%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET595+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 12:41:16 PM UTC 2026
% Result : Theorem 2.97s 1.39s
% Output : Refutation 2.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 58 ( 8 unt; 2 def)
% Number of atoms : 150 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 148 ( 56 ~; 62 |; 19 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 70 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
fof(f5,axiom,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X1)
| member(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
fof(f7,axiom,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( member(X0,X2)
& ~ member(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).
fof(f12,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> equal_set(union(difference(X1,X0),X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI27) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> equal_set(union(difference(X1,X0),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(difference(X1,X0),X0),X1)
& subset(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f20,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f21,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f21]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X1)
& ~ member(X0,X2) ) )
& ( member(X0,X1)
| member(X0,X2)
| ~ member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X1)
& ~ member(X0,X2) ) )
& ( member(X0,X1)
| member(X0,X2)
| ~ member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) )
& ( ( member(X0,X2)
& ~ member(X0,X1) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) )
& ( ( member(X0,X2)
& ~ member(X0,X1) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(flattening,[],[f28]) ).
fof(f39,plain,
( ~ equal_set(union(difference(sK4,sK3),sK3),sK4)
& subset(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f19]) ).
fof(f40,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f42,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f43,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f50,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f51,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| member(X0,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f55,plain,
! [X2,X0,X1] :
( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f67,plain,
subset(sK3,sK4),
inference(cnf_transformation,[],[f39]) ).
fof(f68,plain,
~ equal_set(union(difference(sK4,sK3),sK3),sK4),
inference(cnf_transformation,[],[f39]) ).
fof(f74,plain,
! [X0] :
( member(X0,sK4)
| ~ member(X0,sK3) ),
inference(resolution,[],[f40,f67]) ).
fof(f77,plain,
( ~ subset(union(difference(sK4,sK3),sK3),sK4)
| ~ subset(sK4,union(difference(sK4,sK3),sK3)) ),
inference(resolution,[],[f43,f68]) ).
fof(f79,definition,
( spl5_1
<=> subset(sK4,union(difference(sK4,sK3),sK3)) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f81,plain,
( ~ subset(sK4,union(difference(sK4,sK3),sK3))
| spl5_1 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f83,definition,
( spl5_2
<=> subset(union(difference(sK4,sK3),sK3),sK4) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f85,plain,
( ~ subset(union(difference(sK4,sK3),sK3),sK4)
| spl5_2 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f77,f83,f79]) ).
fof(f87,plain,
( ~ member(sK0(sK4,union(difference(sK4,sK3),sK3)),union(difference(sK4,sK3),sK3))
| spl5_1 ),
inference(resolution,[],[f81,f42]) ).
fof(f88,plain,
( member(sK0(sK4,union(difference(sK4,sK3),sK3)),sK4)
| spl5_1 ),
inference(resolution,[],[f81,f41]) ).
fof(f93,plain,
( ~ member(sK0(sK4,union(difference(sK4,sK3),sK3)),difference(sK4,sK3))
| spl5_1 ),
inference(resolution,[],[f87,f51]) ).
fof(f94,plain,
( ~ member(sK0(sK4,union(difference(sK4,sK3),sK3)),sK3)
| spl5_1 ),
inference(resolution,[],[f87,f50]) ).
fof(f95,plain,
( ~ member(sK0(sK4,union(difference(sK4,sK3),sK3)),sK4)
| member(sK0(sK4,union(difference(sK4,sK3),sK3)),sK3)
| spl5_1 ),
inference(resolution,[],[f93,f55]) ).
fof(f96,plain,
( member(sK0(sK4,union(difference(sK4,sK3),sK3)),sK3)
| spl5_1 ),
inference(forward_subsumption_resolution,[],[f95,f88]) ).
fof(f97,plain,
( $false
| spl5_1 ),
inference(forward_subsumption_resolution,[],[f96,f94]) ).
fof(f98,plain,
spl5_1,
inference(avatar_contradiction_clause,[],[f97]) ).
fof(f100,plain,
( ~ member(sK0(union(difference(sK4,sK3),sK3),sK4),sK4)
| spl5_2 ),
inference(resolution,[],[f85,f42]) ).
fof(f101,plain,
( member(sK0(union(difference(sK4,sK3),sK3),sK4),union(difference(sK4,sK3),sK3))
| spl5_2 ),
inference(resolution,[],[f85,f41]) ).
