%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL050-3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:34:09 PM UTC 2026
% Result : Unsatisfiable 11.72s 2.78s
% Output : Refutation 13.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 17
% Syntax : Number of formulae : 166 ( 166 unt; 3 def)
% Number of atoms : 166 ( 165 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 230 ( 230 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
fof(f2,axiom,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
fof(f4,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
fof(f6,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_associativity_5) ).
fof(f8,negated_conjecture,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity_6) ).
fof(f9,axiom,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f11,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f12,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
fof(f13,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity_11) ).
fof(f14,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top_12) ).
fof(f16,negated_conjecture,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero_13) ).
fof(f23,negated_conjecture,
complement(composition(sk1,top)) != composition(complement(composition(sk1,top)),top),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_17) ).
fof(f24,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f28,definition,
sF0 = composition(sk1,top),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f29,plain,
composition(sk1,top) = sF0,
inference(reorient_equations,[],[f28]) ).
fof(f30,definition,
sF1 = complement(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f31,plain,
complement(sF0) = sF1,
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
sF2 = composition(sF1,top),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f33,plain,
composition(sF1,top) = sF2,
inference(reorient_equations,[],[f32]) ).
fof(f34,plain,
sF1 != sF2,
inference(definition_folding,[],[f23,f33,f31,f29,f31,f29]) ).
fof(f35,plain,
zero = complement(top),
inference(backward_demodulation,[],[f24,f15]) ).
fof(f36,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(backward_demodulation,[],[f4,f1]) ).
fof(f39,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(backward_demodulation,[],[f14,f1]) ).
fof(f43,plain,
! [X0] : join(complement(join(complement(X0),sF0)),complement(join(complement(X0),sF1))) = X0,
inference(superposition,[],[f36,f31]) ).
fof(f45,plain,
! [X0] : join(complement(join(complement(X0),sF0)),complement(join(sF1,complement(X0)))) = X0,
inference(forward_demodulation,[],[f43,f1]) ).
fof(f46,plain,
! [X0] : join(complement(join(sF1,complement(X0))),complement(join(complement(X0),sF0))) = X0,
inference(forward_demodulation,[],[f45,f1]) ).
fof(f47,plain,
! [X0] : join(complement(join(sF1,complement(X0))),complement(join(sF0,complement(X0)))) = X0,
inference(forward_demodulation,[],[f46,f1]) ).
fof(f48,plain,
! [X0] : join(complement(join(sF0,complement(X0))),complement(join(sF1,complement(X0)))) = X0,
inference(forward_demodulation,[],[f47,f1]) ).
fof(f51,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[],[f36,f15]) ).
fof(f52,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f51,f35]) ).
fof(f58,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(superposition,[],[f36,f1]) ).
fof(f60,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(X0,complement(composition(converse(X0),X1)))),
inference(superposition,[],[f39,f10]) ).
fof(f77,plain,
! [X0] : complement(X0) = join(complement(join(complement(complement(X0)),X0)),complement(top)),
inference(superposition,[],[f58,f15]) ).
fof(f83,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(complement(complement(X0)),X0))),
inference(forward_demodulation,[],[f77,f1]) ).
fof(f92,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f83,f1]) ).
fof(f97,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f92,f35]) ).
fof(f101,plain,
! [X0] : complement(complement(X0)) = X0,
inference(backward_demodulation,[],[f52,f97]) ).
fof(f104,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,X0))),
inference(backward_demodulation,[],[f97,f101]) ).
fof(f109,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(X0,complement(X1)))),
inference(superposition,[],[f36,f101]) ).
fof(f113,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0))),
inference(superposition,[],[f58,f101]) ).
fof(f121,plain,
top = join(top,zero),
inference(superposition,[],[f15,f35]) ).
fof(f125,plain,
! [X0] : composition(join(sk1,X0),top) = join(sF0,composition(X0,top)),
inference(superposition,[],[f9,f29]) ).
fof(f139,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f2,f15]) ).
fof(f147,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f155,plain,
! [X0,X1] : composition(X0,converse(X1)) = converse(composition(X1,converse(X0))),
inference(superposition,[],[f12,f10]) ).
fof(f156,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f12,f10]) ).
fof(f158,plain,
! [X2,X0,X1] : composition(join(converse(X1),X2),converse(X0)) = join(converse(composition(X0,X1)),composition(X2,converse(X0))),
inference(superposition,[],[f9,f12]) ).
fof(f159,plain,
! [X0,X1] : complement(converse(X0)) = join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))),
inference(superposition,[],[f39,f12]) ).
