%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET697+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 : n011.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 12:44:27 PM UTC 2026
% Result : Theorem 1.91s 0.80s
% Output : Refutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 15
% Syntax : Number of formulae : 136 ( 11 unt; 6 def)
% Number of atoms : 396 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 421 ( 161 ~; 189 |; 50 &)
% ( 15 <=>; 4 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 190 ( 0 sgn 171 !; 19 ?)
% 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(f4,axiom,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',intersection) ).
fof(f6,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',empty_set) ).
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(f11,axiom,
! [X0,X1] :
( member(X0,product(X1))
<=> ! [X2] :
( member(X2,X1)
=> member(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',product) ).
fof(f12,conjecture,
! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X1,X2) )
=> ( subset(X0,X1)
<=> equal_set(intersection(X0,difference(X2,X1)),empty_set) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI31) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X1,X2) )
=> ( subset(X0,X1)
<=> equal_set(intersection(X0,difference(X2,X1)),empty_set) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f15,plain,
! [X0,X1] :
( member(X0,product(X1))
<=> ! [X2] :
( member(X0,X2)
| ~ member(X2,X1) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f16,plain,
? [X0,X1,X2] :
( ( subset(X0,X1)
<~> equal_set(intersection(X0,difference(X2,X1)),empty_set) )
& subset(X0,X2)
& subset(X1,X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f17,plain,
? [X0,X1,X2] :
( ( subset(X0,X1)
<~> equal_set(intersection(X0,difference(X2,X1)),empty_set) )
& subset(X0,X2)
& subset(X1,X2) ),
inference(flattening,[],[f16]) ).
fof(f18,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,[],[f14]) ).
fof(f19,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,[],[f18]) ).
fof(f20,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))],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| ~ equal_set(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f22,plain,
! [X0,X1] :
( ( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| ~ equal_set(X0,X1) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( member(X0,power_set(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ member(X0,power_set(X1)) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f24]) ).
fof(f28,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(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(flattening,[],[f28]) ).
fof(f33,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(f34,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,[],[f33]) ).
fof(f35,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))],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ( member(X0,product(X1))
| ? [X2] :
( ~ member(X0,X2)
& member(X2,X1) ) )
& ( ! [X2] :
( member(X0,X2)
| ~ member(X2,X1) )
| ~ member(X0,product(X1)) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f37,plain,
! [X0,X1] :
( ( member(X0,product(X1))
| ? [X2] :
( ~ member(X0,X2)
& member(X2,X1) ) )
& ( ! [X3] :
( member(X0,X3)
| ~ member(X3,X1) )
| ~ member(X0,product(X1)) ) ),
inference(rectify,[],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ( member(X0,product(X1))
| ( ~ member(X0,sK2(X0,X1))
& member(sK2(X0,X1),X1) ) )
& ( ! [X3] :
( member(X0,X3)
| ~ member(X3,X1) )
| ~ member(X0,product(X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f37]) ).
fof(f39,plain,
? [X0,X1,X2] :
( ( ~ equal_set(intersection(X0,difference(X2,X1)),empty_set)
| ~ subset(X0,X1) )
& ( equal_set(intersection(X0,difference(X2,X1)),empty_set)
| subset(X0,X1) )
& subset(X0,X2)
& subset(X1,X2) ),
inference(nnf_transformation,[],[f17]) ).
fof(f40,plain,
? [X0,X1,X2] :
( ( ~ equal_set(intersection(X0,difference(X2,X1)),empty_set)
| ~ subset(X0,X1) )
& ( equal_set(intersection(X0,difference(X2,X1)),empty_set)
| subset(X0,X1) )
& subset(X0,X2)
& subset(X1,X2) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
( ( ~ equal_set(intersection(sK3,difference(sK5,sK4)),empty_set)
| ~ subset(sK3,sK4) )
& ( equal_set(intersection(sK3,difference(sK5,sK4)),empty_set)
| subset(sK3,sK4) )
& subset(sK3,sK5)
& subset(sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f40]) ).
fof(f42,plain,
! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f43,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f44,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f46,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f47,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f48,plain,
! [X0,X1] :
( ~ member(X0,power_set(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f49,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f52,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f56,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f6]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f59,plain,
! [X2,X0,X1] :
( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f65,plain,
! [X0,X1] :
( member(X0,sK1(X0,X1))
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f66,plain,
! [X0,X1] :
( member(sK1(X0,X1),X1)
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f67,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X0,sum(X1))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f35]) ).
