%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV539+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 12:57:56 PM UTC 2026
% Result : Theorem 8.54s 2.12s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 27
% Syntax : Number of formulae : 149 ( 60 unt; 16 def)
% Number of atoms : 287 ( 43 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 240 ( 102 ~; 103 |; 18 &)
% ( 12 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 12 con; 0-2 aty)
% Number of variables : 116 ( 0 sgn 110 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subq(X0,X1)
<=> ! [X2] :
( mem(X2,X0)
=> mem(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subq_def) ).
fof(f2,axiom,
! [X0,X1] :
( subq(X0,X1)
=> ( subq(X1,X0)
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext) ).
fof(f4,axiom,
! [X0] : ~ mem(X0,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_ax) ).
fof(f5,axiom,
! [X0,X1] :
( mem(X0,s(X1))
<=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_ax) ).
fof(f6,axiom,
! [X0,X1,X2] :
( mem(X0,u(X1,X2))
<=> ( mem(X0,X1)
| mem(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_ax) ).
fof(f8,axiom,
! [X0,X1] : a(X0,X1) = u(X0,s(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_def) ).
fof(f9,axiom,
! [X0] : n(X0) = a(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_def) ).
fof(f10,axiom,
! [X0,X1] :
( mem(X0,p(X1))
<=> subq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_ax) ).
fof(f11,axiom,
! [X0] :
( atleast2p(X0)
<=> ? [X1] :
( mem(X1,X0)
& ~ subq(X0,p(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',atleast2p_def) ).
fof(f12,axiom,
! [X0] :
( atleast3p(X0)
<=> ? [X1] :
( subq(X1,X0)
& atleast2p(X1)
& ~ subq(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',atleast3p_def) ).
fof(f26,conjecture,
atleast3p(u(n(n(s(n(e)))),p(s(n(n(e)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',atleast3_327) ).
fof(f27,negated_conjecture,
~ atleast3p(u(n(n(s(n(e)))),p(s(n(n(e)))))),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,plain,
~ atleast3p(u(n(n(s(n(e)))),p(s(n(n(e)))))),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0] :
( ? [X1] :
( subq(X1,X0)
& atleast2p(X1)
& ~ subq(X0,X1) )
=> atleast3p(X0) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f30,plain,
! [X0] :
( ? [X1] :
( mem(X1,X0)
& ~ subq(X0,p(X1)) )
=> atleast2p(X0) ),
inference(unused_predicate_definition_removal,[],[f11]) ).
fof(f31,plain,
! [X0,X1] :
( subq(X0,X1)
<=> ! [X2] :
( mem(X2,X1)
| ~ mem(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f32,plain,
! [X0,X1] :
( X0 = X1
| ~ subq(X1,X0)
| ~ subq(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f33,plain,
! [X0,X1] :
( X0 = X1
| ~ subq(X1,X0)
| ~ subq(X0,X1) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0] :
( atleast2p(X0)
| ! [X1] :
( ~ mem(X1,X0)
| subq(X0,p(X1)) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f35,plain,
! [X0] :
( atleast3p(X0)
| ! [X1] :
( ~ subq(X1,X0)
| ~ atleast2p(X1)
| subq(X0,X1) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f36,plain,
! [X0,X1] :
( ( subq(X0,X1)
| ? [X2] :
( ~ mem(X2,X1)
& mem(X2,X0) ) )
& ( ! [X2] :
( mem(X2,X1)
| ~ mem(X2,X0) )
| ~ subq(X0,X1) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f37,plain,
! [X0,X1] :
( ( subq(X0,X1)
| ? [X2] :
( ~ mem(X2,X1)
& mem(X2,X0) ) )
& ( ! [X3] :
( mem(X3,X1)
| ~ mem(X3,X0) )
| ~ subq(X0,X1) ) ),
inference(rectify,[],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ( subq(X0,X1)
| ( ~ mem(sK0(X0,X1),X1)
& mem(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( mem(X3,X1)
| ~ mem(X3,X0) )
| ~ subq(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( ( mem(X0,s(X1))
| X0 != X1 )
& ( X0 = X1
| ~ mem(X0,s(X1)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( mem(X0,u(X1,X2))
| ( ~ mem(X0,X1)
& ~ mem(X0,X2) ) )
& ( mem(X0,X1)
| mem(X0,X2)
| ~ mem(X0,u(X1,X2)) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( mem(X0,u(X1,X2))
| ( ~ mem(X0,X1)
& ~ mem(X0,X2) ) )
& ( mem(X0,X1)
| mem(X0,X2)
| ~ mem(X0,u(X1,X2)) ) ),
inference(flattening,[],[f40]) ).
