%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU158+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 : n009.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 12:47:28 PM UTC 2026
% Result : Theorem 2.57s 1.32s
% Output : Refutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 6 unt; 2 def)
% Number of atoms : 70 ( 2 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 62 ( 27 ~; 26 |; 3 &)
% ( 5 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f41,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f67,conjecture,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
fof(f68,negated_conjecture,
~ ! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f67]) ).
fof(f80,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f122,plain,
? [X0,X1] :
( subset(singleton(X0),X1)
<~> in(X0,X1) ),
inference(ennf_transformation,[],[f68]) ).
fof(f175,plain,
! [X0,X1] :
( ( subset(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| ~ subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f186,plain,
? [X0,X1] :
( ( ~ in(X0,X1)
| ~ subset(singleton(X0),X1) )
& ( in(X0,X1)
| subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f122]) ).
fof(f187,plain,
( ( ~ in(sK19,sK20)
| ~ subset(singleton(sK19),sK20) )
& ( in(sK19,sK20)
| subset(singleton(sK19),sK20) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20]),skolemize(X0,sK19),skolemize(X1,sK20)],[f186]) ).
fof(f265,plain,
! [X0,X1] :
( in(X0,X1)
| ~ subset(singleton(X0),X1) ),
inference(cnf_transformation,[],[f175]) ).
fof(f266,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f175]) ).
fof(f300,plain,
( in(sK19,sK20)
| subset(singleton(sK19),sK20) ),
inference(cnf_transformation,[],[f187]) ).
fof(f301,plain,
( ~ in(sK19,sK20)
| ~ subset(singleton(sK19),sK20) ),
inference(cnf_transformation,[],[f187]) ).
fof(f316,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f80]) ).
fof(f351,plain,
! [X0,X1] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ),
inference(definition_unfolding,[],[f266,f316]) ).
fof(f352,plain,
! [X0,X1] :
( ~ subset(unordered_pair(X0,X0),X1)
| in(X0,X1) ),
inference(definition_unfolding,[],[f265,f316]) ).
fof(f368,plain,
( ~ in(sK19,sK20)
| ~ subset(unordered_pair(sK19,sK19),sK20) ),
inference(definition_unfolding,[],[f301,f316]) ).
fof(f369,plain,
( in(sK19,sK20)
| subset(unordered_pair(sK19,sK19),sK20) ),
inference(definition_unfolding,[],[f300,f316]) ).
fof(f477,definition,
( spl24_1
<=> subset(unordered_pair(sK19,sK19),sK20) ),
introduced(definition,[new_symbols(definition,[spl24_1])],[avatar_definition]) ).
fof(f478,plain,
( subset(unordered_pair(sK19,sK19),sK20)
| ~ spl24_1 ),
inference(avatar_component_clause,[],[f477]) ).
fof(f480,definition,
( spl24_2
<=> in(sK19,sK20) ),
introduced(definition,[new_symbols(definition,[spl24_2])],[avatar_definition]) ).
fof(f482,plain,
( spl24_1
| spl24_2 ),
inference(avatar_split_clause,[],[f369,f480,f477]) ).
fof(f483,plain,
( ~ subset(unordered_pair(sK19,sK19),sK20)
| spl24_1 ),
inference(avatar_component_clause,[],[f477]) ).
fof(f485,plain,
( ~ spl24_1
| ~ spl24_2 ),
inference(avatar_split_clause,[],[f368,f480,f477]) ).
fof(f511,plain,
( ~ in(sK19,sK20)
| spl24_1 ),
inference(resolution,[],[f351,f483]) ).
fof(f514,plain,
( ~ spl24_2
| spl24_1 ),
inference(avatar_split_clause,[],[f511,f477,f480]) ).
fof(f523,plain,
( in(sK19,sK20)
| ~ spl24_1 ),
inference(resolution,[],[f352,f478]) ).
fof(f524,plain,
( spl24_2
| ~ spl24_1 ),
inference(avatar_split_clause,[],[f523,f477,f480]) ).
cnf(s1,plain,
( spl24_1
| spl24_2 ),
inference(sat_conversion,[],[f482]) ).
cnf(s2,plain,
( ~ spl24_1
| ~ spl24_2 ),
inference(sat_conversion,[],[f485]) ).
cnf(s3,plain,
( spl24_1
| ~ spl24_2 ),
inference(sat_conversion,[],[f514]) ).
cnf(s4,plain,
( ~ spl24_1
| spl24_2 ),
inference(sat_conversion,[],[f524]) ).
cnf(s5,plain,
spl24_1,
inference(rat,[],[s1,s3]) ).
cnf(s6,plain,
spl24_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6,s5]) ).
fof(f525,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU158+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n009.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 03:48:00 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.57/1.32 % (2643115)Detected formulas, will run a generic FOF schedule.
% 2.57/1.32 % (2643126)dis-21_1_sil=8000:lcm=predicate:random_seed=11683819: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)
% 2.57/1.32 % (2643126)First to succeed.
% 2.57/1.32 % (2643126)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2643115"
% 2.57/1.32 % (2643120)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=1901116507:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.57/1.32 % (2643124)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4160819312:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.57/1.32 % (2643123)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=616113328:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.57/1.32 % (2643122)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=1904876334:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.57/1.32 % (2643121)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=751551542:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.57/1.32 % (2643124)Also succeeded, but the first one will report.
% 2.57/1.32 % (2643125)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4004585551:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.57/1.32 % (2643123)Also succeeded, but the first one will report.
% 2.57/1.32 % (2643125)Also succeeded, but the first one will report.
% 2.57/1.32 % (2643126)Refutation found. Thanks to Tanya!
% 2.57/1.32 % SZS status Theorem for theBenchmark
% 2.57/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.57/1.32 % (2643126)------------------------------
% 2.57/1.32 % (2643126)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.32 % (2643126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.32 % (2643126)CaDiCaL version: 2.1.3
% 2.57/1.32 % (2643126)Termination reason: Refutation
% 2.57/1.32 % (2643126)Time elapsed: 0.004 s
% 2.57/1.32 % (2643126)Peak memory usage: 89 MB
% 2.57/1.32 % (2643126)Instructions burned: 8 (million)
% 2.57/1.32 % (2643126)------------------------------
% 2.57/1.32 % (2643126)------------------------------
% 2.57/1.32 % (2643115)Success in time 0.277 s
% 2.57/1.32 % Vampire exiting
%------------------------------------------------------------------------------