%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET706+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 12:44:28 PM UTC 2026
% Result : Theorem 2.32s 1.00s
% Output : Refutation 2.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 19
% Syntax : Number of formulae : 157 ( 19 unt; 12 def)
% Number of atoms : 390 ( 8 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 398 ( 165 ~; 181 |; 33 &)
% ( 15 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 149 ( 0 sgn 138 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(f3,axiom,
! [X0,X1] :
( member(X0,power_set(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',power_set) ).
fof(f5,axiom,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X1)
| member(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',union) ).
fof(f7,axiom,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( member(X0,X2)
& ~ member(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',difference) ).
fof(f10,axiom,
! [X0,X1] :
( member(X0,sum(X1))
<=> ? [X2] :
( member(X2,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',sum) ).
fof(f12,conjecture,
! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X1,X0) )
=> equal_set(difference(X0,X2),union(difference(X1,X2),difference(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI49) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X1,X0) )
=> equal_set(difference(X0,X2),union(difference(X1,X2),difference(X0,X1))) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f15,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f16,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f17,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(flattening,[],[f16]) ).
fof(f19,plain,
? [X0,X1,X2] :
( ~ equal_set(difference(X0,X2),union(difference(X1,X2),difference(X0,X1)))
& subset(X2,X1)
& subset(X1,X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f20,plain,
? [X0,X1,X2] :
( ~ equal_set(difference(X0,X2),union(difference(X1,X2),difference(X0,X1)))
& subset(X2,X1)
& subset(X1,X0) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f22,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ( member(X0,power_set(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ member(X0,power_set(X1)) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X1)
& ~ member(X0,X2) ) )
& ( member(X0,X1)
| member(X0,X2)
| ~ member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X1)
& ~ member(X0,X2) ) )
& ( member(X0,X1)
| member(X0,X2)
| ~ member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) )
& ( ( member(X0,X2)
& ~ member(X0,X1) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) )
& ( ( member(X0,X2)
& ~ member(X0,X1) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(flattening,[],[f29]) ).
fof(f34,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ? [X2] :
( member(X2,X1)
& member(X0,X2) )
| ~ member(X0,sum(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f35,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& member(X0,X3) )
| ~ member(X0,sum(X1)) ) ),
inference(rectify,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ( member(sK1(X0,X1),X1)
& member(X0,sK1(X0,X1)) )
| ~ member(X0,sum(X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f35]) ).
fof(f40,plain,
( ~ equal_set(difference(sK3,sK5),union(difference(sK4,sK5),difference(sK3,sK4)))
& subset(sK5,sK4)
& subset(sK4,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f20]) ).
fof(f41,plain,
! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f43,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f44,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f45,plain,
! [X0,X1] :
( ~ member(X0,power_set(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f46,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f51,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f52,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f55,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| member(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f56,plain,
! [X2,X0,X1] :
( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f62,plain,
! [X0,X1] :
( member(X0,sK1(X0,X1))
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f63,plain,
! [X0,X1] :
( member(sK1(X0,X1),X1)
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X0,sum(X1))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f68,plain,
subset(sK4,sK3),
inference(cnf_transformation,[],[f40]) ).
fof(f69,plain,
subset(sK5,sK4),
inference(cnf_transformation,[],[f40]) ).
fof(f70,plain,
~ equal_set(difference(sK3,sK5),union(difference(sK4,sK5),difference(sK3,sK4))),
inference(cnf_transformation,[],[f40]) ).
fof(f74,definition,
sF6 = difference(sK3,sK5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f75,plain,
difference(sK3,sK5) = sF6,
inference(reorient_equations,[],[f74]) ).
fof(f76,definition,
sF7 = difference(sK4,sK5),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f77,plain,
difference(sK4,sK5) = sF7,
inference(reorient_equations,[],[f76]) ).
