%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PHI004^4 : TPTP v9.2.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n024.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 09:27:39 AM UTC 2026
% Result : Theorem 1.27s 1.13s
% Output : Refutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 5
% Syntax : Number of formulae : 70 ( 63 unt; 0 typ; 0 def)
% Number of atoms : 369 ( 62 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 942 ( 46 ~; 13 |; 13 &; 652 @)
% ( 0 <=>; 102 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 280 ( 280 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 11 con; 0-3 aty)
% ( 116 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 216 ( 175 ^; 41 !; 0 ?; 216 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
qML_mu: $tType ).
thf(type_def_6,type,
qML_i: $tType ).
thf(func_def_0,type,
qML_mu: $tType ).
thf(func_def_1,type,
qML_i: $tType ).
thf(func_def_2,type,
scott_G: qML_mu > qML_i > $o ).
thf(func_def_3,type,
scott_NE_QML_mu: qML_mu > qML_i > $o ).
thf(func_def_4,type,
scott_P: ( qML_mu > qML_i > $o ) > qML_i > $o ).
thf(func_def_5,type,
scott_ess_QML_mu: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > $o ).
thf(func_def_23,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
sK2: qML_i > qML_mu ).
thf(func_def_25,type,
sK3: qML_mu ).
thf(func_def_26,type,
sK4: qML_i ).
thf(func_def_27,type,
sK5: qML_i ).
thf(func_def_28,type,
sK6: qML_mu ).
thf(func_def_29,type,
sK7: qML_mu > qML_i > $o ).
thf(func_def_30,type,
sK8: qML_i ).
thf(func_def_31,type,
sK9: qML_mu ).
thf(func_def_32,type,
sK10: qML_mu ).
thf(func_def_33,type,
sK11: qML_i ).
thf(f549,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f548]) ).
thf(f548,plain,
$true = $false,
inference(boolean_simplification,[status(thm)],[f547]) ).
thf(f547,plain,
( $true = ( ~ $true ) ),
inference(forward_demodulation,[status(thm)],[f542,f241]) ).
thf(f241,plain,
( $true
= ( sK7 @ sK6 @ sK5 ) ),
inference(binary_proxy_clausification,[status(thm)],[f239]) ).
thf(f239,plain,
( ( ( sK7 @ sK6 @ sK5 )
=> ( !! @ qML_i
@ ^ [Y0: qML_i] :
( !! @ qML_mu
@ ^ [Y1: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f238]) ).
thf(f238,plain,
( $false
= ( ^ [Y0: qML_mu > qML_i > $o] :
( ( Y0 @ sK6 @ sK5 )
=> ( !! @ qML_i
@ ^ [Y1: qML_i] :
( !! @ qML_mu
@ ^ [Y2: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y3: qML_mu > qML_i > $o] :
( ( scott_P @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK7 ) ),
inference(sigma_clausification,[status(thm)],[f209]) ).
thf(f209,plain,
( $false
= ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( Y0 @ sK6 @ sK5 )
=> ( !! @ qML_i
@ ^ [Y1: qML_i] :
( !! @ qML_mu
@ ^ [Y2: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y3: qML_mu > qML_i > $o] :
( ( scott_P @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f207]) ).
thf(f207,plain,
( ( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( Y0 @ sK6 @ sK5 )
=> ( !! @ qML_i
@ ^ [Y1: qML_i] :
( !! @ qML_mu
@ ^ [Y2: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y3: qML_mu > qML_i > $o] :
( ( scott_P @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& $true )
= $false ),
inference(backward_demodulation,[status(thm)],[f191,f205]) ).
thf(f205,plain,
( $true
= ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK5 )
=> ( Y0 @ sK6 @ sK5 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f194]) ).
thf(f194,plain,
( ( ~ ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK5 )
=> ( Y0 @ sK6 @ sK5 ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f193]) ).
thf(f193,plain,
( $false
= ( ~ ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK5 )
=> ( Y0 @ sK6 @ sK5 ) ) )
| $false ) ),
inference(backward_demodulation,[status(thm)],[f188,f191]) ).
thf(f188,plain,
( $false
= ( ~ ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK5 )
=> ( Y0 @ sK6 @ sK5 ) ) )
| ( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( Y0 @ sK6 @ sK5 )
=> ( !! @ qML_i
@ ^ [Y1: qML_i] :
( !! @ qML_mu
@ ^ [Y2: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y3: qML_mu > qML_i > $o] :
( ( scott_P @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK5 )
=> ( Y0 @ sK6 @ sK5 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f187]) ).
thf(f187,plain,
( $false
= ( ^ [Y0: qML_mu] :
( ~ ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ sK5 )
=> ( Y1 @ Y0 @ sK5 ) ) )
| ( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( Y1 @ Y0 @ sK5 )
=> ( !! @ qML_i
@ ^ [Y2: qML_i] :
( !! @ qML_mu
@ ^ [Y3: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y4: qML_mu > qML_i > $o] :
( ( scott_P @ Y4 @ Y2 )
=> ( Y4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ sK5 )
=> ( Y1 @ Y0 @ sK5 ) ) ) ) )
@ sK6 ) ),
inference(sigma_clausification,[status(thm)],[f183]) ).
thf(f183,plain,
( $false
= ( !! @ qML_mu
@ ^ [Y0: qML_mu] :
( ~ ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ sK5 )
=> ( Y1 @ Y0 @ sK5 ) ) )
| ( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( Y1 @ Y0 @ sK5 )
=> ( !! @ qML_i
@ ^ [Y2: qML_i] :
( !! @ qML_mu
@ ^ [Y3: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y4: qML_mu > qML_i > $o] :
( ( scott_P @ Y4 @ Y2 )
=> ( Y4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ sK5 )
=> ( Y1 @ Y0 @ sK5 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f182]) ).
thf(f182,plain,
( $false
= ( ^ [Y0: qML_i] :
( !! @ qML_mu
@ ^ [Y1: qML_mu] :
( ~ ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( Y2 @ Y1 @ Y0 )
=> ( !! @ qML_i
@ ^ [Y3: qML_i] :
( !! @ qML_mu
@ ^ [Y4: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y5: qML_mu > qML_i > $o] :
( ( scott_P @ Y5 @ Y3 )
=> ( Y5 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
& ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
@ sK5 ) ),
inference(sigma_clausification,[status(thm)],[f177]) ).
thf(f177,plain,
( $false
= ( !! @ qML_i
@ ^ [Y0: qML_i] :
( !! @ qML_mu
@ ^ [Y1: qML_mu] :
( ~ ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( Y2 @ Y1 @ Y0 )
=> ( !! @ qML_i
@ ^ [Y3: qML_i] :
( !! @ qML_mu
@ ^ [Y4: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y5: qML_mu > qML_i > $o] :
( ( scott_P @ Y5 @ Y3 )
=> ( Y5 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
& ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ~ ( !! @ qML_i
@ ^ [Y0: qML_i] :
( !! @ qML_mu
@ ^ [Y1: qML_mu] :
( ~ ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( Y2 @ Y1 @ Y0 )
=> ( !! @ qML_i
@ ^ [Y3: qML_i] :
( !! @ qML_mu
@ ^ [Y4: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y5: qML_mu > qML_i > $o] :
( ( scott_P @ Y5 @ Y3 )
=> ( Y5 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
& ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f49]) ).
thf(f49,plain,
( $true
= ( ~ ( !! @ qML_i
@ ^ [Y0: qML_i] :
( !! @ qML_mu
@ ^ [Y1: qML_mu] :
( ~ ( ^ [Y2: qML_mu,Y3: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y4: qML_mu > qML_i > $o] :
( ( scott_P @ Y4 @ Y3 )
=> ( Y4 @ Y2 @ Y3 ) ) )
@ Y1
@ Y0 )
| ( ^ [Y2: qML_mu > qML_i > $o,Y3: qML_mu,Y4: qML_i] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y5: qML_mu > qML_i > $o] :
( ( Y5 @ Y3 @ Y4 )
=> ( !! @ qML_i
@ ^ [Y6: qML_i] :
( !! @ qML_mu
@ ^ [Y7: qML_mu] :
( ( Y2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ( Y2 @ Y3 @ Y4 ) )
@ ^ [Y2: qML_mu,Y3: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y4: qML_mu > qML_i > $o] :
( ( scott_P @ Y4 @ Y3 )
=> ( Y4 @ Y2 @ Y3 ) ) )
@ Y1
@ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f39,f42,f46,f42]) ).
thf(f46,plain,
( scott_ess_QML_mu
= ( ^ [Y0: qML_mu > qML_i > $o,Y1: qML_mu,Y2: qML_i] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y3: qML_mu > qML_i > $o] :
( ( Y3 @ Y1 @ Y2 )
=> ( !! @ qML_i
@ ^ [Y4: qML_i] :
( !! @ qML_mu
@ ^ [Y5: qML_mu] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
& ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( scott_ess_QML_mu
= ( ^ [Y0: qML_mu > qML_i > $o,Y1: qML_mu,Y2: qML_i] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y3: qML_mu > qML_i > $o] :
( ( Y3 @ Y1 @ Y2 )
=> ( !! @ qML_i
@ ^ [Y4: qML_i] :
( !! @ qML_mu
@ ^ [Y5: qML_mu] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
& ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ^ [X0: qML_mu > qML_i > $o,X1: qML_mu,X2: qML_i] :
( ( X0 @ X1 @ X2 )
& ! [X3: qML_mu > qML_i > $o] :
( ( X3 @ X1 @ X2 )
=> ! [X4: qML_mu,X5: qML_i] :
( ( X0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) ) ) )
= scott_ess_QML_mu ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( ( ^ [X8: qML_mu > qML_i > $o,X0: qML_mu,X1: qML_i] :
( ( X8 @ X0 @ X1 )
& ! [X2: qML_mu > qML_i > $o] :
( ( X2 @ X0 @ X1 )
=> ! [X10: qML_mu,X9: qML_i] :
( ( X8 @ X10 @ X9 )
=> ( X2 @ X10 @ X9 ) ) ) ) )
= scott_ess_QML_mu ),
file('/export/starexec/sandbox/tmp/tmp.lYvwveTElU/DTF2THF_29777.p',fact_4_ess__def) ).
thf(f42,plain,
( scott_G
= ( ^ [Y0: qML_mu,Y1: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( scott_G
= ( ^ [Y0: qML_mu,Y1: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ^ [X0: qML_mu,X1: qML_i] :
! [X2: qML_mu > qML_i > $o] :
( ( scott_P @ X2 @ X1 )
=> ( X2 @ X0 @ X1 ) ) )
= scott_G ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: qML_mu,X1: qML_i] :
! [X2: qML_mu > qML_i > $o] :
( ( scott_P @ X2 @ X1 )
=> ( X2 @ X0 @ X1 ) ) )
= scott_G ),
file('/export/starexec/sandbox/tmp/tmp.lYvwveTElU/DTF2THF_29777.p',fact_0_G__def) ).
