%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL036-2 : 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 : n003.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 16.02s 3.45s
% Output : Refutation 16.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 27
% Syntax : Number of formulae : 179 ( 179 unt; 13 def)
% Number of atoms : 179 ( 178 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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 : 24 ( 24 usr; 19 con; 0-2 aty)
% Number of variables : 164 ( 164 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
fof(f2,axiom,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
fof(f4,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
fof(f6,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(reorient_equations,[],[f5]) ).
fof(f8,negated_conjecture,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity_6) ).
fof(f9,axiom,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f11,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f12,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
fof(f13,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity_11) ).
fof(f14,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top_12) ).
fof(f16,negated_conjecture,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero_13) ).
fof(f23,negated_conjecture,
composition(sk1,top) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_17) ).
fof(f24,plain,
sk1 = composition(sk1,top),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
join(composition(meet(sk2,converse(sk1)),sk3),composition(meet(sk2,converse(sk1)),meet(sk1,sk3))) != composition(meet(sk2,converse(sk1)),meet(sk1,sk3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_18) ).
fof(f26,plain,
composition(meet(sk2,converse(sk1)),meet(sk1,sk3)) != join(composition(meet(sk2,converse(sk1)),sk3),composition(meet(sk2,converse(sk1)),meet(sk1,sk3))),
inference(reorient_equations,[],[f25]) ).
fof(f27,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f31,plain,
composition(complement(join(complement(sk2),complement(converse(sk1)))),complement(join(complement(sk1),complement(sk3)))) != join(composition(complement(join(complement(sk2),complement(converse(sk1)))),sk3),composition(complement(join(complement(sk2),complement(converse(sk1)))),complement(join(complement(sk1),complement(sk3))))),
inference(definition_unfolding,[],[f26,f6,f6,f6,f6,f6]) ).
fof(f32,definition,
sF0 = composition(sk1,top),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f33,plain,
composition(sk1,top) = sF0,
inference(reorient_equations,[],[f32]) ).
fof(f34,plain,
sk1 = sF0,
inference(definition_folding,[],[f24,f33]) ).
fof(f35,definition,
sF1 = complement(sk2),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f36,plain,
complement(sk2) = sF1,
inference(reorient_equations,[],[f35]) ).
fof(f37,definition,
sF2 = converse(sk1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f38,plain,
converse(sk1) = sF2,
inference(reorient_equations,[],[f37]) ).
fof(f39,definition,
sF3 = complement(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f40,plain,
complement(sF2) = sF3,
inference(reorient_equations,[],[f39]) ).
fof(f41,definition,
sF4 = join(sF1,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f42,plain,
join(sF1,sF3) = sF4,
inference(reorient_equations,[],[f41]) ).
fof(f43,definition,
sF5 = complement(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f44,plain,
complement(sF4) = sF5,
inference(reorient_equations,[],[f43]) ).
fof(f45,definition,
sF6 = complement(sk1),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f46,plain,
complement(sk1) = sF6,
inference(reorient_equations,[],[f45]) ).
fof(f47,definition,
sF7 = complement(sk3),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f48,plain,
complement(sk3) = sF7,
inference(reorient_equations,[],[f47]) ).
fof(f49,definition,
sF8 = join(sF6,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f50,plain,
join(sF6,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,definition,
sF10 = composition(sF5,sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f54,plain,
composition(sF5,sF9) = sF10,
inference(reorient_equations,[],[f53]) ).
fof(f55,definition,
sF11 = composition(sF5,sk3),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f56,plain,
composition(sF5,sk3) = sF11,
inference(reorient_equations,[],[f55]) ).
fof(f57,definition,
sF12 = join(sF11,sF10),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f58,plain,
join(sF11,sF10) = sF12,
inference(reorient_equations,[],[f57]) ).
fof(f59,plain,
sF10 != sF12,
inference(definition_folding,[],[f31,f58,f54,f52,f50,f48,f46,f44,f42,f40,f38,f36,f56,f44,f42,f40,f38,f36,f54,f52,f50,f48,f46,f44,f42,f40,f38,f36]) ).
fof(f60,plain,
zero = complement(top),
inference(backward_demodulation,[],[f27,f15]) ).
fof(f61,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(backward_demodulation,[],[f4,f1]) ).
fof(f64,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(backward_demodulation,[],[f14,f1]) ).
fof(f65,plain,
sk1 = composition(sk1,top),
inference(forward_demodulation,[],[f33,f34]) ).
fof(f116,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[],[f61,f15]) ).
fof(f117,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f116,f60]) ).
fof(f145,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(superposition,[],[f61,f1]) ).
