%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL152-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:51:21 AM UTC 2026
% Result : Unsatisfiable 10.56s 2.37s
% Output : Refutation 11.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 7
% Syntax : Number of formulae : 115 ( 115 unt; 0 def)
% Number of atoms : 115 ( 114 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 250 ( 250 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : implies(truth,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_1) ).
fof(f2,axiom,
! [X2,X0,X1] : implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_2) ).
fof(f3,plain,
! [X2,X0,X1] : truth = implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_3) ).
fof(f5,axiom,
! [X0,X1] : implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_4) ).
fof(f6,plain,
! [X0,X1] : truth = implies(implies(not(X0),not(X1)),implies(X1,X0)),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X0,X1] : big_V(X0,X1) = implies(implies(X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',big_V_definition) ).
fof(f8,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = big_V(X0,X1),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0,X1] : big_hat(X0,X1) = not(big_V(not(X0),not(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',big_hat_definition) ).
fof(f14,negated_conjecture,
implies(big_hat(x,y),z) != implies(implies(x,y),implies(x,z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wajsberg_theorem) ).
fof(f15,plain,
! [X0,X1] : big_hat(X0,X1) = not(implies(implies(not(X0),not(X1)),not(X1))),
inference(definition_unfolding,[],[f9,f8]) ).
fof(f16,plain,
implies(implies(x,y),implies(x,z)) != implies(not(implies(implies(not(x),not(y)),not(y))),z),
inference(definition_unfolding,[],[f14,f15]) ).
fof(f17,plain,
! [X2,X3,X0,X1] : truth = implies(truth,implies(implies(implies(implies(X1,X2),implies(X0,X2)),X3),implies(implies(X0,X1),X3))),
inference(superposition,[],[f3,f3]) ).
fof(f22,plain,
! [X2,X3,X0,X1] : truth = implies(implies(implies(implies(X1,X2),implies(X0,X2)),X3),implies(implies(X0,X1),X3)),
inference(forward_demodulation,[],[f17,f1]) ).
fof(f24,plain,
! [X2,X0,X1] : implies(implies(implies(implies(X0,X1),implies(X2,X1)),implies(X2,X0)),implies(X2,X0)) = implies(truth,implies(implies(X0,X1),implies(X2,X1))),
inference(superposition,[],[f4,f3]) ).
fof(f31,plain,
! [X2,X0,X1] : implies(implies(X0,X1),implies(X2,X1)) = implies(implies(implies(implies(X0,X1),implies(X2,X1)),implies(X2,X0)),implies(X2,X0)),
inference(forward_demodulation,[],[f24,f1]) ).
fof(f39,plain,
! [X2,X0,X1] : truth = implies(implies(X0,implies(not(X1),not(X2))),implies(truth,implies(X0,implies(X2,X1)))),
inference(superposition,[],[f3,f6]) ).
fof(f42,plain,
! [X2,X0,X1] : truth = implies(implies(X0,implies(not(X1),not(X2))),implies(X0,implies(X2,X1))),
inference(forward_demodulation,[],[f39,f1]) ).
fof(f43,plain,
! [X0] : truth = implies(implies(not(X0),not(truth)),X0),
inference(superposition,[],[f6,f1]) ).
fof(f48,plain,
! [X0,X1] : truth = implies(X0,implies(implies(X0,X1),implies(truth,X1))),
inference(superposition,[],[f3,f1]) ).
fof(f49,plain,
! [X0,X1] : truth = implies(X0,implies(implies(X0,X1),X1)),
inference(forward_demodulation,[],[f48,f1]) ).
fof(f65,plain,
! [X2,X0,X1,X4] : truth = implies(implies(truth,X4),implies(implies(implies(X2,X0),implies(implies(X0,X1),implies(X2,X1))),X4)),
inference(superposition,[],[f22,f22]) ).
fof(f75,plain,
! [X2,X0,X1] : truth = implies(implies(implies(implies(X0,X1),implies(truth,X1)),X2),implies(X0,X2)),
inference(superposition,[],[f22,f1]) ).
fof(f89,plain,
! [X2,X0,X1] : truth = implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2)),
inference(forward_demodulation,[],[f75,f1]) ).
fof(f95,plain,
! [X4] : truth = implies(implies(truth,X4),implies(truth,X4)),
inference(forward_demodulation,[],[f65,f3]) ).
fof(f105,plain,
! [X4] : truth = implies(X4,X4),
inference(forward_demodulation,[],[f95,f1]) ).
