%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL037-2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 12:34:02 PM UTC 2026
% Result : Unsatisfiable 20.46s 3.70s
% Output : Refutation 20.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 26
% Syntax : Number of formulae : 166 ( 166 unt; 12 def)
% Number of atoms : 166 ( 165 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 23 ( 23 usr; 18 con; 0-2 aty)
% Number of variables : 170 ( 170 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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(f8,negated_conjecture,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f11,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f12,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',def_top_12) ).
fof(f16,negated_conjecture,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero_13) ).
fof(f23,negated_conjecture,
composition(sk1,top) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
fof(f24,plain,
sk1 = composition(sk1,top),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
composition(meet(sk2,converse(sk1)),meet(sk1,sk3)) != composition(meet(sk2,converse(sk1)),sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_18) ).
fof(f26,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f30,plain,
composition(complement(join(complement(sk2),complement(converse(sk1)))),complement(join(complement(sk1),complement(sk3)))) != composition(complement(join(complement(sk2),complement(converse(sk1)))),sk3),
inference(definition_unfolding,[],[f25,f6,f6,f6]) ).
fof(f31,definition,
sF0 = composition(sk1,top),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f32,plain,
composition(sk1,top) = sF0,
inference(reorient_equations,[],[f31]) ).
fof(f33,plain,
sk1 = sF0,
inference(definition_folding,[],[f24,f32]) ).
fof(f34,definition,
sF1 = complement(sk2),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f35,plain,
complement(sk2) = sF1,
inference(reorient_equations,[],[f34]) ).
fof(f36,definition,
sF2 = converse(sk1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f37,plain,
converse(sk1) = sF2,
inference(reorient_equations,[],[f36]) ).
fof(f38,definition,
sF3 = complement(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f39,plain,
complement(sF2) = sF3,
inference(reorient_equations,[],[f38]) ).
fof(f40,definition,
sF4 = join(sF1,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f41,plain,
join(sF1,sF3) = sF4,
inference(reorient_equations,[],[f40]) ).
fof(f42,definition,
sF5 = complement(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f43,plain,
complement(sF4) = sF5,
inference(reorient_equations,[],[f42]) ).
fof(f44,definition,
sF6 = complement(sk1),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f45,plain,
complement(sk1) = sF6,
inference(reorient_equations,[],[f44]) ).
fof(f46,definition,
sF7 = complement(sk3),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f47,plain,
complement(sk3) = sF7,
inference(reorient_equations,[],[f46]) ).
fof(f48,definition,
sF8 = join(sF6,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f49,plain,
join(sF6,sF7) = sF8,
inference(reorient_equations,[],[f48]) ).
fof(f50,definition,
sF9 = complement(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f51,plain,
complement(sF8) = sF9,
inference(reorient_equations,[],[f50]) ).
fof(f52,definition,
sF10 = composition(sF5,sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f53,plain,
composition(sF5,sF9) = sF10,
inference(reorient_equations,[],[f52]) ).
fof(f54,definition,
sF11 = composition(sF5,sk3),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f55,plain,
composition(sF5,sk3) = sF11,
inference(reorient_equations,[],[f54]) ).
fof(f56,plain,
sF10 != sF11,
inference(definition_folding,[],[f30,f55,f43,f41,f39,f37,f35,f53,f51,f49,f47,f45,f43,f41,f39,f37,f35]) ).
fof(f57,plain,
zero = complement(top),
inference(backward_demodulation,[],[f26,f15]) ).
fof(f58,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(backward_demodulation,[],[f4,f1]) ).
fof(f61,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(backward_demodulation,[],[f14,f1]) ).
fof(f62,plain,
sk1 = composition(sk1,top),
inference(forward_demodulation,[],[f32,f33]) ).
fof(f113,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[],[f58,f15]) ).
fof(f114,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f113,f57]) ).
fof(f130,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(superposition,[],[f58,f1]) ).
fof(f154,plain,
complement(top) = join(complement(top),composition(converse(sk1),complement(sk1))),
inference(superposition,[],[f61,f62]) ).
