%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET517-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 12:43:54 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.54s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 69 ( 20 unt; 4 def)
% Number of atoms : 136 ( 34 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 122 ( 55 ~; 63 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f8,axiom,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f48,axiom,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',inductive1) ).
fof(f51,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',omega_is_inductive1) ).
fof(f67,axiom,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f69,axiom,
! [X0] :
( X0 = null_class
| intersection(X0,regular(X0)) = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f122,negated_conjecture,
singleton(member_of(x)) = x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_not_singleton_of_set_1) ).
fof(f123,plain,
x = singleton(member_of(x)),
inference(reorient_equations,[],[f122]) ).
fof(f124,negated_conjecture,
member_of(x) = x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_not_singleton_of_set_2) ).
fof(f125,plain,
x = member_of(x),
inference(reorient_equations,[],[f124]) ).
fof(f188,plain,
x = unordered_pair(member_of(x),member_of(x)),
inference(definition_unfolding,[],[f123,f12]) ).
fof(f199,plain,
x = unordered_pair(x,x),
inference(forward_demodulation,[],[f188,f125]) ).
fof(f222,plain,
member(x,universal_class),
inference(superposition,[],[f11,f199]) ).
fof(f224,definition,
( spl0_9
<=> ! [X0] : ~ inductive(X0) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f225,plain,
( ! [X0] : ~ inductive(X0)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f239,plain,
( $false
| ~ spl0_9 ),
inference(resolution,[],[f225,f51]) ).
fof(f240,plain,
~ spl0_9,
inference(avatar_contradiction_clause,[],[f239]) ).
fof(f258,plain,
! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = null_class ),
inference(resolution,[],[f68,f24]) ).
fof(f353,plain,
( member(x,x)
| ~ member(x,universal_class) ),
inference(superposition,[],[f9,f199]) ).
fof(f354,plain,
member(x,x),
inference(forward_subsumption_resolution,[],[f353,f222]) ).
fof(f502,plain,
! [X0,X1] :
( ~ subclass(X0,X1)
| member(null_class,X1)
| ~ inductive(X0) ),
inference(resolution,[],[f1,f48]) ).
fof(f503,plain,
! [X0,X1] :
( member(regular(X0),X1)
| ~ subclass(X0,X1)
| null_class = X0 ),
inference(resolution,[],[f1,f68]) ).
fof(f601,plain,
! [X0] :
( member(null_class,universal_class)
| ~ inductive(X0) ),
inference(resolution,[],[f502,f4]) ).
fof(f617,definition,
( spl0_35
<=> member(null_class,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f619,plain,
( member(null_class,universal_class)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f617]) ).
fof(f620,plain,
( spl0_9
| spl0_35 ),
inference(avatar_split_clause,[],[f601,f617,f224]) ).
fof(f2235,plain,
! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class
| complement(X0) = null_class ),
inference(resolution,[],[f503,f258]) ).
fof(f2244,plain,
! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class ),
inference(duplicate_literal_removal,[],[f2235]) ).
fof(f2320,plain,
! [X0] :
( ~ member(X0,x)
| x = X0
| x = X0 ),
inference(superposition,[],[f8,f199]) ).
fof(f2321,plain,
! [X0] :
( ~ member(X0,x)
| x = X0 ),
inference(duplicate_literal_removal,[],[f2320]) ).
fof(f2346,plain,
( x = regular(x)
| null_class = x ),
inference(resolution,[],[f2321,f68]) ).
fof(f2599,definition,
( spl0_72
<=> null_class = x ),
introduced(definition,[new_symbols(definition,[spl0_72])],[avatar_definition]) ).
fof(f2600,plain,
( null_class != x
| spl0_72 ),
inference(avatar_component_clause,[],[f2599]) ).
fof(f2601,plain,
( null_class = x
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f2599]) ).
fof(f2604,definition,
( spl0_73
<=> x = regular(x) ),
introduced(definition,[new_symbols(definition,[spl0_73])],[avatar_definition]) ).
fof(f2606,plain,
( x = regular(x)
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f2604]) ).
fof(f2607,plain,
( spl0_72
| spl0_73 ),
inference(avatar_split_clause,[],[f2346,f2604,f2599]) ).
fof(f2622,plain,
( null_class = intersection(x,x)
| null_class = x
| ~ spl0_73 ),
inference(superposition,[],[f70,f2606]) ).
fof(f2624,plain,
( null_class = intersection(x,x)
| spl0_72
| ~ spl0_73 ),
inference(forward_subsumption_resolution,[],[f2622,f2600]) ).
fof(f2911,plain,
null_class = complement(universal_class),
inference(resolution,[],[f2244,f4]) ).
fof(f2914,plain,
! [X0] :
( ~ member(X0,null_class)
| ~ member(X0,universal_class) ),
inference(superposition,[],[f24,f2911]) ).
fof(f2950,plain,
( ! [X0] :
( member(X0,null_class)
| ~ member(X0,x)
| ~ member(X0,x) )
| spl0_72
| ~ spl0_73 ),
inference(superposition,[],[f23,f2624]) ).