fof(f78,definition,
sF8 = difference(sK3,sK4),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f79,plain,
difference(sK3,sK4) = sF8,
inference(reorient_equations,[],[f78]) ).
fof(f80,definition,
sF9 = union(sF7,sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f81,plain,
union(sF7,sF8) = sF9,
inference(reorient_equations,[],[f80]) ).
fof(f82,plain,
~ equal_set(sF6,sF9),
inference(definition_folding,[],[f70,f81,f79,f77,f75]) ).
fof(f83,plain,
member(sK4,power_set(sK3)),
inference(resolution,[],[f46,f68]) ).
fof(f84,plain,
member(sK5,power_set(sK4)),
inference(resolution,[],[f46,f69]) ).
fof(f87,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(resolution,[],[f42,f46]) ).
fof(f89,plain,
! [X2,X0,X1] :
( ~ member(sK0(X0,union(X1,X2)),X2)
| subset(X0,union(X1,X2)) ),
inference(resolution,[],[f51,f43]) ).
fof(f91,plain,
! [X2,X0,X1] :
( ~ member(sK0(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) ),
inference(resolution,[],[f52,f43]) ).
fof(f93,plain,
! [X0] :
( ~ member(X0,sF6)
| ~ member(X0,sK5) ),
inference(superposition,[],[f54,f75]) ).
fof(f94,plain,
! [X0] :
( ~ member(X0,sF7)
| ~ member(X0,sK5) ),
inference(superposition,[],[f54,f77]) ).
fof(f95,plain,
! [X0] :
( ~ member(X0,sF8)
| ~ member(X0,sK4) ),
inference(superposition,[],[f54,f79]) ).
fof(f96,plain,
! [X0] :
( ~ member(X0,sF6)
| member(X0,sK3) ),
inference(superposition,[],[f55,f75]) ).
fof(f97,plain,
! [X0] :
( ~ member(X0,sF7)
| member(X0,sK4) ),
inference(superposition,[],[f55,f77]) ).
fof(f98,plain,
! [X0] :
( ~ member(X0,sF8)
| member(X0,sK3) ),
inference(superposition,[],[f55,f79]) ).
fof(f109,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| equal_set(X0,X1)
| member(sK0(X1,X0),X1) ),
inference(resolution,[],[f44,f42]) ).
fof(f129,plain,
! [X2,X0,X1] :
( ~ subset(sK1(X0,X1),X2)
| member(X0,X2)
| ~ member(X0,sum(X1)) ),
inference(resolution,[],[f62,f41]) ).
fof(f132,plain,
! [X0,X1] :
( subset(sK1(X0,power_set(X1)),X1)
| ~ member(X0,sum(power_set(X1))) ),
inference(resolution,[],[f63,f45]) ).
fof(f166,plain,
! [X0] :
( ~ member(X0,sK4)
| member(X0,sum(power_set(sK3))) ),
inference(resolution,[],[f64,f83]) ).
fof(f167,plain,
! [X0] :
( ~ member(X0,sK5)
| member(X0,sum(power_set(sK4))) ),
inference(resolution,[],[f64,f84]) ).
fof(f186,plain,
! [X0] :
( ~ member(X0,sF9)
| member(X0,sF8)
| member(X0,sF7) ),
inference(superposition,[],[f50,f81]) ).
fof(f193,plain,
! [X2,X0,X1] :
( ~ member(sK0(X0,difference(X1,X2)),X1)
| member(sK0(X0,difference(X1,X2)),X2)
| subset(X0,difference(X1,X2)) ),
inference(resolution,[],[f56,f43]) ).
fof(f195,plain,
! [X0] :
( ~ member(X0,sK4)
| member(X0,sF7)
| member(X0,sK5) ),
inference(superposition,[],[f56,f77]) ).
fof(f196,plain,
! [X0] :
( ~ member(X0,sK3)
| member(X0,sF8)
| member(X0,sK4) ),
inference(superposition,[],[f56,f79]) ).
