%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET597+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 12:44:04 PM UTC 2026
% Result : Theorem 0.15s 5.47s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 83 ( 14 unt; 7 def)
% Number of atoms : 269 ( 30 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 316 ( 130 ~; 135 |; 36 &)
% ( 10 <=>; 3 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 50 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : subset(X0,union(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_of_union) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X2,X1) )
=> subset(union(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_subset) ).
fof(f5,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f6,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f9,conjecture,
! [X0,X1,X2] :
( X0 = union(X1,X2)
<=> ( subset(X1,X0)
& subset(X2,X0)
& ! [X3] :
( ( subset(X1,X3)
& subset(X2,X3) )
=> subset(X0,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th56) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
( X0 = union(X1,X2)
<=> ( subset(X1,X0)
& subset(X2,X0)
& ! [X3] :
( ( subset(X1,X3)
& subset(X2,X3) )
=> subset(X0,X3) ) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( subset(union(X0,X2),X1)
| ~ subset(X0,X1)
| ~ subset(X2,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f12,plain,
! [X0,X1,X2] :
( subset(union(X0,X2),X1)
| ~ subset(X0,X1)
| ~ subset(X2,X1) ),
inference(flattening,[],[f11]) ).
fof(f14,plain,
? [X0,X1,X2] :
( X0 = union(X1,X2)
<~> ( subset(X1,X0)
& subset(X2,X0)
& ! [X3] :
( subset(X0,X3)
| ~ subset(X1,X3)
| ~ subset(X2,X3) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f15,plain,
? [X0,X1,X2] :
( X0 = union(X1,X2)
<~> ( subset(X1,X0)
& subset(X2,X0)
& ! [X3] :
( subset(X0,X3)
| ~ subset(X1,X3)
| ~ subset(X2,X3) ) ) ),
inference(flattening,[],[f14]) ).
fof(f21,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f22,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f21]) ).
fof(f26,plain,
? [X0,X1,X2] :
( ( ~ subset(X1,X0)
| ~ subset(X2,X0)
| ? [X3] :
( ~ subset(X0,X3)
& subset(X1,X3)
& subset(X2,X3) )
| union(X1,X2) != X0 )
& ( ( subset(X1,X0)
& subset(X2,X0)
& ! [X3] :
( subset(X0,X3)
| ~ subset(X1,X3)
| ~ subset(X2,X3) ) )
| X0 = union(X1,X2) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f27,plain,
? [X0,X1,X2] :
( ( ~ subset(X1,X0)
| ~ subset(X2,X0)
| ? [X3] :
( ~ subset(X0,X3)
& subset(X1,X3)
& subset(X2,X3) )
| union(X1,X2) != X0 )
& ( ( subset(X1,X0)
& subset(X2,X0)
& ! [X3] :
( subset(X0,X3)
| ~ subset(X1,X3)
| ~ subset(X2,X3) ) )
| X0 = union(X1,X2) ) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
? [X0,X1,X2] :
( ( ~ subset(X1,X0)
| ~ subset(X2,X0)
| ? [X3] :
( ~ subset(X0,X3)
& subset(X1,X3)
& subset(X2,X3) )
| union(X1,X2) != X0 )
& ( ( subset(X1,X0)
& subset(X2,X0)
& ! [X4] :
( subset(X0,X4)
| ~ subset(X1,X4)
| ~ subset(X2,X4) ) )
| X0 = union(X1,X2) ) ),
inference(rectify,[],[f27]) ).
fof(f29,plain,
( ( ~ subset(sK3,sK2)
| ~ subset(sK4,sK2)
| ( ~ subset(sK2,sK5)
& subset(sK3,sK5)
& subset(sK4,sK5) )
| sK2 != union(sK3,sK4) )
& ( ( subset(sK3,sK2)
& subset(sK4,sK2)
& ! [X4] :
( subset(sK2,X4)
| ~ subset(sK3,X4)
| ~ subset(sK4,X4) ) )
| sK2 = union(sK3,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f28]) ).
fof(f30,plain,
! [X0,X1] : subset(X0,union(X0,X1)),
inference(cnf_transformation,[],[f1]) ).
fof(f31,plain,
! [X2,X0,X1] :
( subset(union(X0,X2),X1)
| ~ subset(X0,X1)
| ~ subset(X2,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f40,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f47,plain,
! [X4] :
( subset(sK2,X4)
| ~ subset(sK3,X4)
| ~ subset(sK4,X4)
| sK2 = union(sK3,sK4) ),
inference(cnf_transformation,[],[f29]) ).
fof(f48,plain,
( subset(sK4,sK2)
| sK2 = union(sK3,sK4) ),
inference(cnf_transformation,[],[f29]) ).
