%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV189^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:37:59 AM UTC 2026
% Result : Theorem 0.23s 0.34s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 7
% Syntax : Number of formulae : 108 ( 26 unt; 0 typ; 6 def)
% Number of atoms : 934 ( 209 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 1119 ( 9 ~; 105 |; 32 &; 731 @)
% ( 0 <=>; 147 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 371 ( 371 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 22 usr; 9 con; 0-4 aty)
% ( 95 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 320 ( 261 ^; 59 !; 0 ?; 320 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cQ: ( b > $o ) > $o ).
thf(func_def_1,type,
cP: ( b > $o ) > $o ).
thf(func_def_3,type,
vNOT: $o > $o ).
thf(func_def_4,type,
vIMP: $o > $o > $o ).
thf(func_def_5,type,
vAND: $o > $o > $o ).
thf(func_def_6,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
sF0: $o ).
thf(func_def_14,type,
sF1: $o ).
thf(func_def_15,type,
sF2: $o ).
thf(func_def_16,type,
sF3: $o ).
thf(func_def_17,type,
sF4: $o ).
thf(func_def_18,type,
sF5: $o ).
thf(func_def_19,type,
sK6: ( b > $o ) > $o ).
thf(func_def_20,type,
sK7: ( b > $o ) > $o ).
thf(func_def_21,type,
sK8: ( b > $o ) > $o ).
thf(func_def_22,type,
sK9: ( ( b > $o ) > $o ) > b > $o ).
thf(func_def_23,type,
sK10: ( ( b > $o ) > $o ) > b > $o ).
thf(f1,conjecture,
( ( ! [X0: ( b > $o ) > $o] :
( ! [X1: b > $o] :
( ( X0 @ X1 )
=> ( cQ @ X1 ) )
=> ( cQ
@ ^ [X1: b] :
! [X2: b > $o] :
( ( X0 @ X2 )
=> ( X2 @ X1 ) ) ) )
& ! [X0: ( b > $o ) > $o] :
( ! [X1: b > $o] :
( ( X0 @ X1 )
=> ( cP @ X1 ) )
=> ( cP
@ ^ [X1: b] :
! [X2: b > $o] :
( ( X0 @ X2 )
=> ( X2 @ X1 ) ) ) ) )
=> ! [X0: ( b > $o ) > $o] :
( ! [X1: b > $o] :
( ( X0 @ X1 )
=> ( ( cP @ X1 )
& ( cQ @ X1 ) ) )
=> ( ( cQ
@ ^ [X1: b] :
! [X2: b > $o] :
( ( X0 @ X2 )
=> ( X2 @ X1 ) ) )
& ( cP
@ ^ [X1: b] :
! [X2: b > $o] :
( ( X0 @ X2 )
=> ( X2 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM567_pme) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: ( b > $o ) > $o] :
( ! [X1: b > $o] :
( ( X0 @ X1 )
=> ( cQ @ X1 ) )
=> ( cQ
@ ^ [X1: b] :
! [X2: b > $o] :
( ( X0 @ X2 )
=> ( X2 @ X1 ) ) ) )
& ! [X0: ( b > $o ) > $o] :
( ! [X1: b > $o] :
( ( X0 @ X1 )
=> ( cP @ X1 ) )
=> ( cP
@ ^ [X1: b] :
! [X2: b > $o] :
( ( X0 @ X2 )
=> ( X2 @ X1 ) ) ) ) )
=> ! [X0: ( b > $o ) > $o] :
( ! [X1: b > $o] :
( ( X0 @ X1 )
=> ( ( cP @ X1 )
& ( cQ @ X1 ) ) )
=> ( ( cQ
@ ^ [X1: b] :
! [X2: b > $o] :
( ( X0 @ X2 )
=> ( X2 @ X1 ) ) )
& ( cP
@ ^ [X1: b] :
! [X2: b > $o] :
( ( X0 @ X2 )
=> ( X2 @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: ( b > $o ) > $o] :
( ! [X1: b > $o] :
( ( X0 @ X1 )
=> ( cQ @ X1 ) )
=> ( cQ
@ ^ [X2: b] :
! [X3: b > $o] :
( ( X0 @ X3 )
=> ( X3 @ X2 ) ) ) )
& ! [X4: ( b > $o ) > $o] :
( ! [X5: b > $o] :
( ( X4 @ X5 )
=> ( cP @ X5 ) )
=> ( cP
@ ^ [X6: b] :
! [X7: b > $o] :
( ( X4 @ X7 )
=> ( X7 @ X6 ) ) ) ) )
=> ! [X8: ( b > $o ) > $o] :
( ! [X9: b > $o] :
( ( X8 @ X9 )
=> ( ( cP @ X9 )
& ( cQ @ X9 ) ) )
=> ( ( cQ
@ ^ [X10: b] :
! [X11: b > $o] :
( ( X8 @ X11 )
=> ( X11 @ X10 ) ) )
& ( cP
@ ^ [X12: b] :
! [X13: b > $o] :
( ( X8 @ X13 )
=> ( X13 @ X12 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ( ~ ( ( ( !! @ ( ( b > $o ) > $o )
@ ^ [Y0: ( b > $o ) > $o] :
( ( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0 @ Y1 )
=> ( cP @ Y1 ) ) )
=> ( cP
@ ^ [Y1: b] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ ( ( b > $o ) > $o )
@ ^ [Y0: ( b > $o ) > $o] :
( ( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0 @ Y1 )
=> ( cQ @ Y1 ) ) )
=> ( cQ
@ ^ [Y1: b] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ Y1 ) ) ) ) ) ) )
=> ( !! @ ( ( b > $o ) > $o )
@ ^ [Y0: ( b > $o ) > $o] :
( ( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0 @ Y1 )
=> ( ( cQ @ Y1 )
& ( cP @ Y1 ) ) ) )
=> ( ( cP
@ ^ [Y1: b] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ Y1 ) ) ) )
& ( cQ