fof(f164,plain,
! [X2,X0,X1] : truth = implies(truth,implies(implies(X2,implies(X0,X1)),implies(X0,implies(X2,X1)))),
inference(superposition,[],[f22,f89]) ).
fof(f165,plain,
! [X2,X0,X1] : truth = implies(implies(X2,implies(X0,X1)),implies(X0,implies(X2,X1))),
inference(forward_demodulation,[],[f164,f1]) ).
fof(f283,plain,
! [X2,X0,X1] : implies(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2))),implies(X1,implies(X0,X2))) = implies(truth,implies(X0,implies(X1,X2))),
inference(superposition,[],[f4,f165]) ).
fof(f300,plain,
! [X2,X0,X1] : implies(X0,implies(X1,X2)) = implies(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2))),implies(X1,implies(X0,X2))),
inference(forward_demodulation,[],[f283,f1]) ).
fof(f323,plain,
! [X2,X0,X1] : implies(X0,implies(X1,X2)) = implies(truth,implies(X1,implies(X0,X2))),
inference(forward_demodulation,[],[f300,f165]) ).
fof(f326,plain,
! [X2,X0,X1] : implies(X0,implies(X1,X2)) = implies(X1,implies(X0,X2)),
inference(forward_demodulation,[],[f323,f1]) ).
fof(f351,plain,
! [X2,X0,X1] : implies(X2,implies(implies(X0,X1),X1)) = implies(implies(X1,X0),implies(X2,X0)),
inference(superposition,[],[f326,f4]) ).
fof(f357,plain,
! [X0,X1] : implies(X0,implies(X1,X0)) = implies(X1,truth),
inference(superposition,[],[f326,f105]) ).
fof(f360,plain,
! [X2,X3,X0,X1] : implies(X3,implies(X0,implies(X1,X2))) = implies(X1,implies(X3,implies(X0,X2))),
inference(superposition,[],[f326,f326]) ).
fof(f655,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),X1)) = implies(implies(X1,X0),truth),
inference(superposition,[],[f357,f4]) ).
fof(f659,plain,
! [X2,X3,X0,X1] : implies(implies(implies(implies(X1,X3),implies(X0,X3)),X2),truth) = implies(implies(implies(X0,X1),X2),truth),
inference(superposition,[],[f357,f22]) ).
fof(f695,plain,
! [X2,X3,X0,X1] : truth = implies(implies(implies(implies(X1,X2),implies(X3,X2)),implies(X0,implies(X3,X1))),implies(X0,truth)),
inference(superposition,[],[f22,f357]) ).
fof(f698,plain,
! [X2,X3,X0,X1] : truth = implies(X0,implies(implies(implies(implies(X1,X2),implies(X3,X2)),implies(X0,implies(X3,X1))),truth)),
inference(forward_demodulation,[],[f695,f326]) ).
fof(f726,plain,
! [X0,X1] : truth = implies(implies(X1,X0),truth),
inference(forward_demodulation,[],[f655,f49]) ).
fof(f728,plain,
! [X3,X0,X1] : truth = implies(X0,implies(implies(implies(X3,X1),implies(X0,implies(X3,X1))),truth)),
inference(forward_demodulation,[],[f698,f659]) ).
fof(f742,plain,
! [X0] : truth = implies(X0,truth),
inference(forward_demodulation,[],[f728,f726]) ).
fof(f777,plain,
! [X0,X1] : truth = implies(implies(truth,X1),implies(X0,X1)),
inference(superposition,[],[f89,f742]) ).
fof(f787,plain,
! [X0,X1] : truth = implies(X1,implies(X0,X1)),
inference(forward_demodulation,[],[f777,f1]) ).
fof(f849,plain,
! [X0,X1] : truth = implies(truth,implies(not(X0),implies(X0,X1))),
inference(superposition,[],[f42,f787]) ).
fof(f862,plain,
! [X2,X0,X1] : truth = implies(implies(implies(truth,implies(X1,X0)),X2),implies(X0,X2)),
inference(superposition,[],[f89,f787]) ).
fof(f879,plain,
! [X2,X0,X1] : truth = implies(X0,implies(implies(implies(truth,implies(X1,X0)),X2),X2)),
inference(forward_demodulation,[],[f862,f326]) ).
fof(f890,plain,
! [X0,X1] : truth = implies(not(X0),implies(X0,X1)),
inference(forward_demodulation,[],[f849,f1]) ).
fof(f901,plain,
! [X2,X0,X1] : truth = implies(X0,implies(implies(implies(X1,X0),X2),X2)),
inference(forward_demodulation,[],[f879,f1]) ).