fof(f49,plain,
( subset(sK3,sK2)
| sK2 = union(sK3,sK4) ),
inference(cnf_transformation,[],[f29]) ).
fof(f50,plain,
( ~ subset(sK3,sK2)
| ~ subset(sK4,sK2)
| subset(sK4,sK5)
| sK2 != union(sK3,sK4) ),
inference(cnf_transformation,[],[f29]) ).
fof(f51,plain,
( ~ subset(sK3,sK2)
| ~ subset(sK4,sK2)
| subset(sK3,sK5)
| sK2 != union(sK3,sK4) ),
inference(cnf_transformation,[],[f29]) ).
fof(f52,plain,
( ~ subset(sK3,sK2)
| ~ subset(sK4,sK2)
| ~ subset(sK2,sK5)
| sK2 != union(sK3,sK4) ),
inference(cnf_transformation,[],[f29]) ).
fof(f58,definition,
( spl6_1
<=> sK2 = union(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f59,plain,
( sK2 != union(sK3,sK4)
| spl6_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f60,plain,
( sK2 = union(sK3,sK4)
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f62,definition,
( spl6_2
<=> ! [X4] :
( subset(sK2,X4)
| ~ subset(sK4,X4)
| ~ subset(sK3,X4) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f63,plain,
( ! [X4] :
( ~ subset(sK4,X4)
| subset(sK2,X4)
| ~ subset(sK3,X4) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f64,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f47,f62,f58]) ).
fof(f66,definition,
( spl6_3
<=> subset(sK4,sK2) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f68,plain,
( subset(sK4,sK2)
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f69,plain,
( spl6_1
| spl6_3 ),
inference(avatar_split_clause,[],[f48,f66,f58]) ).
fof(f71,definition,
( spl6_4
<=> subset(sK3,sK2) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
fof(f73,plain,
( subset(sK3,sK2)
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,plain,
( spl6_1
| spl6_4 ),
inference(avatar_split_clause,[],[f49,f71,f58]) ).
fof(f76,definition,
( spl6_5
<=> subset(sK4,sK5) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
fof(f78,plain,
( subset(sK4,sK5)
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f79,plain,
( ~ spl6_1
| spl6_5
| ~ spl6_3
| ~ spl6_4 ),
inference(avatar_split_clause,[],[f50,f71,f66,f76,f58]) ).
fof(f81,definition,
( spl6_6
<=> subset(sK3,sK5) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
fof(f84,plain,
( ~ spl6_1
| spl6_6
| ~ spl6_3
| ~ spl6_4 ),
inference(avatar_split_clause,[],[f51,f71,f66,f81,f58]) ).
fof(f86,definition,
( spl6_7
<=> subset(sK2,sK5) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
fof(f89,plain,
( ~ spl6_1
| ~ spl6_7
| ~ spl6_3
| ~ spl6_4 ),
inference(avatar_split_clause,[],[f52,f71,f66,f86,f58]) ).
fof(f102,plain,
( ! [X0] :
( ~ subset(sK3,union(sK4,X0))
| subset(sK2,union(sK4,X0)) )
| ~ spl6_2 ),
inference(resolution,[],[f30,f63]) ).
fof(f103,plain,
! [X0,X1] : subset(X1,union(X0,X1)),
inference(superposition,[],[f30,f41]) ).
fof(f104,plain,
( ! [X0] :
( ~ subset(sK3,union(X0,sK4))
| subset(sK2,union(X0,sK4)) )
| ~ spl6_2 ),
inference(superposition,[],[f102,f41]) ).
fof(f107,plain,
( subset(sK2,union(sK3,sK4))
| ~ spl6_2 ),
inference(resolution,[],[f104,f30]) ).
fof(f132,plain,
( ~ subset(union(sK3,sK4),sK2)
| sK2 = union(sK3,sK4)
| ~ spl6_2 ),
inference(resolution,[],[f40,f107]) ).
fof(f133,plain,
( ~ subset(union(sK3,sK4),sK2)
| spl6_1
| ~ spl6_2 ),
inference(forward_subsumption_resolution,[],[f132,f59]) ).
fof(f156,plain,
( ~ subset(sK3,sK2)
| ~ subset(sK4,sK2)
| spl6_1
| ~ spl6_2 ),
inference(resolution,[],[f133,f31]) ).
fof(f157,plain,
( ~ subset(sK4,sK2)
| spl6_1
| ~ spl6_2
| ~ spl6_4 ),
inference(forward_subsumption_resolution,[],[f156,f73]) ).
fof(f158,plain,
( $false
| spl6_1
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4 ),
inference(forward_subsumption_resolution,[],[f157,f68]) ).
fof(f159,plain,
( spl6_1
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4 ),
inference(avatar_contradiction_clause,[],[f158]) ).
