%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN069+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 : n005.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 02:06:40 PM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 82 ( 12 unt; 8 def)
% Number of atoms : 212 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 212 ( 82 ~; 81 |; 38 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 8 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 60 ( 0 sgn 47 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ( big_f(X0)
& ! [X1] :
( ( big_g(X1)
& big_h(X0,X1) )
=> big_j(X0,X1) ) )
=> ! [X2] :
( big_g(X2)
& big_h(X0,X2)
& big_k(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel45_1) ).
fof(f2,axiom,
~ ? [X0] :
( big_l(X0)
& big_k(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel45_2) ).
fof(f3,axiom,
? [X0] :
( big_f(X0)
& ! [X1] :
( big_h(X0,X1)
=> big_l(X1) )
& ! [X2] :
( ( big_g(X2)
& big_h(X0,X2) )
=> big_j(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel45_3) ).
fof(f4,conjecture,
? [X0] :
( big_f(X0)
& ~ ? [X1] :
( big_g(X1)
& big_h(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel45) ).
fof(f5,negated_conjecture,
~ ? [X0] :
( big_f(X0)
& ~ ? [X1] :
( big_g(X1)
& big_h(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [X0] :
( ! [X2] :
( big_g(X2)
& big_h(X0,X2)
& big_k(X2) )
| ~ big_f(X0)
| ? [X1] :
( ~ big_j(X0,X1)
& big_g(X1)
& big_h(X0,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f7,plain,
! [X0] :
( ! [X2] :
( big_g(X2)
& big_h(X0,X2)
& big_k(X2) )
| ~ big_f(X0)
| ? [X1] :
( ~ big_j(X0,X1)
& big_g(X1)
& big_h(X0,X1) ) ),
inference(flattening,[],[f6]) ).
fof(f8,plain,
! [X0] :
( ~ big_l(X0)
| ~ big_k(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
? [X0] :
( big_f(X0)
& ! [X1] :
( big_l(X1)
| ~ big_h(X0,X1) )
& ! [X2] :
( big_j(X0,X2)
| ~ big_g(X2)
| ~ big_h(X0,X2) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f10,plain,
? [X0] :
( big_f(X0)
& ! [X1] :
( big_l(X1)
| ~ big_h(X0,X1) )
& ! [X2] :
( big_j(X0,X2)
| ~ big_g(X2)
| ~ big_h(X0,X2) ) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0] :
( ~ big_f(X0)
| ? [X1] :
( big_g(X1)
& big_h(X0,X1) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f12,definition,
! [X0] :
( ? [X1] :
( ~ big_j(X0,X1)
& big_g(X1)
& big_h(X0,X1) )
| ~ sP0(X0) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f13,plain,
! [X0] :
( ! [X2] :
( big_g(X2)
& big_h(X0,X2)
& big_k(X2) )
| ~ big_f(X0)
| sP0(X0) ),
inference(definition_folding,[],[f7,f12]) ).
fof(f14,plain,
! [X0] :
( ? [X1] :
( ~ big_j(X0,X1)
& big_g(X1)
& big_h(X0,X1) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f12]) ).
fof(f15,plain,
! [X0] :
( ( ~ big_j(X0,sK1(X0))
& big_g(sK1(X0))
& big_h(X0,sK1(X0)) )
| ~ sP0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f14]) ).
fof(f16,plain,
! [X0] :
( ! [X1] :
( big_g(X1)
& big_h(X0,X1)
& big_k(X1) )
| ~ big_f(X0)
| sP0(X0) ),
inference(rectify,[],[f13]) ).
fof(f17,plain,
( big_f(sK2)
& ! [X1] :
( big_l(X1)
| ~ big_h(sK2,X1) )
& ! [X2] :
( big_j(sK2,X2)
| ~ big_g(X2)
| ~ big_h(sK2,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f10]) ).
fof(f18,plain,
! [X0] :
( ~ big_f(X0)
| ( big_g(sK3(X0))
& big_h(X0,sK3(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f11]) ).