fof(f68,plain,
! [X3,X0,X1] :
( ~ member(X0,product(X1))
| ~ member(X3,X1)
| member(X0,X3) ),
inference(cnf_transformation,[],[f38]) ).
fof(f69,plain,
! [X0,X1] :
( member(sK2(X0,X1),X1)
| member(X0,product(X1)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f72,plain,
subset(sK3,sK5),
inference(cnf_transformation,[],[f41]) ).
fof(f73,plain,
( equal_set(intersection(sK3,difference(sK5,sK4)),empty_set)
| subset(sK3,sK4) ),
inference(cnf_transformation,[],[f41]) ).
fof(f74,plain,
( ~ equal_set(intersection(sK3,difference(sK5,sK4)),empty_set)
| ~ subset(sK3,sK4) ),
inference(cnf_transformation,[],[f41]) ).
fof(f78,definition,
sF6 = difference(sK5,sK4),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f79,plain,
difference(sK5,sK4) = sF6,
inference(reorient_equations,[],[f78]) ).
fof(f80,definition,
sF7 = intersection(sK3,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f81,plain,
intersection(sK3,sF6) = sF7,
inference(reorient_equations,[],[f80]) ).
fof(f82,plain,
( ~ equal_set(sF7,empty_set)
| ~ subset(sK3,sK4) ),
inference(definition_folding,[],[f74,f81,f79]) ).
fof(f83,plain,
( equal_set(sF7,empty_set)
| subset(sK3,sK4) ),
inference(definition_folding,[],[f73,f81,f79]) ).
fof(f85,definition,
( spl8_1
<=> subset(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f86,plain,
( ~ subset(sK3,sK4)
| spl8_1 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f87,plain,
( subset(sK3,sK4)
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f89,definition,
( spl8_2
<=> equal_set(sF7,empty_set) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f90,plain,
( ~ equal_set(sF7,empty_set)
| spl8_2 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f91,plain,
( equal_set(sF7,empty_set)
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f92,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f83,f89,f85]) ).
fof(f93,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f82,f89,f85]) ).
fof(f95,plain,
( subset(sF7,empty_set)
| ~ spl8_2 ),
inference(resolution,[],[f46,f91]) ).
fof(f103,plain,
( member(sK0(sK3,sK4),sK3)
| spl8_1 ),
inference(resolution,[],[f43,f86]) ).
fof(f104,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(resolution,[],[f43,f49]) ).
fof(f107,plain,
! [X0] :
( ~ member(X0,sF7)
| member(X0,sF6) ),
inference(superposition,[],[f50,f81]) ).
fof(f108,plain,
! [X0] :
( ~ member(X0,sF7)
| member(X0,sK3) ),
inference(superposition,[],[f51,f81]) ).
fof(f111,plain,
! [X0] :
( ~ member(X0,sF6)
| ~ member(X0,sK4) ),
inference(superposition,[],[f57,f79]) ).
fof(f119,plain,
( ! [X0] :
( ~ subset(sK3,X0)
| member(sK0(sK3,sK4),X0) )
| spl8_1 ),
inference(resolution,[],[f42,f103]) ).
fof(f124,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| equal_set(X0,X1)
| member(sK0(X1,X0),X1) ),
inference(resolution,[],[f47,f43]) ).
fof(f149,plain,
! [X2,X0,X1] :
( ~ subset(sK1(X0,X1),X2)
| member(X0,X2)
| ~ member(X0,sum(X1)) ),
inference(resolution,[],[f65,f42]) ).
fof(f152,plain,
! [X0,X1] :
( subset(sK1(X0,power_set(X1)),X1)
| ~ member(X0,sum(power_set(X1))) ),
inference(resolution,[],[f66,f48]) ).
fof(f160,plain,
! [X0] :
( member(sK1(X0,sF7),sK3)
| ~ member(X0,sum(sF7)) ),
inference(resolution,[],[f66,f108]) ).
fof(f161,plain,
! [X0] :
( member(sK1(X0,sF7),sF6)
| ~ member(X0,sum(sF7)) ),
inference(resolution,[],[f66,f107]) ).
