%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL160-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 0.17s 0.53s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 81
% Number of leaves : 13
% Syntax : Number of formulae : 143 ( 143 unt; 0 def)
% Number of atoms : 143 ( 142 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 79 ( 79 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 24 ( 6 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 : 106 ( 106 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : implies(truth,X0) = X0,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/LCL001-2.ax',or_definition) ).
fof(f9,axiom,
! [X0,X1] : or(X0,X1) = or(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-2.ax',or_commutativity) ).
fof(f10,axiom,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL002-1.ax',xor_definition) ).
fof(f15,axiom,
! [X0,X1] : and_star(X0,X1) = not(or(not(X0),not(X1))),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL002-1.ax',and_star_associativity) ).
fof(f18,axiom,
! [X0,X1] : and_star(X0,X1) = and_star(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax',and_star_commutativity) ).
fof(f19,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax',false_definition) ).
fof(f20,negated_conjecture,
and_star(xor(and_star(xor(truth,x),y),truth),y) != and_star(xor(and_star(xor(truth,y),x),truth),x),
file('/export/starexec/sandbox/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(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,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(not(truth))),not(x)))))),not(y))))),not(not(truth))))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(not(truth))),not(x)))))),not(y)))))),not(truth)))))),not(y))) != not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y)))))),not(x))))),not(not(truth))))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y)))))),not(x)))))),not(truth)))))),not(x))),
inference(definition_unfolding,[],[f20,f23,f22,f23,f22,f23,f22,f23,f22]) ).
fof(f33,plain,
! [X0] : implies(not(X0),truth) = implies(falsehood,X0),
inference(superposition,[],[f25,f19]) ).
fof(f37,plain,
! [X0] : implies(implies(X0,truth),truth) = implies(X0,X0),
inference(superposition,[],[f4,f1]) ).
fof(f39,plain,
! [X0,X1] : implies(implies(X0,not(X1)),not(X1)) = implies(implies(not(X0),X1),X0),
inference(superposition,[],[f4,f25]) ).
fof(f48,plain,
! [X0] : truth = implies(implies(not(X0),not(truth)),X0),
inference(superposition,[],[f6,f1]) ).
fof(f56,plain,
! [X0] : truth = implies(implies(not(X0),falsehood),X0),
inference(forward_demodulation,[],[f48,f19]) ).
fof(f60,plain,
! [X0] : truth = implies(implies(not(falsehood),X0),X0),
inference(superposition,[],[f56,f25]) ).
fof(f80,plain,
! [X0,X1] : truth = implies(implies(truth,X1),implies(implies(X1,X0),X0)),
inference(superposition,[],[f3,f1]) ).
fof(f98,plain,
! [X0,X1] : truth = implies(X1,implies(implies(X1,X0),X0)),
inference(forward_demodulation,[],[f80,f1]) ).
fof(f299,plain,
truth = implies(not(falsehood),not(falsehood)),
inference(superposition,[],[f60,f37]) ).
fof(f479,plain,
truth = implies(truth,not(falsehood)),
inference(superposition,[],[f60,f299]) ).
fof(f491,plain,
truth = not(falsehood),
inference(forward_demodulation,[],[f479,f1]) ).
fof(f497,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(f511,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(f521,plain,
! [X2,X0,X1] : not(implies(not(not(X0)),not(not(implies(not(not(X1)),not(X2)))))) = not(implies(not(not(X2)),not(not(implies(not(not(X0)),not(X1)))))),
inference(superposition,[],[f30,f29]) ).
fof(f522,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(not(truth))),not(x)))))),not(y))))),not(not(truth))))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(not(truth))),not(x)))))),not(y)))))),not(truth)))))),not(y))) != not(implies(not(not(implies(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y)))))),not(not(implies(not(not(x)),not(not(truth)))))))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y)))))),not(x)))))),not(truth)))))),not(x))),
inference(superposition,[],[f31,f29]) ).