fof(f408,plain,
! [X0,X1] :
( equal_set(X0,X1)
| member(sK0(X1,X0),X1)
| member(sK0(X0,X1),X0) ),
inference(resolution,[],[f109,f42]) ).
fof(f466,plain,
! [X0] :
( ~ member(sK0(X0,sF9),sF8)
| subset(X0,sF9) ),
inference(superposition,[],[f89,f81]) ).
fof(f483,plain,
! [X0] :
( ~ member(sK0(X0,sF9),sF7)
| subset(X0,sF9) ),
inference(superposition,[],[f91,f81]) ).
fof(f489,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(X0,sum(power_set(X1)))
| ~ member(X0,sum(power_set(X1))) ),
inference(resolution,[],[f129,f132]) ).
fof(f491,plain,
! [X0,X1] :
( ~ member(X0,sum(power_set(X1)))
| member(X0,X1) ),
inference(duplicate_literal_removal,[],[f489]) ).
fof(f1088,plain,
! [X0] :
( ~ member(sK0(X0,sF6),sK3)
| member(sK0(X0,sF6),sK5)
| subset(X0,sF6) ),
inference(superposition,[],[f193,f75]) ).
fof(f4661,plain,
( member(sK0(sF9,sF6),sF9)
| member(sK0(sF6,sF9),sF6) ),
inference(resolution,[],[f408,f82]) ).
fof(f4663,definition,
( spl10_89
<=> member(sK0(sF6,sF9),sF6) ),
introduced(definition,[new_symbols(definition,[spl10_89])],[avatar_definition]) ).
fof(f4664,plain,
( ~ member(sK0(sF6,sF9),sF6)
| spl10_89 ),
inference(avatar_component_clause,[],[f4663]) ).
fof(f4665,plain,
( member(sK0(sF6,sF9),sF6)
| ~ spl10_89 ),
inference(avatar_component_clause,[],[f4663]) ).
fof(f4667,definition,
( spl10_90
<=> member(sK0(sF9,sF6),sF9) ),
introduced(definition,[new_symbols(definition,[spl10_90])],[avatar_definition]) ).
fof(f4668,plain,
( ~ member(sK0(sF9,sF6),sF9)
| spl10_90 ),
inference(avatar_component_clause,[],[f4667]) ).
fof(f4669,plain,
( member(sK0(sF9,sF6),sF9)
| ~ spl10_90 ),
inference(avatar_component_clause,[],[f4667]) ).
fof(f4670,plain,
( spl10_89
| spl10_90 ),
inference(avatar_split_clause,[],[f4661,f4667,f4663]) ).
fof(f4671,plain,
( member(sK0(sF6,sF9),sK3)
| ~ spl10_89 ),
inference(resolution,[],[f4665,f96]) ).
fof(f4672,plain,
( ~ member(sK0(sF6,sF9),sK5)
| ~ spl10_89 ),
inference(resolution,[],[f4665,f93]) ).
fof(f4709,plain,
( member(sK0(sF6,sF9),sF8)
| member(sK0(sF6,sF9),sK4)
| ~ spl10_89 ),
inference(resolution,[],[f4671,f196]) ).
fof(f4726,definition,
( spl10_91
<=> member(sK0(sF6,sF9),sK4) ),
introduced(definition,[new_symbols(definition,[spl10_91])],[avatar_definition]) ).
fof(f4728,plain,
( member(sK0(sF6,sF9),sK4)
| ~ spl10_91 ),
inference(avatar_component_clause,[],[f4726]) ).
fof(f4730,definition,
( spl10_92
<=> member(sK0(sF6,sF9),sF8) ),
introduced(definition,[new_symbols(definition,[spl10_92])],[avatar_definition]) ).
fof(f4732,plain,
( member(sK0(sF6,sF9),sF8)
| ~ spl10_92 ),
inference(avatar_component_clause,[],[f4730]) ).