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(f161,plain,
complement(top) = join(complement(top),composition(converse(sk1),complement(sk1))),
inference(superposition,[],[f64,f65]) ).
fof(f165,plain,
complement(top) = join(complement(top),composition(converse(sk1),sF6)),
inference(forward_demodulation,[],[f161,f46]) ).
fof(f167,plain,
complement(top) = join(complement(top),composition(sF2,sF6)),
inference(forward_demodulation,[],[f165,f38]) ).
fof(f168,plain,
zero = join(zero,composition(sF2,sF6)),
inference(forward_demodulation,[],[f167,f60]) ).
fof(f171,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f12,f10]) ).
fof(f197,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(complement(join(complement(X0),complement(X1))),X2)),
inference(superposition,[],[f2,f61]) ).
fof(f210,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f234,plain,
! [X0,X1] : join(X0,X1) = join(complement(join(complement(X0),complement(X0))),join(complement(top),X1)),
inference(superposition,[],[f197,f15]) ).
fof(f250,plain,
! [X0,X1] : join(X0,X1) = join(complement(top),join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f234,f210]) ).
fof(f262,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f250,f60]) ).
fof(f426,plain,
! [X0] : complement(X0) = join(complement(join(complement(complement(X0)),X0)),complement(top)),
inference(superposition,[],[f145,f15]) ).
fof(f442,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(complement(complement(X0)),X0))),
inference(forward_demodulation,[],[f426,f1]) ).
fof(f466,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f442,f1]) ).
fof(f479,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f466,f60]) ).
fof(f486,plain,
! [X0] : complement(complement(X0)) = X0,
inference(backward_demodulation,[],[f117,f479]) ).
fof(f497,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,X0))),
inference(backward_demodulation,[],[f479,f486]) ).
fof(f510,plain,
! [X0,X1] : complement(join(X1,X0)) = join(zero,complement(join(X0,join(join(X1,X0),X1)))),
inference(superposition,[],[f497,f210]) ).
fof(f515,plain,
! [X0,X1] : join(complement(X0),X1) = join(zero,join(complement(join(X0,X0)),X1)),
inference(superposition,[],[f2,f497]) ).
fof(f518,plain,
! [X0,X1] : complement(join(X1,X0)) = join(zero,complement(join(X0,join(X1,join(X0,X1))))),
inference(forward_demodulation,[],[f510,f2]) ).
fof(f520,plain,
sk1 = complement(sF6),
inference(superposition,[],[f486,f46]) ).
fof(f521,plain,
sk2 = complement(sF1),
inference(superposition,[],[f486,f36]) ).
fof(f522,plain,
sk3 = complement(sF7),
inference(superposition,[],[f486,f48]) ).
fof(f523,plain,
sF2 = complement(sF3),
inference(superposition,[],[f486,f40]) ).
fof(f527,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(X0,complement(X1)))),
inference(superposition,[],[f61,f486]) ).
fof(f531,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0))),
inference(superposition,[],[f145,f486]) ).
fof(f560,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(X1,complement(X0)))),
inference(superposition,[],[f527,f1]) ).
fof(f663,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,[],[f527,f531]) ).
fof(f664,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,[],[f663,f486]) ).
fof(f687,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,[],[f664,f210]) ).
fof(f701,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,[],[f687,f1]) ).
fof(f713,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f701,f486]) ).
fof(f723,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f713,f486]) ).
fof(f736,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f171,f8]) ).
fof(f747,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f736,f10]) ).
fof(f756,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(one,X0))),
inference(superposition,[],[f64,f747]) ).
fof(f762,plain,
one = converse(one),
inference(superposition,[],[f8,f747]) ).
fof(f763,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f747,f762]) ).
fof(f768,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(backward_demodulation,[],[f756,f763]) ).
fof(f771,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(complement(X0)))),
inference(backward_demodulation,[],[f262,f768]) ).
fof(f772,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,X0)),
inference(forward_demodulation,[],[f771,f486]) ).
fof(f775,plain,
! [X0,X1] : join(complement(X0),X1) = join(X1,complement(join(X0,X0))),
inference(backward_demodulation,[],[f515,f772]) ).