thf(f39,plain,
( ( ~ ( !! @ qML_i
@ ^ [Y0: qML_i] :
( !! @ qML_mu
@ ^ [Y1: qML_mu] :
( ~ ( scott_G @ Y1 @ Y0 )
| ( scott_ess_QML_mu @ scott_G @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ~ ( !! @ qML_i
@ ^ [Y0: qML_i] :
( !! @ qML_mu
@ ^ [Y1: qML_mu] :
( ~ ( scott_G @ Y1 @ Y0 )
| ( scott_ess_QML_mu @ scott_G @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
~ ! [X0: qML_mu,X1: qML_i] :
( ( scott_ess_QML_mu @ scott_G @ X0 @ X1 )
| ~ ( scott_G @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,negated_conjecture,
~ ! [X5: qML_mu,X14: qML_i] :
( ( scott_ess_QML_mu @ scott_G @ X5 @ X14 )
| ~ ( scott_G @ X5 @ X14 ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
thf(f11,conjecture,
! [X5: qML_mu,X14: qML_i] :
( ( scott_ess_QML_mu @ scott_G @ X5 @ X14 )
| ~ ( scott_G @ X5 @ X14 ) ),
file('/export/starexec/sandbox/tmp/tmp.lYvwveTElU/DTF2THF_29777.p',conj_0) ).
thf(f191,plain,
( ( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( Y0 @ sK6 @ sK5 )
=> ( !! @ qML_i
@ ^ [Y1: qML_i] :
( !! @ qML_mu
@ ^ [Y2: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y3: qML_mu > qML_i > $o] :
( ( scott_P @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK5 )
=> ( Y0 @ sK6 @ sK5 ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f188]) ).
thf(f542,plain,
( ( ~ ( sK7 @ sK6 @ sK5 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f541]) ).
thf(f541,plain,
( ( $true
=> ~ ( sK7 @ sK6 @ sK5 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f510]) ).
thf(f510,plain,
( $true
= ( $true
=> ( ^ [Y0: qML_mu,Y1: qML_i] :
~ ( sK7 @ Y0 @ Y1 )
@ sK6
@ sK5 ) ) ),
inference(superposition,[status(thm)],[f211,f492]) ).
thf(f492,plain,
! [X1: qML_i] :
( ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] :
~ ( sK7 @ Y0 @ Y1 )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f406]) ).
thf(f406,plain,
( ( !! @ qML_i
@ ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] :
~ ( sK7 @ Y0 @ Y1 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f391]) ).
thf(f391,plain,
( ( $true
=> ( !! @ qML_i
@ ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] :
~ ( sK7 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f60,f356]) ).
thf(f356,plain,
( ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] :
~ ( sK7 @ Y0 @ Y1 )
@ sK8 )
= $true ),
inference(boolean_simplification,[status(thm)],[f354]) ).
thf(f354,plain,
( $true
= ( $true
=> ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] :
~ ( sK7 @ Y0 @ Y1 )
@ sK8 ) ) ),
inference(superposition,[status(thm)],[f89,f334]) ).
thf(f334,plain,
( $true
= ( ~ ( scott_P @ sK7 @ sK8 ) ) ),
inference(boolean_simplification,[status(thm)],[f323]) ).
thf(f323,plain,
( ( ( scott_P @ sK7 @ sK8 )
=> $false )
= $true ),
inference(superposition,[status(thm)],[f307,f260]) ).
thf(f260,plain,
( $false
= ( sK7 @ sK9 @ sK8 ) ),
inference(binary_proxy_clausification,[status(thm)],[f258]) ).
thf(f258,plain,
( ( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK8 )
=> ( Y0 @ sK9 @ sK8 ) ) )
=> ( sK7 @ sK9 @ sK8 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f257]) ).
thf(f257,plain,
( $false
= ( ^ [Y0: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ sK8 )
=> ( Y1 @ Y0 @ sK8 ) ) )
=> ( sK7 @ Y0 @ sK8 ) )
@ sK9 ) ),
inference(sigma_clausification,[status(thm)],[f254]) ).
thf(f254,plain,
( $false
= ( !! @ qML_mu
@ ^ [Y0: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ sK8 )
=> ( Y1 @ Y0 @ sK8 ) ) )
=> ( sK7 @ Y0 @ sK8 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f253]) ).
thf(f253,plain,
( ( ^ [Y0: qML_i] :
( !! @ qML_mu
@ ^ [Y1: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) )
@ sK8 )
= $false ),
inference(sigma_clausification,[status(thm)],[f240]) ).
thf(f240,plain,
( ( !! @ qML_i
@ ^ [Y0: qML_i] :
( !! @ qML_mu
@ ^ [Y1: qML_mu] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f239]) ).
thf(f307,plain,
! [X1: qML_mu > qML_i > $o] :
( ( ( scott_P @ X1 @ sK8 )
=> ( X1 @ sK9 @ sK8 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f306]) ).
thf(f306,plain,
! [X1: qML_mu > qML_i > $o] :
( ( ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK8 )
=> ( Y0 @ sK9 @ sK8 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f261]) ).
thf(f261,plain,
( $true
= ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK8 )
=> ( Y0 @ sK9 @ sK8 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f258]) ).
thf(f89,plain,
! [X2: qML_i,X1: qML_mu > qML_i > $o] :
( ( ~ ( scott_P @ X1 @ X2 )
=> ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] :
~ ( X1 @ Y0 @ Y1 )
@ X2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f88]) ).
thf(f88,plain,
! [X2: qML_i,X1: qML_mu > qML_i > $o] :
( $true
= ( ^ [Y0: qML_i] :
( ~ ( scott_P @ X1 @ Y0 )
=> ( scott_P
@ ^ [Y1: qML_mu,Y2: qML_i] :
~ ( X1 @ Y1 @ Y2 )
@ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
! [X1: qML_mu > qML_i > $o] :
( $true
= ( !! @ qML_i
@ ^ [Y0: qML_i] :
( ~ ( scott_P @ X1 @ Y0 )
=> ( scott_P
@ ^ [Y1: qML_mu,Y2: qML_i] :
~ ( X1 @ Y1 @ Y2 )
@ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f86]) ).
thf(f86,plain,
! [X1: qML_mu > qML_i > $o] :
( ( ^ [Y0: qML_mu > qML_i > $o] :
( !! @ qML_i
@ ^ [Y1: qML_i] :
( ~ ( scott_P @ Y0 @ Y1 )
=> ( scott_P
@ ^ [Y2: qML_mu,Y3: qML_i] :
~ ( Y0 @ Y2 @ Y3 )
@ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( $true
= ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( !! @ qML_i
@ ^ [Y1: qML_i] :
( ~ ( scott_P @ Y0 @ Y1 )
=> ( scott_P
@ ^ [Y2: qML_mu,Y3: qML_i] :
~ ( Y0 @ Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( $true
= ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( !! @ qML_i
@ ^ [Y1: qML_i] :
( ~ ( scott_P @ Y0 @ Y1 )
=> ( scott_P
@ ^ [Y2: qML_mu,Y3: qML_i] :
~ ( Y0 @ Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ~ ( scott_P @ X1 @ X0 )
=> ( scott_P
@ ^ [X2: qML_mu,X3: qML_i] :
~ ( X1 @ X2 @ X3 )
@ X0 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X3: qML_i,X6: qML_mu > qML_i > $o] :
( ~ ( scott_P @ X6 @ X3 )
=> ( scott_P
@ ^ [X2: qML_mu,X10: qML_i] :
~ ( X6 @ X2 @ X10 )
@ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.lYvwveTElU/DTF2THF_29777.p',fact_5_A1b) ).
thf(f60,plain,
! [X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( ( scott_P @ X2 @ X1 )
=> ( !! @ qML_i @ ( scott_P @ X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: qML_mu > qML_i > $o,X1: qML_i] :
( ( ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ X1 )
=> ( !! @ qML_i @ ( scott_P @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
! [X1: qML_i] :
( ( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ X1 )
=> ( !! @ qML_i @ ( scott_P @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
! [X1: qML_i] :
( ( ^ [Y0: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ Y0 )
=> ( !! @ qML_i @ ( scott_P @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( !! @ qML_i
@ ^ [Y0: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ Y0 )
=> ( !! @ qML_i @ ( scott_P @ Y1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
( ( !! @ qML_i
@ ^ [Y0: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ Y0 )
=> ( !! @ qML_i
@ ^ [Y2: qML_i] : ( scott_P @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( !! @ qML_i
@ ^ [Y0: qML_i] :
( !! @ ( qML_mu > qML_i > $o )
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ Y0 )
=> ( !! @ qML_i
@ ^ [Y2: qML_i] : ( scott_P @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i] :
( ( scott_P @ X0 @ X1 )
=> ! [X2: qML_i] : ( scott_P @ X0 @ X2 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X6: qML_mu > qML_i > $o,X3: qML_i] :
( ( scott_P @ X6 @ X3 )
=> ! [X7: qML_i] : ( scott_P @ X6 @ X7 ) ),
file('/export/starexec/sandbox/tmp/tmp.lYvwveTElU/DTF2THF_29777.p',fact_2_A4) ).
thf(f211,plain,
! [X1: qML_mu > qML_i > $o] :
( $true
= ( ( scott_P @ X1 @ sK5 )
=> ( X1 @ sK6 @ sK5 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f210]) ).
thf(f210,plain,
! [X1: qML_mu > qML_i > $o] :
( $true
= ( ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ sK5 )
=> ( Y0 @ sK6 @ sK5 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f205]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : PHI004^4 : TPTP v9.2.1. Released v6.4.0.
% 0.00/0.08 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.27 % Computer : n024.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Tue Feb 24 06:23:55 EST 2026
% 0.08/0.27 % CPUTime :
% 0.08/0.27 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.34 ---- Original DTF file ---
% 0.14/0.34 thf(spec,logic,$$dhol).
% 0.14/0.34 %------------------------------------------------------------------------------
% 0.14/0.34 % File : PHI004^4 : TPTP v9.2.1. Released v6.4.0.
% 0.14/0.34 % Domain : Philosophy
% 0.14/0.34 % Problem : Being God-like is an essence of any God-like being
% 0.14/0.34 % Version : [Ben16] axioms : Biased.
% 0.14/0.34 % English :
% 0.14/0.34
% 0.14/0.34 % Refs : [Ben16] Benzmueller (2016), Email to Geoff Sutcliffe
% 0.14/0.34 % Source : [Ben16]
% 0.14/0.34 % Names : Sledgehammer_T2_S5U_direct_satallax.p [Ben16]
% 0.14/0.34
% 0.14/0.34 % Status : Theorem
% 0.14/0.34 % Rating : 0.56 v9.1.0, 0.62 v9.0.0, 0.70 v8.2.0, 0.69 v8.1.0, 0.55 v7.5.0, 0.71 v7.4.0, 0.78 v7.2.0, 0.75 v7.0.0, 0.71 v6.4.0
% 0.14/0.34 % Syntax : Number of formulae : 17 ( 4 unt; 6 typ; 0 def)
% 0.14/0.34 % Number of atoms : 24 ( 3 equ; 0 cnn)
% 0.14/0.34 % Maximal formula atoms : 3 ( 2 avg)
% 0.14/0.34 % Number of connectives : 69 ( 5 ~; 1 |; 2 &; 52 @)
% 0.14/0.34 % ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% 0.14/0.34 % Maximal formula depth : 11 ( 6 avg)
% 0.14/0.34 % Number of types : 3 ( 2 usr)
% 0.14/0.34 % Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% 0.14/0.34 % Number of symbols : 5 ( 4 usr; 0 con; 2-3 aty)
% 0.14/0.34 % Number of variables : 37 ( 11 ^; 24 !; 2 ?; 37 :)
% 0.14/0.34 % SPC : TH0_THM_EQU_NAR
% 0.14/0.34
% 0.14/0.34 % Comments : This problem file has been generated by Sledgehammer (satallax
% 0.14/0.34 % translation) in default setting.
