%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL043-2 : 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 : n019.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 25.13s 4.77s
% Output : Refutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 22
% Syntax : Number of formulae : 150 ( 150 unt; 7 def)
% Number of atoms : 150 ( 149 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 : 18 ( 18 usr; 13 con; 0-2 aty)
% Number of variables : 177 ( 177 !; 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(f17,axiom,
! [X2,X0,X1] : join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dedekind_law_14) ).
fof(f18,plain,
! [X2,X0,X1] : composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))) = join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))),
inference(reorient_equations,[],[f17]) ).
fof(f23,negated_conjecture,
join(composition(sk1,converse(sk2)),sk3) = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
fof(f24,plain,
sk3 = join(composition(sk1,converse(sk2)),sk3),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
join(composition(complement(sk3),sk2),complement(sk1)) != complement(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_18) ).
fof(f26,plain,
complement(sk1) != join(composition(complement(sk3),sk2),complement(sk1)),
inference(reorient_equations,[],[f25]) ).
fof(f27,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f28,plain,
! [X2,X0,X1] : composition(complement(join(complement(X0),complement(composition(X2,converse(X1))))),complement(join(complement(X1),complement(composition(converse(X0),X2))))) = join(complement(join(complement(composition(X0,X1)),complement(X2))),composition(complement(join(complement(X0),complement(composition(X2,converse(X1))))),complement(join(complement(X1),complement(composition(converse(X0),X2)))))),
inference(definition_unfolding,[],[f18,f6,f6,f6,f6,f6]) ).
fof(f31,definition,
sF0 = converse(sk2),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f32,plain,
converse(sk2) = sF0,
inference(reorient_equations,[],[f31]) ).
fof(f33,definition,
sF1 = composition(sk1,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f34,plain,
composition(sk1,sF0) = sF1,
inference(reorient_equations,[],[f33]) ).
fof(f35,definition,
sF2 = join(sF1,sk3),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f36,plain,
join(sF1,sk3) = sF2,
inference(reorient_equations,[],[f35]) ).
fof(f37,plain,
sk3 = sF2,
inference(definition_folding,[],[f24,f36,f34,f32]) ).
fof(f38,definition,
sF3 = complement(sk1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f39,plain,
complement(sk1) = sF3,
inference(reorient_equations,[],[f38]) ).
fof(f40,definition,
sF4 = complement(sk3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f41,plain,
complement(sk3) = sF4,
inference(reorient_equations,[],[f40]) ).
fof(f42,definition,
sF5 = composition(sF4,sk2),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f43,plain,
composition(sF4,sk2) = sF5,
inference(reorient_equations,[],[f42]) ).
fof(f44,definition,
sF6 = join(sF5,sF3),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f45,plain,
join(sF5,sF3) = sF6,
inference(reorient_equations,[],[f44]) ).
fof(f46,plain,
sF3 != sF6,
inference(definition_folding,[],[f26,f45,f39,f43,f41,f39]) ).
fof(f47,plain,
zero = complement(top),
inference(backward_demodulation,[],[f27,f15]) ).
fof(f48,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(backward_demodulation,[],[f4,f1]) ).
fof(f51,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(backward_demodulation,[],[f14,f1]) ).
fof(f52,plain,
sk3 = join(sF1,sk3),
inference(forward_demodulation,[],[f36,f37]) ).
fof(f76,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[],[f48,f15]) ).
fof(f77,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f76,f47]) ).
fof(f88,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(superposition,[],[f48,f1]) ).
fof(f91,plain,
! [X0,X1] : converse(join(X1,converse(X0))) = join(converse(X1),X0),
inference(superposition,[],[f11,f10]) ).
fof(f113,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f12,f10]) ).
fof(f118,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f2,f15]) ).
fof(f122,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(complement(join(complement(X0),complement(X1))),X2)),
inference(superposition,[],[f2,f48]) ).
fof(f133,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f149,plain,
! [X0,X1] : join(X0,X1) = join(complement(join(complement(X0),complement(X0))),join(complement(top),X1)),
inference(superposition,[],[f122,f15]) ).
fof(f165,plain,
! [X0,X1] : join(X0,X1) = join(complement(top),join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f149,f133]) ).
fof(f173,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f165,f47]) ).
