%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO894^8 : TPTP v9.3.1. Released v8.1.0.
% 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 08:48:36 AM UTC 2026
% Result : Theorem 0.11s 0.25s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 12
% Syntax : Number of formulae : 93 ( 37 unt; 0 typ; 5 def)
% Number of atoms : 466 ( 102 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 541 ( 78 ~; 73 |; 18 &; 317 @)
% ( 7 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 30 usr; 12 con; 0-4 aty)
% ( 9 !!; 12 ??; 0 @@+; 0 @@-)
% Number of variables : 111 ( 0 sgn 15 !; 2 ?; 111 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
mrel: mworld > mworld > $o ).
thf(func_def_1,type,
mactual: mworld ).
thf(func_def_2,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_4,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_5,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
p: mworld > $o ).
thf(func_def_12,type,
vAND: $o > $o > $o ).
thf(func_def_13,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_17,type,
vIFF: $o > $o > $o ).
thf(func_def_18,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_19,type,
vIMP: $o > $o > $o ).
thf(func_def_22,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_23,type,
vOR: $o > $o > $o ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(func_def_25,type,
sK0: mworld ).
thf(func_def_26,type,
sK1: mworld ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f2,axiom,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot_def) ).
thf(f5,axiom,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(f6,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
<=> ( X0 @ X2 ) ) )
= mequiv ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv_def) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f8,axiom,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( mrel @ X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_def) ).
thf(f10,conjecture,
mlocal @ ( mequiv @ ( mbox @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f11,negated_conjecture,
~ ( mlocal @ ( mequiv @ ( mbox @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia @ p ) ) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
thf(f14,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
<=> ( X0 @ X2 ) ) )
= mequiv ),
inference(rectify,[],[f6]) ).
thf(f15,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f17,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f19,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f20,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
~ ( mlocal @ ( mequiv @ ( mbox @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia @ p ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f22,plain,
( ( mlocal @ ( mequiv @ ( mbox @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia @ p ) ) ) )
!= $true ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( mrel @ X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f24,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f29,plain,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f30,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f29]) ).
thf(f31,plain,
( ( mlocal @ ( mequiv @ ( mbox @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia @ p ) ) ) )
!= $true ),
inference(flattening,[],[f22]) ).
thf(f32,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f34,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f35,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f36,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f37,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f38,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f41,plain,
( ( mlocal @ ( mequiv @ ( mbox @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia @ p ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f31]) ).
thf(f44,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ p
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ p ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ p ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f41,f35,f36,f37,f34,f38,f38,f32]) ).
thf(f45,plain,
( ( ( ~ ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) )
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
=> ~ ( p @ Y0 ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
( ( ( ~ ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) )
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( p @ Y0 ) ) ) )
!= $true ),
inference(boolean_simplification,[],[f45]) ).
thf(f47,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( p @ Y0 ) ) )
!= ( ~ ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) ) ),
inference(iff_proxy_clausification,[],[f46]) ).
thf(f48,plain,
( ( ( ~ ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( p @ Y0 ) ) )
= $true ) ),
inference(xor_proxy_clausification,[],[f47]) ).
thf(f49,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( p @ Y0 ) ) ) )
| ( $false
= ( ~ ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) ) ) ),
inference(xor_proxy_clausification,[],[f47]) ).
thf(f50,plain,
( ( $false
= ( ~ ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( p @ Y0 ) )
@ sK0 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f49]) ).
thf(f51,plain,
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( p @ Y0 ) )
@ sK0 )
= $false ) ),
inference(not_proxy_clausification,[],[f50]) ).
thf(f52,plain,
( ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( p @ Y0 ) )
@ sK0 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) )
@ sK1 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f51]) ).
thf(f53,plain,
( ( ( ( p @ sK1 )
& ( mrel @ mactual @ sK1 ) )
= $true )
| ( ( ( mrel @ mactual @ sK0 )
=> ~ ( p @ sK0 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f54,plain,
( ( ( mrel @ mactual @ sK1 )
= $true )
| ( ( ( mrel @ mactual @ sK0 )
=> ~ ( p @ sK0 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f53]) ).
