%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL005+4 : 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 12:33:38 PM UTC 2026
% Result : Theorem 7.78s 2.41s
% Output : Refutation 11.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 27
% Syntax : Number of formulae : 143 ( 125 unt; 15 def)
% Number of atoms : 163 ( 140 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 23 ~; 16 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 18 con; 0-2 aty)
% Number of variables : 118 ( 0 sgn 116 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',converse_cancellativity) ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
fof(f17,conjecture,
! [X0,X1] :
( join(converse(meet(X0,X1)),meet(converse(X0),converse(X1))) = meet(converse(X0),converse(X1))
& join(meet(converse(X0),converse(X1)),converse(meet(X0,X1))) = converse(meet(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( join(converse(meet(X0,X1)),meet(converse(X0),converse(X1))) = meet(converse(X0),converse(X1))
& join(meet(converse(X0),converse(X1)),converse(meet(X0,X1))) = converse(meet(X0,X1)) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0,X1] :
( meet(converse(X0),converse(X1)) != join(converse(meet(X0,X1)),meet(converse(X0),converse(X1)))
| converse(meet(X0,X1)) != join(meet(converse(X0),converse(X1)),converse(meet(X0,X1))) ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
( meet(converse(sK0),converse(sK1)) != join(converse(meet(sK0,sK1)),meet(converse(sK0),converse(sK1)))
| converse(meet(sK0,sK1)) != join(meet(converse(sK0),converse(sK1)),converse(meet(sK0,sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f19]) ).
fof(f21,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f22,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f23,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f24,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f26,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f28,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f29,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f30,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f31,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f32,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f33,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f37,plain,
( meet(converse(sK0),converse(sK1)) != join(converse(meet(sK0,sK1)),meet(converse(sK0),converse(sK1)))
| converse(meet(sK0,sK1)) != join(meet(converse(sK0),converse(sK1)),converse(meet(sK0,sK1))) ),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f33,f24]) ).
fof(f42,plain,
( complement(join(complement(converse(sK0)),complement(converse(sK1)))) != join(converse(complement(join(complement(sK0),complement(sK1)))),complement(join(complement(converse(sK0)),complement(converse(sK1)))))
| converse(complement(join(complement(sK0),complement(sK1)))) != join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),converse(complement(join(complement(sK0),complement(sK1))))) ),
inference(definition_unfolding,[],[f37,f24,f24,f24,f24,f24,f24]) ).
fof(f43,definition,
sF2 = converse(sK0),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f44,plain,
converse(sK0) = sF2,
inference(reorient_equations,[],[f43]) ).
fof(f45,definition,
sF3 = complement(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f46,plain,
complement(sF2) = sF3,
inference(reorient_equations,[],[f45]) ).
fof(f47,definition,
sF4 = converse(sK1),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f48,plain,
converse(sK1) = sF4,
inference(reorient_equations,[],[f47]) ).
fof(f49,definition,
sF5 = complement(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f50,plain,
complement(sF4) = sF5,
inference(reorient_equations,[],[f49]) ).
fof(f51,definition,
sF6 = join(sF3,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f52,plain,
join(sF3,sF5) = sF6,
inference(reorient_equations,[],[f51]) ).
fof(f53,definition,
sF7 = complement(sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f54,plain,
complement(sF6) = sF7,
inference(reorient_equations,[],[f53]) ).
fof(f55,definition,
sF8 = complement(sK0),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f56,plain,
complement(sK0) = sF8,
inference(reorient_equations,[],[f55]) ).
fof(f57,definition,
sF9 = complement(sK1),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f58,plain,
complement(sK1) = sF9,
inference(reorient_equations,[],[f57]) ).
fof(f59,definition,
sF10 = join(sF8,sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f60,plain,
join(sF8,sF9) = sF10,
inference(reorient_equations,[],[f59]) ).
fof(f61,definition,
sF11 = complement(sF10),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f62,plain,
complement(sF10) = sF11,
inference(reorient_equations,[],[f61]) ).
