%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN063+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 : n013.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 02:06:37 PM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 8 unt; 6 def)
% Number of atoms : 141 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 148 ( 57 ~; 69 |; 8 &)
% ( 8 <=>; 4 =>; 0 <=; 2 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 7 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 20 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] :
( ( big_p(a)
& ( big_p(X0)
=> big_p(b) ) )
=> big_p(c) )
<=> ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| big_p(c) )
& ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel33) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
( ( big_p(a)
& ( big_p(X0)
=> big_p(b) ) )
=> big_p(c) )
<=> ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| big_p(c) )
& ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X0] :
( big_p(c)
| ~ big_p(a)
| ( ~ big_p(b)
& big_p(X0) ) )
<~> ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| big_p(c) )
& ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ! [X0] :
( big_p(c)
| ~ big_p(a)
| ( ~ big_p(b)
& big_p(X0) ) )
<~> ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| big_p(c) )
& ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
! [X1] :
( ~ big_p(c)
| 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(c)
| 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,
( ~ sP2(sK1)
| ~ big_p(c) ),
inference(cnf_transformation,[],[f4]) ).
fof(f20,plain,
! [X0,X1] :
( sP2(X1)
| big_p(X0)
| ~ big_p(a)
| big_p(c) ),
inference(cnf_transformation,[],[f4]) ).
fof(f23,definition,
( spl3_1
<=> ! [X1] : sP2(X1) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f24,plain,
( ! [X1] : sP2(X1)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f23]) ).
fof(f26,definition,
( spl3_2
<=> big_p(c) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f28,plain,
( ~ big_p(c)
| spl3_2 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f29,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f5,f26,f23]) ).
fof(f31,definition,
( spl3_3
<=> big_p(a) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f34,plain,
( spl3_1
| spl3_3 ),
inference(avatar_split_clause,[],[f7,f31,f23]) ).
fof(f36,definition,
( spl3_4
<=> ! [X1] :
( big_p(X1)
| ~ sP2(X1) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f37,plain,
( ! [X1] :
( ~ sP2(X1)
| big_p(X1) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f38,plain,
( ~ spl3_3
| spl3_4
| spl3_2 ),
inference(avatar_split_clause,[],[f8,f26,f36,f31]) ).
fof(f40,definition,
( spl3_5
<=> sP2(sK1) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f42,plain,
( ~ sP2(sK1)
| spl3_5 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f48,plain,
( spl3_3
| ~ spl3_5 ),
inference(avatar_split_clause,[],[f11,f40,f31]) ).
fof(f49,plain,
( ~ spl3_2
| ~ spl3_5 ),
inference(avatar_split_clause,[],[f12,f40,f26]) ).
fof(f53,definition,
( spl3_7
<=> ! [X0] : big_p(X0) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f54,plain,
( ! [X0] : big_p(X0)
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f61,plain,
( spl3_2
| ~ spl3_3
| spl3_7
| spl3_1 ),
inference(avatar_split_clause,[],[f20,f23,f53,f31,f26]) ).
fof(f63,plain,
( $false
| spl3_2
| ~ spl3_7 ),
inference(resolution,[],[f54,f28]) ).
fof(f66,plain,
( spl3_2
| ~ spl3_7 ),
inference(avatar_contradiction_clause,[],[f63]) ).
fof(f67,plain,
( $false
| ~ spl3_1
| spl3_5 ),
inference(resolution,[],[f24,f42]) ).
fof(f68,plain,
( ~ spl3_1
| spl3_5 ),
inference(avatar_contradiction_clause,[],[f67]) ).
fof(f70,plain,
( ! [X0] : big_p(X0)
| ~ spl3_1
| ~ spl3_4 ),
inference(resolution,[],[f37,f24]) ).
fof(f71,plain,
( spl3_7
| ~ spl3_1
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f70,f36,f23,f53]) ).
cnf(s1,plain,
( spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f29]) ).
cnf(s2,plain,
( spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f34]) ).
cnf(s3,plain,
( spl3_2
| ~ spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f38]) ).
cnf(s5,plain,
( spl3_3
| ~ spl3_5 ),
inference(sat_conversion,[],[f48]) ).
cnf(s6,plain,
( ~ spl3_2
| ~ spl3_5 ),
inference(sat_conversion,[],[f49]) ).
cnf(s11,plain,
( spl3_1
| spl3_2
| ~ spl3_3
| spl3_7 ),
inference(sat_conversion,[],[f61]) ).
cnf(s14,plain,
( spl3_2
| ~ spl3_7 ),
inference(sat_conversion,[],[f66]) ).
cnf(s15,plain,
( ~ spl3_1
| spl3_5 ),
inference(sat_conversion,[],[f68]) ).
cnf(s16,plain,
( ~ spl3_1
| ~ spl3_4
| spl3_7 ),
inference(sat_conversion,[],[f71]) ).
cnf(s17,plain,
spl3_1,
inference(rat,[],[s11,s14,s1,s2]) ).
cnf(s18,plain,
spl3_5,
inference(rat,[],[s15,s17]) ).
cnf(s19,plain,
~ spl3_2,
inference(rat,[],[s6,s18]) ).
cnf(s20,plain,
spl3_3,
inference(rat,[],[s5,s18]) ).
cnf(s21,plain,
~ spl3_7,
inference(rat,[],[s14,s19]) ).
cnf(s22,plain,
spl3_4,
inference(rat,[],[s3,s20,s19]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s16,s17,s21,s22]) ).
fof(f72,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN063+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n013.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Mon Sep 28 15:26:51 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 Running first-order model finding
% 0.10/0.22 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
% 0.10/0.26 % (1270830)Will run a generic schedule for satisfiability detection.
% 0.10/0.26 % (1270839)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=346829401:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.26 % (1270839) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1270830-1270839"...
% 0.10/0.26 % (1270839)...printing done.
% 0.10/0.26 % (1270836)% WARNING: option uhcvi not known.
% 0.10/0.26 % (1270839)Refutation found. Thanks to Tanya!
% 0.10/0.26 % SZS status Theorem for theBenchmark
% 0.10/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.26 % (1270839)------------------------------
% 0.10/0.26 % (1270839)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.26 % (1270839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.26 % (1270839)CaDiCaL version: 2.1.3
% 0.10/0.26 % (1270839)Termination reason: Refutation
% 0.10/0.26 % (1270839)Time elapsed: 0.001 s
% 0.10/0.26 % (1270839)Peak memory usage: 12 MB
% 0.10/0.26 % (1270839)Instructions burned: 2 (million)
% 0.10/0.26 % (1270830)Success in time 0.026 s
% 0.10/0.26 % Vampire exiting
%------------------------------------------------------------------------------