@ ^ [Y1: b] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ Y1 ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ~ ( ( ( !! @ ( ( b > $o ) > $o )
@ ^ [Y0: ( b > $o ) > $o] :
( ( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0 @ Y1 )
=> ( cP @ Y1 ) ) )
=> ( cP
@ ^ [Y1: b] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ ( ( b > $o ) > $o )
@ ^ [Y0: ( b > $o ) > $o] :
( ( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0 @ Y1 )
=> ( cQ @ Y1 ) ) )
=> ( cQ
@ ^ [Y1: b] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ Y1 ) ) ) ) ) ) )
=> ( !! @ ( ( b > $o ) > $o )
@ ^ [Y0: ( b > $o ) > $o] :
( ( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0 @ Y1 )
=> ( ( cQ @ Y1 )
& ( cP @ Y1 ) ) ) )
=> ( ( cP
@ ^ [Y1: b] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ Y1 ) ) ) )
& ( cQ
@ ^ [Y1: b] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ Y1 ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f4]) ).
thf(f8,definition,
( sF0
= ( !! @ ( ( b > $o ) > $o )
@ ^ [Y0: ( b > $o ) > $o] :
( ( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0 @ Y1 )
=> ( cP @ Y1 ) ) )
=> ( cP
@ ^ [Y1: b] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ Y1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f9,plain,
( ( !! @ ( ( b > $o ) > $o )
@ ^ [Y0: ( b > $o ) > $o] :
( ( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0 @ Y1 )
=> ( cP @ Y1 ) ) )
=> ( cP
@ ^ [Y1: b] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ Y1 ) ) ) ) ) )
= sF0 ),
inference(reorient_equations,[],[f8]) ).
thf(f10,definition,
( sF1
= ( !! @ ( ( b > $o ) > $o )
@ ^ [Y0: ( b > $o ) > $o] :
( ( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0 @ Y1 )
=> ( cQ @ Y1 ) ) )
=> ( cQ
@ ^ [Y1: b] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ Y1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f11,plain,
( ( !! @ ( ( b > $o ) > $o )
@ ^ [Y0: ( b > $o ) > $o] :
( ( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0 @ Y1 )
=> ( cQ @ Y1 ) ) )
=> ( cQ
@ ^ [Y1: b] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ Y1 ) ) ) ) ) )
= sF1 ),
inference(reorient_equations,[],[f10]) ).
thf(f12,definition,
( sF2
= ( sF0
& sF1 ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f13,definition,
( sF3
= ( !! @ ( ( b > $o ) > $o )
@ ^ [Y0: ( b > $o ) > $o] :
( ( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0 @ Y1 )
=> ( ( cQ @ Y1 )
& ( cP @ Y1 ) ) ) )
=> ( ( cP
@ ^ [Y1: b] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ Y1 ) ) ) )
& ( cQ
@ ^ [Y1: b] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ Y1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f14,definition,
( sF4
= ( sF2
=> sF3 ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f15,plain,
( ( sF2
=> sF3 )
= sF4 ),
inference(reorient_equations,[],[f14]) ).
thf(f16,definition,
( sF5 = ( ~ sF4 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f17,plain,
( ( ~ sF4 ) = sF5 ),
inference(reorient_equations,[],[f16]) ).
thf(f18,plain,
sF5 = $true,
inference(definition_folding,[],[f5,f17,f15,f13,f12,f11,f9]) ).
thf(f20,plain,
( ( $false
= ( sF2
=> sF3 ) )
| ( sF4 = $true ) ),
inference(iff_proxy_clausification,[],[f15]) ).
thf(f21,plain,
( ( ( ~ sF4 ) = $true )
| ( $false = sF5 ) ),
inference(iff_proxy_clausification,[],[f17]) ).
thf(f23,plain,
( ( ( !! @ ( ( b > $o ) > $o )
@ ^ [Y0: ( b > $o ) > $o] :
( ( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0 @ Y1 )
=> ( cP @ Y1 ) ) )
=> ( cP
@ ^ [Y1: b] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ Y1 ) ) ) ) ) )
= $true )
| ( $false = sF0 ) ),
inference(iff_proxy_clausification,[],[f9]) ).
thf(f26,plain,
( ( $false = sF2 )
| ( ( sF0
& sF1 )
= $true ) ),
inference(iff_proxy_clausification,[],[f12]) ).
thf(f27,plain,
( ( sF3 = $true )
| ( $false
= ( !! @ ( ( b > $o ) > $o )
@ ^ [Y0: ( b > $o ) > $o] :
( ( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0 @ Y1 )
=> ( ( cQ @ Y1 )
& ( cP @ Y1 ) ) ) )
=> ( ( cP
@ ^ [Y1: b] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ Y1 ) ) ) )
& ( cQ
@ ^ [Y1: b] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f13]) ).
