%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV089^5 : 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 : n020.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 09:40:15 AM UTC 2026
% Result : Theorem 1.59s 1.63s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 8
% Syntax : Number of formulae : 136 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 1002 ( 524 equ; 13 cnn)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 1609 ( 162 ~; 258 |; 106 &;1051 @)
% ( 2 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 84 ( 84 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 358 ( 107 ^; 203 !; 48 ?; 358 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_9,type,
sK0: a > $o ).
thf(func_def_10,type,
sK1: a > $o ).
thf(func_def_11,type,
sK2: ( a > a ) > a ).
thf(func_def_12,type,
sK3: ( a > a ) > a ).
thf(func_def_13,type,
sK4: a > a ).
thf(func_def_14,type,
sK5: a > a ).
thf(func_def_16,type,
ph7:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK8: a > ( a > a ) > a ).
thf(func_def_18,type,
sK9: a > ( a > a ) > a ).
thf(f1008,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f719,f723,f1007]) ).
thf(f1007,plain,
( spl6_5
| ~ spl6_23 ),
inference(avatar_contradiction_clause,[status(thm)],[f1006]) ).
thf(f1006,plain,
( $false
| spl6_5
| ~ spl6_23 ),
inference(trivial_inequality_removal,[status(thm)],[f1005]) ).
thf(f1005,plain,
( ( $true = $false )
| spl6_5
| ~ spl6_23 ),
inference(backward_demodulation,[status(thm)],[f72,f1004]) ).
thf(f1004,plain,
( ( ( sK0 @ ( sK4 @ ( sK2 @ sK5 ) ) )
= $false )
| spl6_5
| ~ spl6_23 ),
inference(subsumption_resolution,[status(thm)],[f1003,f117]) ).
thf(f117,plain,
( ( $true
!= ( sK0 @ ( sK3 @ sK5 ) ) )
| spl6_5 ),
inference(avatar_component_clause,[status(thm)],[f116]) ).
thf(f116,definition,
( spl6_5
<=> ( $true
= ( sK0 @ ( sK3 @ sK5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_5])],[avatar_definition]) ).
thf(f1003,plain,
( ( ( sK0 @ ( sK4 @ ( sK2 @ sK5 ) ) )
= $false )
| ( $true
= ( sK0 @ ( sK3 @ sK5 ) ) )
| spl6_5
| ~ spl6_23 ),
inference(subsumption_resolution,[status(thm)],[f1002,f382]) ).
thf(f382,plain,
( ( sK2 @ sK5 )
= ( sK5 @ ( sK4 @ ( sK2 @ sK5 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f381]) ).
thf(f381,plain,
( ( ( sK2 @ sK5 )
= ( sK5 @ ( sK4 @ ( sK2 @ sK5 ) ) ) )
| ( $true = $false ) ),
inference(forward_demodulation,[status(thm)],[f371,f70]) ).
thf(f70,plain,
( ( sK1 @ ( sK2 @ sK5 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ( $true != $true )
| ( ( sK1 @ ( sK2 @ sK5 ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f66]) ).
thf(f66,plain,
( ( ( sK1 @ ( sK2 @ sK5 ) )
= $true )
| ( $true != $true )
| ( ( sK1 @ ( sK2 @ sK5 ) )
= $true ) ),
inference(superposition,[status(thm)],[f18,f63]) ).
thf(f63,plain,
! [X0: a > a] :
( ( $true
= ( sK1 @ ( sK5 @ ( sK3 @ X0 ) ) ) )
| ( ( sK1 @ ( sK2 @ X0 ) )
= $true ) ),
inference(equality_resolution,[status(thm)],[f62]) ).
thf(f62,plain,
! [X0: a > a,X1: a] :
( ( ( sK5 @ ( sK3 @ X0 ) )
!= X1 )
| ( $true
= ( sK1 @ X1 ) )
| ( ( sK1 @ ( sK2 @ X0 ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
! [X0: a > a,X1: a] :
( ( $false
= ( ( sK5 @ ( sK3 @ X0 ) )
= X1 ) )
| ( $true
= ( sK1 @ X1 ) )
| ( ( sK1 @ ( sK2 @ X0 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X0: a > a,X1: a] :
( ( ( ( ( sK4 @ X1 )
= ( sK3 @ X0 ) )
& ( sK1 @ X1 ) )
= $true )
| ( $false
= ( ( sK5 @ ( sK3 @ X0 ) )
= X1 ) )
| ( ( sK1 @ ( sK2 @ X0 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
! [X0: a > a,X1: a] :
( ( ( ( ( sK4 @ X1 )
= ( sK3 @ X0 ) )
& ( sK1 @ X1 ) )
= ( ( sK5 @ ( sK3 @ X0 ) )
= X1 ) )
| ( ( sK1 @ ( sK2 @ X0 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
! [X0: a > a,X1: a] :
( ( ( ^ [Y0: a] :
( ( ( sK4 @ Y0 )
= ( sK3 @ X0 ) )
& ( sK1 @ Y0 ) )
@ X1 )
= ( ( sK5 @ ( sK3 @ X0 ) )
= X1 ) )
| ( ( sK1 @ ( sK2 @ X0 ) )
= $true ) ),
inference(argument_congruence,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: a > a] :
( ( ( ^ [Y0: a] :
( ( ( sK4 @ Y0 )
= ( sK3 @ X0 ) )
& ( sK1 @ Y0 ) ) )
= ( (=) @ ( sK5 @ ( sK3 @ X0 ) ) ) )
| ( ( sK1 @ ( sK2 @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: a > a] :
( ( ( ^ [Y0: a] :
( ( ( sK4 @ Y0 )
= ( sK3 @ X0 ) )
& ( sK1 @ Y0 ) ) )
= ( (=) @ ( sK5 @ ( sK3 @ X0 ) ) ) )
| ( ( sK1 @ ( sK2 @ X0 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f23,f17]) ).