fof(f63,definition,
sF12 = converse(sF11),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f64,plain,
converse(sF11) = sF12,
inference(reorient_equations,[],[f63]) ).
fof(f65,definition,
sF13 = join(sF12,sF7),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f66,plain,
join(sF12,sF7) = sF13,
inference(reorient_equations,[],[f65]) ).
fof(f67,definition,
sF14 = join(sF7,sF12),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f68,plain,
join(sF7,sF12) = sF14,
inference(reorient_equations,[],[f67]) ).
fof(f69,plain,
( sF7 != sF13
| sF12 != sF14 ),
inference(definition_folding,[],[f42,f68,f64,f62,f60,f58,f56,f54,f52,f50,f48,f46,f44,f64,f62,f60,f58,f56,f66,f54,f52,f50,f48,f46,f44,f64,f62,f60,f58,f56,f54,f52,f50,f48,f46,f44]) ).
fof(f71,definition,
( spl15_1
<=> sF12 = sF14 ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
fof(f73,plain,
( sF12 != sF14
| spl15_1 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f75,definition,
( spl15_2
<=> sF7 = sF13 ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
fof(f76,plain,
( sF7 = sF13
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f78,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(avatar_split_clause,[],[f69,f75,f71]) ).
fof(f96,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[],[f29,f28]) ).
fof(f115,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X1),X0))) = X1,
inference(superposition,[],[f23,f21]) ).
fof(f116,plain,
! [X0,X1] : join(complement(join(complement(X1),complement(X0))),complement(join(X0,complement(X1)))) = X1,
inference(superposition,[],[f23,f21]) ).
fof(f117,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(superposition,[],[f23,f21]) ).
fof(f119,plain,
sF13 = join(sF7,sF12),
inference(superposition,[],[f66,f21]) ).
fof(f120,plain,
sF13 = sF14,
inference(forward_demodulation,[],[f119,f68]) ).
fof(f128,plain,
( sF12 != sF13
| spl15_1 ),
inference(superposition,[],[f73,f120]) ).
fof(f129,plain,
! [X0,X1] : complement(X1) = join(composition(X0,complement(composition(converse(X0),X1))),complement(X1)),
inference(superposition,[],[f31,f28]) ).
fof(f237,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),complement(X1))),join(complement(join(complement(X0),X1)),X2)),
inference(superposition,[],[f22,f23]) ).
fof(f329,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[],[f30,f28]) ).
fof(f343,plain,
! [X0] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[],[f96,f32]) ).
fof(f617,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f329,f26]) ).
fof(f631,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f617,f28]) ).
fof(f648,plain,
one = converse(one),
inference(superposition,[],[f26,f631]) ).
fof(f653,plain,
! [X0] : composition(one,X0) = X0,
inference(superposition,[],[f631,f648]) ).
fof(f670,plain,
! [X0] : complement(X0) = join(complement(composition(converse(one),X0)),complement(X0)),
inference(superposition,[],[f129,f653]) ).
fof(f671,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f670,f631]) ).
fof(f690,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = join(X0,complement(join(complement(X0),X1))),
inference(superposition,[],[f237,f671]) ).
fof(f697,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = X0,
inference(forward_demodulation,[],[f690,f23]) ).
fof(f717,plain,
! [X0,X1] : join(X1,complement(join(X0,complement(X1)))) = X1,
inference(superposition,[],[f697,f21]) ).
fof(f721,plain,
! [X0] : join(X0,complement(complement(X0))) = X0,
inference(superposition,[],[f697,f697]) ).
fof(f722,plain,
! [X0] : join(X0,complement(converse(top))) = X0,
inference(superposition,[],[f697,f343]) ).
fof(f723,plain,
! [X0] : join(X0,zero) = X0,
inference(superposition,[],[f697,f38]) ).
fof(f771,plain,
! [X0] : join(zero,X0) = X0,
inference(superposition,[],[f21,f723]) ).
fof(f799,plain,
! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),join(complement(join(complement(X0),complement(complement(X0)))),X1)),
inference(superposition,[],[f237,f721]) ).
