hskp13 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a388))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1231,plain,
% 0.88/1.05 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a388) | c0_1(a388) | c3_1(a388))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a388)))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[1230])).
% 0.88/1.05 tff(1232,plain,
% 0.88/1.05 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a388) | c0_1(a388) | c3_1(a388))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a388))),
% 0.88/1.05 inference(transitivity,[status(thm)],[1231, 1229])).
% 0.88/1.05 tff(1233,plain,
% 0.88/1.05 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a388) | c0_1(a388) | c3_1(a388))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(1234,plain,
% 0.88/1.05 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a388)),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1233, 1232])).
% 0.88/1.05 tff(1235,plain,
% 0.88/1.05 (c0_1(a388)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1234, 105, 1228, 30, 46, 38, 312, 311, 122])).
% 0.88/1.05 tff(1236,plain,
% 0.88/1.05 (c2_1(a357)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[323, 1235, 847, 313, 312, 311, 314])).
% 0.88/1.05 tff(1237,plain,
% 0.88/1.05 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.88/1.05 inference(bind,[status(th)],[])).
% 0.88/1.05 tff(1238,plain,
% 0.88/1.05 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.88/1.05 inference(quant_intro,[status(thm)],[1237])).
% 0.88/1.05 tff(1239,plain,
% 0.88/1.05 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1240,plain,
% 0.88/1.05 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.88/1.05 inference(bind,[status(th)],[])).
% 0.88/1.05 tff(1241,plain,
% 0.88/1.05 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.88/1.05 inference(quant_intro,[status(thm)],[1240])).
% 0.88/1.05 tff(1242,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 0.88/1.05 tff(1243,plain,
% 0.88/1.05 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1242, 1241])).
% 0.88/1.05 tff(1244,plain,
% 0.88/1.05 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1243, 1239])).
% 0.88/1.05 tff(1245,plain,(
% 0.88/1.05 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.88/1.05 inference(skolemize,[status(sab)],[1244])).
% 0.88/1.05 tff(1246,plain,
% 0.88/1.05 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1245, 1238])).
% 0.88/1.05 tff(1247,assumption,(~c0_1(a357)), introduced(assumption)).
% 0.88/1.05 tff(1248,plain,
% 0.88/1.05 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357)) | (~c1_1(a388)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357)) | (~c1_1(a388)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1249,plain,
% 0.88/1.05 ((hskp10 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c0_1(a357) | (~c3_1(a357)) | (~c2_1(a357))) <=> (hskp10 | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357)) | (~c1_1(a388)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1250,plain,
% 0.88/1.05 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c0_1(a357) | (~c3_1(a357)) | (~c2_1(a357)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357)) | (~c1_1(a388))))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[1249])).
% 0.88/1.05 tff(1251,plain,
% 0.88/1.05 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c0_1(a357) | (~c3_1(a357)) | (~c2_1(a357)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357)) | (~c1_1(a388)))),
% 0.88/1.05 inference(transitivity,[status(thm)],[1250, 1248])).
% 0.88/1.05 tff(1252,plain,
% 0.88/1.05 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c0_1(a357) | (~c3_1(a357)) | (~c2_1(a357)))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(1253,plain,
% 0.88/1.05 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357)) | (~c1_1(a388))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1252, 1251])).
% 0.88/1.05 tff(1254,plain,
% 0.88/1.05 (hskp10 | (~c2_1(a357))),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1253, 105, 847, 313, 312, 311, 1247, 1246])).
% 0.88/1.05 tff(1255,plain,
% 0.88/1.05 (hskp10),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1254, 1236])).
% 0.88/1.05 tff(1256,plain,
% 0.88/1.05 (((~hskp10) | (~c3_1(a366))) <=> ((~hskp10) | (~c3_1(a366)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1257,plain,
% 0.88/1.05 (((~c3_1(a366)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a366)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1258,axiom,((~c3_1(a366)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 0.88/1.05 tff(1259,plain,
% 0.88/1.05 ((~hskp10) | (~c3_1(a366))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1258, 1257])).
% 0.88/1.05 tff(1260,plain,
% 0.88/1.05 ((~hskp10) | (~c3_1(a366))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1259, 1256])).
% 0.88/1.05 tff(1261,plain,
% 0.88/1.05 (~c3_1(a366)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1260, 1255])).
% 0.88/1.05 tff(1262,plain,
% 0.88/1.05 (((~hskp10) | (~c2_1(a366))) <=> ((~hskp10) | (~c2_1(a366)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1263,plain,
% 0.88/1.05 (((~c2_1(a366)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a366)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1264,axiom,((~c2_1(a366)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 0.88/1.05 tff(1265,plain,
% 0.88/1.05 ((~hskp10) | (~c2_1(a366))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1264, 1263])).
% 0.88/1.05 tff(1266,plain,
% 0.88/1.05 ((~hskp10) | (~c2_1(a366))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1265, 1262])).
% 0.88/1.05 tff(1267,plain,
% 0.88/1.05 (~c2_1(a366)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1266, 1255])).
% 0.88/1.05 tff(1268,plain,
% 0.88/1.05 (((~hskp10) | (~c0_1(a366))) <=> ((~hskp10) | (~c0_1(a366)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1269,plain,
% 0.88/1.05 (((~c0_1(a366)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a366)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1270,axiom,((~c0_1(a366)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 0.88/1.05 tff(1271,plain,
% 0.88/1.05 ((~hskp10) | (~c0_1(a366))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1270, 1269])).