fof(f776,plain,
! [X0] : complement(X0) = join(complement(X0),zero),
inference(backward_demodulation,[],[f497,f775]) ).
fof(f778,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(forward_demodulation,[],[f776,f1]) ).
fof(f782,plain,
! [X0,X1] : complement(join(X1,X0)) = complement(join(X0,join(X1,join(X0,X1)))),
inference(backward_demodulation,[],[f518,f778]) ).
fof(f797,plain,
! [X0] : join(zero,X0) = X0,
inference(superposition,[],[f778,f486]) ).
fof(f826,plain,
zero = composition(sF2,sF6),
inference(backward_demodulation,[],[f168,f797]) ).
fof(f842,plain,
! [X0] : join(X0,zero) = X0,
inference(superposition,[],[f1,f797]) ).
fof(f867,plain,
! [X0] : join(X0,X0) = X0,
inference(superposition,[],[f768,f486]) ).
fof(f910,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1)),
inference(superposition,[],[f2,f867]) ).
fof(f912,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X1,X0)),
inference(superposition,[],[f210,f867]) ).
fof(f918,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X1,join(X0,X1))),
inference(superposition,[],[f2,f867]) ).
fof(f925,plain,
! [X0,X1] : complement(join(X0,X1)) = complement(join(X1,X0)),
inference(backward_demodulation,[],[f782,f918]) ).
fof(f993,plain,
! [X0] : composition(join(X0,sF2),sF6) = join(composition(X0,sF6),zero),
inference(superposition,[],[f9,f826]) ).
fof(f996,plain,
! [X0] : composition(join(X0,sF2),sF6) = join(zero,composition(X0,sF6)),
inference(forward_demodulation,[],[f993,f1]) ).
fof(f998,plain,
! [X0] : composition(join(X0,sF2),sF6) = composition(X0,sF6),
inference(forward_demodulation,[],[f996,f797]) ).
fof(f1206,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(f1220,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f1206,f11]) ).
fof(f1237,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f1220,f11]) ).
fof(f1245,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f1237,f12]) ).
fof(f1268,plain,
complement(sF3) = join(complement(sF4),complement(join(sF3,complement(sF1)))),
inference(superposition,[],[f560,f42]) ).
fof(f1269,plain,
complement(sF7) = join(complement(sF8),complement(join(sF7,complement(sF6)))),
inference(superposition,[],[f560,f50]) ).
fof(f1288,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,[],[f531,f560]) ).
fof(f1295,plain,
! [X0,X1] : complement(X0) = join(complement(join(X1,X0)),complement(X0)),
inference(superposition,[],[f910,f560]) ).
fof(f1296,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0))),
inference(forward_demodulation,[],[f1295,f1]) ).
fof(f1302,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,[],[f1288,f1]) ).
fof(f1311,plain,
complement(sF7) = join(complement(sF8),complement(join(sF7,sk1))),
inference(forward_demodulation,[],[f1269,f520]) ).
fof(f1312,plain,
complement(sF3) = join(complement(sF4),complement(join(sF3,sk2))),
inference(forward_demodulation,[],[f1268,f521]) ).
fof(f1321,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,complement(X1)))),
inference(backward_demodulation,[],[f723,f1296]) ).
fof(f1328,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,[],[f1302,f925]) ).
fof(f1335,plain,
complement(sF7) = join(sF9,complement(join(sF7,sk1))),
inference(forward_demodulation,[],[f1311,f52]) ).
fof(f1336,plain,
complement(sF3) = join(sF5,complement(join(sF3,sk2))),
inference(forward_demodulation,[],[f1312,f44]) ).
fof(f1345,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,[],[f1328,f2]) ).
fof(f1351,plain,
sk3 = join(sF9,complement(join(sF7,sk1))),
inference(forward_demodulation,[],[f1335,f522]) ).
fof(f1352,plain,
sF2 = join(sF5,complement(join(sF3,sk2))),
inference(forward_demodulation,[],[f1336,f523]) ).
fof(f1360,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(X1,join(X0,X1)))),
inference(forward_demodulation,[],[f1345,f1321]) ).
fof(f1371,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(X0,X1))),
inference(forward_demodulation,[],[f1360,f912]) ).
fof(f1379,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f1371,f486]) ).
fof(f1384,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f1379,f486]) ).