fof(f187,plain,
! [X0] : zero = join(zero,composition(converse(X0),complement(composition(X0,top)))),
inference(superposition,[],[f51,f47]) ).
fof(f259,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(X1,top),
inference(superposition,[],[f133,f15]) ).
fof(f334,plain,
! [X0] : complement(X0) = join(complement(join(complement(complement(X0)),X0)),complement(top)),
inference(superposition,[],[f88,f15]) ).
fof(f350,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(complement(complement(X0)),X0))),
inference(forward_demodulation,[],[f334,f1]) ).
fof(f366,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f350,f1]) ).
fof(f375,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f366,f47]) ).
fof(f380,plain,
! [X0] : complement(complement(X0)) = X0,
inference(backward_demodulation,[],[f77,f375]) ).
fof(f391,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,X0))),
inference(backward_demodulation,[],[f375,f380]) ).
fof(f403,plain,
! [X0,X1] : complement(join(X1,X0)) = join(zero,complement(join(X0,join(join(X1,X0),X1)))),
inference(superposition,[],[f391,f133]) ).
fof(f409,plain,
! [X0,X1] : join(complement(X0),X1) = join(zero,join(complement(join(X0,X0)),X1)),
inference(superposition,[],[f2,f391]) ).
fof(f412,plain,
! [X0,X1] : complement(join(X1,X0)) = join(zero,complement(join(X0,join(X1,join(X0,X1))))),
inference(forward_demodulation,[],[f403,f2]) ).
fof(f414,plain,
sk1 = complement(sF3),
inference(superposition,[],[f380,f39]) ).
fof(f415,plain,
sk3 = complement(sF4),
inference(superposition,[],[f380,f41]) ).
fof(f417,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(X0,complement(X1)))),
inference(superposition,[],[f48,f380]) ).
fof(f421,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0))),
inference(superposition,[],[f88,f380]) ).
fof(f442,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(X1,complement(X0)))),
inference(superposition,[],[f417,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,[],[f417,f421]) ).
fof(f531,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,f380]) ).
fof(f553,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,[],[f531,f133]) ).
fof(f567,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,[],[f553,f1]) ).
fof(f577,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f567,f380]) ).
fof(f585,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f577,f380]) ).
fof(f666,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f113,f8]) ).
fof(f681,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f666,f10]) ).
fof(f692,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(one,X0))),
inference(superposition,[],[f51,f681]) ).
fof(f698,plain,
! [X0,X1] : composition(join(X1,converse(one)),X0) = join(composition(X1,X0),X0),
inference(superposition,[],[f9,f681]) ).
fof(f699,plain,
! [X0,X1] : composition(join(converse(one),X1),X0) = join(X0,composition(X1,X0)),
inference(superposition,[],[f9,f681]) ).
fof(f700,plain,
one = converse(one),
inference(superposition,[],[f8,f681]) ).
fof(f703,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f681,f700]) ).
fof(f705,plain,
! [X0,X1] : join(X0,composition(X1,X0)) = composition(join(one,X1),X0),
inference(forward_demodulation,[],[f699,f700]) ).
fof(f706,plain,
! [X0,X1] : composition(join(X1,converse(one)),X0) = join(X0,composition(X1,X0)),
inference(forward_demodulation,[],[f698,f1]) ).
fof(f711,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(backward_demodulation,[],[f692,f703]) ).
fof(f712,plain,
! [X0,X1] : join(X0,composition(X1,X0)) = composition(join(X1,one),X0),
inference(forward_demodulation,[],[f706,f700]) ).
fof(f716,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(complement(X0)))),
inference(backward_demodulation,[],[f173,f711]) ).
fof(f718,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,X0)),
inference(forward_demodulation,[],[f716,f380]) ).
fof(f721,plain,
! [X0,X1] : join(complement(X0),X1) = join(X1,complement(join(X0,X0))),
inference(backward_demodulation,[],[f409,f718]) ).
fof(f722,plain,
! [X0] : complement(X0) = join(complement(X0),zero),
inference(backward_demodulation,[],[f391,f721]) ).
fof(f724,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(forward_demodulation,[],[f722,f1]) ).