fof(f908,plain,
! [X0,X1] : truth = implies(X0,implies(not(X0),X1)),
inference(forward_demodulation,[],[f890,f326]) ).
fof(f1031,plain,
! [X0] : truth = implies(not(truth),X0),
inference(superposition,[],[f1,f908]) ).
fof(f1036,plain,
! [X0,X1] : implies(implies(implies(not(X0),X1),X0),X0) = implies(truth,implies(not(X0),X1)),
inference(superposition,[],[f4,f908]) ).
fof(f1069,plain,
! [X0,X1] : implies(not(X0),X1) = implies(implies(implies(not(X0),X1),X0),X0),
inference(forward_demodulation,[],[f1036,f1]) ).
fof(f1257,plain,
! [X2,X3,X0,X1] : implies(implies(implies(X2,implies(X1,X3)),implies(X1,implies(X2,X3))),implies(X0,implies(X1,implies(X2,X3)))) = implies(X0,implies(truth,implies(X2,implies(X1,X3)))),
inference(superposition,[],[f351,f165]) ).
fof(f1339,plain,
! [X2,X0,X1] : implies(implies(X0,X1),implies(X2,X1)) = implies(implies(X1,X0),implies(X2,X0)),
inference(superposition,[],[f326,f351]) ).
fof(f1518,plain,
! [X2,X3,X0,X1] : implies(X0,implies(X2,implies(X1,X3))) = implies(implies(implies(X2,implies(X1,X3)),implies(X1,implies(X2,X3))),implies(X0,implies(X1,implies(X2,X3)))),
inference(forward_demodulation,[],[f1257,f1]) ).
fof(f1578,plain,
! [X2,X3,X0,X1] : implies(X0,implies(X2,implies(X1,X3))) = implies(X1,implies(implies(implies(X2,implies(X1,X3)),implies(X1,implies(X2,X3))),implies(X0,implies(X2,X3)))),
inference(forward_demodulation,[],[f1518,f360]) ).
fof(f1598,plain,
! [X2,X3,X0,X1] : implies(X0,implies(X2,implies(X1,X3))) = implies(X1,implies(X2,implies(implies(implies(X2,implies(X1,X3)),implies(X1,implies(X2,X3))),implies(X0,X3)))),
inference(forward_demodulation,[],[f1578,f360]) ).
fof(f1605,plain,
! [X2,X3,X0,X1] : implies(X0,implies(X2,implies(X1,X3))) = implies(X1,implies(X2,implies(truth,implies(X0,X3)))),
inference(forward_demodulation,[],[f1598,f165]) ).
fof(f1606,plain,
! [X2,X3,X0,X1] : implies(X0,implies(X2,implies(X1,X3))) = implies(X1,implies(X2,implies(X0,X3))),
inference(forward_demodulation,[],[f1605,f1]) ).
fof(f2150,plain,
! [X2,X0,X1] : implies(implies(implies(X0,X1),X1),implies(X2,X0)) = implies(implies(implies(implies(implies(X0,X1),X1),implies(X2,X0)),implies(X2,implies(X1,X0))),implies(X2,implies(X1,X0))),
inference(superposition,[],[f31,f4]) ).
fof(f2383,plain,
! [X2,X0,X1] : implies(implies(implies(X0,X1),X1),implies(X2,X0)) = implies(X1,implies(implies(implies(implies(implies(X0,X1),X1),implies(X2,X0)),implies(X2,implies(X1,X0))),implies(X2,X0))),
inference(forward_demodulation,[],[f2150,f360]) ).
fof(f2473,plain,
! [X2,X0,X1] : implies(implies(implies(X0,X1),X1),implies(X2,X0)) = implies(X1,implies(X2,implies(implies(implies(implies(implies(X0,X1),X1),implies(X2,X0)),implies(X2,implies(X1,X0))),X0))),
inference(forward_demodulation,[],[f2383,f326]) ).
fof(f2531,plain,
! [X2,X0,X1] : implies(implies(implies(X0,X1),X1),implies(X2,X0)) = implies(X1,implies(X2,implies(implies(X1,implies(implies(implies(implies(X0,X1),X1),implies(X2,X0)),implies(X2,X0))),X0))),
inference(forward_demodulation,[],[f2473,f360]) ).
fof(f2579,plain,
! [X2,X0,X1] : implies(implies(implies(X0,X1),X1),implies(X2,X0)) = implies(X1,implies(X2,implies(truth,X0))),
inference(forward_demodulation,[],[f2531,f901]) ).
