%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET012+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 : n003.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 12:39:30 PM UTC 2026
% Result : Theorem 2.10s 1.70s
% Output : Refutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 73 ( 8 unt; 6 def)
% Number of atoms : 178 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 172 ( 67 ~; 76 |; 15 &)
% ( 10 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 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 : 59 ( 0 sgn 55 !; 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(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(difference(X1,difference(X1,X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI23) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> equal_set(difference(X1,difference(X1,X0)),X0) ),
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] :
( ~ equal_set(difference(X1,difference(X1,X0)),X0)
& subset(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
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(f18,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f19,plain,
( ~ equal_set(difference(sK1,difference(sK1,sK0)),sK0)
& subset(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15]) ).
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,[],[f18]) ).
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,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(f25,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,[],[f24]) ).
fof(f26,plain,
subset(sK0,sK1),
inference(cnf_transformation,[],[f19]) ).
fof(f27,plain,
~ equal_set(difference(sK1,difference(sK1,sK0)),sK0),
inference(cnf_transformation,[],[f19]) ).
fof(f30,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f31,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f32,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f33,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| member(X0,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f36,plain,
! [X2,X0,X1] :
( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f41,plain,
( ~ subset(difference(sK1,difference(sK1,sK0)),sK0)
| ~ subset(sK0,difference(sK1,difference(sK1,sK0))) ),
inference(resolution,[],[f30,f27]) ).
fof(f43,definition,
( spl3_1
<=> subset(sK0,difference(sK1,difference(sK1,sK0))) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f44,plain,
( ~ subset(sK0,difference(sK1,difference(sK1,sK0)))
| spl3_1 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f46,definition,
( spl3_2
<=> subset(difference(sK1,difference(sK1,sK0)),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f47,plain,
( ~ subset(difference(sK1,difference(sK1,sK0)),sK0)
| spl3_2 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f48,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f41,f46,f43]) ).
fof(f49,plain,
( ~ member(sK2(sK0,difference(sK1,difference(sK1,sK0))),difference(sK1,difference(sK1,sK0)))
| spl3_1 ),
inference(resolution,[],[f44,f33]) ).
fof(f50,plain,
( member(sK2(sK0,difference(sK1,difference(sK1,sK0))),sK0)
| spl3_1 ),
inference(resolution,[],[f44,f32]) ).
fof(f52,plain,
! [X0] :
( member(X0,sK1)
| ~ member(X0,sK0) ),
inference(resolution,[],[f31,f26]) ).
fof(f58,plain,
( ~ member(sK2(sK0,difference(sK1,difference(sK1,sK0))),sK1)
| member(sK2(sK0,difference(sK1,difference(sK1,sK0))),difference(sK1,sK0))
| spl3_1 ),
inference(resolution,[],[f36,f49]) ).
fof(f60,definition,
( spl3_3
<=> member(sK2(sK0,difference(sK1,difference(sK1,sK0))),difference(sK1,sK0)) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f61,plain,
( member(sK2(sK0,difference(sK1,difference(sK1,sK0))),difference(sK1,sK0))
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,definition,
( spl3_4
<=> member(sK2(sK0,difference(sK1,difference(sK1,sK0))),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f64,plain,
( ~ member(sK2(sK0,difference(sK1,difference(sK1,sK0))),sK1)
| spl3_4 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f65,plain,
( spl3_3
| ~ spl3_4
| spl3_1 ),
inference(avatar_split_clause,[],[f58,f43,f63,f60]) ).
fof(f66,plain,
( ~ member(sK2(sK0,difference(sK1,difference(sK1,sK0))),sK0)
| spl3_4 ),
inference(resolution,[],[f52,f64]) ).
fof(f67,plain,
( $false
| spl3_1
| spl3_4 ),
inference(resolution,[],[f66,f50]) ).
fof(f68,plain,
( spl3_1
| spl3_4 ),
inference(avatar_contradiction_clause,[],[f67]) ).
fof(f70,plain,
( ~ member(sK2(sK0,difference(sK1,difference(sK1,sK0))),sK0)
| ~ spl3_3 ),
inference(resolution,[],[f61,f34]) ).
fof(f71,plain,
( $false
| spl3_1
| ~ spl3_3 ),
inference(resolution,[],[f70,f50]) ).
fof(f72,plain,
( spl3_1
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f71]) ).
fof(f73,plain,
( ~ member(sK2(difference(sK1,difference(sK1,sK0)),sK0),sK0)
| spl3_2 ),
inference(resolution,[],[f47,f33]) ).
fof(f74,plain,
( member(sK2(difference(sK1,difference(sK1,sK0)),sK0),difference(sK1,difference(sK1,sK0)))
| spl3_2 ),
inference(resolution,[],[f47,f32]) ).
fof(f76,plain,
( member(sK2(difference(sK1,difference(sK1,sK0)),sK0),sK1)
| spl3_2 ),
inference(resolution,[],[f74,f35]) ).
fof(f77,plain,
( ~ member(sK2(difference(sK1,difference(sK1,sK0)),sK0),difference(sK1,sK0))
| spl3_2 ),
inference(resolution,[],[f74,f34]) ).
fof(f78,plain,
( ~ member(sK2(difference(sK1,difference(sK1,sK0)),sK0),sK1)
| member(sK2(difference(sK1,difference(sK1,sK0)),sK0),sK0)
| spl3_2 ),
inference(resolution,[],[f77,f36]) ).
