%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL159-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 11:57:48 AM UTC 2026
% Result : Unsatisfiable 0.24s 0.60s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 14
% Syntax : Number of formulae : 92 ( 92 unt; 0 def)
% Number of atoms : 92 ( 91 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 41 ( 41 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 13 ( 4 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 82 ( 82 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : implies(truth,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',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/Axioms/LCL001-0.ax',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/Axioms/LCL001-0.ax',wajsberg_3) ).
fof(f5,axiom,
! [X0,X1] : implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',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] : or(X0,X1) = implies(not(X0),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-2.ax',or_definition) ).
fof(f9,axiom,
! [X0,X1] : or(X0,X1) = or(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-2.ax',or_commutativity) ).
fof(f10,axiom,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-2.ax',and_definition) ).
fof(f13,axiom,
! [X0,X1] : xor(X0,X1) = or(and(X0,not(X1)),and(not(X0),X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-1.ax',xor_definition) ).
fof(f14,axiom,
! [X0,X1] : xor(X0,X1) = xor(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-1.ax',xor_commutativity) ).
fof(f15,axiom,
! [X0,X1] : and_star(X0,X1) = not(or(not(X0),not(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-1.ax',and_star_definition) ).
fof(f16,plain,
! [X0,X1] : not(or(not(X0),not(X1))) = and_star(X0,X1),
inference(reorient_equations,[],[f15]) ).
fof(f17,axiom,
! [X2,X0,X1] : and_star(and_star(X0,X1),X2) = and_star(X0,and_star(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-1.ax',and_star_associativity) ).
fof(f18,axiom,
! [X0,X1] : and_star(X0,X1) = and_star(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-1.ax',and_star_commutativity) ).
fof(f19,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-1.ax',false_definition) ).
fof(f20,negated_conjecture,
xor(x,xor(truth,y)) != xor(xor(x,truth),y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
fof(f21,plain,
! [X0,X1] : and(X0,X1) = not(implies(not(not(X0)),not(X1))),
inference(definition_unfolding,[],[f10,f7]) ).
fof(f22,plain,
! [X0,X1] : xor(X0,X1) = implies(not(not(implies(not(not(X0)),not(not(X1))))),not(implies(not(not(not(X0))),not(X1)))),
inference(definition_unfolding,[],[f13,f7,f21,f21]) ).
fof(f23,plain,
! [X0,X1] : and_star(X0,X1) = not(implies(not(not(X0)),not(X1))),
inference(definition_unfolding,[],[f16,f7]) ).
fof(f25,plain,
! [X0,X1] : implies(not(X0),X1) = implies(not(X1),X0),
inference(definition_unfolding,[],[f9,f7,f7]) ).
fof(f28,plain,
! [X0,X1] : implies(not(not(implies(not(not(X0)),not(not(X1))))),not(implies(not(not(not(X0))),not(X1)))) = implies(not(not(implies(not(not(X1)),not(not(X0))))),not(implies(not(not(not(X1))),not(X0)))),
inference(definition_unfolding,[],[f14,f22,f22]) ).
fof(f29,plain,
! [X2,X0,X1] : not(implies(not(not(not(implies(not(not(X0)),not(X1))))),not(X2))) = not(implies(not(not(X0)),not(not(implies(not(not(X1)),not(X2)))))),
inference(definition_unfolding,[],[f17,f23,f23,f23,f23]) ).
fof(f30,plain,
! [X0,X1] : not(implies(not(not(X0)),not(X1))) = not(implies(not(not(X1)),not(X0))),
inference(definition_unfolding,[],[f18,f23,f23]) ).
fof(f31,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y)))))))) != implies(not(not(implies(not(not(implies(not(not(implies(not(not(x)),not(not(truth))))),not(implies(not(not(not(x))),not(truth)))))),not(not(y))))),not(implies(not(not(not(implies(not(not(implies(not(not(x)),not(not(truth))))),not(implies(not(not(not(x))),not(truth))))))),not(y)))),
inference(definition_unfolding,[],[f20,f22,f22,f22,f22]) ).
fof(f33,plain,
! [X0] : implies(not(X0),truth) = implies(falsehood,X0),
inference(superposition,[],[f25,f19]) ).
