%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET598+3 : 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 : n002.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 0.16s 15.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 85 ( 14 unt; 7 def)
% Number of atoms : 232 ( 18 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 259 ( 112 ~; 120 |; 12 &)
% ( 10 <=>; 3 =>; 0 <=; 2 <~>)
% Maximal formula depth : 10 ( 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 : 48 ( 0 sgn 42 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : subset(intersection(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_is_subset) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X0,X2) )
=> subset(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_subsets) ).
fof(f5,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f6,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f9,conjecture,
! [X0,X1,X2] :
( X0 = intersection(X1,X2)
<=> ( subset(X0,X1)
& subset(X0,X2)
& ! [X3] :
( ( subset(X3,X1)
& subset(X3,X2) )
=> subset(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th57) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
( X0 = intersection(X1,X2)
<=> ( subset(X0,X1)
& subset(X0,X2)
& ! [X3] :
( ( subset(X3,X1)
& subset(X3,X2) )
=> subset(X3,X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( subset(X0,intersection(X1,X2))
| ~ subset(X0,X1)
| ~ subset(X0,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f12,plain,
! [X0,X1,X2] :
( subset(X0,intersection(X1,X2))
| ~ subset(X0,X1)
| ~ subset(X0,X2) ),
inference(flattening,[],[f11]) ).
fof(f14,plain,
? [X0,X1,X2] :
( X0 = intersection(X1,X2)
<~> ( subset(X0,X1)
& subset(X0,X2)
& ! [X3] :
( subset(X3,X0)
| ~ subset(X3,X1)
| ~ subset(X3,X2) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f15,plain,
? [X0,X1,X2] :
( X0 = intersection(X1,X2)
<~> ( subset(X0,X1)
& subset(X0,X2)
& ! [X3] :
( subset(X3,X0)
| ~ subset(X3,X1)
| ~ subset(X3,X2) ) ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1] : subset(intersection(X0,X1),X0),
inference(cnf_transformation,[],[f1]) ).
fof(f17,plain,
! [X2,X0,X1] :
( subset(X0,intersection(X1,X2))
| ~ subset(X0,X1)
| ~ subset(X0,X2) ),
inference(cnf_transformation,[],[f12]) ).
fof(f26,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f5]) ).
fof(f27,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f33,plain,
! [X3] :
( ~ subset(X3,sK4)
| ~ subset(X3,sK3)
| subset(X3,sK2)
| sK2 = intersection(sK3,sK4) ),
inference(cnf_transformation,[],[f15]) ).
fof(f34,plain,
( subset(sK5,sK4)
| ~ subset(sK2,sK4)
| ~ subset(sK2,sK3)
| sK2 != intersection(sK3,sK4) ),
inference(cnf_transformation,[],[f15]) ).
fof(f35,plain,
( subset(sK5,sK3)
| ~ subset(sK2,sK4)
| ~ subset(sK2,sK3)
| sK2 != intersection(sK3,sK4) ),
inference(cnf_transformation,[],[f15]) ).
fof(f36,plain,
( ~ subset(sK5,sK2)
| ~ subset(sK2,sK4)
| ~ subset(sK2,sK3)
| sK2 != intersection(sK3,sK4) ),
inference(cnf_transformation,[],[f15]) ).
fof(f37,plain,
( subset(sK2,sK4)
| sK2 = intersection(sK3,sK4) ),
inference(cnf_transformation,[],[f15]) ).
fof(f38,plain,
( subset(sK2,sK3)
| sK2 = intersection(sK3,sK4) ),
inference(cnf_transformation,[],[f15]) ).
fof(f44,definition,
( spl6_1
<=> sK2 = intersection(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f45,plain,
( sK2 != intersection(sK3,sK4)
| spl6_1 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f46,plain,
( sK2 = intersection(sK3,sK4)
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f48,definition,
( spl6_2
<=> ! [X3] :
( ~ subset(X3,sK4)
| subset(X3,sK2)
| ~ subset(X3,sK3) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f49,plain,
( ! [X3] :
( ~ subset(X3,sK4)
| subset(X3,sK2)
| ~ subset(X3,sK3) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f50,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f33,f48,f44]) ).
fof(f52,definition,
( spl6_3
<=> subset(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f53,plain,
( subset(sK2,sK3)
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f54,plain,
( ~ subset(sK2,sK3)
| spl6_3 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f56,definition,
( spl6_4
<=> subset(sK2,sK4) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
fof(f57,plain,
( subset(sK2,sK4)
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f58,plain,
( ~ subset(sK2,sK4)
| spl6_4 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f60,definition,
( spl6_5
<=> subset(sK5,sK4) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
fof(f62,plain,
( subset(sK5,sK4)
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,plain,
( ~ spl6_1
| ~ spl6_3
| ~ spl6_4
| spl6_5 ),
inference(avatar_split_clause,[],[f34,f60,f56,f52,f44]) ).
