%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN393+1.003 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 01:50:29 PM UTC 2026
% Result : Theorem 0.21s 1.13s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 2
% Syntax : Number of formulae : 47 ( 4 unt; 1 def)
% Number of atoms : 191 ( 0 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 232 ( 88 ~; 109 |; 14 &)
% ( 19 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of predicates : 5 ( 4 usr; 5 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 ( 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ( p1
<=> p2 )
<=> p3 )
<=> ( p1
<=> ( p2
<=> p3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel12) ).
fof(f2,negated_conjecture,
~ ( ( ( p1
<=> p2 )
<=> p3 )
<=> ( p1
<=> ( p2
<=> p3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( ( p1
<=> p2 )
<=> p3 )
<~> ( p1
<=> ( p2
<=> p3 ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,definition,
( sP0
<=> ( ( p1
<=> p2 )
<=> p3 ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f5,plain,
( sP0
<~> ( p1
<=> ( p2
<=> p3 ) ) ),
inference(definition_folding,[],[f3,f4]) ).
fof(f6,plain,
( ( sP0
| ( ( ~ p3
| ( ( ~ p2
| ~ p1 )
& ( p2
| p1 ) ) )
& ( p3
| ( ( p1
| ~ p2 )
& ( p2
| ~ p1 ) ) ) ) )
& ( ( ( ( ( p1
| ~ p2 )
& ( p2
| ~ p1 ) )
| ~ p3 )
& ( p3
| ( ( ~ p2
| ~ p1 )
& ( p2
| p1 ) ) ) )
| ~ sP0 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f7,plain,
( ( ( ( ( ( ~ p3
| ~ p2 )
& ( p3
| p2 ) )
| ~ p1 )
& ( ( ( p2
| ~ p3 )
& ( p3
| ~ p2 ) )
| p1 ) )
| ~ sP0 )
& ( ( ( p1
| ( ( ~ p3
| ~ p2 )
& ( p3
| p2 ) ) )
& ( ( ( p2
| ~ p3 )
& ( p3
| ~ p2 ) )
| ~ p1 ) )
| sP0 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f8,plain,
( p3
| p2
| p1
| ~ sP0 ),
inference(cnf_transformation,[],[f6]) ).
fof(f9,plain,
( p3
| ~ p2
| ~ p1
| ~ sP0 ),
inference(cnf_transformation,[],[f6]) ).
fof(f10,plain,
( p2
| ~ p1
| ~ p3
| ~ sP0 ),
inference(cnf_transformation,[],[f6]) ).
fof(f11,plain,
( p1
| ~ p2
| ~ p3
| ~ sP0 ),
inference(cnf_transformation,[],[f6]) ).
fof(f12,plain,
( sP0
| p3
| p2
| ~ p1 ),
inference(cnf_transformation,[],[f6]) ).
fof(f13,plain,
( sP0
| p3
| p1
| ~ p2 ),
inference(cnf_transformation,[],[f6]) ).
fof(f14,plain,
( sP0
| ~ p3
| p2
| p1 ),
inference(cnf_transformation,[],[f6]) ).
fof(f15,plain,
( sP0
| ~ p3
| ~ p2
| ~ p1 ),
inference(cnf_transformation,[],[f6]) ).
fof(f16,plain,
( sP0
| ~ p2
| ~ p1
| p3 ),
inference(cnf_transformation,[],[f7]) ).
fof(f17,plain,
( sP0
| ~ p3
| ~ p1
| p2 ),
inference(cnf_transformation,[],[f7]) ).
fof(f18,plain,
( sP0
| p3
| p2
| p1 ),
inference(cnf_transformation,[],[f7]) ).
fof(f19,plain,
( sP0
| ~ p3
| ~ p2
| p1 ),
inference(cnf_transformation,[],[f7]) ).
fof(f20,plain,
( p3
| ~ p2
| p1
| ~ sP0 ),
inference(cnf_transformation,[],[f7]) ).
fof(f21,plain,
( p2
| ~ p3
| p1
| ~ sP0 ),
inference(cnf_transformation,[],[f7]) ).
fof(f22,plain,
( p3
| p2
| ~ p1
| ~ sP0 ),
inference(cnf_transformation,[],[f7]) ).
fof(f23,plain,
( ~ sP0
| ~ p2
| ~ p1
| ~ p3 ),
inference(cnf_transformation,[],[f7]) ).
fof(f31,plain,
( p3
| p2
| ~ sP0 ),
inference(forward_subsumption_resolution,[],[f8,f22]) ).
fof(f32,plain,
( ~ sP0
| ~ p1
| ~ p2 ),
inference(forward_subsumption_resolution,[],[f9,f23]) ).