fof(f156,plain,
complement(top) = join(complement(top),composition(converse(sk1),sF6)),
inference(forward_demodulation,[],[f154,f45]) ).
fof(f158,plain,
complement(top) = join(complement(top),composition(sF2,sF6)),
inference(forward_demodulation,[],[f156,f37]) ).
fof(f159,plain,
zero = join(zero,composition(sF2,sF6)),
inference(forward_demodulation,[],[f158,f57]) ).
fof(f167,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f12,f10]) ).
fof(f170,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(f175,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(complement(join(complement(X0),complement(X1))),X2)),
inference(superposition,[],[f2,f58]) ).
fof(f187,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f211,plain,
! [X0,X1] : join(X0,X1) = join(complement(join(complement(X0),complement(X0))),join(complement(top),X1)),
inference(superposition,[],[f175,f15]) ).
fof(f227,plain,
! [X0,X1] : join(X0,X1) = join(complement(top),join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f211,f187]) ).
fof(f239,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f227,f57]) ).
fof(f269,plain,
! [X0] : join(complement(join(complement(X0),top)),complement(join(complement(X0),zero))) = X0,
inference(superposition,[],[f58,f57]) ).
fof(f271,plain,
! [X0] : join(complement(join(complement(X0),top)),complement(join(zero,complement(X0)))) = X0,
inference(forward_demodulation,[],[f269,f1]) ).
fof(f273,plain,
! [X0] : join(complement(join(zero,complement(X0))),complement(join(complement(X0),top))) = X0,
inference(forward_demodulation,[],[f271,f1]) ).
fof(f275,plain,
! [X0] : join(complement(join(zero,complement(X0))),complement(join(top,complement(X0)))) = X0,
inference(forward_demodulation,[],[f273,f1]) ).
fof(f277,plain,
! [X0] : join(complement(join(top,complement(X0))),complement(join(zero,complement(X0)))) = X0,
inference(forward_demodulation,[],[f275,f1]) ).
fof(f320,plain,
! [X0] : complement(X0) = join(complement(join(complement(complement(X0)),X0)),complement(top)),
inference(superposition,[],[f130,f15]) ).
fof(f323,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),X0) = join(X0,complement(join(complement(complement(X1)),complement(X0)))),
inference(superposition,[],[f175,f130]) ).
fof(f332,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = join(X0,complement(join(complement(complement(X1)),complement(X0)))),
inference(forward_demodulation,[],[f323,f1]) ).
fof(f333,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(complement(complement(X0)),X0))),
inference(forward_demodulation,[],[f320,f1]) ).
fof(f357,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f333,f1]) ).
fof(f370,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f357,f57]) ).
fof(f377,plain,
! [X0] : complement(complement(X0)) = X0,
inference(backward_demodulation,[],[f114,f370]) ).
fof(f387,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = join(X0,complement(join(X1,complement(X0)))),
inference(backward_demodulation,[],[f332,f377]) ).
fof(f388,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,X0))),
inference(backward_demodulation,[],[f370,f377]) ).
fof(f402,plain,
! [X0,X1] : join(complement(X0),X1) = join(zero,join(complement(join(X0,X0)),X1)),
inference(superposition,[],[f2,f388]) ).
fof(f404,plain,
top = complement(zero),
inference(superposition,[],[f377,f57]) ).
fof(f406,plain,
sk2 = complement(sF1),
inference(superposition,[],[f377,f35]) ).
fof(f407,plain,
sk3 = complement(sF7),
inference(superposition,[],[f377,f47]) ).
fof(f408,plain,
sF2 = complement(sF3),
inference(superposition,[],[f377,f39]) ).
fof(f412,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(X0,complement(X1)))),
inference(superposition,[],[f58,f377]) ).
fof(f416,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0))),
inference(superposition,[],[f130,f377]) ).
fof(f443,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(X1,complement(X0)))),
inference(superposition,[],[f412,f1]) ).
fof(f530,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,[],[f412,f416]) ).
fof(f533,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,[],[f530,f377]) ).
fof(f548,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,[],[f533,f187]) ).
fof(f561,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,[],[f548,f1]) ).
