%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU125+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:47:18 PM UTC 2026
% Result : Theorem 3.62s 1.49s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 11 unt; 2 def)
% Number of atoms : 150 ( 10 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 168 ( 62 ~; 63 |; 34 &)
% ( 6 <=>; 3 =>; 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 : 68 ( 0 sgn 57 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
| in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f32,conjecture,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X2,X1) )
=> subset(set_union2(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(f33,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X2,X1) )
=> subset(set_union2(X0,X2),X1) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f40,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f52,plain,
? [X0,X1,X2] :
( ~ subset(set_union2(X0,X2),X1)
& subset(X0,X1)
& subset(X2,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f53,plain,
? [X0,X1,X2] :
( ~ subset(set_union2(X0,X2),X1)
& subset(X0,X1)
& subset(X2,X1) ),
inference(flattening,[],[f52]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(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_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(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_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(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_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f60]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ( ( ( ~ in(sK1(X0,X1,X2),X0)
& ~ in(sK1(X0,X1,X2),X1) )
| ~ in(sK1(X0,X1,X2),X2) )
& ( in(sK1(X0,X1,X2),X0)
| in(sK1(X0,X1,X2),X1)
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f61]) ).
fof(f63,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,[],[f40]) ).
fof(f64,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,[],[f63]) ).
fof(f65,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))],[f64]) ).
fof(f75,plain,
( ~ subset(set_union2(sK8,sK10),sK9)
& subset(sK8,sK9)
& subset(sK10,sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10)],[f53]) ).
fof(f84,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f62]) ).
fof(f90,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f91,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f92,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f123,plain,
subset(sK10,sK9),
inference(cnf_transformation,[],[f75]) ).
fof(f124,plain,
subset(sK8,sK9),
inference(cnf_transformation,[],[f75]) ).
fof(f125,plain,
~ subset(set_union2(sK8,sK10),sK9),
inference(cnf_transformation,[],[f75]) ).
fof(f131,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f84]) ).
fof(f162,plain,
in(sK2(set_union2(sK8,sK10),sK9),set_union2(sK8,sK10)),
inference(resolution,[],[f91,f125]) ).
fof(f165,plain,
~ in(sK2(set_union2(sK8,sK10),sK9),sK9),
inference(resolution,[],[f92,f125]) ).
fof(f212,plain,
! [X0] :
( ~ in(X0,sK10)
| in(X0,sK9) ),
inference(resolution,[],[f90,f123]) ).
fof(f213,plain,
! [X0] :
( ~ in(X0,sK8)
| in(X0,sK9) ),
inference(resolution,[],[f90,f124]) ).
fof(f217,plain,
( in(sK2(set_union2(sK8,sK10),sK9),sK10)
| in(sK2(set_union2(sK8,sK10),sK9),sK8) ),
inference(resolution,[],[f131,f162]) ).
fof(f221,definition,
( spl12_3
<=> in(sK2(set_union2(sK8,sK10),sK9),sK8) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
fof(f222,plain,
( in(sK2(set_union2(sK8,sK10),sK9),sK8)
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f224,definition,
( spl12_4
<=> in(sK2(set_union2(sK8,sK10),sK9),sK10) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
fof(f225,plain,
( in(sK2(set_union2(sK8,sK10),sK9),sK10)
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f226,plain,
( spl12_3
| spl12_4 ),
inference(avatar_split_clause,[],[f217,f224,f221]) ).
fof(f227,plain,
( in(sK2(set_union2(sK8,sK10),sK9),sK9)
| ~ spl12_4 ),
inference(resolution,[],[f225,f212]) ).
fof(f230,plain,
( $false
| ~ spl12_4 ),
inference(resolution,[],[f227,f165]) ).
fof(f233,plain,
~ spl12_4,
inference(avatar_contradiction_clause,[],[f230]) ).
fof(f234,plain,
( in(sK2(set_union2(sK8,sK10),sK9),sK9)
| ~ spl12_3 ),
inference(resolution,[],[f222,f213]) ).
fof(f237,plain,
( $false
| ~ spl12_3 ),
inference(resolution,[],[f234,f165]) ).
fof(f240,plain,
~ spl12_3,
inference(avatar_contradiction_clause,[],[f237]) ).
cnf(s3,plain,
( spl12_3
| spl12_4 ),
inference(sat_conversion,[],[f226]) ).
cnf(s4,plain,
~ spl12_4,
inference(sat_conversion,[],[f233]) ).
cnf(s5,plain,
~ spl12_3,
inference(sat_conversion,[],[f240]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s3,s4,s5]) ).
fof(f241,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU125+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 03:42:01 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.62/1.49 % (2234887)Detected formulas, will run a generic FOF schedule.
