%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU149+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 : n002.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 12:47:25 PM UTC 2026
% Result : Theorem 3.30s 1.34s
% Output : Refutation 3.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 12 unt; 1 def)
% Number of atoms : 94 ( 67 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 107 ( 39 ~; 42 |; 22 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 50 ( 44 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X0
| X3 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f64,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f72,conjecture,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(f73,negated_conjecture,
~ ! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f72]) ).
fof(f101,plain,
? [X0,X1,X2] :
( X0 != X1
& singleton(X0) = unordered_pair(X1,X2) ),
inference(ennf_transformation,[],[f73]) ).
fof(f117,plain,
( sK2 != sK3
& singleton(sK2) = unordered_pair(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f101]) ).
fof(f147,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f148,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(flattening,[],[f147]) ).
fof(f149,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(rectify,[],[f148]) ).
fof(f150,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ( ( ( sK13(X0,X1,X2) != X0
& sK13(X0,X1,X2) != X1 )
| ~ in(sK13(X0,X1,X2),X2) )
& ( sK13(X0,X1,X2) = X0
| sK13(X0,X1,X2) = X1
| in(sK13(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X3,sK13(X0,X1,X2))],[f149]) ).
fof(f184,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f64]) ).
fof(f190,plain,
singleton(sK2) = unordered_pair(sK3,sK4),
inference(cnf_transformation,[],[f117]) ).
fof(f191,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f117]) ).
fof(f244,plain,
! [X2,X0,X1,X4] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f150]) ).
fof(f246,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f150]) ).
fof(f266,plain,
unordered_pair(sK3,sK4) = unordered_pair(sK2,sK2),
inference(definition_unfolding,[],[f190,f184]) ).
fof(f290,definition,
~ sP18(sK2),
introduced(definition,[new_symbols(definition,[sP18])],[inequality_splitting_name_introduction]) ).
fof(f291,plain,
sP18(sK3),
inference(inequality_splitting,[],[f191,f290]) ).
fof(f313,plain,
! [X2,X1,X4] :
( in(X4,X2)
| unordered_pair(X4,X1) != X2 ),
inference(equality_resolution,[],[f246]) ).
fof(f314,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f313]) ).
fof(f317,plain,
! [X0,X1,X4] :
( ~ in(X4,unordered_pair(X0,X1))
| X1 = X4
| X0 = X4 ),
inference(equality_resolution,[],[f244]) ).
fof(f321,plain,
in(sK3,unordered_pair(sK2,sK2)),
inference(superposition,[],[f314,f266]) ).
fof(f329,plain,
( sK2 = sK3
| sK2 = sK3 ),
inference(resolution,[],[f321,f317]) ).
fof(f332,plain,
sK2 = sK3,
inference(duplicate_literal_removal,[],[f329]) ).
fof(f335,plain,
sP18(sK2),
inference(superposition,[],[f291,f332]) ).
fof(f336,plain,
$false,
inference(forward_subsumption_resolution,[],[f335,f290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU149+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % 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 03:48:07 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.30/1.34 % (4128258)Detected formulas, will run a generic FOF schedule.
% 3.30/1.34 % (4128263)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=3128573549:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.30/1.34 % (4128267)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3853707804:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.30/1.34 % (4128266)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1827697525:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.30/1.34 % (4128266)First to succeed.
% 3.30/1.34 % (4128266)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4128258"
% 3.30/1.34 % (4128264)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=470452160:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.30/1.34 % (4128265)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=570324110:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.30/1.34 % (4128267)Also succeeded, but the first one will report.
% 3.30/1.34 % (4128268)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=261880010:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.30/1.34 % (4128269)dis-21_1_sil=8000:lcm=predicate:random_seed=4186779158: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)
% 3.30/1.34 % (4128268)Also succeeded, but the first one will report.
% 3.30/1.34 % (4128269)Instruction limit reached!
% 3.30/1.34 % (4128269)------------------------------
% 3.30/1.34 % (4128269)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.30/1.34 % (4128269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/1.34 % (4128269)CaDiCaL version: 2.1.3
% 3.30/1.34 % (4128269)Termination reason: Instruction limit
% 3.30/1.34 % (4128269)Termination phase: Saturation
% 3.30/1.34 % (4128269)Time elapsed: 0.086 s
% 3.30/1.34 % (4128269)Peak memory usage: 89 MB
% 3.30/1.34 % (4128269)Instructions burned: 130 (million)
% 3.30/1.34 % (4128277)lrs+10_1_sil=8000:sp=occurrence:random_seed=69058920:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.30/1.34 % (4128277)Also succeeded, but the first one will report.
% 3.30/1.34 % (4128266)Refutation found. Thanks to Tanya!
% 3.30/1.34 % SZS status Theorem for theBenchmark
% 3.30/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.30/1.34 % (4128266)------------------------------
% 3.30/1.34 % (4128266)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.30/1.34 % (4128266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/1.34 % (4128266)CaDiCaL version: 2.1.3
% 3.30/1.34 % (4128266)Termination reason: Refutation
% 3.30/1.34 % (4128266)Time elapsed: 0.006 s
% 3.30/1.34 % (4128266)Peak memory usage: 89 MB
% 3.30/1.34 % (4128266)Instructions burned: 8 (million)
% 3.30/1.34 % (4128266)------------------------------
% 3.30/1.34 % (4128266)------------------------------
% 3.30/1.34 % (4128258)Success in time 0.399 s
% 3.30/1.34 % Vampire exiting
%------------------------------------------------------------------------------