%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL042-1 : 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 : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:34:05 PM UTC 2026
% Result : Unsatisfiable 7.93s 3.84s
% Output : Refutation 18.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 26
% Syntax : Number of formulae : 154 ( 76 unt; 12 def)
% Number of atoms : 281 ( 127 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 250 ( 123 ~; 118 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 10 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 136 ( 0 sgn 136 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
fof(f4,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
fof(f6,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_associativity_5) ).
fof(f8,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity_6) ).
fof(f9,axiom,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f11,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f12,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
fof(f13,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity_11) ).
fof(f14,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(reorient_equations,[],[f13]) ).
fof(f15,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top_12) ).
fof(f16,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero_13) ).
fof(f17,negated_conjecture,
! [X0] : meet(composition(sk1,X0),composition(sk1,complement(X0))) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).
fof(f18,plain,
! [X0] : zero = meet(composition(sk1,X0),composition(sk1,complement(X0))),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
join(composition(converse(sk1),sk1),one) != one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_15) ).
fof(f20,plain,
one != join(composition(converse(sk1),sk1),one),
inference(reorient_equations,[],[f19]) ).
fof(f21,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f22,plain,
! [X0] : zero = complement(join(complement(composition(sk1,X0)),complement(composition(sk1,complement(X0))))),
inference(definition_unfolding,[],[f18,f6]) ).
fof(f23,definition,
sF0 = converse(sk1),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f24,plain,
converse(sk1) = sF0,
inference(reorient_equations,[],[f23]) ).
fof(f25,definition,
sF1 = composition(sF0,sk1),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f26,plain,
composition(sF0,sk1) = sF1,
inference(reorient_equations,[],[f25]) ).
fof(f27,definition,
sF2 = join(sF1,one),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f28,plain,
join(sF1,one) = sF2,
inference(reorient_equations,[],[f27]) ).
fof(f29,plain,
one != sF2,
inference(definition_folding,[],[f20,f28,f26,f24]) ).
fof(f30,plain,
zero = complement(top),
inference(backward_demodulation,[],[f21,f15]) ).
fof(f32,definition,
( spl3_1
<=> zero = complement(top) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f34,plain,
( zero = complement(top)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f35,plain,
spl3_1,
inference(avatar_split_clause,[],[f30,f32]) ).
fof(f37,definition,
( spl3_2
<=> composition(sF0,sk1) = sF1 ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f39,plain,
( composition(sF0,sk1) = sF1
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f40,plain,
spl3_2,
inference(avatar_split_clause,[],[f26,f37]) ).
fof(f42,definition,
( spl3_3
<=> converse(sk1) = sF0 ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f44,plain,
( converse(sk1) = sF0
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f45,plain,
spl3_3,
inference(avatar_split_clause,[],[f24,f42]) ).
fof(f47,definition,
( spl3_4
<=> one = sF2 ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f49,plain,
( one != sF2
| spl3_4 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f50,plain,
~ spl3_4,
inference(avatar_split_clause,[],[f29,f47]) ).
fof(f51,plain,
( sk1 = converse(sF0)
| ~ spl3_3 ),
inference(superposition,[],[f10,f44]) ).
fof(f53,definition,
( spl3_5
<=> join(sF1,one) = sF2 ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f55,plain,
( join(sF1,one) = sF2
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f56,plain,
spl3_5,
inference(avatar_split_clause,[],[f28,f53]) ).
fof(f57,plain,
( ! [X0] : complement(X0) = join(composition(sF0,complement(composition(sk1,X0))),complement(X0))
| ~ spl3_3 ),
inference(superposition,[],[f14,f44]) ).
fof(f58,plain,
! [X0,X1] : complement(X1) = join(composition(X0,complement(composition(converse(X0),X1))),complement(X1)),
inference(superposition,[],[f14,f10]) ).
fof(f65,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(X0,complement(composition(converse(X0),X1)))),
inference(forward_demodulation,[],[f58,f1]) ).