% 3.62/1.49 % (2234892)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=4154258969:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.62/1.49 % (2234894)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=444591754:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.62/1.49 % (2234895)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1082013133:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.62/1.49 % (2234898)dis-21_1_sil=8000:lcm=predicate:random_seed=272989982: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)
% 3.62/1.49 % (2234896)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3735288599:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.62/1.49 % (2234893)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=1635771424:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.62/1.49 % (2234897)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3132220244:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.62/1.49 % (2234898)First to succeed.
% 3.62/1.49 % (2234898)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2234887"
% 3.62/1.49 % (2234895)Instruction limit reached!
% 3.62/1.49 % (2234895)------------------------------
% 3.62/1.49 % (2234895)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.49 % (2234895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.49 % (2234895)CaDiCaL version: 2.1.3
% 3.62/1.49 % (2234895)Termination reason: Instruction limit
% 3.62/1.49 % (2234895)Termination phase: Saturation
% 3.62/1.49 % (2234895)Time elapsed: 0.069 s
% 3.62/1.49 % (2234895)Peak memory usage: 89 MB
% 3.62/1.49 % (2234895)Instructions burned: 109 (million)
% 3.62/1.49 % (2234896)Instruction limit reached!
% 3.62/1.49 % (2234896)------------------------------
% 3.62/1.49 % (2234896)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.49 % (2234896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.49 % (2234896)CaDiCaL version: 2.1.3
% 3.62/1.49 % (2234896)Termination reason: Instruction limit
% 3.62/1.49 % (2234896)Termination phase: Saturation
% 3.62/1.49 % (2234896)Time elapsed: 0.075 s
% 3.62/1.49 % (2234896)Peak memory usage: 88 MB
% 3.62/1.49 % (2234896)Instructions burned: 121 (million)
% 3.62/1.49 % (2234897)Instruction limit reached!
% 3.62/1.49 % (2234897)------------------------------
% 3.62/1.49 % (2234897)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.49 % (2234897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.49 % (2234897)CaDiCaL version: 2.1.3
% 3.62/1.49 % (2234897)Termination reason: Instruction limit
% 3.62/1.49 % (2234897)Termination phase: Saturation
% 3.62/1.49 % (2234897)Time elapsed: 0.094 s
% 3.62/1.49 % (2234897)Peak memory usage: 89 MB
% 3.62/1.49 % (2234897)Instructions burned: 140 (million)
% 3.62/1.49 % (2234907)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4191559896:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.62/1.49 % (2234906)lrs+10_1_sil=8000:sp=occurrence:random_seed=1740513487:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.62/1.49 % (2234907)Also succeeded, but the first one will report.
% 3.62/1.49 % (2234908)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4217691283:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.62/1.49 % (2234898)Refutation found. Thanks to Tanya!
% 3.62/1.49 % SZS status Theorem for theBenchmark
% 3.62/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.62/1.49 % (2234898)------------------------------
% 3.62/1.49 % (2234898)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.49 % (2234898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.49 % (2234898)CaDiCaL version: 2.1.3
% 3.62/1.49 % (2234898)Termination reason: Refutation
% 3.62/1.49 % (2234898)Time elapsed: 0.005 s
% 3.62/1.49 % (2234898)Peak memory usage: 89 MB
% 3.62/1.49 % (2234898)Instructions burned: 5 (million)
% 3.62/1.49 % (2234898)------------------------------
% 3.62/1.49 % (2234898)------------------------------
% 3.62/1.49 % (2234887)Success in time 0.431 s
% 3.62/1.49 % Vampire exiting
%------------------------------------------------------------------------------