fof(f38,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y)))))))) != implies(not(not(implies(not(not(implies(not(not(implies(not(not(x)),not(not(truth))))),not(implies(not(not(truth)),not(not(x))))))),not(not(y))))),not(implies(not(not(not(implies(not(not(implies(not(not(x)),not(not(truth))))),not(implies(not(not(truth)),not(not(x)))))))),not(y)))),
inference(superposition,[],[f31,f25]) ).
fof(f43,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(not(x)),not(not(truth))))),not(implies(not(not(truth)),not(not(x)))))))))),not(implies(not(not(not(y))),not(implies(not(not(implies(not(not(x)),not(not(truth))))),not(implies(not(not(truth)),not(not(x))))))))),
inference(forward_demodulation,[],[f38,f28]) ).
fof(f50,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(x)),not(not(truth)))))))))),not(implies(not(not(not(y))),not(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(x)),not(not(truth))))))))),
inference(forward_demodulation,[],[f43,f30]) ).
fof(f57,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(x)),not(falsehood))))))))),not(implies(not(not(not(y))),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(x)),not(falsehood)))))))),
inference(forward_demodulation,[],[f50,f19]) ).
fof(f64,plain,
implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(x)),not(falsehood))))))))),not(implies(not(not(not(y))),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(x)),not(falsehood)))))))) != implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(y)),not(falsehood))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(y)),not(falsehood)))))))),
inference(forward_demodulation,[],[f57,f30]) ).
fof(f84,plain,
! [X0] : implies(implies(X0,truth),truth) = implies(X0,X0),
inference(superposition,[],[f4,f1]) ).
fof(f91,plain,
! [X0] : implies(not(X0),not(X0)) = implies(implies(falsehood,X0),truth),
inference(superposition,[],[f84,f33]) ).
fof(f109,plain,
! [X0] : truth = implies(implies(not(X0),not(truth)),X0),
inference(superposition,[],[f6,f1]) ).
fof(f119,plain,
! [X0] : truth = implies(implies(not(X0),falsehood),X0),
inference(forward_demodulation,[],[f109,f19]) ).
fof(f122,plain,
truth = implies(implies(falsehood,falsehood),truth),
inference(superposition,[],[f119,f19]) ).
fof(f124,plain,
! [X0] : truth = implies(implies(not(falsehood),X0),X0),
inference(superposition,[],[f119,f25]) ).
fof(f126,plain,
truth = implies(not(falsehood),not(falsehood)),
inference(forward_demodulation,[],[f122,f91]) ).
fof(f150,plain,
! [X0,X1] : truth = implies(implies(truth,X1),implies(implies(X1,X0),X0)),
inference(superposition,[],[f3,f1]) ).
fof(f170,plain,
! [X0,X1] : truth = implies(X1,implies(implies(X1,X0),X0)),
inference(forward_demodulation,[],[f150,f1]) ).
fof(f307,plain,
truth = implies(truth,not(falsehood)),
inference(superposition,[],[f124,f126]) ).
fof(f324,plain,
truth = not(falsehood),
inference(forward_demodulation,[],[f307,f1]) ).
fof(f325,plain,
! [X0,X1] : not(implies(not(not(not(implies(not(falsehood),not(X0))))),not(X1))) = not(implies(not(falsehood),not(not(implies(not(not(X0)),not(X1)))))),
inference(superposition,[],[f29,f19]) ).
fof(f339,plain,
! [X0,X1] : not(implies(not(not(not(implies(not(not(X0)),not(X1))))),falsehood)) = not(implies(not(not(X0)),not(not(implies(not(not(X1)),falsehood))))),
inference(superposition,[],[f29,f19]) ).
fof(f369,plain,
! [X0,X1] : not(implies(not(not(X0)),not(not(implies(not(falsehood),not(X1)))))) = not(implies(not(not(not(implies(not(not(X0)),not(X1))))),falsehood)),
inference(forward_demodulation,[],[f339,f25]) ).
fof(f373,plain,
! [X0,X1] : not(implies(not(not(not(implies(truth,not(X0))))),not(X1))) = not(implies(truth,not(not(implies(not(not(X0)),not(X1)))))),
inference(forward_demodulation,[],[f325,f324]) ).
fof(f378,plain,
! [X0,X1] : not(implies(not(falsehood),not(not(implies(not(not(X0)),not(X1)))))) = not(implies(not(not(X0)),not(not(implies(not(falsehood),not(X1)))))),
inference(forward_demodulation,[],[f369,f25]) ).