% 0.14/0.34 %------------------------------------------------------------------------------
% 0.14/0.34 %----Could-be-implicit typings (2)
% 0.14/0.34 thf(ty_n_t__QML____S5U__O__092__060mu__062,type,
% 0.14/0.34 qML_mu: $tType ).
% 0.14/0.34
% 0.14/0.34 thf(ty_n_t__QML____S5U__Oi,type,
% 0.14/0.34 qML_i: $tType ).
% 0.14/0.34
% 0.14/0.34 %----Explicit typings (4)
% 0.14/0.34 thf(sy_c_Scott__S5U_OG,type,
% 0.14/0.34 scott_G: qML_mu > qML_i > $o ).
% 0.14/0.34
% 0.14/0.34 thf(sy_c_Scott__S5U_ONE_001t__QML____S5U__O__092__060mu__062,type,
% 0.14/0.34 scott_NE_QML_mu: qML_mu > qML_i > $o ).
% 0.14/0.34
% 0.14/0.34 thf(sy_c_Scott__S5U_OP,type,
% 0.14/0.34 scott_P: ( qML_mu > qML_i > $o ) > qML_i > $o ).
% 0.14/0.34
% 0.14/0.34 thf(sy_c_Scott__S5U_Oess_001t__QML____S5U__O__092__060mu__062,type,
% 0.14/0.34 scott_ess_QML_mu: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > $o ).
% 0.14/0.34
% 0.14/0.34 %----Relevant facts (10)
% 0.14/0.34 thf(fact_0_G__def,axiom,
% 0.14/0.34 ( scott_G
% 0.14/0.34 = ( ^ [X: qML_mu,W: qML_i] :
% 0.14/0.34 ! [Y: qML_mu > qML_i > $o] :
% 0.14/0.34 ( ( scott_P @ Y @ W )
% 0.14/0.34 => ( Y @ X @ W ) ) ) ) ).
% 0.14/0.34
% 0.14/0.34 % G_def
% 0.14/0.34 thf(fact_1_T3,axiom,
% 0.14/0.34 ! [W2: qML_i,V: qML_i] :
% 0.14/0.34 ? [X2: qML_mu] : ( scott_G @ X2 @ V ) ).
% 0.14/0.34
% 0.14/0.34 % T3
% 0.14/0.34 thf(fact_2_A4,axiom,
% 0.14/0.34 ! [W2: qML_i,X3: qML_mu > qML_i > $o] :
% 0.14/0.34 ( ( scott_P @ X3 @ W2 )
% 0.14/0.34 => ! [X_1: qML_i] : ( scott_P @ X3 @ X_1 ) ) ).
% 0.14/0.34
% 0.14/0.34 % A4
% 0.14/0.34 thf(fact_3_A3,axiom,
% 0.14/0.34 ! [X_1: qML_i] : ( scott_P @ scott_G @ X_1 ) ).
% 0.14/0.34
% 0.14/0.34 % A3
% 0.14/0.34 thf(fact_4_ess__def,axiom,
% 0.14/0.34 ( scott_ess_QML_mu
% 0.14/0.34 = ( ^ [Phi: qML_mu > qML_i > $o,X: qML_mu,W: qML_i] :
% 0.14/0.34 ( ( Phi @ X @ W )
% 0.14/0.34 & ! [Y: qML_mu > qML_i > $o] :
% 0.14/0.34 ( ( Y @ X @ W )
% 0.14/0.34 => ! [V2: qML_i,Z: qML_mu] :
% 0.14/0.34 ( ( Phi @ Z @ V2 )
% 0.14/0.34 => ( Y @ Z @ V2 ) ) ) ) ) ) ).
% 0.14/0.34
% 0.14/0.34 % ess_def
% 0.14/0.34 thf(fact_5_A1b,axiom,
% 0.14/0.34 ! [W2: qML_i,X3: qML_mu > qML_i > $o] :
% 0.14/0.34 ( ~ ( scott_P @ X3 @ W2 )
% 0.14/0.34 => ( scott_P
% 0.14/0.34 @ ^ [Y: qML_mu,Z: qML_i] :
% 0.14/0.34 ~ ( X3 @ Y @ Z )
% 0.14/0.34 @ W2 ) ) ).
% 0.14/0.34
% 0.14/0.34 % A1b
% 0.14/0.34 thf(fact_6_A2,axiom,
% 0.14/0.34 ! [W2: qML_i,X3: qML_mu > qML_i > $o,Xa: qML_mu > qML_i > $o] :
% 0.14/0.34 ( ( ( scott_P @ X3 @ W2 )
% 0.14/0.34 & ! [V3: qML_i,Xb: qML_mu] :
% 0.14/0.34 ( ( X3 @ Xb @ V3 )
% 0.14/0.34 => ( Xa @ Xb @ V3 ) ) )
% 0.14/0.34 => ( scott_P @ Xa @ W2 ) ) ).
% 0.14/0.34
% 0.14/0.34 % A2
% 0.14/0.34 thf(fact_7_A5,axiom,
% 0.14/0.34 ! [X_1: qML_i] : ( scott_P @ scott_NE_QML_mu @ X_1 ) ).
% 0.14/0.34
% 0.14/0.34 % A5
% 0.14/0.34 thf(fact_8_A1a,axiom,
% 0.14/0.34 ! [W2: qML_i,X3: qML_mu > qML_i > $o] :
% 0.14/0.34 ( ( scott_P
% 0.14/0.34 @ ^ [Y: qML_mu,Z: qML_i] :
% 0.14/0.34 ~ ( X3 @ Y @ Z )
% 0.14/0.34 @ W2 )
% 0.14/0.34 => ~ ( scott_P @ X3 @ W2 ) ) ).
% 0.14/0.34
% 0.14/0.34 % A1a
% 0.14/0.34 thf(fact_9_NE__def,axiom,
% 0.14/0.34 ( scott_NE_QML_mu
% 0.14/0.34 = ( ^ [X: qML_mu,W: qML_i] :
% 0.14/0.34 ! [Y: qML_mu > qML_i > $o] :
% 0.14/0.34 ( ( scott_ess_QML_mu @ Y @ X @ W )
% 0.14/0.34 => ! [V2: qML_i] :
% 0.14/0.34 ? [Z: qML_mu] : ( Y @ Z @ V2 ) ) ) ) ).
% 0.14/0.34
% 0.14/0.34 % NE_def
% 0.14/0.34
% 0.14/0.34 %----Conjectures (1)
% 0.14/0.34 thf(conj_0,conjecture,
% 0.14/0.34 ! [W3: qML_i,X2: qML_mu] :
% 0.14/0.34 ( ~ ( scott_G @ X2 @ W3 )
% 0.14/0.34 | ( scott_ess_QML_mu @ scott_G @ X2 @ W3 ) ) ).
% 0.14/0.34
% 0.14/0.34 %------------------------------------------------------------------------------
% 0.14/0.34 ------------------------
% 1.05/1.01 ---- Embedded in THF ---
% 1.05/1.01 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.05/1.01 %%% Generated on Tue Feb 24 06:23:56 EST 2026
% 1.05/1.01 %%% using '$$dhol' embedding, version 1.3.0.
% 1.05/1.01 %%% Logic specification used:
% 1.05/1.01 %%% thf(spec, logic, $$dhol).
% 1.05/1.01
% 1.05/1.01 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.lYvwveTElU/DTF2DTF29777.p
% See solution above
% 1.05/1.01 ------------------------
% 1.27/1.02 ---- Cleaned THF ---
% 1.27/1.02 thf(ty_n_t__QML____S5U__O__092__060mu__062,type,
% 1.27/1.02 qML_mu: $tType ).
% 1.27/1.02
% 1.27/1.02 thf(ty_n_t__QML____S5U__Oi,type,
% 1.27/1.02 qML_i: $tType ).
% 1.27/1.02
% 1.27/1.02 thf(sy_c_Scott__S5U_OG,type,
% 1.27/1.02 scott_G: qML_mu > qML_i > $o ).
% 1.27/1.02
% 1.27/1.02 thf(sy_c_Scott__S5U_ONE_001t__QML____S5U__O__092__060mu__062,type,
% 1.27/1.02 scott_NE_QML_mu: qML_mu > qML_i > $o ).
% 1.27/1.02
% 1.27/1.02 thf(sy_c_Scott__S5U_OP,type,
% 1.27/1.02 scott_P: ( qML_mu > qML_i > $o ) > qML_i > $o ).
% 1.27/1.02
% 1.27/1.02 thf(sy_c_Scott__S5U_Oess_001t__QML____S5U__O__092__060mu__062,type,
% 1.27/1.02 scott_ess_QML_mu: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > $o ).
% 1.27/1.02
% 1.27/1.02 thf(fact_0_G__def,axiom,
% 1.27/1.02 ( scott_G
% 1.27/1.02 = ( ^ [X: qML_mu,W: qML_i] :
% 1.27/1.02 ! [Y: qML_mu > qML_i > $o] :
% 1.27/1.02 ( ( scott_P @ Y @ W )
% 1.27/1.02 => ( Y @ X @ W ) ) ) ) ).
% 1.27/1.02
% 1.27/1.02 thf(fact_1_T3,axiom,
% 1.27/1.02 ! [W2: qML_i,V: qML_i] :
% 1.27/1.02 ? [X2: qML_mu] : ( scott_G @ X2 @ V ) ).
% 1.27/1.02
% 1.27/1.02 thf(fact_2_A4,axiom,
% 1.27/1.02 ! [W2: qML_i,X3: qML_mu > qML_i > $o] :
% 1.27/1.02 ( ( scott_P @ X3 @ W2 )
% 1.27/1.02 => ! [X_1: qML_i] : ( scott_P @ X3 @ X_1 ) ) ).
% 1.27/1.02
% 1.27/1.02 thf(fact_3_A3,axiom,
% 1.27/1.02 ! [X_1: qML_i] : ( scott_P @ scott_G @ X_1 ) ).
% 1.27/1.02
% 1.27/1.02 thf(fact_4_ess__def,axiom,
% 1.27/1.02 ( scott_ess_QML_mu
% 1.27/1.02 = ( ^ [Phi: qML_mu > qML_i > $o,X: qML_mu,W: qML_i] :
% 1.27/1.02 ( ( Phi @ X @ W )
% 1.27/1.02 & ! [Y: qML_mu > qML_i > $o] :
% 1.27/1.02 ( ( Y @ X @ W )
% 1.27/1.02 => ! [V2: qML_i,Z: qML_mu] :
% 1.27/1.02 ( ( Phi @ Z @ V2 )
% 1.27/1.02 => ( Y @ Z @ V2 ) ) ) ) ) ) ).
% 1.27/1.02
% 1.27/1.02 thf(fact_5_A1b,axiom,
% 1.27/1.02 ! [W2: qML_i,X3: qML_mu > qML_i > $o] :
% 1.27/1.02 ( ~ ( scott_P @ X3 @ W2 )
% 1.27/1.02 => ( scott_P
% 1.27/1.02 @ ^ [Y: qML_mu,Z: qML_i] :
% 1.27/1.02 ~ ( X3 @ Y @ Z )
% 1.27/1.02 @ W2 ) ) ).