% 0.88/1.05 tff(1272,plain,
% 0.88/1.05 ((~hskp10) | (~c0_1(a366))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1271, 1268])).
% 0.88/1.05 tff(1273,plain,
% 0.88/1.05 (~c0_1(a366)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1272, 1255])).
% 0.88/1.05 tff(1274,plain,
% 0.88/1.05 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a366) | c2_1(a366) | c3_1(a366) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a366) | c2_1(a366) | c3_1(a366) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1275,plain,
% 0.88/1.05 ((hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a366) | c0_1(a366) | c3_1(a366)) <=> (hskp13 | c0_1(a366) | c2_1(a366) | c3_1(a366) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1276,plain,
% 0.88/1.05 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a366) | c0_1(a366) | c3_1(a366))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a366) | c2_1(a366) | c3_1(a366) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365))))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[1275])).
% 0.88/1.05 tff(1277,plain,
% 0.88/1.05 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a366) | c0_1(a366) | c3_1(a366))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a366) | c2_1(a366) | c3_1(a366) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)))),
% 0.88/1.05 inference(transitivity,[status(thm)],[1276, 1274])).
% 0.88/1.05 tff(1278,plain,
% 0.88/1.05 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a366) | c0_1(a366) | c3_1(a366))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(1279,plain,
% 0.88/1.05 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a366) | c2_1(a366) | c3_1(a366) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1278, 1277])).
% 0.88/1.05 tff(1280,plain,
% 0.88/1.05 ($false),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1279, 105, 1228, 30, 46, 38, 1273, 1267, 1261, 122])).
% 0.88/1.05 tff(1281,plain,((~hskp28) | (~c3_1(a357)) | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~c1_1(a357))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.05 tff(1282,plain,
% 0.88/1.05 (~hskp28),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1281, 1227, 312, 311, 1226, 1225])).
% 0.88/1.05 tff(1283,plain,
% 0.88/1.05 (hskp19),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[549, 1282])).
% 0.88/1.05 tff(1284,plain,
% 0.88/1.05 (~c0_1(a387)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[230, 1283])).
% 0.88/1.05 tff(1285,plain,
% 0.88/1.05 (~c1_1(a387)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[224, 1283])).
% 0.88/1.05 tff(1286,plain,
% 0.88/1.05 (c2_1(a387)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[898, 615, 312, 311, 596, 598])).
% 0.88/1.05 tff(1287,plain,
% 0.88/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a388) | c3_1(a388) | c0_1(a387) | c1_1(a387) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | (~c0_1(a360)) | c3_1(a387) | (~c1_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a388) | c3_1(a388) | c0_1(a387) | c1_1(a387) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | (~c0_1(a360)) | c3_1(a387) | (~c1_1(a388)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1288,plain,
% 0.88/1.05 (((~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a360) | c1_1(a360) | (~c0_1(a360)) | c1_1(a387) | c0_1(a387) | c3_1(a387)) <=> (c2_1(a388) | c3_1(a388) | c0_1(a387) | c1_1(a387) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | (~c0_1(a360)) | c3_1(a387) | (~c1_1(a388)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1289,plain,
% 0.88/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a360) | c1_1(a360) | (~c0_1(a360)) | c1_1(a387) | c0_1(a387) | c3_1(a387))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a388) | c3_1(a388) | c0_1(a387) | c1_1(a387) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | (~c0_1(a360)) | c3_1(a387) | (~c1_1(a388))))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[1288])).
% 0.88/1.05 tff(1290,plain,
% 0.88/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a360) | c1_1(a360) | (~c0_1(a360)) | c1_1(a387) | c0_1(a387) | c3_1(a387))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a388) | c3_1(a388) | c0_1(a387) | c1_1(a387) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | (~c0_1(a360)) | c3_1(a387) | (~c1_1(a388)))),
% 0.88/1.05 inference(transitivity,[status(thm)],[1289, 1287])).
% 0.88/1.05 tff(1291,plain,
% 0.88/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a360) | c1_1(a360) | (~c0_1(a360)) | c1_1(a387) | c0_1(a387) | c3_1(a387))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(1292,plain,
% 0.88/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a388) | c3_1(a388) | c0_1(a387) | c1_1(a387) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | (~c0_1(a360)) | c3_1(a387) | (~c1_1(a388))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1291, 1290])).
% 0.88/1.05 tff(1293,plain,
% 0.88/1.05 ((~c0_1(a360)) | c3_1(a387)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1292, 105, 847, 312, 311, 598, 596, 739, 737, 725])).
% 0.88/1.05 tff(1294,plain,
% 0.88/1.05 (c3_1(a387)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1293, 874])).
% 0.88/1.05 tff(1295,plain,
% 0.88/1.05 (hskp0 | (~c2_1(a387)) | (~c3_1(a387))),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[916, 105, 598, 910])).
% 0.88/1.05 tff(1296,plain,
% 0.88/1.05 ($false),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1295, 1294, 1286, 615])).
% 0.88/1.05 tff(1297,plain,(hskp0 | c0_1(a387) | c2_1(a388) | c3_1(a388) | c1_1(a387) | c1_1(a360) | c2_1(a360) | c3_1(a360)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.05 tff(1298,plain,
% 0.88/1.05 (hskp0),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1297, 596, 312, 311, 598, 739, 737, 738])).
% 0.88/1.05 tff(1299,plain,
% 0.88/1.05 (~c2_1(a353)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[653, 1298])).
% 0.88/1.05 tff(1300,plain,
% 0.88/1.05 (c1_1(a353)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[661, 1298])).
