%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV562+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 : n020.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 12:58:20 PM UTC 2026
% Result : Theorem 8.62s 2.12s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 29
% Syntax : Number of formulae : 151 ( 67 unt; 19 def)
% Number of atoms : 292 ( 53 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 239 ( 98 ~; 108 |; 21 &)
% ( 10 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 17 con; 0-2 aty)
% Number of variables : 120 ( 0 sgn 115 !; 5 ?)
% 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(f3,axiom,
! [X0,X1] :
( disj(X0,X1)
<=> ~ ? [X2] :
( mem(X2,X0)
& mem(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disj_def) ).
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(f7,axiom,
! [X0,X1,X2] :
( mem(X0,m(X1,X2))
<=> ( mem(X0,X1)
& ~ mem(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_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(f26,conjecture,
disj(m(p(a(p(s(n(e))),n(n(e)))),n(a(p(s(n(e))),n(n(e))))),u(s(u(n(e),n(s(n(e))))),n(a(p(s(n(e))),n(n(e)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disj_4914_8333) ).
fof(f27,negated_conjecture,
~ disj(m(p(a(p(s(n(e))),n(n(e)))),n(a(p(s(n(e))),n(n(e))))),u(s(u(n(e),n(s(n(e))))),n(a(p(s(n(e))),n(n(e)))))),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,plain,
~ disj(m(p(a(p(s(n(e))),n(n(e)))),n(a(p(s(n(e))),n(n(e))))),u(s(u(n(e),n(s(n(e))))),n(a(p(s(n(e))),n(n(e)))))),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( ~ ? [X2] :
( mem(X2,X0)
& mem(X2,X1) )
=> disj(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f30,plain,
! [X0,X1] :
( subq(X0,X1)
<=> ! [X2] :
( mem(X2,X1)
| ~ mem(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f33,plain,
! [X0,X1] :
( disj(X0,X1)
| ? [X2] :
( mem(X2,X0)
& mem(X2,X1) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f34,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,[],[f30]) ).
fof(f35,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,[],[f34]) ).
fof(f36,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))],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( disj(X0,X1)
| ( mem(sK1(X0,X1),X0)
& mem(sK1(X0,X1),X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f33]) ).
fof(f38,plain,
! [X0,X1] :
( ( mem(X0,s(X1))
| X0 != X1 )
& ( X0 = X1
| ~ mem(X0,s(X1)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f39,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(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(flattening,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( mem(X0,m(X1,X2))
| ~ mem(X0,X1)
| mem(X0,X2) )
& ( ( mem(X0,X1)
& ~ mem(X0,X2) )
| ~ mem(X0,m(X1,X2)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ( mem(X0,m(X1,X2))
| ~ mem(X0,X1)
| mem(X0,X2) )
& ( ( mem(X0,X1)
& ~ mem(X0,X2) )
| ~ mem(X0,m(X1,X2)) ) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ( mem(X0,p(X1))
| ~ subq(X0,X1) )
& ( subq(X0,X1)
| ~ mem(X0,p(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f44,plain,
! [X3,X0,X1] :
( ~ mem(X3,X0)
| mem(X3,X1)
| ~ subq(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f45,plain,
! [X0,X1] :
( mem(sK0(X0,X1),X0)
| subq(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f48,plain,
! [X0,X1] :
( mem(sK1(X0,X1),X1)
| disj(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f49,plain,
! [X0,X1] :
( mem(sK1(X0,X1),X0)
| disj(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f50,plain,
! [X0] : ~ mem(X0,e),
inference(cnf_transformation,[],[f4]) ).
fof(f51,plain,
! [X0,X1] :
( ~ mem(X0,s(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f38]) ).
fof(f52,plain,
! [X0,X1] :
( mem(X0,s(X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f38]) ).
fof(f53,plain,
! [X2,X0,X1] :
( ~ mem(X0,u(X1,X2))
| mem(X0,X2)
| mem(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f54,plain,
! [X2,X0,X1] :
( mem(X0,u(X1,X2))
| ~ mem(X0,X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f55,plain,
! [X2,X0,X1] :
( mem(X0,u(X1,X2))
| ~ mem(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ mem(X0,m(X1,X2))
| ~ mem(X0,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ~ mem(X0,m(X1,X2))
| mem(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f59,plain,
! [X0,X1] : a(X0,X1) = u(X0,s(X1)),
inference(cnf_transformation,[],[f8]) ).