fof(f728,plain,
! [X0,X1] : complement(join(X1,X0)) = complement(join(X0,join(X1,join(X0,X1)))),
inference(backward_demodulation,[],[f412,f724]) ).
fof(f750,plain,
! [X0] : join(zero,X0) = X0,
inference(superposition,[],[f724,f380]) ).
fof(f775,plain,
! [X0] : zero = composition(converse(X0),complement(composition(X0,top))),
inference(backward_demodulation,[],[f187,f750]) ).
fof(f790,plain,
! [X0] : join(X0,zero) = X0,
inference(superposition,[],[f1,f750]) ).
fof(f816,plain,
! [X0] : join(X0,X0) = X0,
inference(superposition,[],[f711,f380]) ).
fof(f857,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1)),
inference(superposition,[],[f2,f816]) ).
fof(f859,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X1,X0)),
inference(superposition,[],[f133,f816]) ).
fof(f865,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X1,join(X0,X1))),
inference(superposition,[],[f2,f816]) ).
fof(f874,plain,
! [X0,X1] : complement(join(X0,X1)) = complement(join(X1,X0)),
inference(backward_demodulation,[],[f728,f865]) ).
fof(f943,plain,
! [X0] : converse(join(X0,one)) = join(converse(X0),one),
inference(superposition,[],[f11,f700]) ).
fof(f958,plain,
! [X0] : join(one,converse(X0)) = converse(join(X0,one)),
inference(forward_demodulation,[],[f943,f1]) ).
fof(f992,plain,
! [X0] : top = join(X0,top),
inference(superposition,[],[f857,f15]) ).
fof(f1038,plain,
! [X0,X1] : top = join(X0,join(complement(X0),X1)),
inference(backward_demodulation,[],[f259,f992]) ).
fof(f1047,plain,
! [X1] : top = join(top,X1),
inference(backward_demodulation,[],[f118,f1038]) ).
fof(f1347,plain,
complement(sF3) = join(complement(sF6),complement(join(sF3,complement(sF5)))),
inference(superposition,[],[f442,f45]) ).
fof(f1365,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,[],[f421,f442]) ).
fof(f1373,plain,
! [X0,X1] : complement(X0) = join(complement(join(X1,X0)),complement(X0)),
inference(superposition,[],[f857,f442]) ).
fof(f1374,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0))),
inference(forward_demodulation,[],[f1373,f1]) ).
fof(f1381,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,[],[f1365,f1]) ).
fof(f1392,plain,
sk1 = join(complement(sF6),complement(join(sF3,complement(sF5)))),
inference(forward_demodulation,[],[f1347,f414]) ).
fof(f1404,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,complement(X1)))),
inference(backward_demodulation,[],[f585,f1374]) ).
fof(f1411,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,[],[f1381,f874]) ).
fof(f1431,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,[],[f1411,f2]) ).
fof(f1447,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(X1,join(X0,X1)))),
inference(forward_demodulation,[],[f1431,f1404]) ).
fof(f1461,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(X0,X1))),
inference(forward_demodulation,[],[f1447,f859]) ).
fof(f1470,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f1461,f380]) ).
fof(f1476,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f1470,f380]) ).
fof(f1495,plain,
! [X0,X1] : join(X1,complement(join(X0,X1))) = join(X1,complement(X0)),
inference(superposition,[],[f1476,f1]) ).
fof(f1654,plain,
join(sk3,complement(sk3)) = join(sk3,complement(sF1)),
inference(superposition,[],[f1495,f52]) ).
fof(f1698,plain,
top = join(sk3,complement(sF1)),
inference(forward_demodulation,[],[f1654,f15]) ).
fof(f2536,plain,
! [X0] : converse(converse(X0)) = join(converse(zero),X0),
inference(superposition,[],[f91,f750]) ).
fof(f2557,plain,
! [X0] : join(converse(zero),X0) = X0,
inference(forward_demodulation,[],[f2536,f10]) ).
fof(f2607,plain,
zero = converse(zero),
inference(superposition,[],[f790,f2557]) ).
fof(f4366,plain,
! [X0] : composition(complement(join(complement(sF4),complement(composition(X0,converse(sk2))))),complement(join(complement(sk2),complement(composition(converse(sF4),X0))))) = join(complement(join(complement(sF5),complement(X0))),composition(complement(join(complement(sF4),complement(composition(X0,converse(sk2))))),complement(join(complement(sk2),complement(composition(converse(sF4),X0)))))),
inference(superposition,[],[f28,f43]) ).