fof(f66,plain,
( ! [X0] : complement(X0) = join(complement(X0),composition(sF0,complement(composition(sk1,X0))))
| ~ spl3_3 ),
inference(forward_demodulation,[],[f57,f1]) ).
fof(f70,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X1),X0))) = X1,
inference(superposition,[],[f4,f1]) ).
fof(f81,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(forward_demodulation,[],[f70,f1]) ).
fof(f123,plain,
! [X0] : composition(sk1,X0) = join(zero,complement(join(complement(composition(sk1,X0)),composition(sk1,complement(X0))))),
inference(superposition,[],[f4,f22]) ).
fof(f132,plain,
! [X0] : composition(sk1,X0) = join(zero,complement(join(composition(sk1,complement(X0)),complement(composition(sk1,X0))))),
inference(forward_demodulation,[],[f123,f1]) ).
fof(f139,plain,
! [X0] : join(complement(join(complement(X0),complement(complement(complement(X0))))),complement(top)) = X0,
inference(superposition,[],[f4,f15]) ).
fof(f140,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f139,f1]) ).
fof(f143,plain,
( ! [X0] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0
| ~ spl3_1 ),
inference(forward_demodulation,[],[f140,f34]) ).
fof(f156,plain,
( ! [X0] : zero = join(composition(converse(X0),complement(composition(X0,top))),zero)
| ~ spl3_1 ),
inference(superposition,[],[f14,f34]) ).
fof(f157,plain,
( ! [X0] : zero = join(zero,composition(converse(X0),complement(composition(X0,top))))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f156,f1]) ).
fof(f176,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[],[f11,f10]) ).
fof(f200,plain,
! [X0] : complement(X0) = join(complement(join(complement(complement(X0)),X0)),complement(top)),
inference(superposition,[],[f81,f15]) ).
fof(f208,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(complement(complement(X0)),X0))),
inference(forward_demodulation,[],[f200,f1]) ).
fof(f217,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f208,f1]) ).
fof(f222,plain,
( ! [X0] : complement(X0) = join(zero,complement(join(X0,complement(complement(X0)))))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f217,f34]) ).
fof(f226,plain,
( ! [X0] : complement(complement(X0)) = X0
| ~ spl3_1 ),
inference(backward_demodulation,[],[f143,f222]) ).
fof(f227,plain,
( ! [X0] : complement(X0) = join(zero,complement(join(X0,X0)))
| ~ spl3_1 ),
inference(backward_demodulation,[],[f222,f226]) ).
fof(f238,plain,
( ! [X0,X1] : complement(X0) = join(complement(join(X0,complement(X1))),complement(join(X0,X1)))
| ~ spl3_1 ),
inference(superposition,[],[f4,f226]) ).
fof(f244,plain,
( ! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0)))
| ~ spl3_1 ),
inference(superposition,[],[f81,f226]) ).
fof(f249,plain,
( ! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(X0,complement(X1))))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f238,f1]) ).
fof(f316,plain,
( ! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(complement(X0),X1)))
| ~ spl3_1 ),
inference(superposition,[],[f244,f1]) ).
fof(f497,plain,
( ! [X0] : converse(composition(X0,sk1)) = composition(sF0,converse(X0))
| ~ spl3_3 ),
inference(superposition,[],[f12,f44]) ).
fof(f500,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f12,f10]) ).
fof(f503,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(f669,plain,
( ! [X0] : composition(sF0,composition(sk1,X0)) = composition(sF1,X0)
| ~ spl3_2 ),
inference(superposition,[],[f7,f39]) ).
fof(f692,plain,
! [X2,X0,X1] : composition(join(X0,converse(X1)),converse(X2)) = converse(composition(X2,join(converse(X0),X1))),
inference(superposition,[],[f12,f176]) ).
fof(f758,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f500,f8]) ).
fof(f775,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f758,f10]) ).