fof(f539,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(not(truth))),not(x)))))),not(y))))),not(not(truth))))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(not(truth))),not(x)))))),not(y)))))),not(truth)))))),not(y))) != not(implies(not(not(x)),not(implies(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y)))))),not(not(implies(not(not(x)),not(not(truth)))))))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y)))))),not(x)))))),not(truth))))))),
inference(forward_demodulation,[],[f522,f30]) ).
fof(f541,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,[],[f511,f25]) ).
fof(f545,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,[],[f497,f491]) ).
fof(f548,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(not(truth))),not(x)))))),not(y))))),not(not(truth))))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(not(truth))),not(x)))))),not(y)))))),not(truth)))))),not(y))) != not(implies(not(not(x)),not(implies(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y)))))),not(not(implies(not(not(x)),not(not(truth)))))))),not(implies(not(not(truth)),not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y)))))),not(x))))))))))),
inference(forward_demodulation,[],[f539,f30]) ).
fof(f550,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,[],[f541,f25]) ).
fof(f554,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,[],[f545,f1]) ).
fof(f556,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(not(truth))),not(x)))))),not(y))))),not(not(truth))))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(not(truth))),not(x)))))),not(y)))))),not(truth)))))),not(y))) != not(implies(not(not(x)),not(implies(not(not(implies(not(not(truth)),not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y)))))),not(x)))))))),not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y)))))),not(not(implies(not(not(x)),not(not(truth))))))))))),
inference(forward_demodulation,[],[f548,f30]) ).
fof(f557,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,[],[f550,f491]) ).
fof(f560,plain,
! [X0,X1] : not(not(not(implies(not(not(X0)),not(X1))))) = not(implies(not(not(not(not(X0)))),not(X1))),
inference(forward_demodulation,[],[f554,f1]) ).
fof(f561,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(not(truth))),not(x)))))),not(y))))),not(not(truth))))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(not(truth))),not(x)))))),not(y)))))),not(truth)))))),not(y))) != not(implies(not(not(x)),not(implies(not(not(implies(not(not(truth)),not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y)))))),not(x)))))))),not(implies(not(not(not(implies(not(not(x)),not(not(truth)))))),not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y))))))))))),
inference(forward_demodulation,[],[f556,f30]) ).
fof(f562,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,[],[f557,f1]) ).
fof(f565,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(not(truth))),not(x)))))),not(y))))),not(not(truth))))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(not(truth))),not(x)))))),not(y)))))),not(truth)))))),not(y))) != not(implies(not(not(x)),not(implies(not(not(implies(not(not(truth)),not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y)))))),not(x)))))))),not(implies(not(not(x)),not(not(implies(not(not(not(truth))),not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y)))))))))))))),
inference(forward_demodulation,[],[f561,f29]) ).
fof(f566,plain,
! [X0,X1] : not(not(not(implies(not(not(X0)),not(X1))))) = not(implies(not(not(X0)),not(not(not(X1))))),
inference(forward_demodulation,[],[f562,f1]) ).
fof(f568,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(not(truth))),not(x)))))),not(y))))),not(not(truth))))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(x))))),not(implies(not(not(not(truth))),not(x)))))),not(y)))))),not(truth)))))),not(y))) != not(implies(not(not(x)),not(implies(not(not(implies(not(not(truth)),not(not(not(implies(not(not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(y)),not(not(truth))))))),not(x)))))))),not(implies(not(not(x)),not(not(implies(not(not(not(truth))),not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(y)),not(not(truth))))))))))))))),
inference(forward_demodulation,[],[f565,f30]) ).
fof(f570,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))),not(y))))),not(falsehood)))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(falsehood)),not(x)))))),not(y)))))),falsehood))))),not(y))) != not(implies(not(not(x)),not(implies(not(not(implies(not(falsehood),not(not(not(implies(not(not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(y)),not(falsehood)))))),not(x)))))))),not(implies(not(not(x)),not(not(implies(not(not(falsehood)),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(y)),not(falsehood)))))))))))))),
inference(forward_demodulation,[],[f568,f19]) ).