fof(f80,definition,
( spl3_5
<=> member(sK2(difference(sK1,difference(sK1,sK0)),sK0),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f81,plain,
( member(sK2(difference(sK1,difference(sK1,sK0)),sK0),sK0)
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f83,definition,
( spl3_6
<=> member(sK2(difference(sK1,difference(sK1,sK0)),sK0),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f84,plain,
( ~ member(sK2(difference(sK1,difference(sK1,sK0)),sK0),sK1)
| spl3_6 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f85,plain,
( spl3_5
| ~ spl3_6
| spl3_2 ),
inference(avatar_split_clause,[],[f78,f46,f83,f80]) ).
fof(f86,plain,
( $false
| spl3_2
| spl3_6 ),
inference(resolution,[],[f84,f76]) ).
fof(f88,plain,
( spl3_2
| spl3_6 ),
inference(avatar_contradiction_clause,[],[f86]) ).
fof(f89,plain,
( $false
| spl3_2
| ~ spl3_5 ),
inference(resolution,[],[f81,f73]) ).
fof(f90,plain,
( spl3_2
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[],[f89]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f48]) ).
cnf(s2,plain,
( spl3_1
| spl3_3
| ~ spl3_4 ),
inference(sat_conversion,[],[f65]) ).
cnf(s3,plain,
( spl3_1
| spl3_4 ),
inference(sat_conversion,[],[f68]) ).
cnf(s4,plain,
( spl3_1
| ~ spl3_3 ),
inference(sat_conversion,[],[f72]) ).
cnf(s5,plain,
( spl3_2
| spl3_5
| ~ spl3_6 ),
inference(sat_conversion,[],[f85]) ).
cnf(s6,plain,
( spl3_2
| spl3_6 ),
inference(sat_conversion,[],[f88]) ).
cnf(s7,plain,
( spl3_2
| ~ spl3_5 ),
inference(sat_conversion,[],[f90]) ).
cnf(s8,plain,
spl3_1,
inference(rat,[],[s2,s3,s4]) ).
cnf(s9,plain,
~ spl3_2,
inference(rat,[],[s1,s8]) ).
cnf(s10,plain,
~ spl3_5,
inference(rat,[],[s7,s9]) ).
cnf(s11,plain,
spl3_6,
inference(rat,[],[s6,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s5,s10,s11,s9]) ).
fof(f91,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET012+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.79 % Computer : n003.cluster.edu
% 0.11/0.79 % Model : x86_64 x86_64
% 0.11/0.79 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.79 % Memory : 8046.5625MB
% 0.11/0.79 % OS : Linux 6.8.0-71-generic
% 0.11/0.79 % CPULimit : 300
% 0.11/0.79 % WCLimit : 300
% 0.11/0.79 % DateTime : Mon Sep 28 00:05:13 UTC 2026
% 0.11/0.79 % CPUTime :
% 0.11/0.79 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.83 Running first-order theorem proving
% 0.17/0.83 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
% 2.10/1.70 % (1066132)Detected formulas, will run a generic FOF schedule.
% 2.10/1.70 % (1066140)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=104026163:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.10/1.70 % (1066140)Refutation not found, incomplete strategy
% 2.10/1.70 % (1066140)------------------------------
% 2.10/1.70 % (1066140)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.10/1.70 % (1066140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/1.70 % (1066140)CaDiCaL version: 2.1.3
% 2.10/1.70 % (1066140)Termination reason: Refutation not found, incomplete strategy
% 2.10/1.70 % (1066140)Time elapsed: 0.001 s
% 2.10/1.70 % (1066140)Peak memory usage: 88 MB
% 2.10/1.70 % (1066143)dis-21_1_sil=8000:lcm=predicate:random_seed=1642748043: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)
% 2.10/1.70 % (1066142)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1871710784:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.10/1.70 % (1066138)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=265976470:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.10/1.70 % (1066141)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3230468541:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.10/1.70 % (1066137)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=3090072770:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.10/1.70 % (1066139)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=4239118365:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.10/1.70 % (1066143)First to succeed.
% 2.10/1.70 % (1066143)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1066132"
% 2.10/1.70 % (1066142)Also succeeded, but the first one will report.
% 2.10/1.70 % (1066141)Instruction limit reached!
% 2.10/1.70 % (1066141)------------------------------
% 2.10/1.70 % (1066141)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.10/1.70 % (1066141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/1.70 % (1066141)CaDiCaL version: 2.1.3
% 2.10/1.70 % (1066141)Termination reason: Instruction limit
% 2.10/1.70 % (1066141)Termination phase: Saturation
% 2.10/1.70 % (1066141)Time elapsed: 0.073 s
% 2.10/1.70 % (1066141)Peak memory usage: 88 MB
% 2.10/1.70 % (1066141)Instructions burned: 120 (million)
% 2.10/1.70 % (1066140)------------------------------
% 2.10/1.70 % (1066140)------------------------------
% 2.10/1.70 % (1066151)lrs+10_1_sil=8000:sp=occurrence:random_seed=3496548021:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.10/1.70 % (1066152)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2883440084:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.10/1.70 % (1066143)Refutation found. Thanks to Tanya!
% 2.10/1.70 % SZS status Theorem for theBenchmark
% 2.10/1.70 % SZS output start Proof for theBenchmark
% See solution above
% 3.60/1.90 % (1066143)------------------------------
% 3.60/1.90 % (1066143)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.90 % (1066143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.90 % (1066143)CaDiCaL version: 2.1.3
% 3.60/1.90 % (1066143)Termination reason: Refutation
% 3.60/1.90 % (1066143)Time elapsed: 0.003 s
% 3.60/1.90 % (1066143)Peak memory usage: 89 MB
% 3.60/1.90 % (1066143)Instructions burned: 3 (million)
% 3.60/1.90 % (1066143)------------------------------
% 3.60/1.90 % (1066143)------------------------------
% 3.60/1.90 % (1066132)Success in time 0.429 s
% 3.60/1.90 % Vampire exiting
%------------------------------------------------------------------------------