thf(f29,plain,
( ( ( !! @ ( ( b > $o ) > $o )
@ ^ [Y0: ( b > $o ) > $o] :
( ( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0 @ Y1 )
=> ( cQ @ Y1 ) ) )
=> ( cQ
@ ^ [Y1: b] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ Y1 ) ) ) ) ) )
= $true )
| ( $false = sF1 ) ),
inference(iff_proxy_clausification,[],[f11]) ).
thf(f31,plain,
( ( $false = sF3 )
| ( sF4 = $true ) ),
inference(imp_proxy_clausification,[],[f20]) ).
thf(f32,plain,
( ( sF4 = $true )
| ( sF2 = $true ) ),
inference(imp_proxy_clausification,[],[f20]) ).
thf(f34,plain,
( ( ( ~ sF4 ) = $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f21,f18]) ).
thf(f35,plain,
( ( ~ sF4 ) = $true ),
inference(trivial_inequality_removal,[],[f34]) ).
thf(f38,plain,
! [X1: ( b > $o ) > $o] :
( ( $false = sF0 )
| ( ( ^ [Y0: ( b > $o ) > $o] :
( ( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0 @ Y1 )
=> ( cP @ Y1 ) ) )
=> ( cP
@ ^ [Y1: b] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ Y1 ) ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f23]) ).
thf(f39,plain,
! [X1: ( b > $o ) > $o] :
( ( ( ( !! @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( X1 @ Y0 )
=> ( cP @ Y0 ) ) )
=> ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X1 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) )
= $true )
| ( $false = sF0 ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f41,plain,
( ( sF1 = $true )
| ( $false = sF2 ) ),
inference(and_proxy_clausification,[],[f26]) ).
thf(f42,plain,
( ( sF0 = $true )
| ( $false = sF2 ) ),
inference(and_proxy_clausification,[],[f26]) ).
thf(f43,plain,
( ( $false
= ( ^ [Y0: ( b > $o ) > $o] :
( ( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0 @ Y1 )
=> ( ( cQ @ Y1 )
& ( cP @ Y1 ) ) ) )
=> ( ( cP
@ ^ [Y1: b] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ Y1 ) ) ) )
& ( cQ
@ ^ [Y1: b] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ Y1 ) ) ) ) ) )
@ sK7 ) )
| ( sF3 = $true ) ),
inference(sigma_proxy_clausification,[],[f27]) ).
thf(f44,plain,
( ( $false
= ( ( !! @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( sK7 @ Y0 )
=> ( ( cQ @ Y0 )
& ( cP @ Y0 ) ) ) )
=> ( ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK7 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
& ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK7 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) ) ) )
| ( sF3 = $true ) ),
inference(beta-eta_normalization,[],[f43]) ).
thf(f47,plain,
! [X1: ( b > $o ) > $o] :
( ( $false = sF1 )
| ( ( ^ [Y0: ( b > $o ) > $o] :
( ( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0 @ Y1 )
=> ( cQ @ Y1 ) ) )
=> ( cQ
@ ^ [Y1: b] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ Y1 ) ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f29]) ).
thf(f48,plain,
! [X1: ( b > $o ) > $o] :
( ( ( ( !! @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( X1 @ Y0 )
=> ( cQ @ Y0 ) ) )
=> ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X1 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) )
= $true )
| ( $false = sF1 ) ),
inference(beta-eta_normalization,[],[f47]) ).
thf(f51,plain,
$false = sF4,
inference(not_proxy_clausification,[],[f35]) ).
thf(f54,plain,
! [X1: ( b > $o ) > $o] :
( ( $true
= ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X1 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) )
| ( $false = sF0 )
| ( $false
= ( !! @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( X1 @ Y0 )
=> ( cP @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f39]) ).
thf(f55,plain,
( ( $false
= ( ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK7 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
& ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK7 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) ) )
| ( sF3 = $true ) ),
inference(imp_proxy_clausification,[],[f44]) ).
thf(f56,plain,
( ( sF3 = $true )
| ( ( !! @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( sK7 @ Y0 )
=> ( ( cQ @ Y0 )
& ( cP @ Y0 ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f44]) ).
thf(f58,plain,
! [X1: ( b > $o ) > $o] :
( ( ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X1 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true )
| ( $false
= ( !! @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( X1 @ Y0 )
=> ( cQ @ Y0 ) ) ) )
| ( $false = sF1 ) ),
inference(imp_proxy_clausification,[],[f48]) ).
thf(f61,plain,
( ( $false = $true )
| ( $false = sF3 ) ),
inference(backward_demodulation,[],[f31,f51]) ).
thf(f62,plain,
( ( $false = $true )
| ( sF2 = $true ) ),
inference(backward_demodulation,[],[f32,f51]) ).
thf(f63,plain,
$false = sF3,
inference(trivial_inequality_removal,[],[f61]) ).
thf(f64,plain,
sF2 = $true,
inference(trivial_inequality_removal,[],[f62]) ).
thf(f67,plain,
! [X1: ( b > $o ) > $o] :
( ( $false = sF0 )
| ( $false
= ( ^ [Y0: b > $o] :
( ( X1 @ Y0 )
=> ( cP @ Y0 ) )
@ ( sK9 @ X1 ) ) )
| ( $true
= ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X1 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f54]) ).