fof(f4488,plain,
! [X0] : composition(complement(join(complement(sF4),complement(composition(X0,sF0)))),complement(join(complement(sk2),complement(composition(converse(sF4),X0))))) = join(complement(join(complement(sF5),complement(X0))),composition(complement(join(complement(sF4),complement(composition(X0,sF0)))),complement(join(complement(sk2),complement(composition(converse(sF4),X0)))))),
inference(forward_demodulation,[],[f4366,f32]) ).
fof(f4521,plain,
! [X0] : composition(complement(join(sk3,complement(composition(X0,sF0)))),complement(join(complement(sk2),complement(composition(converse(sF4),X0))))) = join(complement(join(complement(sF5),complement(X0))),composition(complement(join(sk3,complement(composition(X0,sF0)))),complement(join(complement(sk2),complement(composition(converse(sF4),X0)))))),
inference(forward_demodulation,[],[f4488,f415]) ).
fof(f7162,plain,
! [X0] : zero = composition(converse(join(X0,one)),complement(join(top,composition(X0,top)))),
inference(superposition,[],[f775,f712]) ).
fof(f7208,plain,
! [X0] : zero = composition(converse(join(X0,one)),complement(top)),
inference(forward_demodulation,[],[f7162,f1047]) ).
fof(f7232,plain,
! [X0] : zero = composition(converse(join(X0,one)),zero),
inference(forward_demodulation,[],[f7208,f47]) ).
fof(f7253,plain,
! [X0] : zero = composition(join(one,converse(X0)),zero),
inference(forward_demodulation,[],[f7232,f958]) ).
fof(f7266,plain,
! [X0] : zero = join(zero,composition(converse(X0),zero)),
inference(forward_demodulation,[],[f7253,f705]) ).
fof(f7274,plain,
! [X0] : zero = composition(converse(X0),zero),
inference(forward_demodulation,[],[f7266,f750]) ).
fof(f7384,plain,
composition(complement(join(sk3,complement(sF1))),complement(join(complement(sk2),complement(composition(converse(sF4),sk1))))) = join(complement(join(complement(sF5),complement(sk1))),composition(complement(join(sk3,complement(sF1))),complement(join(complement(sk2),complement(composition(converse(sF4),sk1)))))),
inference(superposition,[],[f4521,f34]) ).
fof(f7421,plain,
composition(complement(top),complement(join(complement(sk2),complement(composition(converse(sF4),sk1))))) = join(complement(join(complement(sF5),complement(sk1))),composition(complement(top),complement(join(complement(sk2),complement(composition(converse(sF4),sk1)))))),
inference(forward_demodulation,[],[f7384,f1698]) ).
fof(f7440,plain,
composition(zero,complement(join(complement(sk2),complement(composition(converse(sF4),sk1))))) = join(complement(join(complement(sF5),complement(sk1))),composition(zero,complement(join(complement(sk2),complement(composition(converse(sF4),sk1)))))),
inference(forward_demodulation,[],[f7421,f47]) ).
fof(f7449,plain,
composition(zero,complement(join(complement(sk2),complement(composition(converse(sF4),sk1))))) = join(complement(join(complement(sF5),sF3)),composition(zero,complement(join(complement(sk2),complement(composition(converse(sF4),sk1)))))),
inference(forward_demodulation,[],[f7440,f39]) ).
fof(f7457,plain,
composition(zero,complement(join(complement(sk2),complement(composition(converse(sF4),sk1))))) = join(complement(join(sF3,complement(sF5))),composition(zero,complement(join(complement(sk2),complement(composition(converse(sF4),sk1)))))),
inference(forward_demodulation,[],[f7449,f874]) ).
fof(f9565,plain,
! [X0] : converse(zero) = composition(converse(zero),X0),
inference(superposition,[],[f113,f7274]) ).
fof(f9603,plain,
! [X0] : zero = composition(zero,X0),
inference(forward_demodulation,[],[f9565,f2607]) ).
