%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET516-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 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 12:43:54 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.54s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 17
% Syntax : Number of formulae : 66 ( 17 unt; 4 def)
% Number of atoms : 133 ( 31 equ)
% Maximal formula atoms : 5 ( 2 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 : 9 ( 9 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/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f48,axiom,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inductive1) ).
fof(f51,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',omega_is_inductive1) ).
fof(f67,axiom,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
file('/export/starexec/sandbox/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/sandbox/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(x) = x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_no_class_belongs_to_itself_1) ).
fof(f123,plain,
x = singleton(x),
inference(reorient_equations,[],[f122]) ).
fof(f186,plain,
x = unordered_pair(x,x),
inference(definition_unfolding,[],[f123,f12]) ).
fof(f219,plain,
member(x,universal_class),
inference(superposition,[],[f11,f186]) ).
fof(f221,definition,
( spl0_9
<=> ! [X0] : ~ inductive(X0) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f222,plain,
( ! [X0] : ~ inductive(X0)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f229,plain,
( $false
| ~ spl0_9 ),
inference(resolution,[],[f222,f51]) ).
fof(f230,plain,
~ spl0_9,
inference(avatar_contradiction_clause,[],[f229]) ).
fof(f255,plain,
! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = null_class ),
inference(resolution,[],[f68,f24]) ).
fof(f348,plain,
( member(x,x)
| ~ member(x,universal_class) ),
inference(superposition,[],[f9,f186]) ).
fof(f349,plain,
member(x,x),
inference(forward_subsumption_resolution,[],[f348,f219]) ).
fof(f496,plain,
! [X0,X1] :
( ~ subclass(X0,X1)
| member(null_class,X1)
| ~ inductive(X0) ),
inference(resolution,[],[f1,f48]) ).
fof(f497,plain,
! [X0,X1] :
( member(regular(X0),X1)
| ~ subclass(X0,X1)
| null_class = X0 ),
inference(resolution,[],[f1,f68]) ).
fof(f595,plain,
! [X0] :
( member(null_class,universal_class)
| ~ inductive(X0) ),
inference(resolution,[],[f496,f4]) ).
fof(f611,definition,
( spl0_35
<=> member(null_class,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f613,plain,
( member(null_class,universal_class)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f611]) ).
fof(f614,plain,
( spl0_9
| spl0_35 ),
inference(avatar_split_clause,[],[f595,f611,f221]) ).
fof(f2341,plain,
! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class
| complement(X0) = null_class ),
inference(resolution,[],[f497,f255]) ).
fof(f2350,plain,
! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class ),
inference(duplicate_literal_removal,[],[f2341]) ).
fof(f2434,plain,
! [X0] :
( ~ member(X0,x)
| x = X0
| x = X0 ),
inference(superposition,[],[f8,f186]) ).
fof(f2435,plain,
! [X0] :
( ~ member(X0,x)
| x = X0 ),
inference(duplicate_literal_removal,[],[f2434]) ).
fof(f2460,plain,
( x = regular(x)
| null_class = x ),
inference(resolution,[],[f2435,f68]) ).
fof(f2667,definition,
( spl0_79
<=> null_class = x ),
introduced(definition,[new_symbols(definition,[spl0_79])],[avatar_definition]) ).
fof(f2668,plain,
( null_class != x
| spl0_79 ),
inference(avatar_component_clause,[],[f2667]) ).
fof(f2669,plain,
( null_class = x
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f2667]) ).
fof(f2672,definition,
( spl0_80
<=> x = regular(x) ),
introduced(definition,[new_symbols(definition,[spl0_80])],[avatar_definition]) ).
fof(f2674,plain,
( x = regular(x)
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f2672]) ).
fof(f2675,plain,
( spl0_79
| spl0_80 ),
inference(avatar_split_clause,[],[f2460,f2672,f2667]) ).
fof(f2690,plain,
( null_class = intersection(x,x)
| null_class = x
| ~ spl0_80 ),
inference(superposition,[],[f70,f2674]) ).
fof(f2692,plain,
( null_class = intersection(x,x)
| spl0_79
| ~ spl0_80 ),
inference(forward_subsumption_resolution,[],[f2690,f2668]) ).
fof(f2985,plain,
null_class = complement(universal_class),
inference(resolution,[],[f2350,f4]) ).
fof(f2992,plain,
! [X0] :
( ~ member(X0,null_class)
| ~ member(X0,universal_class) ),
inference(superposition,[],[f24,f2985]) ).
fof(f3028,plain,
( ! [X0] :
( member(X0,null_class)
| ~ member(X0,x)
| ~ member(X0,x) )
| spl0_79
| ~ spl0_80 ),
inference(superposition,[],[f23,f2692]) ).
fof(f3029,plain,
( ! [X0] :
( ~ member(X0,x)
| member(X0,null_class) )
| spl0_79
| ~ spl0_80 ),
inference(duplicate_literal_removal,[],[f3028]) ).