thf(f68,plain,
! [X1: ( b > $o ) > $o] :
( ( $false = sF0 )
| ( $true
= ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X1 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) )
| ( $false
= ( ( X1 @ ( sK9 @ X1 ) )
=> ( cP @ ( sK9 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
( ( sF3 = $true )
| ( ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK7 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $false )
| ( $false
= ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK7 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f55]) ).
thf(f70,plain,
! [X1: b > $o] :
( ( sF3 = $true )
| ( ( ^ [Y0: b > $o] :
( ( sK7 @ Y0 )
=> ( ( cQ @ Y0 )
& ( cP @ Y0 ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f56]) ).
thf(f71,plain,
! [X1: b > $o] :
( ( ( ( sK7 @ X1 )
=> ( ( cQ @ X1 )
& ( cP @ X1 ) ) )
= $true )
| ( sF3 = $true ) ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f74,plain,
! [X1: ( b > $o ) > $o] :
( ( $false = sF1 )
| ( $false
= ( ^ [Y0: b > $o] :
( ( X1 @ Y0 )
=> ( cQ @ Y0 ) )
@ ( sK10 @ X1 ) ) )
| ( ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X1 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f58]) ).
thf(f75,plain,
! [X1: ( b > $o ) > $o] :
( ( ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X1 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true )
| ( $false = sF1 )
| ( $false
= ( ( X1 @ ( sK10 @ X1 ) )
=> ( cQ @ ( sK10 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f74]) ).
thf(f78,plain,
( ( $false = $true )
| ( sF1 = $true ) ),
inference(backward_demodulation,[],[f41,f64]) ).
thf(f79,plain,
( ( $false = $true )
| ( sF0 = $true ) ),
inference(backward_demodulation,[],[f42,f64]) ).
thf(f80,plain,
sF0 = $true,
inference(trivial_inequality_removal,[],[f79]) ).
thf(f81,plain,
sF1 = $true,
inference(trivial_inequality_removal,[],[f78]) ).
thf(f83,plain,
! [X1: ( b > $o ) > $o] :
( ( $true
= ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X1 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) )
| ( $false = sF0 )
| ( $false
= ( cP @ ( sK9 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f68]) ).
thf(f84,plain,
! [X1: ( b > $o ) > $o] :
( ( ( X1 @ ( sK9 @ X1 ) )
= $true )
| ( $false = sF0 )
| ( $true
= ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X1 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f68]) ).
thf(f85,plain,
( ( ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK7 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $false )
| ( $false = $true )
| ( $false
= ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK7 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(forward_demodulation,[],[f69,f63]) ).
thf(f86,plain,
( ( $false
= ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK7 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) )
| ( ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK7 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f85]) ).
thf(f87,plain,
! [X1: b > $o] :
( ( ( ( sK7 @ X1 )
=> ( ( cQ @ X1 )
& ( cP @ X1 ) ) )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f71,f63]) ).
thf(f88,plain,
! [X1: b > $o] :
( ( ( sK7 @ X1 )
=> ( ( cQ @ X1 )
& ( cP @ X1 ) ) )
= $true ),
inference(trivial_inequality_removal,[],[f87]) ).
thf(f89,plain,
! [X1: ( b > $o ) > $o] :
( ( $false
= ( cQ @ ( sK10 @ X1 ) ) )
| ( ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X1 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true )
| ( $false = sF1 ) ),
inference(imp_proxy_clausification,[],[f75]) ).
thf(f90,plain,
! [X1: ( b > $o ) > $o] :
( ( ( X1 @ ( sK10 @ X1 ) )
= $true )
| ( $false = sF1 )
| ( ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X1 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f75]) ).
thf(f92,plain,
! [X1: ( b > $o ) > $o] :
( ( $true
= ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X1 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) )
| ( ( X1 @ ( sK9 @ X1 ) )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f84,f80]) ).
thf(f93,plain,
! [X1: ( b > $o ) > $o] :
( ( $true
= ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X1 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) )
| ( ( X1 @ ( sK9 @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f92]) ).
thf(f94,plain,
! [X1: ( b > $o ) > $o] :
( ( $false
= ( cP @ ( sK9 @ X1 ) ) )
| ( $true
= ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X1 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f83,f80]) ).
thf(f95,plain,
! [X1: ( b > $o ) > $o] :
( ( $true
= ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X1 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) )
| ( $false
= ( cP @ ( sK9 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[],[f94]) ).
thf(f96,plain,
! [X1: b > $o] :
( ( $false
= ( sK7 @ X1 ) )
| ( ( ( cQ @ X1 )
& ( cP @ X1 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f88]) ).
thf(f97,plain,
! [X1: ( b > $o ) > $o] :
( ( $false
= ( cQ @ ( sK10 @ X1 ) ) )
| ( ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X1 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f89,f81]) ).
thf(f98,plain,
! [X1: ( b > $o ) > $o] :
( ( ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X1 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true )
| ( $false
= ( cQ @ ( sK10 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[],[f97]) ).
thf(f99,plain,
! [X1: ( b > $o ) > $o] :
( ( ( X1 @ ( sK10 @ X1 ) )
= $true )
| ( ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X1 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f90,f81]) ).
thf(f100,plain,
! [X1: ( b > $o ) > $o] :
( ( ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X1 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true )
| ( ( X1 @ ( sK10 @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f99]) ).
