%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN069-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 : Unsatisfiable 0.07s 0.26s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 78 ( 14 unt; 8 def)
% Number of atoms : 209 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 216 ( 85 ~; 123 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 9 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ big_f(X0)
| big_g(f(X0))
| ~ big_g(X1)
| ~ big_h(X0,X1)
| big_k(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
fof(f2,axiom,
! [X0,X1] :
( ~ big_f(X0)
| big_h(X0,f(X0))
| ~ big_g(X1)
| ~ big_h(X0,X1)
| big_k(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
fof(f3,axiom,
! [X0,X1] :
( ~ big_f(X0)
| ~ big_j(X0,f(X0))
| ~ big_g(X1)
| ~ big_h(X0,X1)
| big_k(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
fof(f4,axiom,
! [X0] :
( ~ big_l(X0)
| ~ big_k(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
fof(f5,axiom,
big_f(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
fof(f6,axiom,
! [X0] :
( ~ big_h(a,X0)
| big_l(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
fof(f7,axiom,
! [X0] :
( ~ big_g(X0)
| ~ big_h(a,X0)
| big_j(a,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
fof(f8,negated_conjecture,
! [X0] :
( ~ big_f(X0)
| big_g(g(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
fof(f9,negated_conjecture,
! [X0] :
( ~ big_f(X0)
| big_h(X0,g(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
fof(f10,plain,
! [X0,X1] :
( big_g(X1)
| ~ big_g(f(X0))
| big_f(X0)
| big_h(X0,X1)
| ~ big_k(X1) ),
inference(consistent_polarity_flipping,[],[f1]) ).
fof(f11,plain,
! [X0,X1] :
( big_g(X1)
| ~ big_h(X0,f(X0))
| big_f(X0)
| big_h(X0,X1)
| ~ big_k(X1) ),
inference(consistent_polarity_flipping,[],[f2]) ).
fof(f12,plain,
! [X0,X1] :
( big_j(X0,f(X0))
| big_f(X0)
| big_g(X1)
| big_h(X0,X1)
| ~ big_k(X1) ),
inference(consistent_polarity_flipping,[],[f3]) ).
fof(f13,plain,
! [X0] :
( ~ big_l(X0)
| big_k(X0) ),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f14,plain,
~ big_f(a),
inference(consistent_polarity_flipping,[],[f5]) ).
fof(f15,plain,
! [X0] :
( big_l(X0)
| big_h(a,X0) ),
inference(consistent_polarity_flipping,[],[f6]) ).
fof(f16,plain,
! [X0] :
( ~ big_j(a,X0)
| big_h(a,X0)
| big_g(X0) ),
inference(consistent_polarity_flipping,[],[f7]) ).
fof(f17,plain,
! [X0] :
( ~ big_g(g(X0))
| big_f(X0) ),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f18,plain,
! [X0] :
( ~ big_h(X0,g(X0))
| big_f(X0) ),
inference(consistent_polarity_flipping,[],[f9]) ).
fof(f19,plain,
! [X0] :
( big_k(X0)
| big_h(a,X0) ),
inference(resolution,[],[f15,f13]) ).
fof(f20,plain,
! [X0,X1] :
( big_f(X1)
| big_f(X0)
| big_h(X0,g(X1))
| ~ big_k(g(X1))
| ~ big_g(f(X0)) ),
inference(resolution,[],[f10,f17]) ).
fof(f21,plain,
! [X0] :
( big_f(X0)
| big_h(X0,g(a))
| ~ big_k(g(a))
| ~ big_g(f(X0)) ),
inference(resolution,[],[f20,f14]) ).
fof(f23,definition,
( spl0_1
<=> big_k(g(a)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f25,plain,
( ~ big_k(g(a))
| spl0_1 ),
inference(avatar_component_clause,[],[f23]) ).
fof(f27,definition,
( spl0_2
<=> ! [X0] :
( big_f(X0)
| ~ big_g(f(X0))
| big_h(X0,g(a)) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f28,plain,
( ! [X0] :
( big_h(X0,g(a))
| ~ big_g(f(X0))
| big_f(X0) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f29,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f21,f27,f23]) ).
fof(f30,plain,
( big_h(a,g(a))
| spl0_1 ),
inference(resolution,[],[f25,f19]) ).
fof(f31,plain,
( big_f(a)
| spl0_1 ),
inference(resolution,[],[f30,f18]) ).
fof(f32,plain,
( $false
| spl0_1 ),
inference(resolution,[],[f31,f14]) ).
fof(f33,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f32]) ).
fof(f34,plain,
( ~ big_g(f(a))
| big_f(a)
| big_f(a)
| ~ spl0_2 ),
inference(resolution,[],[f28,f18]) ).
fof(f35,plain,
( ~ big_g(f(a))
| big_f(a)
| ~ spl0_2 ),
inference(duplicate_literal_removal,[],[f34]) ).
fof(f37,definition,
( spl0_3
<=> big_f(a) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f39,plain,
( big_f(a)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f41,definition,
( spl0_4
<=> big_g(f(a)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f44,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f35,f27,f41,f37]) ).
fof(f47,definition,
( spl0_5
<=> big_k(f(a)) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f49,plain,
( ~ big_k(f(a))
| spl0_5 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f54,plain,
( big_h(a,f(a))
| spl0_5 ),
inference(resolution,[],[f49,f19]) ).