% 0.88/1.05 tff(1301,plain,
% 0.88/1.05 (c0_1(a353)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[940, 1298])).
% 0.88/1.05 tff(1302,plain,
% 0.88/1.05 (~c3_1(a353)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[947, 105, 847, 1301, 1300, 312, 311, 1299, 308])).
% 0.88/1.05 tff(1303,plain,
% 0.88/1.05 (hskp26 | c3_1(a353)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[964, 105, 1301, 1299, 958])).
% 0.88/1.05 tff(1304,plain,
% 0.88/1.05 (hskp26),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1303, 1302])).
% 0.88/1.05 tff(1305,plain,
% 0.88/1.05 (~c3_1(a418)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[971, 1304])).
% 0.88/1.05 tff(1306,plain,
% 0.88/1.05 (~c2_1(a418)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[977, 1304])).
% 0.88/1.05 tff(1307,plain,
% 0.88/1.05 (c0_1(a418)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[985, 1304])).
% 0.88/1.05 tff(1308,plain,
% 0.88/1.05 (c2_1(a387)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1221, 1307, 598, 312, 311, 596, 1306, 1305])).
% 0.88/1.05 tff(1309,plain,
% 0.88/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1310,plain,
% 0.88/1.05 (((~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c2_1(a387)) | c1_1(a360) | c0_1(a360) | c3_1(a360) | c2_1(a360) | c1_1(a360) | c0_1(a360)) <=> (c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1311,plain,
% 0.88/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c2_1(a387)) | c1_1(a360) | c0_1(a360) | c3_1(a360) | c2_1(a360) | c1_1(a360) | c0_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360)))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[1310])).
% 0.88/1.05 tff(1312,plain,
% 0.88/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c2_1(a387)) | c1_1(a360) | c0_1(a360) | c3_1(a360) | c2_1(a360) | c1_1(a360) | c0_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360))),
% 0.88/1.05 inference(transitivity,[status(thm)],[1311, 1309])).
% 0.88/1.05 tff(1313,plain,
% 0.88/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c2_1(a387)) | c1_1(a360) | c0_1(a360) | c3_1(a360) | c2_1(a360) | c1_1(a360) | c0_1(a360))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(1314,plain,
% 0.88/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360)),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1313, 1312])).
% 0.88/1.05 tff(1315,plain,
% 0.88/1.05 ((~c2_1(a387)) | c0_1(a360)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1314, 105, 598, 596, 739, 737, 738, 10])).
% 0.88/1.05 tff(1316,plain,
% 0.88/1.05 (c0_1(a360)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1315, 1308])).
% 0.88/1.05 tff(1317,plain,
% 0.88/1.05 (c3_1(a387)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1293, 1316])).
% 0.88/1.05 tff(1318,plain,
% 0.88/1.05 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.88/1.05 inference(bind,[status(th)],[])).
% 0.88/1.05 tff(1319,plain,
% 0.88/1.05 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.88/1.05 inference(quant_intro,[status(thm)],[1318])).
% 0.88/1.05 tff(1320,plain,
% 0.88/1.05 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1321,plain,
% 0.88/1.05 (^[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)) | hskp10) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~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)) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.88/1.05 inference(bind,[status(th)],[])).
% 0.88/1.05 tff(1322,plain,
% 0.88/1.05 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.88/1.06 inference(quant_intro,[status(thm)],[1321])).
% 0.88/1.06 tff(1323,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)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 0.88/1.06 tff(1324,plain,
% 0.88/1.06 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1323, 1322])).
% 0.88/1.06 tff(1325,plain,
% 0.88/1.06 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1324, 1320])).
% 0.88/1.06 tff(1326,plain,(
% 0.88/1.06 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.88/1.06 inference(skolemize,[status(sab)],[1325])).
% 0.88/1.06 tff(1327,plain,
% 0.88/1.06 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1326, 1319])).
% 0.88/1.06 tff(1328,plain,
% 0.88/1.06 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a387) | c1_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c3_1(a387)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a387) | c1_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c3_1(a387)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1329,plain,
% 0.88/1.06 ((hskp10 | (~ndr1_0) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)) | c1_1(a387) | c0_1(a387) | (~c3_1(a387))) <=> (hskp10 | c0_1(a387) | c1_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c3_1(a387)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1330,plain,
% 0.88/1.06 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)) | c1_1(a387) | c0_1(a387) | (~c3_1(a387)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a387) | c1_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c3_1(a387))))),
% 0.88/1.06 inference(monotonicity,[status(thm)],[1329])).
% 0.88/1.06 tff(1331,plain,
% 0.88/1.06 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)) | c1_1(a387) | c0_1(a387) | (~c3_1(a387)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a387) | c1_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c3_1(a387)))),
% 0.88/1.06 inference(transitivity,[status(thm)],[1330, 1328])).
% 0.88/1.06 tff(1332,plain,
% 0.88/1.06 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)) | c1_1(a387) | c0_1(a387) | (~c3_1(a387)))),
% 0.88/1.06 inference(quant_inst,[status(thm)],[])).
% 0.88/1.06 tff(1333,plain,
% 0.88/1.06 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a387) | c1_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c3_1(a387))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1332, 1331])).
% 0.88/1.06 tff(1334,plain,
% 0.88/1.06 (hskp10 | (~c3_1(a387))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1333, 105, 394, 598, 596, 379, 373, 1327])).
% 0.88/1.06 tff(1335,plain,
% 0.88/1.06 (hskp10),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1334, 1317])).
