%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN375+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 02:07:31 PM UTC 2026
% Result : Theorem 0.11s 0.23s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 7 unt; 6 def)
% Number of atoms : 173 ( 0 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 195 ( 75 ~; 87 |; 15 &)
% ( 17 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 7 prp; 0-1 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 62 ( 0 sgn 40 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] :
( big_p(X0)
<=> ? [X1] : big_p(X1) )
<=> ( ! [X0] : big_p(X0)
<=> ? [X1] : big_p(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2126) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
( big_p(X0)
<=> ? [X1] : big_p(X1) )
<=> ( ! [X0] : big_p(X0)
<=> ? [X1] : big_p(X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ! [X0] :
( big_p(X0)
<=> ? [X1] : big_p(X1) )
<=> ( ! [X2] : big_p(X2)
<=> ? [X3] : big_p(X3) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ! [X0] :
( big_p(X0)
<=> ? [X1] : big_p(X1) )
<~> ( ! [X2] : big_p(X2)
<=> ? [X3] : big_p(X3) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ( ( ( ! [X3] : ~ big_p(X3)
| ? [X2] : ~ big_p(X2) )
& ( ? [X3] : big_p(X3)
| ! [X2] : big_p(X2) ) )
| ? [X0] :
( ( ! [X1] : ~ big_p(X1)
| ~ big_p(X0) )
& ( ? [X1] : big_p(X1)
| big_p(X0) ) ) )
& ( ( ( ! [X2] : big_p(X2)
| ! [X3] : ~ big_p(X3) )
& ( ? [X3] : big_p(X3)
| ? [X2] : ~ big_p(X2) ) )
| ! [X0] :
( ( big_p(X0)
| ! [X1] : ~ big_p(X1) )
& ( ? [X1] : big_p(X1)
| ~ big_p(X0) ) ) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
( ( ( ( ! [X0] : ~ big_p(X0)
| ? [X1] : ~ big_p(X1) )
& ( ? [X2] : big_p(X2)
| ! [X3] : big_p(X3) ) )
| ? [X4] :
( ( ! [X5] : ~ big_p(X5)
| ~ big_p(X4) )
& ( ? [X6] : big_p(X6)
| big_p(X4) ) ) )
& ( ( ( ! [X7] : big_p(X7)
| ! [X8] : ~ big_p(X8) )
& ( ? [X9] : big_p(X9)
| ? [X10] : ~ big_p(X10) ) )
| ! [X11] :
( ( big_p(X11)
| ! [X12] : ~ big_p(X12) )
& ( ? [X13] : big_p(X13)
| ~ big_p(X11) ) ) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ( ( ( ! [X0] : ~ big_p(X0)
| ~ big_p(sK0) )
& ( big_p(sK1)
| ! [X3] : big_p(X3) ) )
| ( ( ! [X5] : ~ big_p(X5)
| ~ big_p(sK2) )
& ( big_p(sK3)
| big_p(sK2) ) ) )
& ( ( ( ! [X7] : big_p(X7)
| ! [X8] : ~ big_p(X8) )
& ( big_p(sK4)
| ~ big_p(sK5) ) )
| ! [X11] :
( ( big_p(X11)
| ! [X12] : ~ big_p(X12) )
& ( big_p(sK6)
| ~ big_p(X11) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X1,sK0),skolemize(X2,sK1),skolemize(X4,sK2),skolemize(X6,sK3),skolemize(X9,sK4),skolemize(X10,sK5),skolemize(X13,sK6)],[f6]) ).
fof(f11,plain,
! [X11,X8,X7,X12] :
( big_p(X7)
| ~ big_p(X8)
| big_p(X11)
| ~ big_p(X12) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X3] :
( big_p(sK1)
| big_p(X3)
| big_p(sK3)
| big_p(sK2) ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X0,X5] :
( ~ big_p(X0)
| ~ big_p(sK0)
| ~ big_p(X5)
| ~ big_p(sK2) ),
inference(cnf_transformation,[],[f7]) ).
