%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU153+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 : n003.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 12:47:27 PM UTC 2026
% Result : Theorem 2.55s 1.33s
% Output : Refutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 8 unt; 0 def)
% Number of atoms : 86 ( 27 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 104 ( 43 ~; 32 |; 27 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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; 2 con; 0-2 aty)
% Number of variables : 50 ( 43 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f32,conjecture,
! [X0,X1] :
~ ( disjoint(singleton(X0),X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f33,negated_conjecture,
~ ! [X0,X1] :
~ ( disjoint(singleton(X0),X1)
& in(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f59,axiom,
! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] :
~ ( in(X2,X0)
& in(X2,X1) ) )
& ~ ( ? [X2] :
( in(X2,X0)
& in(X2,X1) )
& disjoint(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f68,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f82,plain,
! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] :
~ ( in(X2,X0)
& in(X2,X1) ) )
& ~ ( ? [X3] :
( in(X3,X0)
& in(X3,X1) )
& disjoint(X0,X1) ) ),
inference(rectify,[],[f59]) ).
fof(f93,plain,
? [X0,X1] :
( disjoint(singleton(X0),X1)
& in(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f107,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| ? [X2] :
( in(X2,X0)
& in(X2,X1) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X3,X1) )
| ~ disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f82]) ).
fof(f124,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f125,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f124]) ).
fof(f126,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f125]) ).
fof(f153,plain,
( disjoint(singleton(sK8),sK9)
& in(sK8,sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,sK8),skolemize(X1,sK9)],[f93]) ).
fof(f163,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| ( in(sK13(X0,X1),X0)
& in(sK13(X0,X1),X1) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X3,X1) )
| ~ disjoint(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X2,sK13(X0,X1))],[f107]) ).
fof(f175,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f126]) ).
fof(f222,plain,
in(sK8,sK9),
inference(cnf_transformation,[],[f153]) ).
fof(f223,plain,
disjoint(singleton(sK8),sK9),
inference(cnf_transformation,[],[f153]) ).
fof(f255,plain,
! [X3,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X3,X1)
| ~ in(X3,X0) ),
inference(cnf_transformation,[],[f163]) ).
fof(f267,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f68]) ).
fof(f281,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| unordered_pair(X0,X0) != X1 ),
inference(definition_unfolding,[],[f175,f267]) ).
fof(f294,plain,
disjoint(unordered_pair(sK8,sK8),sK9),
inference(definition_unfolding,[],[f223,f267]) ).
fof(f314,plain,
! [X3,X1] :
( in(X3,X1)
| unordered_pair(X3,X3) != X1 ),
inference(equality_resolution,[],[f281]) ).
fof(f315,plain,
! [X3] : in(X3,unordered_pair(X3,X3)),
inference(equality_resolution,[],[f314]) ).
fof(f474,plain,
! [X0] :
( ~ in(X0,unordered_pair(sK8,sK8))
| ~ in(X0,sK9) ),
inference(resolution,[],[f255,f294]) ).
fof(f480,plain,
~ in(sK8,sK9),
inference(resolution,[],[f474,f315]) ).
fof(f484,plain,
$false,
inference(resolution,[],[f480,f222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU153+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n003.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:48:12 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.55/1.33 % (1165557)Detected formulas, will run a generic FOF schedule.
% 2.55/1.33 % (1165568)dis-21_1_sil=8000:lcm=predicate:random_seed=2819835214: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)
% 2.55/1.33 % (1165568)First to succeed.
% 2.55/1.33 % (1165568)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1165557"
% 2.55/1.33 % (1165567)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2225425534:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.55/1.33 % (1165563)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=234231474:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.55/1.33 % (1165566)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3433596470:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.55/1.33 % (1165565)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1267036810:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.55/1.33 % (1165564)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=3285368911:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.55/1.33 % (1165562)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=2999150157:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.55/1.33 % (1165567)Also succeeded, but the first one will report.
% 2.55/1.33 % (1165566)Also succeeded, but the first one will report.
% 2.55/1.33 % (1165565)Also succeeded, but the first one will report.
% 2.55/1.33 % (1165568)Refutation found. Thanks to Tanya!
% 2.55/1.33 % SZS status Theorem for theBenchmark
% 2.55/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.55/1.33 % (1165568)------------------------------
% 2.55/1.33 % (1165568)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.33 % (1165568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.33 % (1165568)CaDiCaL version: 2.1.3
% 2.55/1.33 % (1165568)Termination reason: Refutation
% 2.55/1.33 % (1165568)Time elapsed: 0.003 s
% 2.55/1.33 % (1165568)Peak memory usage: 89 MB
% 2.55/1.33 % (1165568)Instructions burned: 7 (million)
% 2.55/1.33 % (1165568)------------------------------
% 2.55/1.33 % (1165568)------------------------------
% 2.55/1.33 % (1165557)Success in time 0.274 s
% 2.55/1.33 % Vampire exiting
%------------------------------------------------------------------------------