%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL035-1 : 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 : n012.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 12:34:01 PM UTC 2026
% Result : Unsatisfiable 10.48s 2.43s
% Output : Refutation 12.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 27
% Syntax : Number of formulae : 211 ( 211 unt; 12 def)
% Number of atoms : 211 ( 210 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 : 185 ( 185 !; 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(f7,axiom,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity_5) ).
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,negated_conjecture,
composition(sk1,top) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
fof(f18,plain,
sk1 = composition(sk1,top),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
composition(meet(sk2,converse(sk1)),meet(sk1,sk3)) != composition(sk2,meet(sk1,sk3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_15) ).
fof(f20,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f21,plain,
composition(complement(join(complement(sk2),complement(converse(sk1)))),complement(join(complement(sk1),complement(sk3)))) != composition(sk2,complement(join(complement(sk1),complement(sk3)))),
inference(definition_unfolding,[],[f19,f6,f6,f6]) ).
fof(f22,definition,
sF0 = composition(sk1,top),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f23,plain,
composition(sk1,top) = sF0,
inference(reorient_equations,[],[f22]) ).
fof(f24,plain,
sk1 = sF0,
inference(definition_folding,[],[f18,f23]) ).
fof(f25,definition,
sF1 = complement(sk2),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f26,plain,
complement(sk2) = sF1,
inference(reorient_equations,[],[f25]) ).
fof(f27,definition,
sF2 = converse(sk1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f28,plain,
converse(sk1) = sF2,
inference(reorient_equations,[],[f27]) ).
fof(f29,definition,
sF3 = complement(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f30,plain,
complement(sF2) = sF3,
inference(reorient_equations,[],[f29]) ).
fof(f31,definition,
sF4 = join(sF1,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f32,plain,
join(sF1,sF3) = sF4,
inference(reorient_equations,[],[f31]) ).
fof(f33,definition,
sF5 = complement(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f34,plain,
complement(sF4) = sF5,
inference(reorient_equations,[],[f33]) ).
fof(f35,definition,
sF6 = complement(sk1),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f36,plain,
complement(sk1) = sF6,
inference(reorient_equations,[],[f35]) ).
fof(f37,definition,
sF7 = complement(sk3),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f38,plain,
complement(sk3) = sF7,
inference(reorient_equations,[],[f37]) ).
fof(f39,definition,
sF8 = join(sF6,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f40,plain,
join(sF6,sF7) = sF8,
inference(reorient_equations,[],[f39]) ).
fof(f41,definition,
sF9 = complement(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f42,plain,
complement(sF8) = sF9,
inference(reorient_equations,[],[f41]) ).
fof(f43,definition,
sF10 = composition(sF5,sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f44,plain,
composition(sF5,sF9) = sF10,
inference(reorient_equations,[],[f43]) ).
fof(f45,definition,
sF11 = composition(sk2,sF9),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f46,plain,
composition(sk2,sF9) = sF11,
inference(reorient_equations,[],[f45]) ).
fof(f47,plain,
sF10 != sF11,
inference(definition_folding,[],[f21,f46,f42,f40,f38,f36,f44,f42,f40,f38,f36,f34,f32,f30,f28,f26]) ).
fof(f48,plain,
zero = complement(top),
inference(backward_demodulation,[],[f20,f15]) ).
fof(f49,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(backward_demodulation,[],[f14,f1]) ).
fof(f50,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(backward_demodulation,[],[f4,f1]) ).
fof(f51,plain,
sk1 = composition(sk1,top),
inference(forward_demodulation,[],[f23,f24]) ).
fof(f63,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[],[f50,f15]) ).
fof(f70,plain,
! [X0] : join(complement(join(complement(X0),sk1)),complement(join(complement(X0),sF6))) = X0,
inference(superposition,[],[f50,f36]) ).
fof(f85,plain,
! [X0] : join(complement(join(complement(X0),sF6)),complement(join(complement(X0),sk1))) = X0,
inference(forward_demodulation,[],[f70,f1]) ).
fof(f86,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f63,f48]) ).
fof(f93,plain,
! [X0] : join(complement(join(complement(X0),sF6)),complement(join(sk1,complement(X0)))) = X0,
inference(forward_demodulation,[],[f85,f1]) ).
fof(f99,plain,
! [X0] : join(complement(join(sk1,complement(X0))),complement(join(complement(X0),sF6))) = X0,
inference(forward_demodulation,[],[f93,f1]) ).
