%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN047+1 : 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 : n003.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 01:49:06 PM UTC 2026
% Result : Theorem 2.74s 1.17s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 75 ( 11 unt; 7 def)
% Number of atoms : 273 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 329 ( 131 ~; 150 |; 32 &)
% ( 9 <=>; 4 =>; 0 <=; 3 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of predicates : 12 ( 11 usr; 12 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 ) )
=> s )
<=> ( ( ~ p
| q
| s )
& ( ~ p
| ~ r
| s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel17) ).
fof(f2,negated_conjecture,
~ ( ( ( p
& ( q
=> r ) )
=> s )
<=> ( ( ~ p
| q
| s )
& ( ~ p
| ~ r
| s ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( s
| ~ p
| ( ~ r
& q ) )
<~> ( ( ~ p
| q
| s )
& ( ~ p
| ~ r
| s ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ( s
| ~ p
| ( ~ r
& q ) )
<~> ( ( ~ p
| q
| s )
& ( ~ p
| ~ r
| s ) ) ),
inference(flattening,[],[f3]) ).
fof(f5,definition,
( sP0
<=> ( ~ p
| ~ r
| s ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f6,definition,
( sP1
<=> ( s
| ~ p
| ( ~ r
& q ) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f7,plain,
( sP1
<~> ( ( ~ p
| q
| s )
& sP0 ) ),
inference(definition_folding,[],[f4,f6,f5]) ).
fof(f8,plain,
( ( sP1
| ( ~ s
& p
& ( r
| ~ q ) ) )
& ( s
| ~ p
| ( ~ r
& q )
| ~ sP1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f9,plain,
( ( sP1
| ( ~ s
& p
& ( r
| ~ q ) ) )
& ( s
| ~ p
| ( ~ r
& q )
| ~ sP1 ) ),
inference(flattening,[],[f8]) ).
fof(f10,plain,
( ( sP0
| ( p
& r
& ~ s ) )
& ( ~ p
| ~ r
| s
| ~ sP0 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f11,plain,
( ( sP0
| ( p
& r
& ~ s ) )
& ( ~ p
| ~ r
| s
| ~ sP0 ) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
( ( ( p
& ~ q
& ~ s )
| ~ sP0
| ~ sP1 )
& ( ( ( ~ p
| q
| s )
& sP0 )
| sP1 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f13,plain,
( ( ( p
& ~ q
& ~ s )
| ~ sP0
| ~ sP1 )
& ( ( ( ~ p
| q
| s )
& sP0 )
| sP1 ) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
( ~ sP1
| ~ p
| q
| s ),
inference(cnf_transformation,[],[f9]) ).
fof(f15,plain,
( ~ sP1
| ~ p
| ~ r
| s ),
inference(cnf_transformation,[],[f9]) ).
fof(f16,plain,
( ~ q
| r
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f17,plain,
( sP1
| p ),
inference(cnf_transformation,[],[f9]) ).
fof(f18,plain,
( ~ s
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f19,plain,
( ~ sP0
| ~ r
| s
| ~ p ),
inference(cnf_transformation,[],[f11]) ).
fof(f20,plain,
( ~ s
| sP0 ),
inference(cnf_transformation,[],[f11]) ).
fof(f21,plain,
( sP0
| r ),
inference(cnf_transformation,[],[f11]) ).
fof(f22,plain,
( sP0
| p ),
inference(cnf_transformation,[],[f11]) ).
fof(f23,plain,
( sP0
| sP1 ),
inference(cnf_transformation,[],[f13]) ).
fof(f24,plain,
( ~ p
| q
| s
| sP1 ),
inference(cnf_transformation,[],[f13]) ).
fof(f25,plain,
( ~ s
| ~ sP0
| ~ sP1 ),
inference(cnf_transformation,[],[f13]) ).
fof(f26,plain,
( ~ q
| ~ sP0
| ~ sP1 ),
inference(cnf_transformation,[],[f13]) ).
fof(f27,plain,
( p
| ~ sP0
| ~ sP1 ),
inference(cnf_transformation,[],[f13]) ).
fof(f29,definition,
( spl2_1
<=> sP1 ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f30,plain,
( ~ sP1
| spl2_1 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f31,plain,
( sP1
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f33,definition,
( spl2_2
<=> sP0 ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f34,plain,
( ~ sP0
| spl2_2 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f35,plain,
( sP0
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f36,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f23,f33,f29]) ).
fof(f37,plain,
( ~ p
| q
| s ),
inference(forward_subsumption_resolution,[],[f24,f14]) ).
fof(f38,plain,
( ~ s
| ~ sP1 ),
inference(forward_subsumption_resolution,[],[f25,f20]) ).
fof(f40,definition,
( spl2_3
<=> q ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f41,plain,
( q
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f43,plain,
( ~ spl2_1
| ~ spl2_2
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f26,f40,f33,f29]) ).
fof(f44,plain,
( p
| ~ sP1 ),
inference(forward_subsumption_resolution,[],[f27,f22]) ).
fof(f46,definition,
( spl2_4
<=> s ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f47,plain,
( ~ s
| spl2_4 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f50,definition,
( spl2_5
<=> p ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f51,plain,
( p
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f53,plain,
( spl2_4
| spl2_3
| ~ spl2_5 ),
inference(avatar_split_clause,[],[f37,f50,f40,f46]) ).