fof(f2600,plain,
! [X2,X0,X1] : implies(implies(implies(X0,X1),X1),implies(X2,X0)) = implies(X1,implies(X2,X0)),
inference(forward_demodulation,[],[f2579,f1]) ).
fof(f2667,plain,
! [X2,X0,X1] : implies(X0,implies(X2,X1)) = implies(implies(implies(X0,X1),X1),implies(X2,X1)),
inference(superposition,[],[f2600,f4]) ).
fof(f3229,plain,
! [X0] : implies(not(truth),implies(X0,not(not(truth)))) = implies(truth,implies(X0,not(not(truth)))),
inference(superposition,[],[f2600,f43]) ).
fof(f3299,plain,
! [X0] : implies(X0,not(not(truth))) = implies(not(truth),implies(X0,not(not(truth)))),
inference(forward_demodulation,[],[f3229,f1]) ).
fof(f3317,plain,
! [X0] : truth = implies(X0,not(not(truth))),
inference(forward_demodulation,[],[f3299,f1031]) ).
fof(f3333,plain,
truth = not(not(truth)),
inference(superposition,[],[f1,f3317]) ).
fof(f6299,plain,
! [X0] : implies(truth,X0) = implies(not(X0),not(truth)),
inference(superposition,[],[f1069,f43]) ).
fof(f6436,plain,
! [X0] : implies(not(X0),not(truth)) = X0,
inference(forward_demodulation,[],[f6299,f1]) ).
fof(f6504,plain,
! [X0] : implies(X0,not(truth)) = implies(implies(not(truth),not(X0)),not(X0)),
inference(superposition,[],[f4,f6436]) ).
fof(f6505,plain,
! [X0] : truth = implies(implies(not(not(truth)),not(not(X0))),X0),
inference(superposition,[],[f6,f6436]) ).
fof(f6533,plain,
! [X0,X1] : implies(X0,implies(X1,not(truth))) = implies(implies(not(truth),not(X0)),implies(X1,not(X0))),
inference(superposition,[],[f1339,f6436]) ).
fof(f6547,plain,
! [X0,X1] : implies(X0,implies(X1,not(truth))) = implies(truth,implies(X1,not(X0))),
inference(forward_demodulation,[],[f6533,f1031]) ).
fof(f6566,plain,
! [X0] : truth = implies(implies(truth,not(not(X0))),X0),
inference(forward_demodulation,[],[f6505,f3333]) ).
fof(f6567,plain,
! [X0] : implies(X0,not(truth)) = implies(truth,not(X0)),
inference(forward_demodulation,[],[f6504,f1031]) ).
fof(f6575,plain,
! [X0,X1] : implies(X1,not(X0)) = implies(X0,implies(X1,not(truth))),
inference(forward_demodulation,[],[f6547,f1]) ).
fof(f6587,plain,
! [X0] : truth = implies(not(not(X0)),X0),
inference(forward_demodulation,[],[f6566,f1]) ).
fof(f6588,plain,
! [X0] : not(X0) = implies(X0,not(truth)),
inference(forward_demodulation,[],[f6567,f1]) ).
fof(f6662,plain,
! [X0] : truth = implies(truth,implies(X0,not(not(X0)))),
inference(superposition,[],[f6,f6587]) ).
fof(f6665,plain,
! [X0] : truth = implies(X0,not(not(X0))),
inference(forward_demodulation,[],[f6662,f1]) ).
fof(f6745,plain,
! [X0] : implies(truth,not(not(X0))) = implies(implies(not(not(X0)),X0),X0),
inference(superposition,[],[f4,f6665]) ).
fof(f6774,plain,
! [X0,X1] : implies(implies(not(not(X0)),X0),implies(X1,X0)) = implies(truth,implies(X1,not(not(X0)))),
inference(superposition,[],[f1339,f6665]) ).
fof(f6799,plain,
! [X0,X1] : implies(X1,not(not(X0))) = implies(implies(not(not(X0)),X0),implies(X1,X0)),
inference(forward_demodulation,[],[f6774,f1]) ).
fof(f6822,plain,
! [X0] : implies(truth,X0) = implies(truth,not(not(X0))),
inference(forward_demodulation,[],[f6745,f6587]) ).
fof(f6834,plain,
! [X0,X1] : implies(truth,implies(X1,X0)) = implies(X1,not(not(X0))),
inference(forward_demodulation,[],[f6799,f6587]) ).
fof(f6850,plain,
! [X0] : implies(truth,X0) = not(not(X0)),
inference(forward_demodulation,[],[f6822,f1]) ).
fof(f6856,plain,
! [X0,X1] : implies(X1,X0) = implies(X1,not(not(X0))),
inference(forward_demodulation,[],[f6834,f1]) ).