fof(f4733,plain,
( spl10_91
| spl10_92
| ~ spl10_89 ),
inference(avatar_split_clause,[],[f4709,f4663,f4730,f4726]) ).
fof(f4756,plain,
( member(sF6,power_set(sF9))
| spl10_89 ),
inference(resolution,[],[f4664,f87]) ).
fof(f4776,plain,
( subset(sF6,sF9)
| spl10_89 ),
inference(resolution,[],[f4756,f45]) ).
fof(f4803,definition,
( spl10_95
<=> subset(sF9,sF6) ),
introduced(definition,[new_symbols(definition,[spl10_95])],[avatar_definition]) ).
fof(f4804,plain,
( subset(sF9,sF6)
| ~ spl10_95 ),
inference(avatar_component_clause,[],[f4803]) ).
fof(f4805,plain,
( ~ subset(sF9,sF6)
| spl10_95 ),
inference(avatar_component_clause,[],[f4803]) ).
fof(f4909,plain,
( member(sK0(sF9,sF6),sF8)
| member(sK0(sF9,sF6),sF7)
| ~ spl10_90 ),
inference(resolution,[],[f4669,f186]) ).
fof(f4925,definition,
( spl10_104
<=> member(sK0(sF9,sF6),sF7) ),
introduced(definition,[new_symbols(definition,[spl10_104])],[avatar_definition]) ).
fof(f4927,plain,
( member(sK0(sF9,sF6),sF7)
| ~ spl10_104 ),
inference(avatar_component_clause,[],[f4925]) ).
fof(f4929,definition,
( spl10_105
<=> member(sK0(sF9,sF6),sF8) ),
introduced(definition,[new_symbols(definition,[spl10_105])],[avatar_definition]) ).
fof(f4931,plain,
( member(sK0(sF9,sF6),sF8)
| ~ spl10_105 ),
inference(avatar_component_clause,[],[f4929]) ).
fof(f4932,plain,
( spl10_104
| spl10_105
| ~ spl10_90 ),
inference(avatar_split_clause,[],[f4909,f4667,f4929,f4925]) ).
fof(f5008,plain,
( member(sK0(sF9,sF6),sK3)
| ~ spl10_105 ),
inference(resolution,[],[f4931,f98]) ).
fof(f5009,plain,
( ~ member(sK0(sF9,sF6),sK4)
| ~ spl10_105 ),
inference(resolution,[],[f4931,f95]) ).
fof(f5032,plain,
( member(sK0(sF9,sF6),sK4)
| ~ spl10_104 ),
inference(resolution,[],[f4927,f97]) ).
fof(f5033,plain,
( ~ member(sK0(sF9,sF6),sK5)
| ~ spl10_104 ),
inference(resolution,[],[f4927,f94]) ).
fof(f5139,plain,
( member(sK0(sF9,sF6),sum(power_set(sK3)))
| ~ spl10_104 ),
inference(resolution,[],[f5032,f166]) ).
fof(f12082,plain,
( member(sK0(sF9,sF6),sK3)
| ~ spl10_104 ),
inference(resolution,[],[f5139,f491]) ).
fof(f12323,plain,
( member(sK0(sF9,sF6),sK5)
| subset(sF9,sF6)
| ~ spl10_104 ),
inference(resolution,[],[f12082,f1088]) ).
fof(f12360,plain,
( subset(sF9,sF6)
| ~ spl10_104 ),
inference(forward_subsumption_resolution,[],[f12323,f5033]) ).
fof(f12361,plain,
( $false
| spl10_95
| ~ spl10_104 ),
inference(forward_subsumption_resolution,[],[f12360,f4805]) ).
fof(f12362,plain,
( spl10_95
| ~ spl10_104 ),
inference(avatar_contradiction_clause,[],[f12361]) ).
fof(f12454,plain,
( ~ subset(sF6,sF9)
| equal_set(sF6,sF9)
| ~ spl10_95 ),
inference(resolution,[],[f4804,f44]) ).