% 1.27/1.02
% 1.27/1.02 thf(fact_6_A2,axiom,
% 1.27/1.02 ! [W2: qML_i,X3: qML_mu > qML_i > $o,Xa: qML_mu > qML_i > $o] :
% 1.27/1.02 ( ( ( scott_P @ X3 @ W2 )
% 1.27/1.02 & ! [V3: qML_i,Xb: qML_mu] :
% 1.27/1.02 ( ( X3 @ Xb @ V3 )
% 1.27/1.02 => ( Xa @ Xb @ V3 ) ) )
% 1.27/1.02 => ( scott_P @ Xa @ W2 ) ) ).
% 1.27/1.02
% 1.27/1.02 thf(fact_7_A5,axiom,
% 1.27/1.02 ! [X_1: qML_i] : ( scott_P @ scott_NE_QML_mu @ X_1 ) ).
% 1.27/1.02
% 1.27/1.02 thf(fact_8_A1a,axiom,
% 1.27/1.02 ! [W2: qML_i,X3: qML_mu > qML_i > $o] :
% 1.27/1.02 ( ( scott_P
% 1.27/1.02 @ ^ [Y: qML_mu,Z: qML_i] :
% 1.27/1.02 ~ ( X3 @ Y @ Z )
% 1.27/1.02 @ W2 )
% 1.27/1.02 => ~ ( scott_P @ X3 @ W2 ) ) ).
% 1.27/1.02
% 1.27/1.02 thf(fact_9_NE__def,axiom,
% 1.27/1.02 ( scott_NE_QML_mu
% 1.27/1.02 = ( ^ [X: qML_mu,W: qML_i] :
% 1.27/1.02 ! [Y: qML_mu > qML_i > $o] :
% 1.27/1.02 ( ( scott_ess_QML_mu @ Y @ X @ W )
% 1.27/1.02 => ! [V2: qML_i] :
% 1.27/1.02 ? [Z: qML_mu] : ( Y @ Z @ V2 ) ) ) ) ).
% 1.27/1.02
% 1.27/1.02 thf(conj_0,conjecture,
% 1.27/1.02 ! [W3: qML_i,X2: qML_mu] :
% 1.27/1.02 ( ~ ( scott_G @ X2 @ W3 )
% 1.27/1.02 | ( scott_ess_QML_mu @ scott_G @ X2 @ W3 ) ) ).
% 1.27/1.02 ------------------------
% 1.27/1.03 % (29876)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29777 for (3000ds/183Mi)
% 1.27/1.04 % (29878)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_29777 for (3000ds/27Mi)
% 1.27/1.04 % (29877)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_29777 for (3000ds/4Mi)
% 1.27/1.04 % (29879)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29777 for (3000ds/2Mi)
% 1.27/1.04 % (29881)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_29777 for (3000ds/275Mi)
% 1.27/1.04 % (29882)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29777 for (3000ds/18Mi)
% 1.27/1.04 % (29880)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_29777 for (3000ds/2Mi)
% 1.27/1.04 % (29879)Instruction limit reached!
% 1.27/1.04 % (29879)------------------------------
% 1.27/1.04 % (29879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.04 % (29879)Termination reason: Unknown
% 1.27/1.04 % (29880)Instruction limit reached!
% 1.27/1.04 % (29880)------------------------------
% 1.27/1.04 % (29880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.04 % (29880)Termination reason: Unknown
% 1.27/1.04 % (29880)Termination phase: Property scanning
% 1.27/1.04
% 1.27/1.04 % (29880)Memory used [KB]: 1023
% 1.27/1.04 % (29880)Time elapsed: 0.003 s
% 1.27/1.04 % (29880)Instructions burned: 3 (million)
% 1.27/1.04 % (29880)------------------------------
% 1.27/1.04 % (29880)------------------------------
% 1.27/1.04 % (29879)Termination phase: Property scanning
% 1.27/1.04
% 1.27/1.04 % (29879)Memory used [KB]: 1023
% 1.27/1.04 % (29879)Time elapsed: 0.003 s
% 1.27/1.04 % (29879)Instructions burned: 3 (million)
% 1.27/1.04 % (29879)------------------------------
% 1.27/1.04 % (29879)------------------------------
% 1.27/1.04 % (29881)Refutation not found, incomplete strategy
% 1.27/1.04 % (29881)------------------------------
% 1.27/1.04 % (29881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.04 % (29881)Termination reason: Refutation not found, incomplete strategy
% 1.27/1.04
% 1.27/1.04 % (29877)Instruction limit reached!
% 1.27/1.04 % (29877)------------------------------
% 1.27/1.04 % (29877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.04 % (29877)Termination reason: Unknown
% 1.27/1.04 % (29877)Termination phase: Saturation
% 1.27/1.04
% 1.27/1.04 % (29877)Memory used [KB]: 5500
% 1.27/1.04 % (29877)Time elapsed: 0.004 s
% 1.27/1.04 % (29877)Instructions burned: 5 (million)
% 1.27/1.04 % (29877)------------------------------
% 1.27/1.04 % (29877)------------------------------
% 1.27/1.04
% 1.27/1.04 % (29881)Memory used [KB]: 5500
% 1.27/1.04 % (29881)Time elapsed: 0.003 s
% 1.27/1.04 % (29881)Instructions burned: 3 (million)
% 1.27/1.04 % (29881)------------------------------
% 1.27/1.04 % (29881)------------------------------
% 1.27/1.05 % (29882)Instruction limit reached!
% 1.27/1.05 % (29882)------------------------------
% 1.27/1.05 % (29882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.05 % (29882)Termination reason: Unknown
% 1.27/1.05 % (29882)Termination phase: Saturation
% 1.27/1.05
% 1.27/1.05 % (29882)Memory used [KB]: 5756
% 1.27/1.05 % (29882)Time elapsed: 0.011 s
% 1.27/1.05 % (29882)Instructions burned: 18 (million)
% 1.27/1.05 % (29882)------------------------------
% 1.27/1.05 % (29882)------------------------------
% 1.27/1.05 % (29878)Instruction limit reached!
% 1.27/1.05 % (29878)------------------------------
% 1.27/1.05 % (29878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.05 % (29878)Termination reason: Unknown
% 1.27/1.05 % (29878)Termination phase: Saturation
% 1.27/1.05
% 1.27/1.05 % (29878)Memory used [KB]: 5628
% 1.27/1.05 % (29878)Time elapsed: 0.015 s
% 1.27/1.05 % (29878)Instructions burned: 27 (million)
% 1.27/1.05 % (29878)------------------------------
% 1.27/1.05 % (29878)------------------------------
% 1.27/1.05 % (29883)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29777 for (2999ds/3Mi)
% 1.27/1.05 % (29884)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_29777 for (2999ds/37Mi)
% 1.27/1.05 % (29885)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_29777 for (2999ds/15Mi)
% 1.27/1.05 % (29886)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_29777 for (2999ds/3Mi)
% 1.27/1.06 % (29883)Instruction limit reached!
% 1.27/1.06 % (29883)------------------------------
% 1.27/1.06 % (29883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.06 % (29883)Termination reason: Unknown
% 1.27/1.06 % (29883)Termination phase: Function definition elimination
% 1.27/1.06
% 1.27/1.06 % (29883)Memory used [KB]: 1023
% 1.27/1.06 % (29883)Time elapsed: 0.003 s
% 1.27/1.06 % (29883)Instructions burned: 4 (million)
% 1.27/1.06 % (29883)------------------------------
% 1.27/1.06 % (29883)------------------------------
% 1.27/1.06 % (29886)Instruction limit reached!
% 1.27/1.06 % (29886)------------------------------
% 1.27/1.06 % (29886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.06 % (29886)Termination reason: Unknown
% 1.27/1.06 % (29886)Termination phase: Property scanning
% 1.27/1.06
% 1.27/1.06 % (29886)Memory used [KB]: 1023
% 1.27/1.06 % (29886)Time elapsed: 0.003 s
% 1.27/1.06 % (29886)Instructions burned: 4 (million)
% 1.27/1.06 % (29886)------------------------------
% 1.27/1.06 % (29886)------------------------------
% 1.27/1.06 % (29887)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_29777 for (2999ds/1041Mi)
% 1.27/1.06 % (29885)Instruction limit reached!
% 1.27/1.06 % (29885)------------------------------
% 1.27/1.06 % (29885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.06 % (29885)Termination reason: Unknown
% 1.27/1.06 % (29885)Termination phase: Saturation
% 1.27/1.06
% 1.27/1.06 % (29885)Memory used [KB]: 5628
% 1.27/1.06 % (29885)Time elapsed: 0.009 s
% 1.27/1.06 % (29885)Instructions burned: 15 (million)
% 1.27/1.06 % (29885)------------------------------
% 1.27/1.06 % (29885)------------------------------
% 1.27/1.07 % (29888)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_29777 for (2999ds/7Mi)
% 1.27/1.07 % (29888)Instruction limit reached!
% 1.27/1.07 % (29888)------------------------------
% 1.27/1.07 % (29888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.07 % (29888)Termination reason: Unknown
% 1.27/1.07 % (29888)Termination phase: Saturation
% 1.27/1.07
% 1.27/1.07 % (29888)Memory used [KB]: 1023
% 1.27/1.07 % (29888)Time elapsed: 0.005 s
% 1.27/1.07 % (29888)Instructions burned: 8 (million)
% 1.27/1.07 % (29888)------------------------------
% 1.27/1.07 % (29888)------------------------------
% 1.27/1.07 % (29889)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_29777 for (2999ds/16Mi)
% 1.27/1.07 % (29884)Instruction limit reached!
% 1.27/1.07 % (29884)------------------------------
% 1.27/1.07 % (29884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.07 % (29884)Termination reason: Unknown
% 1.27/1.07 % (29884)Termination phase: Saturation
% 1.27/1.07
% 1.27/1.07 % (29884)Memory used [KB]: 6140
% 1.27/1.07 % (29884)Time elapsed: 0.019 s
% 1.27/1.07 % (29884)Instructions burned: 39 (million)
% 1.27/1.07 % (29884)------------------------------
% 1.27/1.07 % (29884)------------------------------
% 1.27/1.07 % (29890)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_29777 for (2999ds/3Mi)
% 1.27/1.07 % (29890)Instruction limit reached!
% 1.27/1.07 % (29890)------------------------------
% 1.27/1.07 % (29890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.07 % (29890)Termination reason: Unknown
% 1.27/1.07 % (29890)Termination phase: Function definition elimination
% 1.27/1.07
% 1.27/1.07 % (29890)Memory used [KB]: 1023
% 1.27/1.07 % (29890)Time elapsed: 0.003 s
% 1.27/1.07 % (29890)Instructions burned: 4 (million)
% 1.27/1.07 % (29890)------------------------------
% 1.27/1.07 % (29890)------------------------------
% 1.27/1.08 % (29891)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_29777 for (2999ds/3Mi)
% 1.27/1.08 % (29891)Instruction limit reached!
% 1.27/1.08 % (29891)------------------------------
% 1.27/1.08 % (29891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.08 % (29891)Termination reason: Unknown
% 1.27/1.08 % (29891)Termination phase: Property scanning
% 1.27/1.08
% 1.27/1.08 % (29891)Memory used [KB]: 1023
% 1.27/1.08 % (29891)Time elapsed: 0.003 s
% 1.27/1.08 % (29891)Instructions burned: 3 (million)
% 1.27/1.08 % (29891)------------------------------
% 1.27/1.08 % (29891)------------------------------
% 1.27/1.08 % (29889)Instruction limit reached!