thf(f55,plain,
( ( ( p @ sK1 )
= $true )
| ( ( ( mrel @ mactual @ sK0 )
=> ~ ( p @ sK0 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f53]) ).
thf(f56,plain,
( ( ( p @ sK1 )
= $true )
| ( ( ~ ( p @ sK0 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f55]) ).
thf(f57,plain,
( ( ( p @ sK1 )
= $true )
| ( ( mrel @ mactual @ sK0 )
= $true ) ),
inference(imp_proxy_clausification,[],[f55]) ).
thf(f58,plain,
( ( ( p @ sK0 )
= $true )
| ( ( p @ sK1 )
= $true ) ),
inference(not_proxy_clausification,[],[f56]) ).
thf(f59,plain,
( ( ( mrel @ mactual @ sK1 )
= $true )
| ( ( ~ ( p @ sK0 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f54]) ).
thf(f60,plain,
( ( ( mrel @ mactual @ sK1 )
= $true )
| ( ( mrel @ mactual @ sK0 )
= $true ) ),
inference(imp_proxy_clausification,[],[f54]) ).
thf(f61,plain,
( ( ( mrel @ mactual @ sK1 )
= $true )
| ( ( p @ sK0 )
= $true ) ),
inference(not_proxy_clausification,[],[f59]) ).
thf(f62,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( p @ Y0 ) ) )
= $true )
| ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f48]) ).
thf(f63,plain,
! [X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f62]) ).
thf(f64,plain,
! [X2: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( p @ Y0 ) )
@ X1 )
= $true )
| ( $false
= ( ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( ( p @ X2 )
& ( mrel @ mactual @ X2 ) ) )
| ( ( ( mrel @ mactual @ X1 )
=> ~ ( p @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( ( ( mrel @ mactual @ X1 )
=> ~ ( p @ X1 ) )
= $true )
| ( ( p @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f67,plain,
! [X2: mworld,X1: mworld] :
( ( ( ~ ( p @ X1 ) )
= $true )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( p @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f66]) ).
thf(f68,plain,
! [X2: mworld,X1: mworld] :
( ( ( p @ X2 )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( p @ X1 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f67]) ).
thf(f70,definition,
( spl2_1
<=> ( ( mrel @ mactual @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f72,plain,
( ( ( mrel @ mactual @ sK0 )
= $true )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f74,definition,
( spl2_2
<=> ( ( p @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f76,plain,
( ( ( p @ sK1 )
= $true )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f74]) ).
thf(f77,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f57,f74,f70]) ).
thf(f79,definition,
( spl2_3
<=> ( ( p @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f81,plain,
( ( ( p @ sK0 )
= $true )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f79]) ).
thf(f82,plain,
( spl2_2
| spl2_3 ),
inference(avatar_split_clause,[],[f58,f79,f74]) ).
thf(f84,definition,
( spl2_4
<=> ( ( mrel @ mactual @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f86,plain,
( ( ( mrel @ mactual @ sK1 )
= $true )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f84]) ).
thf(f87,plain,
( spl2_1
| spl2_4 ),
inference(avatar_split_clause,[],[f60,f84,f70]) ).
thf(f88,plain,
( spl2_4
| spl2_3 ),
inference(avatar_split_clause,[],[f61,f79,f84]) ).
thf(f90,definition,
( spl2_5
<=> ! [X1: mworld] :
( ( ( p @ X1 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
thf(f91,plain,
( ! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( p @ X1 )
= $false ) )
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f90]) ).
thf(f92,plain,
( spl2_5
| spl2_5 ),
inference(avatar_split_clause,[],[f68,f90,f90]) ).
thf(f94,plain,
( ( ( p @ sK1 )
= $false )
| ( $false = $true )
| ~ spl2_4
| ~ spl2_5 ),
inference(constrained_superposition,[],[f91,f86]) ).