fof(f60,plain,
! [X0] : n(X0) = a(X0,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f61,plain,
! [X0,X1] :
( ~ mem(X0,p(X1))
| subq(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f62,plain,
! [X0,X1] :
( mem(X0,p(X1))
| ~ subq(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f63,plain,
~ disj(m(p(a(p(s(n(e))),n(n(e)))),n(a(p(s(n(e))),n(n(e))))),u(s(u(n(e),n(s(n(e))))),n(a(p(s(n(e))),n(n(e)))))),
inference(cnf_transformation,[],[f28]) ).
fof(f64,plain,
! [X0] : n(X0) = u(X0,s(X0)),
inference(definition_unfolding,[],[f60,f59]) ).
fof(f65,plain,
~ disj(m(p(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))),u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))),
inference(definition_unfolding,[],[f63,f59,f64,f64,f64,f64,f59,f64,f64,f64,f64,f64,f64,f64,f59,f64,f64,f64]) ).
fof(f66,plain,
! [X1] : mem(X1,s(X1)),
inference(equality_resolution,[],[f52]) ).
fof(f67,definition,
sF2 = s(e),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f68,plain,
s(e) = sF2,
inference(reorient_equations,[],[f67]) ).
fof(f69,definition,
sF3 = u(e,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f70,plain,
u(e,sF2) = sF3,
inference(reorient_equations,[],[f69]) ).
fof(f71,definition,
sF4 = s(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f72,plain,
s(sF3) = sF4,
inference(reorient_equations,[],[f71]) ).
fof(f73,definition,
sF5 = p(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f74,plain,
p(sF4) = sF5,
inference(reorient_equations,[],[f73]) ).
fof(f75,definition,
sF6 = u(sF3,sF4),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f76,plain,
u(sF3,sF4) = sF6,
inference(reorient_equations,[],[f75]) ).
fof(f77,definition,
sF7 = s(sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f78,plain,
s(sF6) = sF7,
inference(reorient_equations,[],[f77]) ).
fof(f79,definition,
sF8 = u(sF5,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f80,plain,
u(sF5,sF7) = sF8,
inference(reorient_equations,[],[f79]) ).
fof(f81,definition,
sF9 = p(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f82,plain,
p(sF8) = sF9,
inference(reorient_equations,[],[f81]) ).
fof(f83,definition,
sF10 = s(sF8),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f84,plain,
s(sF8) = sF10,
inference(reorient_equations,[],[f83]) ).
fof(f85,definition,
sF11 = u(sF8,sF10),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f86,plain,
u(sF8,sF10) = sF11,
inference(reorient_equations,[],[f85]) ).
fof(f87,definition,
sF12 = m(sF9,sF11),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f88,plain,
m(sF9,sF11) = sF12,
inference(reorient_equations,[],[f87]) ).
fof(f89,definition,
sF13 = s(sF4),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f90,plain,
s(sF4) = sF13,
inference(reorient_equations,[],[f89]) ).
fof(f91,definition,
sF14 = u(sF4,sF13),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f92,plain,
u(sF4,sF13) = sF14,
inference(reorient_equations,[],[f91]) ).
fof(f93,definition,
sF15 = u(sF3,sF14),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f94,plain,
u(sF3,sF14) = sF15,
inference(reorient_equations,[],[f93]) ).
fof(f95,definition,
sF16 = s(sF15),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f96,plain,
s(sF15) = sF16,
inference(reorient_equations,[],[f95]) ).
fof(f97,definition,
sF17 = u(sF16,sF11),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f98,plain,
u(sF16,sF11) = sF17,
inference(reorient_equations,[],[f97]) ).
fof(f99,plain,
~ disj(sF12,sF17),
inference(definition_folding,[],[f65,f98,f86,f84,f80,f78,f76,f72,f70,f68,f70,f68,f74,f72,f70,f68,f80,f78,f76,f72,f70,f68,f70,f68,f74,f72,f70,f68,f96,f94,f92,f90,f72,f70,f68,f72,f70,f68,f70,f68,f88,f86,f84,f80,f78,f76,f72,f70,f68,f70,f68,f74,f72,f70,f68,f80,f78,f76,f72,f70,f68,f70,f68,f74,f72,f70,f68,f82,f80,f78,f76,f72,f70,f68,f70,f68,f74,f72,f70,f68]) ).