fof(f102,plain,
( ~ member(sK0(union(difference(sK4,sK3),sK3),sK4),sK3)
| spl5_2 ),
inference(resolution,[],[f100,f74]) ).
fof(f104,plain,
( member(sK0(union(difference(sK4,sK3),sK3),sK4),sK3)
| member(sK0(union(difference(sK4,sK3),sK3),sK4),difference(sK4,sK3))
| spl5_2 ),
inference(resolution,[],[f101,f49]) ).
fof(f105,plain,
( member(sK0(union(difference(sK4,sK3),sK3),sK4),difference(sK4,sK3))
| spl5_2 ),
inference(forward_subsumption_resolution,[],[f104,f102]) ).
fof(f107,plain,
( member(sK0(union(difference(sK4,sK3),sK3),sK4),sK4)
| spl5_2 ),
inference(resolution,[],[f105,f54]) ).
fof(f109,plain,
( $false
| spl5_2 ),
inference(forward_subsumption_resolution,[],[f107,f100]) ).
fof(f110,plain,
spl5_2,
inference(avatar_contradiction_clause,[],[f109]) ).
cnf(s1,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f86]) ).
cnf(s2,plain,
spl5_1,
inference(sat_conversion,[],[f98]) ).
cnf(s3,plain,
spl5_2,
inference(sat_conversion,[],[f110]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f111,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET595+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 02:19:09 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.97/1.39 % (2926073)Detected formulas, will run a generic FOF schedule.
% 2.97/1.39 % (2926082)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1821898413:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.97/1.39 % (2926082)Instruction limit reached!
% 2.97/1.39 % (2926082)------------------------------
% 2.97/1.39 % (2926082)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.97/1.39 % (2926082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.97/1.39 % (2926082)CaDiCaL version: 2.1.3
% 2.97/1.39 % (2926082)Termination reason: Instruction limit
% 2.97/1.39 % (2926082)Termination phase: Saturation
% 2.97/1.39 % (2926082)Time elapsed: 0.039 s
% 2.97/1.39 % (2926082)Peak memory usage: 88 MB
% 2.97/1.39 % (2926082)Instructions burned: 121 (million)
% 2.97/1.39 % (2926078)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=2719276977:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.97/1.39 % (2926081)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3919352027:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.97/1.39 % (2926080)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=4050670969:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.97/1.39 % (2926079)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=2940647478:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.97/1.39 % (2926081)Refutation not found, incomplete strategy
% 2.97/1.39 % (2926081)------------------------------
% 2.97/1.39 % (2926081)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.97/1.39 % (2926081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.97/1.39 % (2926081)CaDiCaL version: 2.1.3
% 2.97/1.39 % (2926081)Termination reason: Refutation not found, incomplete strategy
% 2.97/1.39 % (2926081)Time elapsed: 0.002 s
% 2.97/1.39 % (2926081)Peak memory usage: 88 MB
% 2.97/1.39 % (2926081)Instructions burned: 1 (million)
% 2.97/1.39 % (2926083)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3705199628:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.97/1.39 % (2926084)dis-21_1_sil=8000:lcm=predicate:random_seed=3194374055: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)
% 2.97/1.39 % (2926083)First to succeed.
% 2.97/1.39 % (2926083)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2926073"
% 2.97/1.39 % (2926084)Also succeeded, but the first one will report.
% 2.97/1.39 % (2926090)lrs+10_1_sil=8000:sp=occurrence:random_seed=1222083429:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.97/1.39 % (2926083)Refutation found. Thanks to Tanya!
% 2.97/1.39 % SZS status Theorem for theBenchmark
% 2.97/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 2.97/1.39 % (2926083)------------------------------
% 2.97/1.39 % (2926083)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.97/1.39 % (2926083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.97/1.39 % (2926083)CaDiCaL version: 2.1.3
% 2.97/1.39 % (2926083)Termination reason: Refutation
% 2.97/1.39 % (2926083)Time elapsed: 0.003 s
% 2.97/1.39 % (2926083)Peak memory usage: 89 MB
% 2.97/1.39 % (2926083)Instructions burned: 4 (million)
% 2.97/1.39 % (2926083)------------------------------
% 2.97/1.39 % (2926083)------------------------------
% 2.97/1.39 % (2926073)Success in time 0.34 s
% 2.97/1.39 % Vampire exiting
%------------------------------------------------------------------------------