%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN377+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 : 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 01:50:25 PM UTC 2026
% Result : Theorem 2.26s 0.86s
% Output : Refutation 2.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 55 ( 6 unt; 6 def)
% Number of atoms : 179 ( 0 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 201 ( 77 ~; 91 |; 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 44 !; 18 ?)
% 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',x2128) ).
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,
( ( ( ( ~ big_p(sK0)
| ! [X1] : ~ big_p(X1) )
& ( ! [X2] : big_p(X2)
| big_p(sK1) ) )
| ( ( ~ big_p(sK3)
| ~ big_p(sK2) )
& ( ! [X6] : big_p(X6)
| big_p(sK2) ) ) )
& ( ( ( big_p(sK4)
| ~ big_p(sK5) )
& ( ! [X9] : big_p(X9)
| ! [X10] : ~ big_p(X10) ) )
| ! [X11] :
( ( big_p(X11)
| ~ big_p(sK6) )
& ( ! [X13] : big_p(X13)
| ~ big_p(X11) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK0),skolemize(X3,sK1),skolemize(X4,sK2),skolemize(X5,sK3),skolemize(X7,sK4),skolemize(X8,sK5),skolemize(X12,sK6)],[f6]) ).
fof(f8,plain,
! [X10,X11,X9,X13] :
( big_p(X9)
| ~ big_p(X10)
| big_p(X13)
| ~ big_p(X11) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X2,X6] :
( big_p(X2)
| big_p(sK1)
| big_p(X6)
| big_p(sK2) ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X1] :
( ~ big_p(sK0)
| ~ big_p(X1)
| ~ big_p(sK3)
| ~ 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(f20,definition,
( spl7_2
<=> ! [X13] : big_p(X13) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f21,plain,
( ! [X13] : big_p(X13)
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f22,plain,
( spl7_1
| spl7_2
| spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f8,f20,f17,f20,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(sK1) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
fof(f45,plain,
( big_p(sK1)
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f46,plain,
( spl7_6
| spl7_2
| spl7_7
| spl7_2 ),
inference(avatar_split_clause,[],[f12,f20,f43,f20,f39]) ).
fof(f48,definition,
( spl7_8
<=> big_p(sK3) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
fof(f50,plain,
( ~ big_p(sK3)
| spl7_8 ),
inference(avatar_component_clause,[],[f48]) ).
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_8
| spl7_1
| ~ spl7_9 ),
inference(avatar_split_clause,[],[f15,f53,f17,f48,f39]) ).
fof(f58,plain,
( $false
| ~ spl7_2
| spl7_9 ),
inference(forward_subsumption_resolution,[],[f55,f21]) ).
fof(f59,plain,
( ~ spl7_2
| spl7_9 ),
inference(avatar_contradiction_clause,[],[f58]) ).
fof(f60,plain,
( $false
| ~ spl7_2
| spl7_6 ),
inference(forward_subsumption_resolution,[],[f40,f21]) ).
fof(f61,plain,
( ~ spl7_2
| spl7_6 ),
inference(avatar_contradiction_clause,[],[f60]) ).
fof(f62,plain,
( $false
| ~ spl7_2
| spl7_8 ),
inference(forward_subsumption_resolution,[],[f50,f21]) ).
fof(f63,plain,
( ~ spl7_2
| spl7_8 ),
inference(avatar_contradiction_clause,[],[f62]) ).
fof(f64,plain,
( $false
| ~ spl7_1
| ~ spl7_2 ),
inference(forward_subsumption_resolution,[],[f18,f21]) ).
fof(f65,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(avatar_contradiction_clause,[],[f64]) ).
fof(f66,plain,
( $false
| ~ spl7_1
| ~ spl7_6 ),
inference(forward_subsumption_resolution,[],[f41,f18]) ).
fof(f67,plain,
( ~ spl7_1
| ~ spl7_6 ),
inference(avatar_contradiction_clause,[],[f66]) ).
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]) ).
cnf(s1,plain,
( spl7_1
| spl7_2
| spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f22]) ).
cnf(s2,plain,
( spl7_1
| spl7_2 ),
inference(rat,[],[s1]) ).
cnf(s7,plain,
( spl7_2
| spl7_2
| spl7_6
| spl7_7 ),
inference(sat_conversion,[],[f46]) ).
cnf(s8,plain,
( spl7_2
| spl7_6
| spl7_7 ),
inference(rat,[],[s7]) ).
cnf(s11,plain,
( spl7_1
| ~ spl7_6
| ~ spl7_8
| ~ spl7_9 ),
inference(sat_conversion,[],[f57]) ).
cnf(s12,plain,
( ~ spl7_2
| spl7_9 ),
inference(sat_conversion,[],[f59]) ).
cnf(s13,plain,
( ~ spl7_2
| spl7_6 ),
inference(sat_conversion,[],[f61]) ).
cnf(s14,plain,
( ~ spl7_2
| spl7_8 ),
inference(sat_conversion,[],[f63]) ).
cnf(s15,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(sat_conversion,[],[f65]) ).
cnf(s16,plain,
( ~ spl7_1
| ~ spl7_6 ),
inference(sat_conversion,[],[f67]) ).
cnf(s17,plain,
( ~ spl7_1
| ~ spl7_7 ),
inference(sat_conversion,[],[f69]) ).
cnf(s18,plain,
spl7_1,
inference(rat,[],[s11,s12,s13,s14,s2]) ).
cnf(s19,plain,
~ spl7_7,
inference(rat,[],[s17,s18]) ).
cnf(s20,plain,
~ spl7_6,
inference(rat,[],[s16,s18]) ).
cnf(s21,plain,
~ spl7_2,
inference(rat,[],[s15,s18]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s8,s21,s19,s20]) ).
fof(f70,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN377+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n007.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 15:48:56 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 2.26/0.86 % (2514371)Detected formulas, will run a generic FOF schedule.
% 2.26/0.86 % (2514381)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=974185039:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.26/0.86 % (2514381)First to succeed.
% 2.26/0.86 % (2514381)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2514371"
% 2.26/0.86 % (2514376)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=1947907164:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.26/0.86 % (2514380)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=353926928:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.26/0.86 % (2514378)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=2158102862:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.26/0.86 % (2514382)dis-21_1_sil=8000:lcm=predicate:random_seed=4111210868: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)
% 2.26/0.86 % (2514377)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=741449515:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.26/0.86 % (2514379)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1834874014:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.26/0.86 % (2514380)Also succeeded, but the first one will report.
% 2.26/0.86 % (2514382)Also succeeded, but the first one will report.
% 2.26/0.86 % (2514379)Also succeeded, but the first one will report.
% 2.26/0.86 % (2514381)Refutation found. Thanks to Tanya!
% 2.26/0.86 % SZS status Theorem for theBenchmark
% 2.26/0.86 % SZS output start Proof for theBenchmark
% See solution above
% 2.26/0.86 % (2514381)------------------------------
% 2.26/0.86 % (2514381)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.26/0.86 % (2514381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.86 % (2514381)CaDiCaL version: 2.1.3
% 2.26/0.86 % (2514381)Termination reason: Refutation
% 2.26/0.86 % (2514381)Time elapsed: 0.001 s
% 2.26/0.86 % (2514381)Peak memory usage: 89 MB
% 2.26/0.86 % (2514381)Instructions burned: 1 (million)
% 2.26/0.86 % (2514381)------------------------------
% 2.26/0.86 % (2514381)------------------------------
% 2.26/0.86 % (2514371)Success in time 0.267 s
% 2.26/0.86 % Vampire exiting
%------------------------------------------------------------------------------