%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN084+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 02:06:44 PM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 97 ( 13 unt; 11 def)
% Number of atoms : 277 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 299 ( 119 ~; 153 |; 8 &)
% ( 13 <=>; 4 =>; 0 <=; 2 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 14 ( 13 usr; 12 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 33 ( 0 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] :
( ( big_p(a)
& ( big_p(X0)
=> big_p(f(X0)) ) )
=> big_p(f(f(X0))) )
<=> ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| big_p(f(f(X1))) )
& ( ~ big_p(a)
| ~ big_p(f(X1))
| big_p(f(f(X1))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel62) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
( ( big_p(a)
& ( big_p(X0)
=> big_p(f(X0)) ) )
=> big_p(f(f(X0))) )
<=> ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| big_p(f(f(X1))) )
& ( ~ big_p(a)
| ~ big_p(f(X1))
| big_p(f(f(X1))) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X0] :
( big_p(f(f(X0)))
| ~ big_p(a)
| ( ~ big_p(f(X0))
& big_p(X0) ) )
<~> ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| big_p(f(f(X1))) )
& ( ~ big_p(a)
| ~ big_p(f(X1))
| big_p(f(f(X1))) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ! [X0] :
( big_p(f(f(X0)))
| ~ big_p(a)
| ( ~ big_p(f(X0))
& big_p(X0) ) )
<~> ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| big_p(f(f(X1))) )
& ( ~ big_p(a)
| ~ big_p(f(X1))
| big_p(f(f(X1))) ) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
! [X1] :
( ~ big_p(f(f(X1)))
| sP2(X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f6,plain,
! [X1] :
( ~ big_p(X1)
| sP2(X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f7,plain,
! [X1] :
( big_p(a)
| sP2(X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f8,plain,
! [X1] :
( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a)
| ~ sP2(X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f11,plain,
( ~ sP2(sK1)
| big_p(a) ),
inference(cnf_transformation,[],[f4]) ).
fof(f12,plain,
( ~ big_p(f(f(sK1)))
| ~ sP2(sK1)
| ~ big_p(f(f(sK0))) ),
inference(cnf_transformation,[],[f4]) ).
fof(f13,plain,
( big_p(f(sK1))
| ~ sP2(sK1)
| ~ big_p(f(f(sK0))) ),
inference(cnf_transformation,[],[f4]) ).
fof(f15,plain,
! [X0,X1] :
( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(f(X0))
| ~ big_p(a)
| big_p(f(f(X0))) ),
inference(cnf_transformation,[],[f4]) ).
fof(f17,plain,
( ~ big_p(f(f(sK1)))
| ~ sP2(sK1)
| ~ big_p(sK0)
| big_p(f(sK0)) ),
inference(cnf_transformation,[],[f4]) ).
fof(f18,plain,
( big_p(f(sK1))
| ~ sP2(sK1)
| ~ big_p(sK0)
| big_p(f(sK0)) ),
inference(cnf_transformation,[],[f4]) ).
fof(f20,plain,
! [X0,X1] :
( sP2(X1)
| big_p(X0)
| ~ big_p(a)
| big_p(f(f(X0))) ),
inference(cnf_transformation,[],[f4]) ).
fof(f23,plain,
! [X0,X1] :
( ~ sP2(X1)
| big_p(X0)
| ~ big_p(a)
| big_p(f(f(X0))) ),
inference(consistent_polarity_flipping,[],[f20]) ).
fof(f25,plain,
( big_p(f(sK1))
| sP2(sK1)
| ~ big_p(sK0)
| big_p(f(sK0)) ),
inference(consistent_polarity_flipping,[],[f18]) ).
fof(f26,plain,
( ~ big_p(f(f(sK1)))
| sP2(sK1)
| ~ big_p(sK0)
| big_p(f(sK0)) ),
inference(consistent_polarity_flipping,[],[f17]) ).
fof(f28,plain,
( big_p(f(sK1))
| sP2(sK1)
| ~ big_p(f(f(sK0))) ),
inference(consistent_polarity_flipping,[],[f13]) ).
fof(f29,plain,
( ~ big_p(f(f(sK1)))
| sP2(sK1)
| ~ big_p(f(f(sK0))) ),
inference(consistent_polarity_flipping,[],[f12]) ).
fof(f30,plain,
( sP2(sK1)
| big_p(a) ),
inference(consistent_polarity_flipping,[],[f11]) ).
fof(f33,plain,
! [X1] :
( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a)
| sP2(X1) ),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f34,plain,
! [X1] :
( big_p(a)
| ~ sP2(X1) ),
inference(consistent_polarity_flipping,[],[f7]) ).
fof(f35,plain,
! [X1] :
( ~ sP2(X1)
| ~ big_p(X1) ),
inference(consistent_polarity_flipping,[],[f6]) ).
fof(f36,plain,
! [X1] :
( ~ big_p(f(f(X1)))
| ~ sP2(X1) ),
inference(consistent_polarity_flipping,[],[f5]) ).