fof(f44,plain,
! [X0,X1] :
( ( mem(X0,p(X1))
| ~ subq(X0,X1) )
& ( subq(X0,X1)
| ~ mem(X0,p(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f45,plain,
! [X3,X0,X1] :
( ~ mem(X3,X0)
| mem(X3,X1)
| ~ subq(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f46,plain,
! [X0,X1] :
( mem(sK0(X0,X1),X0)
| subq(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f47,plain,
! [X0,X1] :
( ~ mem(sK0(X0,X1),X1)
| subq(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f48,plain,
! [X0,X1] :
( ~ subq(X1,X0)
| X0 = X1
| ~ subq(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f49,plain,
! [X0] : ~ mem(X0,e),
inference(cnf_transformation,[],[f4]) ).
fof(f50,plain,
! [X0,X1] :
( ~ mem(X0,s(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f39]) ).
fof(f51,plain,
! [X0,X1] :
( mem(X0,s(X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f39]) ).
fof(f53,plain,
! [X2,X0,X1] :
( mem(X0,u(X1,X2))
| ~ mem(X0,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f54,plain,
! [X2,X0,X1] :
( mem(X0,u(X1,X2))
| ~ mem(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f58,plain,
! [X0,X1] : a(X0,X1) = u(X0,s(X1)),
inference(cnf_transformation,[],[f8]) ).
fof(f59,plain,
! [X0] : n(X0) = a(X0,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f60,plain,
! [X0,X1] :
( ~ mem(X0,p(X1))
| subq(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f61,plain,
! [X0,X1] :
( mem(X0,p(X1))
| ~ subq(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f62,plain,
! [X0,X1] :
( subq(X0,p(X1))
| ~ mem(X1,X0)
| atleast2p(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f63,plain,
! [X0,X1] :
( ~ subq(X1,X0)
| atleast3p(X0)
| ~ atleast2p(X1)
| subq(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f64,plain,
~ atleast3p(u(n(n(s(n(e)))),p(s(n(n(e)))))),
inference(cnf_transformation,[],[f28]) ).
fof(f65,plain,
! [X0] : n(X0) = u(X0,s(X0)),
inference(definition_unfolding,[],[f59,f58]) ).
fof(f66,plain,
~ atleast3p(u(u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e))))))),p(s(u(u(e,s(e)),s(u(e,s(e)))))))),
inference(definition_unfolding,[],[f64,f65,f65,f65,f65,f65]) ).
fof(f67,plain,
! [X1] : mem(X1,s(X1)),
inference(equality_resolution,[],[f51]) ).
fof(f68,definition,
sF1 = s(e),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f69,plain,
s(e) = sF1,
inference(reorient_equations,[],[f68]) ).
fof(f70,definition,
sF2 = u(e,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f71,plain,
u(e,sF1) = sF2,
inference(reorient_equations,[],[f70]) ).
fof(f72,definition,
sF3 = s(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f73,plain,
s(sF2) = sF3,
inference(reorient_equations,[],[f72]) ).
fof(f74,definition,
sF4 = s(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f75,plain,
s(sF3) = sF4,
inference(reorient_equations,[],[f74]) ).
fof(f76,definition,
sF5 = u(sF3,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f77,plain,
u(sF3,sF4) = sF5,
inference(reorient_equations,[],[f76]) ).
fof(f78,definition,
sF6 = s(sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f79,plain,
s(sF5) = sF6,
inference(reorient_equations,[],[f78]) ).
fof(f80,definition,
sF7 = u(sF5,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f81,plain,
u(sF5,sF6) = sF7,
inference(reorient_equations,[],[f80]) ).
