%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET691+4 : 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 : n005.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 12:41:40 PM UTC 2026
% Result : Theorem 2.46s 1.11s
% Output : Refutation 2.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 6 unt; 2 def)
% Number of atoms : 115 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 119 ( 48 ~; 49 |; 13 &)
% ( 7 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 31 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
fof(f6,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
fof(f12,conjecture,
! [X0] :
( subset(X0,empty_set)
<=> equal_set(X0,empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI16) ).
fof(f13,negated_conjecture,
~ ! [X0] :
( subset(X0,empty_set)
<=> equal_set(X0,empty_set) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f16,plain,
? [X0] :
( subset(X0,empty_set)
<~> equal_set(X0,empty_set) ),
inference(ennf_transformation,[],[f13]) ).
fof(f17,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,[],[f14]) ).
fof(f18,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,[],[f17]) ).
fof(f19,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))],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| ~ equal_set(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f21,plain,
! [X0,X1] :
( ( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| ~ equal_set(X0,X1) ) ),
inference(flattening,[],[f20]) ).
fof(f38,plain,
? [X0] :
( ( ~ equal_set(X0,empty_set)
| ~ subset(X0,empty_set) )
& ( equal_set(X0,empty_set)
| subset(X0,empty_set) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f39,plain,
( ( ~ equal_set(sK3,empty_set)
| ~ subset(sK3,empty_set) )
& ( equal_set(sK3,empty_set)
| subset(sK3,empty_set) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f38]) ).
fof(f41,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f44,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f45,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f54,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f6]) ).
fof(f69,plain,
( equal_set(sK3,empty_set)
| subset(sK3,empty_set) ),
inference(cnf_transformation,[],[f39]) ).
fof(f70,plain,
( ~ equal_set(sK3,empty_set)
| ~ subset(sK3,empty_set) ),
inference(cnf_transformation,[],[f39]) ).
fof(f75,definition,
( spl4_1
<=> subset(sK3,empty_set) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f76,plain,
( ~ subset(sK3,empty_set)
| spl4_1 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f77,plain,
( subset(sK3,empty_set)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f79,definition,
( spl4_2
<=> equal_set(sK3,empty_set) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f80,plain,
( ~ equal_set(sK3,empty_set)
| spl4_2 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f81,plain,
( equal_set(sK3,empty_set)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f69,f79,f75]) ).
fof(f83,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f70,f79,f75]) ).
fof(f85,plain,
( subset(sK3,empty_set)
| ~ spl4_2 ),
inference(resolution,[],[f44,f81]) ).
fof(f86,plain,
( $false
| spl4_1
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f85,f76]) ).
fof(f87,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f86]) ).
fof(f96,plain,
( ~ subset(sK3,empty_set)
| ~ subset(empty_set,sK3)
| spl4_2 ),
inference(resolution,[],[f45,f80]) ).
fof(f97,plain,
( ~ subset(empty_set,sK3)
| ~ spl4_1
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f96,f77]) ).
fof(f99,plain,
( member(sK0(empty_set,sK3),empty_set)
| ~ spl4_1
| spl4_2 ),
inference(resolution,[],[f97,f41]) ).
fof(f100,plain,
( $false
| ~ spl4_1
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f99,f54]) ).
fof(f101,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_contradiction_clause,[],[f100]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f82]) ).
cnf(s2,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f83]) ).
cnf(s3,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f87]) ).
cnf(s4,plain,
( ~ spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f101]) ).
cnf(s5,plain,
spl4_1,
inference(rat,[],[s1,s3]) ).
cnf(s6,plain,
spl4_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6,s5]) ).
fof(f102,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET691+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n005.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 02:33:47 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 2.46/1.11 % (376530)Detected formulas, will run a generic FOF schedule.
% 2.46/1.11 % (376540)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=58544838:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.46/1.11 % (376540)First to succeed.
% 2.46/1.11 % (376540)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-376530"
% 2.46/1.11 % (376539)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=349539190:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.46/1.11 % (376541)dis-21_1_sil=8000:lcm=predicate:random_seed=1636659329: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)
% 2.46/1.11 % (376538)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3429908103:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.46/1.11 % (376535)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=501586447:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.46/1.11 % (376536)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=2083299313:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.46/1.11 % (376537)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=71626201:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.46/1.11 % (376539)Also succeeded, but the first one will report.
% 2.46/1.11 % (376538)Refutation not found, incomplete strategy
% 2.46/1.11 % (376538)------------------------------
% 2.46/1.11 % (376538)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.46/1.11 % (376538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/1.11 % (376538)CaDiCaL version: 2.1.3
% 2.46/1.11 % (376538)Termination reason: Refutation not found, incomplete strategy
% 2.46/1.11 % (376538)Time elapsed: 0.001 s
% 2.46/1.11 % (376538)Peak memory usage: 88 MB
% 2.46/1.11 % (376541)Also succeeded, but the first one will report.
% 2.46/1.11 % (376540)Refutation found. Thanks to Tanya!
% 2.46/1.11 % SZS status Theorem for theBenchmark
% 2.46/1.11 % SZS output start Proof for theBenchmark
% See solution above
% 2.46/1.11 % (376540)------------------------------
% 2.46/1.11 % (376540)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.46/1.11 % (376540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/1.11 % (376540)CaDiCaL version: 2.1.3
% 2.46/1.11 % (376540)Termination reason: Refutation
% 2.46/1.11 % (376540)Time elapsed: 0.002 s
% 2.46/1.11 % (376540)Peak memory usage: 89 MB
% 2.46/1.11 % (376540)Instructions burned: 3 (million)
% 2.46/1.11 % (376540)------------------------------
% 2.46/1.11 % (376540)------------------------------
% 2.46/1.11 % (376530)Success in time 0.298 s
% 2.46/1.11 % Vampire exiting
%------------------------------------------------------------------------------