%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL148-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 11:51:20 AM UTC 2026
% Result : Unsatisfiable 38.72s 6.67s
% Output : Refutation 40.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 20
% Syntax : Number of formulae : 192 ( 192 unt; 13 def)
% Number of atoms : 192 ( 191 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 17 con; 0-2 aty)
% Number of variables : 191 ( 191 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : implies(truth,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_1) ).
fof(f4,axiom,
! [X2,X0,X1] : implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_2) ).
fof(f5,plain,
! [X2,X0,X1] : truth = implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),
inference(reorient_equations,[],[f4]) ).
fof(f6,axiom,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_3) ).
fof(f7,axiom,
! [X0,X1] : implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_4) ).
fof(f8,plain,
! [X0,X1] : truth = implies(implies(not(X0),not(X1)),implies(X1,X0)),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0,X1] : big_V(X0,X1) = implies(implies(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',big_V_definition) ).
fof(f10,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = big_V(X0,X1),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
! [X0,X1] : big_hat(X0,X1) = not(big_V(not(X0),not(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',big_hat_definition) ).
fof(f16,negated_conjecture,
implies(x,big_hat(y,z)) != big_hat(implies(x,y),implies(x,z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_theorem) ).
fof(f17,plain,
! [X0,X1] : big_hat(X0,X1) = not(implies(implies(not(X0),not(X1)),not(X1))),
inference(definition_unfolding,[],[f11,f10]) ).
fof(f18,plain,
implies(x,not(implies(implies(not(y),not(z)),not(z)))) != not(implies(implies(not(implies(x,y)),not(implies(x,z))),not(implies(x,z)))),
inference(definition_unfolding,[],[f16,f17,f17]) ).
fof(f19,definition,
sF0 = not(y),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f20,plain,
not(y) = sF0,
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
sF1 = not(z),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f22,plain,
not(z) = sF1,
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
sF2 = implies(sF0,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f24,plain,
implies(sF0,sF1) = sF2,
inference(reorient_equations,[],[f23]) ).
fof(f25,definition,
sF3 = implies(sF2,sF1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f26,plain,
implies(sF2,sF1) = sF3,
inference(reorient_equations,[],[f25]) ).
fof(f27,definition,
sF4 = not(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f28,plain,
not(sF3) = sF4,
inference(reorient_equations,[],[f27]) ).
fof(f29,definition,
sF5 = implies(x,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f30,plain,
implies(x,sF4) = sF5,
inference(reorient_equations,[],[f29]) ).
fof(f31,definition,
sF6 = implies(x,y),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f32,plain,
implies(x,y) = sF6,
inference(reorient_equations,[],[f31]) ).
fof(f33,definition,
sF7 = not(sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f34,plain,
not(sF6) = sF7,
inference(reorient_equations,[],[f33]) ).
fof(f35,definition,
sF8 = implies(x,z),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f36,plain,
implies(x,z) = sF8,
inference(reorient_equations,[],[f35]) ).
fof(f37,definition,
sF9 = not(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f38,plain,
not(sF8) = sF9,
inference(reorient_equations,[],[f37]) ).
fof(f39,definition,
sF10 = implies(sF7,sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f40,plain,
implies(sF7,sF9) = sF10,
inference(reorient_equations,[],[f39]) ).
fof(f41,definition,
sF11 = implies(sF10,sF9),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f42,plain,
implies(sF10,sF9) = sF11,
inference(reorient_equations,[],[f41]) ).
fof(f43,definition,
sF12 = not(sF11),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f44,plain,
not(sF11) = sF12,
inference(reorient_equations,[],[f43]) ).
fof(f45,plain,
sF5 != sF12,
inference(definition_folding,[],[f18,f44,f42,f38,f36,f40,f38,f36,f34,f32,f30,f28,f26,f22,f24,f22,f20]) ).
fof(f46,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,[],[f5,f5]) ).
fof(f51,plain,
! [X2,X3,X0,X1] : truth = implies(implies(implies(implies(X1,X2),implies(X0,X2)),X3),implies(implies(X0,X1),X3)),
inference(forward_demodulation,[],[f46,f3]) ).
fof(f52,plain,
! [X0] : truth = implies(implies(sF1,not(X0)),implies(X0,z)),
inference(superposition,[],[f8,f22]) ).
fof(f53,plain,
! [X0] : truth = implies(implies(not(X0),sF1),implies(z,X0)),
inference(superposition,[],[f8,f22]) ).
fof(f58,plain,
! [X2,X0,X1] : truth = implies(implies(X0,implies(not(X1),not(X2))),implies(truth,implies(X0,implies(X2,X1)))),
inference(superposition,[],[f5,f8]) ).