fof(f100,plain,
mem(e,sF2),
inference(superposition,[],[f66,f68]) ).
fof(f101,plain,
mem(sF3,sF4),
inference(superposition,[],[f66,f72]) ).
fof(f106,plain,
! [X0] :
( ~ mem(X0,sF2)
| mem(X0,sF3) ),
inference(superposition,[],[f54,f70]) ).
fof(f113,plain,
! [X0] :
( ~ mem(X0,sF4)
| mem(X0,sF6) ),
inference(superposition,[],[f54,f76]) ).
fof(f116,plain,
! [X0] :
( ~ mem(X0,sF4)
| mem(X0,sF14) ),
inference(superposition,[],[f55,f92]) ).
fof(f124,plain,
! [X0] :
( ~ mem(X0,sF5)
| subq(X0,sF4) ),
inference(superposition,[],[f61,f74]) ).
fof(f125,plain,
! [X0] :
( ~ mem(X0,sF9)
| subq(X0,sF8) ),
inference(superposition,[],[f61,f82]) ).
fof(f128,plain,
! [X0] :
( ~ mem(X0,sF12)
| ~ mem(X0,sF11) ),
inference(superposition,[],[f56,f88]) ).
fof(f130,plain,
! [X0] :
( ~ mem(sK1(sF12,X0),sF11)
| disj(sF12,X0) ),
inference(resolution,[],[f128,f49]) ).
fof(f134,plain,
! [X0] :
( ~ mem(X0,sF2)
| e = X0 ),
inference(superposition,[],[f51,f68]) ).
fof(f135,plain,
! [X0] :
( ~ mem(X0,sF4)
| sF3 = X0 ),
inference(superposition,[],[f51,f72]) ).
fof(f137,plain,
! [X0] :
( ~ mem(X0,sF7)
| sF6 = X0 ),
inference(superposition,[],[f51,f78]) ).
fof(f139,plain,
! [X0] :
( ~ mem(X0,sF16)
| sF15 = X0 ),
inference(superposition,[],[f51,f96]) ).
fof(f145,plain,
! [X0] :
( ~ mem(X0,sF14)
| mem(X0,sF15) ),
inference(superposition,[],[f54,f94]) ).
fof(f148,plain,
! [X0] :
( ~ mem(X0,sF12)
| mem(X0,sF9) ),
inference(superposition,[],[f57,f88]) ).
fof(f153,plain,
mem(e,sF3),
inference(resolution,[],[f106,f100]) ).
fof(f169,plain,
mem(sF3,sF14),
inference(resolution,[],[f116,f101]) ).
fof(f177,plain,
! [X0] :
( ~ mem(X0,sF3)
| mem(X0,sF2)
| mem(X0,e) ),
inference(superposition,[],[f53,f70]) ).
fof(f181,plain,
! [X0] :
( ~ mem(X0,sF8)
| mem(X0,sF7)
| mem(X0,sF5) ),
inference(superposition,[],[f53,f80]) ).
fof(f183,plain,
! [X0] :
( ~ mem(X0,sF17)
| mem(X0,sF11)
| mem(X0,sF16) ),
inference(superposition,[],[f53,f98]) ).
fof(f184,plain,
! [X0] :
( ~ mem(X0,sF3)
| mem(X0,sF2) ),
inference(forward_subsumption_resolution,[],[f177,f50]) ).
fof(f187,plain,
! [X0] :
( mem(sK1(X0,sF17),sF16)
| mem(sK1(X0,sF17),sF11)
| disj(X0,sF17) ),
inference(resolution,[],[f183,f48]) ).
fof(f199,plain,
mem(sF3,sF6),
inference(resolution,[],[f113,f101]) ).
fof(f204,plain,
! [X0] : subq(e,X0),
inference(resolution,[],[f45,f50]) ).
fof(f239,plain,
! [X0] :
( ~ subq(X0,sF4)
| mem(X0,sF5) ),
inference(superposition,[],[f62,f74]) ).
fof(f272,plain,
mem(sF3,sF15),
inference(resolution,[],[f169,f145]) ).
fof(f335,plain,
! [X0] :
( ~ subq(sF3,X0)
| mem(e,X0) ),
inference(resolution,[],[f44,f153]) ).
