%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL011-1 : 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 : n026.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 12:33:42 PM UTC 2026
% Result : Unsatisfiable 10.69s 2.34s
% Output : Refutation 11.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 25
% Syntax : Number of formulae : 161 ( 161 unt; 11 def)
% Number of atoms : 161 ( 160 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 : 22 ( 22 usr; 17 con; 0-2 aty)
% Number of variables : 182 ( 182 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
fof(f2,axiom,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
fof(f4,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
fof(f6,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(reorient_equations,[],[f5]) ).
fof(f8,negated_conjecture,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity_6) ).
fof(f9,axiom,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f11,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f12,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
fof(f13,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity_11) ).
fof(f14,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top_12) ).
fof(f16,negated_conjecture,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero_13) ).
fof(f17,negated_conjecture,
meet(sk1,composition(converse(sk2),sk3)) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
fof(f18,plain,
zero = meet(sk1,composition(converse(sk2),sk3)),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
meet(composition(sk2,sk1),sk3) != zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_15) ).
fof(f20,plain,
zero != meet(composition(sk2,sk1),sk3),
inference(reorient_equations,[],[f19]) ).
fof(f21,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f22,plain,
zero = complement(join(complement(sk1),complement(composition(converse(sk2),sk3)))),
inference(definition_unfolding,[],[f18,f6]) ).
fof(f23,plain,
zero != complement(join(complement(composition(sk2,sk1)),complement(sk3))),
inference(definition_unfolding,[],[f20,f6]) ).
fof(f24,definition,
sF0 = complement(sk1),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f25,plain,
complement(sk1) = sF0,
inference(reorient_equations,[],[f24]) ).
fof(f26,definition,
sF1 = converse(sk2),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f27,plain,
converse(sk2) = sF1,
inference(reorient_equations,[],[f26]) ).
fof(f28,definition,
sF2 = composition(sF1,sk3),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f29,plain,
composition(sF1,sk3) = sF2,
inference(reorient_equations,[],[f28]) ).
fof(f30,definition,
sF3 = complement(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f31,plain,
complement(sF2) = sF3,
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
sF4 = join(sF0,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f33,plain,
join(sF0,sF3) = sF4,
inference(reorient_equations,[],[f32]) ).
fof(f34,definition,
sF5 = complement(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f35,plain,
complement(sF4) = sF5,
inference(reorient_equations,[],[f34]) ).
fof(f36,plain,
zero = sF5,
inference(definition_folding,[],[f22,f35,f33,f31,f29,f27,f25]) ).
fof(f37,definition,
sF6 = composition(sk2,sk1),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f38,plain,
composition(sk2,sk1) = sF6,
inference(reorient_equations,[],[f37]) ).
fof(f39,definition,
sF7 = complement(sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f40,plain,
complement(sF6) = sF7,
inference(reorient_equations,[],[f39]) ).
fof(f41,definition,
sF8 = complement(sk3),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f42,plain,
complement(sk3) = sF8,
inference(reorient_equations,[],[f41]) ).
fof(f43,definition,
sF9 = join(sF7,sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f44,plain,
join(sF7,sF8) = sF9,
inference(reorient_equations,[],[f43]) ).
fof(f45,definition,
sF10 = complement(sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f46,plain,
complement(sF9) = sF10,
inference(reorient_equations,[],[f45]) ).
fof(f47,plain,
zero != sF10,
inference(definition_folding,[],[f23,f46,f44,f42,f40,f38]) ).
fof(f48,plain,
zero = complement(top),
inference(backward_demodulation,[],[f21,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,
zero = complement(sF4),
inference(forward_demodulation,[],[f35,f36]) ).
fof(f53,plain,
! [X0] : top = join(complement(join(zero,X0)),complement(join(zero,complement(X0)))),
inference(superposition,[],[f50,f48]) ).
fof(f101,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[],[f50,f15]) ).
fof(f102,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f101,f48]) ).
fof(f119,plain,
! [X0] : sF4 = join(complement(join(zero,X0)),complement(join(zero,complement(X0)))),
inference(superposition,[],[f50,f51]) ).