fof(f9658,plain,
zero = join(complement(join(sF3,complement(sF5))),zero),
inference(backward_demodulation,[],[f7457,f9603]) ).
fof(f9710,plain,
zero = join(zero,complement(join(sF3,complement(sF5)))),
inference(forward_demodulation,[],[f9658,f1]) ).
fof(f9741,plain,
zero = complement(join(sF3,complement(sF5))),
inference(forward_demodulation,[],[f9710,f750]) ).
fof(f9760,plain,
sk1 = join(complement(sF6),zero),
inference(backward_demodulation,[],[f1392,f9741]) ).
fof(f9777,plain,
sk1 = join(zero,complement(sF6)),
inference(forward_demodulation,[],[f9760,f1]) ).
fof(f9789,plain,
sk1 = complement(sF6),
inference(forward_demodulation,[],[f9777,f750]) ).
fof(f9849,plain,
complement(sk1) = sF6,
inference(superposition,[],[f380,f9789]) ).
fof(f9880,plain,
sF3 = sF6,
inference(forward_demodulation,[],[f9849,f39]) ).
fof(f9888,plain,
$false,
inference(forward_subsumption_resolution,[],[f9880,f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL043-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.48 % Computer : n019.cluster.edu
% 0.21/0.48 % Model : x86_64 x86_64
% 0.21/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.48 % Memory : 8046.5625MB
% 0.21/0.48 % OS : Linux 6.8.0-71-generic
% 0.21/0.48 % CPULimit : 300
% 0.21/0.48 % WCLimit : 300
% 0.21/0.48 % DateTime : Sun Sep 27 22:57:03 UTC 2026
% 0.21/0.48 % CPUTime :
% 0.21/0.48 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.54 Running first-order theorem proving
% 0.25/0.54 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
% 25.13/4.77 % (3500872)Detected a unit-equality problem, will run specialized UEQ schedule.
% 25.13/4.77 % (3500887)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=3924946832:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 25.13/4.77 % (3500886)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=340114797:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 25.13/4.77 % (3500890)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3831880391:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 25.13/4.77 % (3500888)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3246568686:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 25.13/4.77 % (3500889)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=651528447:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 25.13/4.77 % (3500891)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1790093559:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 25.13/4.77 % (3500892)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1237155404:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 25.13/4.77 % (3500889)Instruction limit reached!
% 25.13/4.77 % (3500889)------------------------------
% 25.13/4.77 % (3500889)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.13/4.77 % (3500889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.13/4.77 % (3500889)CaDiCaL version: 2.1.3
% 25.13/4.77 % (3500889)Termination reason: Instruction limit
% 25.13/4.77 % (3500889)Termination phase: Saturation
% 25.13/4.77 % (3500889)Time elapsed: 0.140 s
% 25.13/4.77 % (3500889)Peak memory usage: 89 MB
% 25.13/4.77 % (3500889)Instructions burned: 136 (million)
% 25.13/4.77 % (3500890)Instruction limit reached!
% 25.13/4.77 % (3500890)------------------------------
% 25.13/4.77 % (3500890)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.13/4.77 % (3500890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.13/4.77 % (3500890)CaDiCaL version: 2.1.3
% 25.13/4.77 % (3500890)Termination reason: Instruction limit
% 25.13/4.77 % (3500890)Termination phase: Saturation
% 25.13/4.77 % (3500890)Time elapsed: 0.173 s
% 25.13/4.77 % (3500890)Peak memory usage: 89 MB
% 25.13/4.77 % (3500890)Instructions burned: 181 (million)
% 25.13/4.77 % (3500891)Instruction limit reached!
% 25.13/4.77 % (3500891)------------------------------
% 25.13/4.77 % (3500891)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.13/4.77 % (3500891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.13/4.77 % (3500891)CaDiCaL version: 2.1.3
% 25.13/4.77 % (3500891)Termination reason: Instruction limit
% 25.13/4.77 % (3500891)Termination phase: Saturation
% 25.13/4.77 % (3500891)Time elapsed: 0.276 s
% 25.13/4.77 % (3500891)Peak memory usage: 90 MB
% 25.13/4.77 % (3500891)Instructions burned: 257 (million)
% 25.13/4.77 % (3500900)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=999164868:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2995 on theBenchmark for (2995ds/2051Mi)
% 25.13/4.77 % (3500901)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1554202973:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 25.13/4.77 % (3500902)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3254774158:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 25.13/4.77 % (3500902)Instruction limit reached!
