%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET703+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 : n018.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 0.17s 0.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 91 ( 16 unt; 6 def)
% Number of atoms : 198 ( 22 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 193 ( 86 ~; 91 |; 2 &)
% ( 12 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 95 ( 0 sgn 93 !; 2 ?)
% 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(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(f8,axiom,
! [X0,X1] :
( member(X0,singleton(X1))
<=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(f9,axiom,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( X0 = X1
| X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',unordered_pair) ).
fof(f12,conjecture,
! [X0,X1] : equal_set(union(singleton(X0),singleton(X1)),unordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI41) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] : equal_set(union(singleton(X0),singleton(X1)),unordered_pair(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] : ~ equal_set(union(singleton(X0),singleton(X1)),unordered_pair(X0,X1)),
inference(ennf_transformation,[],[f13]) ).
fof(f21,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f22,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f23,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f29,plain,
! [X2,X0,X1] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f5]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f5]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f5]) ).
fof(f36,plain,
! [X0,X1] :
( X0 != X1
| member(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f8]) ).
fof(f37,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f8]) ).
fof(f38,plain,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f39,plain,
! [X2,X0,X1] :
( X0 != X2
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f40,plain,
! [X2,X0,X1] :
( X0 != X1
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f47,plain,
~ equal_set(union(singleton(sK3),singleton(sK4)),unordered_pair(sK3,sK4)),
inference(cnf_transformation,[],[f19]) ).
fof(f48,plain,
! [X1] : member(X1,singleton(X1)),
inference(equality_resolution,[],[f36]) ).
fof(f49,plain,
! [X2,X1] : member(X1,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f40]) ).
fof(f50,plain,
! [X2,X1] : member(X2,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f39]) ).
fof(f51,plain,
! [X0,X1] :
( member(sK0(X0,X1),X1)
| ~ subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f22]) ).
fof(f52,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X0)
| ~ subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f21]) ).
fof(f54,plain,
! [X0,X1] :
( equal_set(X0,X1)
| subset(X0,X1)
| subset(X1,X0) ),
inference(consistent_polarity_flipping,[],[f23]) ).
fof(f60,plain,
! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| member(X0,X1) ),
inference(consistent_polarity_flipping,[],[f31]) ).
fof(f61,plain,
! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| member(X0,X2) ),
inference(consistent_polarity_flipping,[],[f30]) ).
fof(f62,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(consistent_polarity_flipping,[],[f29]) ).
fof(f67,plain,
! [X0,X1] :
( member(X0,singleton(X1))
| X0 = X1 ),
inference(consistent_polarity_flipping,[],[f37]) ).
fof(f68,plain,
! [X1] : ~ member(X1,singleton(X1)),
inference(consistent_polarity_flipping,[],[f48]) ).
fof(f69,plain,
! [X2,X1] : ~ member(X1,unordered_pair(X1,X2)),
inference(consistent_polarity_flipping,[],[f49]) ).
fof(f70,plain,
! [X2,X1] : ~ member(X2,unordered_pair(X1,X2)),
inference(consistent_polarity_flipping,[],[f50]) ).
fof(f71,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(consistent_polarity_flipping,[],[f38]) ).
fof(f88,plain,
! [X2,X0,X1] :
( ~ subset(X0,union(X1,X2))
| member(sK0(X0,union(X1,X2)),X1) ),
inference(resolution,[],[f60,f51]) ).
fof(f110,plain,
( subset(union(singleton(sK3),singleton(sK4)),unordered_pair(sK3,sK4))
| subset(unordered_pair(sK3,sK4),union(singleton(sK3),singleton(sK4))) ),
inference(resolution,[],[f54,f47]) ).
fof(f112,definition,
( spl5_1
<=> subset(unordered_pair(sK3,sK4),union(singleton(sK3),singleton(sK4))) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f114,plain,
( subset(unordered_pair(sK3,sK4),union(singleton(sK3),singleton(sK4)))
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f116,definition,
( spl5_2
<=> subset(union(singleton(sK3),singleton(sK4)),unordered_pair(sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f118,plain,
( subset(union(singleton(sK3),singleton(sK4)),unordered_pair(sK3,sK4))
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f119,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f110,f116,f112]) ).
fof(f164,plain,
! [X2,X0,X1] :
( ~ subset(union(X0,X1),X2)
| ~ member(sK0(union(X0,X1),X2),X1)
| ~ member(sK0(union(X0,X1),X2),X0) ),
inference(resolution,[],[f62,f52]) ).
fof(f178,plain,
! [X2,X0,X1] :
( ~ subset(unordered_pair(X0,X1),X2)
| sK0(unordered_pair(X0,X1),X2) = X1
| sK0(unordered_pair(X0,X1),X2) = X0 ),
inference(resolution,[],[f71,f52]) ).
