%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN399+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 : n004.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 02:07:46 PM UTC 2026
% Result : Theorem 0.27s 0.30s
% Output : Refutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 5 unt; 4 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 106 ( 42 ~; 39 |; 13 &)
% ( 9 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 6 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 24 ( 0 sgn 21 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] :
( f(X0)
<=> p )
=> ( ! [X1] : f(X1)
<=> p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kalish223) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
( f(X0)
<=> p )
=> ( ! [X1] : f(X1)
<=> p ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( ! [X1] : f(X1)
<~> p )
& ! [X0] :
( f(X0)
<=> p ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ( ~ p
| ? [X1] : ~ f(X1) )
& ( p
| ! [X1] : f(X1) )
& ! [X0] :
( ( f(X0)
| ~ p )
& ( p
| ~ f(X0) ) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f5,plain,
( ( ~ p
| ? [X1] : ~ f(X1) )
& ( p
| ! [X1] : f(X1) )
& ! [X0] :
( ( f(X0)
| ~ p )
& ( p
| ~ f(X0) ) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
( ( ~ p
| ? [X0] : ~ f(X0) )
& ( p
| ! [X1] : f(X1) )
& ! [X2] :
( ( f(X2)
| ~ p )
& ( p
| ~ f(X2) ) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ( ~ p
| ~ f(sK0) )
& ( p
| ! [X1] : f(X1) )
& ! [X2] :
( ( f(X2)
| ~ p )
& ( p
| ~ f(X2) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f6]) ).
fof(f8,plain,
! [X2] :
( p
| ~ f(X2) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X2] :
( f(X2)
| ~ p ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
! [X1] :
( p
| f(X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
( ~ p
| ~ f(sK0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,definition,
( spl1_1
<=> ! [X2] : ~ f(X2) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f14,plain,
( ! [X2] : ~ f(X2)
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f13]) ).
fof(f16,definition,
( spl1_2
<=> p ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f19,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f8,f16,f13]) ).
fof(f21,definition,
( spl1_3
<=> ! [X2] : f(X2) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f22,plain,
( ! [X2] : f(X2)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f23,plain,
( ~ spl1_2
| spl1_3 ),
inference(avatar_split_clause,[],[f9,f21,f16]) ).
fof(f24,plain,
( spl1_3
| spl1_2 ),
inference(avatar_split_clause,[],[f10,f16,f21]) ).
fof(f26,definition,
( spl1_4
<=> f(sK0) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f28,plain,
( ~ f(sK0)
| spl1_4 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f29,plain,
( ~ spl1_4
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f11,f16,f26]) ).
fof(f30,plain,
( $false
| ~ spl1_3
| spl1_4 ),
inference(forward_subsumption_resolution,[],[f28,f22]) ).
fof(f31,plain,
( ~ spl1_3
| spl1_4 ),
inference(avatar_contradiction_clause,[],[f30]) ).
fof(f32,plain,
( $false
| ~ spl1_1
| ~ spl1_3 ),
inference(forward_subsumption_resolution,[],[f14,f22]) ).
fof(f33,plain,
( ~ spl1_1
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[],[f32]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f19]) ).
cnf(s2,plain,
( ~ spl1_2
| spl1_3 ),
inference(sat_conversion,[],[f23]) ).
cnf(s3,plain,
( spl1_2
| spl1_3 ),
inference(sat_conversion,[],[f24]) ).
cnf(s4,plain,
( ~ spl1_2
| ~ spl1_4 ),
inference(sat_conversion,[],[f29]) ).
cnf(s5,plain,
( ~ spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f31]) ).
cnf(s6,plain,
( ~ spl1_1
| ~ spl1_3 ),
inference(sat_conversion,[],[f33]) ).
cnf(s7,plain,
~ spl1_2,
inference(rat,[],[s5,s2,s4]) ).
cnf(s8,plain,
spl1_3,
inference(rat,[],[s3,s7]) ).
cnf(s9,plain,
spl1_1,
inference(rat,[],[s1,s7]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s6,s8,s9]) ).
fof(f34,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN399+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 % Computer : n004.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Mon Sep 28 15:54:07 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.27 Running first-order model finding
% 0.10/0.27 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
% 0.27/0.30 % (486797)Will run a generic schedule for satisfiability detection.
% 0.27/0.30 % (486805)dis+10_1_sil=32000:sp=arity:random_seed=2478612517:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.27/0.30 % (486805) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-486797-486805"...
% 0.27/0.30 % (486802)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=105248406_3000 on theBenchmark for (3000ds/0Mi)
% 0.27/0.30 % (486805)...printing done.
% 0.27/0.30 % Detected minimum model sizes of [1]
% 0.27/0.30 % Detected maximum model sizes of [1]
% 0.27/0.30 % TRYING [1]
% 0.27/0.30 % (486805)Refutation found. Thanks to Tanya!
% 0.27/0.30 % SZS status Theorem for theBenchmark
% 0.27/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.27/0.30 % (486805)------------------------------
% 0.27/0.30 % (486805)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.30 % (486805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.30 % (486805)CaDiCaL version: 2.1.3
% 0.27/0.30 % (486805)Termination reason: Refutation
% 0.27/0.30 % (486805)Time elapsed: 0.001 s
% 0.27/0.30 % (486805)Peak memory usage: 12 MB
% 0.27/0.30 % (486805)Instructions burned: 1 (million)
% 0.27/0.30 % (486797)Success in time 0.023 s
% 0.27/0.30 % Vampire exiting
%------------------------------------------------------------------------------