%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN318+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 : 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 02:07:17 PM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 7 unt; 2 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 81 ( 32 ~; 20 |; 8 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 32 ( 0 sgn 25 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0] :
( ! [X1] :
( big_f(X1)
=> ( big_f(X0)
=> big_g(X1) ) )
=> ( p
=> ! [X1] :
( big_f(X1)
=> big_g(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_2_4) ).
fof(f2,negated_conjecture,
~ ? [X0] :
( ! [X1] :
( big_f(X1)
=> ( big_f(X0)
=> big_g(X1) ) )
=> ( p
=> ! [X1] :
( big_f(X1)
=> big_g(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ? [X0] :
( ! [X1] :
( big_f(X1)
=> ( big_f(X0)
=> big_g(X1) ) )
=> ( p
=> ! [X2] :
( big_f(X2)
=> big_g(X0) ) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
~ ? [X0] :
( ! [X1] :
( big_f(X1)
=> ( big_f(X0)
=> big_g(X1) ) )
=> ! [X2] :
( big_f(X2)
=> big_g(X0) ) ),
inference(pure_predicate_removal,[],[f3]) ).
fof(f5,plain,
! [X0] :
( ? [X2] :
( ~ big_g(X0)
& big_f(X2) )
& ! [X1] :
( big_g(X1)
| ~ big_f(X0)
| ~ big_f(X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f6,plain,
! [X0] :
( ? [X2] :
( ~ big_g(X0)
& big_f(X2) )
& ! [X1] :
( big_g(X1)
| ~ big_f(X0)
| ~ big_f(X1) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X0] :
( ? [X1] :
( ~ big_g(X0)
& big_f(X1) )
& ! [X2] :
( big_g(X2)
| ~ big_f(X0)
| ~ big_f(X2) ) ),
inference(rectify,[],[f6]) ).
fof(f8,plain,
! [X0] :
( ~ big_g(X0)
& big_f(sK0(X0))
& ! [X2] :
( big_g(X2)
| ~ big_f(X0)
| ~ big_f(X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f7]) ).
fof(f9,plain,
! [X2,X0] :
( big_g(X2)
| ~ big_f(X0)
| ~ big_f(X2) ),
inference(cnf_transformation,[],[f8]) ).
fof(f10,plain,
! [X0] : big_f(sK0(X0)),
inference(cnf_transformation,[],[f8]) ).
fof(f11,plain,
! [X0] : ~ big_g(X0),
inference(cnf_transformation,[],[f8]) ).
fof(f13,definition,
( spl1_1
<=> ! [X0] : ~ big_f(X0) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f14,plain,
( ! [X0] : ~ big_f(X0)
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f13]) ).
fof(f16,definition,
( spl1_2
<=> ! [X2] :
( big_g(X2)
| ~ big_f(X2) ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f17,plain,
( ! [X2] :
( big_g(X2)
| ~ big_f(X2) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f18,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f9,f16,f13]) ).
fof(f19,plain,
( ! [X2] : ~ big_f(X2)
| ~ spl1_2 ),
inference(forward_subsumption_resolution,[],[f17,f11]) ).
fof(f20,plain,
( spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f19,f16,f13]) ).
fof(f21,plain,
( $false
| ~ spl1_1 ),
inference(resolution,[],[f10,f14]) ).
fof(f22,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f21]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f18]) ).
cnf(s2,plain,
( spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f20]) ).
cnf(s3,plain,
~ spl1_1,
inference(sat_conversion,[],[f22]) ).
cnf(s4,plain,
~ spl1_2,
inference(rat,[],[s2,s3]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s3]) ).
fof(f23,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN318+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n026.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 15:44:46 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.20/0.28 % (3962322)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (3962344)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4258479504:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (3962344) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3962322-3962344"...
% 0.20/0.28 % (3962344)...printing done.
% 0.20/0.28 % (3962344)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (3962344)------------------------------
% 0.20/0.28 % (3962344)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3962344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3962344)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3962344)Termination reason: Refutation
% 0.20/0.28 % (3962344)Time elapsed: 0.001 s
% 0.20/0.28 % (3962344)Peak memory usage: 12 MB
% 0.20/0.28 % (3962322)Success in time 0.039 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------