fof(f105,plain,
! [X0] : join(complement(join(sk1,complement(X0))),complement(join(sF6,complement(X0)))) = X0,
inference(forward_demodulation,[],[f99,f1]) ).
fof(f109,plain,
! [X0] : join(complement(join(sF6,complement(X0))),complement(join(sk1,complement(X0)))) = X0,
inference(forward_demodulation,[],[f105,f1]) ).
fof(f110,plain,
! [X0] : converse(join(sk1,X0)) = join(sF2,converse(X0)),
inference(superposition,[],[f11,f28]) ).
fof(f122,plain,
complement(top) = join(complement(top),composition(converse(sk1),complement(sk1))),
inference(superposition,[],[f49,f51]) ).
fof(f124,plain,
complement(top) = join(complement(top),composition(converse(sk1),sF6)),
inference(forward_demodulation,[],[f122,f36]) ).
fof(f125,plain,
complement(top) = join(complement(top),composition(sF2,sF6)),
inference(forward_demodulation,[],[f124,f28]) ).
fof(f126,plain,
zero = join(zero,composition(sF2,sF6)),
inference(forward_demodulation,[],[f125,f48]) ).
fof(f133,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(superposition,[],[f50,f1]) ).
fof(f149,plain,
! [X0] : converse(composition(sk1,X0)) = composition(converse(X0),sF2),
inference(superposition,[],[f12,f28]) ).
fof(f151,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(f154,plain,
sk1 = converse(sF2),
inference(superposition,[],[f10,f28]) ).
fof(f155,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[],[f12,f10]) ).
fof(f158,plain,
! [X0,X1] : converse(join(X1,converse(X0))) = join(converse(X1),X0),
inference(superposition,[],[f11,f10]) ).
fof(f159,plain,
! [X0,X1] : join(X0,converse(X1)) = converse(join(converse(X0),X1)),
inference(superposition,[],[f11,f10]) ).
fof(f165,plain,
! [X0] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[],[f159,f15]) ).
fof(f182,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f2,f15]) ).
fof(f194,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f247,plain,
! [X0] : complement(X0) = join(complement(join(complement(complement(X0)),X0)),complement(top)),
inference(superposition,[],[f133,f15]) ).
fof(f254,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(complement(complement(X0)),X0))),
inference(forward_demodulation,[],[f247,f1]) ).
fof(f276,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f254,f1]) ).
fof(f288,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f276,f48]) ).
fof(f294,plain,
! [X0] : complement(complement(X0)) = X0,
inference(backward_demodulation,[],[f86,f288]) ).
fof(f297,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,X0))),
inference(backward_demodulation,[],[f288,f294]) ).
fof(f309,plain,
sk1 = complement(sF6),
inference(superposition,[],[f294,f36]) ).
fof(f310,plain,
sk2 = complement(sF1),
inference(superposition,[],[f294,f26]) ).
fof(f311,plain,
sk3 = complement(sF7),
inference(superposition,[],[f294,f38]) ).
fof(f317,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(X0,complement(X1)))),
inference(superposition,[],[f50,f294]) ).
fof(f320,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0))),
inference(superposition,[],[f133,f294]) ).
fof(f337,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(X1,complement(X0)))),
inference(superposition,[],[f317,f1]) ).
fof(f346,plain,
complement(sF6) = join(complement(sF8),complement(join(sF6,complement(sF7)))),
inference(superposition,[],[f317,f40]) ).
fof(f372,plain,
complement(sF6) = join(complement(sF8),complement(join(sF6,sk3))),
inference(forward_demodulation,[],[f346,f311]) ).
fof(f383,plain,
complement(sF6) = join(sF9,complement(join(sF6,sk3))),
inference(forward_demodulation,[],[f372,f42]) ).
fof(f390,plain,
sk1 = join(sF9,complement(join(sF6,sk3))),
inference(forward_demodulation,[],[f383,f309]) ).
fof(f425,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,[],[f317,f320]) ).
fof(f428,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,[],[f425,f294]) ).
fof(f443,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,[],[f428,f194]) ).
fof(f456,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,[],[f443,f1]) ).
fof(f468,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f456,f294]) ).
fof(f478,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f468,f294]) ).
fof(f490,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f155,f8]) ).
fof(f503,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f490,f10]) ).