% 0.88/1.06 tff(1336,plain,
% 0.88/1.06 (~c3_1(a366)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1260, 1335])).
% 0.88/1.06 tff(1337,plain,
% 0.88/1.06 (~c2_1(a366)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1266, 1335])).
% 0.88/1.06 tff(1338,plain,
% 0.88/1.06 (~c0_1(a366)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1272, 1335])).
% 0.88/1.06 tff(1339,plain,
% 0.88/1.06 (~hskp19),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[218, 1308])).
% 0.88/1.06 tff(1340,plain,
% 0.88/1.06 (hskp28),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[549, 1339])).
% 0.88/1.06 tff(1341,plain,
% 0.88/1.06 (c3_1(a365)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[37, 1340])).
% 0.88/1.06 tff(1342,plain,
% 0.88/1.06 (c2_1(a365)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[45, 1340])).
% 0.88/1.06 tff(1343,plain,
% 0.88/1.06 (c1_1(a365)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[29, 1340])).
% 0.88/1.06 tff(1344,plain,
% 0.88/1.06 (~hskp13),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[418, 1343, 1342, 1341])).
% 0.88/1.06 tff(1345,plain,
% 0.88/1.06 ($false),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1279, 105, 1344, 1343, 1342, 1341, 1338, 1337, 1336, 122])).
% 0.88/1.06 tff(1346,plain,(c1_1(a387) | c0_1(a387) | c2_1(a388) | c3_1(a388) | c1_1(a360) | c2_1(a360) | c3_1(a360)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.06 tff(1347,plain,
% 0.88/1.06 ($false),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1346, 1285, 1284, 312, 311, 739, 737, 738])).
% 0.88/1.06 tff(1348,plain,(c3_1(a388) | c2_1(a388) | c1_1(a360) | c2_1(a360) | c3_1(a360)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.06 tff(1349,plain,
% 0.88/1.06 (c3_1(a388)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1348, 312, 739, 737, 738])).
% 0.88/1.06 tff(1350,plain,
% 0.88/1.06 (~hskp20),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[274, 1349])).
% 0.88/1.06 tff(1351,assumption,(~hskp20), introduced(assumption)).
% 0.88/1.06 tff(1352,plain,
% 0.88/1.06 ($false),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[268, 105, 1351, 753, 752, 739, 737, 738, 751, 154])).
% 0.88/1.06 tff(1353,plain,((~hskp3) | hskp20 | c1_1(a360) | c2_1(a360) | c3_1(a360)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.06 tff(1354,plain,
% 0.88/1.06 (~hskp3),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1353, 1350, 739, 737, 738])).
% 0.88/1.06 tff(1355,plain,
% 0.88/1.06 (hskp19),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1001, 1354, 738, 739, 737])).
% 0.88/1.06 tff(1356,plain,
% 0.88/1.06 (~c0_1(a387)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[230, 1355])).
% 0.88/1.06 tff(1357,plain,
% 0.88/1.06 (~c1_1(a387)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[224, 1355])).
% 0.88/1.06 tff(1358,plain,
% 0.88/1.06 (c0_1(a388)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[817, 615, 312, 749])).
% 0.88/1.06 tff(1359,plain,
% 0.88/1.06 (hskp0 | (~c3_1(a387))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[621, 105, 598, 596, 597, 614])).
% 0.88/1.06 tff(1360,plain,
% 0.88/1.06 (~c3_1(a387)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1359, 615])).
% 0.88/1.06 tff(1361,plain,
% 0.88/1.06 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.88/1.06 inference(bind,[status(th)],[])).
% 0.88/1.06 tff(1362,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.88/1.06 inference(quant_intro,[status(thm)],[1361])).
% 0.88/1.06 tff(1363,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1364,plain,
% 0.88/1.06 (^[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(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | 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)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.88/1.06 inference(bind,[status(th)],[])).
% 0.88/1.06 tff(1365,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.88/1.06 inference(quant_intro,[status(thm)],[1364])).
% 0.88/1.06 tff(1366,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause199')).
% 0.88/1.06 tff(1367,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1366, 1365])).
% 0.88/1.06 tff(1368,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1367, 1363])).
% 0.88/1.06 tff(1369,plain,(
% 0.88/1.06 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.88/1.06 inference(skolemize,[status(sab)],[1368])).
% 0.88/1.06 tff(1370,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1369, 1362])).
% 0.88/1.06 tff(1371,assumption,(c3_1(a388)), introduced(assumption)).
% 0.88/1.06 tff(1372,plain,
% 0.88/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a388) | (~c3_1(a388)) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c0_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a388) | (~c3_1(a388)) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c0_1(a388)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1373,plain,
% 0.88/1.06 (((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c0_1(a388)) | c2_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a387) | c1_1(a387) | c0_1(a387)) <=> (c2_1(a388) | (~c3_1(a388)) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c0_1(a388)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1374,plain,
% 0.88/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c0_1(a388)) | c2_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a388) | (~c3_1(a388)) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c0_1(a388))))),
% 0.88/1.06 inference(monotonicity,[status(thm)],[1373])).
% 0.88/1.06 tff(1375,plain,
% 0.88/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c0_1(a388)) | c2_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a388) | (~c3_1(a388)) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c0_1(a388)))),
% 0.88/1.06 inference(transitivity,[status(thm)],[1374, 1372])).
% 0.88/1.06 tff(1376,plain,
% 0.88/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c0_1(a388)) | c2_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a387) | c1_1(a387) | c0_1(a387))),
% 0.88/1.06 inference(quant_inst,[status(thm)],[])).