fof(f61,plain,
! [X2,X0,X1] : truth = implies(implies(X0,implies(not(X1),not(X2))),implies(X0,implies(X2,X1))),
inference(forward_demodulation,[],[f58,f3]) ).
fof(f88,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,[],[f6,f5]) ).
fof(f94,plain,
! [X0,X1] : truth = implies(implies(not(X0),not(implies(X1,X0))),implies(implies(X0,X1),X1)),
inference(superposition,[],[f8,f6]) ).
fof(f98,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,[],[f88,f3]) ).
fof(f107,plain,
implies(implies(sF1,sF2),sF2) = implies(sF3,sF1),
inference(superposition,[],[f6,f26]) ).
fof(f117,plain,
! [X0,X1] : truth = implies(X0,implies(implies(X0,X1),implies(truth,X1))),
inference(superposition,[],[f5,f3]) ).
fof(f118,plain,
! [X0,X1] : truth = implies(X0,implies(implies(X0,X1),X1)),
inference(forward_demodulation,[],[f117,f3]) ).
fof(f121,plain,
implies(sF2,sF1) = implies(implies(sF1,sF0),sF0),
inference(superposition,[],[f6,f24]) ).
fof(f126,plain,
sF3 = implies(implies(sF1,sF0),sF0),
inference(forward_demodulation,[],[f121,f26]) ).
fof(f150,plain,
! [X0,X1] : truth = implies(X1,implies(implies(X0,X1),X1)),
inference(superposition,[],[f118,f6]) ).
fof(f152,plain,
! [X2,X0,X1] : truth = implies(truth,implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2))),
inference(superposition,[],[f5,f118]) ).
fof(f158,plain,
! [X0] : truth = implies(implies(truth,X0),X0),
inference(superposition,[],[f3,f118]) ).
fof(f160,plain,
! [X0] : truth = implies(X0,X0),
inference(forward_demodulation,[],[f158,f3]) ).
fof(f164,plain,
! [X2,X0,X1] : truth = implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2)),
inference(forward_demodulation,[],[f152,f3]) ).
fof(f188,plain,
! [X0,X1] : implies(X0,implies(X1,X0)) = implies(implies(implies(X0,implies(X1,X0)),implies(X1,truth)),implies(X1,truth)),
inference(superposition,[],[f98,f3]) ).
fof(f1087,plain,
truth = implies(sF1,sF3),
inference(superposition,[],[f118,f126]) ).
fof(f1235,plain,
! [X2,X0,X1] : truth = implies(truth,implies(implies(X2,implies(X0,X1)),implies(X0,implies(X2,X1)))),
inference(superposition,[],[f51,f164]) ).
fof(f1280,plain,
! [X2,X0,X1] : truth = implies(implies(X2,implies(X0,X1)),implies(X0,implies(X2,X1))),
inference(forward_demodulation,[],[f1235,f3]) ).
fof(f1787,plain,
! [X0] : truth = implies(X0,implies(X0,X0)),
inference(superposition,[],[f150,f3]) ).
fof(f1900,plain,
! [X0] : truth = implies(X0,truth),
inference(forward_demodulation,[],[f1787,f160]) ).
fof(f1912,plain,
! [X0,X1] : implies(X0,implies(X1,X0)) = implies(implies(implies(X0,implies(X1,X0)),truth),truth),
inference(backward_demodulation,[],[f188,f1900]) ).
fof(f2057,plain,
! [X0,X1] : truth = implies(X0,implies(X1,X0)),
inference(forward_demodulation,[],[f1912,f1900]) ).
fof(f2091,plain,
truth = implies(sF1,sF2),
inference(superposition,[],[f2057,f24]) ).
fof(f2099,plain,
! [X0,X1] : truth = implies(truth,implies(not(X0),implies(X0,X1))),
inference(superposition,[],[f61,f2057]) ).
fof(f2106,plain,
! [X0,X1] : implies(implies(implies(X0,X1),X1),X1) = implies(truth,implies(X0,X1)),
inference(superposition,[],[f6,f2057]) ).
fof(f2160,plain,
! [X0,X1] : implies(X0,X1) = implies(implies(implies(X0,X1),X1),X1),
inference(forward_demodulation,[],[f2106,f3]) ).
fof(f2166,plain,
! [X0,X1] : truth = implies(not(X0),implies(X0,X1)),
inference(forward_demodulation,[],[f2099,f3]) ).
fof(f2170,plain,
implies(sF3,sF1) = implies(truth,sF2),
inference(backward_demodulation,[],[f107,f2091]) ).
fof(f2179,plain,
sF2 = implies(sF3,sF1),
inference(forward_demodulation,[],[f2170,f3]) ).
fof(f2199,plain,
! [X0] : truth = implies(not(truth),X0),
inference(superposition,[],[f2166,f3]) ).