fof(f382,plain,
! [X0,X1] : not(not(not(implies(not(not(X0)),not(X1))))) = not(implies(not(not(not(implies(truth,not(X0))))),not(X1))),
inference(forward_demodulation,[],[f373,f1]) ).
fof(f385,plain,
! [X0,X1] : not(implies(not(not(X0)),not(not(implies(truth,not(X1)))))) = not(implies(truth,not(not(implies(not(not(X0)),not(X1)))))),
inference(forward_demodulation,[],[f378,f324]) ).
fof(f387,plain,
! [X0,X1] : not(not(not(implies(not(not(X0)),not(X1))))) = not(implies(not(not(not(not(X0)))),not(X1))),
inference(forward_demodulation,[],[f382,f1]) ).
fof(f389,plain,
! [X0,X1] : not(not(not(implies(not(not(X0)),not(X1))))) = not(implies(not(not(X0)),not(not(implies(truth,not(X1)))))),
inference(forward_demodulation,[],[f385,f1]) ).
fof(f392,plain,
! [X0,X1] : not(not(not(implies(not(not(X0)),not(X1))))) = not(implies(not(not(X0)),not(not(not(X1))))),
inference(forward_demodulation,[],[f389,f1]) ).
fof(f419,plain,
! [X0] : truth = implies(implies(truth,X0),X0),
inference(superposition,[],[f124,f324]) ).
fof(f443,plain,
! [X0] : truth = implies(X0,X0),
inference(forward_demodulation,[],[f419,f1]) ).
fof(f658,plain,
! [X0] : truth = implies(implies(X0,truth),truth),
inference(superposition,[],[f84,f443]) ).
fof(f803,plain,
! [X0] : truth = implies(X0,truth),
inference(superposition,[],[f170,f658]) ).
fof(f869,plain,
! [X0] : truth = implies(falsehood,X0),
inference(superposition,[],[f33,f803]) ).
fof(f900,plain,
implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(not(not(x)),truth)))))))),not(implies(not(not(not(y))),not(implies(not(not(implies(truth,not(not(x))))),not(implies(not(not(x)),truth))))))) != implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(not(not(y)),truth)))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(truth,not(not(y))))),not(implies(not(not(y)),truth))))))),
inference(superposition,[],[f64,f324]) ).
fof(f901,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(not(truth),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(truth,not(not(y))))),not(implies(not(truth),not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(not(not(x)),truth)))))))),not(implies(not(not(not(y))),not(implies(not(not(implies(truth,not(not(x))))),not(implies(not(not(x)),truth))))))),
inference(forward_demodulation,[],[f900,f25]) ).
fof(f902,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(not(truth),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(truth,not(not(y))))),not(implies(not(truth),not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(not(truth),not(x))))))))),not(implies(not(not(not(y))),not(implies(not(not(implies(truth,not(not(x))))),not(implies(not(truth),not(x)))))))),
inference(forward_demodulation,[],[f901,f25]) ).
fof(f903,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x))))))))),not(implies(not(not(not(y))),not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))))),
inference(forward_demodulation,[],[f902,f19]) ).
fof(f904,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(falsehood,not(x)))),not(implies(truth,not(not(x)))))))))),not(implies(not(not(not(y))),not(implies(not(not(implies(falsehood,not(x)))),not(implies(truth,not(not(x))))))))),
inference(forward_demodulation,[],[f903,f30]) ).
fof(f905,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(falsehood,not(x)))),not(not(not(x))))))))),not(implies(not(not(not(y))),not(implies(not(not(implies(falsehood,not(x)))),not(not(not(x)))))))),
inference(forward_demodulation,[],[f904,f1]) ).
fof(f906,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(not(not(x)))),not(implies(falsehood,not(x))))))))),not(implies(not(not(not(y))),not(implies(not(not(not(not(x)))),not(implies(falsehood,not(x)))))))),
inference(forward_demodulation,[],[f905,f30]) ).
fof(f907,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(not(not(implies(not(not(x)),not(implies(falsehood,not(x))))))))))),not(implies(not(not(not(y))),not(not(not(implies(not(not(x)),not(implies(falsehood,not(x)))))))))),
inference(forward_demodulation,[],[f906,f387]) ).
fof(f908,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(not(not(implies(not(not(x)),not(implies(falsehood,not(x))))))))))),not(not(not(implies(not(not(not(y))),not(implies(not(not(x)),not(implies(falsehood,not(x)))))))))),
inference(forward_demodulation,[],[f907,f392]) ).