fof(f12456,plain,
( equal_set(sF6,sF9)
| spl10_89
| ~ spl10_95 ),
inference(forward_subsumption_resolution,[],[f12454,f4776]) ).
fof(f12457,plain,
( $false
| spl10_89
| ~ spl10_95 ),
inference(forward_subsumption_resolution,[],[f12456,f82]) ).
fof(f12458,plain,
( spl10_89
| ~ spl10_95 ),
inference(avatar_contradiction_clause,[],[f12457]) ).
fof(f12459,plain,
( ~ subset(sF6,sF9)
| ~ spl10_95 ),
inference(forward_subsumption_resolution,[],[f12454,f82]) ).
fof(f13129,plain,
( member(sK0(sF6,sF9),sF7)
| member(sK0(sF6,sF9),sK5)
| ~ spl10_91 ),
inference(resolution,[],[f4728,f195]) ).
fof(f13162,plain,
( member(sK0(sF6,sF9),sF7)
| ~ spl10_89
| ~ spl10_91 ),
inference(forward_subsumption_resolution,[],[f13129,f4672]) ).
fof(f13194,plain,
( subset(sF6,sF9)
| ~ spl10_89
| ~ spl10_91 ),
inference(resolution,[],[f13162,f483]) ).
fof(f13230,plain,
( $false
| ~ spl10_89
| ~ spl10_91
| ~ spl10_95 ),
inference(forward_subsumption_resolution,[],[f13194,f12459]) ).
fof(f13231,plain,
( ~ spl10_89
| ~ spl10_91
| ~ spl10_95 ),
inference(avatar_contradiction_clause,[],[f13230]) ).
fof(f13704,plain,
( subset(sF6,sF9)
| ~ spl10_92 ),
inference(resolution,[],[f4732,f466]) ).
fof(f13740,plain,
( $false
| ~ spl10_92
| ~ spl10_95 ),
inference(forward_subsumption_resolution,[],[f13704,f12459]) ).
fof(f13741,plain,
( ~ spl10_92
| ~ spl10_95 ),
inference(avatar_contradiction_clause,[],[f13740]) ).
fof(f13748,plain,
( member(sK0(sF9,sF6),sF9)
| spl10_95 ),
inference(resolution,[],[f4805,f42]) ).
fof(f13749,plain,
( $false
| spl10_90
| spl10_95 ),
inference(forward_subsumption_resolution,[],[f13748,f4668]) ).
fof(f13750,plain,
( spl10_90
| spl10_95 ),
inference(avatar_contradiction_clause,[],[f13749]) ).
fof(f14381,plain,
( member(sK0(sF9,sF6),sK5)
| subset(sF9,sF6)
| ~ spl10_105 ),
inference(resolution,[],[f5008,f1088]) ).
fof(f14418,definition,
( spl10_169
<=> member(sK0(sF9,sF6),sK5) ),
introduced(definition,[new_symbols(definition,[spl10_169])],[avatar_definition]) ).
fof(f14420,plain,
( member(sK0(sF9,sF6),sK5)
| ~ spl10_169 ),
inference(avatar_component_clause,[],[f14418]) ).
fof(f14430,plain,
( member(sK0(sF9,sF6),sK5)
| spl10_95
| ~ spl10_105 ),
inference(forward_subsumption_resolution,[],[f14381,f4805]) ).
fof(f14431,plain,
( spl10_169
| spl10_95
| ~ spl10_105 ),
inference(avatar_split_clause,[],[f14430,f4929,f4803,f14418]) ).
fof(f14694,plain,
( member(sK0(sF9,sF6),sum(power_set(sK4)))
| ~ spl10_169 ),
inference(resolution,[],[f14420,f167]) ).
fof(f15263,plain,
( member(sK0(sF9,sF6),sK4)
| ~ spl10_169 ),
inference(resolution,[],[f14694,f491]) ).
