%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL041-2 : 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 12:34:05 PM UTC 2026
% Result : Unsatisfiable 10.87s 3.72s
% Output : Refutation 20.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 26
% Syntax : Number of formulae : 160 ( 160 unt; 10 def)
% Number of atoms : 160 ( 159 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 20 ( 20 usr; 15 con; 0-2 aty)
% Number of variables : 200 ( 200 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
fof(f2,axiom,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
fof(f4,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
fof(f6,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_associativity_5) ).
fof(f8,negated_conjecture,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity_6) ).
fof(f9,axiom,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f11,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f12,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
fof(f13,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity_11) ).
fof(f14,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top_12) ).
fof(f16,negated_conjecture,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero_13) ).
fof(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/sandbox2/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(converse(sk1),sk1),one) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_17) ).
fof(f24,plain,
one = join(composition(converse(sk1),sk1),one),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
meet(composition(sk1,sk2),composition(sk1,complement(sk2))) != zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_18) ).
fof(f26,plain,
zero != meet(composition(sk1,sk2),composition(sk1,complement(sk2))),
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,plain,
zero != complement(join(complement(composition(sk1,sk2)),complement(composition(sk1,complement(sk2))))),
inference(definition_unfolding,[],[f26,f6]) ).
fof(f32,definition,
sF0 = converse(sk1),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f33,plain,
converse(sk1) = sF0,
inference(reorient_equations,[],[f32]) ).
fof(f34,definition,
sF1 = composition(sF0,sk1),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f35,plain,
composition(sF0,sk1) = sF1,
inference(reorient_equations,[],[f34]) ).
fof(f36,definition,
sF2 = join(sF1,one),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f37,plain,
join(sF1,one) = sF2,
inference(reorient_equations,[],[f36]) ).
fof(f38,plain,
one = sF2,
inference(definition_folding,[],[f24,f37,f35,f33]) ).
fof(f39,definition,
sF3 = composition(sk1,sk2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f40,plain,
composition(sk1,sk2) = sF3,
inference(reorient_equations,[],[f39]) ).
fof(f41,definition,
sF4 = complement(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f42,plain,
complement(sF3) = sF4,
inference(reorient_equations,[],[f41]) ).
fof(f43,definition,
sF5 = complement(sk2),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f44,plain,
complement(sk2) = sF5,
inference(reorient_equations,[],[f43]) ).
fof(f45,definition,
sF6 = composition(sk1,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f46,plain,
composition(sk1,sF5) = sF6,
inference(reorient_equations,[],[f45]) ).
fof(f47,definition,
sF7 = complement(sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f48,plain,
complement(sF6) = sF7,
inference(reorient_equations,[],[f47]) ).
fof(f49,definition,
sF8 = join(sF4,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f50,plain,
join(sF4,sF7) = sF8,
inference(reorient_equations,[],[f49]) ).
fof(f51,definition,
sF9 = complement(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f52,plain,
complement(sF8) = sF9,
inference(reorient_equations,[],[f51]) ).
fof(f53,plain,
zero != sF9,
inference(definition_folding,[],[f31,f52,f50,f48,f46,f44,f42,f40]) ).
fof(f54,plain,
zero = complement(top),
inference(backward_demodulation,[],[f27,f15]) ).
fof(f55,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(backward_demodulation,[],[f4,f1]) ).
fof(f58,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(backward_demodulation,[],[f14,f1]) ).
fof(f59,plain,
one = join(sF1,one),
inference(forward_demodulation,[],[f37,f38]) ).
fof(f101,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[],[f55,f15]) ).
fof(f102,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f101,f54]) ).
fof(f116,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(superposition,[],[f55,f1]) ).
fof(f118,plain,
! [X0] : zero = join(zero,composition(converse(X0),complement(composition(X0,top)))),
inference(superposition,[],[f58,f54]) ).
fof(f149,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(f153,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f12,f10]) ).
fof(f157,plain,
! [X0,X1] : join(X0,converse(X1)) = converse(join(converse(X0),X1)),
inference(superposition,[],[f11,f10]) ).
fof(f186,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(complement(join(complement(X0),complement(X1))),X2)),
inference(superposition,[],[f2,f55]) ).