fof(f120,plain,
top = sF4,
inference(backward_demodulation,[],[f53,f119]) ).
fof(f122,plain,
! [X0] : join(X0,complement(X0)) = sF4,
inference(backward_demodulation,[],[f15,f120]) ).
fof(f145,plain,
complement(sk3) = join(complement(sk3),composition(converse(sF1),complement(sF2))),
inference(superposition,[],[f49,f29]) ).
fof(f146,plain,
complement(sk3) = join(complement(sk3),composition(converse(sF1),sF3)),
inference(forward_demodulation,[],[f145,f31]) ).
fof(f147,plain,
sF8 = join(sF8,composition(converse(sF1),sF3)),
inference(forward_demodulation,[],[f146,f42]) ).
fof(f154,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(superposition,[],[f50,f1]) ).
fof(f179,plain,
sk2 = converse(sF1),
inference(superposition,[],[f10,f27]) ).
fof(f182,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(X0,complement(composition(converse(X0),X1)))),
inference(superposition,[],[f49,f10]) ).
fof(f183,plain,
sF8 = join(sF8,composition(sk2,sF3)),
inference(backward_demodulation,[],[f147,f179]) ).
fof(f185,plain,
! [X2,X0,X1] : join(join(X0,X1),X2) = join(X1,join(X0,X2)),
inference(superposition,[],[f2,f1]) ).
fof(f188,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(sF4,X1),
inference(superposition,[],[f2,f122]) ).
fof(f198,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f211,plain,
! [X0,X1] : join(sF4,X0) = join(X1,join(X0,complement(X1))),
inference(superposition,[],[f188,f1]) ).
fof(f213,plain,
! [X0,X1] : join(sF4,complement(join(complement(X0),complement(X1)))) = join(join(complement(X0),X1),X0),
inference(superposition,[],[f188,f50]) ).
fof(f222,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(sF4,complement(join(complement(X0),complement(X1)))),
inference(forward_demodulation,[],[f213,f1]) ).
fof(f226,plain,
! [X0,X1] : join(sF4,X1) = join(sF4,complement(join(complement(X0),complement(X1)))),
inference(forward_demodulation,[],[f222,f188]) ).
fof(f230,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f12,f10]) ).
fof(f232,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(f262,plain,
! [X0] : complement(X0) = join(complement(join(complement(complement(X0)),X0)),complement(sF4)),
inference(superposition,[],[f154,f122]) ).
fof(f271,plain,
! [X0] : complement(X0) = join(complement(sF4),complement(join(complement(complement(X0)),X0))),
inference(forward_demodulation,[],[f262,f1]) ).
fof(f293,plain,
! [X0] : complement(X0) = join(complement(sF4),complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f271,f1]) ).
fof(f304,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f293,f51]) ).
fof(f311,plain,
! [X0] : complement(complement(X0)) = X0,
inference(backward_demodulation,[],[f102,f304]) ).
fof(f314,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,X0))),
inference(backward_demodulation,[],[f304,f311]) ).
fof(f324,plain,
sk1 = complement(sF0),
inference(superposition,[],[f311,f25]) ).
fof(f335,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0))),
inference(superposition,[],[f154,f311]) ).
fof(f360,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(complement(complement(join(complement(X1),X0))),complement(join(X0,X1))))),
inference(superposition,[],[f335,f335]) ).
fof(f367,plain,
! [X0,X1] : complement(X1) = join(complement(join(X1,complement(X0))),complement(join(X0,X1))),
inference(superposition,[],[f335,f311]) ).
fof(f371,plain,
! [X0] : complement(X0) = join(complement(join(X0,sF4)),complement(join(zero,X0))),
inference(superposition,[],[f335,f51]) ).
fof(f380,plain,
! [X0,X1] : join(sF4,complement(join(complement(X1),X0))) = join(join(X0,X1),complement(X0)),
inference(superposition,[],[f188,f335]) ).