fof(f160,plain,
! [X0,X1] : complement(converse(X0)) = join(complement(converse(X0)),composition(X1,complement(converse(composition(X0,X1))))),
inference(forward_demodulation,[],[f159,f10]) ).
fof(f165,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f158,f12]) ).
fof(f171,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f165,f11]) ).
fof(f174,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f171,f11]) ).
fof(f176,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f174,f12]) ).
fof(f182,plain,
! [X0,X1] : join(X0,converse(X1)) = converse(join(converse(X0),X1)),
inference(superposition,[],[f11,f10]) ).
fof(f183,plain,
! [X0,X1] : converse(join(X1,converse(X0))) = join(converse(X1),X0),
inference(superposition,[],[f11,f10]) ).
fof(f191,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(X1,complement(X0)))),
inference(superposition,[],[f109,f1]) ).
fof(f259,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(complement(join(X0,X1)),complement(complement(join(complement(X1),X0)))))),
inference(superposition,[],[f109,f113]) ).
fof(f261,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(complement(join(X0,X1)),join(complement(X1),X0)))),
inference(forward_demodulation,[],[f259,f101]) ).
fof(f274,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(X0,join(complement(join(X0,X1)),complement(X1))))),
inference(forward_demodulation,[],[f261,f147]) ).
fof(f285,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f274,f1]) ).
fof(f295,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f285,f101]) ).
fof(f303,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f295,f101]) ).
fof(f312,plain,
! [X0] : composition(sk1,composition(top,X0)) = composition(sF0,X0),
inference(superposition,[],[f7,f29]) ).
fof(f332,plain,
! [X0,X1] : converse(composition(X0,join(one,X1))) = converse(join(X0,composition(X0,X1))),
inference(superposition,[],[f176,f8]) ).
fof(f344,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f176]) ).
fof(f355,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f344,f10]) ).
fof(f385,plain,
! [X0,X1] : composition(X0,join(X1,one)) = join(composition(X0,X1),X0),
inference(superposition,[],[f355,f8]) ).
fof(f388,plain,
! [X0] : composition(sk1,join(X0,top)) = join(composition(sk1,X0),sF0),
inference(superposition,[],[f355,f29]) ).
fof(f399,plain,
! [X0] : join(sF0,composition(sk1,X0)) = composition(sk1,join(X0,top)),
inference(forward_demodulation,[],[f388,f1]) ).
fof(f401,plain,
! [X0,X1] : join(X0,composition(X0,X1)) = composition(X0,join(X1,one)),
inference(forward_demodulation,[],[f385,f1]) ).
fof(f503,plain,
! [X0,X1] : join(top,X0) = join(X1,join(X0,complement(X1))),
inference(superposition,[],[f139,f1]) ).
fof(f504,plain,
! [X0,X1] : join(top,join(complement(complement(X1)),X0)) = join(X1,join(top,X0)),
inference(superposition,[],[f139,f139]) ).
fof(f505,plain,
! [X0,X1] : join(top,complement(join(X0,complement(X1)))) = join(join(X0,X1),complement(X0)),
inference(superposition,[],[f139,f109]) ).
fof(f525,plain,
! [X0,X1] : join(top,complement(join(X0,complement(X1)))) = join(X0,join(X1,complement(X0))),
inference(forward_demodulation,[],[f505,f2]) ).
fof(f526,plain,
! [X0,X1] : join(X1,join(top,X0)) = join(top,join(X1,X0)),
inference(forward_demodulation,[],[f504,f101]) ).
fof(f532,plain,
! [X0,X1] : join(top,X1) = join(top,complement(join(X0,complement(X1)))),
inference(forward_demodulation,[],[f525,f503]) ).
fof(f682,plain,
! [X0,X1] : complement(join(X1,X0)) = join(zero,complement(join(X0,join(join(X1,X0),X1)))),
inference(superposition,[],[f104,f147]) ).
fof(f708,plain,
! [X0,X1] : join(zero,complement(join(X0,join(X1,join(X0,X1))))) = complement(join(X1,X0)),
inference(forward_demodulation,[],[f682,f2]) ).
fof(f870,plain,
! [X0] : join(top,complement(join(sF1,complement(X0)))) = join(join(sF0,complement(X0)),X0),
inference(superposition,[],[f139,f48]) ).
fof(f883,plain,
! [X0] : join(top,complement(join(sF1,complement(X0)))) = join(sF0,join(complement(X0),X0)),
inference(forward_demodulation,[],[f870,f2]) ).