fof(f187,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f2,f15]) ).
fof(f198,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f220,plain,
! [X0,X1] : join(X0,X1) = join(complement(join(complement(X0),complement(X0))),join(complement(top),X1)),
inference(superposition,[],[f186,f15]) ).
fof(f236,plain,
! [X0,X1] : join(X0,X1) = join(complement(top),join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f220,f198]) ).
fof(f247,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f236,f54]) ).
fof(f273,plain,
! [X0] : composition(sF0,composition(sk1,X0)) = composition(sF1,X0),
inference(superposition,[],[f7,f35]) ).
fof(f300,plain,
! [X0] : complement(X0) = join(complement(join(complement(complement(X0)),X0)),complement(top)),
inference(superposition,[],[f116,f15]) ).
fof(f313,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(complement(complement(X0)),X0))),
inference(forward_demodulation,[],[f300,f1]) ).
fof(f333,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f313,f1]) ).
fof(f344,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f333,f54]) ).
fof(f351,plain,
! [X0] : complement(complement(X0)) = X0,
inference(backward_demodulation,[],[f102,f344]) ).
fof(f362,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,X0))),
inference(backward_demodulation,[],[f344,f351]) ).
fof(f374,plain,
sk2 = complement(sF5),
inference(superposition,[],[f351,f44]) ).
fof(f379,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(X0,complement(X1)))),
inference(superposition,[],[f55,f351]) ).
fof(f383,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0))),
inference(superposition,[],[f116,f351]) ).
fof(f408,plain,
! [X0,X1] : join(complement(X0),X1) = join(zero,join(complement(join(X0,X0)),X1)),
inference(superposition,[],[f2,f362]) ).
fof(f414,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(X1,complement(X0)))),
inference(superposition,[],[f379,f1]) ).
fof(f498,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,[],[f379,f383]) ).
fof(f501,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,[],[f498,f351]) ).
fof(f517,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,[],[f501,f198]) ).
fof(f530,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,[],[f517,f1]) ).
fof(f541,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f530,f351]) ).
fof(f550,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f541,f351]) ).
fof(f568,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f149,f12]) ).
fof(f578,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f568,f11]) ).
fof(f587,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f578,f11]) ).
fof(f591,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f587,f12]) ).
fof(f599,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f153,f8]) ).
fof(f614,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f599,f10]) ).
fof(f648,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(X1,top),
inference(superposition,[],[f198,f15]) ).
fof(f663,plain,
! [X0,X1] : complement(join(X1,X0)) = join(zero,complement(join(X0,join(join(X1,X0),X1)))),
inference(superposition,[],[f362,f198]) ).
fof(f687,plain,
! [X0,X1] : complement(join(X1,X0)) = join(zero,complement(join(X0,join(X1,join(X0,X1))))),
inference(forward_demodulation,[],[f663,f2]) ).
fof(f717,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(one,X0))),
inference(superposition,[],[f58,f614]) ).
fof(f723,plain,
! [X0,X1] : composition(join(converse(one),X1),X0) = join(X0,composition(X1,X0)),
inference(superposition,[],[f9,f614]) ).
fof(f725,plain,
one = converse(one),
inference(superposition,[],[f8,f614]) ).
fof(f728,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f614,f725]) ).
fof(f731,plain,
! [X0,X1] : join(X0,composition(X1,X0)) = composition(join(one,X1),X0),
inference(forward_demodulation,[],[f723,f725]) ).
fof(f736,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(backward_demodulation,[],[f717,f728]) ).
fof(f741,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(complement(X0)))),
inference(backward_demodulation,[],[f247,f736]) ).
fof(f743,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,X0)),
inference(forward_demodulation,[],[f741,f351]) ).
fof(f746,plain,
! [X0,X1] : join(complement(X0),X1) = join(X1,complement(join(X0,X0))),
inference(backward_demodulation,[],[f408,f743]) ).
fof(f747,plain,
! [X0] : complement(X0) = join(complement(X0),zero),
inference(backward_demodulation,[],[f362,f746]) ).
fof(f749,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(forward_demodulation,[],[f747,f1]) ).