fof(f517,plain,
! [X0] : composition(join(converse(top),X0),converse(sk1)) = join(converse(sk1),composition(X0,converse(sk1))),
inference(superposition,[],[f151,f51]) ).
fof(f525,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f151,f12]) ).
fof(f536,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f525,f11]) ).
fof(f542,plain,
! [X0] : composition(join(converse(top),X0),sF2) = join(sF2,composition(X0,sF2)),
inference(forward_demodulation,[],[f517,f28]) ).
fof(f545,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f536,f11]) ).
fof(f549,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f545,f12]) ).
fof(f589,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(X1,top),
inference(superposition,[],[f194,f15]) ).
fof(f680,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,[],[f320,f337]) ).
fof(f691,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,[],[f680,f1]) ).
fof(f712,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,[],[f691,f1]) ).
fof(f729,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,[],[f712,f2]) ).
fof(f743,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f729,f294]) ).
fof(f755,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f743,f294]) ).
fof(f774,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(one,X0))),
inference(superposition,[],[f49,f503]) ).
fof(f775,plain,
one = converse(one),
inference(superposition,[],[f8,f503]) ).
fof(f780,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f503,f775]) ).
fof(f787,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(backward_demodulation,[],[f774,f780]) ).
fof(f807,plain,
! [X0] : join(X0,X0) = X0,
inference(superposition,[],[f787,f294]) ).
fof(f818,plain,
! [X0] : complement(complement(X0)) = join(zero,complement(complement(X0))),
inference(superposition,[],[f297,f787]) ).
fof(f828,plain,
! [X0] : join(zero,X0) = X0,
inference(forward_demodulation,[],[f818,f294]) ).
fof(f850,plain,
zero = composition(sF2,sF6),
inference(backward_demodulation,[],[f126,f828]) ).
fof(f892,plain,
! [X0] : join(X0,zero) = X0,
inference(superposition,[],[f1,f828]) ).
fof(f931,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1)),
inference(superposition,[],[f2,f807]) ).
fof(f932,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X0,X1)),
inference(superposition,[],[f194,f807]) ).
fof(f933,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X1,X0)),
inference(superposition,[],[f194,f807]) ).
fof(f1049,plain,
! [X0] : composition(join(converse(sF6),X0),converse(sF2)) = join(converse(zero),composition(X0,converse(sF2))),
inference(superposition,[],[f151,f850]) ).
fof(f1052,plain,
! [X0] : composition(join(sF2,X0),sF6) = join(zero,composition(X0,sF6)),
inference(superposition,[],[f9,f850]) ).
fof(f1055,plain,
! [X0] : composition(X0,sF6) = composition(join(sF2,X0),sF6),
inference(forward_demodulation,[],[f1052,f828]) ).
fof(f1057,plain,
! [X0] : composition(join(converse(sF6),X0),sk1) = join(converse(zero),composition(X0,sk1)),
inference(forward_demodulation,[],[f1049,f154]) ).
fof(f1267,plain,
! [X0] : top = join(X0,top),
inference(superposition,[],[f931,f15]) ).
fof(f1270,plain,
! [X0,X1] : complement(X0) = join(complement(join(X1,X0)),complement(X0)),
inference(superposition,[],[f931,f337]) ).
fof(f1311,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0))),
inference(forward_demodulation,[],[f1270,f1]) ).
fof(f1314,plain,
! [X0,X1] : top = join(X0,join(complement(X0),X1)),
inference(backward_demodulation,[],[f589,f1267]) ).
fof(f1335,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,complement(X1)))),
inference(backward_demodulation,[],[f478,f1311]) ).
fof(f1346,plain,
! [X1] : top = join(top,X1),
inference(backward_demodulation,[],[f182,f1314]) ).
fof(f1349,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,X1)))),
inference(backward_demodulation,[],[f755,f1335]) ).
fof(f1363,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f1349,f933]) ).
fof(f1387,plain,
! [X0,X1] : join(X1,complement(join(X0,X1))) = join(X1,complement(X0)),
inference(superposition,[],[f1363,f1]) ).
fof(f1403,plain,
join(sF6,complement(sF7)) = join(sF6,complement(sF8)),
inference(superposition,[],[f1363,f40]) ).
fof(f1435,plain,
join(sF6,complement(sF7)) = join(sF6,sF9),
inference(forward_demodulation,[],[f1403,f42]) ).
