%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET096+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:40:05 PM UTC 2026
% Result : Theorem 3.91s 1.55s
% Output : Refutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 17 unt; 1 def)
% Number of atoms : 142 ( 48 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 141 ( 52 ~; 50 |; 30 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 60 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_defn) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subclass(X0,X1)
& subclass(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality) ).
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_defn) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set_defn) ).
fof(f41,axiom,
! [X0] :
( X0 != null_class
=> ? [X1] :
( member(X1,universal_class)
& member(X1,X0)
& disjoint(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity) ).
fof(f44,conjecture,
! [X0,X1] :
( subclass(X0,singleton(X1))
=> ( X0 = null_class
| singleton(X1) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',two_subsets_of_singleton) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] :
( subclass(X0,singleton(X1))
=> ( X0 = null_class
| singleton(X1) = X0 ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f47,plain,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f57,plain,
! [X0] :
( ? [X1] :
( member(X1,universal_class)
& member(X1,X0)
& disjoint(X1,X0) )
| null_class = X0 ),
inference(ennf_transformation,[],[f41]) ).
fof(f60,plain,
? [X0,X1] :
( null_class != X0
& singleton(X1) != X0
& subclass(X0,singleton(X1)) ),
inference(ennf_transformation,[],[f45]) ).
fof(f61,plain,
? [X0,X1] :
( null_class != X0
& singleton(X1) != X0
& subclass(X0,singleton(X1)) ),
inference(flattening,[],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subclass(X0,X1) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f63,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(rectify,[],[f62]) ).
fof(f64,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X0,X1)
| ~ subclass(X1,X0) )
& ( ( subclass(X0,X1)
& subclass(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f66,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X0,X1)
| ~ subclass(X1,X0) )
& ( ( subclass(X0,X1)
& subclass(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| ( X0 != X1
& X0 != X2 ) )
& ( ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| ( X0 != X1
& X0 != X2 ) )
& ( ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f67]) ).
fof(f102,plain,
! [X0] :
( ( member(sK4(X0),universal_class)
& member(sK4(X0),X0)
& disjoint(sK4(X0),X0) )
| null_class = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f57]) ).
fof(f104,plain,
( null_class != sK6
& sK6 != singleton(sK7)
& subclass(sK6,singleton(sK7)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f61]) ).
fof(f105,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f106,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f107,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f111,plain,
! [X0,X1] :
( ~ subclass(X0,X1)
| X0 = X1
| ~ subclass(X1,X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f68]) ).
fof(f117,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f187,plain,
! [X0] :
( member(sK4(X0),X0)
| null_class = X0 ),
inference(cnf_transformation,[],[f102]) ).
fof(f192,plain,
subclass(sK6,singleton(sK7)),
inference(cnf_transformation,[],[f104]) ).
fof(f193,plain,
sK6 != singleton(sK7),
inference(cnf_transformation,[],[f104]) ).
fof(f194,plain,
null_class != sK6,
inference(cnf_transformation,[],[f104]) ).
fof(f243,plain,
( sK6 = singleton(sK7)
| ~ subclass(singleton(sK7),sK6) ),
inference(resolution,[],[f111,f192]) ).
fof(f245,plain,
~ subclass(singleton(sK7),sK6),
inference(forward_subsumption_resolution,[],[f243,f193]) ).
fof(f264,plain,
~ member(sK0(singleton(sK7),sK6),sK6),
inference(resolution,[],[f245,f107]) ).
fof(f265,plain,
member(sK0(singleton(sK7),sK6),singleton(sK7)),
inference(resolution,[],[f245,f106]) ).
fof(f325,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1
| X0 = X1 ),
inference(superposition,[],[f112,f117]) ).
fof(f326,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f325]) ).
fof(f468,plain,
! [X2,X0,X1] :
( ~ subclass(X2,singleton(X0))
| ~ member(X1,X2)
| X0 = X1 ),
inference(resolution,[],[f326,f105]) ).
fof(f470,plain,
sK7 = sK0(singleton(sK7),sK6),
inference(resolution,[],[f326,f265]) ).
fof(f480,plain,
~ member(sK7,sK6),
inference(superposition,[],[f264,f470]) ).
fof(f489,definition,
( spl8_26
<=> member(sK7,sK6) ),
introduced(definition,[new_symbols(definition,[spl8_26])],[avatar_definition]) ).
fof(f491,plain,
( ~ member(sK7,sK6)
| spl8_26 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f498,plain,
~ spl8_26,
inference(avatar_split_clause,[],[f480,f489]) ).
fof(f2019,plain,
! [X0] :
( ~ member(X0,sK6)
| sK7 = X0 ),
inference(resolution,[],[f468,f192]) ).
fof(f2174,plain,
( sK7 = sK4(sK6)
| null_class = sK6 ),
inference(resolution,[],[f2019,f187]) ).
fof(f2176,plain,
sK7 = sK4(sK6),
inference(forward_subsumption_resolution,[],[f2174,f194]) ).
fof(f2205,plain,
( member(sK7,sK6)
| null_class = sK6 ),
inference(superposition,[],[f187,f2176]) ).