fof(f2227,plain,
! [X0,X1] : truth = implies(truth,implies(not(not(X0)),implies(X1,X0))),
inference(superposition,[],[f61,f2166]) ).
fof(f2286,plain,
! [X0,X1] : truth = implies(not(not(X0)),implies(X1,X0)),
inference(forward_demodulation,[],[f2227,f3]) ).
fof(f2304,plain,
! [X0] : truth = implies(not(not(X0)),X0),
inference(superposition,[],[f2286,f3]) ).
fof(f2413,plain,
! [X0] : truth = implies(truth,implies(X0,not(not(X0)))),
inference(superposition,[],[f8,f2304]) ).
fof(f2473,plain,
! [X0] : truth = implies(X0,not(not(X0))),
inference(forward_demodulation,[],[f2413,f3]) ).
fof(f2506,plain,
! [X0] : implies(implies(not(not(X0)),X0),X0) = implies(truth,not(not(X0))),
inference(superposition,[],[f6,f2473]) ).
fof(f2572,plain,
! [X0] : not(not(X0)) = implies(implies(not(not(X0)),X0),X0),
inference(forward_demodulation,[],[f2506,f3]) ).
fof(f2584,plain,
! [X0] : implies(truth,X0) = not(not(X0)),
inference(forward_demodulation,[],[f2572,f2304]) ).
fof(f2589,plain,
! [X0] : not(not(X0)) = X0,
inference(forward_demodulation,[],[f2584,f3]) ).
fof(f2646,plain,
z = not(sF1),
inference(superposition,[],[f2589,f22]) ).
fof(f2647,plain,
sF3 = not(sF4),
inference(superposition,[],[f2589,f28]) ).
fof(f2648,plain,
sF6 = not(sF7),
inference(superposition,[],[f2589,f34]) ).
fof(f2649,plain,
sF8 = not(sF9),
inference(superposition,[],[f2589,f38]) ).
fof(f2661,plain,
! [X0,X1] : truth = implies(X0,implies(not(X0),X1)),
inference(superposition,[],[f2166,f2589]) ).
fof(f2859,plain,
! [X2,X0,X1] : implies(implies(X0,X1),implies(X2,X1)) = implies(implies(implies(implies(X0,X1),implies(X2,X1)),implies(X2,implies(implies(X0,X1),X1))),implies(X2,implies(implies(X0,X1),X1))),
inference(superposition,[],[f98,f2160]) ).
fof(f2876,plain,
! [X2,X0,X1] : implies(implies(X0,X1),implies(X2,X1)) = implies(truth,implies(X2,implies(implies(X0,X1),X1))),
inference(forward_demodulation,[],[f2859,f1280]) ).
fof(f2918,plain,
! [X2,X0,X1] : implies(implies(X0,X1),implies(X2,X1)) = implies(X2,implies(implies(X0,X1),X1)),
inference(forward_demodulation,[],[f2876,f3]) ).
fof(f3073,plain,
! [X0,X1] : truth = implies(implies(X0,X1),implies(implies(not(X0),not(implies(X1,X0))),X1)),
inference(backward_demodulation,[],[f94,f2918]) ).
fof(f3154,plain,
! [X0] : implies(sF3,implies(X0,sF1)) = implies(X0,implies(sF3,sF1)),
inference(superposition,[],[f2918,f26]) ).
fof(f3160,plain,
! [X2,X0,X1] : implies(X2,implies(implies(X0,X1),X1)) = implies(implies(X1,X0),implies(X2,X0)),
inference(superposition,[],[f2918,f6]) ).
fof(f3275,plain,
! [X0] : implies(X0,sF2) = implies(sF3,implies(X0,sF1)),
inference(forward_demodulation,[],[f3154,f2179]) ).
fof(f3593,plain,
! [X2,X0,X1] : implies(implies(implies(not(X0),X1),X2),implies(X0,X2)) = implies(implies(implies(implies(implies(not(X0),X1),X2),implies(X0,X2)),truth),truth),
inference(superposition,[],[f98,f2661]) ).
fof(f3624,plain,
! [X2,X0,X1] : truth = implies(implies(implies(not(X0),X1),X2),implies(X0,X2)),
inference(forward_demodulation,[],[f3593,f1900]) ).
fof(f3639,plain,
! [X2,X0,X1] : truth = implies(X0,implies(implies(implies(not(X0),X1),X2),X2)),
inference(forward_demodulation,[],[f3624,f2918]) ).
fof(f3838,plain,
! [X2,X0,X1] : implies(truth,implies(X0,implies(X1,X2))) = implies(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2))),implies(X1,implies(X0,X2))),
inference(superposition,[],[f6,f1280]) ).
fof(f3876,plain,
! [X2,X0,X1] : implies(truth,implies(X0,implies(X1,X2))) = implies(truth,implies(X1,implies(X0,X2))),
inference(forward_demodulation,[],[f3838,f1280]) ).