fof(f82,definition,
sF8 = u(sF2,sF3),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f83,plain,
u(sF2,sF3) = sF8,
inference(reorient_equations,[],[f82]) ).
fof(f84,definition,
sF9 = s(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f85,plain,
s(sF8) = sF9,
inference(reorient_equations,[],[f84]) ).
fof(f86,definition,
sF10 = p(sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f87,plain,
p(sF9) = sF10,
inference(reorient_equations,[],[f86]) ).
fof(f88,definition,
sF11 = u(sF7,sF10),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f89,plain,
u(sF7,sF10) = sF11,
inference(reorient_equations,[],[f88]) ).
fof(f90,plain,
~ atleast3p(sF11),
inference(definition_folding,[],[f66,f89,f87,f85,f83,f73,f71,f69,f71,f69,f81,f79,f77,f75,f73,f71,f69,f73,f71,f69,f77,f75,f73,f71,f69,f73,f71,f69]) ).
fof(f91,plain,
mem(e,sF1),
inference(superposition,[],[f67,f69]) ).
fof(f92,plain,
mem(sF2,sF3),
inference(superposition,[],[f67,f73]) ).
fof(f95,plain,
mem(sF8,sF9),
inference(superposition,[],[f67,f85]) ).
fof(f96,plain,
! [X0] :
( ~ mem(X0,sF10)
| subq(X0,sF9) ),
inference(superposition,[],[f60,f87]) ).
fof(f97,plain,
! [X0] :
( ~ mem(X0,sF1)
| mem(X0,sF2) ),
inference(superposition,[],[f53,f71]) ).
fof(f103,plain,
! [X0] :
( ~ mem(X0,sF2)
| mem(X0,sF8) ),
inference(superposition,[],[f54,f83]) ).
fof(f104,plain,
! [X0] :
( ~ mem(X0,sF3)
| mem(X0,sF5) ),
inference(superposition,[],[f54,f77]) ).
fof(f105,plain,
! [X0] :
( ~ mem(X0,sF5)
| mem(X0,sF7) ),
inference(superposition,[],[f54,f81]) ).
fof(f106,plain,
! [X0] :
( ~ mem(X0,sF7)
| mem(X0,sF11) ),
inference(superposition,[],[f54,f89]) ).
fof(f112,plain,
! [X0] :
( ~ mem(X0,sF9)
| sF8 = X0 ),
inference(superposition,[],[f50,f85]) ).
fof(f114,plain,
! [X2,X0,X1] :
( ~ mem(sK0(X0,u(X1,X2)),X2)
| subq(X0,u(X1,X2)) ),
inference(resolution,[],[f47,f53]) ).
fof(f124,plain,
mem(e,sF2),
inference(resolution,[],[f97,f91]) ).
fof(f127,plain,
! [X0] :
( ~ subq(X0,sF9)
| mem(X0,sF10) ),
inference(superposition,[],[f61,f87]) ).
fof(f128,plain,
! [X0] :
( subq(X0,X0)
| subq(X0,X0) ),
inference(resolution,[],[f46,f47]) ).
fof(f137,plain,
! [X0] : subq(X0,X0),
inference(duplicate_literal_removal,[],[f128]) ).
fof(f138,plain,
! [X0] : subq(e,X0),
inference(resolution,[],[f49,f46]) ).
fof(f140,plain,
mem(sF2,sF5),
inference(resolution,[],[f104,f92]) ).
fof(f161,plain,
mem(sF2,sF7),
inference(resolution,[],[f140,f105]) ).
fof(f164,plain,
mem(sF2,sF11),
inference(resolution,[],[f161,f106]) ).
fof(f185,plain,
! [X0] :
( ~ subq(sF2,X0)
| mem(e,X0) ),
inference(resolution,[],[f45,f124]) ).
fof(f200,plain,
! [X0] :
( ~ subq(sF9,X0)
| mem(sF8,X0) ),
inference(resolution,[],[f45,f95]) ).
fof(f201,plain,
mem(e,sF10),
inference(resolution,[],[f127,f138]) ).