fof(f571,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(not(truth),not(x)))))),not(y))))),truth))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(not(truth),not(x)))))),not(y)))))),falsehood))))),not(y))) != not(implies(not(not(x)),not(implies(not(not(implies(truth,not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(not(not(y)),truth))))),not(x)))))))),not(implies(not(not(x)),not(not(implies(not(truth),not(implies(not(not(implies(truth,not(not(y))))),not(implies(not(not(y)),truth))))))))))))),
inference(forward_demodulation,[],[f570,f491]) ).
fof(f572,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(not(truth),not(x)))))),not(y))))),truth))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(not(truth),not(x)))))),not(y)))))),falsehood))))),not(y))) != not(implies(not(not(x)),not(implies(not(not(implies(truth,not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(not(truth),not(y)))))),not(x)))))))),not(implies(not(not(x)),not(not(implies(not(truth),not(implies(not(not(implies(truth,not(not(y))))),not(implies(not(truth),not(y)))))))))))))),
inference(forward_demodulation,[],[f571,f25]) ).
fof(f573,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y))))),truth))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y)))))),falsehood))))),not(y))) != not(implies(not(not(x)),not(implies(not(not(implies(truth,not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))),not(x)))))))),not(implies(not(not(x)),not(not(implies(falsehood,not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))))))))))),
inference(forward_demodulation,[],[f572,f19]) ).
fof(f574,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y))))),truth))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y)))))),falsehood))))),not(y))) != not(implies(not(not(x)),not(implies(not(not(implies(not(not(x)),not(not(implies(falsehood,not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y))))))))))),not(implies(truth,not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))),not(x))))))))))),
inference(forward_demodulation,[],[f573,f30]) ).
fof(f575,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y))))),truth))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y)))))),falsehood))))),not(y))) != not(implies(not(not(x)),not(implies(not(not(implies(not(not(x)),not(not(implies(falsehood,not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y))))))))))),not(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))),not(x)))))))))),
inference(forward_demodulation,[],[f574,f1]) ).
fof(f576,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y))))),truth))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y)))))),falsehood))))),not(y))) != not(implies(not(not(x)),not(implies(not(not(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))),not(x))))))),not(implies(not(not(x)),not(not(implies(falsehood,not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))))))))))),
inference(forward_demodulation,[],[f575,f30]) ).
fof(f577,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y))))),truth))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y)))))),falsehood))))),not(y))) != not(implies(not(not(x)),not(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))),not(x))))),not(implies(not(not(x)),not(not(implies(falsehood,not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))))))))))))),
inference(forward_demodulation,[],[f576,f560]) ).
fof(f578,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y))))),truth))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y)))))),falsehood))))),not(y))) != not(not(not(implies(not(not(x)),not(implies(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))),not(x))))),not(implies(not(not(x)),not(not(implies(falsehood,not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))))))))))))),
inference(forward_demodulation,[],[f577,f566]) ).
fof(f579,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y))))),truth))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y)))))),falsehood))))),not(y))) != not(not(not(implies(not(not(x)),not(implies(not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))),not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(falsehood,not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y))))))))))))))))))),
inference(forward_demodulation,[],[f578,f29]) ).
fof(f580,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y))))),truth))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y)))))),falsehood))))),not(y))) != not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(x)),not(not(implies(falsehood,not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y))))))))))),not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))))))))))),
inference(forward_demodulation,[],[f579,f521]) ).
fof(f581,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y))))),truth))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y)))))),falsehood))))),not(y))) != not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(implies(not(not(implies(truth,not(not(y))))),not(implies(falsehood,not(y))))))))))))))))))),
inference(forward_demodulation,[],[f580,f30]) ).
fof(f582,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y))))),truth))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y)))))),falsehood))))),not(y))) != not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(implies(falsehood,not(y)))),not(implies(truth,not(not(y))))))),not(implies(not(not(x)),not(not(implies(falsehood,not(implies(not(not(implies(falsehood,not(y)))),not(implies(truth,not(not(y)))))))))))))))))))),
inference(forward_demodulation,[],[f581,f30]) ).
fof(f583,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y))))),truth))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y)))))),falsehood))))),not(y))) != not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(implies(falsehood,not(y)))),not(not(not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(implies(not(not(implies(falsehood,not(y)))),not(not(not(y))))))))))))))))))),
inference(forward_demodulation,[],[f582,f1]) ).