fof(f573,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f561,f377]) ).
fof(f583,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f573,f377]) ).
fof(f600,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f170,f12]) ).
fof(f608,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f600,f11]) ).
fof(f613,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f608,f11]) ).
fof(f615,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f613,f12]) ).
fof(f620,plain,
! [X0] : complement(complement(join(X0,X0))) = join(complement(complement(X0)),complement(join(complement(join(X0,X0)),complement(zero)))),
inference(superposition,[],[f443,f388]) ).
fof(f629,plain,
complement(sF3) = join(complement(sF4),complement(join(sF3,complement(sF1)))),
inference(superposition,[],[f443,f41]) ).
fof(f647,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,[],[f416,f443]) ).
fof(f656,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,[],[f647,f1]) ).
fof(f664,plain,
complement(sF3) = join(complement(sF4),complement(join(sF3,sk2))),
inference(forward_demodulation,[],[f629,f406]) ).
fof(f670,plain,
! [X0] : complement(complement(join(X0,X0))) = join(complement(complement(X0)),complement(join(complement(zero),complement(join(X0,X0))))),
inference(forward_demodulation,[],[f620,f1]) ).
fof(f674,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,[],[f656,f1]) ).
fof(f681,plain,
complement(sF3) = join(sF5,complement(join(sF3,sk2))),
inference(forward_demodulation,[],[f664,f43]) ).
fof(f686,plain,
! [X0] : complement(complement(join(X0,X0))) = join(complement(complement(X0)),complement(join(top,complement(join(X0,X0))))),
inference(forward_demodulation,[],[f670,f404]) ).
fof(f690,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,[],[f674,f2]) ).
fof(f696,plain,
sF2 = join(sF5,complement(join(sF3,sk2))),
inference(forward_demodulation,[],[f681,f408]) ).
fof(f700,plain,
! [X0] : complement(complement(join(X0,X0))) = join(X0,complement(join(top,complement(join(X0,X0))))),
inference(forward_demodulation,[],[f686,f377]) ).
fof(f704,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f690,f377]) ).
fof(f712,plain,
! [X0] : join(X0,X0) = join(X0,complement(join(top,complement(join(X0,X0))))),
inference(forward_demodulation,[],[f700,f377]) ).
fof(f716,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f704,f377]) ).
fof(f850,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f167,f8]) ).
fof(f865,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f850,f10]) ).
fof(f876,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(one,X0))),
inference(superposition,[],[f61,f865]) ).
fof(f884,plain,
one = converse(one),
inference(superposition,[],[f8,f865]) ).
fof(f887,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f865,f884]) ).
fof(f895,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(backward_demodulation,[],[f876,f887]) ).
fof(f900,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(complement(X0)))),
inference(backward_demodulation,[],[f239,f895]) ).
fof(f902,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,X0)),
inference(forward_demodulation,[],[f900,f377]) ).
fof(f905,plain,
! [X0,X1] : join(complement(X0),X1) = join(X1,complement(join(X0,X0))),
inference(backward_demodulation,[],[f402,f902]) ).
fof(f906,plain,
! [X0] : join(X0,X0) = join(X0,complement(join(complement(X0),top))),
inference(backward_demodulation,[],[f712,f905]) ).
fof(f907,plain,
! [X0] : complement(X0) = join(complement(X0),zero),
inference(backward_demodulation,[],[f388,f905]) ).
fof(f909,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(forward_demodulation,[],[f907,f1]) ).
fof(f910,plain,
! [X0] : join(X0,X0) = join(X0,complement(join(top,complement(X0)))),
inference(forward_demodulation,[],[f906,f387]) ).
fof(f913,plain,
! [X0] : join(complement(join(top,complement(X0))),complement(complement(X0))) = X0,
inference(backward_demodulation,[],[f277,f909]) ).
fof(f918,plain,
! [X0] : join(complement(complement(X0)),complement(join(top,complement(X0)))) = X0,
inference(forward_demodulation,[],[f913,f1]) ).
fof(f920,plain,
! [X0] : join(X0,complement(join(top,complement(X0)))) = X0,
inference(forward_demodulation,[],[f918,f377]) ).