fof(f6864,plain,
! [X0] : not(not(X0)) = X0,
inference(forward_demodulation,[],[f6850,f1]) ).
fof(f7421,plain,
! [X0,X1] : implies(X1,implies(not(X0),not(truth))) = implies(implies(not(truth),X0),implies(X1,X0)),
inference(superposition,[],[f351,f6588]) ).
fof(f7435,plain,
! [X2,X0,X1] : implies(X0,implies(X1,implies(X2,not(truth)))) = implies(X2,implies(X1,not(X0))),
inference(superposition,[],[f1606,f6588]) ).
fof(f7485,plain,
! [X2,X0,X1] : implies(X2,implies(X1,not(X0))) = implies(X0,implies(X2,not(X1))),
inference(forward_demodulation,[],[f7435,f6575]) ).
fof(f7496,plain,
! [X0,X1] : implies(truth,implies(X1,X0)) = implies(X1,implies(not(X0),not(truth))),
inference(forward_demodulation,[],[f7421,f1031]) ).
fof(f7548,plain,
! [X0,X1] : implies(not(X0),not(X1)) = implies(truth,implies(X1,X0)),
inference(forward_demodulation,[],[f7496,f6575]) ).
fof(f7583,plain,
! [X0,X1] : implies(X1,X0) = implies(not(X0),not(X1)),
inference(forward_demodulation,[],[f7548,f1]) ).
fof(f7601,plain,
! [X0,X1] : implies(X0,not(X1)) = implies(X1,not(X0)),
inference(superposition,[],[f7583,f6864]) ).
fof(f7620,plain,
! [X0,X1] : implies(not(X0),X1) = implies(not(X1),X0),
inference(superposition,[],[f6856,f7583]) ).
fof(f7669,plain,
! [X2,X0,X1] : implies(X2,implies(X0,X1)) = implies(implies(implies(X2,not(X0)),not(X0)),implies(X0,X1)),
inference(superposition,[],[f2667,f7583]) ).
fof(f7672,plain,
! [X2,X0,X1] : implies(X2,implies(X0,X1)) = implies(X0,implies(implies(implies(X2,not(X0)),not(X0)),X1)),
inference(forward_demodulation,[],[f7669,f326]) ).
fof(f7714,plain,
! [X2,X0,X1] : implies(X2,implies(X0,X1)) = implies(X0,implies(implies(X0,not(implies(X2,not(X0)))),X1)),
inference(forward_demodulation,[],[f7672,f7601]) ).
fof(f7924,plain,
! [X2,X0,X1] : implies(implies(X2,not(X0)),implies(X0,not(X1))) = implies(X1,implies(implies(not(X0),X2),X2)),
inference(superposition,[],[f351,f7601]) ).
fof(f7953,plain,
! [X2,X0,X1] : implies(X1,implies(X2,not(X0))) = implies(implies(X0,not(implies(X1,not(X0)))),implies(X2,not(X0))),
inference(superposition,[],[f2667,f7601]) ).
fof(f7971,plain,
! [X2,X0,X1] : implies(X1,implies(X2,not(X0))) = implies(X0,implies(implies(X0,not(implies(X1,not(X0)))),not(X2))),
inference(forward_demodulation,[],[f7953,f7485]) ).
fof(f7990,plain,
! [X2,X0,X1] : implies(X1,implies(implies(not(X0),X2),X2)) = implies(X0,implies(implies(X2,not(X0)),not(X1))),
inference(forward_demodulation,[],[f7924,f326]) ).
fof(f8105,plain,
! [X2,X0,X1] : implies(X1,implies(X2,not(X0))) = implies(X1,implies(X0,not(X2))),
inference(forward_demodulation,[],[f7971,f7714]) ).
fof(f9025,plain,
implies(implies(x,y),implies(x,z)) != implies(not(z),implies(implies(not(x),not(y)),not(y))),
inference(superposition,[],[f16,f7620]) ).
fof(f9026,plain,
implies(implies(x,y),implies(x,z)) != implies(x,implies(implies(not(y),not(x)),not(not(z)))),
inference(forward_demodulation,[],[f9025,f7990]) ).
fof(f9142,plain,
implies(implies(x,y),implies(x,z)) != implies(x,implies(not(z),not(implies(not(y),not(x))))),
inference(forward_demodulation,[],[f9026,f8105]) ).
fof(f9183,plain,
implies(implies(x,y),implies(x,z)) != implies(x,implies(implies(not(y),not(x)),z)),
inference(forward_demodulation,[],[f9142,f7583]) ).
fof(f9206,plain,
implies(implies(x,y),implies(x,z)) != implies(x,implies(implies(x,not(not(y))),z)),
inference(forward_demodulation,[],[f9183,f7601]) ).
fof(f9210,plain,
implies(implies(x,y),implies(x,z)) != implies(x,implies(implies(x,y),z)),
inference(forward_demodulation,[],[f9206,f6856]) ).
fof(f9212,plain,
$false,
inference(forward_subsumption_resolution,[],[f9210,f326]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL152-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 15:21:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.56/2.36 % (1579877)Input is clausal, will run a generic CNF schedule.