fof(f584,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y))))),truth))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y)))))),falsehood))))),not(y))) != not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(not(not(y)))),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(implies(not(not(not(not(y)))),not(implies(falsehood,not(y))))))))))))))))))),
inference(forward_demodulation,[],[f583,f30]) ).
fof(f585,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y))))),truth))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y)))))),falsehood))))),not(y))) != not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))),
inference(forward_demodulation,[],[f584,f560]) ).
fof(f586,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y))))),truth))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y)))))),falsehood))))),not(y))) != not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))),
inference(forward_demodulation,[],[f585,f560]) ).
fof(f587,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y))))),truth))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y)))))),falsehood))))),not(y))) != not(not(not(implies(not(not(x)),not(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))),
inference(forward_demodulation,[],[f586,f566]) ).
fof(f588,plain,
not(implies(not(not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y))))),truth))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y)))))),falsehood))))),not(y))) != not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))),
inference(forward_demodulation,[],[f587,f566]) ).
fof(f589,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y))))),truth))),not(implies(not(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y)))))),falsehood)))))),
inference(forward_demodulation,[],[f588,f30]) ).
fof(f590,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y))))),truth))),not(implies(not(falsehood),not(not(not(implies(not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x)))))),not(y))))))))))),
inference(forward_demodulation,[],[f589,f25]) ).
fof(f591,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(not(not(implies(not(not(y)),not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x))))))))),truth))),not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(truth,not(not(x))))),not(implies(falsehood,not(x))))))))))))))),
inference(forward_demodulation,[],[f590,f30]) ).
fof(f592,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(not(not(implies(not(not(y)),not(implies(not(not(implies(falsehood,not(x)))),not(implies(truth,not(not(x)))))))))),truth))),not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(falsehood,not(x)))),not(implies(truth,not(not(x)))))))))))))))),
inference(forward_demodulation,[],[f591,f30]) ).
fof(f593,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(not(not(implies(not(not(y)),not(implies(not(not(implies(falsehood,not(x)))),not(not(not(x))))))))),truth))),not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(implies(falsehood,not(x)))),not(not(not(x))))))))))))))),
inference(forward_demodulation,[],[f592,f1]) ).
fof(f594,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(not(not(implies(not(not(y)),not(implies(not(not(not(not(x)))),not(implies(falsehood,not(x))))))))),truth))),not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(implies(not(not(not(not(x)))),not(implies(falsehood,not(x))))))))))))))),
inference(forward_demodulation,[],[f593,f30]) ).
fof(f595,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(not(not(implies(not(not(y)),not(not(not(implies(not(not(x)),not(implies(falsehood,not(x))))))))))),truth))),not(implies(not(falsehood),not(not(not(implies(not(not(y)),not(not(not(implies(not(not(x)),not(implies(falsehood,not(x))))))))))))))))),
inference(forward_demodulation,[],[f594,f560]) ).
fof(f596,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(not(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x))))))))))),truth))),not(implies(not(falsehood),not(not(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x))))))))))))))))),
inference(forward_demodulation,[],[f595,f566]) ).
fof(f597,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(not(not(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x))))))))))),truth))),not(implies(truth,not(not(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x))))))))))))))))),
inference(forward_demodulation,[],[f596,f491]) ).
fof(f598,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(truth,not(not(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x)))))))))))))),not(implies(not(not(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x))))))))))),truth)))))),
inference(forward_demodulation,[],[f597,f30]) ).
fof(f599,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(truth,not(not(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x)))))))))))))),not(implies(not(truth),not(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x)))))))))))))))),
inference(forward_demodulation,[],[f598,f25]) ).
fof(f600,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(truth,not(not(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x)))))))))))))),not(implies(falsehood,not(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x)))))))))))))))),
inference(forward_demodulation,[],[f599,f19]) ).
fof(f601,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(falsehood,not(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x))))))))))))),not(implies(truth,not(not(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x))))))))))))))))),
inference(forward_demodulation,[],[f600,f30]) ).