fof(f208,definition,
( spl12_1
<=> subq(sF11,sF10) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f224,definition,
( spl12_3
<=> mem(sF2,sF10) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
fof(f225,plain,
( ~ mem(sF2,sF10)
| spl12_3 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f226,plain,
( mem(sF2,sF10)
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f232,plain,
( subq(sF2,sF9)
| ~ spl12_3 ),
inference(resolution,[],[f226,f96]) ).
fof(f290,plain,
( mem(e,sF9)
| ~ spl12_3 ),
inference(resolution,[],[f185,f232]) ).
fof(f291,plain,
( e = sF8
| ~ spl12_3 ),
inference(resolution,[],[f290,f112]) ).
fof(f293,plain,
( ! [X0] : ~ mem(X0,sF8)
| ~ spl12_3 ),
inference(superposition,[],[f49,f291]) ).
fof(f297,plain,
( mem(sF8,sF2)
| ~ spl12_3 ),
inference(superposition,[],[f124,f291]) ).
fof(f298,plain,
( ! [X0] : subq(sF8,X0)
| ~ spl12_3 ),
inference(superposition,[],[f138,f291]) ).
fof(f425,plain,
! [X0,X1] :
( subq(X0,u(X1,X0))
| subq(X0,u(X1,X0)) ),
inference(resolution,[],[f114,f46]) ).
fof(f436,plain,
! [X0] :
( ~ mem(sK0(X0,sF11),sF10)
| subq(X0,sF11) ),
inference(superposition,[],[f114,f89]) ).
fof(f440,plain,
! [X0,X1] : subq(X0,u(X1,X0)),
inference(duplicate_literal_removal,[],[f425]) ).
fof(f442,plain,
( subq(sF10,sF11)
| subq(sF10,sF11) ),
inference(resolution,[],[f436,f46]) ).
fof(f445,plain,
subq(sF10,sF11),
inference(duplicate_literal_removal,[],[f442]) ).
fof(f459,plain,
subq(sF3,sF8),
inference(superposition,[],[f440,f83]) ).
fof(f480,plain,
( sF3 = sF8
| ~ subq(sF8,sF3) ),
inference(resolution,[],[f459,f48]) ).
fof(f481,plain,
( sF3 = sF8
| ~ spl12_3 ),
inference(forward_subsumption_resolution,[],[f480,f298]) ).
fof(f489,plain,
( mem(sF3,sF2)
| ~ spl12_3 ),
inference(superposition,[],[f297,f481]) ).
fof(f504,plain,
( mem(sF3,sF8)
| ~ spl12_3 ),
inference(resolution,[],[f489,f103]) ).
fof(f508,plain,
( $false
| ~ spl12_3 ),
inference(forward_subsumption_resolution,[],[f504,f293]) ).
fof(f509,plain,
~ spl12_3,
inference(avatar_contradiction_clause,[],[f508]) ).
fof(f611,plain,
mem(sF9,sF10),
inference(resolution,[],[f137,f127]) ).
fof(f625,plain,
! [X0] :
( ~ subq(sF10,X0)
| mem(sF9,X0) ),
inference(resolution,[],[f611,f45]) ).
fof(f629,plain,
( atleast3p(sF11)
| ~ atleast2p(sF10)
| subq(sF11,sF10) ),
inference(resolution,[],[f445,f63]) ).
fof(f630,plain,
( sF10 = sF11
| ~ subq(sF11,sF10) ),
inference(resolution,[],[f445,f48]) ).
fof(f632,definition,
( spl12_43
<=> sF10 = sF11 ),
introduced(definition,[new_symbols(definition,[spl12_43])],[avatar_definition]) ).
fof(f634,plain,
( sF10 = sF11
| ~ spl12_43 ),
inference(avatar_component_clause,[],[f632]) ).
fof(f635,plain,
( ~ spl12_1
| spl12_43 ),
inference(avatar_split_clause,[],[f630,f632,f208]) ).
fof(f636,plain,
( ~ atleast2p(sF10)
| subq(sF11,sF10) ),
inference(forward_subsumption_resolution,[],[f629,f90]) ).
