%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO359^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 : Wed Sep 30 08:47:31 AM UTC 2026
% Result : Theorem 0.10s 0.25s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 8 unt; 0 typ; 4 def)
% Number of atoms : 239 ( 57 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 216 ( 48 ~; 43 |; 8 &; 91 @)
% ( 10 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 23 !; 3 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
gtype: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
g: b > $o ).
thf(func_def_1,type,
h: ( b > $o ) > gtype ).
thf(func_def_2,type,
f: b > $o ).
thf(func_def_6,type,
sK0: b ).
thf(func_def_7,type,
vNOT: $o > $o ).
thf(func_def_9,type,
sK2: b ).
thf(f1,conjecture,
( ( ! [X0: b] :
( ( g @ X0 )
<=> ( f @ X0 ) )
=> ! [X1: ( b > $o ) > $o] :
( ( X1 @ f )
=> ( X1 @ g ) ) )
=> ( ! [X0: b] :
( ( f @ X0 )
<=> ( g @ X0 ) )
=> ( ( h @ f )
= ( h @ g ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEXT1) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: b] :
( ( g @ X0 )
<=> ( f @ X0 ) )
=> ! [X1: ( b > $o ) > $o] :
( ( X1 @ f )
=> ( X1 @ g ) ) )
=> ( ! [X0: b] :
( ( f @ X0 )
<=> ( g @ X0 ) )
=> ( ( h @ f )
= ( h @ g ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: b] :
( ( g @ X0 )
<=> ( f @ X0 ) )
=> ! [X1: ( b > $o ) > $o] :
( ( X1 @ f )
=> ( X1 @ g ) ) )
=> ( ! [X2: b] :
( ( f @ X2 )
<=> ( g @ X2 ) )
=> ( ( h @ f )
= ( h @ g ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) )
=> ! [X1: ( b > $o ) > $o] :
( ( ( X1 @ f )
= $true )
=> ( ( X1 @ g )
= $true ) ) )
=> ( ! [X2: b] :
( ( g @ X2 )
= ( f @ X2 ) )
=> ( ( h @ f )
= ( h @ g ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ( h @ f )
!= ( h @ g ) )
& ! [X2: b] :
( ( g @ X2 )
= ( f @ X2 ) )
& ( ! [X1: ( b > $o ) > $o] :
( ( ( X1 @ g )
= $true )
| ( ( X1 @ f )
!= $true ) )
| ? [X0: b] :
( ( f @ X0 )
!= ( g @ X0 ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ! [X1: ( b > $o ) > $o] :
( ( ( X1 @ g )
= $true )
| ( ( X1 @ f )
!= $true ) )
| ? [X0: b] :
( ( f @ X0 )
!= ( g @ X0 ) ) )
& ( ( h @ f )
!= ( h @ g ) )
& ! [X2: b] :
( ( g @ X2 )
= ( f @ X2 ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ( ! [X0: ( b > $o ) > $o] :
( ( ( X0 @ g )
= $true )
| ( ( X0 @ f )
!= $true ) )
| ? [X1: b] :
( ( f @ X1 )
!= ( g @ X1 ) ) )
& ( ( h @ f )
!= ( h @ g ) )
& ! [X2: b] :
( ( g @ X2 )
= ( f @ X2 ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( ! [X0: ( b > $o ) > $o] :
( ( ( X0 @ g )
= $true )
| ( ( X0 @ f )
!= $true ) )
| ( ( f @ sK0 )
!= ( g @ sK0 ) ) )
& ( ( h @ f )
!= ( h @ g ) )
& ! [X2: b] :
( ( g @ X2 )
= ( f @ X2 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0)],[f7]) ).
thf(f9,plain,
! [X2: b] :
( ( g @ X2 )
= ( f @ X2 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( ( h @ f )
!= ( h @ g ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
! [X2: b] :
( ( $false
= ( f @ X2 ) )
| ( ( g @ X2 )
= $true ) ),
inference(iff_proxy_clausification,[],[f9]) ).
thf(f17,plain,
! [X2: b] :
( ( ( f @ X2 )
= $true )
| ( ( g @ X2 )
= $false ) ),
inference(iff_proxy_clausification,[],[f9]) ).
thf(f43,plain,
f != g,
inference(equality_resolution,[],[f10]) ).
thf(f44,plain,
( ( g @ sK2 )
!= ( f @ sK2 ) ),
inference(negative_extensionality,[],[f43]) ).
thf(f45,plain,
( ( ( f @ sK2 )
= $true )
| ( ( g @ sK2 )
= $true ) ),
inference(xor_proxy_clausification,[],[f44]) ).
thf(f46,plain,
( ( $false
= ( g @ sK2 ) )
| ( $false
= ( f @ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f44]) ).
thf(f48,definition,
( spl1_6
<=> ( $false
= ( f @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
thf(f50,plain,
( ( $false
= ( f @ sK2 ) )
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f48]) ).