fof(f602,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(implies(not(not(y)),not(implies(not(not(implies(falsehood,not(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x))))))))))))),not(not(not(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x)))))))))))))))),
inference(forward_demodulation,[],[f601,f1]) ).
fof(f603,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(implies(not(not(y)),not(implies(not(not(not(not(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x))))))))))))),not(implies(falsehood,not(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x)))))))))))))))),
inference(forward_demodulation,[],[f602,f30]) ).
fof(f604,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(implies(not(not(y)),not(not(not(implies(not(not(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x))))))))))),not(implies(falsehood,not(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x)))))))))))))))))),
inference(forward_demodulation,[],[f603,f560]) ).
fof(f605,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(not(not(implies(not(not(y)),not(implies(not(not(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x))))))))))),not(implies(falsehood,not(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x)))))))))))))))))),
inference(forward_demodulation,[],[f604,f566]) ).
fof(f606,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(not(not(implies(not(not(y)),not(not(not(implies(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x))))))))),not(implies(falsehood,not(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x)))))))))))))))))))),
inference(forward_demodulation,[],[f605,f560]) ).
fof(f607,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(not(not(not(not(implies(not(not(y)),not(implies(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x))))))))),not(implies(falsehood,not(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x)))))))))))))))))))),
inference(forward_demodulation,[],[f606,f566]) ).
fof(f608,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(not(not(not(not(implies(not(not(y)),not(implies(not(not(y)),not(not(implies(not(not(implies(not(not(x)),not(implies(falsehood,not(x)))))),not(implies(falsehood,not(not(not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x))))))))))))))))))))))),
inference(forward_demodulation,[],[f607,f29]) ).
fof(f610,plain,
! [X0] : truth = implies(implies(truth,X0),X0),
inference(superposition,[],[f60,f491]) ).
fof(f615,plain,
! [X0] : implies(truth,X0) = implies(not(X0),falsehood),
inference(superposition,[],[f25,f491]) ).
fof(f618,plain,
! [X0,X1] : not(implies(not(not(not(implies(not(not(X0)),not(X1))))),truth)) = not(implies(not(not(X0)),not(not(implies(not(not(X1)),truth))))),
inference(superposition,[],[f29,f491]) ).
fof(f625,plain,
! [X0,X1] : not(implies(not(not(X0)),not(not(implies(not(truth),not(X1)))))) = not(implies(not(not(not(implies(not(not(X0)),not(X1))))),truth)),
inference(forward_demodulation,[],[f618,f25]) ).
fof(f628,plain,
! [X0] : implies(not(X0),falsehood) = X0,
inference(forward_demodulation,[],[f615,f1]) ).
fof(f633,plain,
! [X0] : truth = implies(X0,X0),
inference(forward_demodulation,[],[f610,f1]) ).
fof(f634,plain,
! [X0,X1] : not(implies(not(truth),not(not(implies(not(not(X0)),not(X1)))))) = not(implies(not(not(X0)),not(not(implies(not(truth),not(X1)))))),
inference(forward_demodulation,[],[f625,f25]) ).
fof(f636,plain,
! [X0,X1] : not(implies(not(not(X0)),not(not(implies(falsehood,not(X1)))))) = not(implies(falsehood,not(not(implies(not(not(X0)),not(X1)))))),
inference(forward_demodulation,[],[f634,f19]) ).
fof(f911,plain,
! [X0] : truth = implies(X0,implies(X0,X0)),
inference(superposition,[],[f98,f37]) ).
fof(f936,plain,
! [X0] : truth = implies(X0,truth),
inference(forward_demodulation,[],[f911,f633]) ).
fof(f975,plain,
! [X0] : truth = implies(falsehood,X0),
inference(superposition,[],[f33,f936]) ).
fof(f1008,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(not(not(not(not(implies(not(not(y)),not(implies(not(not(y)),not(not(implies(not(not(implies(not(not(x)),not(implies(falsehood,not(x)))))),not(truth)))))))))))),
inference(superposition,[],[f608,f975]) ).
fof(f1013,plain,
! [X0] : implies(truth,X0) = implies(implies(X0,falsehood),falsehood),
inference(superposition,[],[f4,f975]) ).