fof(f383,plain,
! [X0,X1] : join(complement(X0),join(X0,X1)) = join(sF4,complement(join(complement(X1),X0))),
inference(forward_demodulation,[],[f380,f1]) ).
fof(f388,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(X1,complement(X0)))),
inference(forward_demodulation,[],[f367,f1]) ).
fof(f393,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(forward_demodulation,[],[f360,f1]) ).
fof(f398,plain,
! [X0,X1] : join(X0,join(X1,complement(X0))) = join(sF4,complement(join(complement(X1),X0))),
inference(forward_demodulation,[],[f383,f198]) ).
fof(f408,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,[],[f393,f311]) ).
fof(f411,plain,
! [X0,X1] : join(sF4,X1) = join(sF4,complement(join(complement(X1),X0))),
inference(forward_demodulation,[],[f398,f211]) ).
fof(f419,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,[],[f408,f198]) ).
fof(f422,plain,
! [X0,X1] : join(sF4,X1) = join(sF4,X0),
inference(backward_demodulation,[],[f226,f411]) ).
fof(f427,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,[],[f419,f1]) ).
fof(f430,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f427,f311]) ).
fof(f431,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f430,f311]) ).
fof(f455,plain,
! [X0,X1] : join(sF4,X0) = join(X1,sF4),
inference(superposition,[],[f1,f422]) ).
fof(f457,plain,
! [X0] : sF4 = join(sF4,X0),
inference(superposition,[],[f122,f422]) ).
fof(f478,plain,
! [X1] : sF4 = join(X1,sF4),
inference(forward_demodulation,[],[f455,f457]) ).
fof(f504,plain,
! [X0] : complement(X0) = join(complement(sF4),complement(join(zero,X0))),
inference(backward_demodulation,[],[f371,f478]) ).
fof(f511,plain,
! [X0] : complement(X0) = join(zero,complement(join(zero,X0))),
inference(forward_demodulation,[],[f504,f51]) ).
fof(f641,plain,
! [X0] : complement(complement(join(X0,X0))) = join(zero,complement(complement(X0))),
inference(superposition,[],[f511,f314]) ).
fof(f657,plain,
! [X0] : join(zero,X0) = complement(complement(join(X0,X0))),
inference(forward_demodulation,[],[f641,f311]) ).
fof(f662,plain,
! [X0] : join(zero,X0) = join(X0,X0),
inference(forward_demodulation,[],[f657,f311]) ).
fof(f681,plain,
! [X0] : join(X0,X0) = join(X0,zero),
inference(superposition,[],[f1,f662]) ).
fof(f735,plain,
! [X0,X1] : join(join(X0,X0),X1) = join(X0,join(zero,X1)),
inference(superposition,[],[f2,f681]) ).
fof(f738,plain,
! [X0,X1] : join(X0,join(X0,X1)) = join(X0,join(zero,X1)),
inference(forward_demodulation,[],[f735,f2]) ).
fof(f819,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,[],[f335,f388]) ).
fof(f827,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,[],[f819,f1]) ).
fof(f858,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,[],[f827,f1]) ).
fof(f886,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,[],[f858,f2]) ).
fof(f908,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f886,f311]) ).
fof(f924,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f908,f311]) ).
fof(f1023,plain,
! [X0,X1] : join(X0,join(X1,X0)) = join(X1,join(zero,X0)),
inference(superposition,[],[f198,f662]) ).
fof(f1076,plain,
! [X0,X1] : join(X0,join(zero,X1)) = join(X1,join(X0,X0)),
inference(superposition,[],[f198,f681]) ).
fof(f1326,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f232,f12]) ).
fof(f1339,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f1326,f11]) ).
fof(f1347,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f1339,f11]) ).
fof(f1350,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f1347,f12]) ).
fof(f1576,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f230,f8]) ).
fof(f1593,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f1576,f10]) ).
fof(f1608,plain,
! [X0] : complement(X0) = join(complement(X0),composition(one,complement(X0))),
inference(superposition,[],[f182,f1593]) ).
fof(f1615,plain,
one = converse(one),
inference(superposition,[],[f8,f1593]) ).