fof(f753,plain,
! [X0,X1] : complement(join(X1,X0)) = complement(join(X0,join(X1,join(X0,X1)))),
inference(backward_demodulation,[],[f687,f749]) ).
fof(f773,plain,
! [X0] : join(zero,X0) = X0,
inference(superposition,[],[f749,f351]) ).
fof(f798,plain,
! [X0] : zero = composition(converse(X0),complement(composition(X0,top))),
inference(backward_demodulation,[],[f118,f773]) ).
fof(f859,plain,
! [X0] : join(X0,X0) = X0,
inference(superposition,[],[f736,f351]) ).
fof(f901,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1)),
inference(superposition,[],[f2,f859]) ).
fof(f903,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X1,X0)),
inference(superposition,[],[f198,f859]) ).
fof(f909,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X1,join(X0,X1))),
inference(superposition,[],[f2,f859]) ).
fof(f916,plain,
! [X0,X1] : complement(join(X0,X1)) = complement(join(X1,X0)),
inference(backward_demodulation,[],[f753,f909]) ).
fof(f1058,plain,
! [X0] : top = join(X0,top),
inference(superposition,[],[f901,f15]) ).
fof(f1106,plain,
! [X0,X1] : top = join(X0,join(complement(X0),X1)),
inference(backward_demodulation,[],[f648,f1058]) ).
fof(f1123,plain,
! [X1] : top = join(top,X1),
inference(backward_demodulation,[],[f187,f1106]) ).
fof(f1207,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,[],[f383,f414]) ).
fof(f1214,plain,
! [X0,X1] : complement(X0) = join(complement(join(X1,X0)),complement(X0)),
inference(superposition,[],[f901,f414]) ).
fof(f1215,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0))),
inference(forward_demodulation,[],[f1214,f1]) ).
fof(f1221,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,[],[f1207,f1]) ).
fof(f1243,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,complement(X1)))),
inference(backward_demodulation,[],[f550,f1215]) ).
fof(f1250,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,[],[f1221,f916]) ).
fof(f1270,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,[],[f1250,f2]) ).
fof(f1285,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(X1,join(X0,X1)))),
inference(forward_demodulation,[],[f1270,f1243]) ).
fof(f1298,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(X0,X1))),
inference(forward_demodulation,[],[f1285,f903]) ).
fof(f1306,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f1298,f351]) ).
fof(f1311,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f1306,f351]) ).
fof(f1706,plain,
! [X0] : zero = composition(converse(join(one,X0)),complement(join(top,composition(X0,top)))),
inference(superposition,[],[f798,f731]) ).
fof(f1723,plain,
! [X0] : zero = composition(converse(join(one,X0)),complement(top)),
inference(forward_demodulation,[],[f1706,f1123]) ).
fof(f1729,plain,
! [X0] : zero = composition(converse(join(one,X0)),zero),
inference(forward_demodulation,[],[f1723,f54]) ).
fof(f2773,plain,
! [X0] : join(one,converse(X0)) = converse(join(one,X0)),
inference(superposition,[],[f157,f725]) ).
fof(f2777,plain,
! [X0] : zero = composition(join(one,converse(X0)),zero),
inference(backward_demodulation,[],[f1729,f2773]) ).
fof(f2792,plain,
! [X0] : zero = join(zero,composition(converse(X0),zero)),
inference(forward_demodulation,[],[f2777,f731]) ).
fof(f2798,plain,
! [X0] : zero = composition(converse(X0),zero),
inference(forward_demodulation,[],[f2792,f773]) ).
fof(f2811,plain,
! [X0] : zero = composition(X0,zero),
inference(superposition,[],[f2798,f10]) ).
fof(f3036,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f591]) ).
fof(f3057,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f3036,f10]) ).
fof(f3145,plain,
! [X0,X1] : join(composition(X0,X1),X0) = composition(X0,join(X1,one)),
inference(superposition,[],[f3057,f8]) ).
fof(f3196,plain,
! [X0,X1] : join(X0,composition(X0,X1)) = composition(X0,join(X1,one)),
inference(forward_demodulation,[],[f3145,f1]) ).
fof(f3343,plain,
! [X0] : composition(X0,one) = join(X0,composition(X0,sF1)),
inference(superposition,[],[f3196,f59]) ).
