%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU972^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:37:52 AM UTC 2026
% Result : Theorem 1.67s 1.76s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 1
% Syntax : Number of formulae : 47 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 385 ( 238 equ; 0 cnn)
% Maximal formula atoms : 11 ( 8 avg)
% Number of connectives : 1140 ( 14 ~; 0 |; 130 &; 806 @)
% ( 6 <=>; 83 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 16 usr; 13 con; 0-2 aty)
% ( 95 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 171 ( 119 ^; 49 !; 3 ?; 171 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cR: a > a ).
thf(func_def_2,type,
cP: a > a > a ).
thf(func_def_3,type,
cL: a > a ).
thf(func_def_4,type,
cZ: a ).
thf(func_def_19,type,
ph0:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
sK1: a ).
thf(func_def_25,type,
sK2: a ).
thf(func_def_26,type,
sK3: a ).
thf(func_def_27,type,
sK4: a ).
thf(func_def_28,type,
sK5: a ).
thf(func_def_29,type,
sK6: a ).
thf(func_def_30,type,
sK7: a ).
thf(func_def_31,type,
sK8: ( a > a > a ) > a ).
thf(func_def_32,type,
sK9: ( a > a > a ) > a ).
thf(func_def_33,type,
sK10: ( a > $o ) > a ).
thf(func_def_34,type,
sK11: a ).
thf(f459,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f435,f267]) ).
thf(f267,plain,
( cZ
!= ( cL @ cZ ) ),
inference(equality_proxy_clausification,[status(thm)],[f176]) ).
thf(f176,plain,
( ( ( cL @ cZ )
= cZ )
= $false ),
inference(boolean_simplification,[status(thm)],[f175]) ).
thf(f175,plain,
( $false
= ( $true
& ( ( cL @ cZ )
= cZ ) ) ),
inference(boolean_simplification,[status(thm)],[f174]) ).
thf(f174,plain,
( $false
= ( ( cZ = cZ )
& ( ( cL @ cZ )
= cZ ) ) ),
inference(forward_demodulation,[status(thm)],[f173,f71]) ).
thf(f71,plain,
( cZ
= ( cR @ cZ ) ),
inference(equality_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
( ( cZ
= ( cR @ cZ ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( cR @ ( cP @ Y1 @ Y0 ) )
= Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ ( cP @ Y1 @ Y2 ) )
=> ( ( Y0 @ ( cP @ ( cL @ Y1 ) @ ( cL @ Y2 ) ) )
& ( ( cZ = Y1 )
= ( cZ = Y2 ) )
& ( Y0 @ ( cP @ ( cR @ Y1 ) @ ( cR @ Y2 ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ ( cP @ Y2 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
& ( cZ
= ( cL @ cZ ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( cZ != Y0 )
= ( ( cP @ ( cL @ Y0 ) @ ( cR @ Y0 ) )
= Y0 ) ) )
& ( cZ
= ( cR @ cZ ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( cR @ ( cP @ Y1 @ Y0 ) )
= Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ ( cP @ Y1 @ Y2 ) )
=> ( ( Y0 @ ( cP @ ( cL @ Y1 ) @ ( cL @ Y2 ) ) )
& ( ( cZ = Y1 )
= ( cZ = Y2 ) )
& ( Y0 @ ( cP @ ( cR @ Y1 ) @ ( cR @ Y2 ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ ( cP @ Y2 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
& ( cZ
= ( cL @ cZ ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( cZ != Y0 )
= ( ( cP @ ( cL @ Y0 ) @ ( cR @ Y0 ) )
= Y0 ) ) )
& ( cZ
= ( cR @ cZ ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( cL @ ( cP @ Y1 @ Y0 ) )
= Y1 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( cR @ ( cP @ Y1 @ Y0 ) )
= Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ ( cP @ Y1 @ Y2 ) )
=> ( ( Y0 @ ( cP @ ( cL @ Y1 ) @ ( cL @ Y2 ) ) )
& ( ( cZ = Y1 )
= ( cZ = Y2 ) )
& ( Y0 @ ( cP @ ( cR @ Y1 ) @ ( cR @ Y2 ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ ( cP @ Y2 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
& ( cZ
= ( cL @ cZ ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( cZ != Y0 )
= ( ( cP @ ( cL @ Y0 ) @ ( cR @ Y0 ) )
= Y0 ) ) )
& ( cZ
= ( cR @ cZ ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( cL @ ( cP @ Y1 @ Y0 ) )
= Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ ( cP @ Y3 @ Y2 ) )
=> ( ( Y1 @ ( cP @ ( cR @ Y3 ) @ ( cR @ Y2 ) ) )
& ( ( cZ = Y2 )
=> ( cZ = Y3 ) )
& ( Y1 @ ( cP @ ( cL @ Y3 ) @ ( cL @ Y2 ) ) ) ) ) ) )
& ( Y1 @ ( cP @ cZ @ Y0 ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( cR @ ( cP @ Y1 @ Y0 ) )
= Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ ( cP @ Y1 @ Y2 ) )
=> ( ( Y0 @ ( cP @ ( cL @ Y1 ) @ ( cL @ Y2 ) ) )
& ( ( cZ = Y1 )
= ( cZ = Y2 ) )
& ( Y0 @ ( cP @ ( cR @ Y1 ) @ ( cR @ Y2 ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ ( cP @ Y2 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
& ( cZ
= ( cL @ cZ ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( cZ != Y0 )
= ( ( cP @ ( cL @ Y0 ) @ ( cR @ Y0 ) )
= Y0 ) ) )
& ( cZ
= ( cR @ cZ ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( cL @ ( cP @ Y1 @ Y0 ) )
= Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ ( cP @ Y3 @ Y2 ) )
=> ( ( Y1 @ ( cP @ ( cR @ Y3 ) @ ( cR @ Y2 ) ) )
& ( ( cZ = Y2 )
=> ( cZ = Y3 ) )
& ( Y1 @ ( cP @ ( cL @ Y3 ) @ ( cL @ Y2 ) ) ) ) ) ) )
& ( Y1 @ ( cP @ cZ @ Y0 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( cR @ ( cP @ Y1 @ Y0 ) )
= Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ ( cP @ Y1 @ Y2 ) )
=> ( ( Y0 @ ( cP @ ( cL @ Y1 ) @ ( cL @ Y2 ) ) )
& ( ( cZ = Y1 )
= ( cZ = Y2 ) )
& ( Y0 @ ( cP @ ( cR @ Y1 ) @ ( cR @ Y2 ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ ( cP @ Y2 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
& ( cZ
= ( cL @ cZ ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( cZ != Y0 )
= ( ( cP @ ( cL @ Y0 ) @ ( cR @ Y0 ) )
= Y0 ) ) )
& ( cZ
= ( cR @ cZ ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( cL @ ( cP @ Y1 @ Y0 ) )
= Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ ( cP @ Y3 @ Y2 ) )
=> ( ( Y1 @ ( cP @ ( cR @ Y3 ) @ ( cR @ Y2 ) ) )
& ( ( cZ = Y2 )
=> ( cZ = Y3 ) )
& ( Y1 @ ( cP @ ( cL @ Y3 ) @ ( cL @ Y2 ) ) ) ) ) ) )
& ( Y1 @ ( cP @ cZ @ Y0 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: a,X1: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ( cZ
= ( cR @ cZ ) )
& ! [X2: a] :
( ( cZ != X2 )
<=> ( ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) )
= X2 ) )
& ( cZ
= ( cL @ cZ ) )
& ! [X3: a > $o] :
( ! [X4: a,X5: a] :
( ( X3 @ ( cP @ X5 @ X4 ) )
=> ( ( X3 @ ( cP @ ( cR @ X5 ) @ ( cR @ X4 ) ) )
& ( ( cZ = X5 )
<=> ( cZ = X4 ) )
& ( X3 @ ( cP @ ( cL @ X5 ) @ ( cL @ X4 ) ) ) ) )
=> ! [X6: a,X7: a] :
( ( X3 @ ( cP @ X6 @ X7 ) )
=> ( X6 = X7 ) ) )
& ! [X8: a,X9: a] :
( ( cR @ ( cP @ X8 @ X9 ) )
= X9 ) )
=> ! [X10: a] :
? [X11: a > $o] :
( ( X11 @ ( cP @ cZ @ X10 ) )
& ! [X12: a,X13: a] :
( ( X11 @ ( cP @ X12 @ X13 ) )
=> ( ( X11 @ ( cP @ ( cL @ X12 ) @ ( cL @ X13 ) ) )
& ( ( cZ = X13 )
=> ( cZ = X12 ) )
& ( X11 @ ( cP @ ( cR @ X12 ) @ ( cR @ X13 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: a,X1: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ( cZ
= ( cR @ cZ ) )
& ! [X2: a] :
( ( cZ != X2 )
<=> ( ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) )
= X2 ) )
& ( cZ
= ( cL @ cZ ) )
& ! [X3: a > $o] :
( ! [X4: a,X2: a] :
( ( X3 @ ( cP @ X2 @ X4 ) )
=> ( ( X3 @ ( cP @ ( cR @ X2 ) @ ( cR @ X4 ) ) )
& ( ( cZ = X2 )
<=> ( cZ = X4 ) )
& ( X3 @ ( cP @ ( cL @ X2 ) @ ( cL @ X4 ) ) ) ) )
=> ! [X2: a,X4: a] :
( ( X3 @ ( cP @ X2 @ X4 ) )
=> ( X2 = X4 ) ) )
& ! [X0: a,X1: a] :
( ( cR @ ( cP @ X0 @ X1 ) )
= X1 ) )
=> ! [X2: a] :
? [X3: a > $o] :
( ( X3 @ ( cP @ cZ @ X2 ) )
& ! [X5: a,X4: a] :
( ( X3 @ ( cP @ X5 @ X4 ) )
=> ( ( X3 @ ( cP @ ( cL @ X5 ) @ ( cL @ X4 ) ) )
& ( ( cZ = X4 )
=> ( cZ = X5 ) )
& ( X3 @ ( cP @ ( cR @ X5 ) @ ( cR @ X4 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: a,X1: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ( cZ
= ( cR @ cZ ) )
& ! [X2: a] :
( ( cZ != X2 )
<=> ( ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) )
= X2 ) )
& ( cZ
= ( cL @ cZ ) )
& ! [X3: a > $o] :
( ! [X4: a,X2: a] :
( ( X3 @ ( cP @ X2 @ X4 ) )
=> ( ( X3 @ ( cP @ ( cR @ X2 ) @ ( cR @ X4 ) ) )
& ( ( cZ = X2 )
<=> ( cZ = X4 ) )
& ( X3 @ ( cP @ ( cL @ X2 ) @ ( cL @ X4 ) ) ) ) )
=> ! [X2: a,X4: a] :
( ( X3 @ ( cP @ X2 @ X4 ) )
=> ( X2 = X4 ) ) )
& ! [X0: a,X1: a] :
( ( cR @ ( cP @ X0 @ X1 ) )
= X1 ) )
=> ! [X2: a] :
? [X3: a > $o] :
( ( X3 @ ( cP @ cZ @ X2 ) )
& ! [X5: a,X4: a] :
( ( X3 @ ( cP @ X5 @ X4 ) )
=> ( ( X3 @ ( cP @ ( cL @ X5 ) @ ( cL @ X4 ) ) )
& ( ( cZ = X4 )
=> ( cZ = X5 ) )
& ( X3 @ ( cP @ ( cR @ X5 ) @ ( cR @ X4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OaApnq3MkH/DTF2THF_31371.p',cPU_LEM2E_pme) ).
