%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET692+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 : n014.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 2.88s 1.29s
% Output : Refutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 79 ( 6 unt; 6 def)
% Number of atoms : 206 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 212 ( 85 ~; 95 |; 18 &)
% ( 12 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 57 !; 6 ?)
% 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(f4,axiom,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
fof(f12,conjecture,
! [X0,X1] :
( equal_set(X0,intersection(X0,X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI19) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] :
( equal_set(X0,intersection(X0,X1))
<=> subset(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
? [X0,X1] :
( equal_set(X0,intersection(X0,X1))
<~> subset(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f16,plain,
? [X0,X1] :
( ( ~ subset(X0,X1)
| ~ equal_set(X0,intersection(X0,X1)) )
& ( subset(X0,X1)
| equal_set(X0,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f17,plain,
( ( ~ subset(sK0,sK1)
| ~ equal_set(sK0,intersection(sK0,sK1)) )
& ( subset(sK0,sK1)
| equal_set(sK0,intersection(sK0,sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16]) ).
fof(f19,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(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(flattening,[],[f19]) ).
fof(f21,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(f22,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,[],[f21]) ).
fof(f23,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))],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
( subset(sK0,sK1)
| equal_set(sK0,intersection(sK0,sK1)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f27,plain,
( ~ subset(sK0,sK1)
| ~ equal_set(sK0,intersection(sK0,sK1)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f31,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f32,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f33,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f34,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f35,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f38,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f40,definition,
( spl3_1
<=> equal_set(sK0,intersection(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f41,plain,
( equal_set(sK0,intersection(sK0,sK1))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f43,definition,
( spl3_2
<=> subset(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f44,plain,
( subset(sK0,sK1)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f45,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f26,f43,f40]) ).
fof(f46,plain,
( ~ equal_set(sK0,intersection(sK0,sK1))
| spl3_1 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f47,plain,
( ~ subset(sK0,sK1)
| spl3_2 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f48,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f27,f43,f40]) ).
fof(f55,plain,
( ~ subset(sK0,intersection(sK0,sK1))
| ~ subset(intersection(sK0,sK1),sK0)
| spl3_1 ),
inference(resolution,[],[f32,f46]) ).
fof(f57,definition,
( spl3_3
<=> subset(intersection(sK0,sK1),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f58,plain,
( ~ subset(intersection(sK0,sK1),sK0)
| spl3_3 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f60,definition,
( spl3_4
<=> subset(sK0,intersection(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f61,plain,
( ~ subset(sK0,intersection(sK0,sK1))
| spl3_4 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f62,plain,
( ~ spl3_3
| ~ spl3_4
| spl3_1 ),
inference(avatar_split_clause,[],[f55,f40,f60,f57]) ).
fof(f63,plain,
( ~ member(sK2(intersection(sK0,sK1),sK0),sK0)
| spl3_3 ),
inference(resolution,[],[f58,f35]) ).
fof(f64,plain,
( member(sK2(intersection(sK0,sK1),sK0),intersection(sK0,sK1))
| spl3_3 ),
inference(resolution,[],[f58,f34]) ).
fof(f66,plain,
( member(sK2(intersection(sK0,sK1),sK0),sK0)
| spl3_3 ),
inference(resolution,[],[f64,f37]) ).
fof(f68,plain,
( $false
| spl3_3 ),
inference(resolution,[],[f66,f63]) ).
fof(f69,plain,
spl3_3,
inference(avatar_contradiction_clause,[],[f68]) ).
fof(f70,plain,
( ! [X0] :
( member(X0,sK1)
| ~ member(X0,sK0) )
| ~ spl3_2 ),
inference(resolution,[],[f33,f44]) ).
fof(f74,plain,
( ~ member(sK2(sK0,intersection(sK0,sK1)),intersection(sK0,sK1))
| spl3_4 ),
inference(resolution,[],[f61,f35]) ).
fof(f75,plain,
( member(sK2(sK0,intersection(sK0,sK1)),sK0)
| spl3_4 ),
inference(resolution,[],[f61,f34]) ).
fof(f81,plain,
( ~ member(sK2(sK0,intersection(sK0,sK1)),sK0)
| ~ member(sK2(sK0,intersection(sK0,sK1)),sK1)
| spl3_4 ),
inference(resolution,[],[f38,f74]) ).
fof(f83,definition,
( spl3_5
<=> member(sK2(sK0,intersection(sK0,sK1)),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f84,plain,
( ~ member(sK2(sK0,intersection(sK0,sK1)),sK1)
| spl3_5 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,definition,
( spl3_6
<=> member(sK2(sK0,intersection(sK0,sK1)),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f87,plain,
( ~ member(sK2(sK0,intersection(sK0,sK1)),sK0)
| spl3_6 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f88,plain,
( ~ spl3_5
| ~ spl3_6
| spl3_4 ),
inference(avatar_split_clause,[],[f81,f60,f86,f83]) ).
fof(f89,plain,
( ~ member(sK2(sK0,intersection(sK0,sK1)),sK0)
| ~ spl3_2
| spl3_5 ),
inference(resolution,[],[f84,f70]) ).