thf(f17,plain,
! [X2: a > a] :
( ( $true
= ( sK0 @ ( sK3 @ X2 ) ) )
| ( ( sK1 @ ( sK2 @ X2 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X2: a > a] :
( ( ! [X4: a] :
( ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X4 )
!= ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
= ( sK2 @ X2 ) )
& ( sK0 @ Y0 ) ) ) )
& ( ( sK1 @ ( sK2 @ X2 ) )
= $true ) )
| ( ( ( sK1 @ ( X2 @ ( sK3 @ X2 ) ) )
!= $true )
& ( $true
= ( sK0 @ ( sK3 @ X2 ) ) ) ) )
& ! [X7: a] :
( ( ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ ( sK5 @ X7 ) )
= ( ^ [Y0: a] :
( ( ( sK4 @ Y0 )
= X7 )
& ( sK1 @ Y0 ) ) ) )
| ( ( sK0 @ X7 )
!= $true ) )
& ! [X9: a] :
( ( ( sK1 @ X9 )
!= $true )
| ( $true
= ( sK0 @ ( sK4 @ X9 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f13,f12,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: a > $o,X1: a > $o] :
( ! [X2: a > a] :
( ? [X3: a] :
( ! [X4: a] :
( ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
= X3 )
& ( X0 @ Y0 ) ) )
!= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X4 ) )
& ( ( X1 @ X3 )
= $true ) )
| ? [X5: a] :
( ( $true
!= ( X1 @ ( X2 @ X5 ) ) )
& ( ( X0 @ X5 )
= $true ) ) )
& ? [X6: a > a] :
( ! [X7: a] :
( ? [X8: a] :
( ( ^ [Y0: a] :
( ( ( X6 @ Y0 )
= X7 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X8 ) )
| ( $true
!= ( X0 @ X7 ) ) )
& ! [X9: a] :
( ( ( X1 @ X9 )
!= $true )
| ( ( X0 @ ( X6 @ X9 ) )
= $true ) ) ) )
=> ( ! [X2: a > a] :
( ? [X3: a] :
( ! [X4: a] :
( ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X4 )
!= ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
= X3 )
& ( sK0 @ Y0 ) ) ) )
& ( ( sK1 @ X3 )
= $true ) )
| ? [X5: a] :
( ( ( sK1 @ ( X2 @ X5 ) )
!= $true )
& ( $true
= ( sK0 @ X5 ) ) ) )
& ? [X6: a > a] :
( ! [X7: a] :
( ? [X8: a] :
( ( ^ [Y0: a] :
( ( ( X6 @ Y0 )
= X7 )
& ( sK1 @ Y0 ) ) )
= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X8 ) )
| ( ( sK0 @ X7 )
!= $true ) )
& ! [X9: a] :
( ( ( sK1 @ X9 )
!= $true )
| ( $true
= ( sK0 @ ( X6 @ X9 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X2: a > a] :
( ? [X3: a] :
( ! [X4: a] :
( ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X4 )
!= ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
= X3 )
& ( sK0 @ Y0 ) ) ) )
& ( ( sK1 @ X3 )
= $true ) )
=> ( ! [X4: a] :
( ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X4 )
!= ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
= ( sK2 @ X2 ) )
& ( sK0 @ Y0 ) ) ) )
& ( ( sK1 @ ( sK2 @ X2 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X2: a > a] :
( ? [X5: a] :
( ( ( sK1 @ ( X2 @ X5 ) )
!= $true )
& ( $true
= ( sK0 @ X5 ) ) )
=> ( ( ( sK1 @ ( X2 @ ( sK3 @ X2 ) ) )
!= $true )
& ( $true
= ( sK0 @ ( sK3 @ X2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X6: a > a] :
( ! [X7: a] :
( ? [X8: a] :
( ( ^ [Y0: a] :
( ( ( X6 @ Y0 )
= X7 )
& ( sK1 @ Y0 ) ) )
= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X8 ) )
| ( ( sK0 @ X7 )
!= $true ) )
& ! [X9: a] :
( ( ( sK1 @ X9 )
!= $true )
| ( $true
= ( sK0 @ ( X6 @ X9 ) ) ) ) )
=> ( ! [X7: a] :
( ? [X8: a] :
( ( ^ [Y0: a] :
( ( ( sK4 @ Y0 )
= X7 )
& ( sK1 @ Y0 ) ) )
= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X8 ) )
| ( ( sK0 @ X7 )
!= $true ) )
& ! [X9: a] :
( ( ( sK1 @ X9 )
!= $true )
| ( $true
= ( sK0 @ ( sK4 @ X9 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X7: a] :
( ? [X8: a] :
( ( ^ [Y0: a] :
( ( ( sK4 @ Y0 )
= X7 )
& ( sK1 @ Y0 ) ) )
= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X8 ) )
=> ( ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ ( sK5 @ X7 ) )
= ( ^ [Y0: a] :
( ( ( sK4 @ Y0 )
= X7 )
& ( sK1 @ Y0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o] :
( ! [X2: a > a] :
( ? [X3: a] :
( ! [X4: a] :
( ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
= X3 )
& ( X0 @ Y0 ) ) )
!= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X4 ) )
& ( ( X1 @ X3 )
= $true ) )
| ? [X5: a] :
( ( $true
!= ( X1 @ ( X2 @ X5 ) ) )
& ( ( X0 @ X5 )
= $true ) ) )
& ? [X6: a > a] :
( ! [X7: a] :
( ? [X8: a] :
( ( ^ [Y0: a] :
( ( ( X6 @ Y0 )
= X7 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X8 ) )
| ( $true
!= ( X0 @ X7 ) ) )
& ! [X9: a] :
( ( ( X1 @ X9 )
!= $true )
| ( ( X0 @ ( X6 @ X9 ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o] :
( ! [X6: a > a] :
( ? [X7: a] :
( ! [X8: a] :
( ( ^ [Y0: a] :
( ( ( X6 @ Y0 )
= X7 )
& ( X0 @ Y0 ) ) )
!= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X8 ) )
& ( ( X1 @ X7 )
= $true ) )
| ? [X9: a] :
( ( $true
!= ( X1 @ ( X6 @ X9 ) ) )
& ( ( X0 @ X9 )
= $true ) ) )
& ? [X2: a > a] :
( ! [X4: a] :
( ? [X5: a] :
( ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
= X4 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X5 ) )
| ( ( X0 @ X4 )
!= $true ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X0 @ ( X2 @ X3 ) )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ? [X2: a > a] :
( ! [X4: a] :
( ( ( X0 @ X4 )
= $true )
=> ? [X5: a] :
( ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
= X4 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X5 ) ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
=> ( ( X0 @ ( X2 @ X3 ) )
= $true ) ) )