% 1.27/1.08 % (29889)------------------------------
% 1.27/1.08 % (29889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.08 % (29889)Termination reason: Unknown
% 1.27/1.08 % (29889)Termination phase: Saturation
% 1.27/1.08
% 1.27/1.08 % (29889)Memory used [KB]: 5756
% 1.27/1.08 % (29889)Time elapsed: 0.010 s
% 1.27/1.08 % (29889)Instructions burned: 16 (million)
% 1.27/1.08 % (29889)------------------------------
% 1.27/1.08 % (29889)------------------------------
% 1.27/1.09 % (29892)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_29777 for (2999ds/7Mi)
% 1.27/1.09 % (29893)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_29777 for (2999ds/3Mi)
% 1.27/1.09 % (29892)Instruction limit reached!
% 1.27/1.09 % (29892)------------------------------
% 1.27/1.09 % (29892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.09 % (29892)Termination reason: Unknown
% 1.27/1.09 % (29892)Termination phase: Saturation
% 1.27/1.09
% 1.27/1.09 % (29892)Memory used [KB]: 5500
% 1.27/1.09 % (29893)Instruction limit reached!
% 1.27/1.09 % (29893)------------------------------
% 1.27/1.09 % (29893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.09 % (29893)Termination reason: Unknown
% 1.27/1.09 % (29893)Termination phase: Property scanning
% 1.27/1.09
% 1.27/1.09 % (29893)Memory used [KB]: 1023
% 1.27/1.09 % (29893)Time elapsed: 0.003 s
% 1.27/1.09 % (29893)Instructions burned: 4 (million)
% 1.27/1.09 % (29893)------------------------------
% 1.27/1.09 % (29893)------------------------------
% 1.27/1.09 % (29892)Time elapsed: 0.005 s
% 1.27/1.09 % (29892)Instructions burned: 8 (million)
% 1.27/1.09 % (29892)------------------------------
% 1.27/1.09 % (29892)------------------------------
% 1.27/1.09 % (29894)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_29777 for (2999ds/4Mi)
% 1.27/1.09 % (29894)Instruction limit reached!
% 1.27/1.09 % (29894)------------------------------
% 1.27/1.09 % (29894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.09 % (29894)Termination reason: Unknown
% 1.27/1.09 % (29894)Termination phase: Function definition elimination
% 1.27/1.09
% 1.27/1.09 % (29894)Memory used [KB]: 1023
% 1.27/1.09 % (29894)Time elapsed: 0.003 s
% 1.27/1.09 % (29894)Instructions burned: 4 (million)
% 1.27/1.09 % (29894)------------------------------
% 1.27/1.09 % (29894)------------------------------
% 1.27/1.09 % (29876)Instruction limit reached!
% 1.27/1.09 % (29876)------------------------------
% 1.27/1.09 % (29876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.09 % (29876)Termination reason: Unknown
% 1.27/1.09 % (29876)Termination phase: Saturation
% 1.27/1.09
% 1.27/1.09 % (29876)Memory used [KB]: 7931
% 1.27/1.09 % (29876)Time elapsed: 0.063 s
% 1.27/1.09 % (29876)Instructions burned: 185 (million)
% 1.27/1.09 % (29876)------------------------------
% 1.27/1.09 % (29876)------------------------------
% 1.27/1.10 % (29895)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_29777 for (2999ds/18Mi)
% 1.27/1.10 % (29896)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_29777 for (2999ds/710Mi)
% 1.27/1.10 % (29900)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_29777 for (2999ds/5Mi)
% 1.27/1.10 % (29900)Instruction limit reached!
% 1.27/1.10 % (29900)------------------------------
% 1.27/1.10 % (29900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.10 % (29900)Termination reason: Unknown
% 1.27/1.10 % (29900)Termination phase: Saturation
% 1.27/1.10
% 1.27/1.10 % (29900)Memory used [KB]: 5500
% 1.27/1.10 % (29900)Time elapsed: 0.003 s
% 1.27/1.10 % (29900)Instructions burned: 7 (million)
% 1.27/1.10 % (29900)------------------------------
% 1.27/1.10 % (29900)------------------------------
% 1.27/1.10 % (29897)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_29777 for (2999ds/6Mi)
% 1.27/1.10 % (29898)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_29777 for (2999ds/902Mi)
% 1.27/1.11 % (29895)Instruction limit reached!
% 1.27/1.11 % (29895)------------------------------
% 1.27/1.11 % (29895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.11 % (29895)Termination reason: Unknown
% 1.27/1.11 % (29895)Termination phase: Saturation
% 1.27/1.11
% 1.27/1.11 % (29895)Memory used [KB]: 5628
% 1.27/1.11 % (29895)Time elapsed: 0.011 s
% 1.27/1.11 % (29895)Instructions burned: 19 (million)
% 1.27/1.11 % (29895)------------------------------
% 1.27/1.11 % (29895)------------------------------
% 1.27/1.11 % (29899)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_29777 for (2999ds/21Mi)
% 1.27/1.11 % (29898)Refutation not found, incomplete strategy
% 1.27/1.11 % (29898)------------------------------
% 1.27/1.11 % (29898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.11 % (29898)Termination reason: Refutation not found, incomplete strategy
% 1.27/1.11
% 1.27/1.11
% 1.27/1.11 % (29898)Memory used [KB]: 5500
% 1.27/1.11 % (29898)Time elapsed: 0.003 s
% 1.27/1.11 % (29898)Instructions burned: 4 (million)
% 1.27/1.11 % (29898)------------------------------
% 1.27/1.11 % (29898)------------------------------
% 1.27/1.11 % (29897)Instruction limit reached!
% 1.27/1.11 % (29897)------------------------------
% 1.27/1.11 % (29897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.11 % (29897)Termination reason: Unknown
% 1.27/1.11 % (29897)Termination phase: Saturation
% 1.27/1.11
% 1.27/1.11 % (29897)Memory used [KB]: 5500
% 1.27/1.11 % (29897)Time elapsed: 0.004 s
% 1.27/1.11 % (29897)Instructions burned: 6 (million)
% 1.27/1.11 % (29897)------------------------------
% 1.27/1.11 % (29897)------------------------------
% 1.27/1.11 % (29901)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_29777 for (2999ds/6Mi)
% 1.27/1.11 % (29901)Instruction limit reached!
% 1.27/1.11 % (29901)------------------------------
% 1.27/1.11 % (29901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.11 % (29901)Termination reason: Unknown
% 1.27/1.11 % (29901)Termination phase: Saturation
% 1.27/1.11
% 1.27/1.11 % (29901)Memory used [KB]: 5500
% 1.27/1.11 % (29901)Time elapsed: 0.003 s
% 1.27/1.11 % (29901)Instructions burned: 6 (million)
% 1.27/1.11 % (29901)------------------------------
% 1.27/1.11 % (29901)------------------------------
% 1.27/1.12 % (29899)Instruction limit reached!
% 1.27/1.12 % (29899)------------------------------
% 1.27/1.12 % (29899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.12 % (29899)Termination reason: Unknown
% 1.27/1.12 % (29899)Termination phase: Saturation
% 1.27/1.12
% 1.27/1.12 % (29899)Memory used [KB]: 5628
% 1.27/1.12 % (29899)Time elapsed: 0.013 s
% 1.27/1.12 % (29899)Instructions burned: 22 (million)
% 1.27/1.12 % (29899)------------------------------
% 1.27/1.12 % (29899)------------------------------
% 1.27/1.12 % (29902)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_29777 for (2999ds/377Mi)
% 1.27/1.12 % (29903)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_29777 for (2999ds/779Mi)
% 1.27/1.12 % (29904)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_29777 for (2999ds/19Mi)
% 1.27/1.12 % (29905)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_29777 for (2999ds/879Mi)
% 1.27/1.13 % (29887)First to succeed.
% 1.27/1.13 % (29904)Refutation not found, incomplete strategy
% 1.27/1.13 % (29904)------------------------------
% 1.27/1.13 % (29904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.13 % (29904)Termination reason: Refutation not found, incomplete strategy
% 1.27/1.13
% 1.27/1.13
% 1.27/1.13 % (29904)Memory used [KB]: 5500
% 1.27/1.13 % (29904)Time elapsed: 0.006 s
% 1.27/1.13 % (29904)Instructions burned: 9 (million)
% 1.27/1.13 % (29904)------------------------------
% 1.27/1.13 % (29904)------------------------------
% 1.27/1.13 % (29887)Refutation found. Thanks to Tanya!
% 1.27/1.13 % SZS status Theorem for DTF2THF_29777
% 1.27/1.13 % SZS output start Proof for DTF2THF_29777
% 1.27/1.13 thf(type_def_5, type, qML_mu: $tType).
% 1.27/1.13 thf(type_def_6, type, qML_i: $tType).
% 1.27/1.13 thf(func_def_0, type, qML_mu: $tType).
% 1.27/1.13 thf(func_def_1, type, qML_i: $tType).
% 1.27/1.13 thf(func_def_2, type, scott_G: qML_mu > qML_i > $o).
% 1.27/1.13 thf(func_def_3, type, scott_NE_QML_mu: qML_mu > qML_i > $o).
% 1.27/1.13 thf(func_def_4, type, scott_P: (qML_mu > qML_i > $o) > qML_i > $o).
% 1.27/1.13 thf(func_def_5, type, scott_ess_QML_mu: (qML_mu > qML_i > $o) > qML_mu > qML_i > $o).
% 1.27/1.13 thf(func_def_23, type, ph1: !>[X0: $tType]:(X0)).
% 1.27/1.13 thf(func_def_24, type, sK2: qML_i > qML_mu).
% 1.27/1.13 thf(func_def_25, type, sK3: qML_mu).
% 1.27/1.13 thf(func_def_26, type, sK4: qML_i).
% 1.27/1.13 thf(func_def_27, type, sK5: qML_i).
% 1.27/1.13 thf(func_def_28, type, sK6: qML_mu).
% 1.27/1.13 thf(func_def_29, type, sK7: qML_mu > qML_i > $o).
% 1.27/1.13 thf(func_def_30, type, sK8: qML_i).
% 1.27/1.13 thf(func_def_31, type, sK9: qML_mu).
% 1.27/1.13 thf(func_def_32, type, sK10: qML_mu).
% 1.27/1.13 thf(func_def_33, type, sK11: qML_i).
% 1.27/1.13 thf(f549,plain,(
% 1.27/1.13 $false),
% 1.27/1.13 inference(trivial_inequality_removal,[status(thm)],[f548])).
% 1.27/1.13 thf(f548,plain,(
% 1.27/1.13 ($true = $false)),
% 1.27/1.13 inference(boolean_simplification,[status(thm)],[f547])).
% 1.27/1.13 thf(f547,plain,(
% 1.27/1.13 ($true = (~ $true))),
% 1.27/1.13 inference(forward_demodulation,[status(thm)],[f542,f241])).
% 1.27/1.13 thf(f241,plain,(
% 1.27/1.13 ($true = (sK7 @ sK6 @ sK5))),
% 1.27/1.13 inference(binary_proxy_clausification,[status(thm)],[f239])).
