%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN358^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 : Wed Sep 30 08:41:51 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 8 unt; 0 typ; 4 def)
% Number of atoms : 242 ( 60 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 163 ( 51 ~; 43 |; 22 &; 38 @)
% ( 8 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 9 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 14 !; 16 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cQ: $i > $o ).
thf(func_def_1,type,
p: $o ).
thf(f1,conjecture,
( ? [X0: $i] :
( ( cQ @ X0 )
& p )
<=> ( ? [X0: $i] : ( cQ @ X0 )
& p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX2109) ).
thf(f2,negated_conjecture,
~ ( ? [X0: $i] :
( ( cQ @ X0 )
& p )
<=> ( ? [X0: $i] : ( cQ @ X0 )
& p ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ? [X0: $i] :
( ( cQ @ X0 )
& p )
<=> ( ? [X1: $i] : ( cQ @ X1 )
& p ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ? [X0: $i] :
( ( ( cQ @ X0 )
= $true )
& ( p = $true ) )
<=> ( ? [X1: $i] :
( ( cQ @ X1 )
= $true )
& ( p = $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ? [X0: $i] :
( ( ( cQ @ X0 )
= $true )
& ( p = $true ) )
<~> ( ? [X1: $i] :
( ( cQ @ X1 )
= $true )
& ( p = $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ! [X1: $i] :
( ( cQ @ X1 )
!= $true )
| ( p != $true )
| ! [X0: $i] :
( ( ( cQ @ X0 )
!= $true )
| ( p != $true ) ) )
& ( ( ? [X1: $i] :
( ( cQ @ X1 )
= $true )
& ( p = $true ) )
| ? [X0: $i] :
( ( ( cQ @ X0 )
= $true )
& ( p = $true ) ) ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f7,plain,
( ( ! [X1: $i] :
( ( cQ @ X1 )
!= $true )
| ( p != $true )
| ! [X0: $i] :
( ( ( cQ @ X0 )
!= $true )
| ( p != $true ) ) )
& ( ( ? [X1: $i] :
( ( cQ @ X1 )
= $true )
& ( p = $true ) )
| ? [X0: $i] :
( ( ( cQ @ X0 )
= $true )
& ( p = $true ) ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
( ( ! [X0: $i] :
( ( cQ @ X0 )
!= $true )
| ( p != $true )
| ! [X1: $i] :
( ( ( cQ @ X1 )
!= $true )
| ( p != $true ) ) )
& ( ( ? [X2: $i] :
( $true
= ( cQ @ X2 ) )
& ( p = $true ) )
| ? [X3: $i] :
( ( $true
= ( cQ @ X3 ) )
& ( p = $true ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ( ! [X0: $i] :
( ( cQ @ X0 )
!= $true )
| ( p != $true )
| ! [X1: $i] :
( ( ( cQ @ X1 )
!= $true )
| ( p != $true ) ) )
& ( ( ( $true
= ( cQ @ sK0 ) )
& ( p = $true ) )
| ( ( $true
= ( cQ @ sK1 ) )
& ( p = $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0),skolemize(X3,sK1)],[f8]) ).
thf(f10,plain,
( ( p = $true )
| ( p = $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
( ( $true
= ( cQ @ sK0 ) )
| ( $true
= ( cQ @ sK1 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f14,plain,
! [X0: $i,X1: $i] :
( ( ( cQ @ X0 )
!= $true )
| ( p != $true )
| ( ( cQ @ X1 )
!= $true )
| ( p != $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f17,plain,
p = $true,
inference(duplicate_literal_removal,[],[f10]) ).
thf(f18,plain,
! [X0: $i,X1: $i] :
( ( ( cQ @ X0 )
!= $true )
| ( p != $true )
| ( ( cQ @ X1 )
!= $true ) ),
inference(duplicate_literal_removal,[],[f14]) ).
thf(f20,definition,
( spl2_1
<=> ( $true
= ( cQ @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f22,plain,
( ( $true
= ( cQ @ sK1 ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f20]) ).
thf(f24,definition,
( spl2_2
<=> ( p = $true ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f29,definition,
( spl2_3
<=> ( $true
= ( cQ @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f31,plain,
( ( $true
= ( cQ @ sK0 ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f29]) ).
thf(f33,plain,
( spl2_1
| spl2_3 ),
inference(avatar_split_clause,[],[f13,f29,f20]) ).
thf(f35,definition,
( spl2_4
<=> ! [X1: $i] :
( ( cQ @ X1 )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f36,plain,
( ! [X1: $i] :
( ( cQ @ X1 )
!= $true )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f37,plain,
( spl2_4
| ~ spl2_2
| spl2_4 ),
inference(avatar_split_clause,[],[f18,f35,f24,f35]) ).
thf(f38,plain,
spl2_2,
inference(avatar_split_clause,[],[f17,f24]) ).
thf(f39,plain,
( ( $true != $true )
| ~ spl2_3
| ~ spl2_4 ),
inference(constrained_superposition,[],[f36,f31]) ).
thf(f40,plain,
( $false
| ~ spl2_3
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f39]) ).
thf(f41,plain,
( ~ spl2_3
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f40]) ).
thf(f42,plain,
( $false
| ~ spl2_1
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f22,f36]) ).
thf(f43,plain,
( ~ spl2_1
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f42]) ).
cnf(s3,plain,
( spl2_1
| spl2_3 ),
inference(sat_conversion,[],[f33]) ).
cnf(s4,plain,
( spl2_4
| ~ spl2_2
| spl2_4 ),
inference(sat_conversion,[],[f37]) ).
cnf(s5,plain,
( ~ spl2_2
| spl2_4 ),
inference(rat,[],[s4]) ).
cnf(s6,plain,
spl2_2,
inference(sat_conversion,[],[f38]) ).
cnf(s7,plain,
( ~ spl2_3
| ~ spl2_4 ),
inference(sat_conversion,[],[f41]) ).
cnf(s8,plain,
( ~ spl2_1
| ~ spl2_4 ),
inference(sat_conversion,[],[f43]) ).
cnf(s9,plain,
spl2_4,
inference(rat,[],[s5,s6]) ).
cnf(s10,plain,
~ spl2_1,
inference(rat,[],[s8,s9]) ).
cnf(s11,plain,
~ spl2_3,
inference(rat,[],[s7,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s3,s11,s10]) ).
thf(f44,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN358^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n016.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 : Tue Sep 29 16:19:50 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.24 Running first-order model finding
% 0.08/0.24 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
% 0.19/0.27 % (543998)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (544012)dis+10_1_sil=32000:sp=arity:random_seed=1242663867:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.27 % (544012) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-543998-544012"...
% 0.19/0.27 % (544012)...printing done.
% 0.19/0.27 % (544012)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (544012)------------------------------
% 0.19/0.27 % (544012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (544012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (544012)CaDiCaL version: 2.1.3
% 0.19/0.27 % (544012)Termination reason: Refutation
% 0.19/0.27 % (544012)Time elapsed: 0.001 s
% 0.19/0.27 % (544012)Peak memory usage: 12 MB
% 0.19/0.27 % (544012)Instructions burned: 1 (million)
% 0.19/0.27 % (543998)Success in time 0.025 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------