fof(f895,plain,
! [X0] : join(top,complement(join(sF1,complement(X0)))) = join(sF0,join(X0,complement(X0))),
inference(forward_demodulation,[],[f883,f1]) ).
fof(f903,plain,
! [X0] : join(sF0,top) = join(top,complement(join(sF1,complement(X0)))),
inference(forward_demodulation,[],[f895,f15]) ).
fof(f911,plain,
! [X0] : join(top,X0) = join(sF0,top),
inference(forward_demodulation,[],[f903,f532]) ).
fof(f925,plain,
! [X0,X1] : join(top,join(X1,X0)) = join(X1,join(sF0,top)),
inference(backward_demodulation,[],[f526,f911]) ).
fof(f948,plain,
top = join(sF0,top),
inference(backward_demodulation,[],[f121,f911]) ).
fof(f951,plain,
! [X0] : top = join(top,X0),
inference(backward_demodulation,[],[f911,f948]) ).
fof(f972,plain,
! [X0,X1] : join(X1,top) = join(top,join(X1,X0)),
inference(forward_demodulation,[],[f925,f948]) ).
fof(f994,plain,
! [X1] : top = join(X1,top),
inference(forward_demodulation,[],[f972,f951]) ).
fof(f1007,plain,
! [X0] : composition(sk1,top) = join(sF0,composition(sk1,X0)),
inference(backward_demodulation,[],[f399,f994]) ).
fof(f1018,plain,
! [X0] : sF0 = join(sF0,composition(sk1,X0)),
inference(forward_demodulation,[],[f1007,f29]) ).
fof(f1054,plain,
! [X0] : composition(X0,top) = join(X0,composition(X0,top)),
inference(superposition,[],[f401,f951]) ).
fof(f1236,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f156,f8]) ).
fof(f1259,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f1236,f10]) ).
fof(f1278,plain,
! [X0] : complement(X0) = join(complement(X0),composition(one,complement(X0))),
inference(superposition,[],[f60,f1259]) ).
fof(f1292,plain,
one = converse(one),
inference(superposition,[],[f8,f1259]) ).
fof(f1300,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f1259,f1292]) ).
fof(f1320,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(backward_demodulation,[],[f1278,f1300]) ).
fof(f1429,plain,
! [X0] : join(X0,X0) = X0,
inference(superposition,[],[f1320,f101]) ).
fof(f1441,plain,
! [X0] : complement(complement(X0)) = join(zero,complement(complement(X0))),
inference(superposition,[],[f104,f1320]) ).
fof(f1450,plain,
! [X0] : join(zero,X0) = X0,
inference(forward_demodulation,[],[f1441,f101]) ).
fof(f1476,plain,
! [X0,X1] : complement(join(X0,join(X1,join(X0,X1)))) = complement(join(X1,X0)),
inference(backward_demodulation,[],[f708,f1450]) ).
fof(f1560,plain,
! [X0] : join(X0,zero) = X0,
inference(superposition,[],[f1,f1450]) ).
fof(f1593,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1)),
inference(superposition,[],[f2,f1429]) ).
fof(f1596,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X0,X1)),
inference(superposition,[],[f147,f1429]) ).
fof(f1597,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X1,X0)),
inference(superposition,[],[f147,f1429]) ).
fof(f1602,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X1,join(X0,X1))),
inference(superposition,[],[f2,f1429]) ).
fof(f1621,plain,
! [X0,X1] : complement(join(X0,X1)) = complement(join(X1,X0)),
inference(backward_demodulation,[],[f1476,f1602]) ).
fof(f1689,plain,
! [X0] : join(one,converse(X0)) = converse(join(one,X0)),
inference(superposition,[],[f11,f1292]) ).
fof(f1950,plain,
! [X0] : converse(top) = join(X0,converse(complement(converse(X0)))),
inference(superposition,[],[f182,f15]) ).
fof(f1956,plain,
! [X0] : converse(top) = join(X0,converse(top)),
inference(superposition,[],[f182,f994]) ).
fof(f2908,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(join(X0,X1),X2)),
inference(superposition,[],[f1593,f9]) ).
fof(f2957,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = composition(join(X0,join(X0,X1)),X2),
inference(forward_demodulation,[],[f2908,f9]) ).
fof(f2971,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = composition(join(X1,X0),X2),
inference(forward_demodulation,[],[f2957,f1596]) ).
fof(f3181,plain,
top = converse(top),
inference(superposition,[],[f951,f1956]) ).