% 1.27/1.13 thf(f239,plain,(
% 1.27/1.13 (((sK7 @ sK6 @ sK5) => (!! @ qML_i @ (^[Y0 : qML_i]: (!! @ qML_mu @ (^[Y1 : qML_mu]: ((!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((scott_P @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))) => (sK7 @ Y1 @ Y0))))))) = $false)),
% 1.27/1.13 inference(beta_eta_normalization,[status(thm)],[f238])).
% 1.27/1.13 thf(f238,plain,(
% 1.27/1.13 ($false = ((^[Y0 : qML_mu > qML_i > $o]: ((Y0 @ sK6 @ sK5) => (!! @ qML_i @ (^[Y1 : qML_i]: (!! @ qML_mu @ (^[Y2 : qML_mu]: ((!! @ (qML_mu > qML_i > $o) @ (^[Y3 : qML_mu > qML_i > $o]: ((scott_P @ Y3 @ Y1) => (Y3 @ Y2 @ Y1)))) => (Y0 @ Y2 @ Y1)))))))) @ sK7))),
% 1.27/1.13 inference(sigma_clausification,[status(thm)],[f209])).
% 1.27/1.13 thf(f209,plain,(
% 1.27/1.13 ($false = (!! @ (qML_mu > qML_i > $o) @ (^[Y0 : qML_mu > qML_i > $o]: ((Y0 @ sK6 @ sK5) => (!! @ qML_i @ (^[Y1 : qML_i]: (!! @ qML_mu @ (^[Y2 : qML_mu]: ((!! @ (qML_mu > qML_i > $o) @ (^[Y3 : qML_mu > qML_i > $o]: ((scott_P @ Y3 @ Y1) => (Y3 @ Y2 @ Y1)))) => (Y0 @ Y2 @ Y1))))))))))),
% 1.27/1.13 inference(boolean_simplification,[status(thm)],[f207])).
% 1.27/1.13 thf(f207,plain,(
% 1.27/1.13 (((!! @ (qML_mu > qML_i > $o) @ (^[Y0 : qML_mu > qML_i > $o]: ((Y0 @ sK6 @ sK5) => (!! @ qML_i @ (^[Y1 : qML_i]: (!! @ qML_mu @ (^[Y2 : qML_mu]: ((!! @ (qML_mu > qML_i > $o) @ (^[Y3 : qML_mu > qML_i > $o]: ((scott_P @ Y3 @ Y1) => (Y3 @ Y2 @ Y1)))) => (Y0 @ Y2 @ Y1))))))))) & $true) = $false)),
% 1.27/1.13 inference(backward_demodulation,[status(thm)],[f191,f205])).
% 1.27/1.13 thf(f205,plain,(
% 1.27/1.13 ($true = (!! @ (qML_mu > qML_i > $o) @ (^[Y0 : qML_mu > qML_i > $o]: ((scott_P @ Y0 @ sK5) => (Y0 @ sK6 @ sK5)))))),
% 1.27/1.13 inference(not_proxy_clausification,[status(thm)],[f194])).
% 1.27/1.13 thf(f194,plain,(
% 1.27/1.13 ((~ (!! @ (qML_mu > qML_i > $o) @ (^[Y0 : qML_mu > qML_i > $o]: ((scott_P @ Y0 @ sK5) => (Y0 @ sK6 @ sK5))))) = $false)),
% 1.27/1.13 inference(boolean_simplification,[status(thm)],[f193])).
% 1.27/1.13 thf(f193,plain,(
% 1.27/1.13 ($false = ((~ (!! @ (qML_mu > qML_i > $o) @ (^[Y0 : qML_mu > qML_i > $o]: ((scott_P @ Y0 @ sK5) => (Y0 @ sK6 @ sK5))))) | $false))),
% 1.27/1.13 inference(backward_demodulation,[status(thm)],[f188,f191])).
% 1.27/1.13 thf(f188,plain,(
% 1.27/1.13 ($false = ((~ (!! @ (qML_mu > qML_i > $o) @ (^[Y0 : qML_mu > qML_i > $o]: ((scott_P @ Y0 @ sK5) => (Y0 @ sK6 @ sK5))))) | ((!! @ (qML_mu > qML_i > $o) @ (^[Y0 : qML_mu > qML_i > $o]: ((Y0 @ sK6 @ sK5) => (!! @ qML_i @ (^[Y1 : qML_i]: (!! @ qML_mu @ (^[Y2 : qML_mu]: ((!! @ (qML_mu > qML_i > $o) @ (^[Y3 : qML_mu > qML_i > $o]: ((scott_P @ Y3 @ Y1) => (Y3 @ Y2 @ Y1)))) => (Y0 @ Y2 @ Y1))))))))) & (!! @ (qML_mu > qML_i > $o) @ (^[Y0 : qML_mu > qML_i > $o]: ((scott_P @ Y0 @ sK5) => (Y0 @ sK6 @ sK5)))))))),
% 1.27/1.13 inference(beta_eta_normalization,[status(thm)],[f187])).
% 1.27/1.13 thf(f187,plain,(
% 1.27/1.13 ($false = ((^[Y0 : qML_mu]: ((~ (!! @ (qML_mu > qML_i > $o) @ (^[Y1 : qML_mu > qML_i > $o]: ((scott_P @ Y1 @ sK5) => (Y1 @ Y0 @ sK5))))) | ((!! @ (qML_mu > qML_i > $o) @ (^[Y1 : qML_mu > qML_i > $o]: ((Y1 @ Y0 @ sK5) => (!! @ qML_i @ (^[Y2 : qML_i]: (!! @ qML_mu @ (^[Y3 : qML_mu]: ((!! @ (qML_mu > qML_i > $o) @ (^[Y4 : qML_mu > qML_i > $o]: ((scott_P @ Y4 @ Y2) => (Y4 @ Y3 @ Y2)))) => (Y1 @ Y3 @ Y2))))))))) & (!! @ (qML_mu > qML_i > $o) @ (^[Y1 : qML_mu > qML_i > $o]: ((scott_P @ Y1 @ sK5) => (Y1 @ Y0 @ sK5))))))) @ sK6))),
% 1.27/1.13 inference(sigma_clausification,[status(thm)],[f183])).
% 1.27/1.13 thf(f183,plain,(
% 1.27/1.13 ($false = (!! @ qML_mu @ (^[Y0 : qML_mu]: ((~ (!! @ (qML_mu > qML_i > $o) @ (^[Y1 : qML_mu > qML_i > $o]: ((scott_P @ Y1 @ sK5) => (Y1 @ Y0 @ sK5))))) | ((!! @ (qML_mu > qML_i > $o) @ (^[Y1 : qML_mu > qML_i > $o]: ((Y1 @ Y0 @ sK5) => (!! @ qML_i @ (^[Y2 : qML_i]: (!! @ qML_mu @ (^[Y3 : qML_mu]: ((!! @ (qML_mu > qML_i > $o) @ (^[Y4 : qML_mu > qML_i > $o]: ((scott_P @ Y4 @ Y2) => (Y4 @ Y3 @ Y2)))) => (Y1 @ Y3 @ Y2))))))))) & (!! @ (qML_mu > qML_i > $o) @ (^[Y1 : qML_mu > qML_i > $o]: ((scott_P @ Y1 @ sK5) => (Y1 @ Y0 @ sK5)))))))))),
% 1.27/1.13 inference(beta_eta_normalization,[status(thm)],[f182])).
% 1.27/1.13 thf(f182,plain,(
% 1.27/1.13 ($false = ((^[Y0 : qML_i]: (!! @ qML_mu @ (^[Y1 : qML_mu]: ((~ (!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((scott_P @ Y2 @ Y0) => (Y2 @ Y1 @ Y0))))) | ((!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((Y2 @ Y1 @ Y0) => (!! @ qML_i @ (^[Y3 : qML_i]: (!! @ qML_mu @ (^[Y4 : qML_mu]: ((!! @ (qML_mu > qML_i > $o) @ (^[Y5 : qML_mu > qML_i > $o]: ((scott_P @ Y5 @ Y3) => (Y5 @ Y4 @ Y3)))) => (Y2 @ Y4 @ Y3))))))))) & (!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((scott_P @ Y2 @ Y0) => (Y2 @ Y1 @ Y0))))))))) @ sK5))),
% 1.27/1.13 inference(sigma_clausification,[status(thm)],[f177])).
% 1.27/1.13 thf(f177,plain,(
% 1.27/1.13 ($false = (!! @ qML_i @ (^[Y0 : qML_i]: (!! @ qML_mu @ (^[Y1 : qML_mu]: ((~ (!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((scott_P @ Y2 @ Y0) => (Y2 @ Y1 @ Y0))))) | ((!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((Y2 @ Y1 @ Y0) => (!! @ qML_i @ (^[Y3 : qML_i]: (!! @ qML_mu @ (^[Y4 : qML_mu]: ((!! @ (qML_mu > qML_i > $o) @ (^[Y5 : qML_mu > qML_i > $o]: ((scott_P @ Y5 @ Y3) => (Y5 @ Y4 @ Y3)))) => (Y2 @ Y4 @ Y3))))))))) & (!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((scott_P @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))))))))))),
% 1.27/1.13 inference(not_proxy_clausification,[status(thm)],[f55])).
% 1.27/1.13 thf(f55,plain,(
% 1.27/1.13 ((~ (!! @ qML_i @ (^[Y0 : qML_i]: (!! @ qML_mu @ (^[Y1 : qML_mu]: ((~ (!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((scott_P @ Y2 @ Y0) => (Y2 @ Y1 @ Y0))))) | ((!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((Y2 @ Y1 @ Y0) => (!! @ qML_i @ (^[Y3 : qML_i]: (!! @ qML_mu @ (^[Y4 : qML_mu]: ((!! @ (qML_mu > qML_i > $o) @ (^[Y5 : qML_mu > qML_i > $o]: ((scott_P @ Y5 @ Y3) => (Y5 @ Y4 @ Y3)))) => (Y2 @ Y4 @ Y3))))))))) & (!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((scott_P @ Y2 @ Y0) => (Y2 @ Y1 @ Y0))))))))))) = $true)),
% 1.27/1.13 inference(beta_eta_normalization,[status(thm)],[f49])).
% 1.27/1.13 thf(f49,plain,(
% 1.27/1.13 ($true = (~ (!! @ qML_i @ (^[Y0 : qML_i]: (!! @ qML_mu @ (^[Y1 : qML_mu]: ((~ ((^[Y2 : qML_mu]: ((^[Y3 : qML_i]: (!! @ (qML_mu > qML_i > $o) @ (^[Y4 : qML_mu > qML_i > $o]: ((scott_P @ Y4 @ Y3) => (Y4 @ Y2 @ Y3))))))) @ Y1 @ Y0)) | ((^[Y2 : qML_mu > qML_i > $o]: ((^[Y3 : qML_mu]: ((^[Y4 : qML_i]: ((!! @ (qML_mu > qML_i > $o) @ (^[Y5 : qML_mu > qML_i > $o]: ((Y5 @ Y3 @ Y4) => (!! @ qML_i @ (^[Y6 : qML_i]: (!! @ qML_mu @ (^[Y7 : qML_mu]: ((Y2 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))))) & (Y2 @ Y3 @ Y4))))))) @ (^[Y2 : qML_mu]: ((^[Y3 : qML_i]: (!! @ (qML_mu > qML_i > $o) @ (^[Y4 : qML_mu > qML_i > $o]: ((scott_P @ Y4 @ Y3) => (Y4 @ Y2 @ Y3))))))) @ Y1 @ Y0))))))))),
% 1.27/1.13 inference(definition_unfolding,[status(thm)],[f39,f42,f46,f42])).