fof(f3413,plain,
! [X0] : join(X0,composition(X0,sF1)) = X0,
inference(forward_demodulation,[],[f3343,f8]) ).
fof(f3482,plain,
! [X0] : composition(one,X0) = join(X0,composition(composition(one,sF1),X0)),
inference(superposition,[],[f731,f3413]) ).
fof(f3492,plain,
! [X0] : composition(one,X0) = join(X0,composition(one,composition(sF1,X0))),
inference(forward_demodulation,[],[f3482,f7]) ).
fof(f3513,plain,
! [X0] : composition(one,X0) = join(X0,composition(sF1,X0)),
inference(forward_demodulation,[],[f3492,f728]) ).
fof(f3522,plain,
! [X0] : join(X0,composition(sF1,X0)) = X0,
inference(forward_demodulation,[],[f3513,f728]) ).
fof(f4924,plain,
composition(sF0,sF3) = composition(sF1,sk2),
inference(superposition,[],[f273,f40]) ).
fof(f5634,plain,
sk2 = join(sk2,composition(sF0,sF3)),
inference(superposition,[],[f3522,f4924]) ).
fof(f11192,plain,
! [X0] : composition(complement(join(complement(sk1),complement(composition(X0,converse(sF5))))),complement(join(complement(sF5),complement(composition(converse(sk1),X0))))) = join(complement(join(complement(sF6),complement(X0))),composition(complement(join(complement(sk1),complement(composition(X0,converse(sF5))))),complement(join(complement(sF5),complement(composition(converse(sk1),X0)))))),
inference(superposition,[],[f28,f46]) ).
fof(f11376,plain,
! [X0] : composition(complement(join(complement(sk1),complement(composition(X0,converse(sF5))))),complement(join(complement(sF5),complement(composition(sF0,X0))))) = join(complement(join(complement(sF6),complement(X0))),composition(complement(join(complement(sk1),complement(composition(X0,converse(sF5))))),complement(join(complement(sF5),complement(composition(sF0,X0)))))),
inference(forward_demodulation,[],[f11192,f33]) ).
fof(f11442,plain,
! [X0] : composition(complement(join(complement(sk1),complement(composition(X0,converse(sF5))))),complement(join(sk2,complement(composition(sF0,X0))))) = join(complement(join(complement(sF6),complement(X0))),composition(complement(join(complement(sk1),complement(composition(X0,converse(sF5))))),complement(join(sk2,complement(composition(sF0,X0)))))),
inference(forward_demodulation,[],[f11376,f374]) ).
fof(f11481,plain,
! [X0] : composition(complement(join(complement(sk1),complement(composition(X0,converse(sF5))))),complement(join(sk2,complement(composition(sF0,X0))))) = join(complement(join(sF7,complement(X0))),composition(complement(join(complement(sk1),complement(composition(X0,converse(sF5))))),complement(join(sk2,complement(composition(sF0,X0)))))),
inference(forward_demodulation,[],[f11442,f48]) ).
fof(f11803,plain,
composition(complement(join(complement(sk1),complement(composition(sF3,converse(sF5))))),complement(join(sk2,complement(composition(sF0,sF3))))) = join(complement(join(sF7,sF4)),composition(complement(join(complement(sk1),complement(composition(sF3,converse(sF5))))),complement(join(sk2,complement(composition(sF0,sF3)))))),
inference(superposition,[],[f11481,f42]) ).
fof(f11878,plain,
composition(complement(join(complement(sk1),complement(composition(sF3,converse(sF5))))),complement(join(sk2,complement(composition(sF0,sF3))))) = join(complement(join(sF4,sF7)),composition(complement(join(complement(sk1),complement(composition(sF3,converse(sF5))))),complement(join(sk2,complement(composition(sF0,sF3)))))),
inference(forward_demodulation,[],[f11803,f916]) ).
fof(f11895,plain,
composition(complement(join(complement(sk1),complement(composition(sF3,converse(sF5))))),complement(join(sk2,complement(composition(sF0,sF3))))) = join(complement(sF8),composition(complement(join(complement(sk1),complement(composition(sF3,converse(sF5))))),complement(join(sk2,complement(composition(sF0,sF3)))))),
inference(forward_demodulation,[],[f11878,f50]) ).