fof(f17,definition,
( spl7_1
<=> ! [X11] : ~ big_p(X11) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f18,plain,
( ! [X11] : ~ big_p(X11)
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f17]) ).
fof(f33,definition,
( spl7_5
<=> ! [X11] : big_p(X11) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
fof(f34,plain,
( ! [X11] : big_p(X11)
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f37,plain,
( spl7_1
| spl7_5
| spl7_1
| spl7_5 ),
inference(avatar_split_clause,[],[f11,f33,f17,f33,f17]) ).
fof(f39,definition,
( spl7_6
<=> big_p(sK2) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
fof(f40,plain,
( ~ big_p(sK2)
| spl7_6 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f41,plain,
( big_p(sK2)
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f43,definition,
( spl7_7
<=> big_p(sK3) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
fof(f45,plain,
( big_p(sK3)
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f47,definition,
( spl7_8
<=> big_p(sK1) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
fof(f49,plain,
( big_p(sK1)
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f50,plain,
( spl7_6
| spl7_7
| spl7_5
| spl7_8 ),
inference(avatar_split_clause,[],[f12,f47,f33,f43,f39]) ).
fof(f53,definition,
( spl7_9
<=> big_p(sK0) ),
introduced(definition,[new_symbols(definition,[spl7_9])],[avatar_definition]) ).
fof(f55,plain,
( ~ big_p(sK0)
| spl7_9 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f57,plain,
( ~ spl7_6
| spl7_1
| ~ spl7_9
| spl7_1 ),
inference(avatar_split_clause,[],[f15,f17,f53,f17,f39]) ).
fof(f60,plain,
( $false
| ~ spl7_5
| spl7_9 ),
inference(forward_subsumption_resolution,[],[f55,f34]) ).
fof(f61,plain,
( ~ spl7_5
| spl7_9 ),
inference(avatar_contradiction_clause,[],[f60]) ).
fof(f62,plain,
( $false
| ~ spl7_5
| spl7_6 ),
inference(forward_subsumption_resolution,[],[f40,f34]) ).
fof(f63,plain,
( ~ spl7_5
| spl7_6 ),
inference(avatar_contradiction_clause,[],[f62]) ).
fof(f68,plain,
( $false
| ~ spl7_1
| ~ spl7_7 ),
inference(forward_subsumption_resolution,[],[f45,f18]) ).
fof(f69,plain,
( ~ spl7_1
| ~ spl7_7 ),
inference(avatar_contradiction_clause,[],[f68]) ).
fof(f70,plain,
( $false
| ~ spl7_1
| ~ spl7_8 ),
inference(forward_subsumption_resolution,[],[f49,f18]) ).
fof(f71,plain,
( ~ spl7_1
| ~ spl7_8 ),
inference(avatar_contradiction_clause,[],[f70]) ).
fof(f72,plain,
( $false
| ~ spl7_1
| ~ spl7_6 ),
inference(forward_subsumption_resolution,[],[f41,f18]) ).
fof(f73,plain,
( ~ spl7_1
| ~ spl7_6 ),
inference(avatar_contradiction_clause,[],[f72]) ).
cnf(s5,plain,
( spl7_1
| spl7_5
| spl7_1
| spl7_5 ),
inference(sat_conversion,[],[f37]) ).
cnf(s6,plain,
( spl7_1
| spl7_5 ),
inference(rat,[],[s5]) ).
cnf(s7,plain,
( spl7_5
| spl7_6
| spl7_7
| spl7_8 ),
inference(sat_conversion,[],[f50]) ).
cnf(s10,plain,
( spl7_1
| spl7_1
| ~ spl7_6
| ~ spl7_9 ),
inference(sat_conversion,[],[f57]) ).
cnf(s11,plain,
( spl7_1
| ~ spl7_6
| ~ spl7_9 ),
inference(rat,[],[s10]) ).