fof(f1400,plain,
! [X0,X1] : join(X1,complement(join(X0,X1))) = join(X1,complement(X0)),
inference(superposition,[],[f1384,f1]) ).
fof(f1415,plain,
join(sF6,complement(sF7)) = join(sF6,complement(sF8)),
inference(superposition,[],[f1384,f50]) ).
fof(f1449,plain,
join(sF6,complement(sF7)) = join(sF6,sF9),
inference(forward_demodulation,[],[f1415,f52]) ).
fof(f1469,plain,
join(sF6,sk3) = join(sF6,sF9),
inference(forward_demodulation,[],[f1449,f522]) ).
fof(f1605,plain,
join(sF3,complement(sF1)) = join(sF3,complement(sF4)),
inference(superposition,[],[f1400,f42]) ).
fof(f1606,plain,
join(sF7,complement(sF6)) = join(sF7,complement(sF8)),
inference(superposition,[],[f1400,f50]) ).
fof(f1641,plain,
join(sF7,complement(sF6)) = join(sF7,sF9),
inference(forward_demodulation,[],[f1606,f52]) ).
fof(f1642,plain,
join(sF3,complement(sF1)) = join(sF3,sF5),
inference(forward_demodulation,[],[f1605,f44]) ).
fof(f1667,plain,
join(sF7,sk1) = join(sF7,sF9),
inference(forward_demodulation,[],[f1641,f520]) ).
fof(f1668,plain,
join(sF3,complement(sF1)) = join(sF5,sF3),
inference(forward_demodulation,[],[f1642,f1]) ).
fof(f1688,plain,
sk3 = join(sF9,complement(join(sF7,sF9))),
inference(backward_demodulation,[],[f1351,f1667]) ).
fof(f1689,plain,
join(sF3,sk2) = join(sF5,sF3),
inference(forward_demodulation,[],[f1668,f521]) ).
fof(f1701,plain,
sk3 = join(sF9,complement(sF7)),
inference(forward_demodulation,[],[f1688,f1400]) ).
fof(f1702,plain,
sF2 = join(sF5,complement(join(sF5,sF3))),
inference(backward_demodulation,[],[f1352,f1689]) ).
fof(f1707,plain,
sk3 = join(sF9,sk3),
inference(forward_demodulation,[],[f1701,f522]) ).
fof(f1708,plain,
sF2 = join(sF5,complement(sF3)),
inference(forward_demodulation,[],[f1702,f1384]) ).
fof(f1713,plain,
sF2 = join(sF5,sF2),
inference(forward_demodulation,[],[f1708,f523]) ).
fof(f2395,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f1245]) ).
fof(f2411,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f2395,f10]) ).
fof(f2472,plain,
! [X0] : composition(sF5,join(sF9,X0)) = join(sF10,composition(sF5,X0)),
inference(superposition,[],[f2411,f54]) ).
fof(f2484,plain,
! [X0] : composition(sF5,join(X0,sF9)) = join(composition(sF5,X0),sF10),
inference(superposition,[],[f2411,f54]) ).
fof(f2485,plain,
! [X0] : composition(sF5,join(X0,sk3)) = join(composition(sF5,X0),sF11),
inference(superposition,[],[f2411,f56]) ).
fof(f2511,plain,
! [X0] : join(sF11,composition(sF5,X0)) = composition(sF5,join(X0,sk3)),
inference(forward_demodulation,[],[f2485,f1]) ).
fof(f2512,plain,
! [X0] : join(sF10,composition(sF5,X0)) = composition(sF5,join(X0,sF9)),
inference(forward_demodulation,[],[f2484,f1]) ).
fof(f4504,plain,
composition(sF5,sk3) = join(sF11,composition(sF5,sF9)),
inference(superposition,[],[f2511,f1707]) ).
fof(f4505,plain,
join(sF11,composition(sF5,sF6)) = composition(sF5,join(sF6,sF9)),
inference(superposition,[],[f2511,f1469]) ).
fof(f4506,plain,
composition(sF5,sk3) = join(sF11,composition(sF5,zero)),
inference(superposition,[],[f2511,f797]) ).
fof(f4534,plain,
sF11 = join(sF11,composition(sF5,zero)),
inference(forward_demodulation,[],[f4506,f56]) ).
fof(f4535,plain,
join(sF11,composition(sF5,sF6)) = join(sF10,composition(sF5,sF6)),
inference(forward_demodulation,[],[f4505,f2512]) ).