fof(f1618,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f1593,f1615]) ).
fof(f1628,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(backward_demodulation,[],[f1608,f1618]) ).
fof(f1634,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(forward_demodulation,[],[f1628,f662]) ).
fof(f1640,plain,
! [X0] : complement(X0) = complement(join(X0,X0)),
inference(backward_demodulation,[],[f314,f1634]) ).
fof(f1699,plain,
! [X0] : complement(complement(X0)) = join(X0,X0),
inference(superposition,[],[f311,f1640]) ).
fof(f1706,plain,
! [X0] : join(X0,X0) = X0,
inference(forward_demodulation,[],[f1699,f311]) ).
fof(f1722,plain,
! [X0] : join(X0,zero) = X0,
inference(backward_demodulation,[],[f681,f1706]) ).
fof(f1728,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(zero,X1)),
inference(backward_demodulation,[],[f1076,f1706]) ).
fof(f1752,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X1,X0)),
inference(backward_demodulation,[],[f1023,f1728]) ).
fof(f1754,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X0,X1)),
inference(backward_demodulation,[],[f738,f1728]) ).
fof(f2066,plain,
! [X0,X1] : join(complement(join(X0,complement(X1))),complement(join(X1,X0))) = join(complement(join(X1,X0)),complement(X0)),
inference(superposition,[],[f1754,f388]) ).
fof(f2125,plain,
! [X0,X1] : join(complement(X0),complement(join(X1,X0))) = join(complement(join(X0,complement(X1))),complement(join(X1,X0))),
inference(forward_demodulation,[],[f2066,f1]) ).
fof(f2155,plain,
! [X0,X1] : join(complement(X0),complement(join(X1,X0))) = join(complement(join(X1,X0)),complement(join(X0,complement(X1)))),
inference(forward_demodulation,[],[f2125,f1]) ).
fof(f2169,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0))),
inference(forward_demodulation,[],[f2155,f388]) ).
fof(f2175,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,complement(X1)))),
inference(backward_demodulation,[],[f431,f2169]) ).
fof(f2180,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,X1)))),
inference(backward_demodulation,[],[f924,f2175]) ).
fof(f2183,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,X0))),
inference(forward_demodulation,[],[f2180,f1752]) ).
fof(f2208,plain,
join(sF3,complement(sF0)) = join(sF3,complement(sF4)),
inference(superposition,[],[f2183,f33]) ).
fof(f2251,plain,
join(sF3,complement(sF0)) = join(sF3,zero),
inference(forward_demodulation,[],[f2208,f51]) ).
fof(f2285,plain,
sF3 = join(sF3,complement(sF0)),
inference(forward_demodulation,[],[f2251,f1722]) ).
fof(f2308,plain,
sF3 = join(sF3,sk1),
inference(forward_demodulation,[],[f2285,f324]) ).
fof(f4168,plain,
! [X0] : join(sF8,X0) = join(composition(sk2,sF3),join(sF8,X0)),
inference(superposition,[],[f185,f183]) ).
fof(f4292,plain,
! [X0] : join(sF8,X0) = join(sF8,join(X0,composition(sk2,sF3))),
inference(forward_demodulation,[],[f4168,f198]) ).
fof(f6815,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f1350]) ).
fof(f6834,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f6815,f10]) ).
fof(f6942,plain,
! [X0] : composition(sk2,join(X0,sk1)) = join(composition(sk2,X0),sF6),
inference(superposition,[],[f6834,f38]) ).
fof(f6997,plain,
! [X0] : join(sF6,composition(sk2,X0)) = composition(sk2,join(X0,sk1)),
inference(forward_demodulation,[],[f6942,f1]) ).
fof(f7304,plain,
composition(sk2,sF3) = join(sF6,composition(sk2,sF3)),
inference(superposition,[],[f6997,f2308]) ).
fof(f7343,plain,
join(sF8,composition(sk2,sF3)) = join(sF8,sF6),
inference(superposition,[],[f4292,f7304]) ).
