%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU230+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 12:52:30 PM UTC 2026
% Result : Theorem 0.18s 0.51s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 14 unt; 0 def)
% Number of atoms : 120 ( 40 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 149 ( 57 ~; 59 |; 29 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-3 aty)
% Number of variables : 61 ( 55 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f21,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f27,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(f143,conjecture,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f144,negated_conjecture,
~ ! [X0] : in(X0,succ(X0)),
inference(negated_conjecture,[status(cth)],[f143]) ).
fof(f233,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f366,plain,
? [X0] : ~ in(X0,succ(X0)),
inference(ennf_transformation,[],[f144]) ).
fof(f533,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,[],[f21]) ).
fof(f534,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,[],[f533]) ).
fof(f535,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK24(X0,X1) != X0
| ~ in(sK24(X0,X1),X1) )
& ( sK24(X0,X1) = X0
| in(sK24(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(X2,sK24(X0,X1))],[f534]) ).
fof(f550,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,[],[f27]) ).
fof(f551,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,[],[f550]) ).
fof(f552,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,[],[f551]) ).
fof(f553,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ( ( ( ~ in(sK30(X0,X1,X2),X0)
& ~ in(sK30(X0,X1,X2),X1) )
| ~ in(sK30(X0,X1,X2),X2) )
& ( in(sK30(X0,X1,X2),X0)
| in(sK30(X0,X1,X2),X1)
| in(sK30(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,[sK30]),skolemize(X3,sK30(X0,X1,X2))],[f552]) ).
fof(f621,plain,
~ in(sK75,succ(sK75)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(X0,sK75)],[f366]) ).
fof(f737,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f18]) ).
fof(f750,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f535]) ).
fof(f774,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f553]) ).
fof(f968,plain,
~ in(sK75,succ(sK75)),
inference(cnf_transformation,[],[f621]) ).
fof(f1110,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f233]) ).
fof(f1147,plain,
! [X0] : succ(X0) = set_union2(X0,unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f737,f1110]) ).
fof(f1179,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| unordered_pair(X0,X0) != X1 ),
inference(definition_unfolding,[],[f750,f1110]) ).
fof(f1241,plain,
~ in(sK75,set_union2(sK75,unordered_pair(sK75,sK75))),
inference(definition_unfolding,[],[f968,f1147]) ).
fof(f1324,plain,
! [X3,X1] :
( in(X3,X1)
| unordered_pair(X3,X3) != X1 ),
inference(equality_resolution,[],[f1179]) ).
fof(f1325,plain,
! [X3] : in(X3,unordered_pair(X3,X3)),
inference(equality_resolution,[],[f1324]) ).
fof(f1338,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f774]) ).
fof(f2080,plain,
~ in(sK75,unordered_pair(sK75,sK75)),
inference(resolution,[],[f1338,f1241]) ).
fof(f2088,plain,
$false,
inference(forward_subsumption_resolution,[],[f2080,f1325]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU230+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n001.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % 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 04:18:32 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.51 % (11173)Will run a generic schedule for satisfiability detection.
% 0.18/0.51 % (11178)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1376353137_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.51 % (11179)% WARNING: option uhcvi not known.
% 0.18/0.51 % (11179)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=496144181:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.51 % (11180)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=509640822:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.51 % (11181)dis+10_1_sil=32000:sp=arity:random_seed=2869209304:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.51 % (11182)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=378123042:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.51 % (11183)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1122190885:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.51 % (11184)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=272390474:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.51 % TRYING [1]
% 0.18/0.51 % TRYING [2]
% 0.18/0.51 % (11181) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-11173-11181"...
% 0.18/0.51 % (11181)...printing done.
% 0.18/0.51 % (11181)Refutation found. Thanks to Tanya!
% 0.18/0.51 % SZS status Theorem for theBenchmark
% 0.18/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.51 % (11181)------------------------------
% 0.18/0.51 % (11181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.51 % (11181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.51 % (11181)CaDiCaL version: 2.1.3
% 0.18/0.51 % (11181)Termination reason: Refutation
% 0.18/0.51 % (11181)Time elapsed: 0.027 s
% 0.18/0.51 % (11181)Peak memory usage: 13 MB
% 0.18/0.51 % (11181)Instructions burned: 43 (million)
% 0.18/0.51 % (11173)Success in time 0.083 s
% 0.18/0.51 % Vampire exiting
%------------------------------------------------------------------------------