=> ? [X6: a > a] :
( ! [X9: a] :
( ( ( X0 @ X9 )
= $true )
=> ( $true
= ( X1 @ ( X6 @ X9 ) ) ) )
& ! [X7: a] :
( ( ( X1 @ X7 )
= $true )
=> ? [X8: a] :
( ( ^ [Y0: a] :
( ( ( X6 @ Y0 )
= X7 )
& ( X0 @ Y0 ) ) )
= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X8 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ? [X2: a > a] :
( ! [X4: a] :
( ( ( X0 @ X4 )
= $true )
=> ? [X5: a] :
( ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
= X4 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X5 ) ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
=> ( ( X0 @ ( X2 @ X3 ) )
= $true ) ) )
=> ? [X9: a > a] :
( ! [X10: a] :
( ( $true
= ( X1 @ X10 ) )
=> ? [X11: a] :
( ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X11 )
= ( ^ [Y0: a] :
( ( ( X9 @ Y0 )
= X10 )
& ( X0 @ Y0 ) ) ) ) )
& ! [X15: a] :
( ( $true
= ( X0 @ X15 ) )
=> ( $true
= ( X1 @ ( X9 @ X15 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ? [X2: a > a] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( X0 @ ( X2 @ X3 ) ) )
& ! [X4: a] :
( ( X0 @ X4 )
=> ? [X5: a] :
( ( ^ [X6: a] :
( ( X1 @ X6 )
& ( ( X2 @ X6 )
= X4 ) ) )
= ( ^ [X7: a,X8: a] : ( X7 = X8 )
@ X5 ) ) ) )
=> ? [X9: a > a] :
( ! [X10: a] :
( ( X1 @ X10 )
=> ? [X11: a] :
( ( ^ [X12: a] :
( ( X0 @ X12 )
& ( ( X9 @ X12 )
= X10 ) ) )
= ( ^ [X13: a,X14: a] : ( X13 = X14 )
@ X11 ) ) )
& ! [X15: a] :
( ( X0 @ X15 )
=> ( X1 @ ( X9 @ X15 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o] :
( ? [X2: a > a] :
( ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) )
& ! [X4: a] :
( ( X1 @ X4 )
=> ? [X5: a] :
( ( ^ [X3: a] :
( ( X0 @ X3 )
& ( ( X2 @ X3 )
= X4 ) ) )
= ( ^ [X0: a,X1: a] : ( X0 = X1 )
@ X5 ) ) ) )
=> ? [X2: a > a] :
( ! [X4: a] :
( ( X0 @ X4 )
=> ? [X6: a] :
( ( ^ [X3: a] :
( ( X1 @ X3 )
& ( ( X2 @ X3 )
= X4 ) ) )
= ( ^ [X0: a,X1: a] : ( X0 = X1 )
@ X6 ) ) )
& ! [X3: a] :
( ( X1 @ X3 )
=> ( X0 @ ( X2 @ X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o] :
( ? [X2: a > a] :
( ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) )
& ! [X4: a] :
( ( X1 @ X4 )
=> ? [X5: a] :
( ( ^ [X3: a] :
( ( X0 @ X3 )
& ( ( X2 @ X3 )
= X4 ) ) )
= ( ^ [X0: a,X1: a] : ( X0 = X1 )
@ X5 ) ) ) )
=> ? [X2: a > a] :
( ! [X4: a] :
( ( X0 @ X4 )
=> ? [X6: a] :
( ( ^ [X3: a] :
( ( X1 @ X3 )
& ( ( X2 @ X3 )
= X4 ) ) )
= ( ^ [X0: a,X1: a] : ( X0 = X1 )
@ X6 ) ) )
& ! [X3: a] :
( ( X1 @ X3 )
=> ( X0 @ ( X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.i5qrV6Zz6N/DTF2THF_6063.p',cEQP_1B_pme) ).
thf(f23,plain,
! [X7: a] :
( ( ( sK0 @ X7 )
!= $true )
| ( ( (=) @ ( sK5 @ X7 ) )
= ( ^ [Y0: a] :
( ( ( sK4 @ Y0 )
= X7 )
& ( sK1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
! [X7: a] :
( ( ( sK0 @ X7 )
!= $true )
| ( ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ ( sK5 @ X7 ) )
= ( ^ [Y0: a] :
( ( ( sK4 @ Y0 )
= X7 )
& ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f18,plain,
! [X2: a > a] :
( ( ( sK1 @ ( X2 @ ( sK3 @ X2 ) ) )
!= $true )
| ( ( sK1 @ ( sK2 @ X2 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f371,plain,
( ( ( sK2 @ sK5 )
= ( sK5 @ ( sK4 @ ( sK2 @ sK5 ) ) ) )
| ( ( sK1 @ ( sK2 @ sK5 ) )
= $false ) ),
inference(equality_resolution,[status(thm)],[f178]) ).
thf(f178,plain,
! [X1: a] :
( ( ( sK4 @ ( sK2 @ sK5 ) )
!= ( sK4 @ X1 ) )
| ( ( sK5 @ ( sK4 @ ( sK2 @ sK5 ) ) )
= X1 )
| ( $false
= ( sK1 @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f177]) ).
thf(f177,plain,
! [X1: a] :
( ( ( sK5 @ ( sK4 @ ( sK2 @ sK5 ) ) )
= X1 )
| ( ( ( sK4 @ X1 )
= ( sK4 @ ( sK2 @ sK5 ) ) )
= $false )
| ( $false
= ( sK1 @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f176]) ).
thf(f176,plain,
! [X1: a] :
( ( $false
= ( sK1 @ X1 ) )
| ( $true
= ( ( sK5 @ ( sK4 @ ( sK2 @ sK5 ) ) )
= X1 ) )
| ( ( ( sK4 @ X1 )
= ( sK4 @ ( sK2 @ sK5 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f175]) ).
thf(f175,plain,
! [X1: a] :
( ( ( ( ( sK4 @ X1 )
= ( sK4 @ ( sK2 @ sK5 ) ) )
& ( sK1 @ X1 ) )
= $false )
| ( $true
= ( ( sK5 @ ( sK4 @ ( sK2 @ sK5 ) ) )
= X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f173]) ).
thf(f173,plain,
! [X1: a] :
( ( ( ( sK4 @ X1 )
= ( sK4 @ ( sK2 @ sK5 ) ) )
& ( sK1 @ X1 ) )
= ( ( sK5 @ ( sK4 @ ( sK2 @ sK5 ) ) )
= X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f172]) ).
thf(f172,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( ( ( sK4 @ Y0 )
= ( sK4 @ ( sK2 @ sK5 ) ) )
& ( sK1 @ Y0 ) )
@ X1 )
= ( ( sK5 @ ( sK4 @ ( sK2 @ sK5 ) ) )
= X1 ) ),
inference(argument_congruence,[status(thm)],[f74]) ).
thf(f74,plain,
( ( ^ [Y0: a] :
( ( ( sK4 @ Y0 )
= ( sK4 @ ( sK2 @ sK5 ) ) )
& ( sK1 @ Y0 ) ) )
= ( (=) @ ( sK5 @ ( sK4 @ ( sK2 @ sK5 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ( $true != $true )
| ( ( ^ [Y0: a] :
( ( ( sK4 @ Y0 )
= ( sK4 @ ( sK2 @ sK5 ) ) )
& ( sK1 @ Y0 ) ) )
= ( (=) @ ( sK5 @ ( sK4 @ ( sK2 @ sK5 ) ) ) ) ) ),
inference(superposition,[status(thm)],[f23,f72]) ).
thf(f1002,plain,
( ( ( sK2 @ sK5 )
!= ( sK5 @ ( sK4 @ ( sK2 @ sK5 ) ) ) )
| ( $true
= ( sK0 @ ( sK3 @ sK5 ) ) )
| ( ( sK0 @ ( sK4 @ ( sK2 @ sK5 ) ) )
= $false )
| spl6_5
| ~ spl6_23 ),
inference(trivial_inequality_removal,[status(thm)],[f968]) ).
