%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET603+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:41:18 PM UTC 2026
% Result : Theorem 3.67s 1.49s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 16 unt; 5 def)
% Number of atoms : 141 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 139 ( 57 ~; 56 |; 16 &)
% ( 9 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 50 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( member(X2,X0)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f6,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f9,conjecture,
! [X0] : difference(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th74) ).
fof(f10,negated_conjecture,
~ ! [X0] : difference(X0,empty_set) = X0,
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f13,plain,
? [X0] : difference(X0,empty_set) != X0,
inference(ennf_transformation,[],[f10]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f19,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f18]) ).
fof(f23,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,[],[f12]) ).
fof(f24,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,[],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f24]) ).
fof(f26,plain,
sK3 != difference(sK3,empty_set),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f13]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f31,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f35,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f41,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f42,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f44,plain,
sK3 != difference(sK3,empty_set),
inference(cnf_transformation,[],[f26]) ).
fof(f49,definition,
! [X0,X1] :
( sQ4_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ4_eqProxy])],[equality_proxy_definition]) ).
fof(f52,plain,
! [X0,X1] :
( sQ4_eqProxy(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(equality_proxy_replacement,[],[f35,f49]) ).
fof(f55,plain,
~ sQ4_eqProxy(sK3,difference(sK3,empty_set)),
inference(equality_proxy_replacement,[],[f44,f49]) ).
fof(f63,plain,
( ~ subset(sK3,difference(sK3,empty_set))
| ~ subset(difference(sK3,empty_set),sK3) ),
inference(resolution,[],[f52,f55]) ).
fof(f66,definition,
( spl5_1
<=> subset(sK3,difference(sK3,empty_set)) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f67,plain,
( ~ subset(sK3,difference(sK3,empty_set))
| spl5_1 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f69,definition,
( spl5_2
<=> subset(difference(sK3,empty_set),sK3) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f70,plain,
( ~ subset(difference(sK3,empty_set),sK3)
| spl5_2 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,plain,
( ~ spl5_2
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f63,f66,f69]) ).
fof(f73,plain,
( ~ member(sK2(sK3,difference(sK3,empty_set)),difference(sK3,empty_set))
| spl5_1 ),
inference(resolution,[],[f67,f42]) ).
fof(f74,plain,
( member(sK2(sK3,difference(sK3,empty_set)),sK3)
| spl5_1 ),
inference(resolution,[],[f67,f41]) ).
fof(f77,plain,
( ~ member(sK2(sK3,difference(sK3,empty_set)),sK3)
| member(sK2(sK3,difference(sK3,empty_set)),empty_set)
| spl5_1 ),
inference(resolution,[],[f31,f73]) ).
fof(f79,definition,
( spl5_3
<=> member(sK2(sK3,difference(sK3,empty_set)),empty_set) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f80,plain,
( member(sK2(sK3,difference(sK3,empty_set)),empty_set)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,definition,
( spl5_4
<=> member(sK2(sK3,difference(sK3,empty_set)),sK3) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f83,plain,
( ~ member(sK2(sK3,difference(sK3,empty_set)),sK3)
| spl5_4 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f84,plain,
( spl5_3
| ~ spl5_4
| spl5_1 ),
inference(avatar_split_clause,[],[f77,f66,f82,f79]) ).
fof(f85,plain,
( $false
| spl5_1
| spl5_4 ),
inference(resolution,[],[f83,f74]) ).
fof(f86,plain,
( spl5_1
| spl5_4 ),
inference(avatar_contradiction_clause,[],[f85]) ).
fof(f87,plain,
( $false
| ~ spl5_3 ),
inference(resolution,[],[f80,f32]) ).
fof(f88,plain,
~ spl5_3,
inference(avatar_contradiction_clause,[],[f87]) ).
fof(f89,plain,
( ~ member(sK2(difference(sK3,empty_set),sK3),sK3)
| spl5_2 ),
inference(resolution,[],[f70,f42]) ).
fof(f90,plain,
( member(sK2(difference(sK3,empty_set),sK3),difference(sK3,empty_set))
| spl5_2 ),
inference(resolution,[],[f70,f41]) ).
fof(f91,plain,
( member(sK2(difference(sK3,empty_set),sK3),sK3)
| spl5_2 ),
inference(resolution,[],[f90,f30]) ).
fof(f93,plain,
( $false
| spl5_2 ),
inference(resolution,[],[f91,f89]) ).
fof(f94,plain,
spl5_2,
inference(avatar_contradiction_clause,[],[f93]) ).