fof(f1455,plain,
join(sF6,complement(sF7)) = join(sF9,sF6),
inference(forward_demodulation,[],[f1435,f1]) ).
fof(f1475,plain,
join(sF6,sk3) = join(sF9,sF6),
inference(forward_demodulation,[],[f1455,f311]) ).
fof(f1488,plain,
sk1 = join(sF9,complement(join(sF9,sF6))),
inference(backward_demodulation,[],[f390,f1475]) ).
fof(f1495,plain,
sk1 = join(sF9,complement(sF6)),
inference(forward_demodulation,[],[f1488,f1363]) ).
fof(f1500,plain,
sk1 = join(sF9,sk1),
inference(forward_demodulation,[],[f1495,f309]) ).
fof(f1599,plain,
join(sF3,complement(sF1)) = join(sF3,complement(sF4)),
inference(superposition,[],[f1387,f32]) ).
fof(f1637,plain,
join(sF3,complement(sF1)) = join(sF3,sF5),
inference(forward_demodulation,[],[f1599,f34]) ).
fof(f1663,plain,
join(sF3,sk2) = join(sF3,sF5),
inference(forward_demodulation,[],[f1637,f310]) ).
fof(f2531,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f549]) ).
fof(f2547,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f2531,f10]) ).
fof(f2612,plain,
! [X0] : composition(sk1,join(top,X0)) = join(sk1,composition(sk1,X0)),
inference(superposition,[],[f2547,f51]) ).
fof(f2694,plain,
! [X0] : composition(sk1,top) = join(sk1,composition(sk1,X0)),
inference(forward_demodulation,[],[f2612,f1346]) ).
fof(f2707,plain,
! [X0] : sk1 = join(sk1,composition(sk1,X0)),
inference(forward_demodulation,[],[f2694,f51]) ).
fof(f3336,plain,
! [X0] : converse(converse(X0)) = join(converse(zero),X0),
inference(superposition,[],[f158,f828]) ).
fof(f3338,plain,
! [X0] : converse(top) = join(converse(top),X0),
inference(superposition,[],[f158,f1346]) ).
fof(f3361,plain,
! [X0] : join(sF2,composition(X0,sF2)) = composition(converse(top),sF2),
inference(backward_demodulation,[],[f542,f3338]) ).
fof(f3363,plain,
! [X0] : join(converse(zero),X0) = X0,
inference(forward_demodulation,[],[f3336,f10]) ).
fof(f3374,plain,
! [X0] : composition(X0,sk1) = composition(join(converse(sF6),X0),sk1),
inference(backward_demodulation,[],[f1057,f3363]) ).
fof(f3414,plain,
zero = converse(zero),
inference(superposition,[],[f892,f3363]) ).
fof(f3543,plain,
! [X0,X1] : join(complement(join(X1,X0)),X0) = join(X0,join(X0,complement(X1))),
inference(superposition,[],[f932,f1387]) ).
fof(f3658,plain,
! [X0,X1] : join(complement(X1),X0) = join(complement(join(X1,X0)),X0),
inference(forward_demodulation,[],[f3543,f932]) ).
fof(f3709,plain,
! [X0,X1] : join(complement(X1),X0) = join(X0,complement(join(X1,X0))),
inference(forward_demodulation,[],[f3658,f1]) ).
fof(f5105,plain,
composition(converse(sF6),sk1) = composition(zero,sk1),
inference(superposition,[],[f3374,f892]) ).
fof(f5482,plain,
! [X0] : complement(X0) = join(complement(join(sF6,X0)),complement(join(sk1,X0))),
inference(superposition,[],[f109,f294]) ).
fof(f7042,plain,
converse(top) = join(sF2,converse(complement(sk1))),
inference(superposition,[],[f110,f15]) ).
fof(f7049,plain,
! [X0] : converse(sk1) = join(sF2,converse(composition(sk1,X0))),
inference(superposition,[],[f110,f2707]) ).
fof(f7075,plain,
! [X0] : converse(sk1) = join(sF2,composition(converse(X0),sF2)),
inference(forward_demodulation,[],[f7049,f149]) ).
fof(f7082,plain,
converse(top) = join(sF2,converse(sF6)),
inference(forward_demodulation,[],[f7042,f36]) ).
fof(f7092,plain,
converse(sk1) = composition(converse(top),sF2),
inference(forward_demodulation,[],[f7075,f3361]) ).