% 0.88/1.06 tff(1377,plain,
% 0.88/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a388) | (~c3_1(a388)) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c0_1(a388))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1376, 1375])).
% 0.88/1.06 tff(1378,plain,
% 0.88/1.06 (c3_1(a387) | (~c0_1(a388))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1377, 105, 312, 1371, 598, 596, 597, 1370])).
% 0.88/1.06 tff(1379,plain,
% 0.88/1.06 ($false),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1378, 1360, 1358])).
% 0.88/1.06 tff(1380,plain,(hskp0 | c2_1(a388) | (~c3_1(a388)) | c0_1(a387) | c1_1(a387) | c2_1(a387) | c1_1(a388)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.06 tff(1381,plain,
% 0.88/1.06 (hskp0),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1380, 1005, 1349, 598, 596, 312, 749])).
% 0.88/1.06 tff(1382,plain,
% 0.88/1.06 (~c2_1(a353)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[653, 1381])).
% 0.88/1.06 tff(1383,plain,
% 0.88/1.06 (c1_1(a353)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[661, 1381])).
% 0.88/1.06 tff(1384,assumption,(~c2_1(a353)), introduced(assumption)).
% 0.88/1.06 tff(1385,assumption,(c1_1(a353)), introduced(assumption)).
% 0.88/1.06 tff(1386,plain,
% 0.88/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a360) | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a360) | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a360))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1387,plain,
% 0.88/1.06 (((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a360) | c0_1(a360) | c3_1(a360)) <=> (c1_1(a360) | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a360))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1388,plain,
% 0.88/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a360) | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a360)))),
% 0.88/1.06 inference(monotonicity,[status(thm)],[1387])).
% 0.88/1.06 tff(1389,plain,
% 0.88/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a360) | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a360))),
% 0.88/1.06 inference(transitivity,[status(thm)],[1388, 1386])).
% 0.88/1.06 tff(1390,plain,
% 0.88/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a360) | c0_1(a360) | c3_1(a360))),
% 0.88/1.06 inference(quant_inst,[status(thm)],[])).
% 0.88/1.06 tff(1391,plain,
% 0.88/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a360) | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a360)),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1390, 1389])).
% 0.88/1.06 tff(1392,plain,
% 0.88/1.06 ((~c3_1(a353)) | c0_1(a360)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1391, 105, 1385, 739, 737, 738, 1384, 595])).
% 0.88/1.06 tff(1393,plain,
% 0.88/1.06 (~c3_1(a353)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1392, 740])).
% 0.88/1.06 tff(1394,plain,
% 0.88/1.06 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1395,plain,
% 0.88/1.06 ((hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a360) | c0_1(a360) | c3_1(a360)) <=> (hskp12 | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1396,plain,
% 0.88/1.06 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360)))),
% 0.88/1.06 inference(monotonicity,[status(thm)],[1395])).
% 0.88/1.06 tff(1397,plain,
% 0.88/1.06 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360))),
% 0.88/1.06 inference(transitivity,[status(thm)],[1396, 1394])).
% 0.88/1.06 tff(1398,plain,
% 0.88/1.06 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a360) | c0_1(a360) | c3_1(a360))),
% 0.88/1.06 inference(quant_inst,[status(thm)],[])).
% 0.88/1.06 tff(1399,plain,
% 0.88/1.06 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360)),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1398, 1397])).
% 0.88/1.06 tff(1400,plain,
% 0.88/1.06 (hskp12 | c3_1(a353) | c0_1(a360)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1399, 105, 1385, 737, 738, 1384, 679])).
% 0.88/1.06 tff(1401,plain,
% 0.88/1.06 (hskp12),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1400, 740, 1393])).
% 0.88/1.06 tff(1402,plain,
% 0.88/1.06 (~c2_1(a369)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[691, 1401])).
% 0.88/1.06 tff(1403,plain,
% 0.88/1.06 (c3_1(a369)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[699, 1401])).
% 0.88/1.06 tff(1404,plain,
% 0.88/1.06 (c0_1(a369)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[707, 1401])).
% 0.88/1.06 tff(1405,plain,
% 0.88/1.06 (~c1_1(a369)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[714, 105, 1404, 1403, 1385, 1402, 1384, 308, 1393])).
% 0.88/1.06 tff(1406,plain,
% 0.88/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a369) | c1_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360) | c1_1(a369) | (~c0_1(a369)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a369) | c1_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360) | c1_1(a369) | (~c0_1(a369)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1407,plain,
% 0.88/1.06 (((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a360) | c0_1(a360) | c3_1(a360)) <=> (c2_1(a369) | c1_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360) | c1_1(a369) | (~c0_1(a369)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1408,plain,
% 0.88/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a369) | c1_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360) | c1_1(a369) | (~c0_1(a369))))),
% 0.88/1.06 inference(monotonicity,[status(thm)],[1407])).
% 0.88/1.06 tff(1409,plain,
% 0.88/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a369) | c1_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360) | c1_1(a369) | (~c0_1(a369)))),
% 0.88/1.06 inference(transitivity,[status(thm)],[1408, 1406])).
% 0.88/1.06 tff(1410,plain,
% 0.88/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a360) | c0_1(a360) | c3_1(a360))),
% 0.88/1.06 inference(quant_inst,[status(thm)],[])).
% 0.88/1.06 tff(1411,plain,
% 0.88/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a369) | c1_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360) | c1_1(a369) | (~c0_1(a369))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1410, 1409])).
