%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN965+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 02:22:58 PM UTC 2026
% Result : Theorem 0.18s 0.26s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 5 unt; 2 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 62 ( 27 ~; 16 |; 13 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 43 ( 0 sgn 35 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0] :
! [X1] :
? [X2] :
( ( p(X2,X1)
=> ? [X3] : p(X3,X2) )
& ( ( p(X0,X2)
& p(X2,X0) )
=> p(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f2,negated_conjecture,
~ ? [X0] :
! [X1] :
? [X2] :
( ( p(X2,X1)
=> ? [X3] : p(X3,X2) )
& ( ( p(X0,X2)
& p(X2,X0) )
=> p(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
! [X0] :
? [X1] :
! [X2] :
( ( ! [X3] : ~ p(X3,X2)
& p(X2,X1) )
| ( ~ p(X2,X1)
& p(X0,X2)
& p(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
! [X0] :
? [X1] :
! [X2] :
( ( ! [X3] : ~ p(X3,X2)
& p(X2,X1) )
| ( ~ p(X2,X1)
& p(X0,X2)
& p(X2,X0) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
! [X0,X2] :
( ( ! [X3] : ~ p(X3,X2)
& p(X2,sK0(X0)) )
| ( ~ p(X2,sK0(X0))
& p(X0,X2)
& p(X2,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f4]) ).
fof(f6,plain,
! [X2,X0] :
( p(X2,sK0(X0))
| p(X2,X0) ),
inference(cnf_transformation,[],[f5]) ).
fof(f9,plain,
! [X2,X3,X0] :
( p(X2,X0)
| ~ p(X3,X2) ),
inference(cnf_transformation,[],[f5]) ).
fof(f11,plain,
! [X2,X3,X0] :
( ~ p(X3,X2)
| ~ p(X2,sK0(X0)) ),
inference(cnf_transformation,[],[f5]) ).
fof(f13,plain,
! [X2,X3,X0,X1] :
( ~ p(X1,sK0(X2))
| ~ p(X3,X0) ),
inference(resolution,[],[f11,f9]) ).
fof(f22,definition,
( spl1_1
<=> ! [X1,X3] : ~ p(X3,sK0(X1)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f23,plain,
( ! [X3,X1] : ~ p(X3,sK0(X1))
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f22]) ).
fof(f25,definition,
( spl1_2
<=> ! [X2,X0] : ~ p(X2,X0) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f26,plain,
( ! [X2,X0] : ~ p(X2,X0)
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f28,plain,
( spl1_2
| spl1_1 ),
inference(avatar_split_clause,[],[f13,f22,f25]) ).
fof(f30,plain,
( ! [X0,X1] : p(X0,X1)
| ~ spl1_2 ),
inference(resolution,[],[f26,f6]) ).
fof(f31,plain,
( $false
| ~ spl1_2 ),
inference(resolution,[],[f30,f26]) ).
fof(f32,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f31]) ).
fof(f33,plain,
( ! [X0,X1] : ~ p(X0,X1)
| ~ spl1_1 ),
inference(resolution,[],[f9,f23]) ).
fof(f34,plain,
( spl1_2
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f33,f22,f25]) ).
cnf(s2,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f28]) ).
cnf(s3,plain,
~ spl1_2,
inference(sat_conversion,[],[f32]) ).
cnf(s4,plain,
( ~ spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f34]) ).
cnf(s5,plain,
~ spl1_1,
inference(rat,[],[s4,s3]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s2,s3,s5]) ).
fof(f35,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN965+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n018.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 17:19:11 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 0.18/0.26 % (3552342)Will run a generic schedule for satisfiability detection.
% 0.18/0.26 % (3552353)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=334720475:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.26 % (3552353) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3552342-3552353"...
% 0.18/0.26 % (3552353)...printing done.
% 0.18/0.26 % (3552353)Refutation found. Thanks to Tanya!
% 0.18/0.26 % SZS status Theorem for theBenchmark
% 0.18/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.26 % (3552353)------------------------------
% 0.18/0.26 % (3552353)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.26 % (3552353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.26 % (3552353)CaDiCaL version: 2.1.3
% 0.18/0.26 % (3552353)Termination reason: Refutation
% 0.18/0.26 % (3552353)Time elapsed: 0.001 s
% 0.18/0.26 % (3552353)Peak memory usage: 12 MB
% 0.18/0.26 % (3552353)Instructions burned: 1 (million)
% 0.18/0.26 % (3552342)Success in time 0.028 s
% 0.18/0.26 % Vampire exiting
%------------------------------------------------------------------------------