thf(f173,plain,
( $false
= ( ( ( cR @ cZ )
= cZ )
& ( ( cL @ cZ )
= cZ ) ) ),
inference(boolean_simplification,[status(thm)],[f172]) ).
thf(f172,plain,
( $false
= ( ( ( cR @ cZ )
= cZ )
& $true
& ( ( cL @ cZ )
= cZ ) ) ),
inference(boolean_simplification,[status(thm)],[f171]) ).
thf(f171,plain,
( $false
= ( ( ( cR @ cZ )
= cZ )
& ( ( cZ = sK3 )
=> $true )
& ( ( cL @ cZ )
= cZ ) ) ),
inference(boolean_simplification,[status(thm)],[f170]) ).
thf(f170,plain,
( $false
= ( $true
=> ( ( ( cR @ cZ )
= cZ )
& ( ( cZ = sK3 )
=> $true )
& ( ( cL @ cZ )
= cZ ) ) ) ),
inference(boolean_simplification,[status(thm)],[f168]) ).
thf(f168,plain,
( ( ( cZ = cZ )
=> ( ( ( cR @ cZ )
= cZ )
& ( ( cZ = sK3 )
=> ( cZ = cZ ) )
& ( ( cL @ cZ )
= cZ ) ) )
= $false ),
inference(superposition,[status(thm)],[f144,f152]) ).
thf(f152,plain,
cZ = sK5,
inference(equality_proxy_clausification,[status(thm)],[f151]) ).
thf(f151,plain,
( ( sK5 = cZ )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f144]) ).
thf(f144,plain,
( ( ( sK5 = cZ )
=> ( ( ( cR @ sK5 )
= cZ )
& ( ( cZ = sK3 )
=> ( cZ = sK5 ) )
& ( ( cL @ sK5 )
= cZ ) ) )
= $false ),
inference(forward_demodulation,[status(thm)],[f143,f51]) ).
thf(f51,plain,
! [X2: a,X1: a] :
( ( cL @ ( cP @ X2 @ X1 ) )
= X2 ),
inference(equality_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: a,X1: a] :
( ( ( cL @ ( cP @ X2 @ X1 ) )
= X2 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( cL @ ( cP @ Y0 @ X1 ) )
= Y0 )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( cL @ ( cP @ Y0 @ X1 ) )
= Y0 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( cL @ ( cP @ Y1 @ Y0 ) )
= Y1 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( cL @ ( cP @ Y1 @ Y0 ) )
= Y1 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f143,plain,
( ( ( sK5 = cZ )
=> ( ( ( cR @ sK5 )
= cZ )
& ( ( cZ = sK3 )
=> ( cZ = sK5 ) )
& ( ( cL @ ( cP @ ( cL @ sK5 ) @ ( cL @ sK3 ) ) )
= cZ ) ) )
= $false ),
inference(forward_demodulation,[status(thm)],[f142,f51]) ).
thf(f142,plain,
( $false
= ( ( sK5 = cZ )
=> ( ( ( cL @ ( cP @ ( cR @ sK5 ) @ ( cR @ sK3 ) ) )
= cZ )
& ( ( cZ = sK3 )
=> ( cZ = sK5 ) )
& ( ( cL @ ( cP @ ( cL @ sK5 ) @ ( cL @ sK3 ) ) )
= cZ ) ) ) ),
inference(forward_demodulation,[status(thm)],[f141,f51]) ).
thf(f141,plain,
( ( ( ( cL @ ( cP @ sK5 @ sK3 ) )
= cZ )
=> ( ( ( cL @ ( cP @ ( cR @ sK5 ) @ ( cR @ sK3 ) ) )
= cZ )
& ( ( cZ = sK3 )
=> ( cZ = sK5 ) )
& ( ( cL @ ( cP @ ( cL @ sK5 ) @ ( cL @ sK3 ) ) )
= cZ ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f140]) ).
thf(f140,plain,
( $false
= ( ^ [Y0: a] :
( ( ( cL @ ( cP @ Y0 @ sK3 ) )
= cZ )
=> ( ( ( cL @ ( cP @ ( cR @ Y0 ) @ ( cR @ sK3 ) ) )
= cZ )
& ( ( cZ = sK3 )
=> ( cZ = Y0 ) )
& ( ( cL @ ( cP @ ( cL @ Y0 ) @ ( cL @ sK3 ) ) )
= cZ ) ) )
@ sK5 ) ),
inference(sigma_clausification,[status(thm)],[f132]) ).
thf(f132,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ( ( cL @ ( cP @ Y0 @ sK3 ) )
= cZ )
=> ( ( ( cL @ ( cP @ ( cR @ Y0 ) @ ( cR @ sK3 ) ) )
= cZ )
& ( ( cZ = sK3 )
=> ( cZ = Y0 ) )
& ( ( cL @ ( cP @ ( cL @ Y0 ) @ ( cL @ sK3 ) ) )
= cZ ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f130]) ).
thf(f130,plain,
( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( cL @ ( cP @ Y1 @ Y0 ) )
= cZ )
=> ( ( ( cL @ ( cP @ ( cR @ Y1 ) @ ( cR @ Y0 ) ) )
= cZ )
& ( ( cZ = Y0 )
=> ( cZ = Y1 ) )
& ( ( cL @ ( cP @ ( cL @ Y1 ) @ ( cL @ Y0 ) ) )
= cZ ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( cL @ ( cP @ Y1 @ Y0 ) )
= cZ )
=> ( ( ( cL @ ( cP @ ( cR @ Y1 ) @ ( cR @ Y0 ) ) )
= cZ )
& ( ( cZ = Y0 )
=> ( cZ = Y1 ) )
& ( ( cL @ ( cP @ ( cL @ Y1 ) @ ( cL @ Y0 ) ) )
= cZ ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f53]) ).
thf(f53,plain,
( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( cL @ ( cP @ Y1 @ Y0 ) )
= cZ )
=> ( ( ( cL @ ( cP @ ( cR @ Y1 ) @ ( cR @ Y0 ) ) )
= cZ )
& ( ( cZ = Y0 )
=> ( cZ = Y1 ) )
& ( ( cL @ ( cP @ ( cL @ Y1 ) @ ( cL @ Y0 ) ) )
= cZ ) ) ) ) )
& $true ) ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ^ [Y2: a] :
( ( ^ [Y3: a] :
( cL
@ ( ^ [Y4: a] : Y4
@ Y3 ) )
@ Y2 )
= ( ^ [Y3: a] : cZ
@ Y2 ) )
@ ( cP @ Y1 @ Y0 ) )
=> ( ( ^ [Y2: a] :
( ( ^ [Y3: a] :
( cL
@ ( ^ [Y4: a] : Y4
@ Y3 ) )
@ Y2 )
= ( ^ [Y3: a] : cZ
@ Y2 ) )
@ ( cP @ ( cR @ Y1 ) @ ( cR @ Y0 ) ) )
& ( ( cZ = Y0 )
=> ( cZ = Y1 ) )
& ( ^ [Y2: a] :
( ( ^ [Y3: a] :
( cL
@ ( ^ [Y4: a] : Y4
@ Y3 ) )
@ Y2 )
= ( ^ [Y3: a] : cZ
@ Y2 ) )
@ ( cP @ ( cL @ Y1 ) @ ( cL @ Y0 ) ) ) ) ) ) )
& $true ) ),
inference(superposition,[status(thm)],[f20,f50]) ).
thf(f20,plain,
! [X1: a > $o] :
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( X1 @ ( cP @ Y1 @ Y0 ) )
=> ( ( X1 @ ( cP @ ( cR @ Y1 ) @ ( cR @ Y0 ) ) )
& ( ( cZ = Y0 )
=> ( cZ = Y1 ) )
& ( X1 @ ( cP @ ( cL @ Y1 ) @ ( cL @ Y0 ) ) ) ) ) ) )
& ( X1 @ ( cP @ cZ @ sK1 ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: a > $o] :
( $false
= ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ ( cP @ Y2 @ Y1 ) )
=> ( ( Y0 @ ( cP @ ( cR @ Y2 ) @ ( cR @ Y1 ) ) )
& ( ( cZ = Y1 )
=> ( cZ = Y2 ) )
& ( Y0 @ ( cP @ ( cL @ Y2 ) @ ( cL @ Y1 ) ) ) ) ) ) )
& ( Y0 @ ( cP @ cZ @ sK1 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ ( cP @ Y2 @ Y1 ) )
=> ( ( Y0 @ ( cP @ ( cR @ Y2 ) @ ( cR @ Y1 ) ) )
& ( ( cZ = Y1 )
=> ( cZ = Y2 ) )
& ( Y0 @ ( cP @ ( cL @ Y2 ) @ ( cL @ Y1 ) ) ) ) ) ) )
& ( Y0 @ ( cP @ cZ @ sK1 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ ( cP @ Y3 @ Y2 ) )
=> ( ( Y1 @ ( cP @ ( cR @ Y3 ) @ ( cR @ Y2 ) ) )
& ( ( cZ = Y2 )
=> ( cZ = Y3 ) )
& ( Y1 @ ( cP @ ( cL @ Y3 ) @ ( cL @ Y2 ) ) ) ) ) ) )
& ( Y1 @ ( cP @ cZ @ Y0 ) ) ) )
@ sK1 ) ),
inference(sigma_clausification,[status(thm)],[f8]) ).
thf(f8,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ ( cP @ Y3 @ Y2 ) )
=> ( ( Y1 @ ( cP @ ( cR @ Y3 ) @ ( cR @ Y2 ) ) )
& ( ( cZ = Y2 )
=> ( cZ = Y3 ) )
& ( Y1 @ ( cP @ ( cL @ Y3 ) @ ( cL @ Y2 ) ) ) ) ) ) )
& ( Y1 @ ( cP @ cZ @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f435,plain,
( cZ
= ( cL @ cZ ) ),
inference(equality_proxy_clausification,[status(thm)],[f403]) ).
thf(f403,plain,
( ( cZ
= ( cL @ cZ ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f228]) ).
thf(f228,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( cR @ ( cP @ Y1 @ Y0 ) )
= Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ ( cP @ Y1 @ Y2 ) )
=> ( ( Y0 @ ( cP @ ( cL @ Y1 ) @ ( cL @ Y2 ) ) )
& ( ( cZ = Y1 )
= ( cZ = Y2 ) )
& ( Y0 @ ( cP @ ( cR @ Y1 ) @ ( cR @ Y2 ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ ( cP @ Y2 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
& ( cZ
= ( cL @ cZ ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( cR @ ( cP @ Y1 @ Y0 ) )
= Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ ( cP @ Y1 @ Y2 ) )
=> ( ( Y0 @ ( cP @ ( cL @ Y1 ) @ ( cL @ Y2 ) ) )
& ( ( cZ = Y1 )
= ( cZ = Y2 ) )
& ( Y0 @ ( cP @ ( cR @ Y1 ) @ ( cR @ Y2 ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ ( cP @ Y2 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
& ( cZ
= ( cL @ cZ ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( cZ != Y0 )
= ( ( cP @ ( cL @ Y0 ) @ ( cR @ Y0 ) )
= Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU972^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n006.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:37:30 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.47 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : SEU972^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.47 % Domain : Set Theory (Relations)
% 0.30/0.47 % Problem : TPS problem from COINDUCTIVE-PU-ALG-THMS
% 0.30/0.47 % Version : Especial.