thf(f101,plain,
! [X1: b > $o] :
( ( $false
= ( sK7 @ X1 ) )
| ( ( cP @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f96]) ).
thf(f102,plain,
! [X1: b > $o] :
( ( $false
= ( sK7 @ X1 ) )
| ( ( cQ @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f96]) ).
thf(f131,plain,
( ( $false = $true )
| ( ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK7 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $false )
| ( ( ^ [Y0: b > $o] :
( sK7
@ ( ^ [Y1: b > $o,Y2: b] :
( Y1
@ ( ^ [Y3: b > $o,Y4: b] : Y4
@ Y1
@ Y2 ) )
@ Y0 ) )
@ ( sK10
@ ^ [Y0: b > $o] :
( sK7
@ ( ^ [Y1: b > $o,Y2: b] :
( Y1
@ ( ^ [Y3: b > $o,Y4: b] : Y4
@ Y1
@ Y2 ) )
@ Y0 ) ) ) )
= $true ) ),
inference(constrained_superposition,[],[f86,f100]) ).
thf(f132,plain,
( ( $false
= ( cQ
@ ( sK10
@ ^ [Y0: b > $o] :
( sK7
@ ( ^ [Y1: b > $o,Y2: b] :
( Y1
@ ( ^ [Y3: b > $o,Y4: b] : Y4
@ Y1
@ Y2 ) )
@ Y0 ) ) ) ) )
| ( $false = $true )
| ( ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK7 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $false ) ),
inference(constrained_superposition,[],[f86,f98]) ).
thf(f135,plain,
( ( ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK7 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $false )
| ( $false
= ( cQ
@ ( sK10
@ ^ [Y0: b > $o] :
( sK7
@ ( ^ [Y1: b > $o,Y2: b] :
( Y1
@ ( ^ [Y3: b > $o,Y4: b] : Y4
@ Y1
@ Y2 ) )
@ Y0 ) ) ) ) ) ),
inference(trivial_inequality_removal,[],[f132]) ).
thf(f136,plain,
( ( ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK7 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $false )
| ( $false
= ( cQ @ ( sK10 @ sK7 ) ) ) ),
inference(beta-eta_normalization,[],[f135]) ).
thf(f140,plain,
( ( ( ^ [Y0: b > $o] :
( sK7
@ ( ^ [Y1: b > $o,Y2: b] :
( Y1
@ ( ^ [Y3: b > $o,Y4: b] : Y4
@ Y1
@ Y2 ) )
@ Y0 ) )
@ ( sK10
@ ^ [Y0: b > $o] :
( sK7
@ ( ^ [Y1: b > $o,Y2: b] :
( Y1
@ ( ^ [Y3: b > $o,Y4: b] : Y4
@ Y1
@ Y2 ) )
@ Y0 ) ) ) )
= $true )
| ( ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK7 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f131]) ).
thf(f141,plain,
( ( ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK7 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $false )
| ( ( sK7 @ ( sK10 @ sK7 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f146,plain,
( ( $false
= ( cQ @ ( sK10 @ sK7 ) ) )
| ( $false = $true )
| ( ( ^ [Y0: b > $o] :
( sK7
@ ( ^ [Y1: b > $o,Y2: b] :
( Y1
@ ( ^ [Y3: b > $o,Y4: b] : Y4
@ Y1
@ Y2 ) )
@ Y0 ) )
@ ( sK9
@ ^ [Y0: b > $o] :
( sK7
@ ( ^ [Y1: b > $o,Y2: b] :
( Y1
@ ( ^ [Y3: b > $o,Y4: b] : Y4
@ Y1
@ Y2 ) )
@ Y0 ) ) ) )
= $true ) ),
inference(constrained_superposition,[],[f136,f93]) ).
thf(f147,plain,
( ( $false = $true )
| ( $false
= ( cP
@ ( sK9
@ ^ [Y0: b > $o] :
( sK7
@ ( ^ [Y1: b > $o,Y2: b] :
( Y1
@ ( ^ [Y3: b > $o,Y4: b] : Y4
@ Y1
@ Y2 ) )
@ Y0 ) ) ) ) )
| ( $false
= ( cQ @ ( sK10 @ sK7 ) ) ) ),
inference(constrained_superposition,[],[f95,f136]) ).
thf(f150,plain,
( ( $false
= ( cQ @ ( sK10 @ sK7 ) ) )
| ( ( ^ [Y0: b > $o] :
( sK7
@ ( ^ [Y1: b > $o,Y2: b] :
( Y1
@ ( ^ [Y3: b > $o,Y4: b] : Y4
@ Y1
@ Y2 ) )
@ Y0 ) )
@ ( sK9
@ ^ [Y0: b > $o] :
( sK7
@ ( ^ [Y1: b > $o,Y2: b] :
( Y1
@ ( ^ [Y3: b > $o,Y4: b] : Y4
@ Y1
@ Y2 ) )
@ Y0 ) ) ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f146]) ).
thf(f151,plain,
( ( $false
= ( cQ @ ( sK10 @ sK7 ) ) )
| ( ( sK7 @ ( sK9 @ sK7 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f150]) ).