% 1.27/1.13 thf(f46,plain,(
% 1.27/1.13 (scott_ess_QML_mu = (^[Y0 : qML_mu > qML_i > $o]: ((^[Y1 : qML_mu]: ((^[Y2 : qML_i]: ((!! @ (qML_mu > qML_i > $o) @ (^[Y3 : qML_mu > qML_i > $o]: ((Y3 @ Y1 @ Y2) => (!! @ qML_i @ (^[Y4 : qML_i]: (!! @ qML_mu @ (^[Y5 : qML_mu]: ((Y0 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))))) & (Y0 @ Y1 @ Y2))))))))),
% 1.27/1.13 inference(cnf_transformation,[status(thm)],[f23])).
% 1.27/1.13 thf(f23,plain,(
% 1.27/1.13 (scott_ess_QML_mu = (^[Y0 : qML_mu > qML_i > $o]: ((^[Y1 : qML_mu]: ((^[Y2 : qML_i]: ((!! @ (qML_mu > qML_i > $o) @ (^[Y3 : qML_mu > qML_i > $o]: ((Y3 @ Y1 @ Y2) => (!! @ qML_i @ (^[Y4 : qML_i]: (!! @ qML_mu @ (^[Y5 : qML_mu]: ((Y0 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))))) & (Y0 @ Y1 @ Y2))))))))),
% 1.27/1.13 inference(fool_elimination,[status(thm)],[f22])).
% 1.27/1.13 thf(f22,plain,(
% 1.27/1.13 ((^[X0 : qML_mu > qML_i > $o, X1 : qML_mu, X2 : qML_i] : ((X0 @ X1 @ X2) & ! [X3 : qML_mu > qML_i > $o] : ((X3 @ X1 @ X2) => ! [X4 : qML_mu,X5 : qML_i] : ((X0 @ X4 @ X5) => (X3 @ X4 @ X5))))) = scott_ess_QML_mu)),
% 1.27/1.13 inference(rectify,[status(thm)],[f5])).
% 1.27/1.13 thf(f5,axiom,(
% 1.27/1.13 ((^[X8 : qML_mu > qML_i > $o, X0 : qML_mu, X1 : qML_i] : ((X8 @ X0 @ X1) & ! [X2 : qML_mu > qML_i > $o] : ((X2 @ X0 @ X1) => ! [X10 : qML_mu,X9 : qML_i] : ((X8 @ X10 @ X9) => (X2 @ X10 @ X9))))) = scott_ess_QML_mu)),
% 1.27/1.13 file('/export/starexec/sandbox/tmp/tmp.lYvwveTElU/DTF2THF_29777.p',fact_4_ess__def)).
% 1.27/1.13 thf(f42,plain,(
% 1.27/1.13 (scott_G = (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((scott_P @ Y2 @ Y1) => (Y2 @ Y0 @ Y1))))))))),
% 1.27/1.13 inference(cnf_transformation,[status(thm)],[f35])).
% 1.27/1.13 thf(f35,plain,(
% 1.27/1.13 (scott_G = (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((scott_P @ Y2 @ Y1) => (Y2 @ Y0 @ Y1))))))))),
% 1.27/1.13 inference(fool_elimination,[status(thm)],[f34])).
% 1.27/1.13 thf(f34,plain,(
% 1.27/1.13 ((^[X0 : qML_mu, X1 : qML_i] : (! [X2 : qML_mu > qML_i > $o] : ((scott_P @ X2 @ X1) => (X2 @ X0 @ X1)))) = scott_G)),
% 1.27/1.13 inference(rectify,[status(thm)],[f1])).
% 1.27/1.13 thf(f1,axiom,(
% 1.27/1.13 ((^[X0 : qML_mu, X1 : qML_i] : (! [X2 : qML_mu > qML_i > $o] : ((scott_P @ X2 @ X1) => (X2 @ X0 @ X1)))) = scott_G)),
% 1.27/1.13 file('/export/starexec/sandbox/tmp/tmp.lYvwveTElU/DTF2THF_29777.p',fact_0_G__def)).
% 1.27/1.13 thf(f39,plain,(
% 1.27/1.13 ((~ (!! @ qML_i @ (^[Y0 : qML_i]: (!! @ qML_mu @ (^[Y1 : qML_mu]: ((~ (scott_G @ Y1 @ Y0)) | (scott_ess_QML_mu @ scott_G @ Y1 @ Y0))))))) = $true)),
% 1.27/1.13 inference(cnf_transformation,[status(thm)],[f19])).
% 1.27/1.13 thf(f19,plain,(
% 1.27/1.13 ((~ (!! @ qML_i @ (^[Y0 : qML_i]: (!! @ qML_mu @ (^[Y1 : qML_mu]: ((~ (scott_G @ Y1 @ Y0)) | (scott_ess_QML_mu @ scott_G @ Y1 @ Y0))))))) = $true)),
% 1.27/1.13 inference(fool_elimination,[status(thm)],[f18])).
% 1.27/1.13 thf(f18,plain,(
% 1.27/1.13 ~! [X0 : qML_mu,X1 : qML_i] : ((scott_ess_QML_mu @ scott_G @ X0 @ X1) | ~(scott_G @ X0 @ X1))),
% 1.27/1.13 inference(rectify,[status(thm)],[f12])).
% 1.27/1.13 thf(f12,negated_conjecture,(
% 1.27/1.13 ~! [X5 : qML_mu,X14 : qML_i] : ((scott_ess_QML_mu @ scott_G @ X5 @ X14) | ~(scott_G @ X5 @ X14))),
% 1.27/1.13 inference(negated_conjecture,[status(cth)],[f11])).
% 1.27/1.13 thf(f11,conjecture,(
% 1.27/1.13 ! [X5 : qML_mu,X14 : qML_i] : ((scott_ess_QML_mu @ scott_G @ X5 @ X14) | ~(scott_G @ X5 @ X14))),
% 1.27/1.13 file('/export/starexec/sandbox/tmp/tmp.lYvwveTElU/DTF2THF_29777.p',conj_0)).
% 1.27/1.13 thf(f191,plain,(
% 1.27/1.13 (((!! @ (qML_mu > qML_i > $o) @ (^[Y0 : qML_mu > qML_i > $o]: ((Y0 @ sK6 @ sK5) => (!! @ qML_i @ (^[Y1 : qML_i]: (!! @ qML_mu @ (^[Y2 : qML_mu]: ((!! @ (qML_mu > qML_i > $o) @ (^[Y3 : qML_mu > qML_i > $o]: ((scott_P @ Y3 @ Y1) => (Y3 @ Y2 @ Y1)))) => (Y0 @ Y2 @ Y1))))))))) & (!! @ (qML_mu > qML_i > $o) @ (^[Y0 : qML_mu > qML_i > $o]: ((scott_P @ Y0 @ sK5) => (Y0 @ sK6 @ sK5))))) = $false)),
% 1.27/1.13 inference(binary_proxy_clausification,[status(thm)],[f188])).
% 1.27/1.13 thf(f542,plain,(
% 1.27/1.13 ((~ (sK7 @ sK6 @ sK5)) = $true)),
% 1.27/1.13 inference(boolean_simplification,[status(thm)],[f541])).
% 1.27/1.13 thf(f541,plain,(
% 1.27/1.13 (($true => (~ (sK7 @ sK6 @ sK5))) = $true)),
% 1.27/1.13 inference(beta_eta_normalization,[status(thm)],[f510])).
% 1.27/1.13 thf(f510,plain,(
% 1.27/1.13 ($true = ($true => ((^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (sK7 @ Y0 @ Y1))))) @ sK6 @ sK5)))),
% 1.27/1.13 inference(superposition,[status(thm)],[f211,f492])).
% 1.27/1.13 thf(f492,plain,(
% 1.27/1.13 ( ! [X1 : qML_i] : (((scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (sK7 @ Y0 @ Y1))))) @ X1) = $true)) )),
% 1.27/1.13 inference(pi_clausification,[status(thm)],[f406])).
% 1.27/1.13 thf(f406,plain,(
% 1.27/1.13 ((!! @ qML_i @ (scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (sK7 @ Y0 @ Y1))))))) = $true)),
% 1.27/1.13 inference(boolean_simplification,[status(thm)],[f391])).
% 1.27/1.13 thf(f391,plain,(
% 1.27/1.13 (($true => (!! @ qML_i @ (scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (sK7 @ Y0 @ Y1)))))))) = $true)),
% 1.27/1.13 inference(superposition,[status(thm)],[f60,f356])).
% 1.27/1.13 thf(f356,plain,(
% 1.27/1.13 ((scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (sK7 @ Y0 @ Y1))))) @ sK8) = $true)),
% 1.27/1.13 inference(boolean_simplification,[status(thm)],[f354])).
% 1.27/1.13 thf(f354,plain,(
% 1.27/1.13 ($true = ($true => (scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (sK7 @ Y0 @ Y1))))) @ sK8)))),
% 1.27/1.13 inference(superposition,[status(thm)],[f89,f334])).
% 1.27/1.13 thf(f334,plain,(
% 1.27/1.13 ($true = (~ (scott_P @ sK7 @ sK8)))),
% 1.27/1.13 inference(boolean_simplification,[status(thm)],[f323])).
% 1.27/1.13 thf(f323,plain,(
% 1.27/1.13 (((scott_P @ sK7 @ sK8) => $false) = $true)),
% 1.27/1.13 inference(superposition,[status(thm)],[f307,f260])).
% 1.27/1.13 thf(f260,plain,(
% 1.27/1.13 ($false = (sK7 @ sK9 @ sK8))),
% 1.27/1.13 inference(binary_proxy_clausification,[status(thm)],[f258])).
% 1.27/1.13 thf(f258,plain,(
% 1.27/1.13 (((!! @ (qML_mu > qML_i > $o) @ (^[Y0 : qML_mu > qML_i > $o]: ((scott_P @ Y0 @ sK8) => (Y0 @ sK9 @ sK8)))) => (sK7 @ sK9 @ sK8)) = $false)),
% 1.27/1.13 inference(beta_eta_normalization,[status(thm)],[f257])).
% 1.27/1.13 thf(f257,plain,(
% 1.27/1.13 ($false = ((^[Y0 : qML_mu]: ((!! @ (qML_mu > qML_i > $o) @ (^[Y1 : qML_mu > qML_i > $o]: ((scott_P @ Y1 @ sK8) => (Y1 @ Y0 @ sK8)))) => (sK7 @ Y0 @ sK8))) @ sK9))),
% 1.27/1.13 inference(sigma_clausification,[status(thm)],[f254])).
% 1.27/1.13 thf(f254,plain,(
% 1.27/1.13 ($false = (!! @ qML_mu @ (^[Y0 : qML_mu]: ((!! @ (qML_mu > qML_i > $o) @ (^[Y1 : qML_mu > qML_i > $o]: ((scott_P @ Y1 @ sK8) => (Y1 @ Y0 @ sK8)))) => (sK7 @ Y0 @ sK8)))))),
% 1.27/1.13 inference(beta_eta_normalization,[status(thm)],[f253])).