fof(f11909,plain,
composition(complement(join(complement(sk1),complement(composition(sF3,converse(sF5))))),complement(join(sk2,complement(composition(sF0,sF3))))) = join(sF9,composition(complement(join(complement(sk1),complement(composition(sF3,converse(sF5))))),complement(join(sk2,complement(composition(sF0,sF3)))))),
inference(forward_demodulation,[],[f11895,f52]) ).
fof(f12508,plain,
join(sk2,complement(sk2)) = join(sk2,complement(composition(sF0,sF3))),
inference(superposition,[],[f1311,f5634]) ).
fof(f12514,plain,
top = join(sk2,complement(composition(sF0,sF3))),
inference(forward_demodulation,[],[f12508,f15]) ).
fof(f12531,plain,
composition(complement(join(complement(sk1),complement(composition(sF3,converse(sF5))))),complement(top)) = join(sF9,composition(complement(join(complement(sk1),complement(composition(sF3,converse(sF5))))),complement(top))),
inference(backward_demodulation,[],[f11909,f12514]) ).
fof(f12548,plain,
composition(complement(join(complement(sk1),complement(composition(sF3,converse(sF5))))),zero) = join(sF9,composition(complement(join(complement(sk1),complement(composition(sF3,converse(sF5))))),zero)),
inference(forward_demodulation,[],[f12531,f54]) ).
fof(f12560,plain,
zero = join(sF9,zero),
inference(forward_demodulation,[],[f12548,f2811]) ).
fof(f12572,plain,
zero = join(zero,sF9),
inference(forward_demodulation,[],[f12560,f1]) ).
fof(f12872,plain,
zero = sF9,
inference(forward_demodulation,[],[f12572,f773]) ).
fof(f12962,plain,
$false,
inference(forward_subsumption_resolution,[],[f12872,f53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL041-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.10 % 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
% 0.23/0.49 % CPULimit : 300
% 0.23/0.49 % WCLimit : 300
% 0.23/0.49 % DateTime : Sun Sep 27 22:56:54 UTC 2026
% 0.23/0.49 % CPUTime :
% 0.23/0.49 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.54 Running first-order theorem proving
% 0.26/0.54 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
% 10.87/3.72 % (1702249)Detected a unit-equality problem, will run specialized UEQ schedule.
% 10.87/3.72 % (1702259)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=217989738:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 10.87/3.72 % (1702257)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=273484032:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 10.87/3.72 % (1702260)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1235857424:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 10.87/3.72 % (1702254)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=2214518542:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 10.87/3.72 % (1702258)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=645183616:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 10.87/3.72 % (1702256)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=271084084:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 10.87/3.72 % (1702255)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=2706976842:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 10.87/3.72 % (1702257)Instruction limit reached!
% 10.87/3.72 % (1702257)------------------------------
% 10.87/3.72 % (1702257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.87/3.72 % (1702257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.87/3.72 % (1702257)CaDiCaL version: 2.1.3
% 10.87/3.72 % (1702257)Termination reason: Instruction limit
% 10.87/3.72 % (1702257)Termination phase: Saturation
% 10.87/3.72 % (1702257)Time elapsed: 0.133 s
% 10.87/3.72 % (1702257)Peak memory usage: 89 MB
% 10.87/3.72 % (1702257)Instructions burned: 137 (million)
% 10.87/3.72 % (1702259)Instruction limit reached!
% 10.87/3.72 % (1702259)------------------------------
% 10.87/3.72 % (1702259)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.87/3.72 % (1702259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.87/3.72 % (1702259)CaDiCaL version: 2.1.3
% 10.87/3.72 % (1702259)Termination reason: Instruction limit
% 10.87/3.72 % (1702259)Termination phase: Saturation
% 10.87/3.72 % (1702259)Time elapsed: 0.150 s
% 10.87/3.72 % (1702259)Peak memory usage: 90 MB
% 10.87/3.72 % (1702259)Instructions burned: 261 (million)
% 10.87/3.72 % (1702258)Instruction limit reached!