fof(f638,definition,
( spl12_44
<=> atleast2p(sF10) ),
introduced(definition,[new_symbols(definition,[spl12_44])],[avatar_definition]) ).
fof(f640,plain,
( ~ atleast2p(sF10)
| spl12_44 ),
inference(avatar_component_clause,[],[f638]) ).
fof(f641,plain,
( spl12_1
| ~ spl12_44 ),
inference(avatar_split_clause,[],[f636,f638,f208]) ).
fof(f846,plain,
( mem(sF2,sF10)
| ~ spl12_43 ),
inference(superposition,[],[f164,f634]) ).
fof(f861,plain,
( $false
| spl12_3
| ~ spl12_43 ),
inference(forward_subsumption_resolution,[],[f846,f225]) ).
fof(f862,plain,
( spl12_3
| ~ spl12_43 ),
inference(avatar_contradiction_clause,[],[f861]) ).
fof(f2626,plain,
! [X0] :
( mem(sF9,p(X0))
| ~ mem(X0,sF10)
| atleast2p(sF10) ),
inference(resolution,[],[f625,f62]) ).
fof(f2628,plain,
( ! [X0] :
( mem(sF9,p(X0))
| ~ mem(X0,sF10) )
| spl12_44 ),
inference(forward_subsumption_resolution,[],[f2626,f640]) ).
fof(f2630,plain,
( ! [X0] :
( ~ mem(X0,sF10)
| subq(sF9,X0) )
| spl12_44 ),
inference(resolution,[],[f2628,f60]) ).
fof(f2634,plain,
( subq(sF9,e)
| spl12_44 ),
inference(resolution,[],[f2630,f201]) ).
fof(f2654,definition,
( spl12_175
<=> subq(sF9,e) ),
introduced(definition,[new_symbols(definition,[spl12_175])],[avatar_definition]) ).
fof(f2656,plain,
( subq(sF9,e)
| ~ spl12_175 ),
inference(avatar_component_clause,[],[f2654]) ).
fof(f2658,plain,
( spl12_175
| spl12_44 ),
inference(avatar_split_clause,[],[f2634,f638,f2654]) ).
fof(f2659,plain,
( mem(sF8,e)
| ~ spl12_175 ),
inference(resolution,[],[f2656,f200]) ).
fof(f2665,plain,
( $false
| ~ spl12_175 ),
inference(forward_subsumption_resolution,[],[f2659,f49]) ).
fof(f2666,plain,
~ spl12_175,
inference(avatar_contradiction_clause,[],[f2665]) ).
cnf(s17,plain,
~ spl12_3,
inference(sat_conversion,[],[f509]) ).
cnf(s28,plain,
( ~ spl12_1
| spl12_43 ),
inference(sat_conversion,[],[f635]) ).
cnf(s29,plain,
( spl12_1
| ~ spl12_44 ),
inference(sat_conversion,[],[f641]) ).
cnf(s38,plain,
( spl12_3
| ~ spl12_43 ),
inference(sat_conversion,[],[f862]) ).
cnf(s193,plain,
( spl12_44
| spl12_175 ),
inference(sat_conversion,[],[f2658]) ).
cnf(s194,plain,
~ spl12_175,
inference(sat_conversion,[],[f2666]) ).
cnf(s195,plain,
spl12_44,
inference(rat,[],[s193,s194]) ).
cnf(s196,plain,
spl12_1,
inference(rat,[],[s29,s195]) ).
cnf(s197,plain,
spl12_43,
inference(rat,[],[s28,s196]) ).
cnf(s198,plain,
spl12_3,
inference(rat,[],[s38,s197]) ).
cnf(s199,plain,
$false,
inference(rat,[],[s17,s198]) ).
fof(f2667,plain,
$false,
inference(avatar_sat_refutation,[],[s199]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV539+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n004.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 06:31:37 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 8.54/2.12 % (148692)Detected formulas, will run a generic FOF schedule.
% 8.54/2.12 % (148701)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=560245221:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.54/2.12 % (148701)Instruction limit reached!