fof(f3055,plain,
( member(x,null_class)
| spl0_79
| ~ spl0_80 ),
inference(resolution,[],[f3029,f349]) ).
fof(f3077,plain,
( ~ member(x,universal_class)
| spl0_79
| ~ spl0_80 ),
inference(resolution,[],[f3055,f2992]) ).
fof(f3080,plain,
( $false
| spl0_79
| ~ spl0_80 ),
inference(forward_subsumption_resolution,[],[f3077,f219]) ).
fof(f3081,plain,
( spl0_79
| ~ spl0_80 ),
inference(avatar_contradiction_clause,[],[f3080]) ).
fof(f3086,plain,
( member(null_class,null_class)
| ~ spl0_79 ),
inference(superposition,[],[f349,f2669]) ).
fof(f3118,plain,
( ~ member(null_class,universal_class)
| ~ spl0_79 ),
inference(resolution,[],[f3086,f2992]) ).
fof(f3121,plain,
( $false
| ~ spl0_35
| ~ spl0_79 ),
inference(forward_subsumption_resolution,[],[f3118,f613]) ).
fof(f3122,plain,
( ~ spl0_35
| ~ spl0_79 ),
inference(avatar_contradiction_clause,[],[f3121]) ).
cnf(s138,plain,
~ spl0_9,
inference(sat_conversion,[],[f230]) ).
cnf(s387,plain,
( spl0_9
| spl0_35 ),
inference(sat_conversion,[],[f614]) ).
cnf(s1464,plain,
( spl0_79
| spl0_80 ),
inference(sat_conversion,[],[f2675]) ).
cnf(s1711,plain,
( spl0_79
| ~ spl0_80 ),
inference(sat_conversion,[],[f3081]) ).
cnf(s1744,plain,
( ~ spl0_35
| ~ spl0_79 ),
inference(sat_conversion,[],[f3122]) ).
cnf(s1748,plain,
spl0_35,
inference(rat,[],[s387,s138]) ).
cnf(s1750,plain,
~ spl0_79,
inference(rat,[],[s1744,s1748]) ).
cnf(s1751,plain,
~ spl0_80,
inference(rat,[],[s1711,s1750]) ).
cnf(s1755,plain,
$false,
inference(rat,[],[s1464,s1751,s1750]) ).
fof(f3123,plain,
$false,
inference(avatar_sat_refutation,[],[s1755]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET516-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n011.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 02:02:16 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 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
% 0.16/0.54 % (2949920)Will run a generic schedule for satisfiability detection.
% 0.16/0.54 % (2949928)dis+10_1_sil=32000:sp=arity:random_seed=1170721722:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.54 % (2949926)% WARNING: option uhcvi not known.
% 0.16/0.54 % (2949926)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3651420006:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.54 % (2949925)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2438745287_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.54 % (2949930)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2369952425:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.54 % (2949927)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1074197099:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.54 % (2949929)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1674374450:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.54 % (2949931)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2891642487:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.54 % (2949928)Instruction limit reached!
% 0.16/0.54 % (2949928)------------------------------
% 0.16/0.54 % (2949928)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.54 % (2949928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.54 % (2949928)CaDiCaL version: 2.1.3
% 0.16/0.54 % (2949928)Termination reason: Instruction limit
% 0.16/0.54 % (2949928)Termination phase: Saturation
% 0.16/0.54 % (2949928)Time elapsed: 0.037 s
% 0.16/0.54 % (2949928)Peak memory usage: 12 MB
% 0.16/0.54 % (2949928)Instructions burned: 105 (million)
% 0.16/0.54 % (2949939)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3558921153:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.16/0.54 % (2949929)Instruction limit reached!
% 0.16/0.54 % (2949929)------------------------------
% 0.16/0.54 % (2949929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.54 % (2949929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.54 % (2949929)CaDiCaL version: 2.1.3
% 0.16/0.54 % (2949929)Termination reason: Instruction limit
% 0.16/0.54 % (2949929)Termination phase: Saturation
% 0.16/0.54 % (2949929)Time elapsed: 0.068 s
% 0.16/0.54 % (2949929)Peak memory usage: 12 MB
% 0.16/0.54 % (2949929)Instructions burned: 116 (million)
% 0.16/0.54 % (2949927) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2949920-2949927"...
% 0.16/0.54 % (2949927)...printing done.
% 0.16/0.54 % (2949927)Refutation found. Thanks to Tanya!
% 0.16/0.54 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.54 % (2949927)------------------------------
% 0.16/0.54 % (2949927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.54 % (2949927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.54 % (2949927)CaDiCaL version: 2.1.3
% 0.16/0.54 % (2949927)Termination reason: Refutation
% 0.16/0.54 % (2949927)Time elapsed: 0.073 s
% 0.16/0.54 % (2949927)Peak memory usage: 14 MB
% 0.16/0.54 % (2949927)Instructions burned: 110 (million)
% 0.16/0.54 % (2949920)Success in time 0.114 s
% 0.16/0.54 % Vampire exiting
%------------------------------------------------------------------------------