%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL016+1 : 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 : n018.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 12:33:44 PM UTC 2026
% Result : Theorem 8.12s 2.14s
% Output : Refutation 9.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 29
% Syntax : Number of formulae : 164 ( 164 unt; 16 def)
% Number of atoms : 164 ( 163 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 22 con; 0-2 aty)
% Number of variables : 130 ( 127 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity) ).
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) ).
fof(f4,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity) ).
fof(f7,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence) ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity) ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity) ).
fof(f11,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity) ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top) ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero) ).
fof(f14,conjecture,
! [X0,X1,X2] : meet(composition(X0,X1),complement(composition(X0,X2))) = meet(composition(X0,meet(X1,complement(X2))),complement(composition(X0,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
~ ! [X0,X1,X2] : meet(composition(X0,X1),complement(composition(X0,X2))) = meet(composition(X0,meet(X1,complement(X2))),complement(composition(X0,X2))),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0,X1,X2] : meet(composition(X0,X1),complement(composition(X0,X2))) != meet(composition(X0,meet(X1,complement(X2))),complement(composition(X0,X2))),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
meet(composition(sK0,sK1),complement(composition(sK0,sK2))) != meet(composition(sK0,meet(sK1,complement(sK2))),complement(composition(sK0,sK2))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f16]) ).
fof(f18,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f19,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f20,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f21,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f23,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f24,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f25,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f26,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f27,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f28,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f29,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f30,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f31,plain,
meet(composition(sK0,sK1),complement(composition(sK0,sK2))) != meet(composition(sK0,meet(sK1,complement(sK2))),complement(composition(sK0,sK2))),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f30,f21]) ).
fof(f33,plain,
complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))) != complement(join(complement(composition(sK0,complement(join(complement(sK1),complement(complement(sK2)))))),complement(complement(composition(sK0,sK2))))),
inference(definition_unfolding,[],[f31,f21,f21,f21]) ).
fof(f34,definition,
sF3 = composition(sK0,sK1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f35,plain,
composition(sK0,sK1) = sF3,
inference(reorient_equations,[],[f34]) ).
fof(f36,definition,
sF4 = complement(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f37,plain,
complement(sF3) = sF4,
inference(reorient_equations,[],[f36]) ).
fof(f38,definition,
sF5 = composition(sK0,sK2),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f39,plain,
composition(sK0,sK2) = sF5,
inference(reorient_equations,[],[f38]) ).
fof(f40,definition,
sF6 = complement(sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f41,plain,
complement(sF5) = sF6,
inference(reorient_equations,[],[f40]) ).
fof(f42,definition,
sF7 = complement(sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f43,plain,
complement(sF6) = sF7,
inference(reorient_equations,[],[f42]) ).
fof(f44,definition,
sF8 = join(sF4,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f45,plain,
join(sF4,sF7) = sF8,
inference(reorient_equations,[],[f44]) ).
fof(f46,definition,
sF9 = complement(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f47,plain,
complement(sF8) = sF9,
inference(reorient_equations,[],[f46]) ).
fof(f48,definition,
sF10 = complement(sK1),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f49,plain,
complement(sK1) = sF10,
inference(reorient_equations,[],[f48]) ).
fof(f50,definition,
sF11 = complement(sK2),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f51,plain,
complement(sK2) = sF11,
inference(reorient_equations,[],[f50]) ).
fof(f52,definition,
sF12 = complement(sF11),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f53,plain,
complement(sF11) = sF12,
inference(reorient_equations,[],[f52]) ).
fof(f54,definition,
sF13 = join(sF10,sF12),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f55,plain,
join(sF10,sF12) = sF13,
inference(reorient_equations,[],[f54]) ).
fof(f56,definition,
sF14 = complement(sF13),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f57,plain,
complement(sF13) = sF14,
inference(reorient_equations,[],[f56]) ).
fof(f58,definition,
sF15 = composition(sK0,sF14),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f59,plain,
composition(sK0,sF14) = sF15,
inference(reorient_equations,[],[f58]) ).
fof(f60,definition,
sF16 = complement(sF15),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f61,plain,
complement(sF15) = sF16,
inference(reorient_equations,[],[f60]) ).
fof(f62,definition,
sF17 = join(sF16,sF7),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f63,plain,
join(sF16,sF7) = sF17,
inference(reorient_equations,[],[f62]) ).