fof(f788,plain,
! [X0] : complement(X0) = join(complement(X0),composition(one,complement(X0))),
inference(superposition,[],[f65,f775]) ).
fof(f794,plain,
one = converse(one),
inference(superposition,[],[f8,f775]) ).
fof(f797,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f775,f794]) ).
fof(f804,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(backward_demodulation,[],[f788,f797]) ).
fof(f826,definition,
( spl3_6
<=> one = converse(one) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f828,plain,
( one = converse(one)
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f826]) ).
fof(f829,plain,
spl3_6,
inference(avatar_split_clause,[],[f794,f826]) ).
fof(f831,plain,
( ! [X0] : join(X0,X0) = X0
| ~ spl3_1 ),
inference(superposition,[],[f804,f226]) ).
fof(f834,plain,
( ! [X0] : complement(complement(X0)) = join(complement(join(X0,complement(X0))),complement(complement(X0)))
| ~ spl3_1 ),
inference(superposition,[],[f316,f804]) ).
fof(f848,plain,
( ! [X0] : complement(complement(X0)) = join(complement(complement(X0)),complement(join(X0,complement(X0))))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f834,f1]) ).
fof(f851,plain,
( ! [X0] : complement(X0) = join(zero,complement(X0))
| ~ spl3_1 ),
inference(backward_demodulation,[],[f227,f831]) ).
fof(f859,plain,
( ! [X0] : complement(complement(X0)) = join(complement(complement(X0)),complement(top))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f848,f15]) ).
fof(f866,plain,
( ! [X0] : composition(sk1,X0) = complement(join(composition(sk1,complement(X0)),complement(composition(sk1,X0))))
| ~ spl3_1 ),
inference(backward_demodulation,[],[f132,f851]) ).
fof(f873,plain,
( ! [X0] : complement(complement(X0)) = join(complement(top),complement(complement(X0)))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f859,f1]) ).
fof(f893,plain,
( ! [X0] : join(complement(top),X0) = X0
| ~ spl3_1 ),
inference(forward_demodulation,[],[f873,f226]) ).
fof(f907,plain,
( ! [X0] : join(zero,X0) = X0
| ~ spl3_1 ),
inference(forward_demodulation,[],[f893,f34]) ).
fof(f922,plain,
( ! [X0] : zero = composition(converse(X0),complement(composition(X0,top)))
| ~ spl3_1 ),
inference(backward_demodulation,[],[f157,f907]) ).
fof(f1201,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f503,f12]) ).
fof(f1218,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f1201,f11]) ).
fof(f1239,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(converse(converse(X2)),X1))),
inference(forward_demodulation,[],[f1218,f692]) ).
fof(f1251,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f1239,f10]) ).
fof(f1281,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f1251]) ).
fof(f1301,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f1281,f10]) ).
fof(f1342,plain,
! [X0,X1] : composition(X0,join(X1,one)) = join(composition(X0,X1),X0),
inference(superposition,[],[f1301,f8]) ).
fof(f1371,plain,
! [X0,X1] : join(X0,composition(X0,X1)) = composition(X0,join(X1,one)),
inference(forward_demodulation,[],[f1342,f1]) ).
fof(f1499,plain,
( ! [X0,X1] : composition(converse(X0),join(X1,complement(composition(X0,top)))) = join(composition(converse(X0),X1),zero)
| ~ spl3_1 ),
inference(superposition,[],[f1301,f922]) ).
fof(f1500,plain,
( ! [X0,X1] : join(zero,composition(converse(X0),X1)) = composition(converse(X0),join(X1,complement(composition(X0,top))))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1499,f1]) ).
fof(f1510,plain,
( ! [X0,X1] : composition(converse(X0),X1) = composition(converse(X0),join(X1,complement(composition(X0,top))))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1500,f907]) ).