fof(f7369,plain,
join(sF8,composition(sk2,sF3)) = join(sF6,sF8),
inference(forward_demodulation,[],[f7343,f1]) ).
fof(f7375,plain,
sF8 = join(sF6,sF8),
inference(forward_demodulation,[],[f7369,f183]) ).
fof(f7401,plain,
join(sF8,complement(sF8)) = join(sF8,complement(sF6)),
inference(superposition,[],[f2183,f7375]) ).
fof(f7405,plain,
join(sF8,sF7) = join(sF8,complement(sF8)),
inference(forward_demodulation,[],[f7401,f40]) ).
fof(f7413,plain,
sF4 = join(sF8,sF7),
inference(forward_demodulation,[],[f7405,f122]) ).
fof(f7419,plain,
sF4 = join(sF7,sF8),
inference(forward_demodulation,[],[f7413,f1]) ).
fof(f7424,plain,
sF4 = sF9,
inference(backward_demodulation,[],[f44,f7419]) ).
fof(f7428,plain,
complement(sF4) = sF10,
inference(backward_demodulation,[],[f46,f7424]) ).
fof(f7539,plain,
zero = sF10,
inference(forward_demodulation,[],[f7428,f51]) ).
fof(f7571,plain,
$false,
inference(forward_subsumption_resolution,[],[f7539,f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL011-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 22:53:57 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 10.69/2.34 % (3297416)Detected a unit-equality problem, will run specialized UEQ schedule.
% 10.69/2.34 % (3297425)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1652642782:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 10.69/2.34 % (3297424)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3581105792:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 10.69/2.34 % (3297426)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=241825359:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 10.69/2.34 % (3297423)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=4283955704:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 10.69/2.34 % (3297427)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4162545051:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 10.69/2.34 % (3297421)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=880230282:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 10.69/2.34 % (3297422)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=104160416:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 10.69/2.34 % (3297425)Instruction limit reached!
% 10.69/2.34 % (3297425)------------------------------
% 10.69/2.34 % (3297425)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.69/2.34 % (3297425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.69/2.34 % (3297425)CaDiCaL version: 2.1.3
% 10.69/2.34 % (3297425)Termination reason: Instruction limit
% 10.69/2.34 % (3297425)Termination phase: Saturation
% 10.69/2.34 % (3297425)Time elapsed: 0.056 s
% 10.69/2.34 % (3297425)Peak memory usage: 89 MB
% 10.69/2.34 % (3297425)Instructions burned: 181 (million)
% 10.69/2.34 % (3297424)Instruction limit reached!
% 10.69/2.34 % (3297424)------------------------------
% 10.69/2.34 % (3297424)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.69/2.34 % (3297424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.69/2.34 % (3297424)CaDiCaL version: 2.1.3
% 10.69/2.34 % (3297424)Termination reason: Instruction limit
% 10.69/2.34 % (3297424)Termination phase: Saturation
% 10.69/2.34 % (3297424)Time elapsed: 0.083 s
% 10.69/2.34 % (3297424)Peak memory usage: 89 MB
% 10.69/2.34 % (3297424)Instructions burned: 136 (million)
% 10.69/2.34 % (3297435)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2090932076:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 10.69/2.34 % (3297426)Instruction limit reached!
% 10.69/2.34 % (3297426)------------------------------
% 10.69/2.34 % (3297426)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.69/2.34 % (3297426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.69/2.34 % (3297426)CaDiCaL version: 2.1.3
% 10.69/2.34 % (3297426)Termination reason: Instruction limit
% 10.69/2.34 % (3297426)Termination phase: Saturation
% 10.69/2.34 % (3297426)Time elapsed: 0.169 s
% 10.69/2.34 % (3297426)Peak memory usage: 90 MB
% 10.69/2.34 % (3297426)Instructions burned: 258 (million)
% 10.69/2.34 % (3297436)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3745558249:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 10.69/2.34 % (3297438)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=204473505:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 10.69/2.34 % (3297438)Instruction limit reached!