% 25.13/4.77 % (3500902)------------------------------
% 25.13/4.77 % (3500902)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.13/4.77 % (3500902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.13/4.77 % (3500902)CaDiCaL version: 2.1.3
% 25.13/4.77 % (3500902)Termination reason: Instruction limit
% 25.13/4.77 % (3500902)Termination phase: Saturation
% 25.13/4.77 % (3500902)Time elapsed: 0.205 s
% 25.13/4.77 % (3500902)Peak memory usage: 92 MB
% 25.13/4.77 % (3500902)Instructions burned: 215 (million)
% 25.13/4.77 % (3500892)Instruction limit reached!
% 25.13/4.77 % (3500892)------------------------------
% 25.13/4.77 % (3500892)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.13/4.77 % (3500892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.13/4.77 % (3500892)CaDiCaL version: 2.1.3
% 25.13/4.77 % (3500892)Termination reason: Instruction limit
% 25.13/4.77 % (3500892)Termination phase: Saturation
% 25.13/4.77 % (3500892)Time elapsed: 1.042 s
% 25.13/4.77 % (3500892)Peak memory usage: 101 MB
% 25.13/4.77 % (3500892)Instructions burned: 1188 (million)
% 25.13/4.77 % (3500906)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=425989752: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)
% 25.13/4.77 % (3500907)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=2810079172:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2986 on theBenchmark for (2986ds/12125Mi)
% 25.13/4.77 % (3500906)Instruction limit reached!
% 25.13/4.77 % (3500906)------------------------------
% 25.13/4.77 % (3500906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.13/4.77 % (3500906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.13/4.77 % (3500906)CaDiCaL version: 2.1.3
% 25.13/4.77 % (3500906)Termination reason: Instruction limit
% 25.13/4.77 % (3500906)Termination phase: Saturation
% 25.13/4.77 % (3500906)Time elapsed: 0.327 s
% 25.13/4.77 % (3500906)Peak memory usage: 93 MB
% 25.13/4.77 % (3500906)Instructions burned: 317 (million)
% 25.13/4.77 % (3500900)Instruction limit reached!
% 25.13/4.77 % (3500900)------------------------------
% 25.13/4.77 % (3500900)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.13/4.77 % (3500900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.13/4.77 % (3500900)CaDiCaL version: 2.1.3
% 25.13/4.77 % (3500900)Termination reason: Instruction limit
% 25.13/4.77 % (3500900)Termination phase: Saturation
% 25.13/4.77 % (3500900)Time elapsed: 1.183 s
% 25.13/4.77 % (3500900)Peak memory usage: 140 MB
% 25.13/4.77 % (3500900)Instructions burned: 2053 (million)
% 25.13/4.77 % (3500910)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=3160349666:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2982 on theBenchmark for (2982ds/2836Mi)
% 25.13/4.77 % (3500911)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=1474955602:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2980 on theBenchmark for (2980ds/14534Mi)
% 25.13/4.77 % (3500888)First to succeed.
% 25.13/4.77 % (3500888)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3500872"
% 25.13/4.77 % (3500888)Refutation found. Thanks to Tanya!
% 25.13/4.77 % SZS status Unsatisfiable for theBenchmark
% 25.13/4.77 % SZS output start Proof for theBenchmark
% See solution above
% 0.29/5.16 % (3500888)------------------------------
% 0.29/5.16 % (3500888)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.29/5.16 % (3500888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/5.16 % (3500888)CaDiCaL version: 2.1.3
% 0.29/5.16 % (3500888)Termination reason: Refutation
% 0.29/5.16 % (3500888)Time elapsed: 2.789 s
% 0.29/5.16 % (3500888)Peak memory usage: 144 MB
% 0.29/5.16 % (3500888)Instructions burned: 2608 (million)
% 0.29/5.16 % (3500888)------------------------------
% 0.29/5.16 % (3500888)------------------------------
% 0.29/5.16 % (3500872)Success in time 3.514 s
% 0.29/5.16 % Vampire exiting
%------------------------------------------------------------------------------