% 8.54/2.12 % (148701)------------------------------
% 8.54/2.12 % (148701)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.54/2.12 % (148701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.54/2.12 % (148701)CaDiCaL version: 2.1.3
% 8.54/2.12 % (148701)Termination reason: Instruction limit
% 8.54/2.12 % (148701)Termination phase: Saturation
% 8.54/2.12 % (148701)Time elapsed: 0.041 s
% 8.54/2.12 % (148701)Peak memory usage: 88 MB
% 8.54/2.12 % (148701)Instructions burned: 121 (million)
% 8.54/2.12 % (148703)dis-21_1_sil=8000:lcm=predicate:random_seed=459520570: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)
% 8.54/2.12 % (148697)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=3952622738:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.54/2.12 % (148698)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=1945041707:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.54/2.12 % (148700)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=897533258:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.54/2.12 % (148702)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1780061267:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.54/2.12 % (148699)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=1583557947:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.54/2.12 % (148700)Refutation not found, incomplete strategy
% 8.54/2.12 % (148700)------------------------------
% 8.54/2.12 % (148700)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.54/2.12 % (148700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.54/2.12 % (148700)CaDiCaL version: 2.1.3
% 8.54/2.12 % (148700)Termination reason: Refutation not found, incomplete strategy
% 8.54/2.12 % (148700)Time elapsed: 0.001 s
% 8.54/2.12 % (148700)Peak memory usage: 88 MB
% 8.54/2.12 % (148703)Instruction limit reached!
% 8.54/2.12 % (148703)------------------------------
% 8.54/2.12 % (148703)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.54/2.12 % (148703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.54/2.12 % (148703)CaDiCaL version: 2.1.3
% 8.54/2.12 % (148703)Termination reason: Instruction limit
% 8.54/2.12 % (148703)Termination phase: Saturation
% 8.54/2.12 % (148703)Time elapsed: 0.082 s
% 8.54/2.12 % (148703)Peak memory usage: 89 MB
% 8.54/2.12 % (148703)Instructions burned: 130 (million)
% 8.54/2.12 % (148705)lrs+10_1_sil=8000:sp=occurrence:random_seed=2136948728:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 8.54/2.12 % (148702)Instruction limit reached!
% 8.54/2.12 % (148702)------------------------------
% 8.54/2.12 % (148702)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.54/2.12 % (148702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.54/2.12 % (148702)CaDiCaL version: 2.1.3
% 8.54/2.12 % (148702)Termination reason: Instruction limit
% 8.54/2.12 % (148702)Termination phase: Saturation
% 8.54/2.12 % (148702)Time elapsed: 0.093 s
% 8.54/2.12 % (148702)Peak memory usage: 89 MB
% 8.54/2.12 % (148702)Instructions burned: 140 (million)
% 8.54/2.12 % (148705)Instruction limit reached!
% 8.54/2.12 % (148705)------------------------------
% 8.54/2.12 % (148705)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.54/2.12 % (148705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.54/2.12 % (148705)CaDiCaL version: 2.1.3
% 8.54/2.12 % (148705)Termination reason: Instruction limit
% 8.54/2.12 % (148705)Termination phase: Saturation
% 8.54/2.12 % (148705)Time elapsed: 0.099 s
% 8.54/2.12 % (148705)Peak memory usage: 91 MB
% 8.54/2.12 % (148705)Instructions burned: 287 (million)
% 8.54/2.12 % (148713)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2922591437:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 8.54/2.12 % (148714)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4160968687:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 8.54/2.12 % (148714)Refutation not found, incomplete strategy
% 8.54/2.12 % (148714)------------------------------
% 8.54/2.12 % (148714)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.54/2.12 % (148714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.54/2.12 % (148714)CaDiCaL version: 2.1.3
% 8.54/2.12 % (148714)Termination reason: Refutation not found, incomplete strategy
% 8.54/2.12 % (148714)Time elapsed: 0.002 s
% 8.54/2.12 % (148714)Peak memory usage: 88 MB
% 8.54/2.12 % (148714)Instructions burned: 1 (million)
% 8.54/2.12 % (148700)------------------------------
% 8.54/2.12 % (148700)------------------------------
% 8.54/2.12 % (148715)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=4183428166:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 8.54/2.12 % (148713)Instruction limit reached!