fof(f3191,plain,
! [X0] : top = join(X0,converse(complement(converse(X0)))),
inference(backward_demodulation,[],[f1950,f3181]) ).
fof(f3253,plain,
! [X0] : composition(top,converse(X0)) = converse(composition(X0,top)),
inference(superposition,[],[f12,f3181]) ).
fof(f3502,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(join(complement(join(X0,complement(X1))),join(X1,X0))),complement(complement(X0))),
inference(superposition,[],[f113,f191]) ).
fof(f3509,plain,
! [X0,X1] : complement(X0) = join(complement(join(X1,X0)),complement(X0)),
inference(superposition,[],[f1593,f191]) ).
fof(f3510,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0))),
inference(forward_demodulation,[],[f3509,f1]) ).
fof(f3515,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(complement(join(X0,complement(X1))),join(X1,X0)))),
inference(forward_demodulation,[],[f3502,f1]) ).
fof(f3555,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,complement(X1)))),
inference(backward_demodulation,[],[f303,f3510]) ).
fof(f3559,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(join(X1,X0),complement(join(X0,complement(X1)))))),
inference(forward_demodulation,[],[f3515,f1621]) ).
fof(f3591,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f3559,f2]) ).
fof(f3612,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(X1,join(X0,X1)))),
inference(forward_demodulation,[],[f3591,f3555]) ).
fof(f3629,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(X0,X1))),
inference(forward_demodulation,[],[f3612,f1597]) ).
fof(f3640,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f3629,f101]) ).
fof(f3647,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f3640,f101]) ).
fof(f3708,plain,
! [X0] : join(X0,complement(top)) = join(X0,complement(converse(complement(converse(X0))))),
inference(superposition,[],[f3647,f3191]) ).
fof(f3712,plain,
! [X0,X1] : join(X1,complement(join(X0,X1))) = join(X1,complement(X0)),
inference(superposition,[],[f3647,f1621]) ).
fof(f3768,plain,
! [X0] : join(X0,zero) = join(X0,complement(converse(complement(converse(X0))))),
inference(forward_demodulation,[],[f3708,f35]) ).
fof(f3805,plain,
! [X0] : join(X0,complement(converse(complement(converse(X0))))) = X0,
inference(forward_demodulation,[],[f3768,f1560]) ).
fof(f4185,plain,
! [X0] : join(converse(complement(converse(X0))),complement(X0)) = join(converse(complement(converse(X0))),complement(top)),
inference(superposition,[],[f3712,f3191]) ).
fof(f4246,plain,
! [X0] : join(converse(complement(converse(X0))),complement(X0)) = join(complement(top),converse(complement(converse(X0)))),
inference(forward_demodulation,[],[f4185,f1]) ).
fof(f4280,plain,
! [X0] : join(converse(complement(converse(X0))),complement(X0)) = join(zero,converse(complement(converse(X0)))),
inference(forward_demodulation,[],[f4246,f35]) ).
fof(f4307,plain,
! [X0] : converse(complement(converse(X0))) = join(converse(complement(converse(X0))),complement(X0)),
inference(forward_demodulation,[],[f4280,f1450]) ).
fof(f4325,plain,
! [X0] : converse(complement(converse(X0))) = join(complement(X0),converse(complement(converse(X0)))),
inference(forward_demodulation,[],[f4307,f1]) ).
fof(f5552,plain,
composition(composition(sk1,top),top) = join(sF0,composition(composition(sk1,top),top)),
inference(superposition,[],[f125,f1054]) ).
fof(f5558,plain,
composition(sk1,composition(top,top)) = join(sF0,composition(sk1,composition(top,top))),
inference(forward_demodulation,[],[f5552,f7]) ).
fof(f5601,plain,
sF0 = composition(sk1,composition(top,top)),
inference(forward_demodulation,[],[f5558,f1018]) ).
fof(f5625,plain,
sF0 = composition(sF0,top),
inference(forward_demodulation,[],[f5601,f312]) ).
fof(f5771,plain,
! [X0] : converse(converse(X0)) = join(X0,converse(complement(converse(complement(converse(converse(X0))))))),
inference(superposition,[],[f182,f3805]) ).
fof(f5782,plain,
! [X0] : join(X0,converse(complement(converse(complement(X0))))) = X0,
inference(forward_demodulation,[],[f5771,f10]) ).
fof(f5832,plain,
! [X0] : complement(X0) = join(complement(X0),converse(complement(converse(X0)))),
inference(superposition,[],[f5782,f101]) ).
