%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN063+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 : n014.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 01:49:11 PM UTC 2026
% Result : Theorem 2.52s 1.13s
% Output : Refutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 40 ( 4 unt; 2 def)
% Number of atoms : 191 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 237 ( 86 ~; 100 |; 40 &)
% ( 4 <=>; 4 =>; 0 <=; 3 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 28 ( 24 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] :
( ( big_p(a)
& ( big_p(X0)
=> big_p(b) ) )
=> big_p(c) )
<=> ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| big_p(c) )
& ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel33) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
( ( big_p(a)
& ( big_p(X0)
=> big_p(b) ) )
=> big_p(c) )
<=> ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| big_p(c) )
& ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X0] :
( big_p(c)
| ~ big_p(a)
| ( ~ big_p(b)
& big_p(X0) ) )
<~> ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| big_p(c) )
& ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ! [X0] :
( big_p(c)
| ~ big_p(a)
| ( ~ big_p(b)
& big_p(X0) ) )
<~> ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| big_p(c) )
& ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ) ) ),
inference(flattening,[],[f3]) ).
fof(f5,definition,
( sP0
<=> ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f6,definition,
( sP1
<=> ! [X0] :
( big_p(c)
| ~ big_p(a)
| ( ~ big_p(b)
& big_p(X0) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f7,plain,
( sP1
<~> ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| big_p(c) )
& sP0 ) ),
inference(definition_folding,[],[f4,f6,f5]) ).
fof(f8,plain,
( ( sP1
| ? [X0] :
( ~ big_p(c)
& big_p(a)
& ( big_p(b)
| ~ big_p(X0) ) ) )
& ( ! [X0] :
( big_p(c)
| ~ big_p(a)
| ( ~ big_p(b)
& big_p(X0) ) )
| ~ sP1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f9,plain,
( ( sP1
| ? [X0] :
( ~ big_p(c)
& big_p(a)
& ( big_p(b)
| ~ big_p(X0) ) ) )
& ( ! [X1] :
( big_p(c)
| ~ big_p(a)
| ( ~ big_p(b)
& big_p(X1) ) )
| ~ sP1 ) ),
inference(rectify,[],[f8]) ).
fof(f10,plain,
( ( sP1
| ( ~ big_p(c)
& big_p(a)
& ( big_p(b)
| ~ big_p(sK2) ) ) )
& ( ! [X1] :
( big_p(c)
| ~ big_p(a)
| ( ~ big_p(b)
& big_p(X1) ) )
| ~ sP1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f9]) ).
fof(f11,plain,
( ( sP0
| ( big_p(a)
& big_p(b)
& ~ big_p(c) ) )
& ( ~ big_p(a)
| ~ big_p(b)
| big_p(c)
| ~ sP0 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f12,plain,
( ( sP0
| ( big_p(a)
& big_p(b)
& ~ big_p(c) ) )
& ( ~ big_p(a)
| ~ big_p(b)
| big_p(c)
| ~ sP0 ) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
( ( ? [X1] :
( ( big_p(a)
& ~ big_p(X1)
& ~ big_p(c) )
| ~ sP0 )
| ~ sP1 )
& ( ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| big_p(c) )
& sP0 )
| sP1 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f14,plain,
( ( ? [X0] :
( ( big_p(a)
& ~ big_p(X0)
& ~ big_p(c) )
| ~ sP0 )
| ~ sP1 )
& ( ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| big_p(c) )
& sP0 )
| sP1 ) ),
inference(rectify,[],[f13]) ).
fof(f15,plain,
( ( ( big_p(a)
& ~ big_p(sK3)
& ~ big_p(c) )
| ~ sP0
| ~ sP1 )
& ( ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| big_p(c) )
& sP0 )
| sP1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f14]) ).
fof(f16,plain,
! [X1] :
( big_p(c)
| ~ big_p(a)
| big_p(X1)
| ~ sP1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f17,plain,
( big_p(c)
| ~ big_p(a)
| ~ big_p(b)
| ~ sP1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f19,plain,
( big_p(a)
| sP1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f20,plain,
( ~ big_p(c)
| sP1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f22,plain,
( ~ big_p(c)
| sP0 ),
inference(cnf_transformation,[],[f12]) ).
fof(f24,plain,
( big_p(a)
| sP0 ),
inference(cnf_transformation,[],[f12]) ).