fof(f1634,plain,
( ! [X0] : complement(composition(sk1,complement(X0))) = join(composition(sk1,X0),complement(join(composition(sk1,complement(X0)),complement(complement(composition(sk1,X0))))))
| ~ spl3_1 ),
inference(superposition,[],[f249,f866]) ).
fof(f1653,plain,
( ! [X0] : complement(composition(sk1,complement(X0))) = join(composition(sk1,X0),complement(join(composition(sk1,complement(X0)),composition(sk1,X0))))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1634,f226]) ).
fof(f1665,plain,
( ! [X0] : complement(composition(sk1,complement(X0))) = join(composition(sk1,X0),complement(join(composition(sk1,X0),composition(sk1,complement(X0)))))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1653,f1]) ).
fof(f1669,plain,
( ! [X0] : complement(composition(sk1,complement(X0))) = join(composition(sk1,X0),complement(composition(sk1,join(X0,complement(X0)))))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1665,f1301]) ).
fof(f1673,plain,
( ! [X0] : complement(composition(sk1,complement(X0))) = join(composition(sk1,X0),complement(composition(sk1,top)))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1669,f15]) ).
fof(f2093,definition,
( spl3_8
<=> sk1 = converse(sF0) ),
introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition]) ).
fof(f2095,plain,
( sk1 = converse(sF0)
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f2093]) ).
fof(f2096,plain,
( spl3_8
| ~ spl3_3 ),
inference(avatar_split_clause,[],[f51,f42,f2093]) ).
fof(f2106,plain,
( composition(sF0,sk1) = converse(composition(sF0,sk1))
| ~ spl3_3
| ~ spl3_8 ),
inference(superposition,[],[f497,f2095]) ).
fof(f2113,plain,
( sF1 = converse(sF1)
| ~ spl3_2
| ~ spl3_3
| ~ spl3_8 ),
inference(forward_demodulation,[],[f2106,f39]) ).
fof(f2121,definition,
( spl3_9
<=> sF1 = converse(sF1) ),
introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition]) ).
fof(f2123,plain,
( sF1 = converse(sF1)
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f2121]) ).
fof(f2124,plain,
( spl3_9
| ~ spl3_2
| ~ spl3_3
| ~ spl3_8 ),
inference(avatar_split_clause,[],[f2113,f2093,f42,f37,f2121]) ).
fof(f2133,plain,
( ! [X0] : converse(join(sF1,X0)) = join(sF1,converse(X0))
| ~ spl3_9 ),
inference(superposition,[],[f176,f2123]) ).
fof(f3863,plain,
( ! [X0] : join(X0,composition(X0,sF1)) = composition(X0,sF2)
| ~ spl3_5 ),
inference(superposition,[],[f1371,f55]) ).
fof(f4320,plain,
( join(sF1,one) = converse(join(sF1,one))
| ~ spl3_6
| ~ spl3_9 ),
inference(superposition,[],[f2133,f828]) ).
fof(f4353,plain,
( sF2 = converse(sF2)
| ~ spl3_5
| ~ spl3_6
| ~ spl3_9 ),
inference(forward_demodulation,[],[f4320,f55]) ).
fof(f4381,definition,
( spl3_17
<=> sF2 = converse(sF2) ),
introduced(definition,[new_symbols(definition,[spl3_17])],[avatar_definition]) ).
fof(f4383,plain,
( sF2 = converse(sF2)
| ~ spl3_17 ),
inference(avatar_component_clause,[],[f4381]) ).
fof(f4384,plain,
( spl3_17
| ~ spl3_5
| ~ spl3_6
| ~ spl3_9 ),
inference(avatar_split_clause,[],[f4353,f2121,f826,f53,f4381]) ).
fof(f4787,plain,
( ! [X0] : join(X0,converse(composition(converse(X0),sF1))) = converse(composition(converse(X0),sF2))
| ~ spl3_5 ),
inference(superposition,[],[f176,f3863]) ).