fof(f5884,plain,
! [X0] : complement(X0) = converse(complement(converse(X0))),
inference(backward_demodulation,[],[f4325,f5832]) ).
fof(f5977,plain,
! [X0] : complement(converse(X0)) = converse(complement(X0)),
inference(superposition,[],[f10,f5884]) ).
fof(f6013,plain,
! [X0,X1] : converse(complement(X0)) = join(converse(complement(X0)),composition(X1,complement(converse(composition(X0,X1))))),
inference(backward_demodulation,[],[f160,f5977]) ).
fof(f6121,plain,
! [X0,X1] : converse(complement(X0)) = join(converse(complement(X0)),composition(X1,converse(complement(composition(X0,X1))))),
inference(forward_demodulation,[],[f6013,f5977]) ).
fof(f9866,plain,
! [X2,X0,X1] : join(converse(X2),composition(X1,converse(X0))) = converse(join(X2,composition(X0,converse(X1)))),
inference(superposition,[],[f183,f155]) ).
fof(f9884,plain,
! [X0,X1] : converse(complement(X0)) = converse(join(complement(X0),composition(complement(composition(X0,X1)),converse(X1)))),
inference(backward_demodulation,[],[f6121,f9866]) ).
fof(f10012,plain,
converse(complement(sF0)) = converse(join(complement(sF0),composition(complement(sF0),converse(top)))),
inference(superposition,[],[f9884,f5625]) ).
fof(f10072,plain,
converse(complement(sF0)) = converse(composition(complement(sF0),join(one,converse(top)))),
inference(forward_demodulation,[],[f10012,f332]) ).
fof(f10110,plain,
converse(complement(sF0)) = converse(composition(complement(sF0),converse(join(one,top)))),
inference(forward_demodulation,[],[f10072,f1689]) ).
fof(f10130,plain,
converse(complement(sF0)) = composition(join(one,top),converse(complement(sF0))),
inference(forward_demodulation,[],[f10110,f155]) ).
fof(f10146,plain,
converse(complement(sF0)) = composition(join(top,one),converse(complement(sF0))),
inference(forward_demodulation,[],[f10130,f2971]) ).
fof(f10161,plain,
converse(sF1) = composition(join(top,one),converse(sF1)),
inference(forward_demodulation,[],[f10146,f31]) ).
fof(f10171,plain,
converse(sF1) = composition(top,converse(sF1)),
inference(forward_demodulation,[],[f10161,f951]) ).
fof(f10179,plain,
converse(sF1) = converse(composition(sF1,top)),
inference(forward_demodulation,[],[f10171,f3253]) ).
fof(f10202,plain,
converse(sF1) = converse(sF2),
inference(forward_demodulation,[],[f10179,f33]) ).
fof(f10223,plain,
sF2 = converse(converse(sF1)),
inference(superposition,[],[f10,f10202]) ).
fof(f10251,plain,
sF1 = sF2,
inference(forward_demodulation,[],[f10223,f10]) ).
fof(f10256,plain,
$false,
inference(forward_subsumption_resolution,[],[f10251,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL050-3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 % Computer : n005.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sun Sep 27 22:57:17 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.46 Running first-order theorem proving
% 0.15/0.46 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.72/2.78 % (274437)Detected a unit-equality problem, will run specialized UEQ schedule.
% 11.72/2.78 % (274450)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1278296967:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 11.72/2.78 % (274454)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1460279351:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 11.72/2.78 % (274452)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2086451492:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 11.72/2.78 % (274451)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2341111933:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 11.72/2.78 % (274449)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=538125208:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 11.72/2.78 % (274448)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=1961306988:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 11.72/2.78 % (274453)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=283833060:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 11.72/2.78 % (274451)Instruction limit reached!
% 11.72/2.78 % (274451)------------------------------
% 11.72/2.78 % (274451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.72/2.78 % (274451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.72/2.78 % (274451)CaDiCaL version: 2.1.3
% 11.72/2.78 % (274451)Termination reason: Instruction limit
% 11.72/2.78 % (274451)Termination phase: Saturation
% 11.72/2.78 % (274451)Time elapsed: 0.133 s
% 11.72/2.78 % (274451)Peak memory usage: 89 MB
% 11.72/2.78 % (274451)Instructions burned: 136 (million)
% 11.72/2.78 % (274452)Instruction limit reached!