fof(f90,plain,
( ~ spl3_6
| ~ spl3_2
| spl3_5 ),
inference(avatar_split_clause,[],[f89,f83,f43,f86]) ).
fof(f91,plain,
( $false
| spl3_4
| spl3_6 ),
inference(resolution,[],[f87,f75]) ).
fof(f93,plain,
( spl3_4
| spl3_6 ),
inference(avatar_contradiction_clause,[],[f91]) ).
fof(f94,plain,
( ~ member(sK2(sK0,sK1),sK1)
| spl3_2 ),
inference(resolution,[],[f47,f35]) ).
fof(f95,plain,
( member(sK2(sK0,sK1),sK0)
| spl3_2 ),
inference(resolution,[],[f47,f34]) ).
fof(f97,plain,
( subset(sK0,intersection(sK0,sK1))
| ~ spl3_1 ),
inference(resolution,[],[f41,f31]) ).
fof(f100,plain,
( ! [X0] :
( member(X0,intersection(sK0,sK1))
| ~ member(X0,sK0) )
| ~ spl3_1 ),
inference(resolution,[],[f97,f33]) ).
fof(f109,plain,
( ! [X0] :
( member(X0,sK1)
| ~ member(X0,sK0) )
| ~ spl3_1 ),
inference(resolution,[],[f100,f36]) ).
fof(f112,plain,
( ~ member(sK2(sK0,sK1),sK0)
| ~ spl3_1
| spl3_2 ),
inference(resolution,[],[f109,f94]) ).
fof(f115,plain,
( $false
| ~ spl3_1
| spl3_2 ),
inference(resolution,[],[f112,f95]) ).
fof(f117,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_contradiction_clause,[],[f115]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f45]) ).
cnf(s2,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f48]) ).
cnf(s3,plain,
( spl3_1
| ~ spl3_3
| ~ spl3_4 ),
inference(sat_conversion,[],[f62]) ).
cnf(s4,plain,
spl3_3,
inference(sat_conversion,[],[f69]) ).
cnf(s5,plain,
( spl3_4
| ~ spl3_5
| ~ spl3_6 ),
inference(sat_conversion,[],[f88]) ).
cnf(s6,plain,
( ~ spl3_2
| spl3_5
| ~ spl3_6 ),
inference(sat_conversion,[],[f90]) ).
cnf(s7,plain,
( spl3_4
| spl3_6 ),
inference(sat_conversion,[],[f93]) ).
cnf(s10,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f117]) ).
cnf(s11,plain,
( spl3_1
| ~ spl3_4 ),
inference(rat,[],[s3,s4]) ).
cnf(s12,plain,
spl3_1,
inference(rat,[],[s6,s5,s7,s1,s11]) ).
cnf(s13,plain,
spl3_2,
inference(rat,[],[s10,s12]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s2,s13,s12]) ).
fof(f118,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET692+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n014.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 02:33:46 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 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
% 2.88/1.29 % (1379145)Detected formulas, will run a generic FOF schedule.
% 2.88/1.29 % (1379150)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=4041355905:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.88/1.29 % (1379153)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3439252521:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.88/1.29 % (1379152)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=1368878076:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.88/1.29 % (1379151)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=2569918167:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.88/1.29 % (1379156)dis-21_1_sil=8000:lcm=predicate:random_seed=3300038490: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)
% 2.88/1.29 % (1379154)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2185371449:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.88/1.29 % (1379155)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=138948152:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.88/1.29 % (1379153)Refutation not found, incomplete strategy
% 2.88/1.29 % (1379153)------------------------------
% 2.88/1.29 % (1379153)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.88/1.29 % (1379153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/1.29 % (1379153)CaDiCaL version: 2.1.3
% 2.88/1.29 % (1379153)Termination reason: Refutation not found, incomplete strategy
% 2.88/1.29 % (1379153)Time elapsed: 0.001 s
% 2.88/1.29 % (1379153)Peak memory usage: 88 MB
% 2.88/1.29 % (1379156)First to succeed.
% 2.88/1.29 % (1379155)Also succeeded, but the first one will report.
% 2.88/1.29 % (1379156)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1379145"
% 2.88/1.29 % (1379154)Also succeeded, but the first one will report.
% 2.88/1.29 % (1379153)------------------------------
% 2.88/1.29 % (1379153)------------------------------
% 2.88/1.29 % (1379156)Refutation found. Thanks to Tanya!
% 2.88/1.29 % SZS status Theorem for theBenchmark
% 2.88/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.66/1.49 % (1379156)------------------------------
% 3.66/1.49 % (1379156)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.49 % (1379156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.49 % (1379156)CaDiCaL version: 2.1.3
% 3.66/1.49 % (1379156)Termination reason: Refutation
% 3.66/1.49 % (1379156)Time elapsed: 0.004 s
% 3.66/1.49 % (1379156)Peak memory usage: 89 MB
% 3.66/1.49 % (1379156)Instructions burned: 3 (million)
% 3.66/1.49 % (1379156)------------------------------
% 3.66/1.49 % (1379156)------------------------------
% 3.66/1.49 % (1379145)Success in time 0.439 s
% 3.66/1.49 % Vampire exiting
%------------------------------------------------------------------------------