%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL044-1 : 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 : n008.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 12:34:06 PM UTC 2026
% Result : Unsatisfiable 15.98s 3.56s
% Output : Refutation 16.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 21
% Syntax : Number of formulae : 142 ( 142 unt; 7 def)
% Number of atoms : 142 ( 141 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 : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 13 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/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(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(f17,negated_conjecture,
join(composition(complement(sk1),sk2),complement(sk3)) = complement(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).
fof(f18,plain,
complement(sk3) = join(composition(complement(sk1),sk2),complement(sk3)),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
join(composition(sk3,converse(sk2)),sk1) != sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_15) ).
fof(f20,plain,
sk1 != join(composition(sk3,converse(sk2)),sk1),
inference(reorient_equations,[],[f19]) ).
fof(f21,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f22,definition,
sF0 = complement(sk3),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f23,plain,
complement(sk3) = sF0,
inference(reorient_equations,[],[f22]) ).
fof(f24,definition,
sF1 = complement(sk1),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f25,plain,
complement(sk1) = sF1,
inference(reorient_equations,[],[f24]) ).
fof(f26,definition,
sF2 = composition(sF1,sk2),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f27,plain,
composition(sF1,sk2) = sF2,
inference(reorient_equations,[],[f26]) ).
fof(f28,definition,
sF3 = join(sF2,sF0),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f29,plain,
join(sF2,sF0) = sF3,
inference(reorient_equations,[],[f28]) ).
fof(f30,plain,
sF0 = sF3,
inference(definition_folding,[],[f18,f29,f23,f27,f25,f23]) ).
fof(f31,definition,
sF4 = converse(sk2),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f32,plain,
converse(sk2) = sF4,
inference(reorient_equations,[],[f31]) ).
fof(f33,definition,
sF5 = composition(sk3,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f34,plain,
composition(sk3,sF4) = sF5,
inference(reorient_equations,[],[f33]) ).
fof(f35,definition,
sF6 = join(sF5,sk1),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f36,plain,
join(sF5,sk1) = sF6,
inference(reorient_equations,[],[f35]) ).
fof(f37,plain,
sk1 != sF6,
inference(definition_folding,[],[f20,f36,f34,f32]) ).
fof(f38,plain,
zero = complement(top),
inference(backward_demodulation,[],[f21,f15]) ).
fof(f39,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(backward_demodulation,[],[f14,f1]) ).
fof(f40,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(backward_demodulation,[],[f4,f1]) ).
fof(f41,plain,
sF0 = join(sF2,sF0),
inference(forward_demodulation,[],[f29,f30]) ).
fof(f64,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[],[f40,f15]) ).
fof(f65,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f64,f38]) ).
fof(f79,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(superposition,[],[f40,f1]) ).
fof(f88,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(X0,complement(composition(converse(X0),X1)))),
inference(superposition,[],[f39,f10]) ).
fof(f90,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[],[f11,f10]) ).
fof(f94,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f12,f10]) ).
fof(f98,plain,
! [X0] : composition(join(sk3,X0),sF4) = join(sF5,composition(X0,sF4)),
inference(superposition,[],[f9,f34]) ).
fof(f117,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f2,f15]) ).
fof(f119,plain,
! [X2,X0,X1] : join(join(X0,X1),X2) = join(X1,join(X0,X2)),
inference(superposition,[],[f2,f1]) ).
fof(f121,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(complement(join(complement(X0),complement(X1))),X2)),
inference(superposition,[],[f2,f40]) ).
fof(f132,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f148,plain,
! [X0,X1] : join(X0,X1) = join(complement(join(complement(X0),complement(X0))),join(complement(top),X1)),
inference(superposition,[],[f121,f15]) ).
fof(f164,plain,
! [X0,X1] : join(X0,X1) = join(complement(top),join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f148,f132]) ).
fof(f173,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f164,f38]) ).
fof(f220,plain,
! [X0] : complement(X0) = join(complement(join(complement(complement(X0)),X0)),complement(top)),
inference(superposition,[],[f79,f15]) ).
fof(f233,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(complement(complement(X0)),X0))),
inference(forward_demodulation,[],[f220,f1]) ).
fof(f249,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f233,f1]) ).
fof(f258,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f249,f38]) ).
fof(f263,plain,
! [X0] : complement(complement(X0)) = X0,
inference(backward_demodulation,[],[f65,f258]) ).
fof(f274,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,X0))),
inference(backward_demodulation,[],[f258,f263]) ).
fof(f288,plain,
! [X0,X1] : join(complement(X0),X1) = join(zero,join(complement(join(X0,X0)),X1)),
inference(superposition,[],[f2,f274]) ).
