%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN045+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 01:49:04 PM UTC 2026
% Result : Theorem 2.53s 0.88s
% Output : Refutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 6 unt; 5 def)
% Number of atoms : 151 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 158 ( 52 ~; 75 |; 22 &)
% ( 7 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of predicates : 9 ( 8 usr; 9 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( p
| ( q
& r ) )
<=> ( ( p
| q )
& ( p
| r ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel13) ).
fof(f2,negated_conjecture,
~ ( ( p
| ( q
& r ) )
<=> ( ( p
| q )
& ( p
| r ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( p
| ( q
& r ) )
<~> ( ( p
| q )
& ( p
| r ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,definition,
( sP0
<=> ( ( p
| q )
& ( p
| r ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f5,plain,
( ( p
| ( q
& r ) )
<~> sP0 ),
inference(definition_folding,[],[f3,f4]) ).
fof(f6,plain,
( ( sP0
| ( ~ p
& ~ q )
| ( ~ p
& ~ r ) )
& ( ( ( p
| q )
& ( p
| r ) )
| ~ sP0 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f7,plain,
( ( sP0
| ( ~ p
& ~ q )
| ( ~ p
& ~ r ) )
& ( ( ( p
| q )
& ( p
| r ) )
| ~ sP0 ) ),
inference(flattening,[],[f6]) ).
fof(f8,plain,
( ( ~ sP0
| ( ~ p
& ( ~ q
| ~ r ) ) )
& ( sP0
| p
| ( q
& r ) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f9,plain,
( ( ~ sP0
| ( ~ p
& ( ~ q
| ~ r ) ) )
& ( sP0
| p
| ( q
& r ) ) ),
inference(flattening,[],[f8]) ).
fof(f10,plain,
( p
| r
| ~ sP0 ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
( p
| q
| ~ sP0 ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
( sP0
| ~ q
| ~ r ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
( sP0
| ~ p
| ~ p ),
inference(cnf_transformation,[],[f7]) ).
fof(f16,plain,
( sP0
| p
| r ),
inference(cnf_transformation,[],[f9]) ).
fof(f17,plain,
( sP0
| p
| q ),
inference(cnf_transformation,[],[f9]) ).
fof(f18,plain,
( ~ sP0
| ~ q
| ~ r ),
inference(cnf_transformation,[],[f9]) ).
fof(f19,plain,
( ~ sP0
| ~ p ),
inference(cnf_transformation,[],[f9]) ).
fof(f20,plain,
( sP0
| ~ p ),
inference(duplicate_literal_removal,[],[f15]) ).
fof(f22,definition,
( spl1_1
<=> r ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f26,definition,
( spl1_2
<=> p ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f30,definition,
( spl1_3
<=> sP0 ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f33,plain,
( spl1_1
| spl1_2
| spl1_3 ),
inference(avatar_split_clause,[],[f16,f30,f26,f22]) ).
fof(f35,definition,
( spl1_4
<=> q ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f38,plain,
( spl1_4
| spl1_2
| spl1_3 ),
inference(avatar_split_clause,[],[f17,f30,f26,f35]) ).
fof(f39,plain,
( ~ spl1_1
| ~ spl1_4
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f18,f30,f35,f22]) ).
fof(f40,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f19,f30,f26]) ).
fof(f41,plain,
( ~ spl1_3
| spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f10,f26,f22,f30]) ).
fof(f42,plain,
( ~ spl1_3
| spl1_4
| spl1_2 ),
inference(avatar_split_clause,[],[f11,f26,f35,f30]) ).
fof(f43,plain,
( ~ spl1_1
| ~ spl1_4
| spl1_3 ),
inference(avatar_split_clause,[],[f12,f30,f35,f22]) ).
fof(f46,plain,
( ~ spl1_2
| spl1_3 ),
inference(avatar_split_clause,[],[f20,f30,f26]) ).
cnf(s1,plain,
( spl1_1
| spl1_2
| spl1_3 ),
inference(sat_conversion,[],[f33]) ).
cnf(s2,plain,
( spl1_2
| spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f38]) ).
cnf(s3,plain,
( ~ spl1_1
| ~ spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f39]) ).
cnf(s4,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(sat_conversion,[],[f40]) ).
cnf(s5,plain,
( spl1_1
| spl1_2
| ~ spl1_3 ),
inference(sat_conversion,[],[f41]) ).
cnf(s6,plain,
( spl1_2
| ~ spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f42]) ).
cnf(s7,plain,
( ~ spl1_1
| spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f43]) ).
cnf(s10,plain,
( ~ spl1_2
| spl1_3 ),
inference(sat_conversion,[],[f46]) ).
cnf(s11,plain,
( spl1_2
| spl1_1 ),
inference(rat,[],[s1,s5]) ).
cnf(s12,plain,
~ spl1_2,
inference(rat,[],[s4,s10]) ).
cnf(s13,plain,
spl1_1,
inference(rat,[],[s11,s12]) ).
cnf(s14,plain,
spl1_3,
inference(rat,[],[s2,s7,s12,s13]) ).
cnf(s15,plain,
spl1_4,
inference(rat,[],[s6,s12,s14]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s3,s13,s14,s15]) ).
fof(f47,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN045+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n018.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 15:25:55 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 2.53/0.88 % (3481455)Detected formulas, will run a generic FOF schedule.
% 2.53/0.88 % (3481491)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2573700986:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.53/0.88 % (3481491)First to succeed.
% 2.53/0.88 % (3481491)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3481455"
% 2.53/0.88 % (3481493)dis-21_1_sil=8000:lcm=predicate:random_seed=1856028740: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)
% 2.53/0.88 % (3481490)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2546985375:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.53/0.88 % (3481488)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1404881972:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.53/0.88 % (3481487)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=2364881536:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.53/0.88 % (3481485)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=1907503936:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.53/0.88 % (3481490)Also succeeded, but the first one will report.
% 2.53/0.88 % (3481493)Also succeeded, but the first one will report.
% 2.53/0.88 % (3481488)Also succeeded, but the first one will report.
% 2.53/0.88 % (3481486)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=2038342475:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.53/0.88 % (3481491)Refutation found. Thanks to Tanya!
% 2.53/0.88 % SZS status Theorem for theBenchmark
% 2.53/0.88 % SZS output start Proof for theBenchmark
% See solution above
% 2.53/0.88 % (3481491)------------------------------
% 2.53/0.88 % (3481491)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/0.88 % (3481491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.88 % (3481491)CaDiCaL version: 2.1.3
% 2.53/0.88 % (3481491)Termination reason: Refutation
% 2.53/0.88 % (3481491)Time elapsed: 0.001 s
% 2.53/0.88 % (3481491)Peak memory usage: 89 MB
% 2.53/0.88 % (3481491)Instructions burned: 1 (million)
% 2.53/0.88 % (3481491)------------------------------
% 2.53/0.88 % (3481491)------------------------------
% 2.53/0.88 % (3481455)Success in time 0.317 s
% 2.53/0.88 % Vampire exiting
%------------------------------------------------------------------------------