fof(f817,plain,
! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),join(zero,X1)),
inference(forward_demodulation,[],[f799,f38]) ).
fof(f821,plain,
! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),X1),
inference(forward_demodulation,[],[f817,f771]) ).
fof(f851,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(complement(X0)),complement(X1)))),
inference(superposition,[],[f117,f821]) ).
fof(f857,plain,
! [X0,X1] : join(X0,X1) = join(X1,complement(complement(X0))),
inference(superposition,[],[f21,f821]) ).
fof(f865,plain,
! [X0] : complement(complement(X0)) = join(X0,zero),
inference(superposition,[],[f723,f821]) ).
fof(f866,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[],[f865,f723]) ).
fof(f873,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(X0,complement(X1)))),
inference(forward_demodulation,[],[f851,f821]) ).
fof(f1973,plain,
! [X0,X1] : join(X0,complement(X1)) = join(complement(join(complement(join(X0,complement(X1))),complement(complement(join(X0,X1))))),complement(complement(X0))),
inference(superposition,[],[f116,f873]) ).
fof(f1984,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(complement(join(X0,complement(X1))),complement(complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f1973,f857]) ).
fof(f2037,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(join(X0,X1),complement(join(X0,complement(X1)))))),
inference(forward_demodulation,[],[f1984,f857]) ).
fof(f2064,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,join(X1,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f2037,f22]) ).
fof(f2079,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f2064,f717]) ).
fof(f2098,plain,
! [X0] : join(X0,complement(converse(top))) = join(X0,complement(converse(complement(converse(X0))))),
inference(superposition,[],[f2079,f343]) ).
fof(f2103,plain,
! [X0,X1] : join(complement(join(complement(X1),complement(X0))),complement(complement(join(complement(X0),X1)))) = join(complement(join(complement(X1),complement(X0))),complement(X0)),
inference(superposition,[],[f2079,f115]) ).
fof(f2197,plain,
! [X0,X1] : join(join(complement(X0),X1),complement(join(complement(X1),complement(X0)))) = join(complement(join(complement(X1),complement(X0))),complement(X0)),
inference(forward_demodulation,[],[f2103,f857]) ).
fof(f2202,plain,
! [X0] : join(X0,complement(converse(complement(converse(X0))))) = X0,
inference(forward_demodulation,[],[f2098,f722]) ).
fof(f2234,plain,
! [X0,X1] : join(complement(X0),join(X1,complement(join(complement(X1),complement(X0))))) = join(complement(join(complement(X1),complement(X0))),complement(X0)),
inference(forward_demodulation,[],[f2197,f22]) ).
fof(f2256,plain,
! [X0,X1] : join(complement(X0),X1) = join(complement(join(complement(X1),complement(X0))),complement(X0)),
inference(forward_demodulation,[],[f2234,f697]) ).
fof(f2277,plain,
! [X0] : converse(complement(converse(X0))) = join(complement(join(complement(converse(complement(converse(X0)))),complement(X0))),complement(X0)),
inference(superposition,[],[f116,f2202]) ).
fof(f2302,plain,
! [X0] : converse(converse(X0)) = join(X0,converse(complement(converse(complement(converse(converse(X0))))))),
inference(superposition,[],[f96,f2202]) ).
fof(f2305,plain,
! [X0] : join(X0,converse(complement(converse(complement(X0))))) = X0,
inference(forward_demodulation,[],[f2302,f28]) ).
fof(f2321,plain,
! [X0] : converse(complement(converse(X0))) = join(complement(X0),converse(complement(converse(X0)))),
inference(forward_demodulation,[],[f2277,f2256]) ).
fof(f2997,plain,
! [X0] : complement(X0) = join(complement(X0),converse(complement(converse(X0)))),
inference(superposition,[],[f2305,f866]) ).
fof(f3045,plain,
! [X0] : complement(X0) = converse(complement(converse(X0))),
inference(forward_demodulation,[],[f2997,f2321]) ).
fof(f4396,plain,
! [X0] : complement(converse(X0)) = converse(complement(X0)),
inference(superposition,[],[f28,f3045]) ).