thf(f968,plain,
( ( ( sK0 @ ( sK4 @ ( sK2 @ sK5 ) ) )
= $false )
| ( ( sK2 @ sK5 )
!= ( sK5 @ ( sK4 @ ( sK2 @ sK5 ) ) ) )
| ( ( sK4 @ ( sK2 @ sK5 ) )
!= ( sK4 @ ( sK2 @ sK5 ) ) )
| ( $true
= ( sK0 @ ( sK3 @ sK5 ) ) )
| spl6_5
| ~ spl6_23 ),
inference(superposition,[status(thm)],[f32,f967]) ).
thf(f967,plain,
( ( ( sK8 @ ( sK4 @ ( sK2 @ sK5 ) ) @ sK5 )
= ( sK4 @ ( sK2 @ sK5 ) ) )
| spl6_5
| ~ spl6_23 ),
inference(equality_resolution,[status(thm)],[f888]) ).
thf(f888,plain,
( ! [X0: a] :
( ( ( sK4 @ ( sK2 @ sK5 ) )
!= X0 )
| ( ( sK8 @ X0 @ sK5 )
= X0 ) )
| spl6_5
| ~ spl6_23 ),
inference(trivial_inequality_removal,[status(thm)],[f887]) ).
thf(f887,plain,
( ! [X0: a] :
( ( ( sK4 @ ( sK2 @ sK5 ) )
!= X0 )
| ( $true = $false )
| ( ( sK8 @ X0 @ sK5 )
= X0 ) )
| spl6_5
| ~ spl6_23 ),
inference(forward_demodulation,[status(thm)],[f886,f72]) ).
thf(f886,plain,
( ! [X0: a] :
( ( ( sK8 @ X0 @ sK5 )
= X0 )
| ( ( sK4 @ ( sK2 @ sK5 ) )
!= X0 )
| ( ( sK0 @ ( sK4 @ ( sK2 @ sK5 ) ) )
= $false ) )
| spl6_5
| ~ spl6_23 ),
inference(subsumption_resolution,[status(thm)],[f885,f117]) ).
thf(f885,plain,
( ! [X0: a] :
( ( ( sK0 @ ( sK4 @ ( sK2 @ sK5 ) ) )
= $false )
| ( ( sK4 @ ( sK2 @ sK5 ) )
!= X0 )
| ( ( sK8 @ X0 @ sK5 )
= X0 )
| ( $true
= ( sK0 @ ( sK3 @ sK5 ) ) ) )
| ~ spl6_23 ),
inference(subsumption_resolution,[status(thm)],[f821,f382]) ).
thf(f821,plain,
( ! [X0: a] :
( ( ( sK2 @ sK5 )
!= ( sK5 @ ( sK4 @ ( sK2 @ sK5 ) ) ) )
| ( ( sK4 @ ( sK2 @ sK5 ) )
!= X0 )
| ( ( sK8 @ X0 @ sK5 )
= X0 )
| ( ( sK0 @ ( sK4 @ ( sK2 @ sK5 ) ) )
= $false )
| ( $true
= ( sK0 @ ( sK3 @ sK5 ) ) ) )
| ~ spl6_23 ),
inference(superposition,[status(thm)],[f32,f722]) ).
thf(f722,plain,
( ! [X0: a] :
( ( ( sK4 @ ( sK2 @ sK5 ) )
= ( sK8 @ X0 @ sK5 ) )
| ( ( sK8 @ X0 @ sK5 )
= X0 ) )
| ~ spl6_23 ),
inference(avatar_component_clause,[status(thm)],[f721]) ).
thf(f721,definition,
( spl6_23
<=> ! [X0: a] :
( ( ( sK8 @ X0 @ sK5 )
= X0 )
| ( ( sK4 @ ( sK2 @ sK5 ) )
= ( sK8 @ X0 @ sK5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_23])],[avatar_definition]) ).
thf(f32,plain,
! [X2: a > a,X4: a] :
( ( ( X2 @ ( sK8 @ X4 @ X2 ) )
!= ( sK2 @ X2 ) )
| ( ( sK8 @ X4 @ X2 )
!= X4 )
| ( $true
= ( sK0 @ ( sK3 @ X2 ) ) )
| ( ( sK0 @ ( sK8 @ X4 @ X2 ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: a > a,X4: a] :
( ( ( sK8 @ X4 @ X2 )
!= X4 )
| ( ( sK0 @ ( sK8 @ X4 @ X2 ) )
= $false )
| ( ( ( X2 @ ( sK8 @ X4 @ X2 ) )
= ( sK2 @ X2 ) )
= $false )
| ( $true
= ( sK0 @ ( sK3 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: a > a,X4: a] :
( ( ( sK8 @ X4 @ X2 )
!= X4 )
| ( $true
= ( sK0 @ ( sK3 @ X2 ) ) )
| ( $false
= ( ( ( X2 @ ( sK8 @ X4 @ X2 ) )
= ( sK2 @ X2 ) )
& ( sK0 @ ( sK8 @ X4 @ X2 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: a > a,X4: a] :
( ( $false
= ( X4
= ( sK8 @ X4 @ X2 ) ) )
| ( $false
= ( ( ( X2 @ ( sK8 @ X4 @ X2 ) )
= ( sK2 @ X2 ) )
& ( sK0 @ ( sK8 @ X4 @ X2 ) ) ) )
| ( $true
= ( sK0 @ ( sK3 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: a > a,X4: a] :
( ( $true
= ( sK0 @ ( sK3 @ X2 ) ) )
| ( ( ( ( X2 @ ( sK8 @ X4 @ X2 ) )
= ( sK2 @ X2 ) )
& ( sK0 @ ( sK8 @ X4 @ X2 ) ) )
!= ( X4
= ( sK8 @ X4 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: a > a,X4: a] :
( ( ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
= ( sK2 @ X2 ) )
& ( sK0 @ Y0 ) )
@ ( sK8 @ X4 @ X2 ) )
!= ( X4
= ( sK8 @ X4 @ X2 ) ) )
| ( $true
= ( sK0 @ ( sK3 @ X2 ) ) ) ),
inference(negative_extensionality,[status(thm)],[f22]) ).
thf(f22,plain,
! [X2: a > a,X4: a] :
( ( ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
= ( sK2 @ X2 ) )
& ( sK0 @ Y0 ) ) )
!= ( (=) @ X4 ) )
| ( $true
= ( sK0 @ ( sK3 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
! [X2: a > a,X4: a] :
( ( $true
= ( sK0 @ ( sK3 @ X2 ) ) )
| ( ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X4 )
!= ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
= ( sK2 @ X2 ) )
& ( sK0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f72,plain,
( ( sK0 @ ( sK4 @ ( sK2 @ sK5 ) ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
( ( $true != $true )
| ( ( sK0 @ ( sK4 @ ( sK2 @ sK5 ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f15,f70]) ).
thf(f15,plain,
! [X9: a] :
( ( ( sK1 @ X9 )
!= $true )
| ( $true
= ( sK0 @ ( sK4 @ X9 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f723,plain,
( spl6_5
| spl6_23 ),
inference(avatar_split_clause,[status(thm)],[f168,f721,f116]) ).