thf(f152,plain,
( ( $false
= ( cP
@ ( sK9
@ ^ [Y0: b > $o] :
( sK7
@ ( ^ [Y1: b > $o,Y2: b] :
( Y1
@ ( ^ [Y3: b > $o,Y4: b] : Y4
@ Y1
@ Y2 ) )
@ Y0 ) ) ) ) )
| ( $false
= ( cQ @ ( sK10 @ sK7 ) ) ) ),
inference(trivial_inequality_removal,[],[f147]) ).
thf(f153,plain,
( ( $false
= ( cP @ ( sK9 @ sK7 ) ) )
| ( $false
= ( cQ @ ( sK10 @ sK7 ) ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f163,plain,
( ( ( sK7 @ ( sK10 @ sK7 ) )
= $true )
| ( $false
= ( cP
@ ( sK9
@ ^ [Y0: b > $o] :
( sK7
@ ( ^ [Y1: b > $o,Y2: b] :
( Y1
@ ( ^ [Y3: b > $o,Y4: b] : Y4
@ Y1
@ Y2 ) )
@ Y0 ) ) ) ) )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f141,f95]) ).
thf(f164,plain,
( ( ( ^ [Y0: b > $o] :
( sK7
@ ( ^ [Y1: b > $o,Y2: b] :
( Y1
@ ( ^ [Y3: b > $o,Y4: b] : Y4
@ Y1
@ Y2 ) )
@ Y0 ) )
@ ( sK9
@ ^ [Y0: b > $o] :
( sK7
@ ( ^ [Y1: b > $o,Y2: b] :
( Y1
@ ( ^ [Y3: b > $o,Y4: b] : Y4
@ Y1
@ Y2 ) )
@ Y0 ) ) ) )
= $true )
| ( $false = $true )
| ( ( sK7 @ ( sK10 @ sK7 ) )
= $true ) ),
inference(constrained_superposition,[],[f141,f93]) ).
thf(f167,plain,
( ( ( sK7 @ ( sK10 @ sK7 ) )
= $true )
| ( ( ^ [Y0: b > $o] :
( sK7
@ ( ^ [Y1: b > $o,Y2: b] :
( Y1
@ ( ^ [Y3: b > $o,Y4: b] : Y4
@ Y1
@ Y2 ) )
@ Y0 ) )
@ ( sK9
@ ^ [Y0: b > $o] :
( sK7
@ ( ^ [Y1: b > $o,Y2: b] :
( Y1
@ ( ^ [Y3: b > $o,Y4: b] : Y4
@ Y1
@ Y2 ) )
@ Y0 ) ) ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f164]) ).
thf(f168,plain,
( ( ( sK7 @ ( sK10 @ sK7 ) )
= $true )
| ( ( sK7 @ ( sK9 @ sK7 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f172,plain,
( ( ( sK7 @ ( sK10 @ sK7 ) )
= $true )
| ( $false
= ( cP
@ ( sK9
@ ^ [Y0: b > $o] :
( sK7
@ ( ^ [Y1: b > $o,Y2: b] :
( Y1
@ ( ^ [Y3: b > $o,Y4: b] : Y4
@ Y1
@ Y2 ) )
@ Y0 ) ) ) ) ) ),
inference(trivial_inequality_removal,[],[f163]) ).
thf(f173,plain,
( ( $false
= ( cP @ ( sK9 @ sK7 ) ) )
| ( ( sK7 @ ( sK10 @ sK7 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f176,plain,
( ( ( sK7 @ ( sK9 @ sK7 ) )
= $true )
| ( ( cQ @ ( sK10 @ sK7 ) )
= $true )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f168,f102]) ).
thf(f181,plain,
( ( ( sK7 @ ( sK9 @ sK7 ) )
= $true )
| ( ( cQ @ ( sK10 @ sK7 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f176]) ).
thf(f187,plain,
( ( ( cQ @ ( sK10 @ sK7 ) )
= $true )
| ( $false = $true )
| ( $true
= ( cP @ ( sK9 @ sK7 ) ) ) ),
inference(constrained_superposition,[],[f181,f101]) ).
thf(f190,plain,
( ( $true
= ( cP @ ( sK9 @ sK7 ) ) )
| ( ( cQ @ ( sK10 @ sK7 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f187]) ).
thf(f196,plain,
( ( $false = $true )
| ( ( sK7 @ ( sK10 @ sK7 ) )
= $true )
| ( ( cQ @ ( sK10 @ sK7 ) )
= $true ) ),
inference(constrained_superposition,[],[f173,f190]) ).
thf(f198,plain,
( ( ( sK7 @ ( sK10 @ sK7 ) )
= $true )
| ( ( cQ @ ( sK10 @ sK7 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f196]) ).
thf(f206,plain,
( ( ( cQ @ ( sK10 @ sK7 ) )
= $true )
| ( ( cQ @ ( sK10 @ sK7 ) )
= $true )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f198,f102]) ).
thf(f211,plain,
( ( ( cQ @ ( sK10 @ sK7 ) )
= $true )
| ( $false = $true ) ),
inference(duplicate_literal_removal,[],[f206]) ).
thf(f212,plain,
( ( cQ @ ( sK10 @ sK7 ) )
= $true ),
inference(trivial_inequality_removal,[],[f211]) ).
thf(f217,plain,
( ( ( sK7 @ ( sK9 @ sK7 ) )
= $true )
| ( $false = $true ) ),
inference(backward_demodulation,[],[f151,f212]) ).