% 10.87/3.72 % (1702258)------------------------------
% 10.87/3.72 % (1702258)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.87/3.72 % (1702258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.87/3.72 % (1702258)CaDiCaL version: 2.1.3
% 10.87/3.72 % (1702258)Termination reason: Instruction limit
% 10.87/3.72 % (1702258)Termination phase: Saturation
% 10.87/3.72 % (1702258)Time elapsed: 0.178 s
% 10.87/3.72 % (1702258)Peak memory usage: 89 MB
% 10.87/3.72 % (1702258)Instructions burned: 181 (million)
% 10.87/3.72 % (1702269)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=554303457:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 10.87/3.72 % (1702268)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=4249330626:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2995 on theBenchmark for (2995ds/2051Mi)
% 10.87/3.72 % (1702270)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1957659622:i=215:ep=RSTC_2995 on theBenchmark for (2995ds/215Mi)
% 10.87/3.72 % (1702270)Instruction limit reached!
% 10.87/3.72 % (1702270)------------------------------
% 10.87/3.72 % (1702270)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.87/3.72 % (1702270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.87/3.72 % (1702270)CaDiCaL version: 2.1.3
% 10.87/3.72 % (1702270)Termination reason: Instruction limit
% 10.87/3.72 % (1702270)Termination phase: Saturation
% 10.87/3.72 % (1702270)Time elapsed: 0.208 s
% 10.87/3.72 % (1702270)Peak memory usage: 92 MB
% 10.87/3.72 % (1702270)Instructions burned: 215 (million)
% 10.87/3.72 % (1702274)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=2823459281:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2990 on theBenchmark for (2990ds/317Mi)
% 10.87/3.72 % (1702260)Instruction limit reached!
% 10.87/3.72 % (1702260)------------------------------
% 10.87/3.72 % (1702260)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.87/3.72 % (1702260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.87/3.72 % (1702260)CaDiCaL version: 2.1.3
% 10.87/3.72 % (1702260)Termination reason: Instruction limit
% 10.87/3.72 % (1702260)Termination phase: Saturation
% 10.87/3.72 % (1702260)Time elapsed: 1.113 s
% 10.87/3.72 % (1702260)Peak memory usage: 101 MB
% 10.87/3.72 % (1702260)Instructions burned: 1187 (million)
% 10.87/3.72 % (1702274)Instruction limit reached!
% 10.87/3.72 % (1702274)------------------------------
% 10.87/3.72 % (1702274)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.87/3.72 % (1702274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.87/3.72 % (1702274)CaDiCaL version: 2.1.3
% 10.87/3.72 % (1702274)Termination reason: Instruction limit
% 10.87/3.72 % (1702274)Termination phase: Saturation
% 10.87/3.72 % (1702274)Time elapsed: 0.337 s
% 10.87/3.72 % (1702274)Peak memory usage: 93 MB
% 10.87/3.72 % (1702274)Instructions burned: 318 (million)
% 10.87/3.72 % (1702276)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=912048476:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2986 on theBenchmark for (2986ds/12125Mi)
% 10.87/3.72 % (1702277)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=905580547:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2983 on theBenchmark for (2983ds/2836Mi)
% 10.87/3.72 % (1702256)First to succeed.
% 10.87/3.72 % (1702256)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1702249"
% 10.87/3.72 % (1702256)Refutation found. Thanks to Tanya!
% 10.87/3.72 % SZS status Unsatisfiable for theBenchmark
% 10.87/3.72 % SZS output start Proof for theBenchmark
% See solution above
% 20.01/3.92 % (1702256)------------------------------
% 20.01/3.92 % (1702256)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.01/3.92 % (1702256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.01/3.92 % (1702256)CaDiCaL version: 2.1.3
% 20.01/3.92 % (1702256)Termination reason: Refutation
% 20.01/3.92 % (1702256)Time elapsed: 2.195 s
% 20.01/3.92 % (1702256)Peak memory usage: 149 MB
% 20.01/3.92 % (1702256)Instructions burned: 3105 (million)
% 20.01/3.92 % (1702256)------------------------------
% 20.01/3.92 % (1702256)------------------------------
% 20.01/3.92 % (1702249)Success in time 2.754 s
% 20.01/3.92 % Vampire exiting
%------------------------------------------------------------------------------