%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n002.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 5.19s 1.61s
% Output : Refutation 5.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 15 unt; 2 def)
% Number of atoms : 165 ( 48 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 187 ( 72 ~; 75 |; 31 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 67 ( 0 sgn 60 !; 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(f39,plain,
? [X0,X1] :
( X0 != X1
& succ(X0) = succ(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f45,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f52,plain,
( sK0 != sK1
& succ(sK0) = succ(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f39]) ).
fof(f55,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(f56,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,[],[f55]) ).
fof(f57,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,[],[f56]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ( ( ( ~ in(sK4(X0,X1,X2),X0)
& ~ in(sK4(X0,X1,X2),X1) )
| ~ in(sK4(X0,X1,X2),X2) )
& ( in(sK4(X0,X1,X2),X0)
| in(sK4(X0,X1,X2),X1)
| in(sK4(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,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f57]) ).
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)
| ( ( sK5(X0,X1) != X0
| ~ in(sK5(X0,X1),X1) )
& ( sK5(X0,X1) = X0
| in(sK5(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f60]) ).
fof(f65,plain,
succ(sK0) = succ(sK1),
inference(cnf_transformation,[],[f52]) ).
fof(f66,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f52]) ).
fof(f68,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f70,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f76,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f58]) ).
fof(f82,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f61]) ).
fof(f86,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f105,plain,
set_union2(sK0,singleton(sK0)) = set_union2(sK1,singleton(sK1)),
inference(definition_unfolding,[],[f65,f70,f70]) ).
fof(f106,plain,
! [X0] : in(X0,set_union2(X0,singleton(X0))),
inference(definition_unfolding,[],[f68,f70]) ).
fof(f110,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f76]) ).
fof(f113,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f82]) ).
fof(f137,plain,
in(sK1,set_union2(sK0,singleton(sK0))),
inference(superposition,[],[f106,f105]) ).
fof(f214,plain,
( in(sK1,singleton(sK0))
| in(sK1,sK0) ),
inference(resolution,[],[f110,f137]) ).
fof(f215,plain,
! [X0] :
( ~ in(X0,set_union2(sK0,singleton(sK0)))
| in(X0,singleton(sK1))
| in(X0,sK1) ),
inference(superposition,[],[f110,f105]) ).
fof(f223,definition,
( spl9_4
<=> in(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
fof(f225,plain,
( in(sK1,sK0)
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f227,definition,
( spl9_5
<=> in(sK1,singleton(sK0)) ),
introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition]) ).
fof(f229,plain,
( in(sK1,singleton(sK0))
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f230,plain,
( spl9_4
| spl9_5 ),
inference(avatar_split_clause,[],[f214,f227,f223]) ).
fof(f231,plain,
( ~ in(sK0,sK1)
| ~ spl9_4 ),
inference(resolution,[],[f225,f86]) ).
fof(f286,plain,
( in(sK0,singleton(sK1))
| in(sK0,sK1) ),
inference(resolution,[],[f215,f106]) ).
fof(f294,plain,
( in(sK0,singleton(sK1))
| ~ spl9_4 ),
inference(forward_subsumption_resolution,[],[f286,f231]) ).
fof(f295,plain,
( sK0 = sK1
| ~ spl9_4 ),
inference(resolution,[],[f294,f113]) ).
fof(f299,plain,
( $false
| ~ spl9_4 ),
inference(forward_subsumption_resolution,[],[f295,f66]) ).
fof(f300,plain,
~ spl9_4,
inference(avatar_contradiction_clause,[],[f299]) ).
fof(f359,plain,
( sK0 = sK1
| ~ spl9_5 ),
inference(resolution,[],[f229,f113]) ).
fof(f363,plain,
( $false
| ~ spl9_5 ),
inference(forward_subsumption_resolution,[],[f359,f66]) ).
fof(f364,plain,
~ spl9_5,
inference(avatar_contradiction_clause,[],[f363]) ).
cnf(s2,plain,
( spl9_4
| spl9_5 ),
inference(sat_conversion,[],[f230]) ).
cnf(s3,plain,
~ spl9_4,
inference(sat_conversion,[],[f300]) ).
cnf(s7,plain,
~ spl9_5,
inference(sat_conversion,[],[f364]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s2,s7,s3]) ).
fof(f365,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM385+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n002.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % 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 19:48:21 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.35/1.51 % (3835075)Detected formulas, will run a generic FOF schedule.
% 3.35/1.51 % (3835081)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=3979840423:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.35/1.51 % (3835084)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=99573800:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.35/1.51 % (3835086)dis-21_1_sil=8000:lcm=predicate:random_seed=966713504: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)
% 3.35/1.51 % (3835083)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=6942345:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.35/1.51 % (3835082)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=229540565:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.35/1.51 % (3835080)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=1217179437:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.35/1.51 % (3835085)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1471287217:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.35/1.51 % (3835083)Refutation not found, incomplete strategy
% 3.35/1.51 % (3835083)------------------------------
% 3.35/1.51 % (3835083)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.51 % (3835083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.51 % (3835083)CaDiCaL version: 2.1.3
% 3.35/1.51 % (3835083)Termination reason: Refutation not found, incomplete strategy
% 3.35/1.51 % (3835083)Time elapsed: 0.001 s
% 3.35/1.51 % (3835083)Peak memory usage: 88 MB
% 3.35/1.51 % (3835084)Instruction limit reached!