fof(f54,plain,
~ s,
inference(forward_subsumption_resolution,[],[f38,f18]) ).
fof(f55,plain,
p,
inference(forward_subsumption_resolution,[],[f44,f17]) ).
fof(f56,plain,
~ spl2_4,
inference(avatar_split_clause,[],[f54,f46]) ).
fof(f57,plain,
spl2_5,
inference(avatar_split_clause,[],[f55,f50]) ).
fof(f59,plain,
( ~ r
| s
| ~ p
| ~ spl2_2 ),
inference(resolution,[],[f35,f19]) ).
fof(f60,plain,
( ~ r
| ~ p
| ~ spl2_2
| spl2_4 ),
inference(forward_subsumption_resolution,[],[f59,f47]) ).
fof(f61,plain,
( ~ r
| ~ spl2_2
| spl2_4
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f60,f51]) ).
fof(f62,plain,
( r
| sP1
| ~ spl2_3 ),
inference(resolution,[],[f41,f16]) ).
fof(f63,plain,
( sP1
| ~ spl2_2
| ~ spl2_3
| spl2_4
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f62,f61]) ).
fof(f64,plain,
( $false
| spl2_1
| ~ spl2_2
| ~ spl2_3
| spl2_4
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f63,f30]) ).
fof(f65,plain,
( spl2_1
| ~ spl2_2
| ~ spl2_3
| spl2_4
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[],[f64]) ).
fof(f67,plain,
( ~ p
| ~ r
| s
| ~ spl2_1 ),
inference(resolution,[],[f31,f15]) ).
fof(f68,plain,
( ~ r
| s
| ~ spl2_1
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f67,f51]) ).
fof(f69,plain,
( ~ r
| ~ spl2_1
| spl2_4
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f68,f47]) ).
fof(f70,plain,
( r
| spl2_2 ),
inference(resolution,[],[f34,f21]) ).
fof(f72,plain,
( $false
| ~ spl2_1
| spl2_2
| spl2_4
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f70,f69]) ).
fof(f73,plain,
( ~ spl2_1
| spl2_2
| spl2_4
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[],[f72]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f36]) ).
cnf(s2,plain,
( ~ spl2_1
| ~ spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f43]) ).
cnf(s3,plain,
( spl2_3
| spl2_4
| ~ spl2_5 ),
inference(sat_conversion,[],[f53]) ).
cnf(s4,plain,
~ spl2_4,
inference(sat_conversion,[],[f56]) ).
cnf(s5,plain,
spl2_5,
inference(sat_conversion,[],[f57]) ).
cnf(s6,plain,
( spl2_1
| ~ spl2_2
| ~ spl2_3
| spl2_4
| ~ spl2_5 ),
inference(sat_conversion,[],[f65]) ).
cnf(s7,plain,
( ~ spl2_1
| spl2_2
| spl2_4
| ~ spl2_5 ),
inference(sat_conversion,[],[f73]) ).
cnf(s8,plain,
spl2_3,
inference(rat,[],[s3,s5,s4]) ).
cnf(s9,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(rat,[],[s2,s8]) ).
cnf(s10,plain,
spl2_1,
inference(rat,[],[s1,s6,s8,s4,s5]) ).
cnf(s11,plain,
spl2_2,
inference(rat,[],[s7,s5,s4,s10]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s9,s11,s10]) ).
fof(f74,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN047+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n003.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Mon Sep 28 15:24:12 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running first-order theorem proving
% 0.10/0.24 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
% 2.74/1.17 % (1696461)Detected formulas, will run a generic FOF schedule.
% 2.74/1.17 % (1696469)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1556354455:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.74/1.17 % (1696469)First to succeed.
% 2.74/1.17 % (1696469)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1696461"
% 2.74/1.17 % (1696468)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=1156274205:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.74/1.17 % (1696472)dis-21_1_sil=8000:lcm=predicate:random_seed=1427437665: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)
% 2.74/1.17 % (1696467)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=551621579:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.74/1.17 % (1696466)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=3977739582:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.74/1.17 % (1696470)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1651590002:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.74/1.17 % (1696471)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=439262266:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.74/1.17 % (1696470)Also succeeded, but the first one will report.
% 2.74/1.17 % (1696471)Also succeeded, but the first one will report.
% 2.74/1.17 % (1696472)Also succeeded, but the first one will report.
% 2.74/1.17 % (1696469)Refutation found. Thanks to Tanya!
% 2.74/1.17 % SZS status Theorem for theBenchmark
% 2.74/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.74/1.17 % (1696469)------------------------------
% 2.74/1.17 % (1696469)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.17 % (1696469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.17 % (1696469)CaDiCaL version: 2.1.3
% 2.74/1.17 % (1696469)Termination reason: Refutation
% 2.74/1.17 % (1696469)Time elapsed: 0.002 s
% 2.74/1.17 % (1696469)Peak memory usage: 89 MB
% 2.74/1.17 % (1696469)Instructions burned: 1 (million)
% 2.74/1.17 % (1696469)------------------------------
% 2.74/1.17 % (1696469)------------------------------
% 2.74/1.17 % (1696461)Success in time 0.297 s
% 2.74/1.17 % Vampire exiting
%------------------------------------------------------------------------------