% 0.88/1.06 tff(1412,plain,
% 0.88/1.06 ($false),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1411, 105, 1404, 1385, 1402, 739, 738, 1384, 725, 740, 1393, 1405])).
% 0.88/1.06 tff(1413,plain,(c0_1(a360) | (~c1_1(a353)) | c1_1(a360) | c3_1(a360) | c2_1(a353) | c2_1(a360)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.06 tff(1414,plain,
% 0.88/1.06 (c0_1(a360)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1413, 1383, 739, 738, 1382, 737])).
% 0.88/1.06 tff(1415,plain,
% 0.88/1.06 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c1_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a360)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c1_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a360)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1416,plain,
% 0.88/1.06 ((hskp3 | (~ndr1_0) | c1_1(a360) | c3_1(a360) | (~c0_1(a360)) | c0_1(a358) | c3_1(a358) | (~c1_1(a358))) <=> (hskp3 | c1_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a360)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1417,plain,
% 0.88/1.06 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a360) | c3_1(a360) | (~c0_1(a360)) | c0_1(a358) | c3_1(a358) | (~c1_1(a358)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c1_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a360))))),
% 0.88/1.06 inference(monotonicity,[status(thm)],[1416])).
% 0.88/1.06 tff(1418,plain,
% 0.88/1.06 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a360) | c3_1(a360) | (~c0_1(a360)) | c0_1(a358) | c3_1(a358) | (~c1_1(a358)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c1_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a360)))),
% 0.88/1.06 inference(transitivity,[status(thm)],[1417, 1415])).
% 0.88/1.06 tff(1419,plain,
% 0.88/1.06 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a360) | c3_1(a360) | (~c0_1(a360)) | c0_1(a358) | c3_1(a358) | (~c1_1(a358)))),
% 0.88/1.06 inference(quant_inst,[status(thm)],[])).
% 0.88/1.06 tff(1420,plain,
% 0.88/1.06 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c1_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a360))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1419, 1418])).
% 0.88/1.06 tff(1421,plain,
% 0.88/1.06 (hskp3 | (~c1_1(a358)) | (~c0_1(a360))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1420, 105, 739, 738, 379, 373, 773])).
% 0.88/1.06 tff(1422,plain,
% 0.88/1.06 (~c1_1(a358)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1421, 1414, 165])).
% 0.88/1.06 tff(1423,plain,
% 0.88/1.06 (((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp26 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360)))) <=> ((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp26 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1424,plain,
% 0.88/1.06 ((hskp26 | (~ndr1_0) | c2_1(a360) | c3_1(a360) | (~c0_1(a360))) <=> (hskp26 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1425,plain,
% 0.88/1.06 (((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp26 | (~ndr1_0) | c2_1(a360) | c3_1(a360) | (~c0_1(a360)))) <=> ((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp26 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360))))),
% 0.88/1.06 inference(monotonicity,[status(thm)],[1424])).
% 0.88/1.06 tff(1426,plain,
% 0.88/1.06 (((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp26 | (~ndr1_0) | c2_1(a360) | c3_1(a360) | (~c0_1(a360)))) <=> ((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp26 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360)))),
% 0.88/1.06 inference(transitivity,[status(thm)],[1425, 1423])).
% 0.88/1.06 tff(1427,plain,
% 0.88/1.06 ((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp26 | (~ndr1_0) | c2_1(a360) | c3_1(a360) | (~c0_1(a360)))),
% 0.88/1.06 inference(quant_inst,[status(thm)],[])).
% 0.88/1.06 tff(1428,plain,
% 0.88/1.06 ((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp26 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1427, 1426])).
% 0.88/1.06 tff(1429,plain,
% 0.88/1.06 (hskp26 | c2_1(a360) | (~c0_1(a360))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1428, 105, 738, 958])).
% 0.88/1.06 tff(1430,plain,
% 0.88/1.06 (hskp26),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1429, 1414, 737])).
% 0.88/1.06 tff(1431,plain,
% 0.88/1.06 (~c3_1(a418)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[971, 1430])).
% 0.88/1.06 tff(1432,plain,
% 0.88/1.06 (~c2_1(a418)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[977, 1430])).
% 0.88/1.06 tff(1433,plain,
% 0.88/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a418) | c3_1(a418) | c1_1(a360) | c2_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c0_1(a360)) | (~c1_1(a418)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c3_1(a418) | c1_1(a360) | c2_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c0_1(a360)) | (~c1_1(a418)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1434,plain,
% 0.88/1.06 (((~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c1_1(a418)) | c2_1(a360) | c1_1(a360) | (~c0_1(a360)) | c1_1(a358) | c0_1(a358) | c3_1(a358)) <=> (c2_1(a418) | c3_1(a418) | c1_1(a360) | c2_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c0_1(a360)) | (~c1_1(a418)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1435,plain,
% 0.88/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c1_1(a418)) | c2_1(a360) | c1_1(a360) | (~c0_1(a360)) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a418) | c3_1(a418) | c1_1(a360) | c2_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c0_1(a360)) | (~c1_1(a418))))),
% 0.88/1.07 inference(monotonicity,[status(thm)],[1434])).
% 0.88/1.07 tff(1436,plain,
% 0.88/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c1_1(a418)) | c2_1(a360) | c1_1(a360) | (~c0_1(a360)) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c3_1(a418) | c1_1(a360) | c2_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c0_1(a360)) | (~c1_1(a418)))),
% 0.88/1.07 inference(transitivity,[status(thm)],[1435, 1433])).