fof(f291,plain,
sk1 = complement(sF1),
inference(superposition,[],[f263,f25]) ).
fof(f292,plain,
sk3 = complement(sF0),
inference(superposition,[],[f263,f23]) ).
fof(f295,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(X0,complement(X1)))),
inference(superposition,[],[f40,f263]) ).
fof(f298,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0))),
inference(superposition,[],[f79,f263]) ).
fof(f320,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(X1,complement(X0)))),
inference(superposition,[],[f295,f1]) ).
fof(f327,plain,
complement(sF2) = join(complement(sF0),complement(join(sF2,complement(sF0)))),
inference(superposition,[],[f295,f41]) ).
fof(f338,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(join(complement(join(X0,X1)),join(X0,complement(X1)))),complement(complement(X0))),
inference(superposition,[],[f295,f295]) ).
fof(f342,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(complement(join(X0,X1)),join(X0,complement(X1))))),
inference(forward_demodulation,[],[f338,f1]) ).
fof(f349,plain,
complement(sF2) = join(sk3,complement(join(sF2,sk3))),
inference(forward_demodulation,[],[f327,f292]) ).
fof(f357,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(join(X0,complement(X1)),complement(join(X0,X1))))),
inference(forward_demodulation,[],[f342,f1]) ).
fof(f364,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,[],[f357,f2]) ).
fof(f367,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f364,f263]) ).
fof(f369,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f367,f263]) ).
fof(f373,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(complement(X0),X1))),
inference(superposition,[],[f298,f1]) ).
fof(f503,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f94,f8]) ).
fof(f517,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f503,f10]) ).
fof(f528,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(one,X0))),
inference(superposition,[],[f39,f517]) ).
fof(f536,plain,
one = converse(one),
inference(superposition,[],[f8,f517]) ).
fof(f539,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f517,f536]) ).
fof(f547,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(backward_demodulation,[],[f528,f539]) ).
fof(f552,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(complement(X0)))),
inference(backward_demodulation,[],[f173,f547]) ).
fof(f554,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,X0)),
inference(forward_demodulation,[],[f552,f263]) ).
fof(f556,plain,
! [X0,X1] : join(complement(X0),X1) = join(X1,complement(join(X0,X0))),
inference(backward_demodulation,[],[f288,f554]) ).
fof(f557,plain,
! [X0] : complement(X0) = join(complement(X0),zero),
inference(backward_demodulation,[],[f274,f556]) ).
fof(f559,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(forward_demodulation,[],[f557,f1]) ).
fof(f584,plain,
! [X0] : join(zero,X0) = X0,
inference(superposition,[],[f559,f263]) ).
fof(f623,plain,
! [X0] : join(X0,zero) = X0,
inference(superposition,[],[f1,f584]) ).
fof(f635,plain,
! [X0] : join(X0,X0) = X0,
inference(superposition,[],[f547,f263]) ).
fof(f675,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1)),
inference(superposition,[],[f2,f635]) ).
fof(f771,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X1,X0)),
inference(superposition,[],[f132,f635]) ).
fof(f800,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(X1,top),
inference(superposition,[],[f132,f15]) ).
fof(f894,plain,
! [X0] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[],[f90,f15]) ).
fof(f1033,plain,
! [X0] : top = join(X0,top),
inference(superposition,[],[f675,f15]) ).
fof(f1084,plain,
! [X0,X1] : top = join(X0,join(complement(X0),X1)),
inference(backward_demodulation,[],[f800,f1033]) ).
fof(f1101,plain,
! [X1] : top = join(top,X1),
inference(backward_demodulation,[],[f117,f1084]) ).
fof(f1253,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,[],[f298,f320]) ).
fof(f1261,plain,
! [X0,X1] : complement(X0) = join(complement(join(X1,X0)),complement(X0)),
inference(superposition,[],[f675,f320]) ).
fof(f1262,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0))),
inference(forward_demodulation,[],[f1261,f1]) ).
fof(f1269,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,[],[f1253,f1]) ).
fof(f1290,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,complement(X1)))),
inference(backward_demodulation,[],[f369,f1262]) ).
fof(f1297,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,[],[f1269,f1]) ).
fof(f1315,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,[],[f1297,f2]) ).
fof(f1329,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(X1,join(X0,X1)))),
inference(forward_demodulation,[],[f1315,f1290]) ).
fof(f1341,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(X0,X1))),
inference(forward_demodulation,[],[f1329,f771]) ).
fof(f1350,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f1341,f263]) ).
fof(f1356,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f1350,f263]) ).