fof(f38,definition,
( spl3_1
<=> ! [X1] : ~ sP2(X1) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f39,plain,
( ! [X1] : ~ sP2(X1)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f41,definition,
( spl3_2
<=> big_p(a) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f44,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f34,f41,f38]) ).
fof(f46,definition,
( spl3_3
<=> ! [X1] :
( big_p(f(f(X1)))
| sP2(X1)
| big_p(X1) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f47,plain,
( ! [X1] :
( big_p(f(f(X1)))
| sP2(X1)
| big_p(X1) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f48,plain,
( ~ spl3_2
| spl3_3 ),
inference(avatar_split_clause,[],[f33,f46,f41]) ).
fof(f50,definition,
( spl3_4
<=> sP2(sK1) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f52,plain,
( sP2(sK1)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f54,definition,
( spl3_5
<=> big_p(f(f(sK1))) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f56,plain,
( ~ big_p(f(f(sK1)))
| spl3_5 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f59,definition,
( spl3_6
<=> big_p(f(sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f61,plain,
( big_p(f(sK1))
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f63,plain,
( spl3_2
| spl3_4 ),
inference(avatar_split_clause,[],[f30,f50,f41]) ).
fof(f65,definition,
( spl3_7
<=> big_p(f(f(sK0))) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f67,plain,
( ~ big_p(f(f(sK0)))
| spl3_7 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f68,plain,
( ~ spl3_7
| spl3_4
| ~ spl3_5 ),
inference(avatar_split_clause,[],[f29,f54,f50,f65]) ).
fof(f69,plain,
( ~ spl3_7
| spl3_4
| spl3_6 ),
inference(avatar_split_clause,[],[f28,f59,f50,f65]) ).
fof(f72,definition,
( spl3_8
<=> ! [X0] :
( ~ big_p(f(X0))
| big_p(f(f(X0))) ) ),
introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition]) ).
fof(f73,plain,
( ! [X0] :
( big_p(f(f(X0)))
| ~ big_p(f(X0)) )
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f74,plain,
( ~ spl3_2
| spl3_8
| spl3_8 ),
inference(avatar_split_clause,[],[f15,f72,f72,f41]) ).
fof(f76,definition,
( spl3_9
<=> ! [X0] :
( big_p(X0)
| big_p(f(f(X0))) ) ),
introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition]) ).
fof(f77,plain,
( ! [X0] :
( big_p(f(f(X0)))
| big_p(X0) )
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f80,definition,
( spl3_10
<=> big_p(f(sK0)) ),
introduced(definition,[new_symbols(definition,[spl3_10])],[avatar_definition]) ).
fof(f84,definition,
( spl3_11
<=> big_p(sK0) ),
introduced(definition,[new_symbols(definition,[spl3_11])],[avatar_definition]) ).
fof(f87,plain,
( spl3_10
| ~ spl3_11
| spl3_4
| ~ spl3_5 ),
inference(avatar_split_clause,[],[f26,f54,f50,f84,f80]) ).
fof(f88,plain,
( spl3_10
| ~ spl3_11
| spl3_4
| spl3_6 ),
inference(avatar_split_clause,[],[f25,f59,f50,f84,f80]) ).
fof(f90,plain,
( ~ spl3_2
| spl3_9
| spl3_1 ),
inference(avatar_split_clause,[],[f23,f38,f76,f41]) ).
fof(f92,plain,
( big_p(sK0)
| spl3_7
| ~ spl3_9 ),
inference(resolution,[],[f77,f67]) ).
fof(f93,plain,
( ! [X0] :
( big_p(X0)
| ~ sP2(X0) )
| ~ spl3_9 ),
inference(resolution,[],[f77,f36]) ).
fof(f94,plain,
( ! [X0] : ~ sP2(X0)
| ~ spl3_9 ),
inference(forward_subsumption_resolution,[],[f93,f35]) ).
fof(f97,plain,
( spl3_1
| ~ spl3_9 ),
inference(avatar_split_clause,[],[f94,f76,f38]) ).
fof(f98,plain,
( ~ big_p(f(sK0))
| spl3_7
| ~ spl3_8 ),
inference(resolution,[],[f73,f67]) ).
fof(f100,plain,
( ~ spl3_10
| spl3_7
| ~ spl3_8 ),
inference(avatar_split_clause,[],[f98,f72,f65,f80]) ).
fof(f101,plain,
( ! [X1] :
( big_p(f(f(X1)))
| big_p(X1) )
| ~ spl3_1
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f47,f39]) ).
fof(f102,plain,
( spl3_9
| ~ spl3_1
| ~ spl3_3 ),
inference(avatar_split_clause,[],[f101,f46,f38,f76]) ).
fof(f103,plain,
( $false
| ~ spl3_1
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f52,f39]) ).
fof(f104,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f103]) ).
fof(f105,plain,
( spl3_11
| spl3_7
| ~ spl3_9 ),
inference(avatar_split_clause,[],[f92,f76,f65,f84]) ).
fof(f106,plain,
( ~ big_p(f(sK1))
| spl3_5
| ~ spl3_8 ),
inference(resolution,[],[f56,f73]) ).