% 0.30/0.47 % English :
% 0.30/0.47
% 0.30/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.47 % Source : [Bro09]
% 0.30/0.47 % Names : tps_1140 [Bro09]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : 0.56 v9.1.0, 0.50 v9.0.0, 0.60 v8.2.0, 0.85 v8.1.0, 0.82 v7.5.0, 0.71 v7.4.0, 0.78 v7.2.0, 0.75 v7.0.0, 0.86 v6.4.0, 0.83 v6.3.0, 1.00 v6.1.0, 0.71 v5.5.0, 1.00 v4.0.0
% 0.30/0.47 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.30/0.47 % Number of atoms : 11 ( 11 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 11 ( 11 avg)
% 0.30/0.47 % Number of connectives : 63 ( 1 ~; 0 |; 10 &; 44 @)
% 0.30/0.47 % ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 18 ( 18 avg)
% 0.30/0.47 % Number of types : 2 ( 1 usr)
% 0.30/0.47 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% 0.30/0.47 % Number of variables : 14 ( 0 ^; 13 !; 1 ?; 14 :)
% 0.30/0.47 % SPC : TH0_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 thf(a_type,type,
% 0.30/0.47 a: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(cR,type,
% 0.30/0.47 cR: a > a ).
% 0.30/0.47
% 0.30/0.47 thf(cP,type,
% 0.30/0.47 cP: a > a > a ).
% 0.30/0.47
% 0.30/0.47 thf(cL,type,
% 0.30/0.47 cL: a > a ).
% 0.30/0.47
% 0.30/0.47 thf(cZ,type,
% 0.30/0.47 cZ: a ).
% 0.30/0.47
% 0.30/0.47 thf(cPU_LEM2E_pme,conjecture,
% 0.30/0.47 ( ( ( ( cL @ cZ )
% 0.30/0.47 = cZ )
% 0.30/0.47 & ( ( cR @ cZ )
% 0.30/0.47 = cZ )
% 0.30/0.47 & ! [Xx: a,Xy: a] :
% 0.30/0.47 ( ( cL @ ( cP @ Xx @ Xy ) )
% 0.30/0.47 = Xx )
% 0.30/0.47 & ! [Xx: a,Xy: a] :
% 0.30/0.47 ( ( cR @ ( cP @ Xx @ Xy ) )
% 0.30/0.47 = Xy )
% 0.30/0.47 & ! [Xt: a] :
% 0.30/0.47 ( ( Xt != cZ )
% 0.30/0.47 <=> ( Xt
% 0.30/0.47 = ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) )
% 0.30/0.47 & ! [X: a > $o] :
% 0.30/0.47 ( ! [Xt: a,Xu: a] :
% 0.30/0.47 ( ( X @ ( cP @ Xt @ Xu ) )
% 0.30/0.47 => ( ( ( Xt = cZ )
% 0.30/0.47 <=> ( Xu = cZ ) )
% 0.30/0.47 & ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
% 0.30/0.47 & ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) )
% 0.30/0.47 => ! [Xt: a,Xu: a] :
% 0.30/0.47 ( ( X @ ( cP @ Xt @ Xu ) )
% 0.30/0.47 => ( Xt = Xu ) ) ) )
% 0.30/0.47 => ! [Xt: a] :
% 0.30/0.47 ? [X: a > $o] :
% 0.30/0.47 ( ( X @ ( cP @ cZ @ Xt ) )
% 0.30/0.47 & ! [Xt0: a,Xu: a] :
% 0.30/0.47 ( ( X @ ( cP @ Xt0 @ Xu ) )
% 0.30/0.47 => ( ( ( Xu = cZ )
% 0.30/0.47 => ( Xt0 = cZ ) )
% 0.30/0.47 & ( X @ ( cP @ ( cL @ Xt0 ) @ ( cL @ Xu ) ) )
% 0.30/0.47 & ( X @ ( cP @ ( cR @ Xt0 ) @ ( cR @ Xu ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 1.48/1.29 ---- Embedded in THF ---
% 1.48/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.29 %%% Generated on Tue Feb 24 12:37:31 EST 2026
% 1.48/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.29 %%% Logic specification used:
% 1.48/1.29 %%% thf(spec, logic, $$dhol).
% 1.48/1.29
% 1.48/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.OaApnq3MkH/DTF2DTF31371.p
% See solution above
% 1.48/1.29 ------------------------
% 1.66/1.30 ---- Cleaned THF ---
% 1.66/1.30 thf(a_type,type,
% 1.66/1.30 a: $tType ).
% 1.66/1.30
% 1.66/1.30 thf(cR,type,
% 1.66/1.30 cR: a > a ).
% 1.66/1.30
% 1.66/1.30 thf(cP,type,
% 1.66/1.30 cP: a > a > a ).
% 1.66/1.30
% 1.66/1.30 thf(cL,type,
% 1.66/1.30 cL: a > a ).
% 1.66/1.30
% 1.66/1.30 thf(cZ,type,
% 1.66/1.30 cZ: a ).
% 1.66/1.30
% 1.66/1.30 thf(cPU_LEM2E_pme,conjecture,
% 1.66/1.30 ( ( ( ( cL @ cZ )
% 1.66/1.30 = cZ )
% 1.66/1.30 & ( ( cR @ cZ )
% 1.66/1.30 = cZ )
% 1.66/1.30 & ! [Xx: a,Xy: a] :
% 1.66/1.30 ( ( cL @ ( cP @ Xx @ Xy ) )
% 1.66/1.30 = Xx )
% 1.66/1.30 & ! [Xx: a,Xy: a] :
% 1.66/1.30 ( ( cR @ ( cP @ Xx @ Xy ) )
% 1.66/1.30 = Xy )
% 1.66/1.30 & ! [Xt: a] :
% 1.66/1.30 ( ( Xt != cZ )
% 1.66/1.30 <=> ( Xt
% 1.66/1.30 = ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) )
% 1.66/1.30 & ! [X: a > $o] :
% 1.66/1.30 ( ! [Xt: a,Xu: a] :
% 1.66/1.30 ( ( X @ ( cP @ Xt @ Xu ) )
% 1.66/1.30 => ( ( ( Xt = cZ )
% 1.66/1.30 <=> ( Xu = cZ ) )
% 1.66/1.30 & ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
% 1.66/1.30 & ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) )
% 1.66/1.30 => ! [Xt: a,Xu: a] :
% 1.66/1.30 ( ( X @ ( cP @ Xt @ Xu ) )
% 1.66/1.30 => ( Xt = Xu ) ) ) )
% 1.66/1.30 => ! [Xt: a] :
% 1.66/1.30 ? [X: a > $o] :
% 1.66/1.30 ( ( X @ ( cP @ cZ @ Xt ) )
% 1.66/1.30 & ! [Xt0: a,Xu: a] :
% 1.66/1.30 ( ( X @ ( cP @ Xt0 @ Xu ) )
% 1.66/1.30 => ( ( ( Xu = cZ )
% 1.66/1.30 => ( Xt0 = cZ ) )
% 1.66/1.30 & ( X @ ( cP @ ( cL @ Xt0 ) @ ( cL @ Xu ) ) )
% 1.66/1.30 & ( X @ ( cP @ ( cR @ Xt0 ) @ ( cR @ Xu ) ) ) ) ) ) ) ).
% 1.66/1.30 ------------------------
% 1.66/1.31 % (31701)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_31371 for (3000ds/4Mi)
% 1.66/1.31 % (31701)Instruction limit reached!
% 1.66/1.31 % (31701)------------------------------
% 1.66/1.31 % (31701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.31 % (31701)Termination reason: Unknown
% 1.66/1.31 % (31701)Termination phase: Saturation
% 1.66/1.31
% 1.66/1.31 % (31701)Memory used [KB]: 5500
% 1.66/1.31 % (31701)Time elapsed: 0.003 s
% 1.66/1.31 % (31701)Instructions burned: 4 (million)
% 1.66/1.31 % (31701)------------------------------
% 1.66/1.31 % (31701)------------------------------
% 1.66/1.32 % (31700)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31371 for (3000ds/183Mi)
% 1.66/1.32 % (31702)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_31371 for (3000ds/27Mi)
% 1.66/1.32 % (31703)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_31371 for (3000ds/2Mi)
% 1.66/1.32 % (31704)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_31371 for (3000ds/2Mi)
% 1.66/1.32 % (31705)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_31371 for (3000ds/275Mi)
% 1.66/1.32 % (31706)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31371 for (3000ds/18Mi)
% 1.66/1.32 % (31703)Instruction limit reached!
% 1.66/1.32 % (31703)------------------------------
% 1.66/1.32 % (31703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (31703)Termination reason: Unknown
% 1.66/1.32 % (31703)Termination phase: Property scanning
% 1.66/1.32
% 1.66/1.32 % (31703)Memory used [KB]: 1023
% 1.66/1.32 % (31703)Time elapsed: 0.004 s
% 1.66/1.32 % (31703)Instructions burned: 3 (million)
% 1.66/1.32 % (31703)------------------------------
% 1.66/1.32 % (31703)------------------------------
% 1.66/1.32 % (31704)Instruction limit reached!
% 1.66/1.32 % (31704)------------------------------
% 1.66/1.32 % (31704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (31704)Termination reason: Unknown
% 1.66/1.32 % (31704)Termination phase: Property scanning
% 1.66/1.32
% 1.66/1.32 % (31704)Memory used [KB]: 1023
% 1.66/1.32 % (31704)Time elapsed: 0.004 s
% 1.66/1.32 % (31704)Instructions burned: 3 (million)
% 1.66/1.32 % (31704)------------------------------
% 1.66/1.32 % (31704)------------------------------
% 1.66/1.32 % (31707)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_31371 for (2999ds/3Mi)
% 1.66/1.33 % (31707)Instruction limit reached!
% 1.66/1.33 % (31707)------------------------------
% 1.66/1.33 % (31707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (31707)Termination reason: Unknown
% 1.66/1.33 % (31707)Termination phase: Property scanning
% 1.66/1.33
% 1.66/1.33 % (31707)Memory used [KB]: 1023
% 1.66/1.33 % (31707)Time elapsed: 0.002 s
% 1.66/1.33 % (31707)Instructions burned: 4 (million)
% 1.66/1.33 % (31707)------------------------------
% 1.66/1.33 % (31707)------------------------------
% 1.66/1.33 % (31702)Refutation not found, incomplete strategy
% 1.66/1.33 % (31702)------------------------------
% 1.66/1.33 % (31702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (31702)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.33
% 1.66/1.33
% 1.66/1.33 % (31702)Memory used [KB]: 5500
% 1.66/1.33 % (31702)Time elapsed: 0.009 s
% 1.66/1.33 % (31702)Instructions burned: 10 (million)
% 1.66/1.33 % (31702)------------------------------
% 1.66/1.33 % (31702)------------------------------
% 1.66/1.33 % (31706)Instruction limit reached!
% 1.66/1.33 % (31706)------------------------------
% 1.66/1.33 % (31706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (31706)Termination reason: Unknown
% 1.66/1.33 % (31706)Termination phase: Saturation
% 1.66/1.33
% 1.66/1.33 % (31706)Memory used [KB]: 5628
% 1.66/1.33 % (31706)Time elapsed: 0.014 s
% 1.66/1.33 % (31706)Instructions burned: 19 (million)
% 1.66/1.33 % (31706)------------------------------
% 1.66/1.33 % (31706)------------------------------
% 1.66/1.33 % (31710)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_31371 for (2999ds/3Mi)
% 1.66/1.34 % (31710)Instruction limit reached!