fof(f15299,plain,
( $false
| ~ spl10_105
| ~ spl10_169 ),
inference(forward_subsumption_resolution,[],[f15263,f5009]) ).
fof(f15300,plain,
( ~ spl10_105
| ~ spl10_169 ),
inference(avatar_contradiction_clause,[],[f15299]) ).
cnf(s90,plain,
( spl10_89
| spl10_90 ),
inference(sat_conversion,[],[f4670]) ).
cnf(s91,plain,
( ~ spl10_89
| spl10_91
| spl10_92 ),
inference(sat_conversion,[],[f4733]) ).
cnf(s103,plain,
( ~ spl10_90
| spl10_104
| spl10_105 ),
inference(sat_conversion,[],[f4932]) ).
cnf(s153,plain,
( spl10_95
| ~ spl10_104 ),
inference(sat_conversion,[],[f12362]) ).
cnf(s154,plain,
( spl10_89
| ~ spl10_95 ),
inference(sat_conversion,[],[f12458]) ).
cnf(s156,plain,
( ~ spl10_89
| ~ spl10_91
| ~ spl10_95 ),
inference(sat_conversion,[],[f13231]) ).
cnf(s166,plain,
( ~ spl10_92
| ~ spl10_95 ),
inference(sat_conversion,[],[f13741]) ).
cnf(s167,plain,
( spl10_90
| spl10_95 ),
inference(sat_conversion,[],[f13750]) ).
cnf(s170,plain,
( spl10_95
| ~ spl10_105
| spl10_169 ),
inference(sat_conversion,[],[f14431]) ).
cnf(s171,plain,
( ~ spl10_105
| ~ spl10_169 ),
inference(sat_conversion,[],[f15300]) ).
cnf(s172,plain,
spl10_89,
inference(rat,[],[s170,s171,s103,s153,s90,s154]) ).
cnf(s173,plain,
( spl10_95
| ~ spl10_90 ),
inference(rat,[],[s170,s171,s103,s153]) ).
cnf(s174,plain,
~ spl10_95,
inference(rat,[],[s91,s156,s166,s172]) ).
cnf(s175,plain,
spl10_90,
inference(rat,[],[s167,s174]) ).
cnf(s177,plain,
$false,
inference(rat,[],[s173,s175,s174]) ).
fof(f15301,plain,
$false,
inference(avatar_sat_refutation,[],[s177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET706+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 02:32:40 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.32/1.00 % (1974013)Will run a generic schedule for satisfiability detection.
% 2.32/1.00 % (1974022)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=435395854:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.32/1.00 % (1974019)% WARNING: option uhcvi not known.
% 2.32/1.00 % (1974020)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2405209696:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.32/1.00 % (1974018)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2073050326_2999 on theBenchmark for (2999ds/0Mi)
% 2.32/1.00 % (1974021)dis+10_1_sil=32000:sp=arity:random_seed=261438132:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.32/1.00 % (1974019)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3359505079:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.32/1.00 % (1974023)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3301012300:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.32/1.00 % (1974024)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=765940125:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.32/1.00 % TRYING [1]
% 2.32/1.00 % TRYING [2]
% 2.32/1.00 % TRYING [3]
% 2.32/1.00 % TRYING [4]
% 2.32/1.00 % TRYING [5]
% 2.32/1.00 % TRYING [6]
% 2.32/1.00 % (1974022)Instruction limit reached!