fof(f1374,plain,
! [X0,X1] : join(X1,complement(join(X0,X1))) = join(X1,complement(X0)),
inference(superposition,[],[f1356,f1]) ).
fof(f1442,plain,
complement(sF2) = join(sk3,complement(sF2)),
inference(backward_demodulation,[],[f349,f1374]) ).
fof(f2978,plain,
composition(complement(sF2),sF4) = join(sF5,composition(complement(sF2),sF4)),
inference(superposition,[],[f98,f1442]) ).
fof(f5441,plain,
! [X0] : join(X0,complement(converse(complement(converse(X0))))) = join(X0,complement(converse(top))),
inference(superposition,[],[f1356,f894]) ).
fof(f5452,plain,
top = converse(top),
inference(superposition,[],[f1101,f894]) ).
fof(f5490,plain,
! [X0] : join(X0,complement(top)) = join(X0,complement(converse(complement(converse(X0))))),
inference(forward_demodulation,[],[f5441,f5452]) ).
fof(f5534,plain,
! [X0] : join(X0,zero) = join(X0,complement(converse(complement(converse(X0))))),
inference(forward_demodulation,[],[f5490,f38]) ).
fof(f5557,plain,
! [X0] : join(X0,complement(converse(complement(converse(X0))))) = X0,
inference(forward_demodulation,[],[f5534,f623]) ).
fof(f5737,plain,
! [X0] : complement(complement(converse(complement(converse(complement(X0)))))) = join(complement(join(X0,complement(converse(complement(converse(complement(X0))))))),complement(complement(X0))),
inference(superposition,[],[f373,f5557]) ).
fof(f5741,plain,
! [X0] : converse(converse(X0)) = join(X0,converse(complement(converse(complement(converse(converse(X0))))))),
inference(superposition,[],[f90,f5557]) ).
fof(f5765,plain,
! [X0] : join(X0,converse(complement(converse(complement(X0))))) = X0,
inference(forward_demodulation,[],[f5741,f10]) ).
fof(f5769,plain,
! [X0] : complement(complement(converse(complement(converse(complement(X0)))))) = join(complement(complement(X0)),complement(join(X0,complement(converse(complement(converse(complement(X0)))))))),
inference(forward_demodulation,[],[f5737,f1]) ).
fof(f5796,plain,
! [X0] : complement(complement(converse(complement(converse(complement(X0)))))) = join(X0,complement(join(X0,complement(converse(complement(converse(complement(X0)))))))),
inference(forward_demodulation,[],[f5769,f263]) ).
fof(f5807,plain,
! [X0] : complement(complement(converse(complement(converse(complement(X0)))))) = join(X0,complement(complement(converse(complement(converse(complement(X0))))))),
inference(forward_demodulation,[],[f5796,f1356]) ).
fof(f5810,plain,
! [X0] : converse(complement(converse(complement(X0)))) = join(X0,converse(complement(converse(complement(X0))))),
inference(forward_demodulation,[],[f5807,f263]) ).
fof(f5811,plain,
! [X0] : converse(complement(converse(complement(X0)))) = X0,
inference(forward_demodulation,[],[f5810,f5765]) ).
fof(f5817,plain,
! [X0] : complement(X0) = converse(complement(converse(X0))),
inference(superposition,[],[f5811,f263]) ).
fof(f5965,plain,
! [X0] : complement(converse(X0)) = converse(complement(X0)),
inference(superposition,[],[f10,f5817]) ).
fof(f5966,plain,
! [X0,X1] : converse(join(complement(converse(X0)),X1)) = join(complement(X0),converse(X1)),
inference(superposition,[],[f11,f5817]) ).
fof(f5969,plain,
! [X0,X1] : converse(composition(X1,complement(converse(X0)))) = composition(complement(X0),converse(X1)),
inference(superposition,[],[f12,f5817]) ).
fof(f6572,plain,
! [X0,X1] : converse(complement(converse(X0))) = join(complement(X0),converse(composition(X1,complement(composition(converse(X1),converse(X0)))))),
inference(superposition,[],[f5966,f88]) ).
fof(f6640,plain,
! [X0,X1] : converse(complement(converse(X0))) = join(complement(X0),converse(composition(X1,complement(converse(composition(X0,X1)))))),
inference(forward_demodulation,[],[f6572,f12]) ).
fof(f6673,plain,
! [X0,X1] : converse(complement(converse(X0))) = join(complement(X0),composition(complement(composition(X0,X1)),converse(X1))),
inference(forward_demodulation,[],[f6640,f5969]) ).