fof(f173,plain,
! [X0] :
( member(sK2(X0,sF7),sK3)
| member(X0,product(sF7)) ),
inference(resolution,[],[f69,f108]) ).
fof(f174,plain,
! [X0] :
( member(sK2(X0,sF7),sF6)
| member(X0,product(sF7)) ),
inference(resolution,[],[f69,f107]) ).
fof(f199,plain,
! [X2,X3,X0,X1] :
( ~ subset(intersection(X1,X2),X3)
| ~ member(X0,X2)
| member(X0,X3)
| ~ member(X0,X1) ),
inference(resolution,[],[f52,f42]) ).
fof(f208,plain,
( member(sK0(sK3,sK4),sK5)
| spl8_1 ),
inference(resolution,[],[f119,f72]) ).
fof(f214,plain,
! [X0] :
( ~ member(X0,sK5)
| member(X0,sF6)
| member(X0,sK4) ),
inference(superposition,[],[f59,f79]) ).
fof(f252,plain,
! [X2,X0,X1] :
( ~ subset(X0,X2)
| member(sK0(X0,X1),X2)
| member(X0,power_set(X1)) ),
inference(resolution,[],[f104,f42]) ).
fof(f295,plain,
( member(sK0(sK3,sK4),sF6)
| member(sK0(sK3,sK4),sK4)
| spl8_1 ),
inference(resolution,[],[f214,f208]) ).
fof(f300,definition,
( spl8_7
<=> member(sK0(sK3,sK4),sK4) ),
introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition]) ).
fof(f301,plain,
( ~ member(sK0(sK3,sK4),sK4)
| spl8_7 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f302,plain,
( member(sK0(sK3,sK4),sK4)
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f304,definition,
( spl8_8
<=> member(sK0(sK3,sK4),sF6) ),
introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition]) ).
fof(f306,plain,
( member(sK0(sK3,sK4),sF6)
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f307,plain,
( spl8_7
| spl8_8
| spl8_1 ),
inference(avatar_split_clause,[],[f295,f85,f304,f300]) ).
fof(f327,plain,
( member(sK3,power_set(sK4))
| ~ spl8_1 ),
inference(resolution,[],[f87,f49]) ).
fof(f345,plain,
( ! [X0] :
( member(X0,sum(power_set(sK4)))
| ~ member(X0,sK3) )
| ~ spl8_1 ),
inference(resolution,[],[f327,f67]) ).
fof(f356,plain,
! [X0,X1] :
( equal_set(X0,X1)
| member(sK0(X1,X0),X1)
| member(sK0(X0,X1),X0) ),
inference(resolution,[],[f124,f43]) ).
fof(f425,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(X0,sum(power_set(X1)))
| ~ member(X0,sum(power_set(X1))) ),
inference(resolution,[],[f149,f152]) ).
fof(f427,plain,
! [X0,X1] :
( ~ member(X0,sum(power_set(X1)))
| member(X0,X1) ),
inference(duplicate_literal_removal,[],[f425]) ).
fof(f885,plain,
! [X0,X1] :
( ~ member(X1,sF6)
| ~ subset(sF7,X0)
| member(X1,X0)
| ~ member(X1,sK3) ),
inference(superposition,[],[f199,f81]) ).
fof(f2497,plain,
( ! [X0] :
( ~ member(X0,sK3)
| member(X0,sK4) )
| ~ spl8_1 ),
inference(resolution,[],[f427,f345]) ).
fof(f2562,plain,
! [X0] :
( ~ member(X0,sum(sF7))
| ~ member(sK1(X0,sF7),sK4) ),
inference(resolution,[],[f161,f111]) ).
fof(f2592,plain,
( ! [X0] :
( member(sK1(X0,sF7),sK4)
| ~ member(X0,sum(sF7)) )
| ~ spl8_1 ),
inference(resolution,[],[f2497,f160]) ).
fof(f2609,plain,
( ! [X0] : ~ member(X0,sum(sF7))
| ~ spl8_1 ),
inference(forward_subsumption_resolution,[],[f2592,f2562]) ).
fof(f2610,plain,
( ! [X0] :
( member(X0,product(sF7))
| member(sK2(X0,sF7),sK4) )
| ~ spl8_1 ),
inference(resolution,[],[f173,f2497]) ).