fof(f7098,plain,
sF2 = composition(converse(top),sF2),
inference(forward_demodulation,[],[f7092,f28]) ).
fof(f7100,plain,
! [X0] : sF2 = join(sF2,composition(X0,sF2)),
inference(backward_demodulation,[],[f3361,f7098]) ).
fof(f7118,plain,
join(complement(sF2),converse(sF6)) = join(converse(sF6),complement(converse(top))),
inference(superposition,[],[f3709,f7082]) ).
fof(f7121,plain,
join(converse(sF6),complement(converse(top))) = join(sF3,converse(sF6)),
inference(forward_demodulation,[],[f7118,f30]) ).
fof(f7207,plain,
! [X0] : composition(sF2,sF6) = composition(composition(X0,sF2),sF6),
inference(superposition,[],[f1055,f7100]) ).
fof(f7233,plain,
! [X0] : composition(sF2,sF6) = composition(X0,composition(sF2,sF6)),
inference(forward_demodulation,[],[f7207,f7]) ).
fof(f7240,plain,
! [X0] : zero = composition(X0,zero),
inference(forward_demodulation,[],[f7233,f850]) ).
fof(f7268,plain,
! [X0] : converse(zero) = composition(converse(zero),X0),
inference(superposition,[],[f155,f7240]) ).
fof(f7273,plain,
! [X0] : zero = composition(zero,X0),
inference(forward_demodulation,[],[f7268,f3414]) ).
fof(f7293,plain,
zero = composition(converse(sF6),sk1),
inference(backward_demodulation,[],[f5105,f7273]) ).
fof(f8972,plain,
! [X0] : composition(converse(sF6),join(X0,sk1)) = join(composition(converse(sF6),X0),zero),
inference(superposition,[],[f2547,f7293]) ).
fof(f8977,plain,
! [X0] : join(zero,composition(converse(sF6),X0)) = composition(converse(sF6),join(X0,sk1)),
inference(forward_demodulation,[],[f8972,f1]) ).
fof(f8988,plain,
! [X0] : composition(converse(sF6),X0) = composition(converse(sF6),join(X0,sk1)),
inference(forward_demodulation,[],[f8977,f828]) ).
fof(f9858,plain,
top = converse(top),
inference(superposition,[],[f1346,f165]) ).
fof(f9862,plain,
complement(converse(complement(converse(sk1)))) = join(complement(join(sF6,converse(complement(converse(sk1))))),complement(converse(top))),
inference(superposition,[],[f5482,f165]) ).
fof(f9884,plain,
complement(converse(complement(converse(sk1)))) = join(complement(converse(top)),complement(join(sF6,converse(complement(converse(sk1)))))),
inference(forward_demodulation,[],[f9862,f1]) ).
fof(f9896,plain,
join(sF3,converse(sF6)) = join(converse(sF6),complement(top)),
inference(backward_demodulation,[],[f7121,f9858]) ).
fof(f9970,plain,
complement(converse(complement(sF2))) = join(complement(converse(top)),complement(join(sF6,converse(complement(sF2))))),
inference(forward_demodulation,[],[f9884,f28]) ).
fof(f9982,plain,
join(sF3,converse(sF6)) = join(complement(top),converse(sF6)),
inference(forward_demodulation,[],[f9896,f1]) ).
fof(f10018,plain,
complement(converse(sF3)) = join(complement(converse(top)),complement(join(sF6,converse(sF3)))),
inference(forward_demodulation,[],[f9970,f30]) ).
fof(f10025,plain,
join(sF3,converse(sF6)) = join(zero,converse(sF6)),
inference(forward_demodulation,[],[f9982,f48]) ).
fof(f10049,plain,
complement(converse(sF3)) = join(complement(top),complement(join(sF6,converse(sF3)))),
inference(forward_demodulation,[],[f10018,f9858]) ).
fof(f10051,plain,
converse(sF6) = join(sF3,converse(sF6)),
inference(forward_demodulation,[],[f10025,f828]) ).
fof(f10064,plain,
complement(converse(sF3)) = join(zero,complement(join(sF6,converse(sF3)))),
inference(forward_demodulation,[],[f10049,f48]) ).
fof(f10070,plain,
complement(converse(sF3)) = complement(join(sF6,converse(sF3))),
inference(forward_demodulation,[],[f10064,f828]) ).