fof(f2208,plain,
( null_class = sK6
| spl8_26 ),
inference(forward_subsumption_resolution,[],[f2205,f491]) ).
fof(f2210,plain,
( $false
| spl8_26 ),
inference(forward_subsumption_resolution,[],[f2208,f194]) ).
fof(f2211,plain,
spl8_26,
inference(avatar_contradiction_clause,[],[f2210]) ).
cnf(s19,plain,
~ spl8_26,
inference(sat_conversion,[],[f498]) ).
cnf(s111,plain,
spl8_26,
inference(sat_conversion,[],[f2211]) ).
cnf(s116,plain,
$false,
inference(rat,[],[s19,s111]) ).
fof(f2212,plain,
$false,
inference(avatar_sat_refutation,[],[s116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET096+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n008.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 00:40:40 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.91/1.55 % (1763542)Detected formulas, will run a generic FOF schedule.
% 3.91/1.55 % (1763547)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=890606525:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.91/1.55 % (1763548)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3161949308:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.91/1.55 % (1763551)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3102727440:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.91/1.55 % (1763552)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=149683590:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.91/1.55 % (1763550)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=791952062:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.91/1.55 % (1763549)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4160031739:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.91/1.55 % (1763553)dis-21_1_sil=8000:lcm=predicate:random_seed=4094435079:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.91/1.55 % (1763550)Refutation not found, incomplete strategy
% 3.91/1.55 % (1763550)------------------------------
% 3.91/1.55 % (1763550)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.55 % (1763550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.55 % (1763550)CaDiCaL version: 2.1.3
% 3.91/1.55 % (1763550)Termination reason: Refutation not found, incomplete strategy
% 3.91/1.55 % (1763550)Time elapsed: 0.001 s
% 3.91/1.55 % (1763550)Peak memory usage: 88 MB
% 3.91/1.55 % (1763551)Instruction limit reached!
% 3.91/1.55 % (1763551)------------------------------
% 3.91/1.55 % (1763551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.55 % (1763551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.55 % (1763551)CaDiCaL version: 2.1.3
% 3.91/1.55 % (1763551)Termination reason: Instruction limit
% 3.91/1.55 % (1763551)Termination phase: Saturation
% 3.91/1.55 % (1763551)Time elapsed: 0.051 s
% 3.91/1.55 % (1763551)Peak memory usage: 88 MB
% 3.91/1.55 % (1763551)Instructions burned: 120 (million)
% 3.91/1.55 % (1763552)First to succeed.
% 3.91/1.55 % (1763552)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1763542"
% 3.91/1.55 % (1763553)Instruction limit reached!
% 3.91/1.55 % (1763553)------------------------------
% 3.91/1.55 % (1763553)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.55 % (1763553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.55 % (1763553)CaDiCaL version: 2.1.3
% 3.91/1.55 % (1763553)Termination reason: Instruction limit
% 3.91/1.55 % (1763553)Termination phase: Saturation
% 3.91/1.55 % (1763553)Time elapsed: 0.080 s
% 3.91/1.55 % (1763553)Peak memory usage: 89 MB
% 3.91/1.55 % (1763553)Instructions burned: 129 (million)
% 3.91/1.55 % (1763561)lrs+10_1_sil=8000:sp=occurrence:random_seed=1945956261:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.91/1.55 % (1763562)lrs+10_1_sil=32000:urr=on:br=off:random_seed=966302941:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.91/1.55 % (1763562)Refutation not found, incomplete strategy
% 3.91/1.55 % (1763562)------------------------------
% 3.91/1.55 % (1763562)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.55 % (1763562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.55 % (1763562)CaDiCaL version: 2.1.3
% 3.91/1.55 % (1763562)Termination reason: Refutation not found, incomplete strategy
% 3.91/1.55 % (1763562)Time elapsed: 0.004 s
% 3.91/1.55 % (1763562)Peak memory usage: 89 MB
% 3.91/1.55 % (1763562)Instructions burned: 4 (million)
% 3.91/1.55 % (1763550)------------------------------
% 3.91/1.55 % (1763550)------------------------------
% 3.91/1.55 % (1763552)Refutation found. Thanks to Tanya!
% 3.91/1.55 % SZS status Theorem for theBenchmark
% 3.91/1.55 % SZS output start Proof for theBenchmark
% See solution above
% 3.91/1.55 % (1763552)------------------------------
% 3.91/1.55 % (1763552)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.55 % (1763552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.55 % (1763552)CaDiCaL version: 2.1.3
% 3.91/1.55 % (1763552)Termination reason: Refutation
% 3.91/1.55 % (1763552)Time elapsed: 0.054 s
% 3.91/1.55 % (1763552)Peak memory usage: 91 MB
% 3.91/1.55 % (1763552)Instructions burned: 70 (million)
% 3.91/1.55 % (1763552)------------------------------
% 3.91/1.55 % (1763552)------------------------------
% 3.91/1.55 % (1763542)Success in time 0.463 s
% 3.91/1.55 % Vampire exiting
%------------------------------------------------------------------------------