fof(f4536,plain,
composition(sF5,sk3) = join(sF11,sF10),
inference(forward_demodulation,[],[f4504,f54]) ).
fof(f4540,plain,
composition(sF5,sk3) = sF12,
inference(forward_demodulation,[],[f4536,f58]) ).
fof(f4543,plain,
sF11 = sF12,
inference(forward_demodulation,[],[f4540,f56]) ).
fof(f4546,plain,
sF10 != sF11,
inference(backward_demodulation,[],[f59,f4543]) ).
fof(f4580,plain,
! [X0] : join(sF10,join(composition(sF5,sF6),X0)) = join(join(sF11,composition(sF5,sF6)),X0),
inference(superposition,[],[f2,f4535]) ).
fof(f4603,plain,
! [X0] : join(sF10,join(composition(sF5,sF6),X0)) = join(sF11,join(composition(sF5,sF6),X0)),
inference(forward_demodulation,[],[f4580,f2]) ).
fof(f4822,plain,
composition(sF5,sF9) = join(sF10,composition(sF5,zero)),
inference(superposition,[],[f2472,f842]) ).
fof(f4854,plain,
sF10 = join(sF10,composition(sF5,zero)),
inference(forward_demodulation,[],[f4822,f54]) ).
fof(f5864,plain,
composition(sF2,sF6) = composition(sF5,sF6),
inference(superposition,[],[f998,f1713]) ).
fof(f5893,plain,
zero = composition(sF5,sF6),
inference(forward_demodulation,[],[f5864,f826]) ).
fof(f5903,plain,
! [X0] : join(sF10,join(zero,X0)) = join(sF11,join(zero,X0)),
inference(backward_demodulation,[],[f4603,f5893]) ).
fof(f5908,plain,
! [X0] : join(sF10,X0) = join(sF11,X0),
inference(forward_demodulation,[],[f5903,f797]) ).
fof(f5962,plain,
sF10 = join(sF11,composition(sF5,zero)),
inference(backward_demodulation,[],[f4854,f5908]) ).
fof(f5970,plain,
sF10 = sF11,
inference(forward_demodulation,[],[f5962,f4534]) ).
fof(f5983,plain,
$false,
inference(forward_subsumption_resolution,[],[f5970,f4546]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL036-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.47 % Computer : n003.cluster.edu
% 0.21/0.47 % Model : x86_64 x86_64
% 0.21/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.47 % Memory : 8046.5625MB
% 0.21/0.47 % OS : Linux 6.8.0-71-generic
% 0.21/0.47 % CPULimit : 300
% 0.21/0.47 % WCLimit : 300
% 0.21/0.47 % DateTime : Sun Sep 27 22:57:11 UTC 2026
% 0.21/0.48 % CPUTime :
% 0.21/0.48 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.53 Running first-order theorem proving
% 0.26/0.53 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
% 16.02/3.45 % (1018569)Detected a unit-equality problem, will run specialized UEQ schedule.
% 16.02/3.45 % (1018586)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1973280804:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 16.02/3.45 % (1018583)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=2764782274:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 16.02/3.45 % (1018582)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=2399516031:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 16.02/3.45 % (1018584)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2869328020:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 16.02/3.45 % (1018585)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=843878421:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 16.02/3.45 % (1018588)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1950364952:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 16.02/3.45 % (1018587)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2144281576:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 16.02/3.45 % (1018586)Instruction limit reached!
% 16.02/3.45 % (1018586)------------------------------
% 16.02/3.45 % (1018586)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.02/3.45 % (1018586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.02/3.45 % (1018586)CaDiCaL version: 2.1.3
% 16.02/3.45 % (1018586)Termination reason: Instruction limit
% 16.02/3.45 % (1018586)Termination phase: Saturation
% 16.02/3.45 % (1018586)Time elapsed: 0.098 s
% 16.02/3.45 % (1018586)Peak memory usage: 90 MB
% 16.02/3.45 % (1018586)Instructions burned: 183 (million)
% 16.02/3.45 % (1018585)Instruction limit reached!