fof(f65,definition,
( spl6_6
<=> subset(sK5,sK3) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
fof(f67,plain,
( subset(sK5,sK3)
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f68,plain,
( ~ spl6_1
| ~ spl6_3
| ~ spl6_4
| spl6_6 ),
inference(avatar_split_clause,[],[f35,f65,f56,f52,f44]) ).
fof(f70,definition,
( spl6_7
<=> subset(sK5,sK2) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
fof(f72,plain,
( ~ subset(sK5,sK2)
| spl6_7 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f73,plain,
( ~ spl6_1
| ~ spl6_3
| ~ spl6_4
| ~ spl6_7 ),
inference(avatar_split_clause,[],[f36,f70,f56,f52,f44]) ).
fof(f74,plain,
( spl6_1
| spl6_4 ),
inference(avatar_split_clause,[],[f37,f56,f44]) ).
fof(f75,plain,
( spl6_1
| spl6_3 ),
inference(avatar_split_clause,[],[f38,f52,f44]) ).
fof(f87,plain,
( ! [X0] :
( ~ subset(intersection(sK4,X0),sK3)
| subset(intersection(sK4,X0),sK2) )
| ~ spl6_2 ),
inference(resolution,[],[f16,f49]) ).
fof(f89,plain,
! [X0,X1] : subset(intersection(X0,X1),X1),
inference(superposition,[],[f16,f27]) ).
fof(f91,plain,
( ! [X0] :
( ~ subset(intersection(X0,sK4),sK3)
| subset(intersection(X0,sK4),sK2) )
| ~ spl6_2 ),
inference(superposition,[],[f87,f27]) ).
fof(f94,plain,
( subset(intersection(sK3,sK4),sK2)
| ~ spl6_2 ),
inference(resolution,[],[f91,f16]) ).
fof(f120,plain,
( ~ subset(sK2,intersection(sK3,sK4))
| sK2 = intersection(sK3,sK4)
| ~ spl6_2 ),
inference(resolution,[],[f26,f94]) ).
fof(f122,plain,
( ~ subset(sK2,intersection(sK3,sK4))
| spl6_1
| ~ spl6_2 ),
inference(forward_subsumption_resolution,[],[f120,f45]) ).
fof(f126,plain,
( ~ subset(sK2,sK3)
| ~ subset(sK2,sK4)
| spl6_1
| ~ spl6_2 ),
inference(resolution,[],[f17,f122]) ).
fof(f129,plain,
( ~ subset(sK2,sK4)
| spl6_1
| ~ spl6_2
| ~ spl6_3 ),
inference(forward_subsumption_resolution,[],[f126,f53]) ).
fof(f130,plain,
( $false
| spl6_1
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4 ),
inference(forward_subsumption_resolution,[],[f129,f57]) ).
fof(f131,plain,
( spl6_1
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4 ),
inference(avatar_contradiction_clause,[],[f130]) ).
fof(f132,plain,
( subset(sK5,sK2)
| ~ subset(sK5,sK3)
| ~ spl6_2
| ~ spl6_5 ),
inference(resolution,[],[f62,f49]) ).
fof(f145,plain,
( ~ subset(sK5,sK3)
| ~ spl6_2
| ~ spl6_5
| spl6_7 ),
inference(forward_subsumption_resolution,[],[f132,f72]) ).
fof(f146,plain,
( $false
| ~ spl6_2
| ~ spl6_5
| ~ spl6_6
| spl6_7 ),
inference(forward_subsumption_resolution,[],[f145,f67]) ).
fof(f147,plain,
( ~ spl6_2
| ~ spl6_5
| ~ spl6_6
| spl6_7 ),
inference(avatar_contradiction_clause,[],[f146]) ).
fof(f174,plain,
( subset(sK2,sK3)
| ~ spl6_1 ),
inference(superposition,[],[f16,f46]) ).
fof(f175,plain,
( ! [X0] :
( subset(X0,sK2)
| ~ subset(X0,sK3)
| ~ subset(X0,sK4) )
| ~ spl6_1 ),
inference(superposition,[],[f17,f46]) ).
fof(f178,plain,
( subset(sK2,sK4)
| ~ spl6_1 ),
inference(superposition,[],[f89,f46]) ).