fof(f10114,plain,
converse(converse(sF6)) = join(converse(sF3),sF6),
inference(superposition,[],[f158,f10051]) ).
fof(f10139,plain,
converse(converse(sF6)) = join(sF6,converse(sF3)),
inference(forward_demodulation,[],[f10114,f1]) ).
fof(f10144,plain,
sF6 = join(sF6,converse(sF3)),
inference(forward_demodulation,[],[f10139,f10]) ).
fof(f10148,plain,
complement(sF6) = complement(converse(sF3)),
inference(backward_demodulation,[],[f10070,f10144]) ).
fof(f10149,plain,
sk1 = complement(converse(sF3)),
inference(forward_demodulation,[],[f10148,f309]) ).
fof(f10157,plain,
complement(sk1) = converse(sF3),
inference(superposition,[],[f294,f10149]) ).
fof(f10173,plain,
sF6 = converse(sF3),
inference(forward_demodulation,[],[f10157,f36]) ).
fof(f10202,plain,
sF3 = converse(sF6),
inference(superposition,[],[f10,f10173]) ).
fof(f10244,plain,
zero = composition(sF3,sk1),
inference(backward_demodulation,[],[f7293,f10202]) ).
fof(f10247,plain,
! [X0] : composition(sF3,X0) = composition(sF3,join(X0,sk1)),
inference(backward_demodulation,[],[f8988,f10202]) ).
fof(f11074,plain,
composition(sF3,sk1) = composition(sF3,sF9),
inference(superposition,[],[f10247,f1500]) ).
fof(f11107,plain,
zero = composition(sF3,sF9),
inference(forward_demodulation,[],[f11074,f10244]) ).
fof(f11138,plain,
! [X0] : composition(join(sF3,X0),sF9) = join(zero,composition(X0,sF9)),
inference(superposition,[],[f9,f11107]) ).
fof(f11147,plain,
! [X0] : composition(X0,sF9) = composition(join(sF3,X0),sF9),
inference(forward_demodulation,[],[f11138,f828]) ).
fof(f11172,plain,
composition(sk2,sF9) = composition(join(sF3,sF5),sF9),
inference(superposition,[],[f11147,f1663]) ).
fof(f11194,plain,
composition(sF5,sF9) = composition(sk2,sF9),
inference(forward_demodulation,[],[f11172,f11147]) ).
fof(f11209,plain,
composition(sF5,sF9) = sF11,
inference(forward_demodulation,[],[f11194,f46]) ).
fof(f11237,plain,
sF10 = sF11,
inference(forward_demodulation,[],[f11209,f44]) ).
fof(f11240,plain,
$false,
inference(forward_subsumption_resolution,[],[f11237,f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL035-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.34 % Computer : n012.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 27 22:55:04 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.37 Running first-order theorem proving
% 0.08/0.37 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
% 10.48/2.43 % (2848047)Detected a unit-equality problem, will run specialized UEQ schedule.
% 10.48/2.43 % (2848058)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1272291774:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 10.48/2.43 % (2848052)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=2659625578:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 10.48/2.43 % (2848056)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3032893140:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 10.48/2.43 % (2848057)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2369794543:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 10.48/2.43 % (2848054)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=4055778779:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 10.48/2.43 % (2848053)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=1566086051:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 10.48/2.43 % (2848055)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3723790845:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 10.48/2.43 % (2848055)Instruction limit reached!
% 10.48/2.43 % (2848055)------------------------------
% 10.48/2.43 % (2848055)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.48/2.43 % (2848055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.48/2.43 % (2848055)CaDiCaL version: 2.1.3
% 10.48/2.43 % (2848055)Termination reason: Instruction limit
% 10.48/2.43 % (2848055)Termination phase: Saturation
% 10.48/2.43 % (2848055)Time elapsed: 0.076 s
% 10.48/2.43 % (2848055)Peak memory usage: 89 MB
% 10.48/2.43 % (2848055)Instructions burned: 136 (million)
% 10.48/2.43 % (2848056)Instruction limit reached!
% 10.48/2.43 % (2848056)------------------------------
% 10.48/2.43 % (2848056)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.48/2.43 % (2848056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.48/2.43 % (2848056)CaDiCaL version: 2.1.3
% 10.48/2.43 % (2848056)Termination reason: Instruction limit
% 10.48/2.43 % (2848056)Termination phase: Saturation
% 10.48/2.43 % (2848056)Time elapsed: 0.095 s
% 10.48/2.43 % (2848056)Peak memory usage: 90 MB
% 10.48/2.43 % (2848056)Instructions burned: 181 (million)
% 10.48/2.43 % (2848057)Instruction limit reached!