fof(f64,definition,
sF18 = complement(sF17),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f65,plain,
complement(sF17) = sF18,
inference(reorient_equations,[],[f64]) ).
fof(f66,plain,
sF9 != sF18,
inference(definition_folding,[],[f33,f65,f63,f43,f41,f39,f61,f59,f57,f55,f53,f51,f49,f47,f45,f43,f41,f39,f37,f35]) ).
fof(f84,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[],[f27,f25]) ).
fof(f87,plain,
! [X2,X0,X1] : composition(join(converse(X1),X2),converse(X0)) = join(converse(composition(X0,X1)),composition(X2,converse(X0))),
inference(superposition,[],[f24,f27]) ).
fof(f142,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X1),X0))) = X1,
inference(superposition,[],[f20,f18]) ).
fof(f143,plain,
! [X0,X1] : join(complement(join(complement(X1),complement(X0))),complement(join(X0,complement(X1)))) = X1,
inference(superposition,[],[f20,f18]) ).
fof(f198,plain,
zero = complement(join(sF18,complement(sF18))),
inference(superposition,[],[f32,f65]) ).
fof(f200,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(superposition,[],[f20,f32]) ).
fof(f213,plain,
zero = complement(top),
inference(forward_demodulation,[],[f198,f29]) ).
fof(f241,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f84,f23]) ).
fof(f247,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f241,f25]) ).
fof(f256,plain,
one = converse(one),
inference(superposition,[],[f23,f247]) ).
fof(f290,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f87,f27]) ).
fof(f301,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f290,f26]) ).
fof(f309,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f301,f26]) ).
fof(f314,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f309,f27]) ).
fof(f331,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f25,f314]) ).
fof(f344,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f331,f25]) ).
fof(f368,plain,
! [X0] : composition(sK0,join(sK1,X0)) = join(sF3,composition(sK0,X0)),
inference(superposition,[],[f344,f35]) ).
fof(f376,plain,
! [X0] : composition(sK0,join(X0,sF14)) = join(composition(sK0,X0),sF15),
inference(superposition,[],[f344,f59]) ).
fof(f463,plain,
! [X0] : composition(one,X0) = X0,
inference(superposition,[],[f247,f256]) ).
fof(f479,plain,
! [X0] : complement(X0) = join(composition(converse(one),complement(X0)),complement(X0)),
inference(superposition,[],[f28,f463]) ).
fof(f492,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f479,f247]) ).
fof(f495,plain,
sF10 = join(sF10,sF10),
inference(superposition,[],[f492,f49]) ).
fof(f496,plain,
sF11 = join(sF11,sF11),
inference(superposition,[],[f492,f51]) ).
fof(f497,plain,
sF4 = join(sF4,sF4),
inference(superposition,[],[f492,f37]) ).
fof(f498,plain,
sF6 = join(sF6,sF6),
inference(superposition,[],[f492,f41]) ).
fof(f499,plain,
sF7 = join(sF7,sF7),
inference(superposition,[],[f492,f43]) ).
fof(f500,plain,
sF9 = join(sF9,sF9),
inference(superposition,[],[f492,f47]) ).
fof(f541,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),complement(X1))),join(complement(join(complement(X0),X1)),X2)),
inference(superposition,[],[f19,f20]) ).
fof(f606,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = join(X0,complement(join(complement(X0),X1))),
inference(superposition,[],[f541,f492]) ).
fof(f615,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = X0,
inference(forward_demodulation,[],[f606,f20]) ).
fof(f654,plain,
! [X0] : join(X0,zero) = X0,
inference(superposition,[],[f615,f32]) ).
fof(f691,plain,
! [X0] : join(zero,X0) = X0,
inference(superposition,[],[f18,f654]) ).
fof(f724,plain,
! [X0,X1] : join(complement(X1),complement(complement(X1))) = join(complement(join(complement(X0),zero)),complement(join(zero,X0))),
inference(superposition,[],[f142,f32]) ).
fof(f751,plain,
! [X0,X1] : join(complement(X1),complement(X0)) = join(complement(X0),complement(join(join(complement(X0),X1),complement(join(complement(X1),complement(X0)))))),
inference(superposition,[],[f143,f142]) ).
fof(f764,plain,
! [X0,X1] : join(complement(X1),complement(X0)) = join(complement(X0),complement(join(complement(X0),join(X1,complement(join(complement(X1),complement(X0))))))),
inference(forward_demodulation,[],[f751,f19]) ).