cnf(s2,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f72]) ).
cnf(s3,plain,
( spl5_1
| spl5_3
| ~ spl5_4 ),
inference(sat_conversion,[],[f84]) ).
cnf(s4,plain,
( spl5_1
| spl5_4 ),
inference(sat_conversion,[],[f86]) ).
cnf(s5,plain,
~ spl5_3,
inference(sat_conversion,[],[f88]) ).
cnf(s6,plain,
spl5_2,
inference(sat_conversion,[],[f94]) ).
cnf(s7,plain,
( spl5_1
| ~ spl5_4 ),
inference(rat,[],[s3,s5]) ).
cnf(s8,plain,
~ spl5_1,
inference(rat,[],[s2,s6]) ).
cnf(s9,plain,
spl5_4,
inference(rat,[],[s4,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s7,s9,s8]) ).
fof(f95,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET603+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n006.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 02:17:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.67/1.49 % (3523512)Detected formulas, will run a generic FOF schedule.
% 3.67/1.49 % (3523520)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=972487904:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.67/1.49 % (3523520)Refutation not found, incomplete strategy
% 3.67/1.49 % (3523520)------------------------------
% 3.67/1.49 % (3523520)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.49 % (3523520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.49 % (3523520)CaDiCaL version: 2.1.3
% 3.67/1.49 % (3523520)Termination reason: Refutation not found, incomplete strategy
% 3.67/1.49 % (3523520)Time elapsed: 0.001 s
% 3.67/1.49 % (3523520)Peak memory usage: 88 MB
% 3.67/1.49 % (3523521)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3532723246:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.67/1.49 % (3523518)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=2790554864:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.67/1.49 % (3523523)dis-21_1_sil=8000:lcm=predicate:random_seed=1467068844: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)
% 3.67/1.49 % (3523519)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=292766686:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.67/1.49 % (3523517)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=801812247:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.67/1.49 % (3523522)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=874492712:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.67/1.49 % (3523523)First to succeed.
% 3.67/1.49 % (3523523)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3523512"
% 3.67/1.49 % (3523521)Also succeeded, but the first one will report.
% 3.67/1.49 % (3523522)Instruction limit reached!
% 3.67/1.49 % (3523522)------------------------------
% 3.67/1.49 % (3523522)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.49 % (3523522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.49 % (3523522)CaDiCaL version: 2.1.3
% 3.67/1.49 % (3523522)Termination reason: Instruction limit
% 3.67/1.49 % (3523522)Termination phase: Saturation
% 3.67/1.49 % (3523522)Time elapsed: 0.090 s
% 3.67/1.49 % (3523522)Peak memory usage: 88 MB
% 3.67/1.49 % (3523522)Instructions burned: 140 (million)
% 3.67/1.49 % (3523520)------------------------------
% 3.67/1.49 % (3523520)------------------------------
% 3.67/1.49 % (3523532)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3739175028:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.67/1.49 % (3523531)lrs+10_1_sil=8000:sp=occurrence:random_seed=3241469734:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.67/1.49 % (3523532)Refutation not found, incomplete strategy
% 3.67/1.49 % (3523532)------------------------------
% 3.67/1.49 % (3523532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.49 % (3523532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.49 % (3523532)CaDiCaL version: 2.1.3
% 3.67/1.49 % (3523532)Termination reason: Refutation not found, incomplete strategy
% 3.67/1.49 % (3523532)Time elapsed: 0.002 s
% 3.67/1.49 % (3523532)Peak memory usage: 89 MB
% 3.67/1.49 % (3523532)Instructions burned: 3 (million)
% 3.67/1.49 % (3523531)Also succeeded, but the first one will report.
% 3.67/1.49 % (3523523)Refutation found. Thanks to Tanya!
% 3.67/1.49 % SZS status Theorem for theBenchmark
% 3.67/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.49 % (3523523)------------------------------
% 3.67/1.49 % (3523523)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.49 % (3523523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.49 % (3523523)CaDiCaL version: 2.1.3
% 3.67/1.49 % (3523523)Termination reason: Refutation
% 3.67/1.49 % (3523523)Time elapsed: 0.003 s
% 3.67/1.49 % (3523523)Peak memory usage: 89 MB
% 3.67/1.49 % (3523523)Instructions burned: 2 (million)
% 3.67/1.49 % (3523523)------------------------------
% 3.67/1.49 % (3523523)------------------------------
% 3.67/1.49 % (3523512)Success in time 0.439 s
% 3.67/1.49 % Vampire exiting
%------------------------------------------------------------------------------