%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU125+1 : 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 : n018.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 3.33s 1.23s
% Output : Refutation 3.33s
% 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(f3,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(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f18,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(f19,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X2,X1) )
=> subset(set_union2(X0,X2),X1) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f29,plain,
? [X0,X1,X2] :
( ~ subset(set_union2(X0,X2),X1)
& subset(X0,X1)
& subset(X2,X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f30,plain,
? [X0,X1,X2] :
( ~ subset(set_union2(X0,X2),X1)
& subset(X0,X1)
& subset(X2,X1) ),
inference(flattening,[],[f29]) ).
fof(f31,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,[],[f3]) ).
fof(f32,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,[],[f31]) ).
fof(f33,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,[],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ( ( ( ~ in(sK0(X0,X1,X2),X0)
& ~ in(sK0(X0,X1,X2),X1) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( in(sK0(X0,X1,X2),X0)
| in(sK0(X0,X1,X2),X1)
| in(sK0(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,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f33]) ).
fof(f35,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,[],[f23]) ).
fof(f36,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,[],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK1(X0,X1),X1)
& in(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f36]) ).
fof(f40,plain,
( ~ subset(set_union2(sK4,sK6),sK5)
& subset(sK4,sK5)
& subset(sK6,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f30]) ).
fof(f43,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f34]) ).
fof(f49,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f50,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f51,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f63,plain,
subset(sK6,sK5),
inference(cnf_transformation,[],[f40]) ).
fof(f64,plain,
subset(sK4,sK5),
inference(cnf_transformation,[],[f40]) ).
fof(f65,plain,
~ subset(set_union2(sK4,sK6),sK5),
inference(cnf_transformation,[],[f40]) ).
fof(f68,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f43]) ).
fof(f83,plain,
in(sK1(set_union2(sK4,sK6),sK5),set_union2(sK4,sK6)),
inference(resolution,[],[f50,f65]) ).
fof(f86,plain,
~ in(sK1(set_union2(sK4,sK6),sK5),sK5),
inference(resolution,[],[f51,f65]) ).
fof(f93,plain,
! [X0] :
( ~ in(X0,sK6)
| in(X0,sK5) ),
inference(resolution,[],[f49,f63]) ).
fof(f94,plain,
! [X0] :
( ~ in(X0,sK4)
| in(X0,sK5) ),
inference(resolution,[],[f49,f64]) ).
fof(f98,plain,
( in(sK1(set_union2(sK4,sK6),sK5),sK6)
| in(sK1(set_union2(sK4,sK6),sK5),sK4) ),
inference(resolution,[],[f68,f83]) ).
fof(f102,definition,
( spl8_1
<=> in(sK1(set_union2(sK4,sK6),sK5),sK4) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f103,plain,
( in(sK1(set_union2(sK4,sK6),sK5),sK4)
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,definition,
( spl8_2
<=> in(sK1(set_union2(sK4,sK6),sK5),sK6) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f106,plain,
( in(sK1(set_union2(sK4,sK6),sK5),sK6)
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f107,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f98,f105,f102]) ).
fof(f108,plain,
( in(sK1(set_union2(sK4,sK6),sK5),sK5)
| ~ spl8_2 ),
inference(resolution,[],[f106,f93]) ).
fof(f111,plain,
( $false
| ~ spl8_2 ),
inference(resolution,[],[f108,f86]) ).
fof(f114,plain,
~ spl8_2,
inference(avatar_contradiction_clause,[],[f111]) ).
fof(f115,plain,
( in(sK1(set_union2(sK4,sK6),sK5),sK5)
| ~ spl8_1 ),
inference(resolution,[],[f103,f94]) ).
fof(f118,plain,
( $false
| ~ spl8_1 ),
inference(resolution,[],[f115,f86]) ).
fof(f121,plain,
~ spl8_1,
inference(avatar_contradiction_clause,[],[f118]) ).
cnf(s1,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f107]) ).
cnf(s2,plain,
~ spl8_2,
inference(sat_conversion,[],[f114]) ).
cnf(s3,plain,
~ spl8_1,
inference(sat_conversion,[],[f121]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f122,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU125+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n018.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 28 03:40:39 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 3.33/1.23 % (2972252)Detected formulas, will run a generic FOF schedule.
% 3.33/1.23 % (2972262)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1911371736:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.33/1.23 % (2972257)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=4292573217:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.33/1.23 % (2972261)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3952258965:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.33/1.23 % (2972260)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=475821902:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.33/1.23 % (2972263)dis-21_1_sil=8000:lcm=predicate:random_seed=1994351526: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)
% 3.33/1.23 % (2972258)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=3244330900:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.33/1.23 % (2972259)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=3152812610:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.33/1.23 % (2972260)Refutation not found, incomplete strategy
% 3.33/1.23 % (2972260)------------------------------
% 3.33/1.23 % (2972260)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.33/1.23 % (2972260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/1.23 % (2972260)CaDiCaL version: 2.1.3
% 3.33/1.23 % (2972260)Termination reason: Refutation not found, incomplete strategy
% 3.33/1.23 % (2972260)Time elapsed: 0.001 s
% 3.33/1.23 % (2972260)Peak memory usage: 88 MB
% 3.33/1.23 % (2972263)First to succeed.
% 3.33/1.23 % (2972263)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2972252"
% 3.33/1.23 % (2972262)Also succeeded, but the first one will report.
% 3.33/1.23 % (2972261)Instruction limit reached!
% 3.33/1.23 % (2972261)------------------------------
% 3.33/1.23 % (2972261)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.33/1.23 % (2972261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/1.23 % (2972261)CaDiCaL version: 2.1.3
% 3.33/1.23 % (2972261)Termination reason: Instruction limit
% 3.33/1.23 % (2972261)Termination phase: Saturation
% 3.33/1.23 % (2972261)Time elapsed: 0.071 s
% 3.33/1.23 % (2972261)Peak memory usage: 88 MB
% 3.33/1.23 % (2972261)Instructions burned: 120 (million)
% 3.33/1.23 % (2972271)lrs+10_1_sil=8000:sp=occurrence:random_seed=1707329443:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.33/1.23 % (2972260)------------------------------
% 3.33/1.23 % (2972260)------------------------------
% 3.33/1.23 % (2972263)Refutation found. Thanks to Tanya!
% 3.33/1.23 % SZS status Theorem for theBenchmark
% 3.33/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 3.33/1.23 % (2972263)------------------------------
% 3.33/1.23 % (2972263)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.33/1.23 % (2972263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/1.23 % (2972263)CaDiCaL version: 2.1.3
% 3.33/1.23 % (2972263)Termination reason: Refutation
% 3.33/1.23 % (2972263)Time elapsed: 0.003 s
% 3.33/1.23 % (2972263)Peak memory usage: 89 MB
% 3.33/1.23 % (2972263)Instructions burned: 3 (million)
% 3.33/1.23 % (2972263)------------------------------
% 3.33/1.23 % (2972263)------------------------------
% 3.33/1.23 % (2972252)Success in time 0.412 s
% 3.33/1.23 % Vampire exiting
%------------------------------------------------------------------------------