fof(f3949,plain,
! [X2,X0,X1] : implies(truth,implies(X0,implies(X1,X2))) = implies(X1,implies(X0,X2)),
inference(forward_demodulation,[],[f3876,f3]) ).
fof(f3967,plain,
! [X2,X0,X1] : implies(X0,implies(X1,X2)) = implies(X1,implies(X0,X2)),
inference(forward_demodulation,[],[f3949,f3]) ).
fof(f4265,plain,
! [X0] : truth = implies(z,implies(implies(not(X0),sF1),X0)),
inference(backward_demodulation,[],[f53,f3967]) ).
fof(f4338,plain,
! [X0] : truth = implies(X0,implies(implies(sF1,not(X0)),z)),
inference(backward_demodulation,[],[f52,f3967]) ).
fof(f4781,plain,
! [X0] : implies(X0,sF5) = implies(x,implies(X0,sF4)),
inference(superposition,[],[f3967,f30]) ).
fof(f4782,plain,
! [X0] : implies(X0,sF6) = implies(x,implies(X0,y)),
inference(superposition,[],[f3967,f32]) ).
fof(f4785,plain,
! [X0] : implies(X0,sF2) = implies(sF0,implies(X0,sF1)),
inference(superposition,[],[f3967,f24]) ).
fof(f4846,plain,
! [X2,X0,X1] : implies(implies(X0,implies(X1,X2)),implies(X0,X2)) = implies(implies(implies(X0,X2),X1),X1),
inference(superposition,[],[f6,f3967]) ).
fof(f4886,plain,
! [X2,X0,X1] : implies(X0,implies(implies(X0,implies(X1,X2)),X2)) = implies(implies(implies(X0,X2),X1),X1),
inference(forward_demodulation,[],[f4846,f3967]) ).
fof(f5907,plain,
truth = implies(sF4,implies(implies(sF1,sF3),z)),
inference(superposition,[],[f4338,f2647]) ).
fof(f5952,plain,
truth = implies(sF4,implies(truth,z)),
inference(forward_demodulation,[],[f5907,f1087]) ).
fof(f5955,plain,
truth = implies(sF4,z),
inference(forward_demodulation,[],[f5952,f3]) ).
fof(f8432,plain,
! [X0] : implies(truth,X0) = implies(implies(X0,not(truth)),not(truth)),
inference(superposition,[],[f6,f2199]) ).
fof(f8505,plain,
! [X0] : implies(implies(X0,not(truth)),not(truth)) = X0,
inference(forward_demodulation,[],[f8432,f3]) ).
fof(f8563,plain,
truth = implies(z,implies(implies(sF3,sF1),sF4)),
inference(superposition,[],[f4265,f2647]) ).
fof(f8633,plain,
truth = implies(z,implies(sF2,sF4)),
inference(forward_demodulation,[],[f8563,f2179]) ).
fof(f8648,plain,
truth = implies(sF2,implies(z,sF4)),
inference(forward_demodulation,[],[f8633,f3967]) ).
fof(f8657,plain,
implies(implies(implies(sF2,sF4),z),z) = implies(sF2,implies(truth,sF4)),
inference(superposition,[],[f4886,f8648]) ).
fof(f8660,plain,
implies(implies(implies(z,sF4),sF2),sF2) = implies(truth,implies(z,sF4)),
inference(superposition,[],[f6,f8648]) ).
fof(f8700,plain,
implies(z,sF4) = implies(implies(implies(z,sF4),sF2),sF2),
inference(forward_demodulation,[],[f8660,f3]) ).
fof(f8702,plain,
implies(sF2,sF4) = implies(implies(implies(sF2,sF4),z),z),
inference(forward_demodulation,[],[f8657,f3]) ).
fof(f10063,plain,
! [X0,X1] : implies(X0,implies(truth,X1)) = implies(implies(X1,not(truth)),implies(X0,not(truth))),
inference(superposition,[],[f3160,f2199]) ).
fof(f10716,plain,
! [X0,X1] : implies(X0,X1) = implies(implies(X1,not(truth)),implies(X0,not(truth))),
inference(forward_demodulation,[],[f10063,f3]) ).
fof(f12138,plain,
truth = implies(truth,implies(implies(not(sF4),not(implies(z,sF4))),z)),
inference(superposition,[],[f3073,f5955]) ).
fof(f12226,plain,
truth = implies(implies(sF1,sF2),implies(implies(not(sF1),not(sF3)),sF2)),
inference(superposition,[],[f3073,f26]) ).