% 11.72/2.78 % (274452)------------------------------
% 11.72/2.78 % (274452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.72/2.78 % (274452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.72/2.78 % (274452)CaDiCaL version: 2.1.3
% 11.72/2.78 % (274452)Termination reason: Instruction limit
% 11.72/2.78 % (274452)Termination phase: Saturation
% 11.72/2.78 % (274452)Time elapsed: 0.173 s
% 11.72/2.78 % (274452)Peak memory usage: 89 MB
% 11.72/2.78 % (274452)Instructions burned: 181 (million)
% 11.72/2.78 % (274453)Instruction limit reached!
% 11.72/2.78 % (274453)------------------------------
% 11.72/2.78 % (274453)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.72/2.78 % (274453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.72/2.78 % (274453)CaDiCaL version: 2.1.3
% 11.72/2.78 % (274453)Termination reason: Instruction limit
% 11.72/2.78 % (274453)Termination phase: Saturation
% 11.72/2.78 % (274453)Time elapsed: 0.269 s
% 11.72/2.78 % (274453)Peak memory usage: 90 MB
% 11.72/2.78 % (274453)Instructions burned: 257 (million)
% 11.72/2.78 % (274464)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3168235894:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 11.72/2.78 % (274465)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3468455267:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 11.72/2.78 % (274466)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=987563007:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 11.72/2.78 % (274466)Instruction limit reached!
% 11.72/2.78 % (274466)------------------------------
% 11.72/2.78 % (274466)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.72/2.78 % (274466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.72/2.78 % (274466)CaDiCaL version: 2.1.3
% 11.72/2.78 % (274466)Termination reason: Instruction limit
% 11.72/2.78 % (274466)Termination phase: Saturation
% 11.72/2.78 % (274466)Time elapsed: 0.200 s
% 11.72/2.78 % (274466)Peak memory usage: 90 MB
% 11.72/2.78 % (274466)Instructions burned: 215 (million)
% 11.72/2.78 % (274470)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=1703651727:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2991 on theBenchmark for (2991ds/317Mi)
% 11.72/2.78 % (274454)Instruction limit reached!
% 11.72/2.78 % (274454)------------------------------
% 11.72/2.78 % (274454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.72/2.78 % (274454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.72/2.78 % (274454)CaDiCaL version: 2.1.3
% 11.72/2.78 % (274454)Termination reason: Instruction limit
% 11.72/2.78 % (274454)Termination phase: Saturation
% 11.72/2.78 % (274454)Time elapsed: 0.947 s
% 11.72/2.78 % (274454)Peak memory usage: 101 MB
% 11.72/2.78 % (274454)Instructions burned: 1187 (million)
% 11.72/2.78 % (274476)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=2494648238:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2988 on theBenchmark for (2988ds/12125Mi)
% 11.72/2.78 % (274470)Instruction limit reached!
% 11.72/2.78 % (274470)------------------------------
% 11.72/2.78 % (274470)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.72/2.78 % (274470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.72/2.78 % (274470)CaDiCaL version: 2.1.3
% 11.72/2.78 % (274470)Termination reason: Instruction limit
% 11.72/2.78 % (274470)Termination phase: Saturation
% 11.72/2.78 % (274470)Time elapsed: 0.326 s
% 11.72/2.78 % (274470)Peak memory usage: 92 MB
% 11.72/2.78 % (274470)Instructions burned: 317 (million)
% 11.72/2.78 % (274450)First to succeed.
% 11.72/2.78 % (274450)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-274437"
% 11.72/2.78 % (274478)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=1443283913:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2985 on theBenchmark for (2985ds/2836Mi)
% 11.72/2.78 % (274450)Refutation found. Thanks to Tanya!
% 11.72/2.78 % SZS status Unsatisfiable for theBenchmark
% 11.72/2.78 % SZS output start Proof for theBenchmark
% See solution above
% 13.38/3.08 % (274450)------------------------------
% 13.38/3.08 % (274450)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.38/3.08 % (274450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.38/3.08 % (274450)CaDiCaL version: 2.1.3
% 13.38/3.08 % (274450)Termination reason: Refutation
% 13.38/3.08 % (274450)Time elapsed: 1.375 s
% 13.38/3.08 % (274450)Peak memory usage: 143 MB
% 13.38/3.08 % (274450)Instructions burned: 2439 (million)
% 13.38/3.08 % (274450)------------------------------
% 13.38/3.08 % (274450)------------------------------
% 13.38/3.08 % (274437)Success in time 1.772 s
% 13.38/3.08 % Vampire exiting
%------------------------------------------------------------------------------