fof(f909,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))))) != implies(not(not(not(not(implies(not(not(not(y))),not(implies(not(not(x)),not(implies(falsehood,not(x)))))))))),not(implies(not(not(y)),not(not(not(not(implies(not(not(x)),not(implies(falsehood,not(x))))))))))),
inference(forward_demodulation,[],[f908,f25]) ).
fof(f910,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))))) != implies(not(not(not(not(implies(not(not(not(y))),not(implies(not(not(x)),not(implies(falsehood,not(x)))))))))),not(not(not(implies(not(not(y)),not(not(implies(not(not(x)),not(implies(falsehood,not(x))))))))))),
inference(forward_demodulation,[],[f909,f392]) ).
fof(f911,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))))) != implies(not(not(not(not(implies(not(not(y)),not(not(implies(not(not(x)),not(implies(falsehood,not(x))))))))))),not(not(not(implies(not(not(not(y))),not(implies(not(not(x)),not(implies(falsehood,not(x)))))))))),
inference(forward_demodulation,[],[f910,f25]) ).
fof(f912,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))))) != implies(not(not(not(not(implies(not(not(y)),not(not(implies(not(not(x)),not(truth))))))))),not(not(not(implies(not(not(not(y))),not(implies(not(not(x)),not(truth)))))))),
inference(forward_demodulation,[],[f911,f869]) ).
fof(f913,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))))) != implies(not(not(not(not(implies(not(not(y)),not(not(implies(not(not(truth)),not(x))))))))),not(not(not(implies(not(not(not(y))),not(implies(not(not(truth)),not(x)))))))),
inference(forward_demodulation,[],[f912,f30]) ).
fof(f914,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))))) != implies(not(not(not(not(implies(not(not(y)),not(not(implies(not(falsehood),not(x))))))))),not(not(not(implies(not(not(not(y))),not(implies(not(falsehood),not(x)))))))),
inference(forward_demodulation,[],[f913,f19]) ).
fof(f915,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))))) != implies(not(not(not(not(implies(not(not(y)),not(not(implies(truth,not(x))))))))),not(not(not(implies(not(not(not(y))),not(implies(truth,not(x)))))))),
inference(forward_demodulation,[],[f914,f324]) ).
fof(f916,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))))) != implies(not(not(not(not(implies(not(not(y)),not(not(not(x)))))))),not(not(not(implies(not(not(not(y))),not(not(x))))))),
inference(forward_demodulation,[],[f915,f1]) ).
fof(f917,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))))) != implies(not(not(not(not(implies(not(not(y)),not(not(not(x)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))),
inference(forward_demodulation,[],[f916,f30]) ).
fof(f918,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))))) != implies(not(not(not(not(not(not(implies(not(not(y)),not(x)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))),
inference(forward_demodulation,[],[f917,f392]) ).
fof(f919,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))))) != implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))),
inference(forward_demodulation,[],[f918,f30]) ).
fof(f920,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(falsehood,not(y)))),not(implies(truth,not(not(y)))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(falsehood,not(y)))),not(implies(truth,not(not(y))))))))) != implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))),
inference(forward_demodulation,[],[f919,f30]) ).
fof(f921,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(falsehood,not(y)))),not(not(not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(falsehood,not(y)))),not(not(not(y)))))))) != implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))),
inference(forward_demodulation,[],[f920,f1]) ).
fof(f922,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(not(not(y)))),not(implies(falsehood,not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(not(not(y)))),not(implies(falsehood,not(y)))))))) != implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))),
inference(forward_demodulation,[],[f921,f30]) ).
fof(f923,plain,
implies(not(not(implies(not(not(x)),not(not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))),not(implies(not(not(not(x))),not(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))))))) != implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))),
inference(forward_demodulation,[],[f922,f387]) ).
fof(f924,plain,
implies(not(not(implies(not(not(x)),not(not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))),not(not(not(implies(not(not(not(x))),not(implies(not(not(y)),not(implies(falsehood,not(y)))))))))) != implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))),
inference(forward_demodulation,[],[f923,f392]) ).
fof(f925,plain,
implies(not(not(not(not(implies(not(not(not(x))),not(implies(not(not(y)),not(implies(falsehood,not(y)))))))))),not(implies(not(not(x)),not(not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))) != implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))),
inference(forward_demodulation,[],[f924,f25]) ).