fof(f12271,plain,
! [X0,X1] : implies(X0,implies(implies(X0,implies(implies(implies(not(X0),not(implies(X1,X0))),X1),X1)),X1)) = implies(truth,implies(implies(not(X0),not(implies(X1,X0))),X1)),
inference(superposition,[],[f4886,f3073]) ).
fof(f12344,plain,
! [X0,X1] : implies(implies(not(X0),not(implies(X1,X0))),X1) = implies(X0,implies(implies(X0,implies(implies(implies(not(X0),not(implies(X1,X0))),X1),X1)),X1)),
inference(forward_demodulation,[],[f12271,f3]) ).
fof(f12365,plain,
truth = implies(implies(sF1,sF2),implies(implies(not(sF1),sF4),sF2)),
inference(forward_demodulation,[],[f12226,f28]) ).
fof(f12404,plain,
truth = implies(implies(not(sF4),not(implies(z,sF4))),z),
inference(forward_demodulation,[],[f12138,f3]) ).
fof(f12486,plain,
! [X0,X1] : implies(implies(not(X0),not(implies(X1,X0))),X1) = implies(X0,implies(truth,X1)),
inference(forward_demodulation,[],[f12344,f3639]) ).
fof(f12498,plain,
truth = implies(implies(sF1,sF2),implies(implies(z,sF4),sF2)),
inference(forward_demodulation,[],[f12365,f2646]) ).
fof(f12530,plain,
truth = implies(implies(sF3,not(implies(z,sF4))),z),
inference(forward_demodulation,[],[f12404,f2647]) ).
fof(f12592,plain,
! [X0,X1] : implies(X0,X1) = implies(implies(not(X0),not(implies(X1,X0))),X1),
inference(forward_demodulation,[],[f12486,f3]) ).
fof(f12597,plain,
truth = implies(truth,implies(implies(z,sF4),sF2)),
inference(forward_demodulation,[],[f12498,f2091]) ).
fof(f12659,plain,
truth = implies(implies(z,sF4),sF2),
inference(forward_demodulation,[],[f12597,f3]) ).
fof(f12686,plain,
implies(truth,sF2) = implies(z,sF4),
inference(backward_demodulation,[],[f8700,f12659]) ).
fof(f12696,plain,
sF2 = implies(z,sF4),
inference(forward_demodulation,[],[f12686,f3]) ).
fof(f12711,plain,
truth = implies(implies(sF3,not(sF2)),z),
inference(backward_demodulation,[],[f12530,f12696]) ).
fof(f12770,plain,
! [X0] : implies(X0,not(truth)) = implies(implies(not(X0),not(truth)),not(truth)),
inference(superposition,[],[f12592,f2199]) ).
fof(f12946,plain,
! [X0] : not(X0) = implies(X0,not(truth)),
inference(forward_demodulation,[],[f12770,f8505]) ).
fof(f13038,plain,
! [X0,X1] : implies(X0,X1) = implies(not(X1),implies(X0,not(truth))),
inference(backward_demodulation,[],[f10716,f12946]) ).
fof(f13258,plain,
! [X0,X1] : implies(X0,X1) = implies(not(X1),not(X0)),
inference(forward_demodulation,[],[f13038,f12946]) ).
fof(f13544,plain,
! [X0,X1] : implies(X0,not(X1)) = implies(X1,not(X0)),
inference(superposition,[],[f13258,f2589]) ).
fof(f13546,plain,
! [X0] : implies(X0,z) = implies(sF1,not(X0)),
inference(superposition,[],[f13258,f22]) ).
fof(f13550,plain,
! [X0] : implies(X0,sF4) = implies(sF3,not(X0)),
inference(superposition,[],[f13258,f2647]) ).
fof(f13551,plain,
! [X0] : implies(X0,sF6) = implies(sF7,not(X0)),
inference(superposition,[],[f13258,f34]) ).
fof(f13554,plain,
! [X0] : implies(X0,sF9) = implies(sF8,not(X0)),
inference(superposition,[],[f13258,f2649]) ).
fof(f13557,plain,
! [X0,X1] : implies(not(X0),X1) = implies(not(X1),X0),
inference(superposition,[],[f13258,f2589]) ).
fof(f13559,plain,
! [X0] : implies(z,X0) = implies(not(X0),sF1),
inference(superposition,[],[f13258,f22]) ).
fof(f13565,plain,
! [X0] : implies(sF7,X0) = implies(not(X0),sF6),
inference(superposition,[],[f13258,f2648]) ).
fof(f13576,plain,
! [X0,X1] : implies(implies(not(X0),not(X1)),not(X1)) = implies(implies(X0,X1),not(X0)),
inference(superposition,[],[f6,f13258]) ).
fof(f13636,plain,
! [X0,X1] : implies(implies(X0,X1),not(X0)) = implies(implies(X1,X0),not(X1)),
inference(forward_demodulation,[],[f13576,f13258]) ).
