%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n008.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 12:24:06 PM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 69 ( 8 unt; 3 def)
% Number of atoms : 242 ( 57 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 282 ( 109 ~; 128 |; 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 : 81 ( 0 sgn 70 !; 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(f136,plain,
( ~ in(sK13,sK14)
| ~ in(sK13,set_union2(sK14,singleton(sK14))) ),
inference(definition_unfolding,[],[f128,f86]) ).
fof(f137,plain,
( sK13 != sK14
| ~ in(sK13,set_union2(sK14,singleton(sK14))) ),
inference(definition_unfolding,[],[f127,f86]) ).
fof(f138,plain,
( in(sK13,sK14)
| sK13 = sK14
| in(sK13,set_union2(sK14,singleton(sK14))) ),
inference(definition_unfolding,[],[f126,f86]) ).
fof(f139,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f88]) ).
fof(f140,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f139]) ).
fof(f141,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f87]) ).
fof(f142,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f93]) ).
fof(f143,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f92]) ).
fof(f144,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f91]) ).
fof(f146,definition,
( spl15_1
<=> in(sK13,set_union2(sK14,singleton(sK14))) ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
fof(f147,plain,
( ~ in(sK13,set_union2(sK14,singleton(sK14)))
| spl15_1 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f148,plain,
( in(sK13,set_union2(sK14,singleton(sK14)))
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f150,definition,
( spl15_2
<=> sK13 = sK14 ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
fof(f151,plain,
( sK13 != sK14
| spl15_2 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f152,plain,
( sK13 = sK14
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f154,definition,
( spl15_3
<=> in(sK13,sK14) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
fof(f155,plain,
( ~ in(sK13,sK14)
| spl15_3 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f156,plain,
( in(sK13,sK14)
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f157,plain,
( spl15_1
| spl15_2
| spl15_3 ),
inference(avatar_split_clause,[],[f138,f154,f150,f146]) ).
fof(f158,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(avatar_split_clause,[],[f137,f150,f146]) ).
fof(f159,plain,
( ~ spl15_1
| ~ spl15_3 ),
inference(avatar_split_clause,[],[f136,f154,f146]) ).
fof(f160,plain,
( ~ in(sK13,set_union2(sK13,singleton(sK13)))
| spl15_1
| ~ spl15_2 ),
inference(forward_demodulation,[],[f147,f152]) ).
fof(f235,plain,
( ~ in(sK13,singleton(sK13))
| spl15_1
| ~ spl15_2 ),
inference(resolution,[],[f143,f160]) ).
fof(f245,plain,
( $false
| spl15_1
| ~ spl15_2 ),
inference(forward_subsumption_resolution,[],[f235,f140]) ).
fof(f246,plain,
( spl15_1
| ~ spl15_2 ),
inference(avatar_contradiction_clause,[],[f245]) ).
fof(f251,plain,
( ~ in(sK13,sK14)
| spl15_1 ),
inference(resolution,[],[f147,f142]) ).
fof(f252,plain,
( $false
| spl15_1
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f251,f156]) ).
fof(f253,plain,
( spl15_1
| ~ spl15_3 ),
inference(avatar_contradiction_clause,[],[f252]) ).
fof(f261,plain,
( in(sK13,singleton(sK14))
| in(sK13,sK14)
| ~ spl15_1 ),
inference(resolution,[],[f144,f148]) ).
fof(f268,plain,
( in(sK13,singleton(sK14))
| ~ spl15_1
| spl15_3 ),
inference(forward_subsumption_resolution,[],[f261,f155]) ).
fof(f269,plain,
( sK13 = sK14
| ~ spl15_1
| spl15_3 ),
inference(resolution,[],[f268,f141]) ).
fof(f273,plain,
( $false
| ~ spl15_1
| spl15_2
| spl15_3 ),
inference(forward_subsumption_resolution,[],[f269,f151]) ).
fof(f274,plain,
( ~ spl15_1
| spl15_2
| spl15_3 ),
inference(avatar_contradiction_clause,[],[f273]) ).
cnf(s1,plain,
( spl15_1
| spl15_2
| spl15_3 ),
inference(sat_conversion,[],[f157]) ).
cnf(s2,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(sat_conversion,[],[f158]) ).
cnf(s3,plain,
( ~ spl15_1
| ~ spl15_3 ),
inference(sat_conversion,[],[f159]) ).
cnf(s4,plain,
( spl15_1
| ~ spl15_2 ),
inference(sat_conversion,[],[f246]) ).
cnf(s5,plain,
( spl15_1
| ~ spl15_3 ),
inference(sat_conversion,[],[f253]) ).
cnf(s6,plain,
( ~ spl15_1
| spl15_2
| spl15_3 ),
inference(sat_conversion,[],[f274]) ).
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(f275,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM386+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n008.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
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 19:46:24 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.11/0.45 % (1552731)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (1552739)dis+10_1_sil=32000:sp=arity:random_seed=3855587220:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.45 % (1552737)% WARNING: option uhcvi not known.
% 0.11/0.45 % (1552739) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1552731-1552739"...
% 0.11/0.45 % (1552739)...printing done.
% 0.11/0.45 % (1552739)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Theorem for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (1552739)------------------------------
% 0.11/0.45 % (1552739)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (1552739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (1552739)CaDiCaL version: 2.1.3
% 0.11/0.45 % (1552739)Termination reason: Refutation
% 0.11/0.45 % (1552739)Time elapsed: 0.004 s
% 0.11/0.45 % (1552739)Peak memory usage: 12 MB
% 0.11/0.45 % (1552739)Instructions burned: 7 (million)
% 0.11/0.45 % (1552731)Success in time 0.029 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------