fof(f1019,plain,
! [X0] : implies(implies(X0,falsehood),falsehood) = X0,
inference(forward_demodulation,[],[f1013,f1]) ).
fof(f1024,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(not(not(not(not(implies(not(not(y)),not(implies(not(not(truth)),not(not(implies(not(not(y)),not(implies(not(not(x)),not(implies(falsehood,not(x)))))))))))))))),
inference(forward_demodulation,[],[f1008,f521]) ).
fof(f1027,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(not(not(not(not(implies(not(not(y)),not(implies(not(not(truth)),not(not(implies(not(not(y)),not(implies(not(not(x)),not(truth)))))))))))))),
inference(forward_demodulation,[],[f1024,f975]) ).
fof(f1029,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(not(not(not(not(implies(not(not(y)),not(implies(not(not(truth)),not(not(implies(not(not(y)),not(implies(not(not(truth)),not(x)))))))))))))),
inference(forward_demodulation,[],[f1027,f30]) ).
fof(f1031,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(not(not(not(not(implies(not(not(y)),not(implies(not(falsehood),not(not(implies(not(not(y)),not(implies(not(falsehood),not(x)))))))))))))),
inference(forward_demodulation,[],[f1029,f19]) ).
fof(f1033,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(not(not(not(not(implies(not(not(y)),not(implies(truth,not(not(implies(not(not(y)),not(implies(truth,not(x)))))))))))))),
inference(forward_demodulation,[],[f1031,f491]) ).
fof(f1035,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(not(not(not(not(implies(not(not(y)),not(not(not(implies(not(not(y)),not(implies(truth,not(x))))))))))))),
inference(forward_demodulation,[],[f1033,f1]) ).
fof(f1037,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(not(not(not(not(not(not(implies(not(not(y)),not(implies(not(not(y)),not(implies(truth,not(x))))))))))))),
inference(forward_demodulation,[],[f1035,f566]) ).
fof(f1039,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(not(not(x)),not(not(implies(falsehood,not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(not(not(not(not(not(not(implies(not(not(y)),not(implies(not(not(y)),not(not(x)))))))))))),
inference(forward_demodulation,[],[f1037,f1]) ).
fof(f1041,plain,
not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(implies(falsehood,not(not(implies(not(not(x)),not(not(not(implies(not(not(y)),not(implies(falsehood,not(y))))))))))))))))))))))) != not(not(not(not(not(not(not(implies(not(not(y)),not(implies(not(not(y)),not(not(x)))))))))))),
inference(forward_demodulation,[],[f1039,f636]) ).
fof(f1043,plain,
not(not(not(not(not(not(not(implies(not(not(y)),not(implies(not(not(y)),not(not(x)))))))))))) != not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(y)),not(implies(falsehood,not(y)))))),not(truth)))))))))))),
inference(forward_demodulation,[],[f1041,f975]) ).
fof(f1045,plain,
not(not(not(not(not(not(not(implies(not(not(y)),not(implies(not(not(y)),not(not(x)))))))))))) != not(not(not(not(not(implies(not(not(x)),not(implies(not(not(truth)),not(not(implies(not(not(x)),not(implies(not(not(y)),not(implies(falsehood,not(y)))))))))))))))),
inference(forward_demodulation,[],[f1043,f521]) ).
fof(f1047,plain,
not(not(not(not(not(not(not(implies(not(not(y)),not(implies(not(not(y)),not(not(x)))))))))))) != not(not(not(not(not(implies(not(not(x)),not(implies(not(not(truth)),not(not(implies(not(not(x)),not(implies(not(not(y)),not(truth)))))))))))))),
inference(forward_demodulation,[],[f1045,f975]) ).
fof(f1049,plain,
not(not(not(not(not(not(not(implies(not(not(y)),not(implies(not(not(y)),not(not(x)))))))))))) != not(not(not(not(not(implies(not(not(x)),not(implies(not(not(truth)),not(not(implies(not(not(x)),not(implies(not(not(truth)),not(y)))))))))))))),
inference(forward_demodulation,[],[f1047,f30]) ).