% 2.32/1.00 % (1974022)------------------------------
% 2.32/1.00 % (1974022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/1.00 % (1974022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/1.00 % (1974022)CaDiCaL version: 2.1.3
% 2.32/1.00 % (1974022)Termination reason: Instruction limit
% 2.32/1.00 % (1974022)Termination phase: Saturation
% 2.32/1.00 % (1974022)Time elapsed: 0.036 s
% 2.32/1.00 % (1974022)Peak memory usage: 12 MB
% 2.32/1.00 % (1974022)Instructions burned: 117 (million)
% 2.32/1.00 % (1974032)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2969690945:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.32/1.00 % TRYING [1]
% 2.32/1.00 % TRYING [2]
% 2.32/1.00 % TRYING [3]
% 2.32/1.00 % TRYING [4]
% 2.32/1.00 % TRYING [5]
% 2.32/1.00 % TRYING [7]
% 2.32/1.00 % TRYING [6]
% 2.32/1.00 % (1974021)Instruction limit reached!
% 2.32/1.00 % (1974021)------------------------------
% 2.32/1.00 % (1974021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/1.00 % (1974021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/1.00 % (1974021)CaDiCaL version: 2.1.3
% 2.32/1.00 % (1974021)Termination reason: Instruction limit
% 2.32/1.00 % (1974021)Termination phase: Saturation
% 2.32/1.00 % (1974021)Time elapsed: 0.063 s
% 2.32/1.00 % (1974021)Peak memory usage: 12 MB
% 2.32/1.00 % (1974021)Instructions burned: 104 (million)
% 2.32/1.00 % (1974023)Instruction limit reached!
% 2.32/1.00 % (1974023)------------------------------
% 2.32/1.00 % (1974023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/1.00 % (1974023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/1.00 % (1974023)CaDiCaL version: 2.1.3
% 2.32/1.00 % (1974023)Termination reason: Instruction limit
% 2.32/1.00 % (1974023)Termination phase: Saturation
% 2.32/1.00 % (1974023)Time elapsed: 0.082 s
% 2.32/1.00 % (1974023)Peak memory usage: 13 MB
% 2.32/1.00 % (1974023)Instructions burned: 131 (million)
% 2.32/1.00 % (1974034)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2807970433:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 2.32/1.00 % TRYING [7]
% 2.32/1.00 % (1974024)Instruction limit reached!
% 2.32/1.00 % (1974024)------------------------------
% 2.32/1.00 % (1974024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/1.00 % (1974024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/1.00 % (1974024)CaDiCaL version: 2.1.3
% 2.32/1.00 % (1974024)Termination reason: Instruction limit
% 2.32/1.00 % (1974024)Termination phase: Saturation
% 2.32/1.00 % (1974024)Time elapsed: 0.092 s
% 2.32/1.00 % (1974024)Peak memory usage: 13 MB
% 2.32/1.00 % (1974024)Instructions burned: 160 (million)
% 2.32/1.00 % (1974036)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=640692481:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.32/1.00 % (1974037)ott-21_1_sil=16000:fs=off:random_seed=4037842595:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.32/1.00 % TRYING [8]
% 2.32/1.00 % (1974034)Instruction limit reached!
% 2.32/1.00 % (1974034)------------------------------
% 2.32/1.00 % (1974034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/1.00 % (1974034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/1.00 % (1974034)CaDiCaL version: 2.1.3
% 2.32/1.00 % (1974034)Termination reason: Instruction limit
% 2.32/1.00 % (1974034)Termination phase: Saturation
% 2.32/1.00 % (1974034)Time elapsed: 0.084 s
% 2.32/1.00 % (1974034)Peak memory usage: 13 MB
% 2.32/1.00 % (1974034)Instructions burned: 131 (million)
% 2.32/1.00 % (1974040)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=819272096:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 2.32/1.00 % TRYING [8]
% 2.32/1.00 % (1974037)Instruction limit reached!
% 2.32/1.00 % (1974037)------------------------------
% 2.32/1.00 % (1974037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/1.00 % (1974037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/1.00 % (1974037)CaDiCaL version: 2.1.3
% 2.32/1.00 % (1974037)Termination reason: Instruction limit
% 2.32/1.00 % (1974037)Termination phase: Saturation
% 2.32/1.00 % (1974037)Time elapsed: 0.097 s
% 2.32/1.00 % (1974037)Peak memory usage: 13 MB
% 2.32/1.00 % (1974037)Instructions burned: 182 (million)
% 2.32/1.00 % (1974042)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1812479906:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 2.32/1.00 % (1974032)Instruction limit reached!