fof(f13798,plain,
truth = implies(implies(sF2,sF4),z),
inference(backward_demodulation,[],[f12711,f13550]) ).
fof(f13962,plain,
! [X0,X1] : implies(implies(X0,X1),not(X0)) = implies(X1,not(implies(X1,X0))),
inference(forward_demodulation,[],[f13636,f13544]) ).
fof(f13995,plain,
implies(truth,z) = implies(sF2,sF4),
inference(backward_demodulation,[],[f8702,f13798]) ).
fof(f14094,plain,
! [X0,X1] : implies(X1,not(implies(X1,X0))) = implies(X0,not(implies(X0,X1))),
inference(forward_demodulation,[],[f13962,f13544]) ).
fof(f14105,plain,
z = implies(sF2,sF4),
inference(forward_demodulation,[],[f13995,f3]) ).
fof(f14796,plain,
implies(x,z) = implies(sF2,sF5),
inference(superposition,[],[f4781,f14105]) ).
fof(f14839,plain,
sF8 = implies(sF2,sF5),
inference(forward_demodulation,[],[f14796,f36]) ).
fof(f15085,plain,
implies(sF7,sF9) = implies(sF8,sF6),
inference(superposition,[],[f13551,f38]) ).
fof(f15143,plain,
sF10 = implies(sF8,sF6),
inference(forward_demodulation,[],[f15085,f40]) ).
fof(f15622,plain,
truth = implies(sF5,sF8),
inference(superposition,[],[f2057,f14839]) ).
fof(f15724,plain,
! [X0] : implies(implies(not(X0),sF1),sF1) = implies(implies(X0,z),not(X0)),
inference(superposition,[],[f6,f13546]) ).
fof(f15774,plain,
! [X0] : implies(implies(not(X0),sF1),sF1) = implies(X0,not(implies(X0,z))),
inference(forward_demodulation,[],[f15724,f13544]) ).
fof(f15806,plain,
! [X0] : implies(implies(z,X0),sF1) = implies(X0,not(implies(X0,z))),
inference(forward_demodulation,[],[f15774,f13559]) ).
fof(f16261,plain,
! [X0] : implies(not(X0),sF6) = implies(x,implies(not(y),X0)),
inference(superposition,[],[f4782,f13557]) ).
fof(f16266,plain,
! [X0] : implies(not(X0),sF5) = implies(x,implies(not(sF4),X0)),
inference(superposition,[],[f4781,f13557]) ).
fof(f16273,plain,
! [X0] : implies(not(X0),sF5) = implies(x,implies(sF3,X0)),
inference(forward_demodulation,[],[f16266,f2647]) ).
fof(f16278,plain,
! [X0] : implies(not(X0),sF6) = implies(x,implies(sF0,X0)),
inference(forward_demodulation,[],[f16261,f20]) ).
fof(f16352,plain,
! [X0] : implies(not(X0),sF5) = implies(sF3,implies(x,X0)),
inference(forward_demodulation,[],[f16273,f3967]) ).
fof(f16355,plain,
! [X0] : implies(not(X0),sF6) = implies(sF0,implies(x,X0)),
inference(forward_demodulation,[],[f16278,f3967]) ).
fof(f16373,plain,
! [X0] : implies(sF7,X0) = implies(sF0,implies(x,X0)),
inference(forward_demodulation,[],[f16355,f13565]) ).
fof(f17160,plain,
implies(sF8,not(implies(sF8,sF5))) = implies(sF5,not(truth)),
inference(superposition,[],[f14094,f15622]) ).
fof(f17161,plain,
not(sF5) = implies(sF8,not(implies(sF8,sF5))),
inference(forward_demodulation,[],[f17160,f12946]) ).
fof(f17189,plain,
not(sF5) = implies(implies(sF8,sF5),sF9),
inference(forward_demodulation,[],[f17161,f13554]) ).
fof(f21890,plain,
implies(implies(z,x),sF1) = implies(x,not(sF8)),
inference(superposition,[],[f15806,f36]) ).
fof(f21952,plain,
implies(sF7,not(implies(x,z))) = implies(sF0,implies(implies(z,x),sF1)),
inference(superposition,[],[f16373,f15806]) ).
fof(f21980,plain,
implies(sF7,not(implies(x,z))) = implies(implies(z,x),sF2),
inference(forward_demodulation,[],[f21952,f4785]) ).
fof(f22027,plain,
implies(sF8,not(x)) = implies(implies(z,x),sF1),
inference(forward_demodulation,[],[f21890,f13544]) ).
fof(f22050,plain,
implies(implies(z,x),sF2) = implies(implies(x,z),sF6),
inference(forward_demodulation,[],[f21980,f13551]) ).