fof(f922,plain,
! [X0] : join(X0,X0) = X0,
inference(backward_demodulation,[],[f910,f920]) ).
fof(f940,plain,
! [X0] : join(zero,X0) = X0,
inference(superposition,[],[f909,f377]) ).
fof(f973,plain,
zero = composition(sF2,sF6),
inference(backward_demodulation,[],[f159,f940]) ).
fof(f992,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1)),
inference(superposition,[],[f2,f922]) ).
fof(f994,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X1,X0)),
inference(superposition,[],[f187,f922]) ).
fof(f1051,plain,
! [X0] : join(X0,zero) = X0,
inference(superposition,[],[f1,f940]) ).
fof(f1163,plain,
! [X0,X1] : complement(X0) = join(complement(join(X1,X0)),complement(X0)),
inference(superposition,[],[f992,f443]) ).
fof(f1208,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0))),
inference(forward_demodulation,[],[f1163,f1]) ).
fof(f1227,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,complement(X1)))),
inference(backward_demodulation,[],[f583,f1208]) ).
fof(f1242,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,X1)))),
inference(backward_demodulation,[],[f716,f1227]) ).
fof(f1252,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f1242,f994]) ).
fof(f1273,plain,
! [X0,X1] : join(X1,complement(join(X0,X1))) = join(X1,complement(X0)),
inference(superposition,[],[f1252,f1]) ).
fof(f1287,plain,
join(sF6,complement(sF7)) = join(sF6,complement(sF8)),
inference(superposition,[],[f1252,f49]) ).
fof(f1317,plain,
join(sF6,complement(sF7)) = join(sF6,sF9),
inference(forward_demodulation,[],[f1287,f51]) ).
fof(f1337,plain,
join(sF6,sk3) = join(sF6,sF9),
inference(forward_demodulation,[],[f1317,f407]) ).
fof(f1460,plain,
! [X0] : composition(join(X0,sF2),sF6) = join(composition(X0,sF6),zero),
inference(superposition,[],[f9,f973]) ).
fof(f1463,plain,
! [X0] : composition(join(X0,sF2),sF6) = join(zero,composition(X0,sF6)),
inference(forward_demodulation,[],[f1460,f1]) ).
fof(f1466,plain,
! [X0] : composition(join(X0,sF2),sF6) = composition(X0,sF6),
inference(forward_demodulation,[],[f1463,f940]) ).
fof(f1510,plain,
join(sF3,complement(sF1)) = join(sF3,complement(sF4)),
inference(superposition,[],[f1273,f41]) ).
fof(f1545,plain,
join(sF3,complement(sF1)) = join(sF3,sF5),
inference(forward_demodulation,[],[f1510,f43]) ).
fof(f1570,plain,
join(sF3,complement(sF1)) = join(sF5,sF3),
inference(forward_demodulation,[],[f1545,f1]) ).
fof(f1591,plain,
join(sF3,sk2) = join(sF5,sF3),
inference(forward_demodulation,[],[f1570,f406]) ).
fof(f1604,plain,
sF2 = join(sF5,complement(join(sF5,sF3))),
inference(backward_demodulation,[],[f696,f1591]) ).
fof(f1610,plain,
sF2 = join(sF5,complement(sF3)),
inference(forward_demodulation,[],[f1604,f1252]) ).
fof(f1615,plain,
sF2 = join(sF5,sF2),
inference(forward_demodulation,[],[f1610,f408]) ).
fof(f3159,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f615]) ).
fof(f3178,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f3159,f10]) ).
fof(f3248,plain,
! [X0] : composition(sF5,join(X0,sF9)) = join(composition(sF5,X0),sF10),
inference(superposition,[],[f3178,f53]) ).
fof(f3278,plain,
! [X0] : join(sF10,composition(sF5,X0)) = composition(sF5,join(X0,sF9)),
inference(forward_demodulation,[],[f3248,f1]) ).
fof(f6031,plain,
composition(sF2,sF6) = composition(sF5,sF6),
inference(superposition,[],[f1466,f1615]) ).