fof(f40,plain,
( p2
| ~ p1
| ~ sP0 ),
inference(forward_subsumption_resolution,[],[f10,f31]) ).
fof(f41,plain,
( ~ sP0
| ~ p1 ),
inference(forward_subsumption_resolution,[],[f40,f32]) ).
fof(f44,plain,
( ~ p1
| ~ p3
| ~ p1
| p2 ),
inference(resolution,[],[f41,f17]) ).
fof(f47,plain,
( p2
| ~ p3
| ~ p1 ),
inference(duplicate_literal_removal,[],[f44]) ).
fof(f48,plain,
( p1
| ~ p3
| ~ sP0 ),
inference(forward_subsumption_resolution,[],[f11,f21]) ).
fof(f49,plain,
( ~ sP0
| ~ p3 ),
inference(forward_subsumption_resolution,[],[f48,f41]) ).
fof(f56,plain,
( sP0
| p3
| p2 ),
inference(forward_subsumption_resolution,[],[f12,f18]) ).
fof(f57,plain,
( p3
| p2 ),
inference(forward_subsumption_resolution,[],[f56,f31]) ).
fof(f58,plain,
( sP0
| p1
| ~ p2 ),
inference(forward_subsumption_resolution,[],[f13,f19]) ).
fof(f65,plain,
( sP0
| p2
| p1 ),
inference(forward_subsumption_resolution,[],[f14,f18]) ).
fof(f66,plain,
( sP0
| p1 ),
inference(forward_subsumption_resolution,[],[f65,f58]) ).
fof(f67,plain,
( p1
| ~ p3 ),
inference(resolution,[],[f66,f49]) ).
fof(f71,plain,
( sP0
| ~ p2
| ~ p1 ),
inference(forward_subsumption_resolution,[],[f15,f16]) ).
fof(f72,plain,
( ~ p2
| ~ p1 ),
inference(forward_subsumption_resolution,[],[f71,f41]) ).
fof(f73,plain,
( ~ p1
| ~ p3
| ~ p1 ),
inference(resolution,[],[f72,f47]) ).
fof(f75,plain,
( ~ p1
| ~ p3 ),
inference(duplicate_literal_removal,[],[f73]) ).
fof(f76,plain,
~ p3,
inference(forward_subsumption_resolution,[],[f75,f67]) ).
fof(f77,plain,
p2,
inference(resolution,[],[f76,f57]) ).
fof(f81,plain,
( ~ p2
| p1
| ~ sP0 ),
inference(resolution,[],[f76,f20]) ).
fof(f82,plain,
( ~ p2
| p1 ),
inference(forward_subsumption_resolution,[],[f81,f58]) ).
fof(f84,plain,
~ p2,
inference(forward_subsumption_resolution,[],[f82,f72]) ).
fof(f86,plain,
$false,
inference(forward_subsumption_resolution,[],[f84,f77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN393+1.003 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n026.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 15:56:42 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 0.21/1.13 % (3973684)Detected formulas, will run a generic FOF schedule.
% 0.21/1.13 % (3973698)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3011770626:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 0.21/1.13 % (3973698)First to succeed.
% 0.21/1.13 % (3973698)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3973684"
% 0.21/1.13 % (3973696)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=293154233:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 0.21/1.13 % (3973697)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3760195905:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 0.21/1.13 % (3973694)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=3030238760:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 0.21/1.13 % (3973695)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=3837886309:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 0.21/1.13 % (3973697)Also succeeded, but the first one will report.
% 0.21/1.13 % (3973699)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=941079944:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 0.21/1.13 % (3973700)dis-21_1_sil=8000:lcm=predicate:random_seed=368178611:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/129Mi)
% 0.21/1.13 % (3973700)Also succeeded, but the first one will report.
% 0.21/1.13 % (3973699)Also succeeded, but the first one will report.
% 0.21/1.13 % (3973698)Refutation found. Thanks to Tanya!
% 0.21/1.13 % SZS status Theorem for theBenchmark
% 0.21/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/1.14 % (3973698)------------------------------
% 0.21/1.14 % (3973698)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.14 % (3973698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.14 % (3973698)CaDiCaL version: 2.1.3
% 0.21/1.14 % (3973698)Termination reason: Refutation
% 0.21/1.14 % (3973698)Time elapsed: 0.001 s
% 0.21/1.14 % (3973698)Peak memory usage: 88 MB
% 0.21/1.14 % (3973698)Instructions burned: 1 (million)
% 0.21/1.14 % (3973698)------------------------------
% 0.21/1.14 % (3973698)------------------------------
% 0.21/1.14 % (3973684)Success in time 0.267 s
% 0.21/1.14 % Vampire exiting
%------------------------------------------------------------------------------