thf(f218,plain,
( ( $false = $true )
| ( $false
= ( cP @ ( sK9 @ sK7 ) ) ) ),
inference(backward_demodulation,[],[f153,f212]) ).
thf(f220,plain,
( $false
= ( cP @ ( sK9 @ sK7 ) ) ),
inference(trivial_inequality_removal,[],[f218]) ).
thf(f221,plain,
( ( sK7 @ ( sK9 @ sK7 ) )
= $true ),
inference(trivial_inequality_removal,[],[f217]) ).
thf(f227,plain,
( ( $false = $true )
| ( $true
= ( cP @ ( sK9 @ sK7 ) ) ) ),
inference(constrained_superposition,[],[f101,f221]) ).
thf(f228,plain,
( $true
= ( cP @ ( sK9 @ sK7 ) ) ),
inference(trivial_inequality_removal,[],[f227]) ).
thf(f232,plain,
$false = $true,
inference(forward_demodulation,[],[f228,f220]) ).
thf(f233,plain,
$false,
inference(trivial_inequality_removal,[],[f232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV189^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n007.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 15:17:41 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.34 % (3494658)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.34 % (3494671)lrs+10_16_si=on:nwc=1.5:random_seed=2612200097:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.34 % (3494676)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.34 % (3494676)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.23/0.34 % (3494671)Instruction limit reached!
% 0.23/0.34 % (3494671)------------------------------
% 0.23/0.34 % (3494671)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (3494671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (3494671)CaDiCaL version: 2.1.3
% 0.23/0.34 % (3494671)Termination reason: Instruction limit
% 0.23/0.34 % (3494671)Termination phase: Saturation
% 0.23/0.34 % (3494671)Time elapsed: 0.006 s
% 0.23/0.34 % (3494671)Peak memory usage: 12 MB
% 0.23/0.34 % (3494671)Instructions burned: 19 (million)
% 0.23/0.34 % (3494675)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=260866509:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.34 % (3494674)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3961941085:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.34 % (3494672)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=115740820:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.34 % (3494673)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2239754934:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.23/0.34 % (3494676)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1990508821:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.34 % (3494670)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=794700459:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.34 % (3494672)Instruction limit reached!
% 0.23/0.34 % (3494672)------------------------------
% 0.23/0.34 % (3494672)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (3494672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (3494672)CaDiCaL version: 2.1.3
% 0.23/0.34 % (3494672)Termination reason: Instruction limit
% 0.23/0.34 % (3494672)Termination phase: Saturation
% 0.23/0.34 % (3494672)Time elapsed: 0.003 s
% 0.23/0.34 % (3494672)Peak memory usage: 12 MB
% 0.23/0.34 % (3494672)Instructions burned: 3 (million)
% 0.23/0.34 % (3494673)Refutation not found, incomplete strategy
% 0.23/0.34 % (3494673)------------------------------
% 0.23/0.34 % (3494673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (3494673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (3494673)CaDiCaL version: 2.1.3
% 0.23/0.34 % (3494673)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.34 % (3494673)Time elapsed: 0.003 s
% 0.23/0.34 % (3494673)Peak memory usage: 12 MB
% 0.23/0.34 % (3494673)Instructions burned: 3 (million)
% 0.23/0.34 % (3494674)Refutation not found, incomplete strategy
% 0.23/0.34 % (3494674)------------------------------
% 0.23/0.34 % (3494674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (3494674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (3494674)CaDiCaL version: 2.1.3
% 0.23/0.34 % (3494674)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.34 % (3494674)Time elapsed: 0.004 s
% 0.23/0.34 % (3494674)Peak memory usage: 12 MB
% 0.23/0.34 % (3494674)Instructions burned: 6 (million)
% 0.23/0.34 % (3494673)------------------------------
% 0.23/0.34 % (3494673)------------------------------
% 0.23/0.34 % (3494674)------------------------------
% 0.23/0.34 % (3494674)------------------------------
% 0.23/0.34 % (3494670)Refutation not found, incomplete strategy
% 0.23/0.34 % (3494670)------------------------------
% 0.23/0.34 % (3494670)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (3494670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (3494670)CaDiCaL version: 2.1.3
% 0.23/0.34 % (3494670)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.34 % (3494670)Time elapsed: 0.004 s
% 0.23/0.34 % (3494670)Peak memory usage: 12 MB
% 0.23/0.34 % (3494670)Instructions burned: 6 (million)
% 0.23/0.34 % (3494670)------------------------------
% 0.23/0.34 % (3494670)------------------------------
% 0.23/0.34 % (3494683)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2514971572:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.34 % (3494683)Instruction limit reached!
% 0.23/0.34 % (3494683)------------------------------
% 0.23/0.34 % (3494683)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (3494683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (3494683)CaDiCaL version: 2.1.3
% 0.23/0.34 % (3494683)Termination reason: Instruction limit
% 0.23/0.34 % (3494683)Termination phase: Saturation
% 0.23/0.34 % (3494683)Time elapsed: 0.002 s
% 0.23/0.34 % (3494683)Peak memory usage: 12 MB
% 0.23/0.34 % (3494683)Instructions burned: 7 (million)
% 0.23/0.34 % (3494676)Refutation not found, incomplete strategy
% 0.23/0.34 % (3494676)------------------------------
% 0.23/0.34 % (3494676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (3494676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (3494676)CaDiCaL version: 2.1.3
% 0.23/0.34 % (3494676)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.34 % (3494676)Time elapsed: 0.016 s
% 0.23/0.34 % (3494676)Peak memory usage: 12 MB
% 0.23/0.34 % (3494676)Instructions burned: 28 (million)
% 0.23/0.34 % (3494676)------------------------------
% 0.23/0.34 % (3494676)------------------------------
% 0.23/0.34 % (3494693)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.23/0.34 % (3494692)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1227279932:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.23/0.34 % (3494696)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.23/0.34 % (3494696)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.23/0.34 % (3494693)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=620961351:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.23/0.34 % (3494694)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2355183738:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.23/0.34 % (3494696)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3699191474:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.23/0.34 % (3494692)Instruction limit reached!