fof(f55,plain,
! [X0,X1] :
( big_f(X1)
| big_f(X0)
| big_h(X0,g(X1))
| ~ big_k(g(X1))
| ~ big_h(X0,f(X0)) ),
inference(resolution,[],[f11,f17]) ).
fof(f57,plain,
! [X0] :
( big_f(a)
| big_g(X0)
| big_h(a,X0)
| ~ big_k(X0)
| big_h(a,f(a))
| big_g(f(a)) ),
inference(resolution,[],[f12,f16]) ).
fof(f58,plain,
! [X0] :
( big_f(X0)
| big_h(X0,g(a))
| ~ big_k(g(a))
| ~ big_h(X0,f(X0)) ),
inference(resolution,[],[f55,f14]) ).
fof(f60,definition,
( spl0_7
<=> ! [X0] :
( big_f(X0)
| ~ big_h(X0,f(X0))
| big_h(X0,g(a)) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f61,plain,
( ! [X0] :
( big_h(X0,g(a))
| ~ big_h(X0,f(X0))
| big_f(X0) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f62,plain,
( ~ spl0_1
| spl0_7 ),
inference(avatar_split_clause,[],[f58,f60,f23]) ).
fof(f63,plain,
( ~ big_h(a,f(a))
| big_f(a)
| big_f(a)
| ~ spl0_7 ),
inference(resolution,[],[f61,f18]) ).
fof(f64,plain,
( ~ big_h(a,f(a))
| big_f(a)
| ~ spl0_7 ),
inference(duplicate_literal_removal,[],[f63]) ).
fof(f66,definition,
( spl0_8
<=> big_h(a,f(a)) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f68,plain,
( ~ big_h(a,f(a))
| spl0_8 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f69,plain,
( spl0_3
| ~ spl0_8
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f64,f60,f66,f37]) ).
fof(f70,plain,
( $false
| spl0_5
| spl0_8 ),
inference(resolution,[],[f68,f54]) ).
fof(f71,plain,
( spl0_5
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f70]) ).
fof(f72,plain,
( $false
| ~ spl0_3 ),
inference(resolution,[],[f39,f14]) ).
fof(f73,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f72]) ).
fof(f79,definition,
( spl0_10
<=> ! [X0] :
( big_g(X0)
| ~ big_k(X0)
| big_h(a,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f80,plain,
( ! [X0] :
( big_h(a,X0)
| ~ big_k(X0)
| big_g(X0) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f81,plain,
( spl0_4
| spl0_8
| spl0_10
| spl0_3 ),
inference(avatar_split_clause,[],[f57,f37,f79,f66,f41]) ).
fof(f84,plain,
( ~ big_k(f(a))
| big_g(f(a))
| spl0_8
| ~ spl0_10 ),
inference(resolution,[],[f80,f68]) ).
fof(f91,plain,
( spl0_4
| ~ spl0_5
| spl0_8
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f84,f79,f66,f47,f41]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f29]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f33]) ).
cnf(s3,plain,
( ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f44]) ).
cnf(s5,plain,
( ~ spl0_1
| spl0_7 ),
inference(sat_conversion,[],[f62]) ).
cnf(s6,plain,
( spl0_3
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f69]) ).
cnf(s7,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f71]) ).
cnf(s8,plain,
~ spl0_3,
inference(sat_conversion,[],[f73]) ).
cnf(s10,plain,
( spl0_3
| spl0_4
| spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f81]) ).
cnf(s12,plain,
( spl0_4
| ~ spl0_5
| spl0_8
| ~ spl0_10 ),
inference(sat_conversion,[],[f91]) ).
cnf(s13,plain,
( ~ spl0_7
| ~ spl0_8 ),
inference(rat,[],[s6,s8]) ).
cnf(s14,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(rat,[],[s3,s8]) ).
cnf(s15,plain,
spl0_7,
inference(rat,[],[s5,s2]) ).
cnf(s16,plain,
~ spl0_8,
inference(rat,[],[s13,s15]) ).
cnf(s17,plain,
spl0_5,
inference(rat,[],[s7,s16]) ).
cnf(s18,plain,
spl0_2,
inference(rat,[],[s1,s2]) ).
cnf(s19,plain,
~ spl0_4,
inference(rat,[],[s14,s18]) ).
cnf(s20,plain,
~ spl0_10,
inference(rat,[],[s12,s17,s16,s19]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s10,s16,s8,s20,s19]) ).
fof(f92,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN069-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n026.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 15:31:30 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.23 Running first-order model finding
% 0.07/0.23 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
% 0.07/0.26 % (3944040)Will run a generic schedule for satisfiability detection.
% 0.07/0.26 % (3944051)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=430124664:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.26 % (3944051) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3944040-3944051"...
% 0.07/0.26 % (3944051)...printing done.
% 0.07/0.26 % (3944051)Refutation found. Thanks to Tanya!
% 0.07/0.26 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.26 % (3944051)------------------------------
% 0.07/0.26 % (3944051)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.26 % (3944051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.26 % (3944051)CaDiCaL version: 2.1.3
% 0.07/0.26 % (3944051)Termination reason: Refutation
% 0.07/0.26 % (3944051)Time elapsed: 0.002 s
% 0.07/0.26 % (3944051)Peak memory usage: 12 MB
% 0.07/0.26 % (3944051)Instructions burned: 2 (million)
% 0.07/0.26 % (3944040)Success in time 0.025 s
% 0.07/0.26 % Vampire exiting
%------------------------------------------------------------------------------