% 10.56/2.36 % (1579906)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=138248338:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 10.56/2.36 % (1579902)lrs+10_1_sil=8000:sp=occurrence:random_seed=549278083:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 10.56/2.36 % (1579899)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2395810374:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 10.56/2.36 % (1579904)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2451594976:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 10.56/2.36 % (1579907)dis-21_1_sil=8000:lcm=predicate:random_seed=753474566:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 10.56/2.36 % (1579897)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2718384812:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 10.56/2.36 % (1579900)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2004565539:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 10.56/2.36 % (1579907)Refutation not found, incomplete strategy
% 10.56/2.36 % (1579907)------------------------------
% 10.56/2.36 % (1579907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.56/2.36 % (1579907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.56/2.36 % (1579907)CaDiCaL version: 2.1.3
% 10.56/2.36 % (1579907)Termination reason: Refutation not found, incomplete strategy
% 10.56/2.36 % (1579907)Time elapsed: 0.001 s
% 10.56/2.36 % (1579907)Peak memory usage: 88 MB
% 10.56/2.36 % (1579906)Instruction limit reached!
% 10.56/2.36 % (1579906)------------------------------
% 10.56/2.36 % (1579906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.56/2.36 % (1579906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.56/2.36 % (1579906)CaDiCaL version: 2.1.3
% 10.56/2.36 % (1579906)Termination reason: Instruction limit
% 10.56/2.36 % (1579906)Termination phase: Saturation
% 10.56/2.36 % (1579906)Time elapsed: 0.057 s
% 10.56/2.36 % (1579906)Peak memory usage: 89 MB
% 10.56/2.36 % (1579906)Instructions burned: 182 (million)
% 10.56/2.36 % (1579902)Instruction limit reached!
% 10.56/2.36 % (1579902)------------------------------
% 10.56/2.36 % (1579902)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.56/2.36 % (1579902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.56/2.36 % (1579902)CaDiCaL version: 2.1.3
% 10.56/2.36 % (1579902)Termination reason: Instruction limit
% 10.56/2.36 % (1579902)Termination phase: Saturation
% 10.56/2.36 % (1579902)Time elapsed: 0.067 s
% 10.56/2.36 % (1579902)Peak memory usage: 88 MB
% 10.56/2.36 % (1579902)Instructions burned: 107 (million)
% 10.56/2.36 % (1579904)Instruction limit reached!
% 10.56/2.36 % (1579904)------------------------------
% 10.56/2.36 % (1579904)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.56/2.36 % (1579904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.56/2.37 % (1579904)CaDiCaL version: 2.1.3
% 10.56/2.37 % (1579904)Termination reason: Instruction limit
% 10.56/2.37 % (1579904)Termination phase: Saturation
% 10.56/2.37 % (1579904)Time elapsed: 0.071 s
% 10.56/2.37 % (1579904)Peak memory usage: 89 MB
% 10.56/2.37 % (1579904)Instructions burned: 116 (million)
% 10.56/2.37 % (1579976)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3784532692:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 10.56/2.37 % (1579976)Refutation not found, incomplete strategy
% 10.56/2.37 % (1579976)------------------------------
% 10.56/2.37 % (1579976)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.56/2.37 % (1579976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.56/2.37 % (1579976)CaDiCaL version: 2.1.3
% 10.56/2.37 % (1579976)Termination reason: Refutation not found, incomplete strategy
% 10.56/2.37 % (1579976)Time elapsed: 0.001 s
% 10.56/2.37 % (1579976)Peak memory usage: 88 MB
% 10.56/2.37 % (1579976)Instructions burned: 1 (million)
% 10.56/2.37 % (1579995)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3475838618:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 10.56/2.37 % (1579992)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1291242477:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 10.56/2.37 % (1579992)Refutation not found, incomplete strategy
% 10.56/2.37 % (1579992)------------------------------
% 10.56/2.37 % (1579992)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.56/2.37 % (1579992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.56/2.37 % (1579992)CaDiCaL version: 2.1.3
% 10.56/2.37 % (1579992)Termination reason: Refutation not found, incomplete strategy
% 10.56/2.37 % (1579992)Time elapsed: 0.002 s
% 10.56/2.37 % (1579992)Peak memory usage: 88 MB
% 10.56/2.37 % (1579992)Instructions burned: 1 (million)
% 10.56/2.37 % (1579907)------------------------------
% 10.56/2.37 % (1579907)------------------------------
% 10.56/2.37 % (1579976)------------------------------
% 10.56/2.37 % (1579976)------------------------------
% 10.56/2.37 % (1579995)Instruction limit reached!