fof(f4428,plain,
complement(converse(sK0)) = converse(sF8),
inference(superposition,[],[f4396,f56]) ).
fof(f4429,plain,
complement(converse(sK1)) = converse(sF9),
inference(superposition,[],[f4396,f58]) ).
fof(f4432,plain,
converse(sF7) = complement(converse(sF6)),
inference(superposition,[],[f4396,f54]) ).
fof(f4461,plain,
complement(sF4) = converse(sF9),
inference(forward_demodulation,[],[f4429,f48]) ).
fof(f4462,plain,
complement(sF2) = converse(sF8),
inference(forward_demodulation,[],[f4428,f44]) ).
fof(f4473,plain,
sF5 = converse(sF9),
inference(forward_demodulation,[],[f4461,f50]) ).
fof(f4474,plain,
sF3 = converse(sF8),
inference(forward_demodulation,[],[f4462,f46]) ).
fof(f4499,plain,
! [X0] : converse(join(sF8,X0)) = join(sF3,converse(X0)),
inference(superposition,[],[f29,f4474]) ).
fof(f4555,plain,
converse(sF10) = join(sF3,converse(sF9)),
inference(superposition,[],[f4499,f60]) ).
fof(f4615,plain,
join(sF3,sF5) = converse(sF10),
inference(forward_demodulation,[],[f4555,f4473]) ).
fof(f4633,plain,
sF6 = converse(sF10),
inference(forward_demodulation,[],[f4615,f52]) ).
fof(f4677,plain,
complement(sF10) = converse(complement(sF6)),
inference(superposition,[],[f3045,f4633]) ).
fof(f4678,plain,
complement(sF10) = complement(converse(sF6)),
inference(forward_demodulation,[],[f4677,f4396]) ).
fof(f4681,plain,
complement(sF10) = converse(sF7),
inference(forward_demodulation,[],[f4678,f4432]) ).
fof(f4684,plain,
sF11 = converse(sF7),
inference(forward_demodulation,[],[f4681,f62]) ).
fof(f4688,plain,
sF7 = converse(sF11),
inference(superposition,[],[f28,f4684]) ).
fof(f4698,plain,
sF7 = join(sF7,complement(converse(complement(sF11)))),
inference(superposition,[],[f2202,f4684]) ).
fof(f4701,plain,
sF7 = join(sF7,complement(complement(converse(sF11)))),
inference(forward_demodulation,[],[f4698,f4396]) ).
fof(f4705,plain,
sF7 = sF12,
inference(forward_demodulation,[],[f4688,f64]) ).
fof(f4707,plain,
sF7 = join(converse(sF11),sF7),
inference(forward_demodulation,[],[f4701,f857]) ).
fof(f4710,plain,
sF7 = join(sF12,sF7),
inference(forward_demodulation,[],[f4707,f64]) ).
fof(f4713,plain,
sF7 = sF13,
inference(forward_demodulation,[],[f4710,f66]) ).
fof(f4715,plain,
spl15_2,
inference(avatar_split_clause,[],[f4713,f75]) ).
fof(f4747,plain,
( sF7 != sF12
| spl15_1
| ~ spl15_2 ),
inference(superposition,[],[f128,f76]) ).
fof(f4748,plain,
( $false
| spl15_1
| ~ spl15_2 ),
inference(forward_subsumption_resolution,[],[f4747,f4705]) ).
fof(f4749,plain,
( spl15_1
| ~ spl15_2 ),
inference(avatar_contradiction_clause,[],[f4748]) ).
cnf(s1,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(sat_conversion,[],[f78]) ).
cnf(s2,plain,
spl15_2,
inference(sat_conversion,[],[f4715]) ).
cnf(s3,plain,
( spl15_1
| ~ spl15_2 ),
inference(sat_conversion,[],[f4749]) ).
cnf(s4,plain,
spl15_1,
inference(rat,[],[s3,s2]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s2,s4]) ).
fof(f4750,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL005+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 22:52:42 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 7.78/2.41 % (3295517)Detected formulas, will run a generic FOF schedule.