fof(f2635,plain,
! [X0] :
( member(X0,product(sF7))
| ~ member(sK2(X0,sF7),sK4) ),
inference(resolution,[],[f174,f111]) ).
fof(f2644,plain,
( ! [X0] : member(X0,product(sF7))
| ~ spl8_1 ),
inference(forward_subsumption_resolution,[],[f2635,f2610]) ).
fof(f2645,plain,
( ! [X0,X1] :
( ~ member(X0,sF7)
| member(X1,X0) )
| ~ spl8_1 ),
inference(resolution,[],[f2644,f68]) ).
fof(f4751,plain,
( member(sK0(empty_set,sF7),empty_set)
| member(sK0(sF7,empty_set),sF7)
| spl8_2 ),
inference(resolution,[],[f356,f90]) ).
fof(f4752,plain,
( member(sK0(sF7,empty_set),sF7)
| spl8_2 ),
inference(forward_subsumption_resolution,[],[f4751,f56]) ).
fof(f4753,plain,
( ! [X0] : member(X0,sK0(sF7,empty_set))
| ~ spl8_1
| spl8_2 ),
inference(resolution,[],[f4752,f2645]) ).
fof(f4757,plain,
( ! [X0] :
( member(X0,sum(sF7))
| ~ member(X0,sK0(sF7,empty_set)) )
| spl8_2 ),
inference(resolution,[],[f4752,f67]) ).
fof(f4770,plain,
( ! [X0] : ~ member(X0,sK0(sF7,empty_set))
| ~ spl8_1
| spl8_2 ),
inference(forward_subsumption_resolution,[],[f4757,f2609]) ).
fof(f4772,plain,
( $false
| ~ spl8_1
| spl8_2 ),
inference(forward_subsumption_resolution,[],[f4770,f4753]) ).
fof(f4773,plain,
( ~ spl8_1
| spl8_2 ),
inference(avatar_contradiction_clause,[],[f4772]) ).
fof(f4782,plain,
( member(sK0(sK3,sK4),sK3)
| spl8_1 ),
inference(resolution,[],[f86,f43]) ).
fof(f4785,plain,
( ! [X0] :
( member(sK0(sF7,X0),empty_set)
| member(sF7,power_set(X0)) )
| ~ spl8_2 ),
inference(resolution,[],[f95,f252]) ).
fof(f4791,plain,
( ! [X0] : member(sF7,power_set(X0))
| ~ spl8_2 ),
inference(forward_subsumption_resolution,[],[f4785,f56]) ).
fof(f4854,plain,
( ! [X0] : subset(sF7,X0)
| ~ spl8_2 ),
inference(resolution,[],[f4791,f48]) ).
fof(f4948,plain,
( subset(sK3,sK4)
| ~ spl8_7 ),
inference(resolution,[],[f302,f44]) ).
fof(f4965,plain,
( $false
| spl8_1
| ~ spl8_7 ),
inference(forward_subsumption_resolution,[],[f4948,f86]) ).
fof(f4966,plain,
( spl8_1
| ~ spl8_7 ),
inference(avatar_contradiction_clause,[],[f4965]) ).
fof(f4984,plain,
( ! [X0] :
( ~ subset(sF7,X0)
| member(sK0(sK3,sK4),X0)
| ~ member(sK0(sK3,sK4),sK3) )
| ~ spl8_8 ),
inference(resolution,[],[f306,f885]) ).
fof(f5219,plain,
( ! [X0] :
( ~ subset(sF7,X0)
| member(sK0(sK3,sK4),X0) )
| spl8_1
| ~ spl8_8 ),
inference(forward_subsumption_resolution,[],[f4984,f4782]) ).
fof(f5235,plain,
( ! [X0] : member(sK0(sK3,sK4),X0)
| spl8_1
| ~ spl8_2
| ~ spl8_8 ),
inference(forward_subsumption_resolution,[],[f5219,f4854]) ).
fof(f5560,plain,
( $false
| spl8_1
| ~ spl8_2
| spl8_7
| ~ spl8_8 ),
inference(resolution,[],[f5235,f301]) ).
fof(f5633,plain,
( spl8_1
| ~ spl8_2
| spl8_7
| ~ spl8_8 ),
inference(avatar_contradiction_clause,[],[f5560]) ).
cnf(s1,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f92]) ).