fof(f874,plain,
( ~ member(sK0(union(singleton(sK3),singleton(sK4)),unordered_pair(sK3,sK4)),singleton(sK4))
| ~ member(sK0(union(singleton(sK3),singleton(sK4)),unordered_pair(sK3,sK4)),singleton(sK3))
| ~ spl5_2 ),
inference(resolution,[],[f164,f118]) ).
fof(f891,definition,
( spl5_5
<=> member(sK0(union(singleton(sK3),singleton(sK4)),unordered_pair(sK3,sK4)),singleton(sK3)) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f893,plain,
( ~ member(sK0(union(singleton(sK3),singleton(sK4)),unordered_pair(sK3,sK4)),singleton(sK3))
| spl5_5 ),
inference(avatar_component_clause,[],[f891]) ).
fof(f895,definition,
( spl5_6
<=> member(sK0(union(singleton(sK3),singleton(sK4)),unordered_pair(sK3,sK4)),singleton(sK4)) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
fof(f897,plain,
( ~ member(sK0(union(singleton(sK3),singleton(sK4)),unordered_pair(sK3,sK4)),singleton(sK4))
| spl5_6 ),
inference(avatar_component_clause,[],[f895]) ).
fof(f898,plain,
( ~ spl5_5
| ~ spl5_6
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f874,f116,f895,f891]) ).
fof(f961,plain,
( sK4 = sK0(union(singleton(sK3),singleton(sK4)),unordered_pair(sK3,sK4))
| spl5_6 ),
inference(resolution,[],[f897,f67]) ).
fof(f970,plain,
( member(sK4,unordered_pair(sK3,sK4))
| ~ subset(union(singleton(sK3),singleton(sK4)),unordered_pair(sK3,sK4))
| spl5_6 ),
inference(superposition,[],[f51,f961]) ).
fof(f971,plain,
( ~ subset(union(singleton(sK3),singleton(sK4)),unordered_pair(sK3,sK4))
| spl5_6 ),
inference(forward_subsumption_resolution,[],[f970,f70]) ).
fof(f974,plain,
( $false
| ~ spl5_2
| spl5_6 ),
inference(forward_subsumption_resolution,[],[f971,f118]) ).
fof(f975,plain,
( ~ spl5_2
| spl5_6 ),
inference(avatar_contradiction_clause,[],[f974]) ).
fof(f976,plain,
( sK3 = sK0(union(singleton(sK3),singleton(sK4)),unordered_pair(sK3,sK4))
| spl5_5 ),
inference(resolution,[],[f893,f67]) ).
fof(f985,plain,
( member(sK3,unordered_pair(sK3,sK4))
| ~ subset(union(singleton(sK3),singleton(sK4)),unordered_pair(sK3,sK4))
| spl5_5 ),
inference(superposition,[],[f51,f976]) ).
fof(f986,plain,
( ~ subset(union(singleton(sK3),singleton(sK4)),unordered_pair(sK3,sK4))
| spl5_5 ),
inference(forward_subsumption_resolution,[],[f985,f69]) ).
fof(f988,plain,
( $false
| ~ spl5_2
| spl5_5 ),
inference(forward_subsumption_resolution,[],[f986,f118]) ).
fof(f989,plain,
( ~ spl5_2
| spl5_5 ),
inference(avatar_contradiction_clause,[],[f988]) ).
fof(f1000,plain,
( member(sK0(unordered_pair(sK3,sK4),union(singleton(sK3),singleton(sK4))),singleton(sK3))
| ~ spl5_1 ),
inference(resolution,[],[f114,f88]) ).
fof(f1005,plain,
( sK4 = sK0(unordered_pair(sK3,sK4),union(singleton(sK3),singleton(sK4)))
| sK3 = sK0(unordered_pair(sK3,sK4),union(singleton(sK3),singleton(sK4)))
| ~ spl5_1 ),
inference(resolution,[],[f114,f178]) ).
fof(f1007,definition,
( spl5_9
<=> sK3 = sK0(unordered_pair(sK3,sK4),union(singleton(sK3),singleton(sK4))) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
fof(f1009,plain,
( sK3 = sK0(unordered_pair(sK3,sK4),union(singleton(sK3),singleton(sK4)))
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f1007]) ).
fof(f1011,definition,
( spl5_10
<=> sK4 = sK0(unordered_pair(sK3,sK4),union(singleton(sK3),singleton(sK4))) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
fof(f1013,plain,
( sK4 = sK0(unordered_pair(sK3,sK4),union(singleton(sK3),singleton(sK4)))
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f1011]) ).