% 16.02/3.45 % (1018585)------------------------------
% 16.02/3.45 % (1018585)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.02/3.45 % (1018585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.02/3.45 % (1018585)CaDiCaL version: 2.1.3
% 16.02/3.45 % (1018585)Termination reason: Instruction limit
% 16.02/3.45 % (1018585)Termination phase: Saturation
% 16.02/3.45 % (1018585)Time elapsed: 0.139 s
% 16.02/3.45 % (1018585)Peak memory usage: 89 MB
% 16.02/3.45 % (1018585)Instructions burned: 136 (million)
% 16.02/3.45 % (1018596)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3579004283:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 16.02/3.45 % (1018587)Instruction limit reached!
% 16.02/3.45 % (1018587)------------------------------
% 16.02/3.45 % (1018587)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.02/3.45 % (1018587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.02/3.45 % (1018587)CaDiCaL version: 2.1.3
% 16.02/3.45 % (1018587)Termination reason: Instruction limit
% 16.02/3.45 % (1018587)Termination phase: Saturation
% 16.02/3.45 % (1018587)Time elapsed: 0.291 s
% 16.02/3.45 % (1018587)Peak memory usage: 91 MB
% 16.02/3.45 % (1018587)Instructions burned: 257 (million)
% 16.02/3.45 % (1018597)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=327598595:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 16.02/3.45 % (1018599)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3646176244:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 16.02/3.45 % (1018599)Instruction limit reached!
% 16.02/3.45 % (1018599)------------------------------
% 16.02/3.45 % (1018599)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.02/3.45 % (1018599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.02/3.45 % (1018599)CaDiCaL version: 2.1.3
% 16.02/3.45 % (1018599)Termination reason: Instruction limit
% 16.02/3.45 % (1018599)Termination phase: Saturation
% 16.02/3.45 % (1018599)Time elapsed: 0.203 s
% 16.02/3.45 % (1018599)Peak memory usage: 92 MB
% 16.02/3.45 % (1018599)Instructions burned: 215 (million)
% 16.02/3.45 % (1018602)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=2728747752: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)
% 16.02/3.45 % (1018588)Instruction limit reached!
% 16.02/3.45 % (1018588)------------------------------
% 16.02/3.45 % (1018588)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.02/3.45 % (1018588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.02/3.45 % (1018588)CaDiCaL version: 2.1.3
% 16.02/3.45 % (1018588)Termination reason: Instruction limit
% 16.02/3.45 % (1018588)Termination phase: Saturation
% 16.02/3.45 % (1018588)Time elapsed: 1.110 s
% 16.02/3.45 % (1018588)Peak memory usage: 102 MB
% 16.02/3.45 % (1018588)Instructions burned: 1188 (million)
% 16.02/3.45 % (1018602)Instruction limit reached!
% 16.02/3.45 % (1018602)------------------------------
% 16.02/3.45 % (1018602)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.02/3.45 % (1018602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.02/3.45 % (1018602)CaDiCaL version: 2.1.3
% 16.02/3.45 % (1018602)Termination reason: Instruction limit
% 16.02/3.45 % (1018602)Termination phase: Saturation
% 16.02/3.45 % (1018602)Time elapsed: 0.309 s
% 16.02/3.45 % (1018602)Peak memory usage: 92 MB
% 16.02/3.45 % (1018602)Instructions burned: 317 (million)
% 16.02/3.45 % (1018604)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=1303640986:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2985 on theBenchmark for (2985ds/12125Mi)
% 16.02/3.45 % (1018584)First to succeed.
% 16.02/3.45 % (1018584)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1018569"
% 16.02/3.45 % (1018605)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=620752540:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2983 on theBenchmark for (2983ds/2836Mi)
% 16.02/3.45 % (1018584)Refutation found. Thanks to Tanya!
% 16.02/3.45 % SZS status Unsatisfiable for theBenchmark
% 16.02/3.45 % SZS output start Proof for theBenchmark
% See solution above
% 16.58/3.65 % (1018584)------------------------------
% 16.58/3.65 % (1018584)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.58/3.65 % (1018584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.58/3.65 % (1018584)CaDiCaL version: 2.1.3
% 16.58/3.65 % (1018584)Termination reason: Refutation
% 16.58/3.65 % (1018584)Time elapsed: 1.662 s
% 16.58/3.65 % (1018584)Peak memory usage: 138 MB
% 16.58/3.65 % (1018584)Instructions burned: 1960 (million)
% 16.58/3.65 % (1018584)------------------------------
% 16.58/3.65 % (1018584)------------------------------
% 16.58/3.65 % (1018569)Success in time 2.237 s
% 16.58/3.65 % Vampire exiting
%------------------------------------------------------------------------------