cnf(s2,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(sat_conversion,[],[f93]) ).
cnf(s5,plain,
( spl8_1
| spl8_7
| spl8_8 ),
inference(sat_conversion,[],[f307]) ).
cnf(s33,plain,
( ~ spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f4773]) ).
cnf(s36,plain,
( spl8_1
| ~ spl8_7 ),
inference(sat_conversion,[],[f4966]) ).
cnf(s77,plain,
( spl8_1
| ~ spl8_2
| spl8_7
| ~ spl8_8 ),
inference(sat_conversion,[],[f5633]) ).
cnf(s83,plain,
spl8_1,
inference(rat,[],[s77,s5,s1,s36]) ).
cnf(s84,plain,
spl8_2,
inference(rat,[],[s33,s83]) ).
cnf(s85,plain,
$false,
inference(rat,[],[s2,s84,s83]) ).
fof(f5640,plain,
$false,
inference(avatar_sat_refutation,[],[s85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET697+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 02:33:30 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 1.91/0.80 % (2964704)Will run a generic schedule for satisfiability detection.
% 1.91/0.80 % (2964714)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2219333799:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.91/0.80 % (2964710)% WARNING: option uhcvi not known.
% 1.91/0.80 % (2964711)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2125635519:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.91/0.80 % (2964709)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3300180151_2999 on theBenchmark for (2999ds/0Mi)
% 1.91/0.80 % (2964715)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2606493014:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.91/0.80 % (2964712)dis+10_1_sil=32000:sp=arity:random_seed=951716467:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.91/0.80 % (2964713)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3160428603:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.91/0.80 % (2964710)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2947701148:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.91/0.80 % TRYING [1]
% 1.91/0.80 % TRYING [2]
% 1.91/0.80 % TRYING [3]
% 1.91/0.80 % TRYING [4]
% 1.91/0.80 % TRYING [5]
% 1.91/0.80 % TRYING [6]
% 1.91/0.80 % (2964714)Instruction limit reached!
% 1.91/0.80 % (2964714)------------------------------
% 1.91/0.80 % (2964714)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.91/0.80 % (2964714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.91/0.80 % (2964714)CaDiCaL version: 2.1.3
% 1.91/0.80 % (2964714)Termination reason: Instruction limit
% 1.91/0.80 % (2964714)Termination phase: Saturation
% 1.91/0.80 % (2964714)Time elapsed: 0.047 s
% 1.91/0.80 % (2964714)Peak memory usage: 13 MB
% 1.91/0.80 % (2964714)Instructions burned: 133 (million)
% 1.91/0.80 % TRYING [7]
% 1.91/0.80 % (2964723)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2615871507:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.91/0.80 % TRYING [1]
% 1.91/0.80 % TRYING [2]
% 1.91/0.80 % TRYING [3]
% 1.91/0.80 % TRYING [4]
% 1.91/0.80 % TRYING [5]
% 1.91/0.80 % (2964712)Instruction limit reached!
% 1.91/0.80 % (2964712)------------------------------
% 1.91/0.80 % (2964712)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.91/0.80 % (2964712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.91/0.80 % (2964712)CaDiCaL version: 2.1.3
% 1.91/0.80 % (2964712)Termination reason: Instruction limit
% 1.91/0.80 % (2964712)Termination phase: Saturation
% 1.91/0.80 % (2964712)Time elapsed: 0.066 s
% 1.91/0.80 % (2964712)Peak memory usage: 12 MB
% 1.91/0.80 % (2964712)Instructions burned: 104 (million)
% 1.91/0.80 % (2964713)Instruction limit reached!
% 1.91/0.80 % (2964713)------------------------------
% 1.91/0.80 % (2964713)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.91/0.80 % (2964713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.91/0.80 % (2964713)CaDiCaL version: 2.1.3
% 1.91/0.80 % (2964713)Termination reason: Instruction limit
% 1.91/0.80 % (2964713)Termination phase: Saturation
% 1.91/0.80 % (2964713)Time elapsed: 0.069 s
% 1.91/0.80 % (2964713)Peak memory usage: 12 MB
% 1.91/0.80 % (2964713)Instructions burned: 117 (million)
% 1.91/0.80 % TRYING [6]
% 1.91/0.80 % (2964725)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2004085414:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.91/0.80 % (2964726)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=934422696:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.91/0.80 % TRYING [7]
% 1.91/0.80 % (2964715)Instruction limit reached!