fof(f347,plain,
! [X0] :
( ~ subq(sF15,X0)
| mem(sF3,X0) ),
inference(resolution,[],[f44,f272]) ).
fof(f393,plain,
! [X0] :
( mem(sK1(X0,sF17),sF11)
| disj(X0,sF17)
| sF15 = sK1(X0,sF17) ),
inference(resolution,[],[f187,f139]) ).
fof(f397,plain,
( disj(sF12,sF17)
| sF15 = sK1(sF12,sF17)
| disj(sF12,sF17) ),
inference(resolution,[],[f393,f130]) ).
fof(f401,plain,
( disj(sF12,sF17)
| sF15 = sK1(sF12,sF17) ),
inference(duplicate_literal_removal,[],[f397]) ).
fof(f402,plain,
sF15 = sK1(sF12,sF17),
inference(forward_subsumption_resolution,[],[f401,f99]) ).
fof(f405,plain,
( mem(sF15,sF12)
| disj(sF12,sF17) ),
inference(superposition,[],[f49,f402]) ).
fof(f407,plain,
mem(sF15,sF12),
inference(forward_subsumption_resolution,[],[f405,f99]) ).
fof(f409,plain,
mem(sF15,sF9),
inference(resolution,[],[f407,f148]) ).
fof(f412,plain,
subq(sF15,sF8),
inference(resolution,[],[f409,f125]) ).
fof(f438,plain,
mem(e,sF5),
inference(resolution,[],[f239,f204]) ).
fof(f596,definition,
( spl18_27
<=> mem(sF3,sF5) ),
introduced(definition,[new_symbols(definition,[spl18_27])],[avatar_definition]) ).
fof(f597,plain,
( ~ mem(sF3,sF5)
| spl18_27 ),
inference(avatar_component_clause,[],[f596]) ).
fof(f598,plain,
( mem(sF3,sF5)
| ~ spl18_27 ),
inference(avatar_component_clause,[],[f596]) ).
fof(f616,plain,
( subq(sF3,sF4)
| ~ spl18_27 ),
inference(resolution,[],[f598,f124]) ).
fof(f800,definition,
( spl18_39
<=> mem(e,sF4) ),
introduced(definition,[new_symbols(definition,[spl18_39])],[avatar_definition]) ).
fof(f801,plain,
( ~ mem(e,sF4)
| spl18_39 ),
inference(avatar_component_clause,[],[f800]) ).
fof(f802,plain,
( mem(e,sF4)
| ~ spl18_39 ),
inference(avatar_component_clause,[],[f800]) ).
fof(f932,plain,
( e = sF3
| ~ spl18_39 ),
inference(resolution,[],[f802,f135]) ).
fof(f1053,definition,
( spl18_51
<=> mem(sF3,sF8) ),
introduced(definition,[new_symbols(definition,[spl18_51])],[avatar_definition]) ).
fof(f1055,plain,
( mem(sF3,sF8)
| ~ spl18_51 ),
inference(avatar_component_clause,[],[f1053]) ).
fof(f1155,plain,
( ! [X0] : ~ mem(X0,sF3)
| ~ spl18_39 ),
inference(superposition,[],[f50,f932]) ).
fof(f1161,plain,
( mem(sF3,sF3)
| ~ spl18_39 ),
inference(superposition,[],[f153,f932]) ).
fof(f1607,plain,
mem(sF3,sF8),
inference(resolution,[],[f347,f412]) ).
fof(f1609,plain,
spl18_51,
inference(avatar_split_clause,[],[f1607,f1053]) ).
fof(f1610,plain,
( mem(sF3,sF7)
| mem(sF3,sF5)
| ~ spl18_51 ),
inference(resolution,[],[f1055,f181]) ).
fof(f1615,plain,
( mem(sF3,sF7)
| spl18_27
| ~ spl18_51 ),
inference(forward_subsumption_resolution,[],[f1610,f597]) ).
fof(f1621,plain,
( sF3 = sF6
| spl18_27
| ~ spl18_51 ),
inference(resolution,[],[f1615,f137]) ).
fof(f1628,plain,
( mem(sF3,sF3)
| spl18_27
| ~ spl18_51 ),
inference(superposition,[],[f199,f1621]) ).
fof(f1650,plain,
( mem(sF3,sF2)
| spl18_27
| ~ spl18_51 ),
inference(resolution,[],[f1628,f184]) ).