fof(f768,plain,
! [X0,X1] : join(complement(X1),complement(complement(X1))) = join(complement(join(complement(X0),zero)),complement(X0)),
inference(forward_demodulation,[],[f724,f691]) ).
fof(f772,plain,
! [X0,X1] : join(complement(X1),complement(X0)) = join(complement(X0),complement(join(complement(X0),X1))),
inference(forward_demodulation,[],[f764,f615]) ).
fof(f774,plain,
! [X0,X1] : join(complement(complement(X0)),complement(X0)) = join(complement(X1),complement(complement(X1))),
inference(forward_demodulation,[],[f768,f654]) ).
fof(f777,plain,
! [X0] : top = join(complement(complement(X0)),complement(X0)),
inference(forward_demodulation,[],[f774,f29]) ).
fof(f778,plain,
top = join(complement(zero),zero),
inference(superposition,[],[f777,f32]) ).
fof(f818,plain,
top = complement(zero),
inference(forward_demodulation,[],[f778,f654]) ).
fof(f850,plain,
! [X0] : join(complement(X0),complement(complement(X0))) = join(complement(zero),complement(X0)),
inference(superposition,[],[f772,f654]) ).
fof(f872,plain,
! [X0] : join(complement(X0),complement(complement(X0))) = join(top,complement(X0)),
inference(forward_demodulation,[],[f850,f818]) ).
fof(f880,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[],[f872,f29]) ).
fof(f921,plain,
sK1 = join(zero,complement(join(sF10,sF10))),
inference(superposition,[],[f200,f49]) ).
fof(f922,plain,
sK2 = join(zero,complement(join(sF11,sF11))),
inference(superposition,[],[f200,f51]) ).
fof(f923,plain,
sF3 = join(zero,complement(join(sF4,sF4))),
inference(superposition,[],[f200,f37]) ).
fof(f924,plain,
sF5 = join(zero,complement(join(sF6,sF6))),
inference(superposition,[],[f200,f41]) ).
fof(f925,plain,
sF6 = join(zero,complement(join(sF7,sF7))),
inference(superposition,[],[f200,f43]) ).
fof(f926,plain,
sF8 = join(zero,complement(join(sF9,sF9))),
inference(superposition,[],[f200,f47]) ).
fof(f940,plain,
sF8 = complement(join(sF9,sF9)),
inference(forward_demodulation,[],[f926,f691]) ).
fof(f941,plain,
sF6 = complement(join(sF7,sF7)),
inference(forward_demodulation,[],[f925,f691]) ).
fof(f942,plain,
sF5 = complement(join(sF6,sF6)),
inference(forward_demodulation,[],[f924,f691]) ).
fof(f943,plain,
sF3 = complement(join(sF4,sF4)),
inference(forward_demodulation,[],[f923,f691]) ).
fof(f944,plain,
sK2 = complement(join(sF11,sF11)),
inference(forward_demodulation,[],[f922,f691]) ).
fof(f945,plain,
sK1 = complement(join(sF10,sF10)),
inference(forward_demodulation,[],[f921,f691]) ).
fof(f953,plain,
sF8 = complement(sF9),
inference(forward_demodulation,[],[f940,f500]) ).
fof(f954,plain,
sF6 = complement(sF7),
inference(forward_demodulation,[],[f941,f499]) ).
fof(f955,plain,
sF5 = complement(sF6),
inference(forward_demodulation,[],[f942,f498]) ).
fof(f956,plain,
sF3 = complement(sF4),
inference(forward_demodulation,[],[f943,f497]) ).
fof(f957,plain,
sK2 = complement(sF11),
inference(forward_demodulation,[],[f944,f496]) ).
fof(f958,plain,
sK1 = complement(sF10),
inference(forward_demodulation,[],[f945,f495]) ).
fof(f961,plain,
sF5 = sF7,
inference(forward_demodulation,[],[f955,f43]) ).
fof(f962,plain,
sK2 = sF12,
inference(forward_demodulation,[],[f957,f53]) ).
fof(f965,plain,
sF5 = composition(sK0,sF12),
inference(superposition,[],[f39,f962]) ).
fof(f967,plain,
sF7 = composition(sK0,sF12),
inference(forward_demodulation,[],[f965,f961]) ).