% 7.78/2.41 % (3295626)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3766193315:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.78/2.41 % (3295626)Refutation not found, incomplete strategy
% 7.78/2.41 % (3295626)------------------------------
% 7.78/2.41 % (3295626)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.78/2.41 % (3295626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.78/2.41 % (3295626)CaDiCaL version: 2.1.3
% 7.78/2.41 % (3295626)Termination reason: Refutation not found, incomplete strategy
% 7.78/2.41 % (3295626)Time elapsed: 0.001 s
% 7.78/2.41 % (3295626)Peak memory usage: 88 MB
% 7.78/2.41 % (3295626)Instructions burned: 1 (million)
% 7.78/2.41 % (3295625)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=980012688:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.78/2.41 % (3295623)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=1954505140:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.78/2.41 % (3295627)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=936801165:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.78/2.41 % (3295624)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=472692000:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.78/2.41 % (3295628)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3487231280:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.78/2.41 % (3295629)dis-21_1_sil=8000:lcm=predicate:random_seed=3504764324: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)
% 7.78/2.41 % (3295629)Refutation not found, incomplete strategy
% 7.78/2.41 % (3295629)------------------------------
% 7.78/2.41 % (3295629)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.78/2.41 % (3295629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.78/2.41 % (3295629)CaDiCaL version: 2.1.3
% 7.78/2.41 % (3295629)Termination reason: Refutation not found, incomplete strategy
% 7.78/2.41 % (3295629)Time elapsed: 0.002 s
% 7.78/2.41 % (3295629)Peak memory usage: 88 MB
% 7.78/2.41 % (3295629)Instructions burned: 1 (million)
% 7.78/2.41 % (3295627)Instruction limit reached!
% 7.78/2.41 % (3295627)------------------------------
% 7.78/2.41 % (3295627)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.78/2.41 % (3295627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.78/2.41 % (3295627)CaDiCaL version: 2.1.3
% 7.78/2.41 % (3295627)Termination reason: Instruction limit
% 7.78/2.41 % (3295627)Termination phase: Saturation
% 7.78/2.41 % (3295627)Time elapsed: 0.067 s
% 7.78/2.41 % (3295627)Peak memory usage: 88 MB
% 7.78/2.41 % (3295627)Instructions burned: 120 (million)
% 7.78/2.41 % (3295628)Instruction limit reached!
% 7.78/2.41 % (3295628)------------------------------
% 7.78/2.41 % (3295628)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.78/2.41 % (3295628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.78/2.41 % (3295628)CaDiCaL version: 2.1.3
% 7.78/2.41 % (3295628)Termination reason: Instruction limit
% 7.78/2.41 % (3295628)Termination phase: Saturation
% 7.78/2.41 % (3295628)Time elapsed: 0.096 s
% 7.78/2.41 % (3295628)Peak memory usage: 90 MB
% 7.78/2.41 % (3295628)Instructions burned: 141 (million)
% 7.78/2.41 % (3295626)------------------------------
% 7.78/2.41 % (3295626)------------------------------
% 7.78/2.41 % (3295650)lrs+10_1_sil=8000:sp=occurrence:random_seed=2109572167:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 7.78/2.41 % (3295651)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3447886629:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 7.78/2.41 % (3295629)------------------------------
% 7.78/2.41 % (3295629)------------------------------
% 7.78/2.41 % (3295652)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3175931454:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 7.78/2.41 % (3295651)Instruction limit reached!
% 7.78/2.41 % (3295651)------------------------------
% 7.78/2.41 % (3295651)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.78/2.41 % (3295651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.78/2.41 % (3295651)CaDiCaL version: 2.1.3
% 7.78/2.41 % (3295651)Termination reason: Instruction limit
% 7.78/2.41 % (3295651)Termination phase: Saturation
% 7.78/2.41 % (3295651)Time elapsed: 0.092 s
% 7.78/2.41 % (3295651)Peak memory usage: 90 MB
% 7.78/2.41 % (3295651)Instructions burned: 158 (million)
% 7.78/2.41 % (3295650)Instruction limit reached!