cnf(s13,plain,
( ~ spl7_5
| spl7_9 ),
inference(sat_conversion,[],[f61]) ).
cnf(s14,plain,
( ~ spl7_5
| spl7_6 ),
inference(sat_conversion,[],[f63]) ).
cnf(s17,plain,
( ~ spl7_1
| ~ spl7_7 ),
inference(sat_conversion,[],[f69]) ).
cnf(s18,plain,
( ~ spl7_1
| ~ spl7_8 ),
inference(sat_conversion,[],[f71]) ).
cnf(s19,plain,
( ~ spl7_1
| ~ spl7_6 ),
inference(sat_conversion,[],[f73]) ).
cnf(s20,plain,
spl7_1,
inference(rat,[],[s11,s13,s14,s6]) ).
cnf(s21,plain,
~ spl7_6,
inference(rat,[],[s19,s20]) ).
cnf(s22,plain,
~ spl7_8,
inference(rat,[],[s18,s20]) ).
cnf(s23,plain,
~ spl7_7,
inference(rat,[],[s17,s20]) ).
cnf(s26,plain,
~ spl7_5,
inference(rat,[],[s14,s21]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s7,s22,s26,s23,s21]) ).
fof(f74,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN375+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.16 % Computer : n007.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Mon Sep 28 15:48:40 UTC 2026
% 0.11/0.16 % CPUTime :
% 0.11/0.16 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.19 Running first-order model finding
% 0.11/0.19 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.23 % (2513941)Will run a generic schedule for satisfiability detection.
% 0.11/0.23 % (2513947)% WARNING: option uhcvi not known.
% 0.11/0.23 % (2513949)dis+10_1_sil=32000:sp=arity:random_seed=3520591991:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.23 % (2513946)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1862139669_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.23 % (2513952)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2498406739:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.23 % (2513947)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3064377499:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.23 % (2513948)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=652027129:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.23 % (2513950)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3291956550:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.23 % (2513951)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2717428122:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.23 % Detected minimum model sizes of [1]
% 0.11/0.23 % Detected maximum model sizes of [7]
% 0.11/0.23 % TRYING [1]
% 0.11/0.23 % (2513949) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2513941-2513949"...
% 0.11/0.23 % TRYING [2]
% 0.11/0.23 % (2513947) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2513941-2513947"...
% 0.11/0.23 % (2513952) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2513941-2513952"...
% 0.11/0.23 % (2513951) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2513941-2513951"...
% 0.11/0.23 % TRYING [3]
% 0.11/0.23 % (2513950) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2513941-2513950"...
% 0.11/0.23 % (2513948) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2513941-2513948"...
% 0.11/0.23 % TRYING [4]
% 0.11/0.23 % TRYING [5]
% 0.11/0.23 % (2513949)...printing done.
% 0.11/0.23 % (2513947)...printing done.
% 0.11/0.23 % TRYING [6]
% 0.11/0.23 % (2513952)...printing done.
% 0.11/0.23 % (2513950)...printing done.
% 0.11/0.23 % (2513951)...printing done.
% 0.11/0.23 % (2513948)...printing done.
% 0.11/0.23 % (2513949)Refutation found. Thanks to Tanya!
% 0.11/0.23 % SZS status Theorem for theBenchmark
% 0.11/0.23 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.23 % (2513949)------------------------------
% 0.11/0.23 % (2513949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.23 % (2513949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.23 % (2513949)CaDiCaL version: 2.1.3
% 0.11/0.23 % (2513949)Termination reason: Refutation
% 0.11/0.23 % (2513949)Time elapsed: 0.002 s
% 0.11/0.23 % (2513949)Peak memory usage: 12 MB
% 0.11/0.23 % (2513949)Instructions burned: 1 (million)
% 0.11/0.23 % (2513941)Success in time 0.034 s
% 0.11/0.23 % Vampire exiting
%------------------------------------------------------------------------------