%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN051^5 : 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 : n009.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 08:41:49 AM UTC 2026
% Result : Theorem 0.26s 0.32s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 5 unt; 0 typ; 5 def)
% Number of atoms : 257 ( 59 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 182 ( 49 ~; 40 |; 24 &; 44 @)
% ( 5 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 13 ( 10 usr; 10 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 10 !; 18 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
p: $o ).
thf(func_def_1,type,
cF: $i > $o ).
thf(f1,conjecture,
( ( ? [X0: $i] :
( ( cF @ X0 )
=> p )
& ? [X0: $i] :
( p
=> ( cF @ X0 ) ) )
=> ? [X0: $i] :
( ( ( cF @ X0 )
=> p )
& ( p
=> ( cF @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPELL21) ).
thf(f2,negated_conjecture,
~ ( ( ? [X0: $i] :
( ( cF @ X0 )
=> p )
& ? [X0: $i] :
( p
=> ( cF @ X0 ) ) )
=> ? [X0: $i] :
( ( ( cF @ X0 )
=> p )
& ( p
=> ( cF @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ? [X0: $i] :
( ( cF @ X0 )
=> p )
& ? [X1: $i] :
( p
=> ( cF @ X1 ) ) )
=> ? [X2: $i] :
( ( ( cF @ X2 )
=> p )
& ( p
=> ( cF @ X2 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ? [X0: $i] :
( ( ( cF @ X0 )
= $true )
=> ( p = $true ) )
& ? [X1: $i] :
( ( p = $true )
=> ( ( cF @ X1 )
= $true ) ) )
=> ? [X2: $i] :
( ( ( ( cF @ X2 )
= $true )
=> ( p = $true ) )
& ( ( p = $true )
=> ( ( cF @ X2 )
= $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X2: $i] :
( ( ( p != $true )
& ( ( cF @ X2 )
= $true ) )
| ( ( ( cF @ X2 )
!= $true )
& ( p = $true ) ) )
& ? [X0: $i] :
( ( p = $true )
| ( ( cF @ X0 )
!= $true ) )
& ? [X1: $i] :
( ( ( cF @ X1 )
= $true )
| ( p != $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ! [X2: $i] :
( ( ( p != $true )
& ( ( cF @ X2 )
= $true ) )
| ( ( ( cF @ X2 )
!= $true )
& ( p = $true ) ) )
& ? [X0: $i] :
( ( p = $true )
| ( ( cF @ X0 )
!= $true ) )
& ? [X1: $i] :
( ( ( cF @ X1 )
= $true )
| ( p != $true ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ! [X0: $i] :
( ( ( p != $true )
& ( ( cF @ X0 )
= $true ) )
| ( ( ( cF @ X0 )
!= $true )
& ( p = $true ) ) )
& ? [X1: $i] :
( ( p = $true )
| ( ( cF @ X1 )
!= $true ) )
& ? [X2: $i] :
( ( ( cF @ X2 )
= $true )
| ( p != $true ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ! [X0: $i] :
( ( ( p != $true )
& ( ( cF @ X0 )
= $true ) )
| ( ( ( cF @ X0 )
!= $true )
& ( p = $true ) ) )
& ( ( p = $true )
| ( $true
!= ( cF @ sK0 ) ) )
& ( ( $true
= ( cF @ sK1 ) )
| ( p != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X1,sK0),skolemize(X2,sK1)],[f7]) ).
thf(f9,plain,
( ( $true
= ( cF @ sK1 ) )
| ( p != $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( ( p = $true )
| ( $true
!= ( cF @ sK0 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
! [X0: $i] :
( ( ( cF @ X0 )
= $true )
| ( p = $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
! [X0: $i] :
( ( p != $true )
| ( ( cF @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f18,definition,
( spl2_1
<=> ( p = $true ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f22,definition,
( spl2_2
<=> ( $true
= ( cF @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f24,plain,
( ( $true
= ( cF @ sK1 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f22]) ).