fof(f19,plain,
! [X0] :
( big_h(X0,sK1(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f20,plain,
! [X0] :
( big_g(sK1(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f21,plain,
! [X0] :
( ~ big_j(X0,sK1(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f22,plain,
! [X0,X1] :
( big_k(X1)
| ~ big_f(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f25,plain,
! [X0] :
( ~ big_l(X0)
| ~ big_k(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f26,plain,
! [X2] :
( big_j(sK2,X2)
| ~ big_g(X2)
| ~ big_h(sK2,X2) ),
inference(cnf_transformation,[],[f17]) ).
fof(f27,plain,
! [X1] :
( big_l(X1)
| ~ big_h(sK2,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f28,plain,
big_f(sK2),
inference(cnf_transformation,[],[f17]) ).
fof(f29,plain,
! [X0] :
( ~ big_f(X0)
| big_h(X0,sK3(X0)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
! [X0] :
( sP0(X0)
| ~ big_j(X0,sK1(X0)) ),
inference(consistent_polarity_flipping,[],[f21]) ).
fof(f32,plain,
! [X0] :
( big_g(sK1(X0))
| sP0(X0) ),
inference(consistent_polarity_flipping,[],[f20]) ).
fof(f33,plain,
! [X0] :
( sP0(X0)
| ~ big_h(X0,sK1(X0)) ),
inference(consistent_polarity_flipping,[],[f19]) ).
fof(f36,plain,
! [X0,X1] :
( big_k(X1)
| big_f(X0)
| ~ sP0(X0) ),
inference(consistent_polarity_flipping,[],[f22]) ).
fof(f37,plain,
~ big_f(sK2),
inference(consistent_polarity_flipping,[],[f28]) ).
fof(f38,plain,
! [X1] :
( big_l(X1)
| big_h(sK2,X1) ),
inference(consistent_polarity_flipping,[],[f27]) ).
fof(f39,plain,
! [X2] :
( big_j(sK2,X2)
| ~ big_g(X2)
| big_h(sK2,X2) ),
inference(consistent_polarity_flipping,[],[f26]) ).
fof(f41,plain,
! [X0] :
( ~ big_h(X0,sK3(X0))
| big_f(X0) ),
inference(consistent_polarity_flipping,[],[f29]) ).
fof(f43,definition,
( spl4_1
<=> ! [X0] :
( big_f(X0)
| ~ sP0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f44,plain,
( ! [X0] :
( ~ sP0(X0)
| big_f(X0) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f46,definition,
( spl4_2
<=> ! [X1] : big_k(X1) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f47,plain,
( ! [X1] : big_k(X1)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f48,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f36,f46,f43]) ).
fof(f53,plain,
! [X0] :
( big_h(sK2,X0)
| ~ big_k(X0) ),
inference(resolution,[],[f38,f25]) ).
fof(f54,plain,
( ~ big_k(sK3(sK2))
| big_f(sK2) ),
inference(resolution,[],[f53,f41]) ).
fof(f56,definition,
( spl4_4
<=> big_f(sK2) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f58,plain,
( big_f(sK2)
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f60,definition,
( spl4_5
<=> big_k(sK3(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f62,plain,
( ~ big_k(sK3(sK2))
| spl4_5 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,plain,
( spl4_4
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f54,f60,f56]) ).
fof(f64,plain,
( $false
| ~ spl4_2
| spl4_5 ),
inference(resolution,[],[f62,f47]) ).
fof(f65,plain,
( ~ spl4_2
| spl4_5 ),
inference(avatar_contradiction_clause,[],[f64]) ).
fof(f66,plain,
( $false
| ~ spl4_4 ),
inference(resolution,[],[f58,f37]) ).
fof(f67,plain,
~ spl4_4,
inference(avatar_contradiction_clause,[],[f66]) ).
fof(f72,definition,
( spl4_6
<=> sP0(sK2) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f73,plain,
( sP0(sK2)
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f74,plain,
( ~ sP0(sK2)
| spl4_6 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f80,plain,
( ~ big_j(sK2,sK1(sK2))
| spl4_6 ),
inference(resolution,[],[f74,f31]) ).
