%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM385+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 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 68 ( 18 unt; 4 def)
% Number of atoms : 206 ( 56 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 231 ( 93 ~; 96 |; 31 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 84 ( 0 sgn 77 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
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,axiom,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f29,conjecture,
! [X0,X1] :
( succ(X0) = succ(X1)
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_ordinal1) ).
fof(f30,negated_conjecture,
~ ! [X0,X1] :
( succ(X0) = succ(X1)
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f44,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f53,plain,
? [X0,X1] :
( X0 != X1
& succ(X0) = succ(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f60,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(f61,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,[],[f60]) ).
fof(f62,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))],[f61]) ).
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(nnf_transformation,[],[f8]) ).
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) ) ) )
& ( ! [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,[],[f63]) ).
fof(f65,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,[],[f64]) ).
fof(f66,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))],[f65]) ).
fof(f78,plain,
( sK13 != sK14
& succ(sK13) = succ(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X0,sK13),skolemize(X1,sK14)],[f53]) ).
fof(f79,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f85,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f86,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f62]) ).
fof(f87,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f62]) ).
fof(f90,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f66]) ).
fof(f91,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f66]) ).
fof(f125,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f126,plain,
succ(sK13) = succ(sK14),
inference(cnf_transformation,[],[f78]) ).
fof(f127,plain,
sK13 != sK14,
inference(cnf_transformation,[],[f78]) ).
fof(f135,plain,
! [X0] : in(X0,set_union2(X0,singleton(X0))),
inference(definition_unfolding,[],[f125,f85]) ).
fof(f136,plain,
set_union2(sK13,singleton(sK13)) = set_union2(sK14,singleton(sK14)),
inference(definition_unfolding,[],[f126,f85,f85]) ).
fof(f137,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f87]) ).
fof(f138,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f137]) ).
fof(f139,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f86]) ).
fof(f141,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f91]) ).
fof(f142,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f90]) ).
fof(f447,plain,
! [X0] :
( in(X0,set_union2(sK13,singleton(sK13)))
| ~ in(X0,singleton(sK14)) ),
inference(superposition,[],[f141,f136]) ).
fof(f920,plain,
! [X0] :
( in(X0,sK13)
| in(X0,singleton(sK13))
| ~ in(X0,singleton(sK14)) ),
inference(resolution,[],[f142,f447]) ).
fof(f923,plain,
! [X0] :
( in(X0,sK14)
| in(X0,singleton(sK14))
| ~ in(X0,set_union2(sK13,singleton(sK13))) ),
inference(superposition,[],[f142,f136]) ).
fof(f991,plain,
! [X0] :
( in(X0,singleton(sK13))
| ~ in(X0,singleton(sK14))
| ~ in(sK13,X0) ),
inference(resolution,[],[f920,f79]) ).
fof(f1009,plain,
! [X0] :
( ~ in(sK13,X0)
| ~ in(X0,singleton(sK14))
| sK13 = X0 ),
inference(resolution,[],[f991,f139]) ).
fof(f1030,plain,
( ~ in(sK13,sK14)
| sK13 = sK14 ),
inference(resolution,[],[f1009,f138]) ).
fof(f1082,definition,
( spl15_13
<=> in(sK13,set_union2(sK13,singleton(sK13))) ),
introduced(definition,[new_symbols(definition,[spl15_13])],[avatar_definition]) ).
fof(f1084,plain,
( ~ in(sK13,set_union2(sK13,singleton(sK13)))
| spl15_13 ),
inference(avatar_component_clause,[],[f1082]) ).
fof(f1086,definition,
( spl15_14
<=> in(sK13,singleton(sK14)) ),
introduced(definition,[new_symbols(definition,[spl15_14])],[avatar_definition]) ).
fof(f1088,plain,
( in(sK13,singleton(sK14))
| ~ spl15_14 ),
inference(avatar_component_clause,[],[f1086]) ).
fof(f1111,plain,
( $false
| spl15_13 ),
inference(resolution,[],[f1084,f135]) ).
fof(f1114,plain,
spl15_13,
inference(avatar_contradiction_clause,[],[f1111]) ).
