%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO359^5 : 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 : n017.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 08:49:47 AM UTC 2026
% Result : Theorem 0.10s 0.25s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 61 ( 10 unt; 0 typ; 5 def)
% Number of atoms : 299 ( 69 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 264 ( 61 ~; 65 |; 8 &; 103 @)
% ( 11 <=>; 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 : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 8 con; 0-4 aty)
% Number of variables : 31 ( 0 sgn 28 !; 3 ?; 31 :)
% 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,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
( ( ! [X0: b] :
( ( f @ X0 )
<=> ( g @ X0 ) )
=> ! [X1: ( b > $o ) > $o] :
( ( X1 @ f )
=> ( X1 @ g ) ) )
=> ( ! [X0: b] :
( ( f @ X0 )
<=> ( g @ X0 ) )
=> ( ( h @ f )
= ( h @ g ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEXT1) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: b] :
( ( f @ X0 )
<=> ( g @ 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] :
( ( f @ X0 )
<=> ( g @ 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] :
( ( f @ X2 )
= ( g @ X2 ) )
=> ( ( h @ f )
= ( h @ g ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ( h @ f )
!= ( h @ g ) )
& ! [X2: b] :
( ( f @ X2 )
= ( g @ X2 ) )
& ( ! [X1: ( b > $o ) > $o] :
( ( ( X1 @ g )
= $true )
| ( ( X1 @ f )
!= $true ) )
| ? [X0: b] :
( ( f @ X0 )
!= ( g @ X0 ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ( h @ f )
!= ( h @ g ) )
& ! [X2: b] :
( ( f @ X2 )
= ( g @ X2 ) )
& ( ! [X1: ( b > $o ) > $o] :
( ( ( X1 @ g )
= $true )
| ( ( X1 @ f )
!= $true ) )
| ? [X0: b] :
( ( f @ X0 )
!= ( g @ X0 ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ( ( h @ f )
!= ( h @ g ) )
& ! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) )
& ( ! [X1: ( b > $o ) > $o] :
( ( ( X1 @ g )
= $true )
| ( ( X1 @ f )
!= $true ) )
| ? [X2: b] :
( ( f @ X2 )
!= ( g @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( ( h @ f )
!= ( h @ g ) )
& ! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) )
& ( ! [X1: ( b > $o ) > $o] :
( ( ( X1 @ g )
= $true )
| ( ( X1 @ f )
!= $true ) )
| ( ( f @ sK0 )
!= ( g @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0)],[f7]) ).
thf(f9,plain,
! [X1: ( b > $o ) > $o] :
( ( ( X1 @ g )
= $true )
| ( ( X1 @ f )
!= $true )
| ( ( f @ sK0 )
!= ( g @ sK0 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( ( h @ f )
!= ( h @ g ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
! [X1: ( b > $o ) > $o] :
( ( ( X1 @ g )
= $true )
| ( ( X1 @ f )
!= $true )
| ( $true
= ( f @ sK0 ) )
| ( $true
= ( g @ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f9]) ).
thf(f15,plain,
! [X1: ( b > $o ) > $o] :
( ( ( X1 @ g )
= $true )
| ( ( X1 @ f )
!= $true )
| ( ( f @ sK0 )
= $false )
| ( ( g @ sK0 )
= $false ) ),
inference(xor_proxy_clausification,[],[f9]) ).
thf(f16,plain,
! [X0: b] :
( ( ( f @ X0 )
= $true )
| ( ( g @ X0 )
= $false ) ),
inference(iff_proxy_clausification,[],[f10]) ).
thf(f17,plain,
! [X0: b] :
( ( ( f @ X0 )
= $false )
| ( ( g @ X0 )
= $true ) ),
inference(iff_proxy_clausification,[],[f10]) ).
thf(f19,definition,
( spl1_1
<=> ( ( g @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f21,plain,
( ( ( g @ sK0 )
= $false )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f23,definition,
( spl1_2
<=> ( ( f @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f24,plain,
( ( ( f @ sK0 )
!= $false )
| spl1_2 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f25,plain,
( ( ( f @ sK0 )
= $false )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f27,definition,
( spl1_3
<=> ! [X1: ( b > $o ) > $o] :
( ( ( X1 @ g )
= $true )
| ( ( X1 @ f )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
thf(f28,plain,
( ! [X1: ( b > $o ) > $o] :
( ( ( X1 @ f )
!= $true )
| ( ( X1 @ g )
= $true ) )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f29,plain,
( spl1_1
| spl1_2
| spl1_3 ),
inference(avatar_split_clause,[],[f15,f27,f23,f19]) ).
thf(f31,definition,
( spl1_4
<=> ( $true
= ( g @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
thf(f33,plain,
( ( $true
= ( g @ sK0 ) )
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f35,definition,
( spl1_5
<=> ( $true
= ( f @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
thf(f37,plain,
( ( $true
= ( f @ sK0 ) )
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f38,plain,
( spl1_4
| spl1_5
| spl1_3 ),
inference(avatar_split_clause,[],[f14,f27,f35,f31]) ).