fof(f1019,plain,
! [X0] : join(complement(join(complement(X0),complement(top))),complement(top)) = X0,
inference(superposition,[],[f143,f880]) ).
fof(f1021,plain,
! [X0] : join(complement(join(complement(X0),zero)),zero) = X0,
inference(forward_demodulation,[],[f1019,f213]) ).
fof(f1022,plain,
! [X0] : complement(join(complement(X0),zero)) = X0,
inference(forward_demodulation,[],[f1021,f654]) ).
fof(f1023,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[],[f1022,f654]) ).
fof(f1043,plain,
! [X0,X1] : complement(X0) = join(complement(join(complement(X1),X0)),complement(join(X0,X1))),
inference(superposition,[],[f142,f1023]) ).
fof(f1052,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X0,X1))),
inference(superposition,[],[f615,f1023]) ).
fof(f1053,plain,
! [X0,X1] : join(complement(X1),X0) = join(X0,complement(join(X0,X1))),
inference(superposition,[],[f772,f1023]) ).
fof(f1075,plain,
! [X0,X1] : complement(X1) = join(complement(X1),complement(join(X0,X1))),
inference(superposition,[],[f1052,f18]) ).
fof(f1169,plain,
! [X0,X1] : join(complement(X0),X1) = join(X1,complement(join(X0,X1))),
inference(superposition,[],[f1053,f18]) ).
fof(f1301,plain,
complement(sF7) = join(complement(sF7),complement(sF8)),
inference(superposition,[],[f1075,f45]) ).
fof(f1340,plain,
complement(sF7) = join(complement(sF7),sF9),
inference(forward_demodulation,[],[f1301,f47]) ).
fof(f1367,plain,
sF6 = join(sF6,sF9),
inference(forward_demodulation,[],[f1340,f954]) ).
fof(f1513,plain,
! [X0,X1] : complement(X1) = join(complement(join(complement(X0),X1)),complement(join(X0,X1))),
inference(superposition,[],[f1043,f18]) ).
fof(f1723,plain,
join(complement(sF4),sF7) = join(sF7,complement(sF8)),
inference(superposition,[],[f1169,f45]) ).
fof(f1724,plain,
join(complement(sF10),sF12) = join(sF12,complement(sF13)),
inference(superposition,[],[f1169,f55]) ).
fof(f1779,plain,
join(complement(sF10),sF12) = join(sF12,sF14),
inference(forward_demodulation,[],[f1724,f57]) ).
fof(f1780,plain,
join(complement(sF4),sF7) = join(sF7,sF9),
inference(forward_demodulation,[],[f1723,f47]) ).
fof(f1805,plain,
join(sF12,sF14) = join(sK1,sF12),
inference(forward_demodulation,[],[f1779,f958]) ).
fof(f1806,plain,
join(sF7,sF9) = join(sF3,sF7),
inference(forward_demodulation,[],[f1780,f956]) ).
fof(f2896,plain,
join(sF3,composition(sK0,sF12)) = composition(sK0,join(sF12,sF14)),
inference(superposition,[],[f368,f1805]) ).
fof(f2915,plain,
join(sF3,composition(sK0,sF12)) = join(composition(sK0,sF12),sF15),
inference(forward_demodulation,[],[f2896,f376]) ).
fof(f2920,plain,
join(sF3,sF7) = join(sF7,sF15),
inference(forward_demodulation,[],[f2915,f967]) ).
fof(f2923,plain,
join(sF7,sF9) = join(sF7,sF15),
inference(forward_demodulation,[],[f2920,f1806]) ).
fof(f3398,plain,
complement(sF9) = join(complement(join(complement(sF7),sF9)),complement(join(sF7,sF15))),
inference(superposition,[],[f1513,f2923]) ).
fof(f3400,plain,
complement(sF9) = join(complement(join(sF6,sF9)),complement(join(sF7,sF15))),
inference(forward_demodulation,[],[f3398,f954]) ).
fof(f3407,plain,
complement(sF9) = join(complement(sF6),complement(join(sF7,sF15))),
inference(forward_demodulation,[],[f3400,f1367]) ).
fof(f3412,plain,
complement(sF9) = join(sF7,complement(join(sF7,sF15))),
inference(forward_demodulation,[],[f3407,f43]) ).
fof(f3414,plain,
complement(sF9) = join(complement(sF15),sF7),
inference(forward_demodulation,[],[f3412,f1053]) ).