fof(f22085,plain,
implies(x,sF9) = implies(implies(z,x),sF1),
inference(forward_demodulation,[],[f22027,f13554]) ).
fof(f22103,plain,
implies(sF8,sF6) = implies(implies(z,x),sF2),
inference(forward_demodulation,[],[f22050,f36]) ).
fof(f22135,plain,
sF10 = implies(implies(z,x),sF2),
inference(forward_demodulation,[],[f22103,f15143]) ).
fof(f22177,plain,
implies(implies(z,x),sF2) = implies(sF3,implies(x,sF9)),
inference(superposition,[],[f3275,f22085]) ).
fof(f22228,plain,
implies(implies(z,x),sF2) = implies(not(sF9),sF5),
inference(forward_demodulation,[],[f22177,f16352]) ).
fof(f22240,plain,
implies(sF8,sF5) = implies(implies(z,x),sF2),
inference(forward_demodulation,[],[f22228,f2649]) ).
fof(f22245,plain,
sF10 = implies(sF8,sF5),
inference(forward_demodulation,[],[f22240,f22135]) ).
fof(f22253,plain,
implies(sF10,sF9) = not(sF5),
inference(backward_demodulation,[],[f17189,f22245]) ).
fof(f22258,plain,
sF11 = not(sF5),
inference(forward_demodulation,[],[f22253,f42]) ).
fof(f22261,plain,
sF5 = not(sF11),
inference(superposition,[],[f2589,f22258]) ).
fof(f22328,plain,
sF5 = sF12,
inference(backward_demodulation,[],[f44,f22261]) ).
fof(f22501,plain,
$false,
inference(forward_subsumption_resolution,[],[f22328,f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL148-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.48 % Computer : n026.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Sun Sep 27 15:26:11 UTC 2026
% 0.22/0.48 % CPUTime :
% 0.22/0.48 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.53 Running first-order theorem proving
% 0.26/0.53 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 38.72/6.67 % (2990461)Detected a unit-equality problem, will run specialized UEQ schedule.
% 38.72/6.67 % (2990466)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=3397990221:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 38.72/6.67 % (2990467)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=607050761:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 38.72/6.67 % (2990469)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=212480609:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 38.72/6.67 % (2990468)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=908307617:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 38.72/6.67 % (2990472)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1436431424:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 38.72/6.67 % (2990471)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=54610251:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 38.72/6.67 % (2990470)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3527273231:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 38.72/6.67 % (2990469)Instruction limit reached!
% 38.72/6.67 % (2990469)------------------------------
% 38.72/6.67 % (2990469)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 38.72/6.67 % (2990469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.72/6.67 % (2990469)CaDiCaL version: 2.1.3
% 38.72/6.67 % (2990469)Termination reason: Instruction limit
% 38.72/6.67 % (2990469)Termination phase: Saturation
% 38.72/6.67 % (2990469)Time elapsed: 0.126 s
% 38.72/6.67 % (2990469)Peak memory usage: 89 MB
% 38.72/6.67 % (2990469)Instructions burned: 136 (million)
% 38.72/6.67 % (2990470)Instruction limit reached!
% 38.72/6.67 % (2990470)------------------------------
% 38.72/6.67 % (2990470)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 38.72/6.67 % (2990470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.72/6.67 % (2990470)CaDiCaL version: 2.1.3
% 38.72/6.67 % (2990470)Termination reason: Instruction limit
% 38.72/6.67 % (2990470)Termination phase: Saturation
% 38.72/6.67 % (2990470)Time elapsed: 0.177 s
% 38.72/6.67 % (2990470)Peak memory usage: 90 MB
% 38.72/6.67 % (2990470)Instructions burned: 181 (million)
% 38.72/6.67 % (2990471)Instruction limit reached!
% 38.72/6.67 % (2990471)------------------------------
% 38.72/6.67 % (2990471)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 38.72/6.67 % (2990471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.72/6.67 % (2990471)CaDiCaL version: 2.1.3
% 38.72/6.67 % (2990471)Termination reason: Instruction limit
% 38.72/6.67 % (2990471)Termination phase: Saturation
% 38.72/6.67 % (2990471)Time elapsed: 0.275 s
% 38.72/6.67 % (2990471)Peak memory usage: 91 MB
% 38.72/6.67 % (2990471)Instructions burned: 258 (million)
% 38.72/6.67 % (2990480)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3972916010:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 38.72/6.67 % (2990481)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1360447750:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 38.72/6.67 % (2990482)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3597182154:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 38.72/6.67 % (2990482)Instruction limit reached!