fof(f1014,plain,
( spl5_9
| spl5_10
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f1005,f112,f1011,f1007]) ).
fof(f1018,plain,
( member(sK4,union(singleton(sK3),singleton(sK4)))
| ~ subset(unordered_pair(sK3,sK4),union(singleton(sK3),singleton(sK4)))
| ~ spl5_10 ),
inference(superposition,[],[f51,f1013]) ).
fof(f1019,plain,
( member(sK4,union(singleton(sK3),singleton(sK4)))
| ~ spl5_1
| ~ spl5_10 ),
inference(forward_subsumption_resolution,[],[f1018,f114]) ).
fof(f1021,plain,
( member(sK4,singleton(sK4))
| ~ spl5_1
| ~ spl5_10 ),
inference(resolution,[],[f1019,f61]) ).
fof(f1033,plain,
( $false
| ~ spl5_1
| ~ spl5_10 ),
inference(forward_subsumption_resolution,[],[f1021,f68]) ).
fof(f1034,plain,
( ~ spl5_1
| ~ spl5_10 ),
inference(avatar_contradiction_clause,[],[f1033]) ).
fof(f1063,plain,
( member(sK3,singleton(sK3))
| ~ spl5_1
| ~ spl5_9 ),
inference(forward_demodulation,[],[f1000,f1009]) ).
fof(f1064,plain,
( $false
| ~ spl5_1
| ~ spl5_9 ),
inference(forward_subsumption_resolution,[],[f1063,f68]) ).
fof(f1065,plain,
( ~ spl5_1
| ~ spl5_9 ),
inference(avatar_contradiction_clause,[],[f1064]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f119]) ).
cnf(s3,plain,
( ~ spl5_2
| ~ spl5_5
| ~ spl5_6 ),
inference(sat_conversion,[],[f898]) ).
cnf(s4,plain,
( ~ spl5_2
| spl5_6 ),
inference(sat_conversion,[],[f975]) ).
cnf(s5,plain,
( ~ spl5_2
| spl5_5 ),
inference(sat_conversion,[],[f989]) ).
cnf(s7,plain,
( ~ spl5_1
| spl5_9
| spl5_10 ),
inference(sat_conversion,[],[f1014]) ).
cnf(s8,plain,
( ~ spl5_1
| ~ spl5_10 ),
inference(sat_conversion,[],[f1034]) ).
cnf(s10,plain,
( ~ spl5_1
| ~ spl5_9 ),
inference(sat_conversion,[],[f1065]) ).
cnf(s11,plain,
~ spl5_2,
inference(rat,[],[s3,s4,s5]) ).
cnf(s12,plain,
spl5_1,
inference(rat,[],[s1,s11]) ).
cnf(s13,plain,
~ spl5_9,
inference(rat,[],[s10,s12]) ).
cnf(s14,plain,
~ spl5_10,
inference(rat,[],[s8,s12]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s7,s14,s13,s12]) ).
fof(f1066,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET703+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n018.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 02:36:24 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.17/0.50 % (2939322)Will run a generic schedule for satisfiability detection.
% 0.17/0.50 % (2939329)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3393439954:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.50 % (2939328)% WARNING: option uhcvi not known.
% 0.17/0.50 % (2939327)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2603504852_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.50 % (2939328)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=527840225:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.50 % (2939330)dis+10_1_sil=32000:sp=arity:random_seed=1908648061:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.50 % (2939332)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1092386106:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.50 % TRYING [1]
% 0.17/0.50 % TRYING [2]
% 0.17/0.50 % TRYING [3]
% 0.17/0.50 % TRYING [4]
% 0.17/0.50 % (2939333)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=385221700:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.50 % (2939331)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1208552748:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.50 % TRYING [5]
% 0.17/0.50 % TRYING [6]
% 0.17/0.50 % (2939328) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2939322-2939328"...
% 0.17/0.50 % (2939328)...printing done.
% 0.17/0.50 % (2939328)Refutation found. Thanks to Tanya!
% 0.17/0.50 % SZS status Theorem for theBenchmark
% 0.17/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.50 % (2939328)------------------------------
% 0.17/0.50 % (2939328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.50 % (2939328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.50 % (2939328)CaDiCaL version: 2.1.3
% 0.17/0.50 % (2939328)Termination reason: Refutation
% 0.17/0.50 % (2939328)Time elapsed: 0.031 s
% 0.17/0.50 % (2939328)Peak memory usage: 13 MB
% 0.17/0.50 % (2939328)Instructions burned: 46 (million)
% 0.17/0.50 % (2939322)Success in time 0.07 s
% 0.17/0.50 % Vampire exiting
%------------------------------------------------------------------------------