fof(f3416,plain,
join(sF16,sF7) = complement(sF9),
inference(forward_demodulation,[],[f3414,f61]) ).
fof(f3417,plain,
sF8 = join(sF16,sF7),
inference(forward_demodulation,[],[f3416,f953]) ).
fof(f3418,plain,
sF8 = sF17,
inference(forward_demodulation,[],[f3417,f63]) ).
fof(f3419,plain,
complement(sF8) = sF18,
inference(superposition,[],[f65,f3418]) ).
fof(f3420,plain,
sF9 = sF18,
inference(forward_demodulation,[],[f3419,f47]) ).
fof(f3421,plain,
$false,
inference(forward_subsumption_resolution,[],[f3420,f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : REL016+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n018.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sun Sep 27 22:52:54 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.49 Running first-order theorem proving
% 0.22/0.49 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
% 8.12/2.14 % (2816834)Detected formulas, will run a generic FOF schedule.
% 8.12/2.14 % (2816839)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=375923658:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.12/2.14 % (2816844)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2706684929:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.12/2.14 % (2816840)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2451286657:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.12/2.14 % (2816842)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2727590355:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.12/2.14 % (2816843)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2143718417:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.12/2.14 % (2816841)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1604537259:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.12/2.14 % (2816842)Refutation not found, incomplete strategy
% 8.12/2.14 % (2816842)------------------------------
% 8.12/2.14 % (2816842)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.12/2.14 % (2816842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.12/2.14 % (2816842)CaDiCaL version: 2.1.3
% 8.12/2.14 % (2816842)Termination reason: Refutation not found, incomplete strategy
% 8.12/2.14 % (2816842)Time elapsed: 0.002 s
% 8.12/2.14 % (2816842)Peak memory usage: 88 MB
% 8.12/2.14 % (2816845)dis-21_1_sil=8000:lcm=predicate:random_seed=2241255283:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 8.12/2.14 % (2816845)Refutation not found, incomplete strategy
% 8.12/2.14 % (2816845)------------------------------
% 8.12/2.14 % (2816845)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.12/2.14 % (2816845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.12/2.14 % (2816845)CaDiCaL version: 2.1.3
% 8.12/2.14 % (2816845)Termination reason: Refutation not found, incomplete strategy
% 8.12/2.14 % (2816845)Time elapsed: 0.002 s
% 8.12/2.14 % (2816845)Peak memory usage: 88 MB
% 8.12/2.14 % (2816845)Instructions burned: 1 (million)
% 8.12/2.14 % (2816844)Instruction limit reached!
% 8.12/2.14 % (2816844)------------------------------
% 8.12/2.14 % (2816844)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.12/2.14 % (2816844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.12/2.14 % (2816844)CaDiCaL version: 2.1.3
% 8.12/2.14 % (2816844)Termination reason: Instruction limit
% 8.12/2.14 % (2816844)Termination phase: Saturation
% 8.12/2.14 % (2816844)Time elapsed: 0.139 s
% 8.12/2.14 % (2816844)Peak memory usage: 90 MB
% 8.12/2.14 % (2816844)Instructions burned: 140 (million)
% 8.12/2.14 % (2816843)Instruction limit reached!
% 8.12/2.14 % (2816843)------------------------------
% 8.12/2.14 % (2816843)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.12/2.14 % (2816843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.12/2.14 % (2816843)CaDiCaL version: 2.1.3
% 8.12/2.14 % (2816843)Termination reason: Instruction limit
% 8.12/2.14 % (2816843)Termination phase: Saturation
% 8.12/2.14 % (2816843)Time elapsed: 0.107 s
% 8.12/2.14 % (2816843)Peak memory usage: 88 MB
% 8.12/2.14 % (2816843)Instructions burned: 120 (million)
% 8.12/2.14 % (2816853)lrs+10_1_sil=8000:sp=occurrence:random_seed=1093044488:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 8.12/2.14 % (2816842)------------------------------
% 8.12/2.14 % (2816842)------------------------------
% 8.12/2.14 % (2816854)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2080382734:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 8.12/2.14 % (2816845)------------------------------
% 8.12/2.14 % (2816845)------------------------------
% 8.12/2.14 % (2816853)Instruction limit reached!