% 10.56/2.37 % (1579995)------------------------------
% 10.56/2.37 % (1579995)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.56/2.37 % (1579995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.56/2.37 % (1579995)CaDiCaL version: 2.1.3
% 10.56/2.37 % (1579995)Termination reason: Instruction limit
% 10.56/2.37 % (1579995)Termination phase: Saturation
% 10.56/2.37 % (1579995)Time elapsed: 0.148 s
% 10.56/2.37 % (1579995)Peak memory usage: 91 MB
% 10.56/2.37 % (1579995)Instructions burned: 220 (million)
% 10.56/2.37 % (1580055)lrs+10_64_to=lpo:sil=8000:random_seed=2987684080:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 10.56/2.37 % (1580056)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=157596631:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 10.56/2.37 % (1579992)------------------------------
% 10.56/2.37 % (1579992)------------------------------
% 10.56/2.37 % (1580056)Instruction limit reached!
% 10.56/2.37 % (1580056)------------------------------
% 10.56/2.37 % (1580056)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.56/2.37 % (1580056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.56/2.37 % (1580056)CaDiCaL version: 2.1.3
% 10.56/2.37 % (1580056)Termination reason: Instruction limit
% 10.56/2.37 % (1580056)Termination phase: Saturation
% 10.56/2.37 % (1580056)Time elapsed: 0.067 s
% 10.56/2.37 % (1580056)Peak memory usage: 90 MB
% 10.56/2.37 % (1580056)Instructions burned: 195 (million)
% 10.56/2.37 % (1580055)Instruction limit reached!
% 10.56/2.37 % (1580055)------------------------------
% 10.56/2.37 % (1580055)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.56/2.37 % (1580055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.56/2.37 % (1580055)CaDiCaL version: 2.1.3
% 10.56/2.37 % (1580055)Termination reason: Instruction limit
% 10.56/2.37 % (1580055)Termination phase: Saturation
% 10.56/2.37 % (1580055)Time elapsed: 0.079 s
% 10.56/2.37 % (1580055)Peak memory usage: 89 MB
% 10.56/2.37 % (1580055)Instructions burned: 126 (million)
% 10.56/2.37 % (1580057)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3295644452:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 10.56/2.37 % (1580060)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=926424161:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 10.56/2.37 % (1580061)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=2865164991:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 10.56/2.37 % (1580057)Instruction limit reached!
% 10.56/2.37 % (1580057)------------------------------
% 10.56/2.37 % (1580057)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.56/2.37 % (1580057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.56/2.37 % (1580057)CaDiCaL version: 2.1.3
% 10.56/2.37 % (1580057)Termination reason: Instruction limit
% 10.56/2.37 % (1580057)Termination phase: Saturation
% 10.56/2.37 % (1580057)Time elapsed: 0.098 s
% 10.56/2.37 % (1580057)Peak memory usage: 91 MB
% 10.56/2.37 % (1580057)Instructions burned: 157 (million)
% 10.56/2.37 % (1580062)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=939428974:i=107_2993 on theBenchmark for (2993ds/107Mi)
% 10.56/2.37 % (1580062)Refutation not found, incomplete strategy
% 10.56/2.37 % (1580062)------------------------------
% 10.56/2.37 % (1580062)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.56/2.37 % (1580062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.56/2.37 % (1580062)CaDiCaL version: 2.1.3
% 10.56/2.37 % (1580062)Termination reason: Refutation not found, incomplete strategy
% 10.56/2.37 % (1580062)Time elapsed: 0.001 s
% 10.56/2.37 % (1580062)Peak memory usage: 88 MB
% 10.56/2.37 % (1580061)Instruction limit reached!