% 1.66/1.34 % (31710)------------------------------
% 1.66/1.34 % (31710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.34 % (31710)Termination reason: Unknown
% 1.66/1.34 % (31710)Termination phase: Saturation
% 1.66/1.34
% 1.66/1.34 % (31710)Memory used [KB]: 5500
% 1.66/1.34 % (31710)Time elapsed: 0.002 s
% 1.66/1.34 % (31710)Instructions burned: 4 (million)
% 1.66/1.34 % (31710)------------------------------
% 1.66/1.34 % (31710)------------------------------
% 1.66/1.34 % (31708)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_31371 for (2999ds/37Mi)
% 1.66/1.34 % (31709)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_31371 for (2999ds/15Mi)
% 1.66/1.34 % (31713)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_31371 for (2999ds/16Mi)
% 1.66/1.35 % (31711)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_31371 for (2999ds/1041Mi)
% 1.66/1.35 % (31712)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_31371 for (2999ds/7Mi)
% 1.66/1.35 % (31709)Instruction limit reached!
% 1.66/1.35 % (31709)------------------------------
% 1.66/1.35 % (31709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (31709)Termination reason: Unknown
% 1.66/1.35 % (31709)Termination phase: Saturation
% 1.66/1.35
% 1.66/1.35 % (31709)Memory used [KB]: 5628
% 1.66/1.35 % (31709)Time elapsed: 0.012 s
% 1.66/1.35 % (31709)Instructions burned: 16 (million)
% 1.66/1.35 % (31709)------------------------------
% 1.66/1.35 % (31709)------------------------------
% 1.66/1.35 % (31713)Instruction limit reached!
% 1.66/1.35 % (31713)------------------------------
% 1.66/1.35 % (31713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (31713)Termination reason: Unknown
% 1.66/1.35 % (31713)Termination phase: Saturation
% 1.66/1.35
% 1.66/1.35 % (31713)Memory used [KB]: 5628
% 1.66/1.35 % (31713)Time elapsed: 0.007 s
% 1.66/1.35 % (31713)Instructions burned: 18 (million)
% 1.66/1.35 % (31713)------------------------------
% 1.66/1.35 % (31713)------------------------------
% 1.66/1.35 % (31712)Instruction limit reached!
% 1.66/1.35 % (31712)------------------------------
% 1.66/1.35 % (31712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (31712)Termination reason: Unknown
% 1.66/1.35 % (31712)Termination phase: Saturation
% 1.66/1.35
% 1.66/1.35 % (31712)Memory used [KB]: 1023
% 1.66/1.35 % (31712)Time elapsed: 0.005 s
% 1.66/1.35 % (31712)Instructions burned: 8 (million)
% 1.66/1.35 % (31712)------------------------------
% 1.66/1.35 % (31712)------------------------------
% 1.66/1.35 % (31708)Instruction limit reached!
% 1.66/1.35 % (31708)------------------------------
% 1.66/1.35 % (31708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (31708)Termination reason: Unknown
% 1.66/1.35 % (31708)Termination phase: Saturation
% 1.66/1.35
% 1.66/1.35 % (31708)Memory used [KB]: 5628
% 1.66/1.35 % (31708)Time elapsed: 0.015 s
% 1.66/1.35 % (31708)Instructions burned: 39 (million)
% 1.66/1.35 % (31708)------------------------------
% 1.66/1.35 % (31708)------------------------------
% 1.66/1.36 % (31715)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_31371 for (2999ds/3Mi)
% 1.66/1.36 % (31715)Instruction limit reached!
% 1.66/1.36 % (31715)------------------------------
% 1.66/1.36 % (31715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (31715)Termination reason: Unknown
% 1.66/1.36 % (31715)Termination phase: Property scanning
% 1.66/1.36
% 1.66/1.36 % (31715)Memory used [KB]: 1023
% 1.66/1.36 % (31715)Time elapsed: 0.002 s
% 1.66/1.36 % (31715)Instructions burned: 3 (million)
% 1.66/1.36 % (31715)------------------------------
% 1.66/1.36 % (31715)------------------------------
% 1.66/1.36 % (31717)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_31371 for (2999ds/3Mi)
% 1.66/1.36 % (31716)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_31371 for (2999ds/7Mi)
% 1.66/1.36 % (31717)Instruction limit reached!
% 1.66/1.36 % (31717)------------------------------
% 1.66/1.36 % (31717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (31717)Termination reason: Unknown
% 1.66/1.36 % (31717)Termination phase: Saturation
% 1.66/1.36
% 1.66/1.36 % (31717)Memory used [KB]: 5500
% 1.66/1.36 % (31717)Time elapsed: 0.003 s
% 1.66/1.36 % (31717)Instructions burned: 4 (million)
% 1.66/1.36 % (31717)------------------------------
% 1.66/1.36 % (31717)------------------------------
% 1.66/1.37 % (31716)Instruction limit reached!
% 1.66/1.37 % (31716)------------------------------
% 1.66/1.37 % (31716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (31716)Termination reason: Unknown
% 1.66/1.37 % (31716)Termination phase: Saturation
% 1.66/1.37
% 1.66/1.37 % (31716)Memory used [KB]: 5500
% 1.66/1.37 % (31716)Time elapsed: 0.004 s
% 1.66/1.37 % (31716)Instructions burned: 7 (million)
% 1.66/1.37 % (31716)------------------------------
% 1.66/1.37 % (31716)------------------------------
% 1.66/1.37 % (31714)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_31371 for (2999ds/3Mi)
% 1.66/1.37 % (31714)Instruction limit reached!
% 1.66/1.37 % (31714)------------------------------
% 1.66/1.37 % (31714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (31714)Termination reason: Unknown
% 1.66/1.37 % (31714)Termination phase: Twee Goal Transformation
% 1.66/1.37
% 1.66/1.37 % (31714)Memory used [KB]: 1023
% 1.66/1.37 % (31714)Time elapsed: 0.004 s
% 1.66/1.37 % (31714)Instructions burned: 4 (million)
% 1.66/1.37 % (31714)------------------------------
% 1.66/1.37 % (31714)------------------------------
% 1.66/1.37 % (31718)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_31371 for (2999ds/4Mi)
% 1.66/1.37 % (31718)Instruction limit reached!
% 1.66/1.37 % (31718)------------------------------
% 1.66/1.37 % (31718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (31718)Termination reason: Unknown
% 1.66/1.37 % (31718)Termination phase: Saturation
% 1.66/1.37
% 1.66/1.37 % (31718)Memory used [KB]: 1023
% 1.66/1.37 % (31718)Time elapsed: 0.002 s
% 1.66/1.37 % (31718)Instructions burned: 4 (million)
% 1.66/1.37 % (31718)------------------------------
% 1.66/1.37 % (31718)------------------------------
% 1.66/1.37 % (31719)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_31371 for (2999ds/18Mi)
% 1.66/1.38 % (31720)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_31371 for (2999ds/710Mi)
% 1.66/1.38 % (31719)Refutation not found, incomplete strategy
% 1.66/1.38 % (31719)------------------------------
% 1.66/1.38 % (31719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.38 % (31719)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.38
% 1.66/1.38
% 1.66/1.38 % (31719)Memory used [KB]: 5500
% 1.66/1.38 % (31719)Time elapsed: 0.005 s
% 1.66/1.38 % (31719)Instructions burned: 9 (million)
% 1.66/1.38 % (31719)------------------------------
% 1.66/1.38 % (31719)------------------------------
% 1.66/1.38 % (31722)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_31371 for (2999ds/902Mi)
% 1.66/1.39 % (31721)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_31371 for (2999ds/6Mi)
% 1.66/1.39 % (31723)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_31371 for (2999ds/21Mi)
% 1.66/1.39 % (31721)Instruction limit reached!
% 1.66/1.39 % (31721)------------------------------
% 1.66/1.39 % (31721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.39 % (31721)Termination reason: Unknown
% 1.66/1.39 % (31721)Termination phase: Saturation
% 1.66/1.39
% 1.66/1.39 % (31721)Memory used [KB]: 5500
% 1.66/1.39 % (31721)Time elapsed: 0.006 s
% 1.66/1.39 % (31721)Instructions burned: 7 (million)
% 1.66/1.39 % (31721)------------------------------
% 1.66/1.39 % (31721)------------------------------
% 1.67/1.40 % (31723)Instruction limit reached!
% 1.67/1.40 % (31723)------------------------------
% 1.67/1.40 % (31723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.40 % (31723)Termination reason: Unknown
% 1.67/1.40 % (31723)Termination phase: Saturation
% 1.67/1.40
% 1.67/1.40 % (31723)Memory used [KB]: 5628
% 1.67/1.40 % (31723)Time elapsed: 0.010 s
% 1.67/1.40 % (31723)Instructions burned: 23 (million)
% 1.67/1.40 % (31723)------------------------------
% 1.67/1.40 % (31723)------------------------------
% 1.67/1.41 % (31725)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_31371 for (2999ds/6Mi)
% 1.67/1.41 % (31724)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_31371 for (2999ds/5Mi)
% 1.67/1.41 % (31725)Instruction limit reached!
% 1.67/1.41 % (31725)------------------------------
% 1.67/1.41 % (31725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.41 % (31725)Termination reason: Unknown
% 1.67/1.41 % (31725)Termination phase: Saturation
% 1.67/1.41
% 1.67/1.41 % (31725)Memory used [KB]: 5500
% 1.67/1.41 % (31725)Time elapsed: 0.004 s
% 1.67/1.41 % (31725)Instructions burned: 8 (million)
% 1.67/1.41 % (31725)------------------------------
% 1.67/1.41 % (31725)------------------------------
% 1.67/1.41 % (31724)Instruction limit reached!
% 1.67/1.41 % (31724)------------------------------
% 1.67/1.41 % (31724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.41 % (31724)Termination reason: Unknown
% 1.67/1.41 % (31724)Termination phase: Saturation
% 1.67/1.41
% 1.67/1.41 % (31724)Memory used [KB]: 5500
% 1.67/1.41 % (31724)Time elapsed: 0.005 s
% 1.67/1.41 % (31724)Instructions burned: 5 (million)
% 1.67/1.41 % (31724)------------------------------
% 1.67/1.41 % (31724)------------------------------
% 1.67/1.42 % (31726)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_31371 for (2999ds/377Mi)
% 1.67/1.43 % (31727)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_31371 for (2999ds/779Mi)
% 1.67/1.43 % (31700)Instruction limit reached!
% 1.67/1.43 % (31700)------------------------------
% 1.67/1.43 % (31700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.43 % (31700)Termination reason: Unknown
% 1.67/1.43 % (31700)Termination phase: Saturation
% 1.67/1.43
% 1.67/1.43 % (31700)Memory used [KB]: 6396
% 1.67/1.43 % (31700)Time elapsed: 0.109 s
% 1.67/1.43 % (31700)Instructions burned: 184 (million)
% 1.67/1.43 % (31700)------------------------------
% 1.67/1.43 % (31700)------------------------------
% 1.67/1.44 % (31728)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_31371 for (2998ds/19Mi)
% 1.67/1.44 % (31727)Refutation not found, incomplete strategy
% 1.67/1.44 % (31727)------------------------------
% 1.67/1.44 % (31727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.44 % (31727)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.44
% 1.67/1.44
% 1.67/1.44 % (31727)Memory used [KB]: 5628
% 1.67/1.44 % (31727)Time elapsed: 0.013 s
% 1.67/1.44 % (31727)Instructions burned: 35 (million)
% 1.67/1.44 % (31727)------------------------------
% 1.67/1.44 % (31727)------------------------------
% 1.67/1.44 % (31728)Instruction limit reached!