fof(f107,plain,
( $false
| spl3_5
| ~ spl3_6
| ~ spl3_8 ),
inference(forward_subsumption_resolution,[],[f106,f61]) ).
fof(f108,plain,
( spl3_5
| ~ spl3_6
| ~ spl3_8 ),
inference(avatar_contradiction_clause,[],[f107]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f44]) ).
cnf(s2,plain,
( ~ spl3_2
| spl3_3 ),
inference(sat_conversion,[],[f48]) ).
cnf(s5,plain,
( spl3_2
| spl3_4 ),
inference(sat_conversion,[],[f63]) ).
cnf(s6,plain,
( spl3_4
| ~ spl3_5
| ~ spl3_7 ),
inference(sat_conversion,[],[f68]) ).
cnf(s7,plain,
( spl3_4
| spl3_6
| ~ spl3_7 ),
inference(sat_conversion,[],[f69]) ).
cnf(s9,plain,
( spl3_8
| ~ spl3_2
| spl3_8 ),
inference(sat_conversion,[],[f74]) ).
cnf(s10,plain,
( ~ spl3_2
| spl3_8 ),
inference(rat,[],[s9]) ).
cnf(s12,plain,
( spl3_4
| ~ spl3_5
| spl3_10
| ~ spl3_11 ),
inference(sat_conversion,[],[f87]) ).
cnf(s13,plain,
( spl3_4
| spl3_6
| spl3_10
| ~ spl3_11 ),
inference(sat_conversion,[],[f88]) ).
cnf(s15,plain,
( spl3_1
| ~ spl3_2
| spl3_9 ),
inference(sat_conversion,[],[f90]) ).
cnf(s18,plain,
( spl3_1
| ~ spl3_9 ),
inference(sat_conversion,[],[f97]) ).
cnf(s19,plain,
( spl3_7
| ~ spl3_8
| ~ spl3_10 ),
inference(sat_conversion,[],[f100]) ).
cnf(s20,plain,
( ~ spl3_1
| ~ spl3_3
| spl3_9 ),
inference(sat_conversion,[],[f102]) ).
cnf(s21,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(sat_conversion,[],[f104]) ).
cnf(s22,plain,
( spl3_7
| ~ spl3_9
| spl3_11 ),
inference(sat_conversion,[],[f105]) ).
cnf(s23,plain,
( spl3_5
| ~ spl3_6
| ~ spl3_8 ),
inference(sat_conversion,[],[f108]) ).
cnf(s24,plain,
( spl3_1
| spl3_9 ),
inference(rat,[],[s1,s15]) ).
cnf(s25,plain,
spl3_1,
inference(rat,[],[s24,s18]) ).
cnf(s26,plain,
~ spl3_4,
inference(rat,[],[s21,s25]) ).
cnf(s27,plain,
spl3_2,
inference(rat,[],[s5,s26]) ).
cnf(s28,plain,
spl3_8,
inference(rat,[],[s10,s27]) ).
cnf(s29,plain,
spl3_3,
inference(rat,[],[s2,s27]) ).
cnf(s30,plain,
spl3_9,
inference(rat,[],[s20,s25,s29]) ).
cnf(s31,plain,
spl3_6,
inference(rat,[],[s13,s19,s22,s7,s26,s28,s30]) ).
cnf(s32,plain,
spl3_5,
inference(rat,[],[s23,s28,s31]) ).
cnf(s33,plain,
~ spl3_7,
inference(rat,[],[s6,s26,s32]) ).
cnf(s34,plain,
spl3_11,
inference(rat,[],[s22,s30,s33]) ).
cnf(s35,plain,
~ spl3_10,
inference(rat,[],[s19,s28,s33]) ).
cnf(s36,plain,
$false,
inference(rat,[],[s12,s32,s26,s34,s35]) ).
fof(f109,plain,
$false,
inference(avatar_sat_refutation,[],[s36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN084+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n002.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 15:35:37 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 Running first-order model finding
% 0.07/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.25 % (454380)Will run a generic schedule for satisfiability detection.
% 0.07/0.25 % (454386)% WARNING: option uhcvi not known.
% 0.07/0.25 % (454386)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1180039791:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.25 % (454386) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-454380-454386"...
% 0.07/0.25 % (454386)...printing done.
% 0.07/0.25 % (454385)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3226172113_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.25 % (454387)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1750745041:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.25 % (454388)dis+10_1_sil=32000:sp=arity:random_seed=3607716487:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.25 % (454386)Refutation found. Thanks to Tanya!
% 0.07/0.25 % SZS status Theorem for theBenchmark
% 0.07/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.25 % (454386)------------------------------
% 0.07/0.25 % (454386)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.25 % (454386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.25 % (454386)CaDiCaL version: 2.1.3
% 0.07/0.25 % (454386)Termination reason: Refutation
% 0.07/0.25 % (454386)Time elapsed: 0.002 s
% 0.07/0.25 % (454386)Peak memory usage: 12 MB
% 0.07/0.25 % (454386)Instructions burned: 2 (million)
% 0.07/0.25 % (454380)Success in time 0.037 s
% 0.07/0.25 % Vampire exiting
%------------------------------------------------------------------------------