% 8.12/2.14 % (2816853)------------------------------
% 8.12/2.14 % (2816853)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.12/2.14 % (2816853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.12/2.14 % (2816853)CaDiCaL version: 2.1.3
% 8.12/2.14 % (2816853)Termination reason: Instruction limit
% 8.12/2.14 % (2816853)Termination phase: Saturation
% 8.12/2.14 % (2816853)Time elapsed: 0.280 s
% 8.12/2.14 % (2816853)Peak memory usage: 91 MB
% 8.12/2.14 % (2816853)Instructions burned: 286 (million)
% 8.12/2.14 % (2816854)Instruction limit reached!
% 8.12/2.14 % (2816854)------------------------------
% 8.12/2.14 % (2816854)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.12/2.14 % (2816854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.12/2.14 % (2816854)CaDiCaL version: 2.1.3
% 8.12/2.14 % (2816854)Termination reason: Instruction limit
% 8.12/2.14 % (2816854)Termination phase: Saturation
% 8.12/2.14 % (2816854)Time elapsed: 0.155 s
% 8.12/2.14 % (2816854)Peak memory usage: 91 MB
% 8.12/2.14 % (2816854)Instructions burned: 157 (million)
% 8.12/2.14 % (2816856)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4245442383:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 8.12/2.14 % (2816858)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2473218751:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 8.12/2.14 % (2816839)First to succeed.
% 8.12/2.14 % (2816839)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2816834"
% 8.12/2.14 % (2816860)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1141860954:i=2350_2991 on theBenchmark for (2991ds/2350Mi)
% 8.12/2.14 % (2816859)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2609223254:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2991 on theBenchmark for (2991ds/294Mi)
% 8.12/2.14 % (2816859)Refutation not found, incomplete strategy
% 8.12/2.14 % (2816859)------------------------------
% 8.12/2.14 % (2816859)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.12/2.14 % (2816859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.12/2.14 % (2816859)CaDiCaL version: 2.1.3
% 8.12/2.14 % (2816859)Termination reason: Refutation not found, incomplete strategy
% 8.12/2.14 % (2816859)Time elapsed: 0.003 s
% 8.12/2.14 % (2816859)Peak memory usage: 88 MB
% 8.12/2.14 % (2816859)Instructions burned: 1 (million)
% 8.12/2.14 % (2816841)Refutation not found, incomplete strategy
% 8.12/2.14 % (2816841)------------------------------
% 8.12/2.14 % (2816841)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.12/2.14 % (2816841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.12/2.14 % (2816841)CaDiCaL version: 2.1.3
% 8.12/2.14 % (2816841)Termination reason: Refutation not found, incomplete strategy
% 8.12/2.14 % (2816841)Time elapsed: 0.850 s
% 8.12/2.14 % (2816841)Peak memory usage: 128 MB
% 8.12/2.14 % (2816841)Instructions burned: 890 (million)
% 8.12/2.14 % (2816858)Instruction limit reached!
% 8.12/2.14 % (2816858)------------------------------
% 8.12/2.14 % (2816858)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.12/2.14 % (2816858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.12/2.14 % (2816858)CaDiCaL version: 2.1.3
% 8.12/2.14 % (2816858)Termination reason: Instruction limit
% 8.12/2.14 % (2816858)Termination phase: Saturation
% 8.12/2.14 % (2816858)Time elapsed: 0.248 s
% 8.12/2.14 % (2816858)Peak memory usage: 92 MB
% 8.12/2.14 % (2816858)Instructions burned: 248 (million)
% 8.12/2.14 % (2816839)Refutation found. Thanks to Tanya!
% 8.12/2.14 % SZS status Theorem for theBenchmark
% 8.12/2.14 % SZS output start Proof for theBenchmark
% See solution above
% 9.69/2.46 % (2816839)------------------------------
% 9.69/2.46 % (2816839)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.69/2.46 % (2816839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.69/2.46 % (2816839)CaDiCaL version: 2.1.3
% 9.69/2.46 % (2816839)Termination reason: Refutation
% 9.69/2.46 % (2816839)Time elapsed: 0.829 s
% 9.69/2.46 % (2816839)Peak memory usage: 133 MB
% 9.69/2.46 % (2816839)Instructions burned: 1370 (million)
% 9.69/2.46 % (2816839)------------------------------
% 9.69/2.46 % (2816839)------------------------------
% 9.69/2.46 % (2816834)Success in time 1.275 s
% 9.69/2.46 % Vampire exiting
%------------------------------------------------------------------------------