% 10.69/2.34 % (3297438)------------------------------
% 10.69/2.34 % (3297438)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.69/2.34 % (3297438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.69/2.34 % (3297438)CaDiCaL version: 2.1.3
% 10.69/2.34 % (3297438)Termination reason: Instruction limit
% 10.69/2.34 % (3297438)Termination phase: Saturation
% 10.69/2.34 % (3297438)Time elapsed: 0.119 s
% 10.69/2.34 % (3297438)Peak memory usage: 92 MB
% 10.69/2.34 % (3297438)Instructions burned: 217 (million)
% 10.69/2.34 % (3297441)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=4191758355:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 10.69/2.34 % (3297427)Instruction limit reached!
% 10.69/2.34 % (3297427)------------------------------
% 10.69/2.34 % (3297427)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.69/2.34 % (3297427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.69/2.34 % (3297427)CaDiCaL version: 2.1.3
% 10.69/2.34 % (3297427)Termination reason: Instruction limit
% 10.69/2.34 % (3297427)Termination phase: Saturation
% 10.69/2.34 % (3297427)Time elapsed: 0.667 s
% 10.69/2.34 % (3297427)Peak memory usage: 101 MB
% 10.69/2.34 % (3297427)Instructions burned: 1188 (million)
% 10.69/2.34 % (3297441)Instruction limit reached!
% 10.69/2.34 % (3297441)------------------------------
% 10.69/2.34 % (3297441)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.69/2.34 % (3297441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.69/2.34 % (3297441)CaDiCaL version: 2.1.3
% 10.69/2.34 % (3297441)Termination reason: Instruction limit
% 10.69/2.34 % (3297441)Termination phase: Saturation
% 10.69/2.34 % (3297441)Time elapsed: 0.202 s
% 10.69/2.34 % (3297441)Peak memory usage: 93 MB
% 10.69/2.34 % (3297441)Instructions burned: 317 (million)
% 10.69/2.34 % (3297443)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=2994746390:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/12125Mi)
% 10.69/2.34 % (3297444)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=4278587017:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2990 on theBenchmark for (2990ds/2836Mi)
% 10.69/2.34 % (3297435)Instruction limit reached!
% 10.69/2.34 % (3297435)------------------------------
% 10.69/2.34 % (3297435)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.69/2.34 % (3297435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.69/2.34 % (3297435)CaDiCaL version: 2.1.3
% 10.69/2.34 % (3297435)Termination reason: Instruction limit
% 10.69/2.34 % (3297435)Termination phase: Saturation
% 10.69/2.34 % (3297435)Time elapsed: 0.778 s
% 10.69/2.34 % (3297435)Peak memory usage: 141 MB
% 10.69/2.34 % (3297435)Instructions burned: 2053 (million)
% 10.69/2.34 % (3297447)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=1318746517:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2989 on theBenchmark for (2989ds/14534Mi)
% 10.69/2.34 % (3297423)First to succeed.
% 10.69/2.34 % (3297423)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3297416"
% 10.69/2.34 % (3297421)Also succeeded, but the first one will report.
% 10.69/2.34 % (3297423)Refutation found. Thanks to Tanya!
% 10.69/2.34 % SZS status Unsatisfiable for theBenchmark
% 10.69/2.34 % SZS output start Proof for theBenchmark
% See solution above
% 11.16/2.53 % (3297423)------------------------------
% 11.16/2.53 % (3297423)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.16/2.53 % (3297423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.16/2.53 % (3297423)CaDiCaL version: 2.1.3
% 11.16/2.53 % (3297423)Termination reason: Refutation
% 11.16/2.53 % (3297423)Time elapsed: 1.091 s
% 11.16/2.53 % (3297423)Peak memory usage: 135 MB
% 11.16/2.53 % (3297423)Instructions burned: 1686 (million)
% 11.16/2.53 % (3297423)------------------------------
% 11.16/2.53 % (3297423)------------------------------
% 11.16/2.53 % (3297416)Success in time 1.494 s
% 11.16/2.53 % Vampire exiting
%------------------------------------------------------------------------------