%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU129+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 12:47:20 PM UTC 2026
% Result : Theorem 2.33s 0.92s
% Output : Refutation 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 10 unt; 2 def)
% Number of atoms : 164 ( 10 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 184 ( 70 ~; 72 |; 31 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 89 ( 0 sgn 81 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f8,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f23,axiom,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(f24,axiom,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X0,X2) )
=> subset(X0,set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
fof(f26,axiom,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X1,X2) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f27,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
fof(f28,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f45,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f50,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X1)
| ~ subset(X0,X2) ),
inference(ennf_transformation,[],[f24]) ).
fof(f51,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X1)
| ~ subset(X0,X2) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(ennf_transformation,[],[f26]) ).
fof(f53,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
? [X0,X1,X2] :
( ~ subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
& subset(X0,X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f72,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f73,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK2(X0,X1),X1)
& in(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f73]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f76]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK3(X0,X1,X2),X0)
| ~ in(sK3(X0,X1,X2),X1)
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( in(sK3(X0,X1,X2),X0)
& in(sK3(X0,X1,X2),X1) )
| in(sK3(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f77]) ).
fof(f82,plain,
( ~ subset(set_intersection2(sK6,sK8),set_intersection2(sK7,sK8))
& subset(sK6,sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8)],[f54]) ).
fof(f100,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f101,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f102,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f78]) ).
fof(f120,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[],[f23]) ).
fof(f121,plain,
! [X2,X0,X1] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X1)
| ~ subset(X0,X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f123,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f124,plain,
subset(sK6,sK7),
inference(cnf_transformation,[],[f82]) ).
fof(f125,plain,
~ subset(set_intersection2(sK6,sK8),set_intersection2(sK7,sK8)),
inference(cnf_transformation,[],[f82]) ).
fof(f147,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f102]) ).
fof(f229,plain,
( ~ subset(set_intersection2(sK6,sK8),sK7)
| ~ subset(set_intersection2(sK6,sK8),sK8) ),
inference(resolution,[],[f121,f125]) ).
fof(f232,definition,
( spl12_3
<=> subset(set_intersection2(sK6,sK8),sK8) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
fof(f233,plain,
( ~ subset(set_intersection2(sK6,sK8),sK8)
| spl12_3 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f235,definition,
( spl12_4
<=> subset(set_intersection2(sK6,sK8),sK7) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
fof(f236,plain,
( ~ subset(set_intersection2(sK6,sK8),sK7)
| spl12_4 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f237,plain,
( ~ spl12_3
| ~ spl12_4 ),
inference(avatar_split_clause,[],[f229,f235,f232]) ).
fof(f239,plain,
( ~ in(sK2(set_intersection2(sK6,sK8),sK8),sK8)
| spl12_3 ),
inference(resolution,[],[f233,f101]) ).
fof(f240,plain,
( in(sK2(set_intersection2(sK6,sK8),sK8),set_intersection2(sK6,sK8))
| spl12_3 ),
inference(resolution,[],[f233,f100]) ).
fof(f251,plain,
( in(sK2(set_intersection2(sK6,sK8),sK8),sK8)
| spl12_3 ),
inference(resolution,[],[f240,f147]) ).
fof(f261,plain,
( $false
| spl12_3 ),
inference(resolution,[],[f251,f239]) ).
fof(f264,plain,
spl12_3,
inference(avatar_contradiction_clause,[],[f261]) ).
fof(f265,plain,
( ! [X0] :
( ~ subset(set_intersection2(sK6,sK8),X0)
| ~ subset(X0,sK7) )
| spl12_4 ),
inference(resolution,[],[f236,f123]) ).
fof(f269,plain,
( ~ subset(sK6,sK7)
| spl12_4 ),
inference(resolution,[],[f265,f120]) ).
fof(f276,plain,
( $false
| spl12_4 ),
inference(resolution,[],[f269,f124]) ).
fof(f280,plain,
spl12_4,
inference(avatar_contradiction_clause,[],[f276]) ).
cnf(s3,plain,
( ~ spl12_3
| ~ spl12_4 ),
inference(sat_conversion,[],[f237]) ).
cnf(s4,plain,
spl12_3,
inference(sat_conversion,[],[f264]) ).
cnf(s5,plain,
spl12_4,
inference(sat_conversion,[],[f280]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s3,s5,s4]) ).
fof(f281,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU129+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Mon Sep 28 03:39:04 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.32 Running first-order theorem proving
% 0.07/0.32 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
% 2.33/0.92 % (2994427)Detected formulas, will run a generic FOF schedule.
% 2.33/0.92 % (2994436)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4156310580:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.33/0.92 % (2994437)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2542022090:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.33/0.92 % (2994433)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=231695566:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.33/0.92 % (2994435)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2807344798:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.33/0.92 % (2994438)dis-21_1_sil=8000:lcm=predicate:random_seed=3487894740: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)
% 2.33/0.92 % (2994432)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=1450677712:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.33/0.92 % (2994434)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=1862848202:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.33/0.92 % (2994438)First to succeed.
% 2.33/0.92 % (2994438)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2994427"
% 2.33/0.92 % (2994435)Also succeeded, but the first one will report.
% 2.33/0.92 % (2994436)Also succeeded, but the first one will report.
% 2.33/0.92 % (2994437)Instruction limit reached!
% 2.33/0.92 % (2994437)------------------------------
% 2.33/0.92 % (2994437)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.33/0.92 % (2994437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.92 % (2994437)CaDiCaL version: 2.1.3
% 2.33/0.92 % (2994437)Termination reason: Instruction limit
% 2.33/0.92 % (2994437)Termination phase: Saturation
% 2.33/0.92 % (2994437)Time elapsed: 0.053 s
% 2.33/0.92 % (2994437)Peak memory usage: 89 MB
% 2.33/0.92 % (2994437)Instructions burned: 141 (million)
% 2.33/0.92 % (2994438)Refutation found. Thanks to Tanya!
% 2.33/0.92 % SZS status Theorem for theBenchmark
% 2.33/0.92 % SZS output start Proof for theBenchmark
% See solution above
% 2.33/0.92 % (2994438)------------------------------
% 2.33/0.92 % (2994438)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.33/0.92 % (2994438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.92 % (2994438)CaDiCaL version: 2.1.3
% 2.33/0.92 % (2994438)Termination reason: Refutation
% 2.33/0.92 % (2994438)Time elapsed: 0.003 s
% 2.33/0.92 % (2994438)Peak memory usage: 89 MB
% 2.33/0.92 % (2994438)Instructions burned: 6 (million)
% 2.33/0.92 % (2994438)------------------------------
% 2.33/0.92 % (2994438)------------------------------
% 2.33/0.92 % (2994427)Success in time 0.298 s
% 2.33/0.92 % Vampire exiting
%------------------------------------------------------------------------------