% 1.67/1.44 % (31728)------------------------------
% 1.67/1.44 % (31728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.44 % (31728)Termination reason: Unknown
% 1.67/1.44 % (31728)Termination phase: Saturation
% 1.67/1.44
% 1.67/1.44 % (31728)Memory used [KB]: 5500
% 1.67/1.44 % (31728)Time elapsed: 0.007 s
% 1.67/1.44 % (31728)Instructions burned: 19 (million)
% 1.67/1.44 % (31728)------------------------------
% 1.67/1.44 % (31728)------------------------------
% 1.67/1.45 % (31729)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_31371 for (2998ds/879Mi)
% 1.67/1.45 % (31730)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_31371 for (2998ds/17Mi)
% 1.67/1.46 % (31705)Instruction limit reached!
% 1.67/1.46 % (31705)------------------------------
% 1.67/1.46 % (31705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.46 % (31705)Termination reason: Unknown
% 1.67/1.46 % (31705)Termination phase: Saturation
% 1.67/1.46
% 1.67/1.46 % (31705)Memory used [KB]: 6140
% 1.67/1.46 % (31705)Time elapsed: 0.139 s
% 1.67/1.46 % (31705)Instructions burned: 278 (million)
% 1.67/1.46 % (31705)------------------------------
% 1.67/1.46 % (31705)------------------------------
% 1.67/1.46 % (31730)Instruction limit reached!
% 1.67/1.46 % (31730)------------------------------
% 1.67/1.46 % (31730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.46 % (31730)Termination reason: Unknown
% 1.67/1.46 % (31730)Termination phase: Saturation
% 1.67/1.46
% 1.67/1.46 % (31730)Memory used [KB]: 5628
% 1.67/1.46 % (31730)Time elapsed: 0.008 s
% 1.67/1.46 % (31730)Instructions burned: 17 (million)
% 1.67/1.46 % (31730)------------------------------
% 1.67/1.46 % (31730)------------------------------
% 1.67/1.47 % (31731)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_31371 for (2998ds/3Mi)
% 1.67/1.47 % (31731)Instruction limit reached!
% 1.67/1.47 % (31731)------------------------------
% 1.67/1.47 % (31731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.47 % (31731)Termination reason: Unknown
% 1.67/1.47 % (31731)Termination phase: Saturation
% 1.67/1.47
% 1.67/1.47 % (31731)Memory used [KB]: 1023
% 1.67/1.47 % (31731)Time elapsed: 0.003 s
% 1.67/1.47 % (31731)Instructions burned: 4 (million)
% 1.67/1.47 % (31731)------------------------------
% 1.67/1.47 % (31731)------------------------------
% 1.67/1.47 % (31732)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_31371 for (2998ds/30Mi)
% 1.67/1.48 % (31733)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_31371 for (2998ds/127Mi)
% 1.67/1.48 % (31732)Instruction limit reached!
% 1.67/1.48 % (31732)------------------------------
% 1.67/1.48 % (31732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.48 % (31732)Termination reason: Unknown
% 1.67/1.48 % (31732)Termination phase: Saturation
% 1.67/1.48
% 1.67/1.48 % (31732)Memory used [KB]: 5628
% 1.67/1.48 % (31732)Time elapsed: 0.035 s
% 1.67/1.48 % (31732)Instructions burned: 32 (million)
% 1.67/1.48 % (31732)------------------------------
% 1.67/1.48 % (31732)------------------------------
% 1.67/1.49 % (31734)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_31371 for (2998ds/100Mi)
% 1.67/1.50 % (31734)Refutation not found, incomplete strategy
% 1.67/1.50 % (31734)------------------------------
% 1.67/1.50 % (31734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.50 % (31734)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.50
% 1.67/1.50
% 1.67/1.50 % (31734)Memory used [KB]: 5500
% 1.67/1.50 % (31734)Time elapsed: 0.028 s
% 1.67/1.50 % (31734)Instructions burned: 10 (million)
% 1.67/1.50 % (31734)------------------------------
% 1.67/1.50 % (31734)------------------------------
% 1.67/1.51 % (31735)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_31371 for (2998ds/3Mi)
% 1.67/1.51 % (31735)Instruction limit reached!
% 1.67/1.51 % (31735)------------------------------
% 1.67/1.51 % (31735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.51 % (31735)Termination reason: Unknown
% 1.67/1.51 % (31735)Termination phase: Saturation
% 1.67/1.51
% 1.67/1.51 % (31735)Memory used [KB]: 5500
% 1.67/1.51 % (31735)Time elapsed: 0.003 s
% 1.67/1.51 % (31735)Instructions burned: 4 (million)
% 1.67/1.51 % (31735)------------------------------
% 1.67/1.51 % (31735)------------------------------
% 1.67/1.52 % (31736)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_31371 for (2997ds/20Mi)
% 1.67/1.52 % (31733)Instruction limit reached!
% 1.67/1.52 % (31733)------------------------------
% 1.67/1.52 % (31733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.52 % (31733)Termination reason: Unknown
% 1.67/1.52 % (31733)Termination phase: Saturation
% 1.67/1.52
% 1.67/1.52 % (31733)Memory used [KB]: 5884
% 1.67/1.52 % (31733)Time elapsed: 0.067 s
% 1.67/1.52 % (31733)Instructions burned: 128 (million)
% 1.67/1.52 % (31733)------------------------------
% 1.67/1.52 % (31733)------------------------------
% 1.67/1.52 % (31736)Instruction limit reached!
% 1.67/1.52 % (31736)------------------------------
% 1.67/1.52 % (31736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.52 % (31736)Termination reason: Unknown
% 1.67/1.52 % (31736)Termination phase: Saturation
% 1.67/1.52
% 1.67/1.52 % (31736)Memory used [KB]: 5628
% 1.67/1.52 % (31736)Time elapsed: 0.009 s
% 1.67/1.52 % (31736)Instructions burned: 20 (million)
% 1.67/1.52 % (31736)------------------------------
% 1.67/1.52 % (31736)------------------------------
% 1.67/1.53 % (31737)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_31371 for (2997ds/86Mi)
% 1.67/1.53 % (31738)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_31371 for (2997ds/107Mi)
% 1.67/1.54 % (31738)Refutation not found, incomplete strategy
% 1.67/1.54 % (31738)------------------------------
% 1.67/1.54 % (31738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.54 % (31738)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.54
% 1.67/1.54
% 1.67/1.54 % (31738)Memory used [KB]: 5628
% 1.67/1.54 % (31738)Time elapsed: 0.008 s
% 1.67/1.54 % (31738)Instructions burned: 18 (million)
% 1.67/1.54 % (31738)------------------------------
% 1.67/1.54 % (31738)------------------------------
% 1.67/1.55 % (31726)Instruction limit reached!
% 1.67/1.55 % (31726)------------------------------
% 1.67/1.55 % (31726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.55 % (31726)Termination reason: Unknown
% 1.67/1.55 % (31726)Termination phase: Saturation
% 1.67/1.55
% 1.67/1.55 % (31726)Memory used [KB]: 6268
% 1.67/1.55 % (31726)Time elapsed: 0.128 s
% 1.67/1.55 % (31726)Instructions burned: 378 (million)
% 1.67/1.55 % (31726)------------------------------
% 1.67/1.55 % (31726)------------------------------
% 1.67/1.55 % (31739)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_31371 for (2997ds/39Mi)
% 1.67/1.55 % (31737)Refutation not found, incomplete strategy
% 1.67/1.55 % (31737)------------------------------
% 1.67/1.55 % (31737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.55 % (31737)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.55
% 1.67/1.55
% 1.67/1.55 % (31737)Memory used [KB]: 5756
% 1.67/1.55 % (31737)Time elapsed: 0.022 s
% 1.67/1.55 % (31737)Instructions burned: 59 (million)
% 1.67/1.55 % (31737)------------------------------
% 1.67/1.55 % (31737)------------------------------
% 1.67/1.56 % (31740)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_31371 for (2997ds/448Mi)
% 1.67/1.56 % (31739)Instruction limit reached!
% 1.67/1.56 % (31739)------------------------------
% 1.67/1.56 % (31739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.56 % (31739)Termination reason: Unknown
% 1.67/1.56 % (31739)Termination phase: Saturation
% 1.67/1.56
% 1.67/1.56 % (31739)Memory used [KB]: 5884
% 1.67/1.56 % (31739)Time elapsed: 0.014 s
% 1.67/1.56 % (31739)Instructions burned: 41 (million)
% 1.67/1.56 % (31739)------------------------------
% 1.67/1.56 % (31739)------------------------------
% 1.67/1.56 % (31741)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_31371 for (2997ds/46Mi)
% 1.67/1.57 % (31742)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_31371 for (2997ds/98Mi)
% 1.67/1.58 % (31741)Instruction limit reached!
% 1.67/1.58 % (31741)------------------------------
% 1.67/1.58 % (31741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.58 % (31741)Termination reason: Unknown
% 1.67/1.58 % (31741)Termination phase: Saturation
% 1.67/1.58
% 1.67/1.58 % (31741)Memory used [KB]: 5756
% 1.67/1.58 % (31741)Time elapsed: 0.019 s
% 1.67/1.58 % (31741)Instructions burned: 48 (million)
% 1.67/1.58 % (31741)------------------------------
% 1.67/1.58 % (31741)------------------------------
% 1.67/1.59 % (31743)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_31371 for (2997ds/507Mi)
% 1.67/1.60 % (31720)Refutation not found, non-redundant clauses discarded% (31720)------------------------------
% 1.67/1.60 % (31720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.60 % (31720)Termination reason: Refutation not found, non-redundant clauses discarded
% 1.67/1.60
% 1.67/1.60 % (31720)Memory used [KB]: 6652
% 1.67/1.60 % (31720)Time elapsed: 0.227 s
% 1.67/1.60 % (31720)Instructions burned: 696 (million)
% 1.67/1.60 % (31720)------------------------------
% 1.67/1.60 % (31720)------------------------------
% 1.67/1.61 % (31742)Instruction limit reached!
% 1.67/1.61 % (31742)------------------------------
% 1.67/1.61 % (31742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.61 % (31742)Termination reason: Unknown
% 1.67/1.61 % (31742)Termination phase: Saturation
% 1.67/1.61
% 1.67/1.61 % (31742)Memory used [KB]: 1279
% 1.67/1.61 % (31742)Time elapsed: 0.034 s
% 1.67/1.61 % (31742)Instructions burned: 98 (million)
% 1.67/1.61 % (31742)------------------------------
% 1.67/1.61 % (31742)------------------------------
% 1.67/1.61 % (31744)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_31371 for (2996ds/149Mi)
% 1.67/1.62 % (31745)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_31371 for (2996ds/39Mi)
% 1.67/1.63 % (31745)Instruction limit reached!
% 1.67/1.63 % (31745)------------------------------
% 1.67/1.63 % (31745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.63 % (31745)Termination reason: Unknown
% 1.67/1.63 % (31745)Termination phase: Saturation
% 1.67/1.63
% 1.67/1.63 % (31745)Memory used [KB]: 5628
% 1.67/1.63 % (31745)Time elapsed: 0.015 s
% 1.67/1.63 % (31745)Instructions burned: 39 (million)
% 1.67/1.63 % (31745)------------------------------
% 1.67/1.63 % (31745)------------------------------
% 1.67/1.64 % (31746)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_31371 for (2996ds/6Mi)
% 1.67/1.64 % (31746)Instruction limit reached!