fof(f82,plain,
( ~ big_g(sK1(sK2))
| big_h(sK2,sK1(sK2))
| spl4_6 ),
inference(resolution,[],[f39,f80]) ).
fof(f84,definition,
( spl4_8
<=> big_h(sK2,sK1(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
fof(f88,definition,
( spl4_9
<=> big_g(sK1(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition]) ).
fof(f90,plain,
( ~ big_g(sK1(sK2))
| spl4_9 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,plain,
( spl4_8
| ~ spl4_9
| spl4_6 ),
inference(avatar_split_clause,[],[f82,f72,f88,f84]) ).
fof(f94,plain,
( sP0(sK2)
| spl4_9 ),
inference(resolution,[],[f32,f90]) ).
fof(f95,plain,
( spl4_6
| spl4_9 ),
inference(avatar_split_clause,[],[f94,f88,f72]) ).
fof(f96,plain,
( big_f(sK2)
| ~ spl4_1
| ~ spl4_6 ),
inference(resolution,[],[f73,f44]) ).
fof(f97,plain,
( spl4_4
| ~ spl4_1
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f96,f72,f43,f56]) ).
fof(f98,plain,
( ~ big_h(sK2,sK1(sK2))
| spl4_6 ),
inference(resolution,[],[f74,f33]) ).
fof(f104,plain,
( ~ spl4_8
| spl4_6 ),
inference(avatar_split_clause,[],[f98,f72,f84]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f48]) ).
cnf(s3,plain,
( spl4_4
| ~ spl4_5 ),
inference(sat_conversion,[],[f63]) ).
cnf(s4,plain,
( ~ spl4_2
| spl4_5 ),
inference(sat_conversion,[],[f65]) ).
cnf(s5,plain,
~ spl4_4,
inference(sat_conversion,[],[f67]) ).
cnf(s7,plain,
( spl4_6
| spl4_8
| ~ spl4_9 ),
inference(sat_conversion,[],[f91]) ).
cnf(s9,plain,
( spl4_6
| spl4_9 ),
inference(sat_conversion,[],[f95]) ).
cnf(s10,plain,
( ~ spl4_1
| spl4_4
| ~ spl4_6 ),
inference(sat_conversion,[],[f97]) ).
cnf(s12,plain,
( spl4_6
| ~ spl4_8 ),
inference(sat_conversion,[],[f104]) ).
cnf(s13,plain,
~ spl4_5,
inference(rat,[],[s3,s5]) ).
cnf(s14,plain,
~ spl4_2,
inference(rat,[],[s4,s13]) ).
cnf(s15,plain,
spl4_1,
inference(rat,[],[s1,s14]) ).
cnf(s16,plain,
~ spl4_6,
inference(rat,[],[s10,s5,s15]) ).
cnf(s17,plain,
~ spl4_8,
inference(rat,[],[s12,s16]) ).
cnf(s18,plain,
spl4_9,
inference(rat,[],[s9,s16]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s7,s18,s17,s16]) ).
fof(f105,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN069+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n005.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 15:28:35 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 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
% 0.07/0.26 % (867100)Will run a generic schedule for satisfiability detection.
% 0.07/0.26 % (867111)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4046930646:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.26 % (867111) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-867100-867111"...
% 0.07/0.26 % (867111)...printing done.
% 0.07/0.26 % (867106)% WARNING: option uhcvi not known.
% 0.07/0.26 % (867111)Refutation found. Thanks to Tanya!
% 0.07/0.26 % SZS status Theorem for theBenchmark
% 0.07/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.26 % (867111)------------------------------
% 0.07/0.26 % (867111)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.26 % (867111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.26 % (867111)CaDiCaL version: 2.1.3
% 0.07/0.26 % (867111)Termination reason: Refutation
% 0.07/0.26 % (867111)Time elapsed: 0.002 s
% 0.07/0.26 % (867111)Peak memory usage: 12 MB
% 0.07/0.26 % (867111)Instructions burned: 2 (million)
% 0.07/0.26 % (867100)Success in time 0.029 s
% 0.07/0.26 % Vampire exiting
%------------------------------------------------------------------------------