% 10.56/2.37 % (1580061)------------------------------
% 10.56/2.37 % (1580061)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.56/2.37 % (1580061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.56/2.37 % (1580061)CaDiCaL version: 2.1.3
% 10.56/2.37 % (1580061)Termination reason: Instruction limit
% 10.56/2.37 % (1580061)Termination phase: Saturation
% 10.56/2.37 % (1580061)Time elapsed: 0.067 s
% 10.56/2.37 % (1580061)Peak memory usage: 88 MB
% 10.56/2.37 % (1580061)Instructions burned: 107 (million)
% 10.56/2.37 % (1580066)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=505749746:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2992 on theBenchmark for (2992ds/242Mi)
% 10.56/2.37 % (1580068)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=3577622146:cond=fast:i=5208:av=off_2991 on theBenchmark for (2991ds/5208Mi)
% 10.56/2.37 % (1580062)------------------------------
% 10.56/2.37 % (1580062)------------------------------
% 10.56/2.37 % (1580066)Instruction limit reached!
% 10.56/2.37 % (1580066)------------------------------
% 10.56/2.37 % (1580066)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.56/2.37 % (1580066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.56/2.37 % (1580066)CaDiCaL version: 2.1.3
% 10.56/2.37 % (1580066)Termination reason: Instruction limit
% 10.56/2.37 % (1580066)Termination phase: Saturation
% 10.56/2.37 % (1580066)Time elapsed: 0.138 s
% 10.56/2.37 % (1580066)Peak memory usage: 91 MB
% 10.56/2.37 % (1580066)Instructions burned: 243 (million)
% 10.56/2.37 % (1580071)lrs+1011_16_sil=32000:erd=off:bce=on:random_seed=1841338205:i=134:sd=2:doe=on:ss=axioms:sgt=14_2989 on theBenchmark for (2989ds/134Mi)
% 10.56/2.37 % (1580071)Instruction limit reached!
% 10.56/2.37 % (1580071)------------------------------
% 10.56/2.37 % (1580071)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.56/2.37 % (1580071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.56/2.37 % (1580071)CaDiCaL version: 2.1.3
% 10.56/2.37 % (1580071)Termination reason: Instruction limit
% 10.56/2.37 % (1580071)Termination phase: Saturation
% 10.56/2.37 % (1580071)Time elapsed: 0.044 s
% 10.56/2.37 % (1580071)Peak memory usage: 89 MB
% 10.56/2.37 % (1580071)Instructions burned: 137 (million)
% 10.56/2.37 % (1579899)First to succeed.
% 10.56/2.37 % (1579899)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1579877"
% 10.56/2.37 % (1580072)ott+10_5:4_to=lpo:sil=8000:prc=on:fde=unused:sp=unary_frequency:spb=goal:urr=on:random_seed=2245387870:i=499:bd=all_2989 on theBenchmark for (2989ds/499Mi)
% 10.56/2.37 % (1580074)lrs+10_64_to=lpo:sil=8000:prc=on:sp=reverse_frequency:nwc=5:alpa=false:flr=on:random_seed=3873292508:i=191:fgj=on:bd=all_2987 on theBenchmark for (2987ds/191Mi)
% 10.56/2.37 % (1580074)Instruction limit reached!
% 10.56/2.37 % (1580074)------------------------------
% 10.56/2.37 % (1580074)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.56/2.37 % (1580074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.56/2.37 % (1580074)CaDiCaL version: 2.1.3
% 10.56/2.37 % (1580074)Termination reason: Instruction limit
% 10.56/2.37 % (1580074)Termination phase: Saturation
% 10.56/2.37 % (1580074)Time elapsed: 0.068 s
% 10.56/2.37 % (1580074)Peak memory usage: 92 MB
% 10.56/2.37 % (1580074)Instructions burned: 193 (million)
% 10.56/2.37 % (1579899)Refutation found. Thanks to Tanya!
% 10.56/2.37 % SZS status Unsatisfiable for theBenchmark
% 10.56/2.37 % SZS output start Proof for theBenchmark
% See solution above
% 11.10/2.46 % (1579899)------------------------------
% 11.10/2.46 % (1579899)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.10/2.46 % (1579899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.10/2.46 % (1579899)CaDiCaL version: 2.1.3
% 11.10/2.46 % (1579899)Termination reason: Refutation
% 11.10/2.46 % (1579899)Time elapsed: 1.080 s
% 11.10/2.46 % (1579899)Peak memory usage: 134 MB
% 11.10/2.46 % (1579899)Instructions burned: 1701 (million)
% 11.10/2.46 % (1579899)------------------------------
% 11.10/2.46 % (1579899)------------------------------
% 11.10/2.46 % (1579877)Success in time 1.508 s
% 11.10/2.46 % Vampire exiting
%------------------------------------------------------------------------------