fof(f1051,plain,
not(not(not(not(not(not(not(implies(not(not(y)),not(implies(not(not(y)),not(not(x)))))))))))) != not(not(not(not(not(implies(not(not(x)),not(implies(not(falsehood),not(not(implies(not(not(x)),not(implies(not(falsehood),not(y)))))))))))))),
inference(forward_demodulation,[],[f1049,f19]) ).
fof(f1053,plain,
not(not(not(not(not(not(not(implies(not(not(y)),not(implies(not(not(y)),not(not(x)))))))))))) != not(not(not(not(not(implies(not(not(x)),not(implies(truth,not(not(implies(not(not(x)),not(implies(truth,not(y)))))))))))))),
inference(forward_demodulation,[],[f1051,f491]) ).
fof(f1055,plain,
not(not(not(not(not(not(not(implies(not(not(y)),not(implies(not(not(y)),not(not(x)))))))))))) != not(not(not(not(not(implies(not(not(x)),not(not(not(implies(not(not(x)),not(implies(truth,not(y))))))))))))),
inference(forward_demodulation,[],[f1053,f1]) ).
fof(f1057,plain,
not(not(not(not(not(not(not(implies(not(not(y)),not(implies(not(not(y)),not(not(x)))))))))))) != not(not(not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(implies(truth,not(y))))))))))))),
inference(forward_demodulation,[],[f1055,f566]) ).
fof(f1059,plain,
not(not(not(not(not(not(not(implies(not(not(y)),not(implies(not(not(y)),not(not(x)))))))))))) != not(not(not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),not(not(y)))))))))))),
inference(forward_demodulation,[],[f1057,f1]) ).
fof(f1529,plain,
! [X0] : not(X0) = implies(X0,falsehood),
inference(superposition,[],[f1019,f628]) ).
fof(f1667,plain,
! [X0] : not(not(X0)) = X0,
inference(superposition,[],[f628,f1529]) ).
fof(f1809,plain,
! [X0,X1] : not(not(implies(not(not(X0)),not(X1)))) = implies(not(not(X1)),not(X0)),
inference(superposition,[],[f1667,f30]) ).
fof(f1869,plain,
not(not(not(not(not(not(not(implies(y,not(implies(y,not(not(x)))))))))))) != not(not(not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),y)))))))))),
inference(superposition,[],[f1059,f1667]) ).
fof(f1877,plain,
! [X0,X1] : implies(X0,X1) = implies(not(X1),not(X0)),
inference(superposition,[],[f25,f1667]) ).
fof(f1907,plain,
not(not(not(not(not(not(not(implies(y,not(implies(y,not(not(x)))))))))))) != not(not(not(not(not(implies(not(not(x)),not(implies(not(not(x)),y)))))))),
inference(forward_demodulation,[],[f1869,f1667]) ).
fof(f1961,plain,
! [X0,X1] : not(not(implies(not(not(X0)),not(X1)))) = implies(X0,not(X1)),
inference(forward_demodulation,[],[f1809,f1877]) ).
fof(f1971,plain,
not(not(not(not(not(not(not(implies(y,not(implies(y,not(not(x)))))))))))) != not(not(not(implies(not(not(x)),not(implies(not(not(x)),y)))))),
inference(forward_demodulation,[],[f1907,f1667]) ).
fof(f2024,plain,
! [X0,X1] : implies(not(not(X0)),not(X1)) = implies(X0,not(X1)),
inference(forward_demodulation,[],[f1961,f1667]) ).
fof(f2034,plain,
not(not(not(not(not(not(not(implies(y,not(implies(y,not(not(x)))))))))))) != not(implies(not(not(x)),not(implies(not(not(x)),y)))),
inference(forward_demodulation,[],[f1971,f1667]) ).
fof(f2087,plain,
! [X0,X1] : implies(X0,not(X1)) = implies(X1,not(X0)),
inference(forward_demodulation,[],[f2024,f1877]) ).