fof(f4791,plain,
( ! [X0] : composition(converse(sF2),X0) = join(X0,converse(composition(converse(X0),sF1)))
| ~ spl3_5 ),
inference(forward_demodulation,[],[f4787,f500]) ).
fof(f4812,plain,
( ! [X0] : composition(converse(sF2),X0) = join(X0,composition(converse(sF1),X0))
| ~ spl3_5 ),
inference(forward_demodulation,[],[f4791,f500]) ).
fof(f4823,plain,
( ! [X0] : composition(converse(sF2),X0) = join(X0,composition(sF1,X0))
| ~ spl3_5
| ~ spl3_9 ),
inference(forward_demodulation,[],[f4812,f2123]) ).
fof(f4827,plain,
( ! [X0] : composition(sF2,X0) = join(X0,composition(sF1,X0))
| ~ spl3_5
| ~ spl3_9
| ~ spl3_17 ),
inference(forward_demodulation,[],[f4823,f4383]) ).
fof(f4971,plain,
( ! [X0] : join(X0,composition(sF0,complement(composition(sk1,complement(X0))))) = X0
| ~ spl3_1
| ~ spl3_3 ),
inference(superposition,[],[f66,f226]) ).
fof(f5951,plain,
( ! [X0] : composition(converse(sk1),composition(sk1,X0)) = composition(converse(sk1),complement(composition(sk1,complement(X0))))
| ~ spl3_1 ),
inference(superposition,[],[f1510,f1673]) ).
fof(f5982,plain,
( ! [X0] : composition(sF0,composition(sk1,X0)) = composition(sF0,complement(composition(sk1,complement(X0))))
| ~ spl3_1
| ~ spl3_3 ),
inference(forward_demodulation,[],[f5951,f44]) ).
fof(f6000,plain,
( ! [X0] : composition(sF1,X0) = composition(sF0,complement(composition(sk1,complement(X0))))
| ~ spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f5982,f669]) ).
fof(f6010,plain,
( ! [X0] : join(X0,composition(sF1,X0)) = X0
| ~ spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f4971,f6000]) ).
fof(f6015,plain,
( ! [X0] : composition(sF2,X0) = X0
| ~ spl3_1
| ~ spl3_2
| ~ spl3_3
| ~ spl3_5
| ~ spl3_9
| ~ spl3_17 ),
inference(forward_demodulation,[],[f6010,f4827]) ).
fof(f6053,plain,
( one = sF2
| ~ spl3_1
| ~ spl3_2
| ~ spl3_3
| ~ spl3_5
| ~ spl3_9
| ~ spl3_17 ),
inference(superposition,[],[f6015,f8]) ).
fof(f6096,plain,
( $false
| ~ spl3_1
| ~ spl3_2
| ~ spl3_3
| spl3_4
| ~ spl3_5
| ~ spl3_9
| ~ spl3_17 ),
inference(forward_subsumption_resolution,[],[f6053,f49]) ).
fof(f6097,plain,
( ~ spl3_1
| ~ spl3_2
| ~ spl3_3
| spl3_4
| ~ spl3_5
| ~ spl3_9
| ~ spl3_17 ),
inference(avatar_contradiction_clause,[],[f6096]) ).
cnf(s1,plain,
spl3_1,
inference(sat_conversion,[],[f35]) ).
cnf(s2,plain,
spl3_2,
inference(sat_conversion,[],[f40]) ).
cnf(s3,plain,
spl3_3,
inference(sat_conversion,[],[f45]) ).
cnf(s4,plain,
~ spl3_4,
inference(sat_conversion,[],[f50]) ).
cnf(s5,plain,
spl3_5,
inference(sat_conversion,[],[f56]) ).
cnf(s6,plain,
spl3_6,
inference(sat_conversion,[],[f829]) ).
cnf(s8,plain,
( ~ spl3_3
| spl3_8 ),
inference(sat_conversion,[],[f2096]) ).
