%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM386+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 12:15:02 PM UTC 2026
% Result : Theorem 0.60s 0.84s
% Output : Refutation 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 69 ( 10 unt; 3 def)
% Number of atoms : 239 ( 55 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 275 ( 105 ~; 125 |; 35 &)
% ( 9 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 87 ( 0 sgn 76 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f7,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f28,conjecture,
! [X0,X1] :
( in(X0,succ(X1))
<=> ( in(X0,X1)
| X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_ordinal1) ).
fof(f29,negated_conjecture,
~ ! [X0,X1] :
( in(X0,succ(X1))
<=> ( in(X0,X1)
| X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f52,plain,
? [X0,X1] :
( in(X0,succ(X1))
<~> ( in(X0,X1)
| X0 = X1 ) ),
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,
? [X0,X1] :
( ( ( ~ in(X0,X1)
& X0 != X1 )
| ~ in(X0,succ(X1)) )
& ( in(X0,X1)
| X0 = X1
| in(X0,succ(X1)) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f78,plain,
? [X0,X1] :
( ( ( ~ in(X0,X1)
& X0 != X1 )
| ~ in(X0,succ(X1)) )
& ( in(X0,X1)
| X0 = X1
| in(X0,succ(X1)) ) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
( ( ( ~ in(sK13,sK14)
& sK13 != sK14 )
| ~ in(sK13,succ(sK14)) )
& ( in(sK13,sK14)
| sK13 = sK14
| in(sK13,succ(sK14)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X0,sK13),skolemize(X1,sK14)],[f78]) ).
fof(f86,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f87,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f61]) ).
fof(f88,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f61]) ).
fof(f91,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f65]) ).
fof(f92,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f65]) ).
fof(f93,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f65]) ).
fof(f126,plain,
( in(sK13,sK14)
| sK13 = sK14
| in(sK13,succ(sK14)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f127,plain,
( sK13 != sK14
| ~ in(sK13,succ(sK14)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f128,plain,
( ~ in(sK13,sK14)
| ~ in(sK13,succ(sK14)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f135,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f88]) ).
fof(f136,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f135]) ).
fof(f137,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f87]) ).
fof(f138,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f93]) ).
fof(f139,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f92]) ).
fof(f140,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f91]) ).
fof(f142,definition,
( spl15_1
<=> in(sK13,succ(sK14)) ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
fof(f143,plain,
( ~ in(sK13,succ(sK14))
| spl15_1 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f144,plain,
( in(sK13,succ(sK14))
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f146,definition,
( spl15_2
<=> sK13 = sK14 ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
fof(f147,plain,
( sK13 != sK14
| spl15_2 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f148,plain,
( sK13 = sK14
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f150,definition,
( spl15_3
<=> in(sK13,sK14) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
fof(f151,plain,
( ~ in(sK13,sK14)
| spl15_3 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f152,plain,
( in(sK13,sK14)
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f153,plain,
( spl15_1
| spl15_2
| spl15_3 ),
inference(avatar_split_clause,[],[f126,f150,f146,f142]) ).
fof(f154,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(avatar_split_clause,[],[f127,f146,f142]) ).
fof(f155,plain,
( ~ spl15_1
| ~ spl15_3 ),
inference(avatar_split_clause,[],[f128,f150,f142]) ).
fof(f156,plain,
( ~ in(sK13,succ(sK13))
| spl15_1
| ~ spl15_2 ),
inference(forward_demodulation,[],[f143,f148]) ).
fof(f179,plain,
! [X0,X1] : in(X0,set_union2(X1,singleton(X0))),
inference(resolution,[],[f139,f136]) ).
fof(f183,plain,
! [X0,X1] :
( ~ in(X1,succ(X0))
| in(X1,singleton(X0))
| in(X1,X0) ),
inference(superposition,[],[f140,f86]) ).
fof(f248,plain,
! [X0] : in(X0,succ(X0)),
inference(superposition,[],[f179,f86]) ).
fof(f256,plain,
( $false
| spl15_1
| ~ spl15_2 ),
inference(resolution,[],[f248,f156]) ).
fof(f257,plain,
( spl15_1
| ~ spl15_2 ),
inference(avatar_contradiction_clause,[],[f256]) ).
fof(f259,plain,
( ! [X0] : in(sK13,set_union2(sK14,X0))
| ~ spl15_3 ),
inference(resolution,[],[f152,f138]) ).
fof(f276,plain,
( in(sK13,succ(sK14))
| ~ spl15_3 ),
inference(superposition,[],[f259,f86]) ).
fof(f278,plain,
( $false
| spl15_1
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f276,f143]) ).
fof(f279,plain,
( spl15_1
| ~ spl15_3 ),
inference(avatar_contradiction_clause,[],[f278]) ).
fof(f312,plain,
( in(sK13,singleton(sK14))
| in(sK13,sK14)
| ~ spl15_1 ),
inference(resolution,[],[f183,f144]) ).
fof(f314,plain,
( in(sK13,singleton(sK14))
| ~ spl15_1
| spl15_3 ),
inference(forward_subsumption_resolution,[],[f312,f151]) ).
fof(f315,plain,
( sK13 = sK14
| ~ spl15_1
| spl15_3 ),
inference(resolution,[],[f314,f137]) ).
fof(f319,plain,
( $false
| ~ spl15_1
| spl15_2
| spl15_3 ),
inference(forward_subsumption_resolution,[],[f315,f147]) ).
