%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN358+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 : n010.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 01:50:22 PM UTC 2026
% Result : Theorem 0.22s 1.14s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 8 unt; 6 def)
% Number of atoms : 119 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 131 ( 55 ~; 46 |; 20 &)
% ( 9 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 8 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 30 ( 0 sgn 16 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X0] :
( p
& big_q(X0) )
<=> ( p
& ? [X0] : big_q(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2109) ).
fof(f2,negated_conjecture,
~ ( ? [X0] :
( p
& big_q(X0) )
<=> ( p
& ? [X0] : big_q(X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ? [X0] :
( p
& big_q(X0) )
<=> ( p
& ? [X1] : big_q(X1) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ? [X0] :
( p
& big_q(X0) )
<~> ( p
& ? [X1] : big_q(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ( ~ p
| ! [X1] : ~ big_q(X1)
| ! [X0] :
( ~ p
| ~ big_q(X0) ) )
& ( ( p
& ? [X1] : big_q(X1) )
| ? [X0] :
( p
& big_q(X0) ) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
( ( ~ p
| ! [X1] : ~ big_q(X1)
| ! [X0] :
( ~ p
| ~ big_q(X0) ) )
& ( ( p
& ? [X1] : big_q(X1) )
| ? [X0] :
( p
& big_q(X0) ) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
( ( ~ p
| ! [X0] : ~ big_q(X0)
| ! [X1] :
( ~ p
| ~ big_q(X1) ) )
& ( ( p
& ? [X2] : big_q(X2) )
| ? [X3] :
( p
& big_q(X3) ) ) ),
inference(rectify,[],[f6]) ).
fof(f8,plain,
( ( ~ p
| ! [X0] : ~ big_q(X0)
| ! [X1] :
( ~ p
| ~ big_q(X1) ) )
& ( ( p
& big_q(sK0) )
| ( p
& big_q(sK1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0),skolemize(X3,sK1)],[f7]) ).
fof(f9,plain,
( big_q(sK0)
| big_q(sK1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f12,plain,
( p
| p ),
inference(cnf_transformation,[],[f8]) ).
fof(f13,plain,
! [X0,X1] :
( ~ p
| ~ big_q(X0)
| ~ p
| ~ big_q(X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f14,plain,
! [X0] :
( ~ big_q(X0)
| sP2 ),
inference(cnf_transformation,[],[f14_D]) ).
fof(f14_D,definition,
( ! [X0] : ~ big_q(X0)
<=> ~ sP2 ),
introduced(definition,[new_symbols(definition,[sP2])],[general_splitting_component_introduction]) ).
fof(f15,plain,
! [X1] :
( ~ p
| ~ p
| ~ big_q(X1)
| ~ sP2 ),
inference(general_splitting,[],[f13,f14_D]) ).
fof(f16,plain,
p,
inference(duplicate_literal_removal,[],[f12]) ).
fof(f17,plain,
! [X1] :
( ~ p
| ~ big_q(X1)
| ~ sP2 ),
inference(duplicate_literal_removal,[],[f15]) ).
fof(f19,definition,
( spl3_1
<=> big_q(sK1) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f21,plain,
( big_q(sK1)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f23,definition,
( spl3_2
<=> big_q(sK0) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f25,plain,
( big_q(sK0)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f23]) ).
fof(f26,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f9,f23,f19]) ).
fof(f28,definition,
( spl3_3
<=> p ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f33,plain,
spl3_3,
inference(avatar_split_clause,[],[f16,f28]) ).
fof(f35,definition,
( spl3_4
<=> sP2 ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f39,definition,
( spl3_5
<=> ! [X0] : ~ big_q(X0) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f40,plain,
( ! [X0] : ~ big_q(X0)
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f41,plain,
( spl3_4
| spl3_5 ),
inference(avatar_split_clause,[],[f14,f39,f35]) ).
fof(f42,plain,
( ~ spl3_4
| spl3_5
| ~ spl3_3 ),
inference(avatar_split_clause,[],[f17,f28,f39,f35]) ).
fof(f43,plain,
( $false
| ~ spl3_2
| ~ spl3_5 ),
inference(resolution,[],[f40,f25]) ).
fof(f44,plain,
( ~ spl3_2
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[],[f43]) ).
fof(f45,plain,
( $false
| ~ spl3_1
| ~ spl3_5 ),
inference(forward_subsumption_resolution,[],[f21,f40]) ).
fof(f46,plain,
( ~ spl3_1
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[],[f45]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f26]) ).
cnf(s4,plain,
spl3_3,
inference(sat_conversion,[],[f33]) ).
cnf(s5,plain,
( spl3_4
| spl3_5 ),
inference(sat_conversion,[],[f41]) ).
cnf(s6,plain,
( ~ spl3_3
| ~ spl3_4
| spl3_5 ),
inference(sat_conversion,[],[f42]) ).
cnf(s7,plain,
( ~ spl3_2
| ~ spl3_5 ),
inference(sat_conversion,[],[f44]) ).
cnf(s8,plain,
( ~ spl3_1
| ~ spl3_5 ),
inference(sat_conversion,[],[f46]) ).
cnf(s9,plain,
spl3_5,
inference(rat,[],[s6,s5,s4]) ).
cnf(s10,plain,
~ spl3_1,
inference(rat,[],[s8,s9]) ).
cnf(s11,plain,
~ spl3_2,
inference(rat,[],[s7,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s11,s10]) ).
fof(f47,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN358+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 : n010.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 15:48:33 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
% 0.22/1.14 % (2030284)Detected formulas, will run a generic FOF schedule.
% 0.22/1.14 % (2030299)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3183408899:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.22/1.14 % (2030299)First to succeed.
% 0.22/1.14 % (2030299)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2030284"
% 0.22/1.14 % (2030302)dis-21_1_sil=8000:lcm=predicate:random_seed=374475186: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)
% 0.22/1.14 % (2030300)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2177690139:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.22/1.14 % (2030301)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3651963395:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.22/1.14 % (2030298)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=3816155609:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.22/1.14 % (2030297)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=3875494321:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.22/1.14 % (2030296)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=2853901911:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.22/1.14 % (2030300)Also succeeded, but the first one will report.
% 0.22/1.14 % (2030302)Also succeeded, but the first one will report.
% 0.22/1.14 % (2030301)Also succeeded, but the first one will report.
% 0.22/1.14 % (2030299)Refutation found. Thanks to Tanya!
% 0.22/1.14 % SZS status Theorem for theBenchmark
% 0.22/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/1.14 % (2030299)------------------------------
% 0.22/1.14 % (2030299)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.22/1.14 % (2030299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/1.14 % (2030299)CaDiCaL version: 2.1.3
% 0.22/1.14 % (2030299)Termination reason: Refutation
% 0.22/1.14 % (2030299)Time elapsed: 0.001 s
% 0.22/1.14 % (2030299)Peak memory usage: 89 MB
% 0.22/1.14 % (2030299)Instructions burned: 1 (million)
% 0.22/1.14 % (2030299)------------------------------
% 0.22/1.14 % (2030299)------------------------------
% 0.22/1.14 % (2030284)Success in time 0.267 s
% 0.22/1.14 % Vampire exiting
%------------------------------------------------------------------------------