fof(f1652,plain,
( e = sF3
| spl18_27
| ~ spl18_51 ),
inference(resolution,[],[f1650,f134]) ).
fof(f1665,plain,
( mem(sF3,sF5)
| spl18_27
| ~ spl18_51 ),
inference(superposition,[],[f438,f1652]) ).
fof(f1683,plain,
( $false
| spl18_27
| ~ spl18_51 ),
inference(forward_subsumption_resolution,[],[f1665,f597]) ).
fof(f1684,plain,
( spl18_27
| ~ spl18_51 ),
inference(avatar_contradiction_clause,[],[f1683]) ).
fof(f1689,plain,
( mem(e,sF4)
| ~ spl18_27 ),
inference(resolution,[],[f616,f335]) ).
fof(f1701,plain,
( $false
| ~ spl18_27
| spl18_39 ),
inference(forward_subsumption_resolution,[],[f1689,f801]) ).
fof(f1702,plain,
( ~ spl18_27
| spl18_39 ),
inference(avatar_contradiction_clause,[],[f1701]) ).
fof(f1704,plain,
( $false
| ~ spl18_39 ),
inference(forward_subsumption_resolution,[],[f1161,f1155]) ).
fof(f1705,plain,
~ spl18_39,
inference(avatar_contradiction_clause,[],[f1704]) ).
cnf(s80,plain,
spl18_51,
inference(sat_conversion,[],[f1609]) ).
cnf(s86,plain,
( spl18_27
| ~ spl18_51 ),
inference(sat_conversion,[],[f1684]) ).
cnf(s88,plain,
( ~ spl18_27
| spl18_39 ),
inference(sat_conversion,[],[f1702]) ).
cnf(s89,plain,
~ spl18_39,
inference(sat_conversion,[],[f1705]) ).
cnf(s90,plain,
~ spl18_27,
inference(rat,[],[s88,s89]) ).
cnf(s91,plain,
~ spl18_51,
inference(rat,[],[s86,s90]) ).
cnf(s92,plain,
$false,
inference(rat,[],[s80,s91]) ).
fof(f1708,plain,
$false,
inference(avatar_sat_refutation,[],[s92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV562+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n020.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 06:37:34 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 8.62/2.12 % (4191848)Detected formulas, will run a generic FOF schedule.
% 8.62/2.12 % (4191859)dis-21_1_sil=8000:lcm=predicate:random_seed=1681856818: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)
% 8.62/2.12 % (4191859)Instruction limit reached!
% 8.62/2.12 % (4191859)------------------------------
% 8.62/2.12 % (4191859)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.12 % (4191859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.12 % (4191859)CaDiCaL version: 2.1.3
% 8.62/2.12 % (4191859)Termination reason: Instruction limit
% 8.62/2.12 % (4191859)Termination phase: Saturation
% 8.62/2.12 % (4191859)Time elapsed: 0.037 s
% 8.62/2.12 % (4191859)Peak memory usage: 89 MB
% 8.62/2.12 % (4191859)Instructions burned: 132 (million)
% 8.62/2.12 % (4191855)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=3160940106:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.62/2.12 % (4191858)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1856433394:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.62/2.12 % (4191853)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=3251901291:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.62/2.12 % (4191854)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=2659678574:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.62/2.12 % (4191857)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2611581034:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.62/2.12 % (4191856)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1683593859:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.62/2.12 % (4191856)Refutation not found, incomplete strategy
% 8.62/2.12 % (4191856)------------------------------
% 8.62/2.12 % (4191856)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.12 % (4191856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.12 % (4191856)CaDiCaL version: 2.1.3
% 8.62/2.12 % (4191856)Termination reason: Refutation not found, incomplete strategy
% 8.62/2.12 % (4191856)Time elapsed: 0.001 s
% 8.62/2.12 % (4191856)Peak memory usage: 88 MB
% 8.62/2.12 % (4191856)Instructions burned: 1 (million)
% 8.62/2.12 % (4191857)Instruction limit reached!
