%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU230+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:47:53 PM UTC 2026
% Result : Theorem 3.49s 1.45s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 11 unt; 0 def)
% Number of atoms : 114 ( 35 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 145 ( 55 ~; 57 |; 29 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-3 aty)
% Number of variables : 55 ( 49 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f7,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f8,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
| in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f28,conjecture,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f29,negated_conjecture,
~ ! [X0] : in(X0,succ(X0)),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f52,plain,
? [X0] : ~ in(X0,succ(X0)),
inference(ennf_transformation,[],[f29]) ).
fof(f59,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(f60,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,[],[f59]) ).
fof(f61,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))],[f60]) ).
fof(f62,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,[],[f8]) ).
fof(f63,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,[],[f62]) ).
fof(f64,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,[],[f63]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ( ( ( ~ in(sK1(X0,X1,X2),X0)
& ~ in(sK1(X0,X1,X2),X1) )
| ~ in(sK1(X0,X1,X2),X2) )
& ( in(sK1(X0,X1,X2),X0)
| in(sK1(X0,X1,X2),X1)
| in(sK1(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,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f64]) ).
fof(f77,plain,
~ in(sK13,succ(sK13)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X0,sK13)],[f52]) ).
fof(f84,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f86,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f61]) ).
fof(f90,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f65]) ).
fof(f124,plain,
~ in(sK13,succ(sK13)),
inference(cnf_transformation,[],[f77]) ).
fof(f132,plain,
~ in(sK13,set_union2(sK13,singleton(sK13))),
inference(definition_unfolding,[],[f124,f84]) ).
fof(f133,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f86]) ).
fof(f134,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f133]) ).
fof(f137,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f90]) ).
fof(f165,plain,
~ in(sK13,singleton(sK13)),
inference(resolution,[],[f137,f132]) ).
fof(f170,plain,
$false,
inference(resolution,[],[f165,f134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU230+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 04:12:11 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 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
% 3.49/1.45 % (3572171)Detected formulas, will run a generic FOF schedule.
% 3.49/1.45 % (3572179)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3180935224:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.49/1.45 % (3572179)Refutation not found, incomplete strategy
% 3.49/1.45 % (3572179)------------------------------
% 3.49/1.45 % (3572179)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.45 % (3572179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.45 % (3572179)CaDiCaL version: 2.1.3
% 3.49/1.45 % (3572179)Termination reason: Refutation not found, incomplete strategy
% 3.49/1.45 % (3572179)Time elapsed: 0.001 s
% 3.49/1.45 % (3572179)Peak memory usage: 88 MB
% 3.49/1.45 % (3572180)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3021348602:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.49/1.45 % (3572181)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=534269102:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.49/1.45 % (3572182)dis-21_1_sil=8000:lcm=predicate:random_seed=2739129723: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)
% 3.49/1.45 % (3572176)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=4193249309:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.49/1.45 % (3572177)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=2747322764:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.49/1.45 % (3572178)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=110088834:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.49/1.45 % (3572182)First to succeed.
% 3.49/1.45 % (3572182)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3572171"
% 3.49/1.45 % (3572181)Also succeeded, but the first one will report.
% 3.49/1.45 % (3572180)Instruction limit reached!
% 3.49/1.45 % (3572180)------------------------------
% 3.49/1.45 % (3572180)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.45 % (3572180)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.45 % (3572180)CaDiCaL version: 2.1.3
% 3.49/1.45 % (3572180)Termination reason: Instruction limit
% 3.49/1.45 % (3572180)Termination phase: Saturation
% 3.49/1.45 % (3572180)Time elapsed: 0.064 s
% 3.49/1.45 % (3572180)Peak memory usage: 88 MB
% 3.49/1.45 % (3572180)Instructions burned: 120 (million)
% 3.49/1.45 % (3572179)------------------------------
% 3.49/1.45 % (3572179)------------------------------
% 3.49/1.45 % (3572190)lrs+10_1_sil=8000:sp=occurrence:random_seed=1557109099:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.49/1.45 % (3572190)Also succeeded, but the first one will report.
% 3.49/1.45 % (3572191)lrs+10_1_sil=32000:urr=on:br=off:random_seed=324471546:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.49/1.45 % (3572191)Also succeeded, but the first one will report.
% 3.49/1.45 % (3572182)Refutation found. Thanks to Tanya!
% 3.49/1.45 % SZS status Theorem for theBenchmark
% 3.49/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.45 % (3572182)------------------------------
% 3.49/1.45 % (3572182)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.45 % (3572182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.45 % (3572182)CaDiCaL version: 2.1.3
% 3.49/1.45 % (3572182)Termination reason: Refutation
% 3.49/1.45 % (3572182)Time elapsed: 0.003 s
% 3.49/1.45 % (3572182)Peak memory usage: 88 MB
% 3.49/1.45 % (3572182)Instructions burned: 3 (million)
% 3.49/1.45 % (3572182)------------------------------
% 3.49/1.45 % (3572182)------------------------------
% 3.49/1.45 % (3572171)Success in time 0.408 s
% 3.49/1.45 % Vampire exiting
%------------------------------------------------------------------------------