fof(f26,plain,
! [X1] :
( big_p(c)
| big_p(X1)
| ~ big_p(a)
| sP1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
( ~ big_p(c)
| ~ sP0
| ~ sP1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
( big_p(a)
| ~ sP0
| ~ sP1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f31,plain,
! [X0] :
( sP1
| big_p(X0)
| ~ big_p(a)
| sP1 ),
inference(resolution,[],[f20,f26]) ).
fof(f32,plain,
! [X0] :
( sP1
| big_p(X0)
| ~ big_p(a) ),
inference(duplicate_literal_removal,[],[f31]) ).
fof(f33,plain,
! [X0] :
( big_p(X0)
| sP1 ),
inference(forward_subsumption_resolution,[],[f32,f19]) ).
fof(f34,plain,
( sP1
| sP1 ),
inference(resolution,[],[f33,f20]) ).
fof(f37,plain,
sP1,
inference(duplicate_literal_removal,[],[f34]) ).
fof(f40,plain,
! [X1] :
( big_p(c)
| ~ big_p(a)
| big_p(X1) ),
inference(forward_subsumption_resolution,[],[f16,f33]) ).
fof(f41,plain,
! [X0] :
( ~ big_p(a)
| big_p(X0)
| sP0 ),
inference(resolution,[],[f40,f22]) ).
fof(f45,plain,
! [X0] :
( big_p(X0)
| sP0 ),
inference(forward_subsumption_resolution,[],[f41,f24]) ).
fof(f47,plain,
( sP0
| sP0 ),
inference(resolution,[],[f45,f22]) ).
fof(f51,plain,
sP0,
inference(duplicate_literal_removal,[],[f47]) ).
fof(f52,plain,
( big_p(c)
| ~ big_p(a)
| ~ sP1 ),
inference(forward_subsumption_resolution,[],[f17,f40]) ).
fof(f53,plain,
( big_p(c)
| ~ big_p(a) ),
inference(forward_subsumption_resolution,[],[f52,f33]) ).
fof(f56,plain,
( ~ big_p(a)
| ~ sP0
| ~ sP1 ),
inference(resolution,[],[f53,f27]) ).
fof(f57,plain,
( ~ sP0
| ~ sP1 ),
inference(forward_subsumption_resolution,[],[f56,f29]) ).
fof(f58,plain,
~ sP1,
inference(forward_subsumption_resolution,[],[f57,f51]) ).
fof(f59,plain,
$false,
inference(forward_subsumption_resolution,[],[f58,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN063+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n014.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 15:27:16 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 2.52/1.13 % (1853138)Detected formulas, will run a generic FOF schedule.
% 2.52/1.13 % (1853147)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3453144118:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.52/1.13 % (1853147)First to succeed.
% 2.52/1.13 % (1853147)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1853138"
% 2.52/1.13 % (1853144)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=2414194105:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.52/1.13 % (1853145)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=4022896710:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.52/1.13 % (1853143)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=3637946458:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.52/1.13 % (1853146)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=311411901:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.52/1.13 % (1853146)Also succeeded, but the first one will report.
% 2.52/1.13 % (1853149)dis-21_1_sil=8000:lcm=predicate:random_seed=22044195: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)
% 2.52/1.13 % (1853148)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1967428652:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.52/1.13 % (1853148)Also succeeded, but the first one will report.
% 2.52/1.13 % (1853149)Also succeeded, but the first one will report.
% 2.52/1.13 % (1853147)Refutation found. Thanks to Tanya!
% 2.52/1.13 % SZS status Theorem for theBenchmark
% 2.52/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 2.52/1.13 % (1853147)------------------------------
% 2.52/1.13 % (1853147)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.52/1.13 % (1853147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/1.13 % (1853147)CaDiCaL version: 2.1.3
% 2.52/1.13 % (1853147)Termination reason: Refutation
% 2.52/1.13 % (1853147)Time elapsed: 0.001 s
% 2.52/1.13 % (1853147)Peak memory usage: 88 MB
% 2.52/1.13 % (1853147)Instructions burned: 1 (million)
% 2.52/1.13 % (1853147)------------------------------
% 2.52/1.13 % (1853147)------------------------------
% 2.52/1.13 % (1853138)Success in time 0.271 s
% 2.52/1.13 % Vampire exiting
%------------------------------------------------------------------------------