% 0.23/0.34 % (3494692)------------------------------
% 0.23/0.34 % (3494692)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (3494692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (3494692)CaDiCaL version: 2.1.3
% 0.23/0.34 % (3494692)Termination reason: Instruction limit
% 0.23/0.34 % (3494692)Termination phase: Saturation
% 0.23/0.34 % (3494692)Time elapsed: 0.004 s
% 0.23/0.34 % (3494692)Peak memory usage: 12 MB
% 0.23/0.34 % (3494692)Instructions burned: 6 (million)
% 0.23/0.34 % (3494693)Instruction limit reached!
% 0.23/0.34 % (3494693)------------------------------
% 0.23/0.34 % (3494693)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (3494693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (3494693)CaDiCaL version: 2.1.3
% 0.23/0.34 % (3494693)Termination reason: Instruction limit
% 0.23/0.34 % (3494693)Termination phase: Saturation
% 0.23/0.34 % (3494693)Time elapsed: 0.004 s
% 0.23/0.34 % (3494693)Peak memory usage: 12 MB
% 0.23/0.34 % (3494693)Instructions burned: 7 (million)
% 0.23/0.34 % (3494701)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=3336905578:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.23/0.34 % (3494694)Instruction limit reached!
% 0.23/0.34 % (3494694)------------------------------
% 0.23/0.34 % (3494694)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (3494694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (3494694)CaDiCaL version: 2.1.3
% 0.23/0.34 % (3494694)Termination reason: Instruction limit
% 0.23/0.34 % (3494694)Termination phase: Saturation
% 0.23/0.34 % (3494694)Time elapsed: 0.009 s
% 0.23/0.34 % (3494694)Peak memory usage: 12 MB
% 0.23/0.34 % (3494694)Instructions burned: 14 (million)
% 0.23/0.34 % (3494703)lrs+10_1_si=on:cs=on:random_seed=162716678:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.23/0.34 % (3494696) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3494658-3494696"...
% 0.23/0.34 % (3494701)Refutation not found, incomplete strategy
% 0.23/0.34 % (3494701)------------------------------
% 0.23/0.34 % (3494701)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (3494701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (3494701)CaDiCaL version: 2.1.3
% 0.23/0.34 % (3494701)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.34 % (3494701)Time elapsed: 0.009 s
% 0.23/0.34 % (3494701)Peak memory usage: 12 MB
% 0.23/0.34 % (3494701)Instructions burned: 18 (million)
% 0.23/0.34 % (3494701)------------------------------
% 0.23/0.34 % (3494701)------------------------------
% 0.23/0.34 % (3494675)Instruction limit reached!
% 0.23/0.34 % (3494675)------------------------------
% 0.23/0.34 % (3494675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (3494675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (3494675)CaDiCaL version: 2.1.3
% 0.23/0.34 % (3494675)Termination reason: Instruction limit
% 0.23/0.34 % (3494675)Termination phase: Saturation
% 0.23/0.34 % (3494675)Time elapsed: 0.042 s
% 0.23/0.34 % (3494675)Peak memory usage: 12 MB
% 0.23/0.34 % (3494675)Instructions burned: 76 (million)
% 0.23/0.34 % (3494708)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.23/0.34 % (3494696)...printing done.
% 0.23/0.34 % (3494703)Instruction limit reached!
% 0.23/0.34 % (3494703)------------------------------
% 0.23/0.34 % (3494703)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (3494703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (3494703)CaDiCaL version: 2.1.3
% 0.23/0.34 % (3494703)Termination reason: Instruction limit
% 0.23/0.34 % (3494703)Termination phase: Saturation
% 0.23/0.34 % (3494703)Time elapsed: 0.005 s
% 0.23/0.34 % (3494703)Peak memory usage: 12 MB
% 0.23/0.34 % (3494703)Instructions burned: 9 (million)
% 0.23/0.34 % (3494696)Refutation found. Thanks to Tanya!
% 0.23/0.34 % SZS status Theorem for theBenchmark
% 0.23/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.34 % (3494696)------------------------------
% 0.23/0.34 % (3494696)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (3494696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (3494696)CaDiCaL version: 2.1.3
% 0.23/0.34 % (3494696)Termination reason: Refutation
% 0.23/0.34 % (3494696)Time elapsed: 0.015 s
% 0.23/0.34 % (3494696)Peak memory usage: 12 MB
% 0.23/0.34 % (3494696)Instructions burned: 29 (million)
% 0.23/0.34 % (3494658)Success in time 0.083 s
% 0.23/0.34 % Vampire exiting
%------------------------------------------------------------------------------