fof(f165,plain,
( subset(sK2,sK5)
| ~ subset(sK3,sK5)
| ~ spl6_2
| ~ spl6_5 ),
inference(resolution,[],[f78,f63]) ).
fof(f176,plain,
( ~ spl6_6
| spl6_7
| ~ spl6_2
| ~ spl6_5 ),
inference(avatar_split_clause,[],[f165,f76,f62,f86,f81]) ).
fof(f179,plain,
( subset(sK3,sK2)
| ~ spl6_1 ),
inference(superposition,[],[f30,f60]) ).
fof(f180,plain,
( ! [X0] :
( subset(sK2,X0)
| ~ subset(sK3,X0)
| ~ subset(sK4,X0) )
| ~ spl6_1 ),
inference(superposition,[],[f31,f60]) ).
fof(f184,plain,
( subset(sK4,sK2)
| ~ spl6_1 ),
inference(superposition,[],[f103,f60]) ).
fof(f187,plain,
( spl6_4
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f179,f58,f71]) ).
fof(f188,plain,
( spl6_3
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f184,f58,f66]) ).
fof(f189,plain,
( spl6_2
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f180,f58,f62]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f64]) ).
cnf(s2,plain,
( spl6_1
| spl6_3 ),
inference(sat_conversion,[],[f69]) ).
cnf(s3,plain,
( spl6_1
| spl6_4 ),
inference(sat_conversion,[],[f74]) ).
cnf(s4,plain,
( ~ spl6_1
| ~ spl6_3
| ~ spl6_4
| spl6_5 ),
inference(sat_conversion,[],[f79]) ).
cnf(s5,plain,
( ~ spl6_1
| ~ spl6_3
| ~ spl6_4
| spl6_6 ),
inference(sat_conversion,[],[f84]) ).
cnf(s6,plain,
( ~ spl6_1
| ~ spl6_3
| ~ spl6_4
| ~ spl6_7 ),
inference(sat_conversion,[],[f89]) ).
cnf(s10,plain,
( spl6_1
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4 ),
inference(sat_conversion,[],[f159]) ).
cnf(s13,plain,
( ~ spl6_2
| ~ spl6_5
| ~ spl6_6
| spl6_7 ),
inference(sat_conversion,[],[f176]) ).
cnf(s15,plain,
( ~ spl6_1
| spl6_4 ),
inference(sat_conversion,[],[f187]) ).
cnf(s16,plain,
( ~ spl6_1
| spl6_3 ),
inference(sat_conversion,[],[f188]) ).
cnf(s17,plain,
( ~ spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f189]) ).
cnf(s18,plain,
spl6_1,
inference(rat,[],[s10,s1,s2,s3]) ).
cnf(s19,plain,
spl6_2,
inference(rat,[],[s17,s18]) ).
cnf(s20,plain,
spl6_3,
inference(rat,[],[s16,s18]) ).
cnf(s21,plain,
spl6_4,
inference(rat,[],[s15,s18]) ).
cnf(s22,plain,
spl6_6,
inference(rat,[],[s5,s20,s21,s18]) ).
cnf(s23,plain,
spl6_5,
inference(rat,[],[s4,s20,s21,s18]) ).
cnf(s24,plain,
~ spl6_7,
inference(rat,[],[s6,s20,s21,s18]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s13,s19,s22,s24,s23]) ).
fof(f190,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET597+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/5.39 % Computer : n016.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Mon Sep 28 02:22:10 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/5.43 Running first-order model finding
% 0.15/5.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.47 % (3190296)Will run a generic schedule for satisfiability detection.
% 0.15/5.47 % (3190304)dis+10_1_sil=32000:sp=arity:random_seed=3832795284:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/5.47 % (3190304) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3190296-3190304"...
% 0.15/5.47 % (3190302)% WARNING: option uhcvi not known.
% 0.15/5.47 % (3190304)...printing done.
% 0.15/5.47 % (3190304)Refutation found. Thanks to Tanya!
% 0.15/5.47 % SZS status Theorem for theBenchmark
% 0.15/5.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/5.47 % (3190304)------------------------------
% 0.15/5.47 % (3190304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/5.47 % (3190304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/5.47 % (3190304)CaDiCaL version: 2.1.3
% 0.15/5.47 % (3190304)Termination reason: Refutation
% 0.15/5.47 % (3190304)Time elapsed: 0.003 s
% 0.15/5.47 % (3190304)Peak memory usage: 12 MB
% 0.15/5.47 % (3190304)Instructions burned: 5 (million)
% 0.15/5.47 % (3190296)Success in time 0.032 s
% 0.15/5.47 % Vampire exiting
%------------------------------------------------------------------------------