thf(f168,plain,
! [X0: a] :
( ( ( sK8 @ X0 @ sK5 )
= X0 )
| ( $true
= ( sK0 @ ( sK3 @ sK5 ) ) )
| ( ( sK4 @ ( sK2 @ sK5 ) )
= ( sK8 @ X0 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f165]) ).
thf(f165,plain,
! [X0: a] :
( ( ( sK8 @ X0 @ sK5 )
= X0 )
| ( $true
= ( sK0 @ ( sK3 @ sK5 ) ) )
| ( ( sK8 @ X0 @ sK5 )
= X0 )
| ( $true
= ( sK0 @ ( sK3 @ sK5 ) ) )
| ( ( sK4 @ ( sK2 @ sK5 ) )
= ( sK8 @ X0 @ sK5 ) ) ),
inference(superposition,[status(thm)],[f134,f36]) ).
thf(f36,plain,
! [X2: a > a,X4: a] :
( ( ( X2 @ ( sK8 @ X4 @ X2 ) )
= ( sK2 @ X2 ) )
| ( $true
= ( sK0 @ ( sK3 @ X2 ) ) )
| ( ( sK8 @ X4 @ X2 )
= X4 ) ),
inference(equality_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: a > a,X4: a] :
( ( $true
= ( sK0 @ ( sK3 @ X2 ) ) )
| ( ( ( X2 @ ( sK8 @ X4 @ X2 ) )
= ( sK2 @ X2 ) )
= $true )
| ( ( sK8 @ X4 @ X2 )
= X4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: a > a,X4: a] :
( ( ( sK8 @ X4 @ X2 )
= X4 )
| ( $true
= ( ( ( X2 @ ( sK8 @ X4 @ X2 ) )
= ( sK2 @ X2 ) )
& ( sK0 @ ( sK8 @ X4 @ X2 ) ) ) )
| ( $true
= ( sK0 @ ( sK3 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: a > a,X4: a] :
( ( $true
= ( sK0 @ ( sK3 @ X2 ) ) )
| ( $true
= ( X4
= ( sK8 @ X4 @ X2 ) ) )
| ( $true
= ( ( ( X2 @ ( sK8 @ X4 @ X2 ) )
= ( sK2 @ X2 ) )
& ( sK0 @ ( sK8 @ X4 @ X2 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f134,plain,
! [X0: a,X1: a > a] :
( ( ( sK8 @ X0 @ X1 )
= ( sK4 @ ( sK5 @ ( sK8 @ X0 @ X1 ) ) ) )
| ( ( sK8 @ X0 @ X1 )
= X0 )
| ( ( sK0 @ ( sK3 @ X1 ) )
= $true ) ),
inference(equality_resolution,[status(thm)],[f101]) ).
thf(f101,plain,
! [X2: a,X0: a,X1: a > a] :
( ( ( sK5 @ ( sK8 @ X0 @ X1 ) )
!= X2 )
| ( ( sK4 @ X2 )
= ( sK8 @ X0 @ X1 ) )
| ( ( sK8 @ X0 @ X1 )
= X0 )
| ( ( sK0 @ ( sK3 @ X1 ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
! [X2: a,X0: a,X1: a > a] :
( ( $true
= ( ( sK4 @ X2 )
= ( sK8 @ X0 @ X1 ) ) )
| ( ( sK8 @ X0 @ X1 )
= X0 )
| ( ( sK0 @ ( sK3 @ X1 ) )
= $true )
| ( ( sK5 @ ( sK8 @ X0 @ X1 ) )
!= X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
! [X2: a,X0: a,X1: a > a] :
( ( ( ( sK5 @ ( sK8 @ X0 @ X1 ) )
= X2 )
= $false )
| ( $true
= ( ( sK4 @ X2 )
= ( sK8 @ X0 @ X1 ) ) )
| ( ( sK8 @ X0 @ X1 )
= X0 )
| ( ( sK0 @ ( sK3 @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
! [X2: a,X0: a,X1: a > a] :
( ( ( sK0 @ ( sK3 @ X1 ) )
= $true )
| ( ( sK8 @ X0 @ X1 )
= X0 )
| ( ( ( ( sK4 @ X2 )
= ( sK8 @ X0 @ X1 ) )
& ( sK1 @ X2 ) )
= $true )
| ( ( ( sK5 @ ( sK8 @ X0 @ X1 ) )
= X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
! [X2: a,X0: a,X1: a > a] :
( ( ( sK0 @ ( sK3 @ X1 ) )
= $true )
| ( ( ( sK5 @ ( sK8 @ X0 @ X1 ) )
= X2 )
= ( ( ( sK4 @ X2 )
= ( sK8 @ X0 @ X1 ) )
& ( sK1 @ X2 ) ) )
| ( ( sK8 @ X0 @ X1 )
= X0 ) ),
inference(beta_eta_normalization,[status(thm)],[f94]) ).
thf(f94,plain,
! [X2: a,X0: a,X1: a > a] :
( ( ( ^ [Y0: a] :
( ( ( sK4 @ Y0 )
= ( sK8 @ X0 @ X1 ) )
& ( sK1 @ Y0 ) )
@ X2 )
= ( ( sK5 @ ( sK8 @ X0 @ X1 ) )
= X2 ) )
| ( ( sK0 @ ( sK3 @ X1 ) )
= $true )
| ( ( sK8 @ X0 @ X1 )
= X0 ) ),
inference(argument_congruence,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: a,X1: a > a] :
( ( ( ^ [Y0: a] :
( ( ( sK4 @ Y0 )
= ( sK8 @ X0 @ X1 ) )
& ( sK1 @ Y0 ) ) )
= ( (=) @ ( sK5 @ ( sK8 @ X0 @ X1 ) ) ) )
| ( ( sK0 @ ( sK3 @ X1 ) )
= $true )
| ( ( sK8 @ X0 @ X1 )
= X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: a,X1: a > a] :
( ( $true != $true )
| ( ( sK8 @ X0 @ X1 )
= X0 )
| ( ( sK0 @ ( sK3 @ X1 ) )
= $true )
| ( ( ^ [Y0: a] :
( ( ( sK4 @ Y0 )
= ( sK8 @ X0 @ X1 ) )
& ( sK1 @ Y0 ) ) )
= ( (=) @ ( sK5 @ ( sK8 @ X0 @ X1 ) ) ) ) ),
inference(superposition,[status(thm)],[f23,f34]) ).
thf(f34,plain,
! [X2: a > a,X4: a] :
( ( ( sK0 @ ( sK8 @ X4 @ X2 ) )
= $true )
| ( $true
= ( sK0 @ ( sK3 @ X2 ) ) )
| ( ( sK8 @ X4 @ X2 )
= X4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f719,plain,
~ spl6_5,
inference(avatar_contradiction_clause,[status(thm)],[f718]) ).
thf(f718,plain,
( $false
| ~ spl6_5 ),
inference(trivial_inequality_removal,[status(thm)],[f717]) ).
thf(f717,plain,
( ( $true = $false )
| ~ spl6_5 ),
inference(backward_demodulation,[status(thm)],[f72,f716]) ).