fof(f6060,plain,
zero = composition(sF5,sF6),
inference(forward_demodulation,[],[f6031,f973]) ).
fof(f6073,plain,
! [X0] : composition(sF5,join(sF6,X0)) = join(zero,composition(sF5,X0)),
inference(superposition,[],[f3178,f6060]) ).
fof(f6076,plain,
! [X0] : composition(sF5,X0) = composition(sF5,join(sF6,X0)),
inference(forward_demodulation,[],[f6073,f940]) ).
fof(f6192,plain,
composition(sF5,sk3) = composition(sF5,join(sF6,sF9)),
inference(superposition,[],[f6076,f1337]) ).
fof(f6220,plain,
composition(sF5,sk3) = join(sF10,composition(sF5,sF6)),
inference(forward_demodulation,[],[f6192,f3278]) ).
fof(f6233,plain,
composition(sF5,sk3) = join(sF10,zero),
inference(forward_demodulation,[],[f6220,f6060]) ).
fof(f6253,plain,
sF10 = composition(sF5,sk3),
inference(forward_demodulation,[],[f6233,f1051]) ).
fof(f6260,plain,
sF10 = sF11,
inference(backward_demodulation,[],[f55,f6253]) ).
fof(f6261,plain,
$false,
inference(forward_subsumption_resolution,[],[f6260,f56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL037-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n017.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 22:51:20 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.79/3.70 % (3045687)Detected a unit-equality problem, will run specialized UEQ schedule.
% 19.79/3.70 % (3045770)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3962097621:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 19.79/3.70 % (3045757)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=4204619807:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 19.79/3.70 % (3045765)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2311141997:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 19.79/3.70 % (3045766)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3533900299:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 19.79/3.70 % (3045764)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=2462022687:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 20.46/3.70 % (3045767)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=175888378:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 20.46/3.70 % (3045768)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3916651104:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 20.46/3.70 % (3045766)Instruction limit reached!
% 20.46/3.70 % (3045766)------------------------------
% 20.46/3.70 % (3045766)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.46/3.70 % (3045766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.46/3.70 % (3045766)CaDiCaL version: 2.1.3
% 20.46/3.70 % (3045766)Termination reason: Instruction limit
% 20.46/3.70 % (3045766)Termination phase: Saturation
% 20.46/3.70 % (3045766)Time elapsed: 0.142 s
% 20.46/3.70 % (3045766)Peak memory usage: 89 MB
% 20.46/3.70 % (3045766)Instructions burned: 136 (million)
% 20.46/3.70 % (3045767)Instruction limit reached!
% 20.46/3.70 % (3045767)------------------------------
% 20.46/3.70 % (3045767)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.46/3.70 % (3045767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.46/3.70 % (3045767)CaDiCaL version: 2.1.3
% 20.46/3.70 % (3045767)Termination reason: Instruction limit
% 20.46/3.70 % (3045767)Termination phase: Saturation
% 20.46/3.70 % (3045767)Time elapsed: 0.182 s
% 20.46/3.70 % (3045767)Peak memory usage: 90 MB
% 20.46/3.70 % (3045767)Instructions burned: 181 (million)
% 20.46/3.70 % (3045768)Instruction limit reached!
% 20.46/3.70 % (3045768)------------------------------
% 20.46/3.70 % (3045768)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.46/3.70 % (3045768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.46/3.70 % (3045768)CaDiCaL version: 2.1.3
% 20.46/3.70 % (3045768)Termination reason: Instruction limit
% 20.46/3.70 % (3045768)Termination phase: Saturation
% 20.46/3.70 % (3045768)Time elapsed: 0.278 s
% 20.46/3.70 % (3045768)Peak memory usage: 91 MB
% 20.46/3.70 % (3045768)Instructions burned: 258 (million)
% 20.46/3.70 % (3045797)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2287143867:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2995 on theBenchmark for (2995ds/2051Mi)
% 20.46/3.70 % (3045799)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3593672892:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 20.46/3.70 % (3045770)Instruction limit reached!