cnf(s9,plain,
( ~ spl3_2
| ~ spl3_3
| ~ spl3_8
| spl3_9 ),
inference(sat_conversion,[],[f2124]) ).
cnf(s17,plain,
( ~ spl3_5
| ~ spl3_6
| ~ spl3_9
| spl3_17 ),
inference(sat_conversion,[],[f4384]) ).
cnf(s23,plain,
( ~ spl3_1
| ~ spl3_2
| ~ spl3_3
| spl3_4
| ~ spl3_5
| ~ spl3_9
| ~ spl3_17 ),
inference(sat_conversion,[],[f6097]) ).
cnf(s24,plain,
spl3_8,
inference(rat,[],[s8,s3]) ).
cnf(s26,plain,
spl3_9,
inference(rat,[],[s9,s24,s3,s2]) ).
cnf(s27,plain,
spl3_17,
inference(rat,[],[s17,s5,s6,s26]) ).
cnf(s28,plain,
~ spl3_1,
inference(rat,[],[s23,s27,s2,s5,s4,s3,s26]) ).
cnf(s29,plain,
$false,
inference(rat,[],[s1,s28]) ).
fof(f6281,plain,
$false,
inference(avatar_sat_refutation,[],[s29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL042-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.48 % Computer : n015.cluster.edu
% 0.21/0.48 % Model : x86_64 x86_64
% 0.21/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.48 % Memory : 8046.5625MB
% 0.21/0.48 % OS : Linux 6.8.0-71-generic
% 0.21/0.48 % CPULimit : 300
% 0.21/0.48 % WCLimit : 300
% 0.21/0.48 % DateTime : Sun Sep 27 22:59:46 UTC 2026
% 0.21/0.49 % CPUTime :
% 0.21/0.49 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.54 Running first-order theorem proving
% 0.26/0.55 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
% 7.93/3.84 % (2109340)Detected a unit-equality problem, will run specialized UEQ schedule.
% 7.93/3.84 % (2109351)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2955615148:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 7.93/3.84 % (2109346)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=47743484:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 7.93/3.84 % (2109345)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=604720743:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 7.93/3.84 % (2109347)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=342142856:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 7.93/3.84 % (2109348)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1488591326:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 7.93/3.84 % (2109349)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1353223200:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 7.93/3.84 % (2109350)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4004384953:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 7.93/3.84 % (2109348)Instruction limit reached!
% 7.93/3.84 % (2109348)------------------------------
% 7.93/3.84 % (2109348)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.93/3.84 % (2109348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.93/3.84 % (2109348)CaDiCaL version: 2.1.3
% 7.93/3.84 % (2109348)Termination reason: Instruction limit
% 7.93/3.84 % (2109348)Termination phase: Saturation
% 7.93/3.84 % (2109348)Time elapsed: 0.140 s
% 7.93/3.84 % (2109348)Peak memory usage: 89 MB
% 7.93/3.84 % (2109348)Instructions burned: 136 (million)
% 7.93/3.84 % (2109349)Instruction limit reached!
% 7.93/3.84 % (2109349)------------------------------
% 7.93/3.84 % (2109349)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.93/3.84 % (2109349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.93/3.84 % (2109349)CaDiCaL version: 2.1.3
% 7.93/3.84 % (2109349)Termination reason: Instruction limit
% 7.93/3.84 % (2109349)Termination phase: Saturation
% 7.93/3.84 % (2109349)Time elapsed: 0.178 s
% 7.93/3.84 % (2109349)Peak memory usage: 89 MB
% 7.93/3.84 % (2109349)Instructions burned: 181 (million)
% 7.93/3.84 % (2109350)Instruction limit reached!