thf(f716,plain,
( ( ( sK0 @ ( sK4 @ ( sK2 @ sK5 ) ) )
= $false )
| ~ spl6_5 ),
inference(subsumption_resolution,[status(thm)],[f715,f382]) ).
thf(f715,plain,
( ( ( sK2 @ sK5 )
!= ( sK5 @ ( sK4 @ ( sK2 @ sK5 ) ) ) )
| ( ( sK0 @ ( sK4 @ ( sK2 @ sK5 ) ) )
= $false )
| ~ spl6_5 ),
inference(subsumption_resolution,[status(thm)],[f714,f311]) ).
thf(f311,plain,
( ( $true
= ( sK1 @ ( sK5 @ ( sK3 @ sK5 ) ) ) )
| ~ spl6_5 ),
inference(equality_resolution,[status(thm)],[f305]) ).
thf(f305,plain,
( ! [X1: a] :
( ( ( sK5 @ ( sK3 @ sK5 ) )
!= X1 )
| ( $true
= ( sK1 @ X1 ) ) )
| ~ spl6_5 ),
inference(binary_proxy_clausification,[status(thm)],[f304]) ).
thf(f304,plain,
( ! [X1: a] :
( ( $true
= ( ( ( sK4 @ X1 )
= ( sK3 @ sK5 ) )
& ( sK1 @ X1 ) ) )
| ( ( sK5 @ ( sK3 @ sK5 ) )
!= X1 ) )
| ~ spl6_5 ),
inference(equality_proxy_clausification,[status(thm)],[f303]) ).
thf(f303,plain,
( ! [X1: a] :
( ( ( ( sK5 @ ( sK3 @ sK5 ) )
= X1 )
= $false )
| ( $true
= ( ( ( sK4 @ X1 )
= ( sK3 @ sK5 ) )
& ( sK1 @ X1 ) ) ) )
| ~ spl6_5 ),
inference(binary_proxy_clausification,[status(thm)],[f301]) ).
thf(f301,plain,
( ! [X1: a] :
( ( ( sK5 @ ( sK3 @ sK5 ) )
= X1 )
= ( ( ( sK4 @ X1 )
= ( sK3 @ sK5 ) )
& ( sK1 @ X1 ) ) )
| ~ spl6_5 ),
inference(beta_eta_normalization,[status(thm)],[f300]) ).
thf(f300,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( ( sK4 @ Y0 )
= ( sK3 @ sK5 ) )
& ( sK1 @ Y0 ) )
@ X1 )
= ( ( sK5 @ ( sK3 @ sK5 ) )
= X1 ) )
| ~ spl6_5 ),
inference(argument_congruence,[status(thm)],[f141]) ).
thf(f141,plain,
( ( ( ^ [Y0: a] :
( ( ( sK4 @ Y0 )
= ( sK3 @ sK5 ) )
& ( sK1 @ Y0 ) ) )
= ( (=) @ ( sK5 @ ( sK3 @ sK5 ) ) ) )
| ~ spl6_5 ),
inference(trivial_inequality_removal,[status(thm)],[f140]) ).
thf(f140,plain,
( ( ( ^ [Y0: a] :
( ( ( sK4 @ Y0 )
= ( sK3 @ sK5 ) )
& ( sK1 @ Y0 ) ) )
= ( (=) @ ( sK5 @ ( sK3 @ sK5 ) ) ) )
| ( $true != $true )
| ~ spl6_5 ),
inference(superposition,[status(thm)],[f23,f118]) ).
thf(f118,plain,
( ( $true
= ( sK0 @ ( sK3 @ sK5 ) ) )
| ~ spl6_5 ),
inference(avatar_component_clause,[status(thm)],[f116]) ).
thf(f714,plain,
( ( $true
!= ( sK1 @ ( sK5 @ ( sK3 @ sK5 ) ) ) )
| ( ( sK2 @ sK5 )
!= ( sK5 @ ( sK4 @ ( sK2 @ sK5 ) ) ) )
| ( ( sK0 @ ( sK4 @ ( sK2 @ sK5 ) ) )
= $false )
| ~ spl6_5 ),
inference(trivial_inequality_removal,[status(thm)],[f707]) ).
thf(f707,plain,
( ( ( sK0 @ ( sK4 @ ( sK2 @ sK5 ) ) )
= $false )
| ( ( sK2 @ sK5 )
!= ( sK5 @ ( sK4 @ ( sK2 @ sK5 ) ) ) )
| ( ( sK4 @ ( sK2 @ sK5 ) )
!= ( sK4 @ ( sK2 @ sK5 ) ) )
| ( $true
!= ( sK1 @ ( sK5 @ ( sK3 @ sK5 ) ) ) )
| ~ spl6_5 ),
inference(superposition,[status(thm)],[f45,f700]) ).
thf(f700,plain,
( ( ( sK4 @ ( sK2 @ sK5 ) )
= ( sK9 @ ( sK4 @ ( sK2 @ sK5 ) ) @ sK5 ) )
| ~ spl6_5 ),
inference(equality_resolution,[status(thm)],[f693]) ).
thf(f693,plain,
( ! [X0: a] :
( ( ( sK4 @ ( sK2 @ sK5 ) )
!= X0 )
| ( ( sK9 @ X0 @ sK5 )
= X0 ) )
| ~ spl6_5 ),
inference(trivial_inequality_removal,[status(thm)],[f692]) ).
thf(f692,plain,
( ! [X0: a] :
( ( ( sK9 @ X0 @ sK5 )
= X0 )
| ( $true = $false )
| ( ( sK4 @ ( sK2 @ sK5 ) )
!= X0 ) )
| ~ spl6_5 ),
inference(forward_demodulation,[status(thm)],[f691,f72]) ).
thf(f691,plain,
( ! [X0: a] :
( ( ( sK0 @ ( sK4 @ ( sK2 @ sK5 ) ) )
= $false )
| ( ( sK4 @ ( sK2 @ sK5 ) )
!= X0 )
| ( ( sK9 @ X0 @ sK5 )
= X0 ) )
| ~ spl6_5 ),
inference(subsumption_resolution,[status(thm)],[f690,f382]) ).
thf(f690,plain,
( ! [X0: a] :
( ( ( sK2 @ sK5 )
!= ( sK5 @ ( sK4 @ ( sK2 @ sK5 ) ) ) )
| ( ( sK9 @ X0 @ sK5 )
= X0 )
| ( ( sK4 @ ( sK2 @ sK5 ) )
!= X0 )
| ( ( sK0 @ ( sK4 @ ( sK2 @ sK5 ) ) )
= $false ) )
| ~ spl6_5 ),
inference(subsumption_resolution,[status(thm)],[f681,f311]) ).