% 20.46/3.70 % (3045770)------------------------------
% 20.46/3.70 % (3045770)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.46/3.70 % (3045770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.46/3.70 % (3045770)CaDiCaL version: 2.1.3
% 20.46/3.70 % (3045770)Termination reason: Instruction limit
% 20.46/3.70 % (3045770)Termination phase: Saturation
% 20.46/3.70 % (3045770)Time elapsed: 0.589 s
% 20.46/3.70 % (3045770)Peak memory usage: 102 MB
% 20.46/3.70 % (3045770)Instructions burned: 1189 (million)
% 20.46/3.70 % (3045800)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2743690471:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 20.46/3.70 % (3045807)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=3377206383:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2992 on theBenchmark for (2992ds/317Mi)
% 20.46/3.70 % (3045800)Instruction limit reached!
% 20.46/3.70 % (3045800)------------------------------
% 20.46/3.70 % (3045800)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.46/3.70 % (3045800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.46/3.70 % (3045800)CaDiCaL version: 2.1.3
% 20.46/3.70 % (3045800)Termination reason: Instruction limit
% 20.46/3.70 % (3045800)Termination phase: Saturation
% 20.46/3.70 % (3045800)Time elapsed: 0.215 s
% 20.46/3.70 % (3045800)Peak memory usage: 92 MB
% 20.46/3.70 % (3045800)Instructions burned: 215 (million)
% 20.46/3.70 % (3045807)Instruction limit reached!
% 20.46/3.70 % (3045807)------------------------------
% 20.46/3.70 % (3045807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.46/3.70 % (3045807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.46/3.70 % (3045807)CaDiCaL version: 2.1.3
% 20.46/3.70 % (3045807)Termination reason: Instruction limit
% 20.46/3.70 % (3045807)Termination phase: Saturation
% 20.46/3.70 % (3045807)Time elapsed: 0.171 s
% 20.46/3.70 % (3045807)Peak memory usage: 93 MB
% 20.46/3.70 % (3045807)Instructions burned: 319 (million)
% 20.46/3.70 % (3045814)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=4211532785:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2989 on theBenchmark for (2989ds/12125Mi)
% 20.46/3.70 % (3045815)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=371849868:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2988 on theBenchmark for (2988ds/2836Mi)
% 20.46/3.70 % (3045765)First to succeed.
% 20.46/3.70 % (3045765)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3045687"
% 20.46/3.70 % (3045757)Also succeeded, but the first one will report.
% 20.46/3.70 % (3045797)Instruction limit reached!
% 20.46/3.70 % (3045797)------------------------------
% 20.46/3.70 % (3045797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.46/3.70 % (3045797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.46/3.70 % (3045797)CaDiCaL version: 2.1.3
% 20.46/3.70 % (3045797)Termination reason: Instruction limit
% 20.46/3.70 % (3045797)Termination phase: Saturation
% 20.46/3.70 % (3045797)Time elapsed: 2.133 s
% 20.46/3.70 % (3045797)Peak memory usage: 140 MB
% 20.46/3.70 % (3045797)Instructions burned: 2051 (million)
% 20.46/3.70 % (3045765)Refutation found. Thanks to Tanya!
% 20.46/3.70 % SZS status Unsatisfiable for theBenchmark
% 20.46/3.70 % SZS output start Proof for theBenchmark
% See solution above
% 20.66/3.96 % (3045765)------------------------------
% 20.66/3.96 % (3045765)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.66/3.96 % (3045765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.66/3.96 % (3045765)CaDiCaL version: 2.1.3
% 20.66/3.96 % (3045765)Termination reason: Refutation
% 20.66/3.96 % (3045765)Time elapsed: 2.125 s
% 20.66/3.96 % (3045765)Peak memory usage: 139 MB
% 20.66/3.96 % (3045765)Instructions burned: 1989 (million)
% 20.66/3.96 % (3045765)------------------------------
% 20.66/3.96 % (3045765)------------------------------
% 20.66/3.96 % (3045687)Success in time 2.838 s
% 20.66/3.96 % Vampire exiting
%------------------------------------------------------------------------------