% 8.54/2.12 % (148713)------------------------------
% 8.54/2.12 % (148713)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.54/2.12 % (148713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.54/2.12 % (148713)CaDiCaL version: 2.1.3
% 8.54/2.12 % (148713)Termination reason: Instruction limit
% 8.54/2.12 % (148713)Termination phase: Saturation
% 8.54/2.12 % (148713)Time elapsed: 0.077 s
% 8.54/2.12 % (148713)Peak memory usage: 89 MB
% 8.54/2.12 % (148713)Instructions burned: 158 (million)
% 8.54/2.12 % (148715)Instruction limit reached!
% 8.54/2.12 % (148715)------------------------------
% 8.54/2.12 % (148715)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.54/2.12 % (148715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.54/2.12 % (148715)CaDiCaL version: 2.1.3
% 8.54/2.12 % (148715)Termination reason: Instruction limit
% 8.54/2.12 % (148715)Termination phase: Saturation
% 8.54/2.12 % (148715)Time elapsed: 0.077 s
% 8.54/2.12 % (148715)Peak memory usage: 91 MB
% 8.54/2.12 % (148715)Instructions burned: 250 (million)
% 8.54/2.12 % (148718)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3222670449:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 8.54/2.12 % (148718)Refutation not found, incomplete strategy
% 8.54/2.12 % (148718)------------------------------
% 8.54/2.12 % (148718)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.54/2.12 % (148718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.54/2.12 % (148718)CaDiCaL version: 2.1.3
% 8.54/2.12 % (148718)Termination reason: Refutation not found, incomplete strategy
% 8.54/2.12 % (148718)Time elapsed: 0.001 s
% 8.54/2.12 % (148718)Peak memory usage: 88 MB
% 8.54/2.12 % (148718)Instructions burned: 1 (million)
% 8.54/2.12 % (148720)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1358604399:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 8.54/2.12 % (148721)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1954754809:cts=off:i=113:fsr=off:ss=included:sgt=4_2995 on theBenchmark for (2995ds/113Mi)
% 8.54/2.12 % (148721)Instruction limit reached!
% 8.54/2.12 % (148721)------------------------------
% 8.54/2.12 % (148721)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.54/2.12 % (148721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.54/2.12 % (148721)CaDiCaL version: 2.1.3
% 8.54/2.12 % (148721)Termination reason: Instruction limit
% 8.54/2.12 % (148721)Termination phase: Saturation
% 8.54/2.12 % (148721)Time elapsed: 0.037 s
% 8.54/2.12 % (148721)Peak memory usage: 89 MB
% 8.54/2.12 % (148721)Instructions burned: 116 (million)
% 8.54/2.12 % (148714)------------------------------
% 8.54/2.12 % (148714)------------------------------
% 8.54/2.12 % (148725)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=698445598:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 8.54/2.12 % (148699)Refutation not found, incomplete strategy
% 8.54/2.12 % (148699)------------------------------
% 8.54/2.12 % (148699)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.54/2.12 % (148699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.54/2.12 % (148699)CaDiCaL version: 2.1.3
% 8.54/2.12 % (148699)Termination reason: Refutation not found, incomplete strategy
% 8.54/2.12 % (148699)Time elapsed: 0.561 s
% 8.54/2.12 % (148699)Peak memory usage: 126 MB
% 8.54/2.12 % (148699)Instructions burned: 828 (million)
% 8.54/2.12 % (148725)Instruction limit reached!
% 8.54/2.12 % (148725)------------------------------
% 8.54/2.12 % (148725)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.54/2.12 % (148725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.54/2.12 % (148725)CaDiCaL version: 2.1.3
% 8.54/2.12 % (148725)Termination reason: Instruction limit
% 8.54/2.12 % (148725)Termination phase: Saturation
% 8.54/2.12 % (148725)Time elapsed: 0.034 s
% 8.54/2.12 % (148725)Peak memory usage: 88 MB
% 8.54/2.12 % (148725)Instructions burned: 130 (million)
% 8.54/2.12 % (148718)------------------------------
% 8.54/2.12 % (148718)------------------------------
% 8.54/2.12 % (148726)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1293065460:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 8.54/2.12 % (148728)lrs+10_1_sil=8000:sp=occurrence:random_seed=647828706:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 8.54/2.12 % (148726)Instruction limit reached!