% 3.35/1.51 % (3835084)------------------------------
% 3.35/1.51 % (3835084)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.51 % (3835084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.51 % (3835084)CaDiCaL version: 2.1.3
% 3.35/1.51 % (3835084)Termination reason: Instruction limit
% 3.35/1.51 % (3835084)Termination phase: Saturation
% 3.35/1.51 % (3835084)Time elapsed: 0.067 s
% 3.35/1.51 % (3835084)Peak memory usage: 88 MB
% 3.35/1.51 % (3835084)Instructions burned: 119 (million)
% 3.35/1.51 % (3835086)Instruction limit reached!
% 3.35/1.51 % (3835086)------------------------------
% 3.35/1.51 % (3835086)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.51 % (3835086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.51 % (3835086)CaDiCaL version: 2.1.3
% 3.35/1.51 % (3835086)Termination reason: Instruction limit
% 3.35/1.51 % (3835086)Termination phase: Saturation
% 3.35/1.51 % (3835086)Time elapsed: 0.072 s
% 3.35/1.51 % (3835086)Peak memory usage: 89 MB
% 3.35/1.51 % (3835086)Instructions burned: 130 (million)
% 3.35/1.51 % (3835085)Instruction limit reached!
% 3.35/1.51 % (3835085)------------------------------
% 3.35/1.51 % (3835085)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.51 % (3835085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.51 % (3835085)CaDiCaL version: 2.1.3
% 3.35/1.51 % (3835085)Termination reason: Instruction limit
% 3.35/1.51 % (3835085)Termination phase: Saturation
% 3.35/1.51 % (3835085)Time elapsed: 0.091 s
% 3.35/1.51 % (3835085)Peak memory usage: 89 MB
% 3.35/1.51 % (3835085)Instructions burned: 140 (million)
% 3.35/1.51 % (3835095)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3435051672:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.35/1.51 % (3835094)lrs+10_1_sil=8000:sp=occurrence:random_seed=4293077368:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.35/1.51 % (3835095)Refutation not found, incomplete strategy
% 3.35/1.51 % (3835095)------------------------------
% 3.35/1.51 % (3835095)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.51 % (3835095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.51 % (3835095)CaDiCaL version: 2.1.3
% 3.35/1.51 % (3835095)Termination reason: Refutation not found, incomplete strategy
% 3.35/1.51 % (3835095)Time elapsed: 0.001 s
% 5.19/1.61 % (3835095)Peak memory usage: 88 MB
% 5.19/1.61 % (3835094)First to succeed.
% 5.19/1.61 % (3835094)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3835075"
% 5.19/1.61 % (3835096)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1161438466:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.19/1.61 % (3835083)------------------------------
% 5.19/1.61 % (3835083)------------------------------
% 5.19/1.61 % (3835081)Also succeeded, but the first one will report.
% 5.19/1.61 % (3835100)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=437648363:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 5.19/1.61 % (3835096)Instruction limit reached!
% 5.19/1.61 % (3835096)------------------------------
% 5.19/1.61 % (3835096)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.19/1.61 % (3835096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.61 % (3835096)CaDiCaL version: 2.1.3
% 5.19/1.61 % (3835096)Termination reason: Instruction limit
% 5.19/1.61 % (3835096)Termination phase: Saturation
% 5.19/1.61 % (3835096)Time elapsed: 0.210 s
% 5.19/1.61 % (3835096)Peak memory usage: 91 MB
% 5.19/1.61 % (3835096)Instructions burned: 325 (million)
% 5.19/1.61 % (3835095)------------------------------
% 5.19/1.61 % (3835095)------------------------------
% 5.19/1.61 % (3835094)Refutation found. Thanks to Tanya!
% 5.19/1.61 % SZS status Theorem for theBenchmark
% 5.19/1.61 % SZS output start Proof for theBenchmark
% See solution above
% 5.19/1.61 % (3835094)------------------------------
% 5.19/1.61 % (3835094)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.19/1.61 % (3835094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.61 % (3835094)CaDiCaL version: 2.1.3
% 5.19/1.61 % (3835094)Termination reason: Refutation
% 5.19/1.61 % (3835094)Time elapsed: 0.010 s
% 5.19/1.61 % (3835094)Peak memory usage: 89 MB
% 5.19/1.61 % (3835094)Instructions burned: 11 (million)
% 5.19/1.61 % (3835094)------------------------------
% 5.19/1.61 % (3835094)------------------------------
% 5.19/1.61 % (3835075)Success in time 0.658 s
% 5.19/1.61 % Vampire exiting
%------------------------------------------------------------------------------