% 7.78/2.41 % (3295650)------------------------------
% 7.78/2.41 % (3295650)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.78/2.41 % (3295650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.78/2.41 % (3295650)CaDiCaL version: 2.1.3
% 7.78/2.41 % (3295650)Termination reason: Instruction limit
% 7.78/2.41 % (3295650)Termination phase: Saturation
% 7.78/2.41 % (3295650)Time elapsed: 0.171 s
% 7.78/2.41 % (3295650)Peak memory usage: 91 MB
% 7.78/2.41 % (3295650)Instructions burned: 285 (million)
% 7.78/2.41 % (3295655)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=749256747:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 7.78/2.41 % (3295657)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1147576614:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 7.78/2.41 % (3295652)Instruction limit reached!
% 7.78/2.41 % (3295652)------------------------------
% 7.78/2.41 % (3295652)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.78/2.41 % (3295652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.78/2.41 % (3295652)CaDiCaL version: 2.1.3
% 7.78/2.41 % (3295652)Termination reason: Instruction limit
% 7.78/2.41 % (3295652)Termination phase: Saturation
% 7.78/2.41 % (3295652)Time elapsed: 0.213 s
% 7.78/2.41 % (3295652)Peak memory usage: 92 MB
% 7.78/2.41 % (3295652)Instructions burned: 325 (million)
% 7.78/2.41 % (3295657)Refutation not found, incomplete strategy
% 7.78/2.41 % (3295657)------------------------------
% 7.78/2.41 % (3295657)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.78/2.41 % (3295657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.78/2.41 % (3295657)CaDiCaL version: 2.1.3
% 7.78/2.41 % (3295657)Termination reason: Refutation not found, incomplete strategy
% 7.78/2.41 % (3295657)Time elapsed: 0.004 s
% 7.78/2.41 % (3295657)Peak memory usage: 88 MB
% 7.78/2.41 % (3295657)Instructions burned: 2 (million)
% 7.78/2.41 % (3295658)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3057140052:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 7.78/2.41 % (3295655)Instruction limit reached!
% 7.78/2.41 % (3295655)------------------------------
% 7.78/2.41 % (3295655)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.78/2.41 % (3295655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.78/2.41 % (3295655)CaDiCaL version: 2.1.3
% 7.78/2.41 % (3295655)Termination reason: Instruction limit
% 7.78/2.41 % (3295655)Termination phase: Saturation
% 7.78/2.41 % (3295655)Time elapsed: 0.227 s
% 7.78/2.41 % (3295655)Peak memory usage: 92 MB
% 7.78/2.41 % (3295655)Instructions burned: 248 (million)
% 7.78/2.41 % (3295670)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3859592568:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 7.78/2.41 % (3295670)Refutation not found, incomplete strategy
% 7.78/2.41 % (3295670)------------------------------
% 7.78/2.41 % (3295670)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.78/2.41 % (3295670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.78/2.41 % (3295670)CaDiCaL version: 2.1.3
% 7.78/2.41 % (3295670)Termination reason: Refutation not found, incomplete strategy
% 7.78/2.41 % (3295670)Time elapsed: 0.002 s
% 7.78/2.41 % (3295670)Peak memory usage: 88 MB
% 7.78/2.41 % (3295670)Instructions burned: 1 (million)
% 7.78/2.41 % (3295625)Refutation not found, incomplete strategy
% 7.78/2.41 % (3295625)------------------------------
% 7.78/2.41 % (3295625)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.78/2.41 % (3295625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.78/2.41 % (3295625)CaDiCaL version: 2.1.3
% 7.78/2.41 % (3295625)Termination reason: Refutation not found, incomplete strategy
% 7.78/2.41 % (3295625)Time elapsed: 0.705 s
% 7.78/2.41 % (3295625)Peak memory usage: 127 MB
% 7.78/2.41 % (3295625)Instructions burned: 891 (million)
% 7.78/2.41 % (3295678)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1173593570:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 7.78/2.41 % (3295678)Refutation not found, incomplete strategy
% 7.78/2.41 % (3295678)------------------------------
% 7.78/2.41 % (3295678)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.78/2.41 % (3295678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.78/2.41 % (3295678)CaDiCaL version: 2.1.3
% 7.78/2.41 % (3295678)Termination reason: Refutation not found, incomplete strategy
% 7.78/2.41 % (3295678)Time elapsed: 0.002 s
% 7.78/2.41 % (3295678)Peak memory usage: 88 MB
% 7.78/2.41 % (3295678)Instructions burned: 1 (million)
% 7.78/2.41 % (3295657)------------------------------
% 7.78/2.41 % (3295657)------------------------------
% 7.78/2.41 % (3295670)------------------------------
% 7.78/2.41 % (3295670)------------------------------
% 7.78/2.41 % (3295688)lrs+10_1_sil=8000:sp=occurrence:random_seed=4282676317:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2989 on theBenchmark for (2989ds/907Mi)
% 7.78/2.41 % (3295623)First to succeed.