fof(f2951,plain,
( ! [X0] :
( ~ member(X0,x)
| member(X0,null_class) )
| spl0_72
| ~ spl0_73 ),
inference(duplicate_literal_removal,[],[f2950]) ).
fof(f2977,plain,
( member(x,null_class)
| spl0_72
| ~ spl0_73 ),
inference(resolution,[],[f2951,f354]) ).
fof(f2999,plain,
( ~ member(x,universal_class)
| spl0_72
| ~ spl0_73 ),
inference(resolution,[],[f2977,f2914]) ).
fof(f3002,plain,
( $false
| spl0_72
| ~ spl0_73 ),
inference(forward_subsumption_resolution,[],[f2999,f222]) ).
fof(f3003,plain,
( spl0_72
| ~ spl0_73 ),
inference(avatar_contradiction_clause,[],[f3002]) ).
fof(f3009,plain,
( member(null_class,null_class)
| ~ spl0_72 ),
inference(superposition,[],[f354,f2601]) ).
fof(f3040,plain,
( ~ member(null_class,universal_class)
| ~ spl0_72 ),
inference(resolution,[],[f3009,f2914]) ).
fof(f3043,plain,
( $false
| ~ spl0_35
| ~ spl0_72 ),
inference(forward_subsumption_resolution,[],[f3040,f619]) ).
fof(f3044,plain,
( ~ spl0_35
| ~ spl0_72 ),
inference(avatar_contradiction_clause,[],[f3043]) ).
cnf(s145,plain,
~ spl0_9,
inference(sat_conversion,[],[f240]) ).
cnf(s390,plain,
( spl0_9
| spl0_35 ),
inference(sat_conversion,[],[f620]) ).
cnf(s1399,plain,
( spl0_72
| spl0_73 ),
inference(sat_conversion,[],[f2607]) ).
cnf(s1642,plain,
( spl0_72
| ~ spl0_73 ),
inference(sat_conversion,[],[f3003]) ).
cnf(s1676,plain,
( ~ spl0_35
| ~ spl0_72 ),
inference(sat_conversion,[],[f3044]) ).
cnf(s1679,plain,
spl0_35,
inference(rat,[],[s390,s145]) ).
cnf(s1681,plain,
~ spl0_72,
inference(rat,[],[s1676,s1679]) ).
cnf(s1682,plain,
~ spl0_73,
inference(rat,[],[s1642,s1681]) ).
cnf(s1686,plain,
$false,
inference(rat,[],[s1399,s1682,s1681]) ).
fof(f3045,plain,
$false,
inference(avatar_sat_refutation,[],[s1686]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET517-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n004.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 02:02:07 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 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
% 0.18/0.54 % (4075245)Will run a generic schedule for satisfiability detection.
% 0.18/0.54 % (4075253)dis+10_1_sil=32000:sp=arity:random_seed=3257825412:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.54 % (4075251)% WARNING: option uhcvi not known.
% 0.18/0.54 % (4075250)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2717819624_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.54 % (4075251)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=165578914:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.54 % (4075255)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3217546700:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.54 % (4075252)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1782237544:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.54 % (4075254)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1684283193:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.54 % (4075256)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1472417055:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.54 % (4075253)Instruction limit reached!
% 0.18/0.54 % (4075253)------------------------------
% 0.18/0.54 % (4075253)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.54 % (4075253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.54 % (4075253)CaDiCaL version: 2.1.3
% 0.18/0.54 % (4075253)Termination reason: Instruction limit
% 0.18/0.54 % (4075253)Termination phase: Saturation
% 0.18/0.54 % (4075253)Time elapsed: 0.036 s
% 0.18/0.54 % (4075253)Peak memory usage: 12 MB
% 0.18/0.54 % (4075253)Instructions burned: 106 (million)
% 0.18/0.54 % (4075264)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2286367011:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.18/0.54 % (4075252) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4075245-4075252"...
% 0.18/0.54 % (4075254)Instruction limit reached!
% 0.18/0.54 % (4075254)------------------------------
% 0.18/0.54 % (4075254)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.54 % (4075254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.54 % (4075254)CaDiCaL version: 2.1.3
% 0.18/0.54 % (4075254)Termination reason: Instruction limit
% 0.18/0.54 % (4075254)Termination phase: Saturation
% 0.18/0.54 % (4075254)Time elapsed: 0.069 s
% 0.18/0.54 % (4075254)Peak memory usage: 12 MB
% 0.18/0.54 % (4075254)Instructions burned: 117 (million)
% 0.18/0.54 % (4075252)...printing done.
% 0.18/0.54 % (4075252)Refutation found. Thanks to Tanya!
% 0.18/0.54 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.54 % (4075252)------------------------------
% 0.18/0.54 % (4075252)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.54 % (4075252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.54 % (4075252)CaDiCaL version: 2.1.3
% 0.18/0.54 % (4075252)Termination reason: Refutation
% 0.18/0.54 % (4075252)Time elapsed: 0.069 s
% 0.18/0.54 % (4075252)Peak memory usage: 14 MB
% 0.18/0.54 % (4075252)Instructions burned: 108 (million)
% 0.18/0.54 % (4075245)Success in time 0.104 s
% 0.18/0.54 % Vampire exiting
%------------------------------------------------------------------------------