% 7.93/3.84 % (2109350)------------------------------
% 7.93/3.84 % (2109350)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.93/3.84 % (2109350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.93/3.84 % (2109350)CaDiCaL version: 2.1.3
% 7.93/3.84 % (2109350)Termination reason: Instruction limit
% 7.93/3.84 % (2109350)Termination phase: Saturation
% 7.93/3.84 % (2109350)Time elapsed: 0.277 s
% 7.93/3.84 % (2109350)Peak memory usage: 90 MB
% 7.93/3.84 % (2109350)Instructions burned: 257 (million)
% 7.93/3.84 % (2109359)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2221405517:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 7.93/3.84 % (2109360)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1489329687:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 7.93/3.84 % (2109351)Instruction limit reached!
% 7.93/3.84 % (2109351)------------------------------
% 7.93/3.84 % (2109351)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.93/3.84 % (2109351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.93/3.84 % (2109351)CaDiCaL version: 2.1.3
% 7.93/3.84 % (2109351)Termination reason: Instruction limit
% 7.93/3.84 % (2109351)Termination phase: Saturation
% 7.93/3.84 % (2109351)Time elapsed: 0.571 s
% 7.93/3.84 % (2109351)Peak memory usage: 100 MB
% 7.93/3.84 % (2109351)Instructions burned: 1188 (million)
% 7.93/3.84 % (2109361)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1537175448:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 7.93/3.84 % (2109361)Instruction limit reached!
% 7.93/3.84 % (2109361)------------------------------
% 7.93/3.84 % (2109361)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.93/3.84 % (2109361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.93/3.84 % (2109361)CaDiCaL version: 2.1.3
% 7.93/3.84 % (2109361)Termination reason: Instruction limit
% 7.93/3.84 % (2109361)Termination phase: Saturation
% 7.93/3.84 % (2109361)Time elapsed: 0.196 s
% 7.93/3.84 % (2109361)Peak memory usage: 91 MB
% 7.93/3.84 % (2109361)Instructions burned: 215 (million)
% 7.93/3.84 % (2109365)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=2269614326:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2992 on theBenchmark for (2992ds/317Mi)
% 7.93/3.84 % (2109365)Instruction limit reached!
% 7.93/3.84 % (2109365)------------------------------
% 7.93/3.84 % (2109365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.93/3.84 % (2109365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.93/3.84 % (2109365)CaDiCaL version: 2.1.3
% 7.93/3.84 % (2109365)Termination reason: Instruction limit
% 7.93/3.84 % (2109365)Termination phase: Saturation
% 7.93/3.84 % (2109365)Time elapsed: 0.183 s
% 7.93/3.84 % (2109365)Peak memory usage: 93 MB
% 7.93/3.84 % (2109365)Instructions burned: 318 (million)
% 7.93/3.84 % (2109366)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=2221212257:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2990 on theBenchmark for (2990ds/12125Mi)
% 7.93/3.84 % (2109368)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=3116329117:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2988 on theBenchmark for (2988ds/2836Mi)
% 7.93/3.84 % (2109345)First to succeed.
% 7.93/3.84 % (2109345)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2109340"
% 7.93/3.84 % (2109360)Also succeeded, but the first one will report.
% 7.93/3.84 % (2109345)Refutation found. Thanks to Tanya!
% 7.93/3.84 % SZS status Unsatisfiable for theBenchmark
% 7.93/3.84 % SZS output start Proof for theBenchmark
% See solution above
% 18.77/4.22 % (2109345)------------------------------
% 18.77/4.22 % (2109345)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.77/4.22 % (2109345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.77/4.22 % (2109345)CaDiCaL version: 2.1.3
% 18.77/4.22 % (2109345)Termination reason: Refutation
% 18.77/4.22 % (2109345)Time elapsed: 1.828 s
% 18.77/4.22 % (2109345)Peak memory usage: 136 MB
% 18.77/4.22 % (2109345)Instructions burned: 1649 (million)
% 18.77/4.22 % (2109345)------------------------------
% 18.77/4.22 % (2109345)------------------------------
% 18.77/4.22 % (2109340)Success in time 2.522 s
% 18.77/4.22 % Vampire exiting
%------------------------------------------------------------------------------