thf(f25,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f9,f22,f18]) ).
thf(f27,definition,
( spl2_3
<=> ( $true
= ( cF @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f29,plain,
( ( $true
!= ( cF @ sK0 ) )
| spl2_3 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f30,plain,
( ~ spl2_3
| spl2_1 ),
inference(avatar_split_clause,[],[f10,f18,f27]) ).
thf(f32,definition,
( spl2_4
<=> ! [X0: $i] :
( ( cF @ X0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f33,plain,
( ! [X0: $i] :
( ( cF @ X0 )
= $true )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f34,plain,
( spl2_1
| spl2_4 ),
inference(avatar_split_clause,[],[f11,f32,f18]) ).
thf(f36,definition,
( spl2_5
<=> ! [X0: $i] :
( ( cF @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
thf(f37,plain,
( ! [X0: $i] :
( ( cF @ X0 )
!= $true )
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f38,plain,
( spl2_5
| ~ spl2_1 ),
inference(avatar_split_clause,[],[f14,f18,f36]) ).
thf(f39,plain,
( ( $true != $true )
| spl2_3
| ~ spl2_4 ),
inference(constrained_superposition,[],[f29,f33]) ).
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,
( ( $true != $true )
| ~ spl2_2
| ~ spl2_5 ),
inference(constrained_superposition,[],[f37,f24]) ).
thf(f43,plain,
( $false
| ~ spl2_2
| ~ spl2_5 ),
inference(trivial_inequality_removal,[],[f42]) ).
thf(f44,plain,
( ~ spl2_2
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[],[f43]) ).
cnf(s1,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f25]) ).
cnf(s2,plain,
( spl2_1
| ~ spl2_3 ),
inference(sat_conversion,[],[f30]) ).
cnf(s3,plain,
( spl2_1
| spl2_4 ),
inference(sat_conversion,[],[f34]) ).
cnf(s4,plain,
( ~ spl2_1
| spl2_5 ),
inference(sat_conversion,[],[f38]) ).
cnf(s5,plain,
( spl2_3
| ~ spl2_4 ),
inference(sat_conversion,[],[f41]) ).
cnf(s6,plain,
( ~ spl2_2
| ~ spl2_5 ),
inference(sat_conversion,[],[f44]) ).
cnf(s7,plain,
spl2_1,
inference(rat,[],[s5,s2,s3]) ).
cnf(s8,plain,
spl2_5,
inference(rat,[],[s4,s7]) ).
cnf(s9,plain,
spl2_2,
inference(rat,[],[s1,s7]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s6,s8,s9]) ).
thf(f45,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN051^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 % Computer : n009.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 16:14:15 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.28 Running first-order model finding
% 0.09/0.28 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
% 0.26/0.32 % (4192247)Will run a generic schedule for satisfiability detection.
% 0.26/0.32 % (4192256)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2741276030:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.26/0.32 % (4192256)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.26/0.32 % (4192256) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4192247-4192256"...
% 0.26/0.32 % (4192256)...printing done.
% 0.26/0.32 % (4192252)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=182092827_2999 on theBenchmark for (2999ds/0Mi)
% 0.26/0.32 % (4192256)Refutation found. Thanks to Tanya!
% 0.26/0.32 % SZS status Theorem for theBenchmark
% 0.26/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.32 % (4192256)------------------------------
% 0.26/0.32 % (4192256)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.32 % (4192256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.32 % (4192256)CaDiCaL version: 2.1.3
% 0.26/0.32 % (4192256)Termination reason: Refutation
% 0.26/0.32 % (4192256)Time elapsed: 0.002 s
% 0.26/0.32 % (4192256)Peak memory usage: 12 MB
% 0.26/0.32 % (4192256)Instructions burned: 2 (million)
% 0.26/0.32 % (4192247)Success in time 0.025 s
% 0.26/0.32 % Vampire exiting
%------------------------------------------------------------------------------