% 1.67/1.64 % (31746)------------------------------
% 1.67/1.64 % (31746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.64 % (31746)Termination reason: Unknown
% 1.67/1.64 % (31746)Termination phase: Saturation
% 1.67/1.64
% 1.67/1.64 % (31746)Memory used [KB]: 9978
% 1.67/1.64 % (31746)Time elapsed: 0.004 s
% 1.67/1.64 % (31746)Instructions burned: 6 (million)
% 1.67/1.64 % (31746)------------------------------
% 1.67/1.64 % (31746)------------------------------
% 1.67/1.64 % (31722)Instruction limit reached!
% 1.67/1.64 % (31722)------------------------------
% 1.67/1.64 % (31722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.64 % (31722)Termination reason: Unknown
% 1.67/1.64 % (31722)Termination phase: Saturation
% 1.67/1.64
% 1.67/1.64 % (31722)Memory used [KB]: 7036
% 1.67/1.64 % (31722)Time elapsed: 0.265 s
% 1.67/1.64 % (31722)Instructions burned: 905 (million)
% 1.67/1.64 % (31722)------------------------------
% 1.67/1.64 % (31722)------------------------------
% 1.67/1.65 % (31747)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_31371 for (2996ds/1087Mi)
% 1.67/1.65 % (31748)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_31371 for (2996ds/47Mi)
% 1.67/1.66 % (31744)Instruction limit reached!
% 1.67/1.66 % (31744)------------------------------
% 1.67/1.66 % (31744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.66 % (31744)Termination reason: Unknown
% 1.67/1.66 % (31744)Termination phase: Saturation
% 1.67/1.66
% 1.67/1.66 % (31744)Memory used [KB]: 6012
% 1.67/1.66 % (31744)Time elapsed: 0.049 s
% 1.67/1.66 % (31744)Instructions burned: 150 (million)
% 1.67/1.66 % (31744)------------------------------
% 1.67/1.66 % (31744)------------------------------
% 1.67/1.67 % (31748)Instruction limit reached!
% 1.67/1.67 % (31748)------------------------------
% 1.67/1.67 % (31748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.67 % (31748)Termination reason: Unknown
% 1.67/1.67 % (31748)Termination phase: Saturation
% 1.67/1.67
% 1.67/1.67 % (31748)Memory used [KB]: 5628
% 1.67/1.67 % (31748)Time elapsed: 0.016 s
% 1.67/1.67 % (31748)Instructions burned: 48 (million)
% 1.67/1.67 % (31748)------------------------------
% 1.67/1.67 % (31748)------------------------------
% 1.67/1.67 % (31749)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_31371 for (2996ds/44Mi)
% 1.67/1.68 % (31750)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_31371 for (2996ds/432Mi)
% 1.67/1.68 % (31749)Refutation not found, incomplete strategy
% 1.67/1.68 % (31749)------------------------------
% 1.67/1.68 % (31749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.68 % (31749)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.68
% 1.67/1.68
% 1.67/1.68 % (31749)Memory used [KB]: 1151
% 1.67/1.68 % (31749)Time elapsed: 0.014 s
% 1.67/1.68 % (31749)Instructions burned: 38 (million)
% 1.67/1.68 % (31749)------------------------------
% 1.67/1.68 % (31749)------------------------------
% 1.67/1.69 % (31751)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_31371 for (2996ds/62Mi)
% 1.67/1.71 % (31740)Instruction limit reached!
% 1.67/1.71 % (31740)------------------------------
% 1.67/1.71 % (31740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.71 % (31740)Termination reason: Unknown
% 1.67/1.71 % (31740)Termination phase: Saturation
% 1.67/1.71
% 1.67/1.71 % (31740)Memory used [KB]: 6140
% 1.67/1.71 % (31740)Time elapsed: 0.151 s
% 1.67/1.71 % (31740)Instructions burned: 448 (million)
% 1.67/1.71 % (31740)------------------------------
% 1.67/1.71 % (31740)------------------------------
% 1.67/1.71 % (31751)Instruction limit reached!
% 1.67/1.71 % (31751)------------------------------
% 1.67/1.71 % (31751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.71 % (31751)Termination reason: Unknown
% 1.67/1.71 % (31751)Termination phase: Saturation
% 1.67/1.71
% 1.67/1.71 % (31751)Memory used [KB]: 5884
% 1.67/1.71 % (31751)Time elapsed: 0.021 s
% 1.67/1.71 % (31751)Instructions burned: 63 (million)
% 1.67/1.71 % (31751)------------------------------
% 1.67/1.71 % (31751)------------------------------
% 1.67/1.72 % (31752)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_31371 for (2996ds/31Mi)
% 1.67/1.72 % (31711)Instruction limit reached!
% 1.67/1.72 % (31711)------------------------------
% 1.67/1.72 % (31711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.72 % (31711)Termination reason: Unknown
% 1.67/1.72 % (31711)Termination phase: Saturation
% 1.67/1.72
% 1.67/1.72 % (31711)Memory used [KB]: 6908
% 1.67/1.72 % (31711)Time elapsed: 0.372 s
% 1.67/1.72 % (31711)Instructions burned: 1041 (million)
% 1.67/1.72 % (31711)------------------------------
% 1.67/1.72 % (31711)------------------------------
% 1.67/1.72 % (31753)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_31371 for (2995ds/96Mi)
% 1.67/1.73 % (31752)Instruction limit reached!
% 1.67/1.73 % (31752)------------------------------
% 1.67/1.73 % (31752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.73 % (31752)Termination reason: Unknown
% 1.67/1.73 % (31752)Termination phase: Saturation
% 1.67/1.73
% 1.67/1.73 % (31752)Memory used [KB]: 5628
% 1.67/1.73 % (31752)Time elapsed: 0.013 s
% 1.67/1.73 % (31752)Instructions burned: 32 (million)
% 1.67/1.73 % (31752)------------------------------
% 1.67/1.73 % (31752)------------------------------
% 1.67/1.73 % (31754)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_31371 for (2995ds/453Mi)
% 1.67/1.73 % (31729)Refutation not found, non-redundant clauses discarded% (31729)------------------------------
% 1.67/1.73 % (31729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.73 % (31729)Termination reason: Refutation not found, non-redundant clauses discarded
% 1.67/1.73
% 1.67/1.73 % (31729)Memory used [KB]: 6908
% 1.67/1.73 % (31729)Time elapsed: 0.282 s
% 1.67/1.73 % (31729)Instructions burned: 859 (million)
% 1.67/1.73 % (31729)------------------------------
% 1.67/1.73 % (31729)------------------------------
% 1.67/1.74 % (31755)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_31371 for (2995ds/71Mi)
% 1.67/1.74 % (31756)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_31371 for (2995ds/83Mi)
% 1.67/1.75 % (31754)Refutation not found, incomplete strategy
% 1.67/1.75 % (31754)------------------------------
% 1.67/1.75 % (31754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.75 % (31754)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.75
% 1.67/1.75
% 1.67/1.75 % (31754)Memory used [KB]: 5628
% 1.67/1.75 % (31754)Time elapsed: 0.021 s
% 1.67/1.75 % (31754)Instructions burned: 57 (million)
% 1.67/1.75 % (31754)------------------------------
% 1.67/1.75 % (31754)------------------------------
% 1.67/1.75 % (31750)First to succeed.
% 1.67/1.75 % (31753)Instruction limit reached!
% 1.67/1.75 % (31753)------------------------------
% 1.67/1.75 % (31753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.75 % (31753)Termination reason: Unknown
% 1.67/1.75 % (31753)Termination phase: Saturation
% 1.67/1.75
% 1.67/1.75 % (31753)Memory used [KB]: 5628
% 1.67/1.75 % (31753)Time elapsed: 0.033 s
% 1.67/1.75 % (31753)Instructions burned: 96 (million)
% 1.67/1.75 % (31753)------------------------------
% 1.67/1.75 % (31753)------------------------------
% 1.67/1.76 % (31750)Refutation found. Thanks to Tanya!
% 1.67/1.76 % SZS status Theorem for DTF2THF_31371
% 1.67/1.76 % SZS output start Proof for DTF2THF_31371
% 1.67/1.76 thf(type_def_5, type, a: $tType).
% 1.67/1.76 thf(func_def_0, type, a: $tType).
% 1.67/1.76 thf(func_def_1, type, cR: a > a).
% 1.67/1.76 thf(func_def_2, type, cP: a > a > a).
% 1.67/1.76 thf(func_def_3, type, cL: a > a).
% 1.67/1.76 thf(func_def_4, type, cZ: a).
% 1.67/1.76 thf(func_def_19, type, ph0: !>[X0: $tType]:(X0)).
% 1.67/1.76 thf(func_def_20, type, sK1: a).
% 1.67/1.76 thf(func_def_25, type, sK2: a).
% 1.67/1.76 thf(func_def_26, type, sK3: a).
% 1.67/1.76 thf(func_def_27, type, sK4: a).
% 1.67/1.76 thf(func_def_28, type, sK5: a).
% 1.67/1.76 thf(func_def_29, type, sK6: a).
% 1.67/1.76 thf(func_def_30, type, sK7: a).
% 1.67/1.76 thf(func_def_31, type, sK8: (a > a > a) > a).
% 1.67/1.76 thf(func_def_32, type, sK9: (a > a > a) > a).
% 1.67/1.76 thf(func_def_33, type, sK10: (a > $o) > a).
% 1.67/1.76 thf(func_def_34, type, sK11: a).
% 1.67/1.76 thf(f459,plain,(
% 1.67/1.76 $false),
% 1.67/1.76 inference(subsumption_resolution,[status(thm)],[f435,f267])).
% 1.67/1.76 thf(f267,plain,(
% 1.67/1.76 (cZ != (cL @ cZ))),
% 1.67/1.76 inference(equality_proxy_clausification,[status(thm)],[f176])).
% 1.67/1.76 thf(f176,plain,(
% 1.67/1.76 (((cL @ cZ) = cZ) = $false)),
% 1.67/1.76 inference(boolean_simplification,[status(thm)],[f175])).
% 1.67/1.76 thf(f175,plain,(
% 1.67/1.76 ($false = ($true & ((cL @ cZ) = cZ)))),
% 1.67/1.76 inference(boolean_simplification,[status(thm)],[f174])).
% 1.67/1.76 thf(f174,plain,(
% 1.67/1.76 ($false = ((cZ = cZ) & ((cL @ cZ) = cZ)))),
% 1.67/1.76 inference(forward_demodulation,[status(thm)],[f173,f71])).
% 1.67/1.76 thf(f71,plain,(
% 1.67/1.76 (cZ = (cR @ cZ))),
% 1.67/1.76 inference(equality_proxy_clausification,[status(thm)],[f57])).