% 1.91/0.80 % (2964715)------------------------------
% 1.91/0.80 % (2964715)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.91/0.80 % (2964715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.91/0.80 % (2964715)CaDiCaL version: 2.1.3
% 1.91/0.80 % (2964715)Termination reason: Instruction limit
% 1.91/0.80 % (2964715)Termination phase: Saturation
% 1.91/0.80 % (2964715)Time elapsed: 0.100 s
% 1.91/0.80 % (2964715)Peak memory usage: 13 MB
% 1.91/0.80 % (2964715)Instructions burned: 159 (million)
% 1.91/0.80 % (2964729)ott-21_1_sil=16000:fs=off:random_seed=3922181020:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.91/0.80 % TRYING [8]
% 1.91/0.80 % (2964725)Instruction limit reached!
% 1.91/0.80 % (2964725)------------------------------
% 1.91/0.80 % (2964725)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.91/0.80 % (2964725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.91/0.80 % (2964725)CaDiCaL version: 2.1.3
% 1.91/0.80 % (2964725)Termination reason: Instruction limit
% 1.91/0.80 % (2964725)Termination phase: Saturation
% 1.91/0.80 % (2964725)Time elapsed: 0.085 s
% 1.91/0.80 % (2964725)Peak memory usage: 13 MB
% 1.91/0.80 % (2964725)Instructions burned: 132 (million)
% 1.91/0.80 % (2964731)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3548942279:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 1.91/0.80 % TRYING [8]
% 1.91/0.80 % (2964729)Instruction limit reached!
% 1.91/0.80 % (2964729)------------------------------
% 1.91/0.80 % (2964729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.91/0.80 % (2964729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.91/0.80 % (2964729)CaDiCaL version: 2.1.3
% 1.91/0.80 % (2964729)Termination reason: Instruction limit
% 1.91/0.80 % (2964729)Termination phase: Saturation
% 1.91/0.80 % (2964729)Time elapsed: 0.094 s
% 1.91/0.80 % (2964729)Peak memory usage: 13 MB
% 1.91/0.80 % (2964729)Instructions burned: 181 (million)
% 1.91/0.80 % (2964733)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2983279266:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.91/0.80 % TRYING [1]
% 1.91/0.80 % TRYING [2]
% 1.91/0.80 % TRYING [3]
% 1.91/0.80 % TRYING [4]
% 1.91/0.80 % (2964723)Instruction limit reached!
% 1.91/0.80 % (2964723)------------------------------
% 1.91/0.80 % (2964723)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.91/0.80 % (2964723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.91/0.80 % (2964723)CaDiCaL version: 2.1.3
% 1.91/0.80 % (2964723)Termination reason: Instruction limit
% 1.91/0.80 % (2964723)Termination phase: Finite model building SAT solving
% 1.91/0.80 % (2964723)Time elapsed: 0.190 s
% 1.91/0.80 % (2964723)Peak memory usage: 20 MB
% 1.91/0.80 % (2964723)Instructions burned: 716 (million)
% 1.91/0.80 % TRYING [5]
% 1.91/0.80 % (2964735)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=451366296:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 1.91/0.80 % TRYING [6]
% 1.91/0.80 % TRYING [7]
% 1.91/0.80 % (2964735) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2964704-2964735"...
% 1.91/0.80 % (2964735)...printing done.
% 1.91/0.80 % (2964735)Refutation found. Thanks to Tanya!
% 1.91/0.80 % SZS status Theorem for theBenchmark
% 1.91/0.80 % SZS output start Proof for theBenchmark
% See solution above
% 2.82/0.80 % (2964735)------------------------------
% 2.82/0.80 % (2964735)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.82/0.80 % (2964735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/0.80 % (2964735)CaDiCaL version: 2.1.3
% 2.82/0.80 % (2964735)Termination reason: Refutation
% 2.82/0.80 % (2964735)Time elapsed: 0.097 s
% 2.82/0.80 % (2964735)Peak memory usage: 15 MB
% 2.82/0.80 % (2964735)Instructions burned: 294 (million)
% 2.82/0.80 % (2964704)Success in time 0.389 s
% 2.82/0.80 % Vampire exiting
%------------------------------------------------------------------------------