% 1.27/1.13 thf(f253,plain,(
% 1.27/1.13 (((^[Y0 : qML_i]: (!! @ qML_mu @ (^[Y1 : qML_mu]: ((!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((scott_P @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))) => (sK7 @ Y1 @ Y0))))) @ sK8) = $false)),
% 1.27/1.13 inference(sigma_clausification,[status(thm)],[f240])).
% 1.27/1.13 thf(f240,plain,(
% 1.27/1.13 ((!! @ qML_i @ (^[Y0 : qML_i]: (!! @ qML_mu @ (^[Y1 : qML_mu]: ((!! @ (qML_mu > qML_i > $o) @ (^[Y2 : qML_mu > qML_i > $o]: ((scott_P @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))) => (sK7 @ Y1 @ Y0)))))) = $false)),
% 1.27/1.13 inference(binary_proxy_clausification,[status(thm)],[f239])).
% 1.27/1.13 thf(f307,plain,(
% 1.27/1.13 ( ! [X1 : qML_mu > qML_i > $o] : ((((scott_P @ X1 @ sK8) => (X1 @ sK9 @ sK8)) = $true)) )),
% 1.27/1.13 inference(beta_eta_normalization,[status(thm)],[f306])).
% 1.27/1.13 thf(f306,plain,(
% 1.27/1.13 ( ! [X1 : qML_mu > qML_i > $o] : ((((^[Y0 : qML_mu > qML_i > $o]: ((scott_P @ Y0 @ sK8) => (Y0 @ sK9 @ sK8))) @ X1) = $true)) )),
% 1.27/1.13 inference(pi_clausification,[status(thm)],[f261])).
% 1.27/1.13 thf(f261,plain,(
% 1.27/1.13 ($true = (!! @ (qML_mu > qML_i > $o) @ (^[Y0 : qML_mu > qML_i > $o]: ((scott_P @ Y0 @ sK8) => (Y0 @ sK9 @ sK8)))))),
% 1.27/1.13 inference(binary_proxy_clausification,[status(thm)],[f258])).
% 1.27/1.13 thf(f89,plain,(
% 1.27/1.13 ( ! [X2 : qML_i,X1 : qML_mu > qML_i > $o] : ((((~ (scott_P @ X1 @ X2)) => (scott_P @ (^[Y0 : qML_mu]: ((^[Y1 : qML_i]: (~ (X1 @ Y0 @ Y1))))) @ X2)) = $true)) )),
% 1.27/1.13 inference(beta_eta_normalization,[status(thm)],[f88])).
% 1.27/1.13 thf(f88,plain,(
% 1.27/1.13 ( ! [X2 : qML_i,X1 : qML_mu > qML_i > $o] : (($true = ((^[Y0 : qML_i]: ((~ (scott_P @ X1 @ Y0)) => (scott_P @ (^[Y1 : qML_mu]: ((^[Y2 : qML_i]: (~ (X1 @ Y1 @ Y2))))) @ Y0))) @ X2))) )),
% 1.27/1.13 inference(pi_clausification,[status(thm)],[f87])).
% 1.27/1.13 thf(f87,plain,(
% 1.27/1.13 ( ! [X1 : qML_mu > qML_i > $o] : (($true = (!! @ qML_i @ (^[Y0 : qML_i]: ((~ (scott_P @ X1 @ Y0)) => (scott_P @ (^[Y1 : qML_mu]: ((^[Y2 : qML_i]: (~ (X1 @ Y1 @ Y2))))) @ Y0)))))) )),
% 1.27/1.13 inference(beta_eta_normalization,[status(thm)],[f86])).
% 1.27/1.13 thf(f86,plain,(
% 1.27/1.13 ( ! [X1 : qML_mu > qML_i > $o] : ((((^[Y0 : qML_mu > qML_i > $o]: (!! @ qML_i @ (^[Y1 : qML_i]: ((~ (scott_P @ Y0 @ Y1)) => (scott_P @ (^[Y2 : qML_mu]: ((^[Y3 : qML_i]: (~ (Y0 @ Y2 @ Y3))))) @ Y1))))) @ X1) = $true)) )),
% 1.27/1.13 inference(pi_clausification,[status(thm)],[f43])).
% 1.27/1.13 thf(f43,plain,(
% 1.27/1.13 ($true = (!! @ (qML_mu > qML_i > $o) @ (^[Y0 : qML_mu > qML_i > $o]: (!! @ qML_i @ (^[Y1 : qML_i]: ((~ (scott_P @ Y0 @ Y1)) => (scott_P @ (^[Y2 : qML_mu]: ((^[Y3 : qML_i]: (~ (Y0 @ Y2 @ Y3))))) @ Y1)))))))),
% 1.27/1.13 inference(cnf_transformation,[status(thm)],[f27])).
% 1.27/1.13 thf(f27,plain,(
% 1.27/1.13 ($true = (!! @ (qML_mu > qML_i > $o) @ (^[Y0 : qML_mu > qML_i > $o]: (!! @ qML_i @ (^[Y1 : qML_i]: ((~ (scott_P @ Y0 @ Y1)) => (scott_P @ (^[Y2 : qML_mu]: ((^[Y3 : qML_i]: (~ (Y0 @ Y2 @ Y3))))) @ Y1)))))))),
% 1.27/1.13 inference(fool_elimination,[status(thm)],[f26])).
% 1.27/1.13 thf(f26,plain,(
% 1.27/1.13 ! [X0 : qML_i,X1 : qML_mu > qML_i > $o] : (~(scott_P @ X1 @ X0) => (scott_P @ (^[X2 : qML_mu, X3 : qML_i] : (~(X1 @ X2 @ X3))) @ X0))),
% 1.27/1.13 inference(rectify,[status(thm)],[f6])).
% 1.27/1.13 thf(f6,axiom,(
% 1.27/1.13 ! [X3 : qML_i,X6 : qML_mu > qML_i > $o] : (~(scott_P @ X6 @ X3) => (scott_P @ (^[X2 : qML_mu, X10 : qML_i] : (~(X6 @ X2 @ X10))) @ X3))),
% 1.27/1.13 file('/export/starexec/sandbox/tmp/tmp.lYvwveTElU/DTF2THF_29777.p',fact_5_A1b)).
% 1.27/1.13 thf(f60,plain,(
% 1.27/1.13 ( ! [X2 : qML_mu > qML_i > $o,X1 : qML_i] : ((((scott_P @ X2 @ X1) => (!! @ qML_i @ (scott_P @ X2))) = $true)) )),
% 1.27/1.13 inference(beta_eta_normalization,[status(thm)],[f59])).
% 1.27/1.13 thf(f59,plain,(
% 1.27/1.13 ( ! [X2 : qML_mu > qML_i > $o,X1 : qML_i] : ((((^[Y0 : qML_mu > qML_i > $o]: ((scott_P @ Y0 @ X1) => (!! @ qML_i @ (scott_P @ Y0)))) @ X2) = $true)) )),
% 1.27/1.13 inference(pi_clausification,[status(thm)],[f58])).
% 1.27/1.13 thf(f58,plain,(
% 1.27/1.13 ( ! [X1 : qML_i] : (((!! @ (qML_mu > qML_i > $o) @ (^[Y0 : qML_mu > qML_i > $o]: ((scott_P @ Y0 @ X1) => (!! @ qML_i @ (scott_P @ Y0))))) = $true)) )),
% 1.27/1.13 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.27/1.13 thf(f57,plain,(
% 1.27/1.13 ( ! [X1 : qML_i] : ((((^[Y0 : qML_i]: (!! @ (qML_mu > qML_i > $o) @ (^[Y1 : qML_mu > qML_i > $o]: ((scott_P @ Y1 @ Y0) => (!! @ qML_i @ (scott_P @ Y1)))))) @ X1) = $true)) )),
% 1.27/1.13 inference(pi_clausification,[status(thm)],[f56])).
% 1.27/1.13 thf(f56,plain,(
% 1.27/1.13 ((!! @ qML_i @ (^[Y0 : qML_i]: (!! @ (qML_mu > qML_i > $o) @ (^[Y1 : qML_mu > qML_i > $o]: ((scott_P @ Y1 @ Y0) => (!! @ qML_i @ (scott_P @ Y1))))))) = $true)),
% 1.27/1.13 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.27/1.13 thf(f41,plain,(
% 1.27/1.13 ((!! @ qML_i @ (^[Y0 : qML_i]: (!! @ (qML_mu > qML_i > $o) @ (^[Y1 : qML_mu > qML_i > $o]: ((scott_P @ Y1 @ Y0) => (!! @ qML_i @ (^[Y2 : qML_i]: (scott_P @ Y1 @ Y2)))))))) = $true)),
% 1.27/1.13 inference(cnf_transformation,[status(thm)],[f29])).
% 1.27/1.13 thf(f29,plain,(
% 1.27/1.13 ((!! @ qML_i @ (^[Y0 : qML_i]: (!! @ (qML_mu > qML_i > $o) @ (^[Y1 : qML_mu > qML_i > $o]: ((scott_P @ Y1 @ Y0) => (!! @ qML_i @ (^[Y2 : qML_i]: (scott_P @ Y1 @ Y2)))))))) = $true)),
% 1.27/1.13 inference(fool_elimination,[status(thm)],[f28])).
% 1.27/1.13 thf(f28,plain,(
% 1.27/1.13 ! [X0 : qML_mu > qML_i > $o,X1 : qML_i] : ((scott_P @ X0 @ X1) => ! [X2 : qML_i] : (scott_P @ X0 @ X2))),
% 1.27/1.13 inference(rectify,[status(thm)],[f3])).
% 1.27/1.13 thf(f3,axiom,(
% 1.27/1.13 ! [X6 : qML_mu > qML_i > $o,X3 : qML_i] : ((scott_P @ X6 @ X3) => ! [X7 : qML_i] : (scott_P @ X6 @ X7))),
% 1.27/1.13 file('/export/starexec/sandbox/tmp/tmp.lYvwveTElU/DTF2THF_29777.p',fact_2_A4)).
% 1.27/1.13 thf(f211,plain,(
% 1.27/1.13 ( ! [X1 : qML_mu > qML_i > $o] : (($true = ((scott_P @ X1 @ sK5) => (X1 @ sK6 @ sK5)))) )),
% 1.27/1.13 inference(beta_eta_normalization,[status(thm)],[f210])).
% 1.27/1.13 thf(f210,plain,(
% 1.27/1.13 ( ! [X1 : qML_mu > qML_i > $o] : (($true = ((^[Y0 : qML_mu > qML_i > $o]: ((scott_P @ Y0 @ sK5) => (Y0 @ sK6 @ sK5))) @ X1))) )),
% 1.27/1.13 inference(pi_clausification,[status(thm)],[f205])).
% 1.27/1.13 % SZS output end Proof for DTF2THF_29777
% 1.27/1.13 % (29887)------------------------------
% 1.27/1.13 % (29887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.13 % (29887)Termination reason: Refutation
% 1.27/1.13
% 1.27/1.13 % (29887)Memory used [KB]: 6140
% 1.27/1.13 % (29887)Time elapsed: 0.069 s
% 1.27/1.13 % (29887)Instructions burned: 137 (million)
% 1.27/1.13 % (29887)------------------------------
% 1.27/1.13 % (29887)------------------------------
% 1.27/1.13 % (29875)Success in time 0.097 s
%------------------------------------------------------------------------------