% 1.67/1.76 thf(f57,plain,(
% 1.67/1.76 ((cZ = (cR @ cZ)) = $true)),
% 1.67/1.76 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.67/1.76 thf(f23,plain,(
% 1.67/1.76 ((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((cR @ (cP @ Y1 @ Y0)) = Y0))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ (cP @ Y1 @ Y2)) => (((Y0 @ (cP @ (cL @ Y1) @ (cL @ Y2))) & ((cZ = Y1) = (cZ = Y2))) & (Y0 @ (cP @ (cR @ Y1) @ (cR @ Y2))))))))) => (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ (cP @ Y2 @ Y1)) => (Y2 = Y1)))))))))) & (cZ = (cL @ cZ))) & (!! @ a @ (^[Y0 : a]: ((~ (cZ = Y0)) = ((cP @ (cL @ Y0) @ (cR @ Y0)) = Y0))))) & (cZ = (cR @ cZ))) = $true)),
% 1.67/1.76 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.67/1.76 thf(f9,plain,(
% 1.67/1.76 (((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((cR @ (cP @ Y1 @ Y0)) = Y0))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ (cP @ Y1 @ Y2)) => (((Y0 @ (cP @ (cL @ Y1) @ (cL @ Y2))) & ((cZ = Y1) = (cZ = Y2))) & (Y0 @ (cP @ (cR @ Y1) @ (cR @ Y2))))))))) => (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ (cP @ Y2 @ Y1)) => (Y2 = Y1)))))))))) & (cZ = (cL @ cZ))) & (!! @ a @ (^[Y0 : a]: ((~ (cZ = Y0)) = ((cP @ (cL @ Y0) @ (cR @ Y0)) = Y0))))) & (cZ = (cR @ cZ))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((cL @ (cP @ Y1 @ Y0)) = Y1)))))) = $true)),
% 1.67/1.76 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.67/1.76 thf(f7,plain,(
% 1.67/1.76 ((((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((cR @ (cP @ Y1 @ Y0)) = Y0))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ (cP @ Y1 @ Y2)) => (((Y0 @ (cP @ (cL @ Y1) @ (cL @ Y2))) & ((cZ = Y1) = (cZ = Y2))) & (Y0 @ (cP @ (cR @ Y1) @ (cR @ Y2))))))))) => (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ (cP @ Y2 @ Y1)) => (Y2 = Y1)))))))))) & (cZ = (cL @ cZ))) & (!! @ a @ (^[Y0 : a]: ((~ (cZ = Y0)) = ((cP @ (cL @ Y0) @ (cR @ Y0)) = Y0))))) & (cZ = (cR @ cZ))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((cL @ (cP @ Y1 @ Y0)) = Y1)))))) => (!! @ a @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ (cP @ Y3 @ Y2)) => (((Y1 @ (cP @ (cR @ Y3) @ (cR @ Y2))) & ((cZ = Y2) => (cZ = Y3))) & (Y1 @ (cP @ (cL @ Y3) @ (cL @ Y2))))))))) & (Y1 @ (cP @ cZ @ Y0)))))))) = $false)),
% 1.67/1.76 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.67/1.76 thf(f6,plain,(
% 1.67/1.76 ((~ (((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((cR @ (cP @ Y1 @ Y0)) = Y0))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ (cP @ Y1 @ Y2)) => (((Y0 @ (cP @ (cL @ Y1) @ (cL @ Y2))) & ((cZ = Y1) = (cZ = Y2))) & (Y0 @ (cP @ (cR @ Y1) @ (cR @ Y2))))))))) => (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ (cP @ Y2 @ Y1)) => (Y2 = Y1)))))))))) & (cZ = (cL @ cZ))) & (!! @ a @ (^[Y0 : a]: ((~ (cZ = Y0)) = ((cP @ (cL @ Y0) @ (cR @ Y0)) = Y0))))) & (cZ = (cR @ cZ))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((cL @ (cP @ Y1 @ Y0)) = Y1)))))) => (!! @ a @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ (cP @ Y3 @ Y2)) => (((Y1 @ (cP @ (cR @ Y3) @ (cR @ Y2))) & ((cZ = Y2) => (cZ = Y3))) & (Y1 @ (cP @ (cL @ Y3) @ (cL @ Y2))))))))) & (Y1 @ (cP @ cZ @ Y0))))))))) = $true)),
% 1.67/1.76 inference(cnf_transformation,[status(thm)],[f5])).
% 1.67/1.76 thf(f5,plain,(
% 1.67/1.76 ((~ (((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((cR @ (cP @ Y1 @ Y0)) = Y0))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ (cP @ Y1 @ Y2)) => (((Y0 @ (cP @ (cL @ Y1) @ (cL @ Y2))) & ((cZ = Y1) = (cZ = Y2))) & (Y0 @ (cP @ (cR @ Y1) @ (cR @ Y2))))))))) => (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ (cP @ Y2 @ Y1)) => (Y2 = Y1)))))))))) & (cZ = (cL @ cZ))) & (!! @ a @ (^[Y0 : a]: ((~ (cZ = Y0)) = ((cP @ (cL @ Y0) @ (cR @ Y0)) = Y0))))) & (cZ = (cR @ cZ))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((cL @ (cP @ Y1 @ Y0)) = Y1)))))) => (!! @ a @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ (cP @ Y3 @ Y2)) => (((Y1 @ (cP @ (cR @ Y3) @ (cR @ Y2))) & ((cZ = Y2) => (cZ = Y3))) & (Y1 @ (cP @ (cL @ Y3) @ (cL @ Y2))))))))) & (Y1 @ (cP @ cZ @ Y0))))))))) = $true)),
% 1.67/1.76 inference(fool_elimination,[status(thm)],[f4])).
% 1.67/1.76 thf(f4,plain,(
% 1.67/1.76 ~((! [X0 : a,X1 : a] : ((cL @ (cP @ X0 @ X1)) = X0) & (cZ = (cR @ cZ)) & ! [X2 : a] : ((cZ != X2) <=> ((cP @ (cL @ X2) @ (cR @ X2)) = X2)) & (cZ = (cL @ cZ)) & ! [X3 : a > $o] : (! [X4 : a,X5 : a] : ((X3 @ (cP @ X5 @ X4)) => ((X3 @ (cP @ (cR @ X5) @ (cR @ X4))) & ((cZ = X5) <=> (cZ = X4)) & (X3 @ (cP @ (cL @ X5) @ (cL @ X4))))) => ! [X6 : a,X7 : a] : ((X3 @ (cP @ X6 @ X7)) => (X6 = X7))) & ! [X8 : a,X9 : a] : ((cR @ (cP @ X8 @ X9)) = X9)) => ! [X10 : a] : ? [X11 : a > $o] : ((X11 @ (cP @ cZ @ X10)) & ! [X12 : a,X13 : a] : ((X11 @ (cP @ X12 @ X13)) => ((X11 @ (cP @ (cL @ X12) @ (cL @ X13))) & ((cZ = X13) => (cZ = X12)) & (X11 @ (cP @ (cR @ X12) @ (cR @ X13)))))))),
% 1.67/1.76 inference(rectify,[status(thm)],[f2])).
% 1.67/1.76 thf(f2,negated_conjecture,(
% 1.67/1.76 ~((! [X0 : a,X1 : a] : ((cL @ (cP @ X0 @ X1)) = X0) & (cZ = (cR @ cZ)) & ! [X2 : a] : ((cZ != X2) <=> ((cP @ (cL @ X2) @ (cR @ X2)) = X2)) & (cZ = (cL @ cZ)) & ! [X3 : a > $o] : (! [X4 : a,X2 : a] : ((X3 @ (cP @ X2 @ X4)) => ((X3 @ (cP @ (cR @ X2) @ (cR @ X4))) & ((cZ = X2) <=> (cZ = X4)) & (X3 @ (cP @ (cL @ X2) @ (cL @ X4))))) => ! [X2 : a,X4 : a] : ((X3 @ (cP @ X2 @ X4)) => (X2 = X4))) & ! [X0 : a,X1 : a] : ((cR @ (cP @ X0 @ X1)) = X1)) => ! [X2 : a] : ? [X3 : a > $o] : ((X3 @ (cP @ cZ @ X2)) & ! [X5 : a,X4 : a] : ((X3 @ (cP @ X5 @ X4)) => ((X3 @ (cP @ (cL @ X5) @ (cL @ X4))) & ((cZ = X4) => (cZ = X5)) & (X3 @ (cP @ (cR @ X5) @ (cR @ X4)))))))),
% 1.67/1.76 inference(negated_conjecture,[status(cth)],[f1])).
% 1.67/1.76 thf(f1,conjecture,(
% 1.67/1.76 (! [X0 : a,X1 : a] : ((cL @ (cP @ X0 @ X1)) = X0) & (cZ = (cR @ cZ)) & ! [X2 : a] : ((cZ != X2) <=> ((cP @ (cL @ X2) @ (cR @ X2)) = X2)) & (cZ = (cL @ cZ)) & ! [X3 : a > $o] : (! [X4 : a,X2 : a] : ((X3 @ (cP @ X2 @ X4)) => ((X3 @ (cP @ (cR @ X2) @ (cR @ X4))) & ((cZ = X2) <=> (cZ = X4)) & (X3 @ (cP @ (cL @ X2) @ (cL @ X4))))) => ! [X2 : a,X4 : a] : ((X3 @ (cP @ X2 @ X4)) => (X2 = X4))) & ! [X0 : a,X1 : a] : ((cR @ (cP @ X0 @ X1)) = X1)) => ! [X2 : a] : ? [X3 : a > $o] : ((X3 @ (cP @ cZ @ X2)) & ! [X5 : a,X4 : a] : ((X3 @ (cP @ X5 @ X4)) => ((X3 @ (cP @ (cL @ X5) @ (cL @ X4))) & ((cZ = X4) => (cZ = X5)) & (X3 @ (cP @ (cR @ X5) @ (cR @ X4))))))),
% 1.67/1.76 file('/export/starexec/sandbox/tmp/tmp.OaApnq3MkH/DTF2THF_31371.p',cPU_LEM2E_pme)).
% 1.67/1.76 thf(f173,plain,(
% 1.67/1.76 ($false = (((cR @ cZ) = cZ) & ((cL @ cZ) = cZ)))),
% 1.67/1.76 inference(boolean_simplification,[status(thm)],[f172])).
% 1.67/1.76 thf(f172,plain,(
% 1.67/1.76 ($false = ((((cR @ cZ) = cZ) & $true) & ((cL @ cZ) = cZ)))),
% 1.67/1.76 inference(boolean_simplification,[status(thm)],[f171])).
% 1.67/1.76 thf(f171,plain,(
% 1.67/1.76 ($false = ((((cR @ cZ) = cZ) & ((cZ = sK3) => $true)) & ((cL @ cZ) = cZ)))),
% 1.67/1.76 inference(boolean_simplification,[status(thm)],[f170])).
% 1.67/1.76 thf(f170,plain,(
% 1.67/1.76 ($false = ($true => ((((cR @ cZ) = cZ) & ((cZ = sK3) => $true)) & ((cL @ cZ) = cZ))))),
% 1.67/1.76 inference(boolean_simplification,[status(thm)],[f168])).
% 1.67/1.76 thf(f168,plain,(
% 1.67/1.76 (((cZ = cZ) => ((((cR @ cZ) = cZ) & ((cZ = sK3) => (cZ = cZ))) & ((cL @ cZ) = cZ))) = $false)),
% 1.67/1.76 inference(superposition,[status(thm)],[f144,f152])).
% 1.67/1.76 thf(f152,plain,(
% 1.67/1.76 (cZ = sK5)),
% 1.67/1.76 inference(equality_proxy_clausification,[status(thm)],[f151])).
% 1.67/1.76 thf(f151,plain,(
% 1.67/1.76 ((sK5 = cZ) = $true)),
% 1.67/1.76 inference(binary_proxy_clausification,[status(thm)],[f144])).