thf(f52,definition,
( spl1_7
<=> ( $false
= ( g @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
thf(f53,plain,
( ( $false
!= ( g @ sK2 ) )
| spl1_7 ),
inference(avatar_component_clause,[],[f52]) ).
thf(f54,plain,
( ( $false
= ( g @ sK2 ) )
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f52]) ).
thf(f55,plain,
( spl1_6
| spl1_7 ),
inference(avatar_split_clause,[],[f46,f52,f48]) ).
thf(f57,definition,
( spl1_8
<=> ( ( f @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
thf(f59,plain,
( ( ( f @ sK2 )
= $true )
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f57]) ).
thf(f61,definition,
( spl1_9
<=> ( ( g @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
thf(f63,plain,
( ( ( g @ sK2 )
= $true )
| ~ spl1_9 ),
inference(avatar_component_clause,[],[f61]) ).
thf(f64,plain,
( spl1_8
| spl1_9 ),
inference(avatar_split_clause,[],[f45,f61,f57]) ).
thf(f72,plain,
( ( ( g @ sK2 )
= $true )
| ( $false = $true )
| ~ spl1_8 ),
inference(constrained_superposition,[],[f59,f16]) ).
thf(f76,plain,
( ( ( g @ sK2 )
= $true )
| ~ spl1_8 ),
inference(trivial_inequality_removal,[],[f72]) ).
thf(f86,plain,
( ( $false = $true )
| ~ spl1_7
| ~ spl1_8 ),
inference(forward_demodulation,[],[f76,f54]) ).
thf(f87,plain,
( $false
| ~ spl1_7
| ~ spl1_8 ),
inference(trivial_inequality_removal,[],[f86]) ).
thf(f88,plain,
( ~ spl1_7
| ~ spl1_8 ),
inference(avatar_contradiction_clause,[],[f87]) ).
thf(f93,plain,
( ( $false = $true )
| ~ spl1_7
| ~ spl1_9 ),
inference(forward_demodulation,[],[f63,f54]) ).
thf(f94,plain,
( $false
| ~ spl1_7
| ~ spl1_9 ),
inference(trivial_inequality_removal,[],[f93]) ).
thf(f95,plain,
( ~ spl1_7
| ~ spl1_9 ),
inference(avatar_contradiction_clause,[],[f94]) ).
thf(f109,plain,
( ( $false
= ( g @ sK2 ) )
| ( $false = $true )
| ~ spl1_6 ),
inference(constrained_superposition,[],[f17,f50]) ).
thf(f117,plain,
( ( $false
= ( g @ sK2 ) )
| ~ spl1_6 ),
inference(trivial_inequality_removal,[],[f109]) ).
thf(f125,plain,
( $false
| ~ spl1_6
| spl1_7 ),
inference(forward_subsumption_resolution,[],[f117,f53]) ).
thf(f126,plain,
( ~ spl1_6
| spl1_7 ),
inference(avatar_contradiction_clause,[],[f125]) ).
cnf(s4,plain,
( spl1_6
| spl1_7 ),
inference(sat_conversion,[],[f55]) ).
cnf(s5,plain,
( spl1_8
| spl1_9 ),
inference(sat_conversion,[],[f64]) ).
cnf(s10,plain,
( ~ spl1_7
| ~ spl1_8 ),
inference(sat_conversion,[],[f88]) ).
cnf(s13,plain,
( ~ spl1_7
| ~ spl1_9 ),
inference(sat_conversion,[],[f95]) ).
cnf(s19,plain,
( ~ spl1_6
| spl1_7 ),
inference(sat_conversion,[],[f126]) ).
cnf(s23,plain,
~ spl1_7,
inference(rat,[],[s5,s10,s13]) ).
cnf(s24,plain,
~ spl1_6,
inference(rat,[],[s19,s23]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s4,s23,s24]) ).
thf(f129,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO359^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n018.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 16:50:56 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running higher-order theorem proving
% 0.10/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.25 % (333447)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.10/0.25 % (333453)lrs+10_16_si=on:nwc=1.5:random_seed=2974337440:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.10/0.25 % (333453) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-333447-333453"...
% 0.10/0.25 % (333453)...printing done.
% 0.10/0.25 % (333453)Refutation found. Thanks to Tanya!
% 0.10/0.25 % SZS status Theorem for theBenchmark
% 0.10/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.25 % (333453)------------------------------
% 0.10/0.25 % (333453)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.25 % (333453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.25 % (333453)CaDiCaL version: 2.1.3
% 0.10/0.25 % (333453)Termination reason: Refutation
% 0.10/0.25 % (333453)Time elapsed: 0.002 s
% 0.10/0.25 % (333453)Peak memory usage: 13 MB
% 0.10/0.25 % (333453)Instructions burned: 4 (million)
% 0.10/0.25 % (333447)Success in time 0.027 s
% 0.10/0.25 % Vampire exiting
%------------------------------------------------------------------------------