fof(f179,plain,
( $false
| ~ spl6_1
| spl6_3 ),
inference(forward_subsumption_resolution,[],[f174,f54]) ).
fof(f180,plain,
( ~ spl6_1
| spl6_3 ),
inference(avatar_contradiction_clause,[],[f179]) ).
fof(f181,plain,
( $false
| ~ spl6_1
| spl6_4 ),
inference(forward_subsumption_resolution,[],[f178,f58]) ).
fof(f182,plain,
( ~ spl6_1
| spl6_4 ),
inference(avatar_contradiction_clause,[],[f181]) ).
fof(f183,plain,
( spl6_2
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f175,f44,f48]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f50]) ).
cnf(s2,plain,
( ~ spl6_1
| ~ spl6_3
| ~ spl6_4
| spl6_5 ),
inference(sat_conversion,[],[f63]) ).
cnf(s3,plain,
( ~ spl6_1
| ~ spl6_3
| ~ spl6_4
| spl6_6 ),
inference(sat_conversion,[],[f68]) ).
cnf(s4,plain,
( ~ spl6_1
| ~ spl6_3
| ~ spl6_4
| ~ spl6_7 ),
inference(sat_conversion,[],[f73]) ).
cnf(s5,plain,
( spl6_1
| spl6_4 ),
inference(sat_conversion,[],[f74]) ).
cnf(s6,plain,
( spl6_1
| spl6_3 ),
inference(sat_conversion,[],[f75]) ).
cnf(s8,plain,
( spl6_1
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4 ),
inference(sat_conversion,[],[f131]) ).
cnf(s11,plain,
( ~ spl6_2
| ~ spl6_5
| ~ spl6_6
| spl6_7 ),
inference(sat_conversion,[],[f147]) ).
cnf(s16,plain,
( ~ spl6_1
| spl6_3 ),
inference(sat_conversion,[],[f180]) ).
cnf(s17,plain,
( ~ spl6_1
| spl6_4 ),
inference(sat_conversion,[],[f182]) ).
cnf(s18,plain,
( ~ spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f183]) ).
cnf(s19,plain,
spl6_1,
inference(rat,[],[s8,s1,s5,s6]) ).
cnf(s20,plain,
spl6_2,
inference(rat,[],[s18,s19]) ).
cnf(s21,plain,
spl6_4,
inference(rat,[],[s17,s19]) ).
cnf(s22,plain,
spl6_3,
inference(rat,[],[s16,s19]) ).
cnf(s23,plain,
spl6_6,
inference(rat,[],[s3,s22,s21,s19]) ).
cnf(s24,plain,
spl6_5,
inference(rat,[],[s2,s22,s21,s19]) ).
cnf(s25,plain,
~ spl6_7,
inference(rat,[],[s4,s22,s21,s19]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s11,s20,s23,s25,s24]) ).
fof(f184,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET598+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/15.39 % Computer : n002.cluster.edu
% 0.10/15.39 % Model : x86_64 x86_64
% 0.10/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.39 % Memory : 8046.5625MB
% 0.10/15.39 % OS : Linux 6.8.0-71-generic
% 0.10/15.39 % CPULimit : 300
% 0.10/15.39 % WCLimit : 300
% 0.10/15.39 % DateTime : Mon Sep 28 02:20:08 UTC 2026
% 0.10/15.39 % CPUTime :
% 0.10/15.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.16/15.42 Running first-order model finding
% 0.16/15.43 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
% 0.16/15.48 % (4091950)Will run a generic schedule for satisfiability detection.
% 0.16/15.48 % (4091959)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2093275728:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/15.48 % (4091956)% WARNING: option uhcvi not known.
% 0.16/15.48 % (4091959) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4091950-4091959"...
% 0.16/15.48 % (4091959)...printing done.
% 0.16/15.48 % (4091959)Refutation found. Thanks to Tanya!
% 0.16/15.48 % SZS status Theorem for theBenchmark
% 0.16/15.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/15.48 % (4091959)------------------------------
% 0.16/15.48 % (4091959)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/15.48 % (4091959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/15.48 % (4091959)CaDiCaL version: 2.1.3
% 0.16/15.48 % (4091959)Termination reason: Refutation
% 0.16/15.48 % (4091959)Time elapsed: 0.003 s
% 0.16/15.48 % (4091959)Peak memory usage: 12 MB
% 0.16/15.48 % (4091959)Instructions burned: 5 (million)
% 0.16/15.48 % (4091950)Success in time 0.041 s
% 0.16/15.48 % Vampire exiting
%------------------------------------------------------------------------------