% 1.67/1.76 thf(f144,plain,(
% 1.67/1.76 (((sK5 = cZ) => ((((cR @ sK5) = cZ) & ((cZ = sK3) => (cZ = sK5))) & ((cL @ sK5) = cZ))) = $false)),
% 1.67/1.76 inference(forward_demodulation,[status(thm)],[f143,f51])).
% 1.67/1.76 thf(f51,plain,(
% 1.67/1.76 ( ! [X2 : a,X1 : a] : (((cL @ (cP @ X2 @ X1)) = X2)) )),
% 1.67/1.76 inference(equality_proxy_clausification,[status(thm)],[f50])).
% 1.67/1.76 thf(f50,plain,(
% 1.67/1.76 ( ! [X2 : a,X1 : a] : ((((cL @ (cP @ X2 @ X1)) = X2) = $true)) )),
% 1.67/1.76 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.67/1.76 thf(f46,plain,(
% 1.67/1.76 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: ((cL @ (cP @ Y0 @ X1)) = Y0)) @ X2) = $true)) )),
% 1.67/1.76 inference(pi_clausification,[status(thm)],[f36])).
% 1.67/1.76 thf(f36,plain,(
% 1.67/1.76 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: ((cL @ (cP @ Y0 @ X1)) = Y0))) = $true)) )),
% 1.67/1.76 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.67/1.76 thf(f30,plain,(
% 1.67/1.76 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((cL @ (cP @ Y1 @ Y0)) = Y1)))) @ X1) = $true)) )),
% 1.67/1.76 inference(pi_clausification,[status(thm)],[f22])).
% 1.67/1.76 thf(f22,plain,(
% 1.67/1.76 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((cL @ (cP @ Y1 @ Y0)) = Y1))))) = $true)),
% 1.67/1.76 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.67/1.76 thf(f143,plain,(
% 1.67/1.76 (((sK5 = cZ) => ((((cR @ sK5) = cZ) & ((cZ = sK3) => (cZ = sK5))) & ((cL @ (cP @ (cL @ sK5) @ (cL @ sK3))) = cZ))) = $false)),
% 1.67/1.76 inference(forward_demodulation,[status(thm)],[f142,f51])).
% 1.67/1.76 thf(f142,plain,(
% 1.67/1.76 ($false = ((sK5 = cZ) => ((((cL @ (cP @ (cR @ sK5) @ (cR @ sK3))) = cZ) & ((cZ = sK3) => (cZ = sK5))) & ((cL @ (cP @ (cL @ sK5) @ (cL @ sK3))) = cZ))))),
% 1.67/1.76 inference(forward_demodulation,[status(thm)],[f141,f51])).
% 1.67/1.76 thf(f141,plain,(
% 1.67/1.76 ((((cL @ (cP @ sK5 @ sK3)) = cZ) => ((((cL @ (cP @ (cR @ sK5) @ (cR @ sK3))) = cZ) & ((cZ = sK3) => (cZ = sK5))) & ((cL @ (cP @ (cL @ sK5) @ (cL @ sK3))) = cZ))) = $false)),
% 1.67/1.76 inference(beta_eta_normalization,[status(thm)],[f140])).
% 1.67/1.76 thf(f140,plain,(
% 1.67/1.76 ($false = ((^[Y0 : a]: (((cL @ (cP @ Y0 @ sK3)) = cZ) => ((((cL @ (cP @ (cR @ Y0) @ (cR @ sK3))) = cZ) & ((cZ = sK3) => (cZ = Y0))) & ((cL @ (cP @ (cL @ Y0) @ (cL @ sK3))) = cZ)))) @ sK5))),
% 1.67/1.76 inference(sigma_clausification,[status(thm)],[f132])).
% 1.67/1.76 thf(f132,plain,(
% 1.67/1.76 ((!! @ a @ (^[Y0 : a]: (((cL @ (cP @ Y0 @ sK3)) = cZ) => ((((cL @ (cP @ (cR @ Y0) @ (cR @ sK3))) = cZ) & ((cZ = sK3) => (cZ = Y0))) & ((cL @ (cP @ (cL @ Y0) @ (cL @ sK3))) = cZ))))) = $false)),
% 1.67/1.76 inference(beta_eta_normalization,[status(thm)],[f130])).
% 1.67/1.76 thf(f130,plain,(
% 1.67/1.76 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((cL @ (cP @ Y1 @ Y0)) = cZ) => ((((cL @ (cP @ (cR @ Y1) @ (cR @ Y0))) = cZ) & ((cZ = Y0) => (cZ = Y1))) & ((cL @ (cP @ (cL @ Y1) @ (cL @ Y0))) = cZ)))))) @ sK3))),
% 1.67/1.76 inference(sigma_clausification,[status(thm)],[f54])).
% 1.67/1.76 thf(f54,plain,(
% 1.67/1.76 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((cL @ (cP @ Y1 @ Y0)) = cZ) => ((((cL @ (cP @ (cR @ Y1) @ (cR @ Y0))) = cZ) & ((cZ = Y0) => (cZ = Y1))) & ((cL @ (cP @ (cL @ Y1) @ (cL @ Y0))) = cZ))))))))),
% 1.67/1.76 inference(boolean_simplification,[status(thm)],[f53])).
% 1.67/1.76 thf(f53,plain,(
% 1.67/1.76 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((cL @ (cP @ Y1 @ Y0)) = cZ) => ((((cL @ (cP @ (cR @ Y1) @ (cR @ Y0))) = cZ) & ((cZ = Y0) => (cZ = Y1))) & ((cL @ (cP @ (cL @ Y1) @ (cL @ Y0))) = cZ))))))) & $true))),
% 1.67/1.76 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.67/1.76 thf(f52,plain,(
% 1.67/1.76 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((^[Y2 : a]: (((^[Y3 : a]: (cL @ ((^[Y4 : a]: (Y4)) @ Y3))) @ Y2) = ((^[Y3 : a]: (cZ)) @ Y2))) @ (cP @ Y1 @ Y0)) => ((((^[Y2 : a]: (((^[Y3 : a]: (cL @ ((^[Y4 : a]: (Y4)) @ Y3))) @ Y2) = ((^[Y3 : a]: (cZ)) @ Y2))) @ (cP @ (cR @ Y1) @ (cR @ Y0))) & ((cZ = Y0) => (cZ = Y1))) & ((^[Y2 : a]: (((^[Y3 : a]: (cL @ ((^[Y4 : a]: (Y4)) @ Y3))) @ Y2) = ((^[Y3 : a]: (cZ)) @ Y2))) @ (cP @ (cL @ Y1) @ (cL @ Y0))))))))) & $true))),
% 1.67/1.76 inference(superposition,[status(thm)],[f20,f50])).
% 1.67/1.76 thf(f20,plain,(
% 1.67/1.76 ( ! [X1 : a > $o] : ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((X1 @ (cP @ Y1 @ Y0)) => (((X1 @ (cP @ (cR @ Y1) @ (cR @ Y0))) & ((cZ = Y0) => (cZ = Y1))) & (X1 @ (cP @ (cL @ Y1) @ (cL @ Y0))))))))) & (X1 @ (cP @ cZ @ sK1))) = $false)) )),
% 1.67/1.76 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.67/1.76 thf(f19,plain,(
% 1.67/1.76 ( ! [X1 : a > $o] : (($false = ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ (cP @ Y2 @ Y1)) => (((Y0 @ (cP @ (cR @ Y2) @ (cR @ Y1))) & ((cZ = Y1) => (cZ = Y2))) & (Y0 @ (cP @ (cL @ Y2) @ (cL @ Y1))))))))) & (Y0 @ (cP @ cZ @ sK1)))) @ X1))) )),
% 1.67/1.76 inference(pi_clausification,[status(thm)],[f15])).
% 1.67/1.76 thf(f15,plain,(
% 1.67/1.76 ((?? @ (a > $o) @ (^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ (cP @ Y2 @ Y1)) => (((Y0 @ (cP @ (cR @ Y2) @ (cR @ Y1))) & ((cZ = Y1) => (cZ = Y2))) & (Y0 @ (cP @ (cL @ Y2) @ (cL @ Y1))))))))) & (Y0 @ (cP @ cZ @ sK1))))) = $false)),
% 1.67/1.76 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.67/1.76 thf(f12,plain,(
% 1.67/1.76 ($false = ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ (cP @ Y3 @ Y2)) => (((Y1 @ (cP @ (cR @ Y3) @ (cR @ Y2))) & ((cZ = Y2) => (cZ = Y3))) & (Y1 @ (cP @ (cL @ Y3) @ (cL @ Y2))))))))) & (Y1 @ (cP @ cZ @ Y0)))))) @ sK1))),
% 1.67/1.76 inference(sigma_clausification,[status(thm)],[f8])).
% 1.67/1.76 thf(f8,plain,(
% 1.67/1.76 ($false = (!! @ a @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ (cP @ Y3 @ Y2)) => (((Y1 @ (cP @ (cR @ Y3) @ (cR @ Y2))) & ((cZ = Y2) => (cZ = Y3))) & (Y1 @ (cP @ (cL @ Y3) @ (cL @ Y2))))))))) & (Y1 @ (cP @ cZ @ Y0))))))))),
% 1.67/1.76 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.67/1.76 thf(f435,plain,(
% 1.67/1.76 (cZ = (cL @ cZ))),
% 1.67/1.76 inference(equality_proxy_clausification,[status(thm)],[f403])).
% 1.67/1.76 thf(f403,plain,(
% 1.67/1.76 ((cZ = (cL @ cZ)) = $true)),
% 1.67/1.76 inference(binary_proxy_clausification,[status(thm)],[f228])).
% 1.67/1.76 thf(f228,plain,(
% 1.67/1.76 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((cR @ (cP @ Y1 @ Y0)) = Y0))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ (cP @ Y1 @ Y2)) => (((Y0 @ (cP @ (cL @ Y1) @ (cL @ Y2))) & ((cZ = Y1) = (cZ = Y2))) & (Y0 @ (cP @ (cR @ Y1) @ (cR @ Y2))))))))) => (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ (cP @ Y2 @ Y1)) => (Y2 = Y1)))))))))) & (cZ = (cL @ cZ))) = $true)),
% 1.67/1.76 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.67/1.76 thf(f58,plain,(
% 1.67/1.76 (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((cR @ (cP @ Y1 @ Y0)) = Y0))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ (cP @ Y1 @ Y2)) => (((Y0 @ (cP @ (cL @ Y1) @ (cL @ Y2))) & ((cZ = Y1) = (cZ = Y2))) & (Y0 @ (cP @ (cR @ Y1) @ (cR @ Y2))))))))) => (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ (cP @ Y2 @ Y1)) => (Y2 = Y1)))))))))) & (cZ = (cL @ cZ))) & (!! @ a @ (^[Y0 : a]: ((~ (cZ = Y0)) = ((cP @ (cL @ Y0) @ (cR @ Y0)) = Y0))))) = $true)),
% 1.67/1.76 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.67/1.76 % SZS output end Proof for DTF2THF_31371
% 1.67/1.76 % (31750)------------------------------
% 1.67/1.76 % (31750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.76 % (31750)Termination reason: Refutation
% 1.67/1.76
% 1.67/1.76 % (31750)Memory used [KB]: 2302
% 1.67/1.76 % (31750)Time elapsed: 0.077 s
% 1.67/1.76 % (31750)Instructions burned: 251 (million)
% 1.67/1.76 % (31750)------------------------------
% 1.67/1.76 % (31750)------------------------------
% 1.67/1.76 % (31699)Success in time 0.444 s
%------------------------------------------------------------------------------