thf(f681,plain,
( ! [X0: a] :
( ( ( sK9 @ X0 @ sK5 )
= X0 )
| ( ( sK4 @ ( sK2 @ sK5 ) )
!= X0 )
| ( $true
!= ( sK1 @ ( sK5 @ ( sK3 @ sK5 ) ) ) )
| ( ( sK2 @ sK5 )
!= ( sK5 @ ( sK4 @ ( sK2 @ sK5 ) ) ) )
| ( ( sK0 @ ( sK4 @ ( sK2 @ sK5 ) ) )
= $false ) )
| ~ spl6_5 ),
inference(superposition,[status(thm)],[f45,f676]) ).
thf(f676,plain,
( ! [X0: a] :
( ( ( sK4 @ ( sK2 @ sK5 ) )
= ( sK9 @ X0 @ sK5 ) )
| ( ( sK9 @ X0 @ sK5 )
= X0 ) )
| ~ spl6_5 ),
inference(equality_resolution,[status(thm)],[f671]) ).
thf(f671,plain,
( ! [X0: a,X1: a] :
( ( ( sK2 @ sK5 )
!= X1 )
| ( ( sK9 @ X0 @ sK5 )
= ( sK4 @ X1 ) )
| ( ( sK9 @ X0 @ sK5 )
= X0 ) )
| ~ spl6_5 ),
inference(duplicate_literal_removal,[status(thm)],[f669]) ).
thf(f669,plain,
( ! [X0: a,X1: a] :
( ( ( sK9 @ X0 @ sK5 )
= ( sK4 @ X1 ) )
| ( ( sK9 @ X0 @ sK5 )
= X0 )
| ( ( sK9 @ X0 @ sK5 )
= X0 )
| ( ( sK2 @ sK5 )
!= X1 ) )
| ~ spl6_5 ),
inference(superposition,[status(thm)],[f581,f317]) ).
thf(f317,plain,
( ! [X0: a] :
( ( ( sK2 @ sK5 )
= ( sK5 @ ( sK9 @ X0 @ sK5 ) ) )
| ( ( sK9 @ X0 @ sK5 )
= X0 ) )
| ~ spl6_5 ),
inference(trivial_inequality_removal,[status(thm)],[f313]) ).
thf(f313,plain,
( ! [X0: a] :
( ( ( sK2 @ sK5 )
= ( sK5 @ ( sK9 @ X0 @ sK5 ) ) )
| ( ( sK9 @ X0 @ sK5 )
= X0 )
| ( $true != $true ) )
| ~ spl6_5 ),
inference(superposition,[status(thm)],[f49,f311]) ).
thf(f49,plain,
! [X2: a > a,X4: a] :
( ( ( sK1 @ ( X2 @ ( sK3 @ X2 ) ) )
!= $true )
| ( ( X2 @ ( sK9 @ X4 @ X2 ) )
= ( sK2 @ X2 ) )
| ( ( sK9 @ X4 @ X2 )
= X4 ) ),
inference(equality_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
! [X2: a > a,X4: a] :
( ( ( X4
= ( sK9 @ X4 @ X2 ) )
= $true )
| ( ( X2 @ ( sK9 @ X4 @ X2 ) )
= ( sK2 @ X2 ) )
| ( ( sK1 @ ( X2 @ ( sK3 @ X2 ) ) )
!= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X2: a > a,X4: a] :
( ( $true
= ( ( X2 @ ( sK9 @ X4 @ X2 ) )
= ( sK2 @ X2 ) ) )
| ( ( X4
= ( sK9 @ X4 @ X2 ) )
= $true )
| ( ( sK1 @ ( X2 @ ( sK3 @ X2 ) ) )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: a > a,X4: a] :
( ( ( sK1 @ ( X2 @ ( sK3 @ X2 ) ) )
!= $true )
| ( $true
= ( ( ( X2 @ ( sK9 @ X4 @ X2 ) )
= ( sK2 @ X2 ) )
& ( sK0 @ ( sK9 @ X4 @ X2 ) ) ) )
| ( ( X4
= ( sK9 @ X4 @ X2 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: a > a,X4: a] :
( ( ( X4
= ( sK9 @ X4 @ X2 ) )
!= ( ( ( X2 @ ( sK9 @ X4 @ X2 ) )
= ( sK2 @ X2 ) )
& ( sK0 @ ( sK9 @ X4 @ X2 ) ) ) )
| ( ( sK1 @ ( X2 @ ( sK3 @ X2 ) ) )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: a > a,X4: a] :
( ( ( X4
= ( sK9 @ X4 @ X2 ) )
!= ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
= ( sK2 @ X2 ) )
& ( sK0 @ Y0 ) )
@ ( sK9 @ X4 @ X2 ) ) )
| ( ( sK1 @ ( X2 @ ( sK3 @ X2 ) ) )
!= $true ) ),
inference(negative_extensionality,[status(thm)],[f21]) ).
thf(f21,plain,
! [X2: a > a,X4: a] :
( ( ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
= ( sK2 @ X2 ) )
& ( sK0 @ Y0 ) ) )
!= ( (=) @ X4 ) )
| ( ( sK1 @ ( X2 @ ( sK3 @ X2 ) ) )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
! [X2: a > a,X4: a] :
( ( ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X4 )
!= ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
= ( sK2 @ X2 ) )
& ( sK0 @ Y0 ) ) ) )
| ( ( sK1 @ ( X2 @ ( sK3 @ X2 ) ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f581,plain,
( ! [X0: a,X1: a] :
( ( ( sK5 @ ( sK9 @ X0 @ sK5 ) )
!= X1 )
| ( ( sK9 @ X0 @ sK5 )
= ( sK4 @ X1 ) )
| ( ( sK9 @ X0 @ sK5 )
= X0 ) )
| ~ spl6_5 ),
inference(equality_proxy_clausification,[status(thm)],[f580]) ).
thf(f580,plain,
( ! [X0: a,X1: a] :
( ( $true
= ( ( sK4 @ X1 )
= ( sK9 @ X0 @ sK5 ) ) )
| ( ( sK9 @ X0 @ sK5 )
= X0 )
| ( ( sK5 @ ( sK9 @ X0 @ sK5 ) )
!= X1 ) )
| ~ spl6_5 ),
inference(binary_proxy_clausification,[status(thm)],[f578]) ).
thf(f578,plain,
( ! [X0: a,X1: a] :
( ( ( sK9 @ X0 @ sK5 )
= X0 )
| ( ( sK5 @ ( sK9 @ X0 @ sK5 ) )
!= X1 )
| ( $true
= ( ( ( sK4 @ X1 )
= ( sK9 @ X0 @ sK5 ) )
& ( sK1 @ X1 ) ) ) )
| ~ spl6_5 ),
inference(equality_proxy_clausification,[status(thm)],[f577]) ).
thf(f577,plain,
( ! [X0: a,X1: a] :
( ( ( ( sK5 @ ( sK9 @ X0 @ sK5 ) )
= X1 )
= $false )
| ( $true
= ( ( ( sK4 @ X1 )
= ( sK9 @ X0 @ sK5 ) )
& ( sK1 @ X1 ) ) )
| ( ( sK9 @ X0 @ sK5 )
= X0 ) )
| ~ spl6_5 ),
inference(binary_proxy_clausification,[status(thm)],[f575]) ).