% 2.32/1.00 % (1974032)------------------------------
% 2.32/1.00 % (1974032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/1.00 % (1974032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/1.00 % (1974032)CaDiCaL version: 2.1.3
% 2.32/1.00 % (1974032)Termination reason: Instruction limit
% 2.32/1.00 % (1974032)Termination phase: Finite model building SAT solving
% 2.32/1.00 % (1974032)Time elapsed: 0.191 s
% 2.32/1.00 % (1974032)Peak memory usage: 20 MB
% 2.32/1.00 % (1974032)Instructions burned: 715 (million)
% 2.32/1.00 % TRYING [1]
% 2.32/1.00 % TRYING [2]
% 2.32/1.00 % TRYING [3]
% 2.32/1.00 % TRYING [4]
% 2.32/1.00 % (1974044)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1429838015:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 2.32/1.00 % TRYING [5]
% 2.32/1.00 % TRYING [6]
% 2.32/1.00 % TRYING [7]
% 2.32/1.00 % TRYING [9]
% 2.32/1.00 % TRYING [8]
% 2.32/1.00 % (1974040)Instruction limit reached!
% 2.32/1.00 % (1974040)------------------------------
% 2.32/1.00 % (1974040)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/1.00 % (1974040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/1.00 % (1974040)CaDiCaL version: 2.1.3
% 2.32/1.00 % (1974040)Termination reason: Instruction limit
% 2.32/1.00 % (1974040)Termination phase: Saturation
% 2.32/1.00 % (1974040)Time elapsed: 0.297 s
% 2.32/1.00 % (1974040)Peak memory usage: 15 MB
% 2.32/1.00 % (1974040)Instructions burned: 477 (million)
% 2.32/1.00 % (1974036)Instruction limit reached!
% 2.32/1.00 % (1974036)------------------------------
% 2.32/1.00 % (1974036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/1.00 % (1974036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/1.00 % (1974036)CaDiCaL version: 2.1.3
% 2.32/1.00 % (1974036)Termination reason: Instruction limit
% 2.32/1.00 % (1974036)Termination phase: Saturation
% 2.32/1.00 % (1974036)Time elapsed: 0.393 s
% 2.32/1.00 % (1974036)Peak memory usage: 19 MB
% 2.32/1.00 % (1974036)Instructions burned: 684 (million)
% 2.32/1.00 % (1974046)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3982990239:i=889:ins=1_2994 on theBenchmark for (2994ds/889Mi)
% 2.32/1.00 % (1974047)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=3879073390:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2994 on theBenchmark for (2994ds/692Mi)
% 2.32/1.00 % TRYING [14]
% 2.32/1.00 % (1974044) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1974013-1974044"...
% 2.32/1.00 % (1974044)...printing done.
% 2.32/1.00 % (1974044)Refutation found. Thanks to Tanya!
% 2.32/1.00 % SZS status Theorem for theBenchmark
% 2.32/1.00 % SZS output start Proof for theBenchmark
% See solution above
% 2.32/1.00 % (1974044)------------------------------
% 2.32/1.00 % (1974044)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/1.00 % (1974044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/1.00 % (1974044)CaDiCaL version: 2.1.3
% 2.32/1.00 % (1974044)Termination reason: Refutation
% 2.32/1.00 % (1974044)Time elapsed: 0.294 s
% 2.32/1.00 % (1974044)Peak memory usage: 23 MB
% 2.32/1.00 % (1974044)Instructions burned: 933 (million)
% 2.32/1.00 % (1974013)Success in time 0.582 s
% 2.32/1.00 % Vampire exiting
%------------------------------------------------------------------------------