fof(f320,plain,
( ~ spl15_1
| spl15_2
| spl15_3 ),
inference(avatar_contradiction_clause,[],[f319]) ).
cnf(s1,plain,
( spl15_1
| spl15_2
| spl15_3 ),
inference(sat_conversion,[],[f153]) ).
cnf(s2,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(sat_conversion,[],[f154]) ).
cnf(s3,plain,
( ~ spl15_1
| ~ spl15_3 ),
inference(sat_conversion,[],[f155]) ).
cnf(s4,plain,
( spl15_1
| ~ spl15_2 ),
inference(sat_conversion,[],[f257]) ).
cnf(s5,plain,
( spl15_1
| ~ spl15_3 ),
inference(sat_conversion,[],[f279]) ).
cnf(s6,plain,
( ~ spl15_1
| spl15_2
| spl15_3 ),
inference(sat_conversion,[],[f320]) ).
cnf(s7,plain,
spl15_1,
inference(rat,[],[s1,s4,s5]) ).
cnf(s8,plain,
~ spl15_3,
inference(rat,[],[s3,s7]) ).
cnf(s9,plain,
~ spl15_2,
inference(rat,[],[s2,s7]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s6,s8,s7,s9]) ).
fof(f321,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM386+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 % Computer : n012.cluster.edu
% 0.04/0.32 % Model : x86_64 x86_64
% 0.04/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.32 % Memory : 8046.5625MB
% 0.04/0.32 % OS : Linux 6.8.0-71-generic
% 0.04/0.32 % CPULimit : 300
% 0.04/0.32 % WCLimit : 300
% 0.04/0.32 % DateTime : Sun Sep 27 19:45:04 UTC 2026
% 0.04/0.32 % CPUTime :
% 0.04/0.32 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.34 Running first-order theorem proving
% 0.08/0.34 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
% 0.60/0.84 % (2693174)Detected formulas, will run a generic FOF schedule.
% 0.60/0.84 % (2693183)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1337189874:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.60/0.84 % (2693182)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2405574941:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.60/0.84 % (2693180)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=2749556478:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.60/0.84 % (2693181)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=2185092346:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.60/0.84 % (2693179)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=4106716411:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.60/0.84 % (2693185)dis-21_1_sil=8000:lcm=predicate:random_seed=3855299152: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)
% 0.60/0.84 % (2693184)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=422237448:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.60/0.84 % (2693182)Refutation not found, incomplete strategy
% 0.60/0.84 % (2693182)------------------------------
% 0.60/0.84 % (2693182)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.60/0.84 % (2693182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.84 % (2693182)CaDiCaL version: 2.1.3
% 0.60/0.84 % (2693182)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.84 % (2693182)Time elapsed: 0.001 s
% 0.60/0.84 % (2693182)Peak memory usage: 88 MB
% 0.60/0.84 % (2693182)Instructions burned: 1 (million)
% 0.60/0.84 % (2693184)First to succeed.
% 0.60/0.84 % (2693184)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2693174"
% 0.60/0.84 % (2693183)Instruction limit reached!
% 0.60/0.84 % (2693183)------------------------------
% 0.60/0.84 % (2693183)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.60/0.84 % (2693183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.84 % (2693183)CaDiCaL version: 2.1.3
% 0.60/0.84 % (2693183)Termination reason: Instruction limit
% 0.60/0.84 % (2693183)Termination phase: Saturation
% 0.60/0.84 % (2693183)Time elapsed: 0.034 s
% 0.60/0.84 % (2693183)Peak memory usage: 88 MB
% 0.60/0.84 % (2693183)Instructions burned: 120 (million)
% 0.60/0.84 % (2693185)Instruction limit reached!
% 0.60/0.84 % (2693185)------------------------------
% 0.60/0.84 % (2693185)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.60/0.84 % (2693185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.84 % (2693185)CaDiCaL version: 2.1.3
% 0.60/0.84 % (2693185)Termination reason: Instruction limit
% 0.60/0.84 % (2693185)Termination phase: Saturation
% 0.60/0.84 % (2693185)Time elapsed: 0.041 s
% 0.60/0.84 % (2693185)Peak memory usage: 89 MB
% 0.60/0.84 % (2693185)Instructions burned: 131 (million)
% 0.60/0.84 % (2693182)------------------------------
% 0.60/0.84 % (2693182)------------------------------
% 0.60/0.84 % (2693193)lrs+10_1_sil=8000:sp=occurrence:random_seed=1360439516:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.60/0.84 % (2693193)Also succeeded, but the first one will report.
% 0.60/0.84 % (2693184)Refutation found. Thanks to Tanya!
% 0.60/0.84 % SZS status Theorem for theBenchmark
% 0.60/0.84 % SZS output start Proof for theBenchmark
% See solution above
% 2.33/0.94 % (2693184)------------------------------
% 2.33/0.94 % (2693184)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.33/0.94 % (2693184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.94 % (2693184)CaDiCaL version: 2.1.3
% 2.33/0.94 % (2693184)Termination reason: Refutation
% 2.33/0.94 % (2693184)Time elapsed: 0.005 s
% 2.33/0.94 % (2693184)Peak memory usage: 89 MB
% 2.33/0.94 % (2693184)Instructions burned: 10 (million)
% 2.33/0.94 % (2693184)------------------------------
% 2.33/0.94 % (2693184)------------------------------
% 2.33/0.94 % (2693174)Success in time 0.298 s
% 2.33/0.94 % Vampire exiting
%------------------------------------------------------------------------------