fof(f6693,plain,
! [X0,X1] : complement(converse(converse(X0))) = join(complement(X0),composition(complement(composition(X0,X1)),converse(X1))),
inference(forward_demodulation,[],[f6673,f5965]) ).
fof(f6704,plain,
! [X0,X1] : complement(X0) = join(complement(X0),composition(complement(composition(X0,X1)),converse(X1))),
inference(forward_demodulation,[],[f6693,f10]) ).
fof(f7990,plain,
complement(sF1) = join(complement(sF1),composition(complement(sF2),converse(sk2))),
inference(superposition,[],[f6704,f27]) ).
fof(f8048,plain,
complement(sF1) = join(complement(sF1),composition(complement(sF2),sF4)),
inference(forward_demodulation,[],[f7990,f32]) ).
fof(f8077,plain,
sk1 = join(sk1,composition(complement(sF2),sF4)),
inference(forward_demodulation,[],[f8048,f291]) ).
fof(f8107,plain,
! [X0] : join(sk1,X0) = join(composition(complement(sF2),sF4),join(sk1,X0)),
inference(superposition,[],[f119,f8077]) ).
fof(f8127,plain,
! [X0] : join(sk1,X0) = join(sk1,join(X0,composition(complement(sF2),sF4))),
inference(forward_demodulation,[],[f8107,f132]) ).
fof(f8169,plain,
join(sk1,sF5) = join(sk1,composition(complement(sF2),sF4)),
inference(superposition,[],[f8127,f2978]) ).
fof(f8216,plain,
sk1 = join(sk1,sF5),
inference(forward_demodulation,[],[f8169,f8077]) ).
fof(f8233,plain,
sk1 = join(sF5,sk1),
inference(forward_demodulation,[],[f8216,f1]) ).
fof(f8238,plain,
sk1 = sF6,
inference(backward_demodulation,[],[f36,f8233]) ).
fof(f8240,plain,
$false,
inference(forward_subsumption_resolution,[],[f8238,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL044-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.48 % Computer : n008.cluster.edu
% 0.23/0.48 % Model : x86_64 x86_64
% 0.23/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.48 % Memory : 8046.5625MB
% 0.23/0.48 % OS : Linux 6.8.0-71-generic
% 0.23/0.48 % CPULimit : 300
% 0.23/0.48 % WCLimit : 300
% 0.23/0.48 % DateTime : Sun Sep 27 22:57:39 UTC 2026
% 0.23/0.48 % CPUTime :
% 0.23/0.48 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.28/0.54 Running first-order theorem proving
% 0.28/0.54 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
% 15.98/3.56 % (1704410)Detected a unit-equality problem, will run specialized UEQ schedule.
% 15.98/3.56 % (1704418)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3913710308:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 15.98/3.56 % (1704415)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=845995829:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 15.98/3.56 % (1704416)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=3704801465:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 15.98/3.56 % (1704418)Instruction limit reached!
% 15.98/3.56 % (1704418)------------------------------
% 15.98/3.56 % (1704418)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.98/3.56 % (1704418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.98/3.56 % (1704418)CaDiCaL version: 2.1.3
% 15.98/3.56 % (1704418)Termination reason: Instruction limit
% 15.98/3.56 % (1704418)Termination phase: Saturation
% 15.98/3.56 % (1704418)Time elapsed: 0.075 s
% 15.98/3.56 % (1704418)Peak memory usage: 89 MB
% 15.98/3.56 % (1704418)Instructions burned: 136 (million)
% 15.98/3.56 % (1704421)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3434667798:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 15.98/3.56 % (1704419)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3663412376:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 15.98/3.56 % (1704417)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2956867584:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 15.98/3.56 % (1704420)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1020871622:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 15.98/3.56 % (1704419)Instruction limit reached!
% 15.98/3.56 % (1704419)------------------------------
% 15.98/3.56 % (1704419)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.98/3.56 % (1704419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.98/3.56 % (1704419)CaDiCaL version: 2.1.3
% 15.98/3.56 % (1704419)Termination reason: Instruction limit
% 15.98/3.56 % (1704419)Termination phase: Saturation
% 15.98/3.56 % (1704419)Time elapsed: 0.182 s
% 15.98/3.56 % (1704419)Peak memory usage: 89 MB
% 15.98/3.56 % (1704419)Instructions burned: 182 (million)
% 15.98/3.56 % (1704425)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3529534889:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 15.98/3.56 % (1704420)Instruction limit reached!