% 8.62/2.12 % (4191857)------------------------------
% 8.62/2.12 % (4191857)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.12 % (4191857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.12 % (4191857)CaDiCaL version: 2.1.3
% 8.62/2.12 % (4191857)Termination reason: Instruction limit
% 8.62/2.12 % (4191857)Termination phase: Saturation
% 8.62/2.12 % (4191857)Time elapsed: 0.077 s
% 8.62/2.12 % (4191857)Peak memory usage: 89 MB
% 8.62/2.12 % (4191857)Instructions burned: 119 (million)
% 8.62/2.12 % (4191858)Instruction limit reached!
% 8.62/2.12 % (4191858)------------------------------
% 8.62/2.12 % (4191858)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.12 % (4191858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.12 % (4191858)CaDiCaL version: 2.1.3
% 8.62/2.12 % (4191858)Termination reason: Instruction limit
% 8.62/2.12 % (4191858)Termination phase: Saturation
% 8.62/2.12 % (4191858)Time elapsed: 0.092 s
% 8.62/2.12 % (4191858)Peak memory usage: 89 MB
% 8.62/2.12 % (4191858)Instructions burned: 139 (million)
% 8.62/2.12 % (4191861)lrs+10_1_sil=8000:sp=occurrence:random_seed=686963561:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 8.62/2.12 % (4191861)Instruction limit reached!
% 8.62/2.12 % (4191861)------------------------------
% 8.62/2.12 % (4191861)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.12 % (4191861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.12 % (4191861)CaDiCaL version: 2.1.3
% 8.62/2.12 % (4191861)Termination reason: Instruction limit
% 8.62/2.12 % (4191861)Termination phase: Saturation
% 8.62/2.12 % (4191861)Time elapsed: 0.099 s
% 8.62/2.12 % (4191861)Peak memory usage: 92 MB
% 8.62/2.12 % (4191861)Instructions burned: 288 (million)
% 8.62/2.12 % (4191868)lrs+10_1_sil=32000:urr=on:br=off:random_seed=710053006:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 8.62/2.12 % (4191856)------------------------------
% 8.62/2.12 % (4191856)------------------------------
% 8.62/2.12 % (4191869)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1944391469:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 8.62/2.12 % (4191869)Refutation not found, incomplete strategy
% 8.62/2.12 % (4191869)------------------------------
% 8.62/2.12 % (4191869)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.12 % (4191869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.12 % (4191869)CaDiCaL version: 2.1.3
% 8.62/2.12 % (4191869)Termination reason: Refutation not found, incomplete strategy
% 8.62/2.12 % (4191869)Time elapsed: 0.004 s
% 8.62/2.12 % (4191869)Peak memory usage: 88 MB
% 8.62/2.12 % (4191869)Instructions burned: 4 (million)
% 8.62/2.12 % (4191868)Instruction limit reached!
% 8.62/2.12 % (4191868)------------------------------
% 8.62/2.12 % (4191868)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.12 % (4191868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.12 % (4191868)CaDiCaL version: 2.1.3
% 8.62/2.12 % (4191868)Termination reason: Instruction limit
% 8.62/2.12 % (4191868)Termination phase: Saturation
% 8.62/2.12 % (4191868)Time elapsed: 0.083 s
% 8.62/2.12 % (4191868)Peak memory usage: 90 MB
% 8.62/2.12 % (4191868)Instructions burned: 158 (million)
% 8.62/2.12 % (4191871)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=3122918273:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 8.62/2.12 % (4191873)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1370755690:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 8.62/2.12 % (4191873)Refutation not found, incomplete strategy
% 8.62/2.12 % (4191873)------------------------------
% 8.62/2.12 % (4191873)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.12 % (4191873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.12 % (4191873)CaDiCaL version: 2.1.3
% 8.62/2.12 % (4191873)Termination reason: Refutation not found, incomplete strategy
% 8.62/2.12 % (4191873)Time elapsed: 0.002 s
% 8.62/2.12 % (4191873)Peak memory usage: 88 MB
% 8.62/2.12 % (4191873)Instructions burned: 1 (million)
% 8.62/2.12 % (4191871)Instruction limit reached!
% 8.62/2.12 % (4191871)------------------------------
% 8.62/2.12 % (4191871)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.12 % (4191871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.12 % (4191871)CaDiCaL version: 2.1.3
% 8.62/2.12 % (4191871)Termination reason: Instruction limit
% 8.62/2.12 % (4191871)Termination phase: Saturation
% 8.62/2.12 % (4191871)Time elapsed: 0.078 s
% 8.62/2.12 % (4191871)Peak memory usage: 91 MB
% 8.62/2.12 % (4191871)Instructions burned: 249 (million)
% 8.62/2.12 % (4191875)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3340553947:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 8.62/2.12 % (4191869)------------------------------
% 8.62/2.12 % (4191869)------------------------------
% 8.62/2.12 % (4191878)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1184913086:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 8.62/2.12 % (4191878)Instruction limit reached!