thf(f96,plain,
( ( ( p @ sK1 )
= $false )
| ~ spl2_4
| ~ spl2_5 ),
inference(trivial_inequality_removal,[],[f94]) ).
thf(f100,plain,
( ( $false = $true )
| ~ spl2_2
| ~ spl2_4
| ~ spl2_5 ),
inference(forward_demodulation,[],[f96,f76]) ).
thf(f101,plain,
( $false
| ~ spl2_2
| ~ spl2_4
| ~ spl2_5 ),
inference(trivial_inequality_removal,[],[f100]) ).
thf(f102,plain,
( ~ spl2_2
| ~ spl2_4
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[],[f101]) ).
thf(f104,plain,
( ( ( p @ sK0 )
= $false )
| ( $false = $true )
| ~ spl2_1
| ~ spl2_5 ),
inference(constrained_superposition,[],[f91,f72]) ).
thf(f106,plain,
( ( ( p @ sK0 )
= $false )
| ~ spl2_1
| ~ spl2_5 ),
inference(trivial_inequality_removal,[],[f104]) ).
thf(f110,plain,
( ( $false = $true )
| ~ spl2_1
| ~ spl2_3
| ~ spl2_5 ),
inference(forward_demodulation,[],[f106,f81]) ).
thf(f111,plain,
( $false
| ~ spl2_1
| ~ spl2_3
| ~ spl2_5 ),
inference(trivial_inequality_removal,[],[f110]) ).
thf(f112,plain,
( ~ spl2_1
| ~ spl2_3
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[],[f111]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f77]) ).
cnf(s2,plain,
( spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f82]) ).
cnf(s3,plain,
( spl2_1
| spl2_4 ),
inference(sat_conversion,[],[f87]) ).
cnf(s4,plain,
( spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f88]) ).
cnf(s5,plain,
( spl2_5
| spl2_5 ),
inference(sat_conversion,[],[f92]) ).
cnf(s6,plain,
spl2_5,
inference(rat,[],[s5]) ).
cnf(s8,plain,
( ~ spl2_2
| ~ spl2_4
| ~ spl2_5 ),
inference(sat_conversion,[],[f102]) ).
cnf(s10,plain,
( ~ spl2_1
| ~ spl2_3
| ~ spl2_5 ),
inference(sat_conversion,[],[f112]) ).
cnf(s11,plain,
spl2_1,
inference(rat,[],[s8,s1,s3,s6]) ).
cnf(s12,plain,
~ spl2_3,
inference(rat,[],[s10,s6,s11]) ).
cnf(s13,plain,
spl2_4,
inference(rat,[],[s4,s12]) ).
cnf(s14,plain,
spl2_2,
inference(rat,[],[s2,s12]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s8,s6,s13,s14]) ).
thf(f113,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO894^8 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.17 % Computer : n018.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Sep 29 17:28:26 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.20 Running higher-order theorem proving
% 0.11/0.21 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
% 0.11/0.25 % (382723)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.11/0.25 % (382728)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2864012062:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.11/0.25 % (382728) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-382723-382728"...
% 0.11/0.25 % (382728)...printing done.
% 0.11/0.25 % (382728)Refutation found. Thanks to Tanya!
% 0.11/0.25 % SZS status Theorem for theBenchmark
% 0.11/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.25 % (382728)------------------------------
% 0.11/0.25 % (382728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.25 % (382728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.25 % (382728)CaDiCaL version: 2.1.3
% 0.11/0.25 % (382728)Termination reason: Refutation
% 0.11/0.25 % (382728)Time elapsed: 0.003 s
% 0.11/0.25 % (382728)Peak memory usage: 13 MB
% 0.11/0.25 % (382728)Instructions burned: 7 (million)
% 0.11/0.25 % (382723)Success in time 0.026 s
% 0.11/0.25 % Vampire exiting
%------------------------------------------------------------------------------