% 10.48/2.43 % (2848057)------------------------------
% 10.48/2.43 % (2848057)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.48/2.43 % (2848057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.48/2.43 % (2848057)CaDiCaL version: 2.1.3
% 10.48/2.43 % (2848057)Termination reason: Instruction limit
% 10.48/2.43 % (2848057)Termination phase: Saturation
% 10.48/2.43 % (2848057)Time elapsed: 0.151 s
% 10.48/2.43 % (2848057)Peak memory usage: 90 MB
% 10.48/2.43 % (2848057)Instructions burned: 257 (million)
% 10.48/2.43 % (2848066)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2833270024:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 10.48/2.43 % (2848067)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2251726599:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 10.48/2.43 % (2848068)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1766919630:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 10.48/2.43 % (2848058)Instruction limit reached!
% 10.48/2.43 % (2848058)------------------------------
% 10.48/2.43 % (2848058)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.48/2.43 % (2848058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.48/2.43 % (2848058)CaDiCaL version: 2.1.3
% 10.48/2.43 % (2848058)Termination reason: Instruction limit
% 10.48/2.43 % (2848058)Termination phase: Saturation
% 10.48/2.43 % (2848058)Time elapsed: 0.506 s
% 10.48/2.43 % (2848058)Peak memory usage: 99 MB
% 10.48/2.43 % (2848058)Instructions burned: 1188 (million)
% 10.48/2.43 % (2848068)Instruction limit reached!
% 10.48/2.43 % (2848068)------------------------------
% 10.48/2.43 % (2848068)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.48/2.43 % (2848068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.48/2.43 % (2848068)CaDiCaL version: 2.1.3
% 10.48/2.43 % (2848068)Termination reason: Instruction limit
% 10.48/2.43 % (2848068)Termination phase: Saturation
% 10.48/2.43 % (2848068)Time elapsed: 0.111 s
% 10.48/2.43 % (2848068)Peak memory usage: 92 MB
% 10.48/2.43 % (2848068)Instructions burned: 216 (million)
% 10.48/2.43 % (2848073)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=1974656255:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2992 on theBenchmark for (2992ds/12125Mi)
% 10.48/2.43 % (2848072)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=2181274263:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2993 on theBenchmark for (2993ds/317Mi)
% 10.48/2.43 % (2848072)Instruction limit reached!
% 10.48/2.43 % (2848072)------------------------------
% 10.48/2.43 % (2848072)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.48/2.43 % (2848072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.48/2.43 % (2848072)CaDiCaL version: 2.1.3
% 10.48/2.43 % (2848072)Termination reason: Instruction limit
% 10.48/2.43 % (2848072)Termination phase: Saturation
% 10.48/2.43 % (2848072)Time elapsed: 0.156 s
% 10.48/2.43 % (2848072)Peak memory usage: 91 MB
% 10.48/2.43 % (2848072)Instructions burned: 318 (million)
% 10.48/2.43 % (2848076)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=1159619603:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2989 on theBenchmark for (2989ds/2836Mi)
% 10.48/2.43 % (2848054)First to succeed.
% 10.48/2.43 % (2848054)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2848047"
% 10.48/2.43 % (2848054)Refutation found. Thanks to Tanya!
% 10.48/2.43 % SZS status Unsatisfiable for theBenchmark
% 10.48/2.43 % SZS output start Proof for theBenchmark
% See solution above
% 12.48/2.56 % (2848054)------------------------------
% 12.48/2.56 % (2848054)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.48/2.56 % (2848054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.48/2.56 % (2848054)CaDiCaL version: 2.1.3
% 12.48/2.56 % (2848054)Termination reason: Refutation
% 12.48/2.56 % (2848054)Time elapsed: 1.245 s
% 12.48/2.56 % (2848054)Peak memory usage: 138 MB
% 12.48/2.56 % (2848054)Instructions burned: 2175 (million)
% 12.48/2.56 % (2848054)------------------------------
% 12.48/2.56 % (2848054)------------------------------
% 12.48/2.56 % (2848047)Success in time 1.714 s
% 12.48/2.56 % Vampire exiting
%------------------------------------------------------------------------------