% 8.62/2.12 % (4191878)------------------------------
% 8.62/2.12 % (4191878)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.12 % (4191878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.12 % (4191878)CaDiCaL version: 2.1.3
% 8.62/2.12 % (4191878)Termination reason: Instruction limit
% 8.62/2.12 % (4191878)Termination phase: Saturation
% 8.62/2.12 % (4191878)Time elapsed: 0.036 s
% 8.62/2.12 % (4191878)Peak memory usage: 89 MB
% 8.62/2.12 % (4191878)Instructions burned: 116 (million)
% 8.62/2.12 % (4191873)------------------------------
% 8.62/2.12 % (4191873)------------------------------
% 8.62/2.12 % (4191880)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3937350451:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 8.62/2.12 % (4191882)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3932118392:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 8.62/2.12 % (4191882)Instruction limit reached!
% 8.62/2.12 % (4191882)------------------------------
% 8.62/2.12 % (4191882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.12 % (4191882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.12 % (4191882)CaDiCaL version: 2.1.3
% 8.62/2.12 % (4191882)Termination reason: Instruction limit
% 8.62/2.12 % (4191882)Termination phase: Saturation
% 8.62/2.12 % (4191882)Time elapsed: 0.030 s
% 8.62/2.12 % (4191882)Peak memory usage: 88 MB
% 8.62/2.12 % (4191882)Instructions burned: 118 (million)
% 8.62/2.12 % (4191880)Instruction limit reached!
% 8.62/2.12 % (4191880)------------------------------
% 8.62/2.12 % (4191880)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.12 % (4191880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.12 % (4191880)CaDiCaL version: 2.1.3
% 8.62/2.12 % (4191880)Termination reason: Instruction limit
% 8.62/2.12 % (4191880)Termination phase: Saturation
% 8.62/2.12 % (4191880)Time elapsed: 0.054 s
% 8.62/2.12 % (4191880)Peak memory usage: 88 MB
% 8.62/2.12 % (4191880)Instructions burned: 128 (million)
% 8.62/2.12 % (4191853)First to succeed.
% 8.62/2.12 % (4191853)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4191848"
% 8.62/2.12 % (4191883)lrs+10_1_sil=8000:sp=occurrence:random_seed=528654443:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 8.62/2.12 % (4191886)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1881701751:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 8.62/2.12 % (4191886)Refutation not found, incomplete strategy
% 8.62/2.12 % (4191886)------------------------------
% 8.62/2.12 % (4191886)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.12 % (4191886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.12 % (4191886)CaDiCaL version: 2.1.3
% 8.62/2.12 % (4191886)Termination reason: Refutation not found, incomplete strategy
% 8.62/2.12 % (4191886)Time elapsed: 0.001 s
% 8.62/2.12 % (4191886)Peak memory usage: 88 MB
% 8.62/2.12 % (4191886)Instructions burned: 1 (million)
% 8.62/2.12 % (4191887)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2180160455:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 8.62/2.12 % (4191886)------------------------------
% 8.62/2.12 % (4191886)------------------------------
% 8.62/2.12 % (4191853)Refutation found. Thanks to Tanya!
% 8.62/2.12 % SZS status Theorem for theBenchmark
% 8.62/2.12 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/2.31 % (4191853)------------------------------
% 0.17/2.31 % (4191853)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/2.31 % (4191853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/2.31 % (4191853)CaDiCaL version: 2.1.3
% 0.17/2.31 % (4191853)Termination reason: Refutation
% 0.17/2.31 % (4191853)Time elapsed: 0.806 s
% 0.17/2.31 % (4191853)Peak memory usage: 130 MB
% 0.17/2.31 % (4191853)Instructions burned: 1184 (million)
% 0.17/2.31 % (4191853)------------------------------
% 0.17/2.31 % (4191853)------------------------------
% 0.17/2.31 % (4191848)Success in time 1.246 s
% 0.17/2.31 % Vampire exiting
%------------------------------------------------------------------------------