% 8.54/2.12 % (148726)------------------------------
% 8.54/2.12 % (148726)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.54/2.12 % (148726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.54/2.12 % (148726)CaDiCaL version: 2.1.3
% 8.54/2.12 % (148726)Termination reason: Instruction limit
% 8.54/2.12 % (148726)Termination phase: Saturation
% 8.54/2.12 % (148726)Time elapsed: 0.072 s
% 8.54/2.12 % (148726)Peak memory usage: 89 MB
% 8.54/2.12 % (148726)Instructions burned: 115 (million)
% 8.54/2.12 % (148730)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=4048693028:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 8.54/2.12 % (148730)Refutation not found, incomplete strategy
% 8.54/2.12 % (148730)------------------------------
% 8.54/2.12 % (148730)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.54/2.12 % (148730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.54/2.12 % (148730)CaDiCaL version: 2.1.3
% 8.54/2.12 % (148730)Termination reason: Refutation not found, incomplete strategy
% 8.54/2.12 % (148730)Time elapsed: 0.001 s
% 8.54/2.12 % (148730)Peak memory usage: 88 MB
% 8.54/2.12 % (148699)------------------------------
% 8.54/2.12 % (148699)------------------------------
% 8.54/2.12 % (148732)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2387170894:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 8.54/2.12 % (148697)First to succeed.
% 8.54/2.12 % (148697)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-148692"
% 8.54/2.12 % (148735)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1738518604:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2990 on theBenchmark for (2990ds/134Mi)
% 8.54/2.12 % (148728)Instruction limit reached!
% 8.54/2.12 % (148728)------------------------------
% 8.54/2.12 % (148728)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.54/2.12 % (148728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.54/2.12 % (148728)CaDiCaL version: 2.1.3
% 8.54/2.12 % (148728)Termination reason: Instruction limit
% 8.54/2.12 % (148728)Termination phase: Saturation
% 8.54/2.12 % (148728)Time elapsed: 0.310 s
% 8.54/2.12 % (148728)Peak memory usage: 96 MB
% 8.54/2.12 % (148728)Instructions burned: 910 (million)
% 8.54/2.12 % (148730)------------------------------
% 8.54/2.12 % (148730)------------------------------
% 8.54/2.12 % (148735)Instruction limit reached!
% 8.54/2.12 % (148735)------------------------------
% 8.54/2.12 % (148735)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.54/2.12 % (148735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.54/2.12 % (148735)CaDiCaL version: 2.1.3
% 8.54/2.12 % (148735)Termination reason: Instruction limit
% 8.54/2.12 % (148735)Termination phase: Saturation
% 8.54/2.12 % (148735)Time elapsed: 0.071 s
% 8.54/2.12 % (148735)Peak memory usage: 90 MB
% 8.54/2.12 % (148735)Instructions burned: 134 (million)
% 8.54/2.12 % (148697)Refutation found. Thanks to Tanya!
% 8.54/2.12 % SZS status Theorem for theBenchmark
% 8.54/2.12 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/2.31 % (148697)------------------------------
% 0.15/2.31 % (148697)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/2.31 % (148697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/2.31 % (148697)CaDiCaL version: 2.1.3
% 0.15/2.31 % (148697)Termination reason: Refutation
% 0.15/2.31 % (148697)Time elapsed: 0.854 s
% 0.15/2.31 % (148697)Peak memory usage: 131 MB
% 0.15/2.31 % (148697)Instructions burned: 1230 (million)
% 0.15/2.31 % (148697)------------------------------
% 0.15/2.31 % (148697)------------------------------
% 0.15/2.31 % (148692)Success in time 1.268 s
% 0.15/2.31 % Vampire exiting
%------------------------------------------------------------------------------