fof(f926,plain,
implies(not(not(not(not(implies(not(not(not(x))),not(implies(not(not(y)),not(implies(falsehood,not(y)))))))))),not(not(not(implies(not(not(x)),not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))) != implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))),
inference(forward_demodulation,[],[f925,f392]) ).
fof(f927,plain,
implies(not(not(not(not(implies(not(not(x)),not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))),not(not(not(implies(not(not(not(x))),not(implies(not(not(y)),not(implies(falsehood,not(y)))))))))) != implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))),
inference(forward_demodulation,[],[f926,f25]) ).
fof(f928,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(not(not(implies(not(not(x)),not(not(implies(not(not(y)),not(truth))))))))),not(not(not(implies(not(not(not(x))),not(implies(not(not(y)),not(truth)))))))),
inference(forward_demodulation,[],[f927,f869]) ).
fof(f929,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(not(not(implies(not(not(x)),not(not(implies(not(not(truth)),not(y))))))))),not(not(not(implies(not(not(not(x))),not(implies(not(not(truth)),not(y)))))))),
inference(forward_demodulation,[],[f928,f30]) ).
fof(f930,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(not(not(implies(not(not(x)),not(not(implies(not(falsehood),not(y))))))))),not(not(not(implies(not(not(not(x))),not(implies(not(falsehood),not(y)))))))),
inference(forward_demodulation,[],[f929,f19]) ).
fof(f931,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(not(not(implies(not(not(x)),not(not(implies(truth,not(y))))))))),not(not(not(implies(not(not(not(x))),not(implies(truth,not(y)))))))),
inference(forward_demodulation,[],[f930,f324]) ).
fof(f932,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(not(not(implies(not(not(x)),not(not(not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))),
inference(forward_demodulation,[],[f931,f1]) ).
fof(f933,plain,
implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))) != implies(not(not(not(not(not(not(implies(not(not(x)),not(y)))))))),not(not(not(implies(not(not(not(x))),not(not(y))))))),
inference(forward_demodulation,[],[f932,f392]) ).
fof(f934,plain,
$false,
inference(trivial_inequality_removal,[],[f933]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL159-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.21/0.45 % Computer : n020.cluster.edu
% 0.21/0.45 % Model : x86_64 x86_64
% 0.21/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.45 % Memory : 8046.5625MB
% 0.21/0.45 % OS : Linux 6.8.0-71-generic
% 0.21/0.45 % CPULimit : 300
% 0.21/0.45 % WCLimit : 300
% 0.21/0.45 % DateTime : Sun Sep 27 15:25:19 UTC 2026
% 0.21/0.46 % CPUTime :
% 0.21/0.46 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.24/0.51 Running first-order model finding
% 0.24/0.51 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/0.60 % (3531078)Will run a generic schedule for satisfiability detection.
% 0.24/0.60 % (3531087)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=754994230:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.24/0.60 % (3531085)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1108659578:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.24/0.60 % (3531088)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2794147734:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.24/0.60 % (3531083)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2020266914_2999 on theBenchmark for (2999ds/0Mi)
% 0.24/0.60 % (3531086)dis+10_1_sil=32000:sp=arity:random_seed=4054644851:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.24/0.60 % (3531089)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=818727823:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.24/0.60 % TRYING [1]
% 0.24/0.60 % (3531087) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3531078-3531087"...
% 0.24/0.60 % TRYING [2]
% 0.24/0.60 % (3531087)...printing done.
% 0.24/0.60 % (3531084)% WARNING: option uhcvi not known.
% 0.24/0.60 % TRYING [3]
% 0.24/0.60 % (3531087)Refutation found. Thanks to Tanya!
% 0.24/0.60 % SZS status Unsatisfiable for theBenchmark
% 0.24/0.60 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.60 % (3531087)------------------------------
% 0.24/0.60 % (3531087)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.60 % (3531087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.60 % (3531087)CaDiCaL version: 2.1.3
% 0.24/0.60 % (3531087)Termination reason: Refutation
% 0.24/0.60 % (3531087)Time elapsed: 0.028 s
% 0.24/0.60 % (3531087)Peak memory usage: 12 MB
% 0.24/0.60 % (3531087)Instructions burned: 57 (million)
% 0.24/0.60 % (3531078)Success in time 0.074 s
% 0.24/0.60 % Vampire exiting
%------------------------------------------------------------------------------