% 0.88/1.07 tff(1437,plain,
% 0.88/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c1_1(a418)) | c2_1(a360) | c1_1(a360) | (~c0_1(a360)) | c1_1(a358) | c0_1(a358) | c3_1(a358))),
% 0.88/1.07 inference(quant_inst,[status(thm)],[])).
% 0.88/1.07 tff(1438,plain,
% 0.88/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c3_1(a418) | c1_1(a360) | c2_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c0_1(a360)) | (~c1_1(a418))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[1437, 1436])).
% 0.88/1.07 tff(1439,plain,
% 0.88/1.07 (~c1_1(a418)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1438, 105, 1432, 1431, 739, 737, 379, 373, 725, 1414, 1422])).
% 0.88/1.07 tff(1440,plain,
% 0.88/1.07 (c0_1(a418)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[985, 1430])).
% 0.88/1.07 tff(1441,plain,
% 0.88/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418) | (~c0_1(a418)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418) | (~c0_1(a418)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(1442,plain,
% 0.88/1.07 (((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a418) | c1_1(a418) | (~c0_1(a418)) | c1_1(a358) | c0_1(a358) | c3_1(a358)) <=> (c2_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418) | (~c0_1(a418)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(1443,plain,
% 0.88/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a418) | c1_1(a418) | (~c0_1(a418)) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418) | (~c0_1(a418))))),
% 0.88/1.07 inference(monotonicity,[status(thm)],[1442])).
% 0.88/1.07 tff(1444,plain,
% 0.88/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a418) | c1_1(a418) | (~c0_1(a418)) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418) | (~c0_1(a418)))),
% 0.88/1.07 inference(transitivity,[status(thm)],[1443, 1441])).
% 0.88/1.07 tff(1445,plain,
% 0.88/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a418) | c1_1(a418) | (~c0_1(a418)) | c1_1(a358) | c0_1(a358) | c3_1(a358))),
% 0.88/1.07 inference(quant_inst,[status(thm)],[])).
% 0.88/1.07 tff(1446,plain,
% 0.88/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418) | (~c0_1(a418))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[1445, 1444])).
% 0.88/1.07 tff(1447,plain,
% 0.88/1.07 (c3_1(a353)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1446, 105, 1440, 1383, 1432, 379, 373, 1382, 725, 1422, 1439])).
% 0.88/1.07 tff(1448,plain,
% 0.88/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a418) | c3_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c3_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(1449,plain,
% 0.88/1.07 (((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a418) | c1_1(a418) | c3_1(a418) | c1_1(a358) | c0_1(a358) | c3_1(a358)) <=> (c2_1(a418) | c3_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(1450,plain,
% 0.88/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a418) | c1_1(a418) | c3_1(a418) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a418) | c3_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418)))),
% 0.88/1.07 inference(monotonicity,[status(thm)],[1449])).
% 0.88/1.07 tff(1451,plain,
% 0.88/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a418) | c1_1(a418) | c3_1(a418) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c3_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418))),
% 0.88/1.07 inference(transitivity,[status(thm)],[1450, 1448])).
% 0.88/1.07 tff(1452,plain,
% 0.88/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a418) | c1_1(a418) | c3_1(a418) | c1_1(a358) | c0_1(a358) | c3_1(a358))),
% 0.88/1.07 inference(quant_inst,[status(thm)],[])).
% 0.88/1.07 tff(1453,plain,
% 0.88/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c3_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[1452, 1451])).
% 0.88/1.07 tff(1454,plain,
% 0.88/1.07 ($false),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1453, 105, 1383, 1432, 1431, 379, 373, 1382, 595, 1422, 1447, 1439])).
% 0.88/1.07 tff(1455,plain,(hskp3 | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a387) | c1_1(a387) | c2_1(a388) | c1_1(a388)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.07 tff(1456,plain,
% 0.88/1.07 (c1_1(a388)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1455, 1357, 737, 738, 1354, 739, 312, 1356])).
% 0.88/1.07 tff(1457,plain,
% 0.88/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a388) | (~c3_1(a388)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a388) | (~c3_1(a388)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(1458,plain,
% 0.88/1.07 (((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c1_1(a388)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a360) | c0_1(a360) | c3_1(a360)) <=> (c2_1(a388) | (~c3_1(a388)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(1459,plain,
% 0.88/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c1_1(a388)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a388) | (~c3_1(a388)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388))))),
% 0.88/1.07 inference(monotonicity,[status(thm)],[1458])).
% 0.88/1.07 tff(1460,plain,
% 0.88/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c1_1(a388)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a388) | (~c3_1(a388)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388)))),
% 0.88/1.07 inference(transitivity,[status(thm)],[1459, 1457])).
% 0.88/1.07 tff(1461,plain,
% 0.88/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c1_1(a388)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a360) | c0_1(a360) | c3_1(a360))),
% 0.88/1.07 inference(quant_inst,[status(thm)],[])).
% 0.88/1.07 tff(1462,plain,
% 0.88/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a388) | (~c3_1(a388)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[1461, 1460])).
% 0.88/1.07 tff(1463,plain,
% 0.88/1.07 ((~c3_1(a388)) | c0_1(a360) | (~c1_1(a388))),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1462, 105, 312, 739, 737, 738, 595])).
% 0.88/1.07 tff(1464,plain,
% 0.88/1.07 (c0_1(a360)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1463, 1456, 1349])).
% 0.88/1.07 tff(1465,plain,
% 0.88/1.07 (~c1_1(a358)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1421, 1464, 1354])).