% 15.98/3.56 % (1704420)------------------------------
% 15.98/3.56 % (1704420)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.98/3.56 % (1704420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.98/3.56 % (1704420)CaDiCaL version: 2.1.3
% 15.98/3.56 % (1704420)Termination reason: Instruction limit
% 15.98/3.56 % (1704420)Termination phase: Saturation
% 15.98/3.56 % (1704420)Time elapsed: 0.284 s
% 15.98/3.56 % (1704420)Peak memory usage: 90 MB
% 15.98/3.56 % (1704420)Instructions burned: 258 (million)
% 15.98/3.56 % (1704430)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2089888605:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 15.98/3.56 % (1704432)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3003372534:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 15.98/3.56 % (1704432)Instruction limit reached!
% 15.98/3.56 % (1704432)------------------------------
% 15.98/3.56 % (1704432)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.98/3.56 % (1704432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.98/3.56 % (1704432)CaDiCaL version: 2.1.3
% 15.98/3.56 % (1704432)Termination reason: Instruction limit
% 15.98/3.56 % (1704432)Termination phase: Saturation
% 15.98/3.56 % (1704432)Time elapsed: 0.204 s
% 15.98/3.56 % (1704432)Peak memory usage: 92 MB
% 15.98/3.56 % (1704432)Instructions burned: 215 (million)
% 15.98/3.56 % (1704435)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=4088341506:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2989 on theBenchmark for (2989ds/317Mi)
% 15.98/3.56 % (1704421)Instruction limit reached!
% 15.98/3.56 % (1704421)------------------------------
% 15.98/3.56 % (1704421)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.98/3.56 % (1704421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.98/3.56 % (1704421)CaDiCaL version: 2.1.3
% 15.98/3.56 % (1704421)Termination reason: Instruction limit
% 15.98/3.56 % (1704421)Termination phase: Saturation
% 15.98/3.56 % (1704421)Time elapsed: 1.091 s
% 15.98/3.56 % (1704421)Peak memory usage: 99 MB
% 15.98/3.56 % (1704421)Instructions burned: 1187 (million)
% 15.98/3.56 % (1704437)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=777779347:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2986 on theBenchmark for (2986ds/12125Mi)
% 15.98/3.56 % (1704435)Instruction limit reached!
% 15.98/3.56 % (1704435)------------------------------
% 15.98/3.56 % (1704435)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.98/3.56 % (1704435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.98/3.56 % (1704435)CaDiCaL version: 2.1.3
% 15.98/3.56 % (1704435)Termination reason: Instruction limit
% 15.98/3.56 % (1704435)Termination phase: Saturation
% 15.98/3.56 % (1704435)Time elapsed: 0.194 s
% 15.98/3.56 % (1704435)Peak memory usage: 93 MB
% 15.98/3.56 % (1704435)Instructions burned: 317 (million)
% 15.98/3.56 % (1704489)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=4223709441:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2984 on theBenchmark for (2984ds/2836Mi)
% 15.98/3.56 % (1704417)First to succeed.
% 15.98/3.56 % (1704417)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1704410"
% 15.98/3.56 % (1704425)Instruction limit reached!
% 15.98/3.56 % (1704425)------------------------------
% 15.98/3.56 % (1704425)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.98/3.56 % (1704425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.98/3.56 % (1704425)CaDiCaL version: 2.1.3
% 15.98/3.56 % (1704425)Termination reason: Instruction limit
% 15.98/3.56 % (1704425)Termination phase: Saturation
% 15.98/3.56 % (1704425)Time elapsed: 1.445 s
% 15.98/3.56 % (1704425)Peak memory usage: 141 MB
% 15.98/3.56 % (1704425)Instructions burned: 2052 (million)
% 15.98/3.56 % (1704593)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=94111277:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2980 on theBenchmark for (2980ds/14534Mi)
% 15.98/3.56 % (1704417)Refutation found. Thanks to Tanya!
% 15.98/3.56 % SZS status Unsatisfiable for theBenchmark
% 15.98/3.56 % SZS output start Proof for theBenchmark
% See solution above
% 16.75/3.76 % (1704417)------------------------------
% 16.75/3.76 % (1704417)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.75/3.76 % (1704417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.75/3.76 % (1704417)CaDiCaL version: 2.1.3
% 16.75/3.76 % (1704417)Termination reason: Refutation
% 16.75/3.76 % (1704417)Time elapsed: 1.646 s
% 16.75/3.76 % (1704417)Peak memory usage: 137 MB
% 16.75/3.76 % (1704417)Instructions burned: 1896 (million)
% 16.75/3.76 % (1704417)------------------------------
% 16.75/3.76 % (1704417)------------------------------
% 16.75/3.76 % (1704410)Success in time 2.237 s
% 16.75/3.76 % Vampire exiting
%------------------------------------------------------------------------------