fof(f1117,definition,
( spl15_16
<=> sK13 = sK14 ),
introduced(definition,[new_symbols(definition,[spl15_16])],[avatar_definition]) ).
fof(f1119,plain,
( sK13 = sK14
| ~ spl15_16 ),
inference(avatar_component_clause,[],[f1117]) ).
fof(f1121,definition,
( spl15_17
<=> in(sK13,sK14) ),
introduced(definition,[new_symbols(definition,[spl15_17])],[avatar_definition]) ).
fof(f1123,plain,
( ~ in(sK13,sK14)
| spl15_17 ),
inference(avatar_component_clause,[],[f1121]) ).
fof(f1124,plain,
( spl15_16
| ~ spl15_17 ),
inference(avatar_split_clause,[],[f1030,f1121,f1117]) ).
fof(f1127,plain,
( in(sK13,singleton(sK14))
| ~ in(sK13,set_union2(sK13,singleton(sK13)))
| spl15_17 ),
inference(resolution,[],[f1123,f923]) ).
fof(f1128,plain,
( ~ spl15_13
| spl15_14
| spl15_17 ),
inference(avatar_split_clause,[],[f1127,f1121,f1086,f1082]) ).
fof(f1136,plain,
( sK13 = sK14
| ~ spl15_14 ),
inference(resolution,[],[f1088,f139]) ).
fof(f1137,plain,
( spl15_16
| ~ spl15_14 ),
inference(avatar_split_clause,[],[f1136,f1086,f1117]) ).
fof(f1138,plain,
( sK13 != sK13
| ~ spl15_16 ),
inference(superposition,[],[f127,f1119]) ).
fof(f1201,plain,
( $false
| ~ spl15_16 ),
inference(trivial_inequality_removal,[],[f1138]) ).
fof(f1202,plain,
~ spl15_16,
inference(avatar_contradiction_clause,[],[f1201]) ).
cnf(s10,plain,
spl15_13,
inference(sat_conversion,[],[f1114]) ).
cnf(s12,plain,
( spl15_16
| ~ spl15_17 ),
inference(sat_conversion,[],[f1124]) ).
cnf(s13,plain,
( ~ spl15_13
| spl15_14
| spl15_17 ),
inference(sat_conversion,[],[f1128]) ).
cnf(s15,plain,
( ~ spl15_14
| spl15_16 ),
inference(sat_conversion,[],[f1137]) ).
cnf(s16,plain,
~ spl15_16,
inference(sat_conversion,[],[f1202]) ).
cnf(s18,plain,
~ spl15_14,
inference(rat,[],[s15,s16]) ).
cnf(s20,plain,
( ~ spl15_13
| spl15_17 ),
inference(rat,[],[s13,s18]) ).
cnf(s21,plain,
~ spl15_17,
inference(rat,[],[s12,s16]) ).
cnf(s22,plain,
~ spl15_13,
inference(rat,[],[s20,s21]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s10,s22]) ).
fof(f1204,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM385+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n008.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 19:46:10 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 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
% 0.17/0.48 % (1552333)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (1552344)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3248920569:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % (1552339)% WARNING: option uhcvi not known.
% 0.17/0.48 % (1552338)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3616006355_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (1552341)dis+10_1_sil=32000:sp=arity:random_seed=317219065:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (1552340)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=67440695:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (1552339)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1095221317:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (1552342)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1267499581:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (1552343)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3515002818:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % TRYING [1]
% 0.17/0.48 % TRYING [2]
% 0.17/0.48 % TRYING [3]
% 0.17/0.48 % TRYING [4]
% 0.17/0.48 % (1552344) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1552333-1552344"...
% 0.17/0.48 % (1552344)...printing done.
% 0.17/0.48 % (1552344)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (1552344)------------------------------
% 0.17/0.48 % (1552344)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (1552344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (1552344)CaDiCaL version: 2.1.3
% 0.17/0.48 % (1552344)Termination reason: Refutation
% 0.17/0.48 % (1552344)Time elapsed: 0.013 s
% 0.17/0.48 % (1552344)Peak memory usage: 13 MB
% 0.17/0.48 % (1552344)Instructions burned: 39 (million)
% 0.17/0.48 % (1552333)Success in time 0.041 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------