% 7.78/2.41 % (3295623)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3295517"
% 7.78/2.41 % (3295686)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2509923963:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2989 on theBenchmark for (2989ds/114Mi)
% 7.78/2.41 % (3295625)------------------------------
% 7.78/2.41 % (3295625)------------------------------
% 7.78/2.41 % (3295624)Also succeeded, but the first one will report.
% 7.78/2.41 % (3295686)Instruction limit reached!
% 7.78/2.41 % (3295686)------------------------------
% 7.78/2.41 % (3295686)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.78/2.41 % (3295686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.78/2.41 % (3295686)CaDiCaL version: 2.1.3
% 7.78/2.41 % (3295686)Termination reason: Instruction limit
% 7.78/2.41 % (3295686)Termination phase: Saturation
% 7.78/2.41 % (3295686)Time elapsed: 0.091 s
% 7.78/2.41 % (3295686)Peak memory usage: 89 MB
% 7.78/2.41 % (3295686)Instructions burned: 114 (million)
% 7.78/2.41 % (3295678)------------------------------
% 7.78/2.41 % (3295678)------------------------------
% 7.78/2.41 % (3295694)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1400489479:i=437:sd=1:aac=none:ss=included_2987 on theBenchmark for (2987ds/437Mi)
% 7.78/2.41 % (3295694)Refutation not found, incomplete strategy
% 7.78/2.41 % (3295694)------------------------------
% 7.78/2.41 % (3295694)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.78/2.41 % (3295694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.78/2.41 % (3295694)CaDiCaL version: 2.1.3
% 7.78/2.41 % (3295694)Termination reason: Refutation not found, incomplete strategy
% 7.78/2.41 % (3295694)Time elapsed: 0.003 s
% 7.78/2.41 % (3295694)Peak memory usage: 88 MB
% 7.78/2.41 % (3295694)Instructions burned: 1 (million)
% 7.78/2.41 % (3295696)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3548032425:i=5202:ss=axioms:sgt=16_2986 on theBenchmark for (2986ds/5202Mi)
% 7.78/2.41 % (3295623)Refutation found. Thanks to Tanya!
% 7.78/2.41 % SZS status Theorem for theBenchmark
% 7.78/2.41 % SZS output start Proof for theBenchmark
% See solution above
% 11.52/2.65 % (3295623)------------------------------
% 11.52/2.65 % (3295623)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.52/2.65 % (3295623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.52/2.65 % (3295623)CaDiCaL version: 2.1.3
% 11.52/2.65 % (3295623)Termination reason: Refutation
% 11.52/2.65 % (3295623)Time elapsed: 1.067 s
% 11.52/2.65 % (3295623)Peak memory usage: 133 MB
% 11.52/2.65 % (3295623)Instructions burned: 1471 (million)
% 11.52/2.65 % (3295623)------------------------------
% 11.52/2.65 % (3295623)------------------------------
% 11.52/2.65 % (3295517)Success in time 1.546 s
% 11.52/2.65 % Vampire exiting
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