fof(f2097,plain,
not(not(not(not(not(not(not(implies(y,not(implies(y,not(not(x)))))))))))) != not(implies(implies(not(not(x)),y),not(x))),
inference(forward_demodulation,[],[f2034,f1877]) ).
fof(f2158,plain,
not(not(not(not(not(not(not(implies(y,not(implies(y,not(not(x)))))))))))) != not(implies(implies(not(x),not(y)),not(y))),
inference(forward_demodulation,[],[f2097,f39]) ).
fof(f2216,plain,
not(not(not(not(not(not(not(implies(y,not(implies(y,not(not(x)))))))))))) != not(implies(y,not(implies(not(x),not(y))))),
inference(forward_demodulation,[],[f2158,f2087]) ).
fof(f2270,plain,
not(not(not(not(not(not(not(implies(y,not(implies(y,not(not(x)))))))))))) != not(implies(y,not(implies(y,x)))),
inference(forward_demodulation,[],[f2216,f1877]) ).
fof(f2321,plain,
not(not(not(not(not(implies(y,not(implies(y,not(not(x)))))))))) != not(implies(y,not(implies(y,x)))),
inference(forward_demodulation,[],[f2270,f1667]) ).
fof(f2371,plain,
not(not(not(implies(y,not(implies(y,not(not(x)))))))) != not(implies(y,not(implies(y,x)))),
inference(forward_demodulation,[],[f2321,f1667]) ).
fof(f2419,plain,
not(implies(y,not(implies(y,not(not(x)))))) != not(implies(y,not(implies(y,x)))),
inference(forward_demodulation,[],[f2371,f1667]) ).
fof(f2467,plain,
not(implies(y,not(implies(y,x)))) != not(implies(y,not(implies(y,x)))),
inference(forward_demodulation,[],[f2419,f1667]) ).
fof(f2468,plain,
$false,
inference(trivial_inequality_removal,[],[f2467]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL160-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 15:29:17 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.15/0.41 Running first-order model finding
% 0.15/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.53 % (2781918)Will run a generic schedule for satisfiability detection.
% 0.17/0.53 % (2781924)% WARNING: option uhcvi not known.
% 0.17/0.53 % (2781924)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1559225496:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.53 % (2781923)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4210658591_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.53 % (2781925)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4012715183:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.53 % (2781926)dis+10_1_sil=32000:sp=arity:random_seed=2432001813:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.53 % (2781928)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1530302626:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.53 % (2781927)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3348978731:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.53 % (2781929)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1748940359:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.53 % TRYING [1]
% 0.17/0.53 % TRYING [2]
% 0.17/0.53 % TRYING [3]
% 0.17/0.53 % TRYING [4]
% 0.17/0.53 % (2781926)Instruction limit reached!
% 0.17/0.53 % (2781926)------------------------------
% 0.17/0.53 % (2781926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.53 % (2781926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.53 % (2781926)CaDiCaL version: 2.1.3
% 0.17/0.53 % (2781926)Termination reason: Instruction limit
% 0.17/0.53 % (2781926)Termination phase: Saturation
% 0.17/0.53 % (2781926)Time elapsed: 0.055 s
% 0.17/0.53 % (2781926)Peak memory usage: 12 MB
% 0.17/0.53 % (2781926)Instructions burned: 104 (million)
% 0.17/0.53 % (2781927) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2781918-2781927"...
% 0.17/0.53 % (2781925) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2781918-2781925"...
% 0.17/0.53 % (2781927)...printing done.
% 0.17/0.53 % (2781927)Refutation found. Thanks to Tanya!
% 0.17/0.53 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.53 % (2781927)------------------------------
% 0.17/0.53 % (2781927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.53 % (2781927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.53 % (2781927)CaDiCaL version: 2.1.3
% 0.17/0.53 % (2781927)Termination reason: Refutation
% 0.17/0.53 % (2781927)Time elapsed: 0.065 s
% 0.17/0.53 % (2781927)Peak memory usage: 13 MB
% 0.17/0.53 % (2781927)Instructions burned: 130 (million)
% 0.17/0.53 % (2781918)Success in time 0.113 s
% 0.17/0.53 % Vampire exiting
%------------------------------------------------------------------------------