% 0.88/1.07 tff(1466,plain,
% 0.88/1.07 (hskp26),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1429, 1464, 737])).
% 0.88/1.07 tff(1467,plain,
% 0.88/1.07 (~c3_1(a418)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[971, 1466])).
% 0.88/1.07 tff(1468,plain,
% 0.88/1.07 (~c2_1(a418)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[977, 1466])).
% 0.88/1.07 tff(1469,plain,
% 0.88/1.07 (~c1_1(a418)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1438, 105, 1468, 1467, 739, 737, 379, 373, 725, 1464, 1465])).
% 0.88/1.07 tff(1470,plain,
% 0.88/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a418) | c3_1(a418) | c2_1(a388) | (~c3_1(a388)) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c1_1(a388)) | c1_1(a418))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c3_1(a418) | c2_1(a388) | (~c3_1(a388)) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c1_1(a388)) | c1_1(a418))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(1471,plain,
% 0.88/1.07 (((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c1_1(a388)) | c2_1(a418) | c1_1(a418) | c3_1(a418) | c1_1(a358) | c0_1(a358) | c3_1(a358)) <=> (c2_1(a418) | c3_1(a418) | c2_1(a388) | (~c3_1(a388)) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c1_1(a388)) | c1_1(a418))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(1472,plain,
% 0.88/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c1_1(a388)) | c2_1(a418) | c1_1(a418) | c3_1(a418) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a418) | c3_1(a418) | c2_1(a388) | (~c3_1(a388)) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c1_1(a388)) | c1_1(a418)))),
% 0.88/1.07 inference(monotonicity,[status(thm)],[1471])).
% 0.88/1.07 tff(1473,plain,
% 0.88/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c1_1(a388)) | c2_1(a418) | c1_1(a418) | c3_1(a418) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c3_1(a418) | c2_1(a388) | (~c3_1(a388)) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c1_1(a388)) | c1_1(a418))),
% 0.88/1.07 inference(transitivity,[status(thm)],[1472, 1470])).
% 0.88/1.07 tff(1474,plain,
% 0.88/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c1_1(a388)) | c2_1(a418) | c1_1(a418) | c3_1(a418) | c1_1(a358) | c0_1(a358) | c3_1(a358))),
% 0.88/1.07 inference(quant_inst,[status(thm)],[])).
% 0.88/1.07 tff(1475,plain,
% 0.88/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c3_1(a418) | c2_1(a388) | (~c3_1(a388)) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c1_1(a388)) | c1_1(a418)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[1474, 1473])).
% 0.88/1.07 tff(1476,plain,
% 0.88/1.07 ($false),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1475, 105, 1456, 1468, 1467, 312, 1349, 379, 373, 595, 1465, 1469])).
% 0.88/1.07 tff(1477,plain,(c2_1(a388) | c1_1(a360) | c2_1(a360) | c3_1(a360)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.07 tff(1478,plain,
% 0.88/1.07 (c2_1(a388)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1477, 739, 737, 738])).
% 0.88/1.07 tff(1479,plain,
% 0.88/1.07 (~hskp20),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[280, 1478])).
% 0.88/1.07 tff(1480,plain,
% 0.88/1.07 (~hskp3),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1353, 1479, 739, 737, 738])).
% 0.88/1.07 tff(1481,plain,
% 0.88/1.07 (hskp19),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1001, 1480, 738, 739, 737])).
% 0.88/1.07 tff(1482,plain,
% 0.88/1.07 (~c2_1(a387)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[218, 1481])).
% 0.88/1.07 tff(1483,plain,
% 0.88/1.07 (~c1_1(a387)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[224, 1481])).
% 0.88/1.07 tff(1484,plain,
% 0.88/1.07 (~c0_1(a387)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[230, 1481])).
% 0.88/1.07 tff(1485,assumption,(~c1_1(a358)), introduced(assumption)).
% 0.88/1.07 tff(1486,plain,
% 0.88/1.07 ($false),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[798, 105, 394, 598, 596, 597, 379, 373, 10, 1485])).
% 0.88/1.07 tff(1487,plain,(c1_1(a358) | c0_1(a387) | c1_1(a387) | c2_1(a387)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.07 tff(1488,plain,
% 0.88/1.07 (c1_1(a358)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1487, 1484, 1483, 1482])).
% 0.88/1.07 tff(1489,plain,
% 0.88/1.07 (~c0_1(a360)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1421, 1488, 1480])).
% 0.88/1.07 tff(1490,plain,
% 0.88/1.07 (hskp0 | (~c1_1(a358))),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[638, 105, 394, 1484, 1483, 1482, 379, 632])).
% 0.88/1.07 tff(1491,plain,
% 0.88/1.07 (hskp0),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1490, 1488])).
% 0.88/1.07 tff(1492,plain,
% 0.88/1.07 (c1_1(a353)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[661, 1491])).
% 0.88/1.07 tff(1493,plain,
% 0.88/1.07 (~c2_1(a353)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[653, 1491])).
% 0.88/1.07 tff(1494,plain,
% 0.88/1.07 ($false),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1413, 1493, 1492, 739, 738, 1489, 737])).
% 0.88/1.08 tff(1495,plain,(c1_1(a360) | c3_1(a360) | c2_1(a360)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.08 tff(1496,plain,
% 0.88/1.08 ($false),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[1495, 736, 735, 734])).
% 0.88/1.08 % SZS output end Proof
% 0.88/1.08 % E exiting
%------------------------------------------------------------------------------