thf(f53,plain,
( ( f = g )
| ~ spl1_3 ),
inference(leibniz_equality_elimination,[],[f28]) ).
thf(f84,plain,
( ( ( h @ g )
!= ( h @ g ) )
| ~ spl1_3 ),
inference(constrained_superposition,[],[f11,f53]) ).
thf(f85,plain,
( $false
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f84]) ).
thf(f86,plain,
~ spl1_3,
inference(avatar_contradiction_clause,[],[f85]) ).
thf(f91,plain,
( ( $true = $false )
| ( ( g @ sK0 )
= $false )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f16,f25]) ).
thf(f92,plain,
( ( ( g @ sK0 )
= $false )
| ~ spl1_2 ),
inference(trivial_inequality_removal,[],[f91]) ).
thf(f95,plain,
( spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f92,f23,f19]) ).
thf(f100,plain,
( ( $true = $false )
| ~ spl1_1
| ~ spl1_4 ),
inference(forward_demodulation,[],[f33,f21]) ).
thf(f101,plain,
( $false
| ~ spl1_1
| ~ spl1_4 ),
inference(trivial_inequality_removal,[],[f100]) ).
thf(f102,plain,
( ~ spl1_1
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f101]) ).
thf(f104,plain,
( ( $true = $false )
| ~ spl1_2
| ~ spl1_5 ),
inference(forward_demodulation,[],[f37,f25]) ).
thf(f105,plain,
( $false
| ~ spl1_2
| ~ spl1_5 ),
inference(trivial_inequality_removal,[],[f104]) ).
thf(f106,plain,
( ~ spl1_2
| ~ spl1_5 ),
inference(avatar_contradiction_clause,[],[f105]) ).
thf(f107,plain,
( ( $false != $false )
| ( $true
= ( g @ sK0 ) )
| spl1_2 ),
inference(constrained_superposition,[],[f24,f17]) ).
thf(f110,plain,
( ( $true
= ( g @ sK0 ) )
| spl1_2 ),
inference(trivial_inequality_removal,[],[f107]) ).
thf(f111,plain,
( ( $true = $false )
| ~ spl1_1
| spl1_2 ),
inference(forward_demodulation,[],[f110,f21]) ).
thf(f112,plain,
( $false
| ~ spl1_1
| spl1_2 ),
inference(trivial_inequality_removal,[],[f111]) ).
thf(f113,plain,
( ~ spl1_1
| spl1_2 ),
inference(avatar_contradiction_clause,[],[f112]) ).
cnf(s1,plain,
( spl1_1
| spl1_2
| spl1_3 ),
inference(sat_conversion,[],[f29]) ).
cnf(s2,plain,
( spl1_3
| spl1_4
| spl1_5 ),
inference(sat_conversion,[],[f38]) ).
cnf(s3,plain,
~ spl1_3,
inference(sat_conversion,[],[f86]) ).
cnf(s4,plain,
( spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f95]) ).
cnf(s6,plain,
( ~ spl1_1
| ~ spl1_4 ),
inference(sat_conversion,[],[f102]) ).
cnf(s7,plain,
( ~ spl1_2
| ~ spl1_5 ),
inference(sat_conversion,[],[f106]) ).
cnf(s8,plain,
( ~ spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f113]) ).
cnf(s9,plain,
( spl1_4
| spl1_5 ),
inference(rat,[],[s2,s3]) ).
cnf(s10,plain,
( spl1_1
| spl1_2 ),
inference(rat,[],[s1,s3]) ).
cnf(s11,plain,
spl1_1,
inference(rat,[],[s10,s4]) ).
cnf(s12,plain,
spl1_2,
inference(rat,[],[s8,s11]) ).
cnf(s13,plain,
~ spl1_4,
inference(rat,[],[s6,s11]) ).
cnf(s14,plain,
~ spl1_5,
inference(rat,[],[s7,s12]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s9,s14,s13]) ).
thf(f114,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO359^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 % Computer : n017.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 16:44:07 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 Running first-order model finding
% 0.10/0.20 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
% 0.10/0.25 % (586064)Will run a generic schedule for satisfiability detection.
% 0.10/0.25 % (586072)dis+10_1_sil=32000:sp=arity:random_seed=34449014:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.25 % (586072) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-586064-586072"...
% 0.10/0.25 % (586070)% WARNING: option uhcvi not known.
% 0.10/0.25 % (586072)...printing done.
% 0.10/0.25 % (586072)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 % (586072)------------------------------
% 0.10/0.25 % (586072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.25 % (586072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.25 % (586072)CaDiCaL version: 2.1.3
% 0.10/0.25 % (586072)Termination reason: Refutation
% 0.10/0.25 % (586072)Time elapsed: 0.003 s
% 0.10/0.25 % (586072)Peak memory usage: 12 MB
% 0.10/0.25 % (586072)Instructions burned: 5 (million)
% 0.10/0.25 % (586064)Success in time 0.031 s
% 0.10/0.25 % Vampire exiting
%------------------------------------------------------------------------------