% 38.72/6.67 % (2990482)------------------------------
% 38.72/6.67 % (2990482)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 38.72/6.67 % (2990482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.72/6.67 % (2990482)CaDiCaL version: 2.1.3
% 38.72/6.67 % (2990482)Termination reason: Instruction limit
% 38.72/6.67 % (2990482)Termination phase: Saturation
% 38.72/6.67 % (2990482)Time elapsed: 0.177 s
% 38.72/6.67 % (2990482)Peak memory usage: 89 MB
% 38.72/6.67 % (2990482)Instructions burned: 215 (million)
% 38.72/6.67 % (2990486)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=840459276:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2990 on theBenchmark for (2990ds/317Mi)
% 38.72/6.67 % (2990472)Instruction limit reached!
% 38.72/6.67 % (2990472)------------------------------
% 38.72/6.67 % (2990472)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 38.72/6.67 % (2990472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.72/6.67 % (2990472)CaDiCaL version: 2.1.3
% 38.72/6.67 % (2990472)Termination reason: Instruction limit
% 38.72/6.67 % (2990472)Termination phase: Saturation
% 38.72/6.67 % (2990472)Time elapsed: 1.046 s
% 38.72/6.67 % (2990472)Peak memory usage: 100 MB
% 38.72/6.67 % (2990472)Instructions burned: 1188 (million)
% 38.72/6.67 % (2990486)Instruction limit reached!
% 38.72/6.67 % (2990486)------------------------------
% 38.72/6.67 % (2990486)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 38.72/6.67 % (2990486)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.72/6.67 % (2990486)CaDiCaL version: 2.1.3
% 38.72/6.67 % (2990486)Termination reason: Instruction limit
% 38.72/6.67 % (2990486)Termination phase: Saturation
% 38.72/6.67 % (2990486)Time elapsed: 0.321 s
% 38.72/6.67 % (2990486)Peak memory usage: 94 MB
% 38.72/6.67 % (2990486)Instructions burned: 317 (million)
% 38.72/6.67 % (2990488)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=2905229030:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2986 on theBenchmark for (2986ds/12125Mi)
% 38.72/6.67 % (2990490)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=1106610431:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2984 on theBenchmark for (2984ds/2836Mi)
% 38.72/6.67 % (2990480)Instruction limit reached!
% 38.72/6.67 % (2990480)------------------------------
% 38.72/6.67 % (2990480)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 38.72/6.67 % (2990480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.72/6.67 % (2990480)CaDiCaL version: 2.1.3
% 38.72/6.67 % (2990480)Termination reason: Instruction limit
% 38.72/6.67 % (2990480)Termination phase: Saturation
% 38.72/6.67 % (2990480)Time elapsed: 2.197 s
% 38.72/6.67 % (2990480)Peak memory usage: 143 MB
% 38.72/6.67 % (2990480)Instructions burned: 2051 (million)
% 38.72/6.67 % (2990492)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=3149771349:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2971 on theBenchmark for (2971ds/14534Mi)
% 38.72/6.67 % (2990490)Instruction limit reached!
% 38.72/6.67 % (2990490)------------------------------
% 38.72/6.67 % (2990490)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 38.72/6.67 % (2990490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.72/6.67 % (2990490)CaDiCaL version: 2.1.3
% 38.72/6.67 % (2990490)Termination reason: Instruction limit
% 38.72/6.67 % (2990490)Termination phase: Saturation
% 38.72/6.67 % (2990490)Time elapsed: 2.993 s
% 38.72/6.67 % (2990490)Peak memory usage: 149 MB
% 38.72/6.67 % (2990490)Instructions burned: 2836 (million)
% 38.72/6.67 % (2990468)First to succeed.
% 38.72/6.67 % (2990468)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2990461"
% 38.72/6.67 % (2990494)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:sas=cadical:sp=reverse_frequency:bsr=on:alpa=false:sac=on:random_seed=1216708754:i=11832:s2at=3:bs=on:bd=preordered:fsd=on_2951 on theBenchmark for (2951ds/11832Mi)
% 38.72/6.67 % (2990468)Refutation found. Thanks to Tanya!
% 38.72/6.67 % SZS status Unsatisfiable for theBenchmark
% 38.72/6.67 % SZS output start Proof for theBenchmark
% See solution above
% 40.04/7.01 % (2990468)------------------------------
% 40.04/7.01 % (2990468)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 40.04/7.01 % (2990468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.04/7.01 % (2990468)CaDiCaL version: 2.1.3
% 40.04/7.01 % (2990468)Termination reason: Refutation
% 40.04/7.01 % (2990468)Time elapsed: 4.817 s
% 40.04/7.01 % (2990468)Peak memory usage: 159 MB
% 40.04/7.01 % (2990468)Instructions burned: 4800 (million)
% 40.04/7.01 % (2990468)------------------------------
% 40.04/7.01 % (2990468)------------------------------
% 40.04/7.01 % (2990461)Success in time 5.499 s
% 40.04/7.01 % Vampire exiting
%------------------------------------------------------------------------------