thf(f575,plain,
( ! [X0: a,X1: a] :
( ( ( sK9 @ X0 @ sK5 )
= X0 )
| ( ( ( sK5 @ ( sK9 @ X0 @ sK5 ) )
= X1 )
= ( ( ( sK4 @ X1 )
= ( sK9 @ X0 @ sK5 ) )
& ( sK1 @ X1 ) ) ) )
| ~ spl6_5 ),
inference(beta_eta_normalization,[status(thm)],[f574]) ).
thf(f574,plain,
( ! [X0: a,X1: a] :
( ( ( ( sK5 @ ( sK9 @ X0 @ sK5 ) )
= X1 )
= ( ^ [Y0: a] :
( ( ( sK4 @ Y0 )
= ( sK9 @ X0 @ sK5 ) )
& ( sK1 @ Y0 ) )
@ X1 ) )
| ( ( sK9 @ X0 @ sK5 )
= X0 ) )
| ~ spl6_5 ),
inference(argument_congruence,[status(thm)],[f471]) ).
thf(f471,plain,
( ! [X0: a] :
( ( ( (=) @ ( sK5 @ ( sK9 @ X0 @ sK5 ) ) )
= ( ^ [Y0: a] :
( ( ( sK4 @ Y0 )
= ( sK9 @ X0 @ sK5 ) )
& ( sK1 @ Y0 ) ) ) )
| ( ( sK9 @ X0 @ sK5 )
= X0 ) )
| ~ spl6_5 ),
inference(trivial_inequality_removal,[status(thm)],[f470]) ).
thf(f470,plain,
( ! [X0: a] :
( ( $true != $true )
| ( ( (=) @ ( sK5 @ ( sK9 @ X0 @ sK5 ) ) )
= ( ^ [Y0: a] :
( ( ( sK4 @ Y0 )
= ( sK9 @ X0 @ sK5 ) )
& ( sK1 @ Y0 ) ) ) )
| ( ( sK9 @ X0 @ sK5 )
= X0 ) )
| ~ spl6_5 ),
inference(superposition,[status(thm)],[f23,f318]) ).
thf(f318,plain,
( ! [X0: a] :
( ( ( sK0 @ ( sK9 @ X0 @ sK5 ) )
= $true )
| ( ( sK9 @ X0 @ sK5 )
= X0 ) )
| ~ spl6_5 ),
inference(trivial_inequality_removal,[status(thm)],[f314]) ).
thf(f314,plain,
( ! [X0: a] :
( ( ( sK0 @ ( sK9 @ X0 @ sK5 ) )
= $true )
| ( $true != $true )
| ( ( sK9 @ X0 @ sK5 )
= X0 ) )
| ~ spl6_5 ),
inference(superposition,[status(thm)],[f50,f311]) ).
thf(f50,plain,
! [X2: a > a,X4: a] :
( ( ( sK1 @ ( X2 @ ( sK3 @ X2 ) ) )
!= $true )
| ( $true
= ( sK0 @ ( sK9 @ X4 @ X2 ) ) )
| ( ( sK9 @ X4 @ X2 )
= X4 ) ),
inference(equality_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: a > a,X4: a] :
( ( ( sK1 @ ( X2 @ ( sK3 @ X2 ) ) )
!= $true )
| ( ( X4
= ( sK9 @ X4 @ X2 ) )
= $true )
| ( $true
= ( sK0 @ ( sK9 @ X4 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f45,plain,
! [X2: a > a,X4: a] :
( ( ( X2 @ ( sK9 @ X4 @ X2 ) )
!= ( sK2 @ X2 ) )
| ( ( sK9 @ X4 @ X2 )
!= X4 )
| ( $false
= ( sK0 @ ( sK9 @ X4 @ X2 ) ) )
| ( ( sK1 @ ( X2 @ ( sK3 @ X2 ) ) )
!= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: a > a,X4: a] :
( ( $false
= ( ( X2 @ ( sK9 @ X4 @ X2 ) )
= ( sK2 @ X2 ) ) )
| ( ( sK1 @ ( X2 @ ( sK3 @ X2 ) ) )
!= $true )
| ( $false
= ( sK0 @ ( sK9 @ X4 @ X2 ) ) )
| ( ( sK9 @ X4 @ X2 )
!= X4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: a > a,X4: a] :
( ( ( sK9 @ X4 @ X2 )
!= X4 )
| ( ( sK1 @ ( X2 @ ( sK3 @ X2 ) ) )
!= $true )
| ( $false
= ( ( ( X2 @ ( sK9 @ X4 @ X2 ) )
= ( sK2 @ X2 ) )
& ( sK0 @ ( sK9 @ X4 @ X2 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: a > a,X4: a] :
( ( ( X4
= ( sK9 @ X4 @ X2 ) )
= $false )
| ( ( sK1 @ ( X2 @ ( sK3 @ X2 ) ) )
!= $true )
| ( $false
= ( ( ( X2 @ ( sK9 @ X4 @ X2 ) )
= ( sK2 @ X2 ) )
& ( sK0 @ ( sK9 @ X4 @ X2 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV089^5 : 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 : n020.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 12:40:12 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
% 0.33/0.49 ---- Original DTF file ---
% 0.33/0.49 thf(spec,logic,$$dhol).
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 % File : SEV089^5 : TPTP v9.2.1. Released v4.0.0.
% 0.33/0.49 % Domain : Set Theory (Relations)
% 0.33/0.49 % Problem : TPS problem from RELN-THMS
% 0.33/0.49 % Version : Especial.
% 0.33/0.49 % English :
% 0.33/0.49
% 0.33/0.49 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.33/0.49 % Source : [Bro09]
% 0.33/0.49 % Names : tps_1003 [Bro09]
% 0.33/0.49
% 0.33/0.49 % Status : Theorem
% 0.33/0.49 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.60 v8.2.0, 0.54 v8.1.0, 0.55 v7.5.0, 0.57 v7.4.0, 0.78 v7.2.0, 0.75 v7.0.0, 0.71 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 1.00 v6.1.0, 0.86 v5.5.0, 0.83 v5.4.0, 0.80 v5.1.0, 1.00 v5.0.0, 0.80 v4.1.0, 0.67 v4.0.0
% 0.33/0.49 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.33/0.49 % Number of atoms : 6 ( 6 equ; 0 cnn)
% 0.33/0.49 % Maximal formula atoms : 2 ( 6 avg)
% 0.33/0.49 % Number of connectives : 23 ( 0 ~; 0 |; 4 &; 14 @)
% 0.33/0.49 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.33/0.49 % Maximal formula depth : 10 ( 10 avg)
% 0.33/0.49 % Number of types : 2 ( 1 usr)
% 0.33/0.49 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.33/0.49 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.33/0.49 % Number of variables : 16 ( 6 ^; 6 !; 4 ?; 16 :)
% 0.33/0.49 % SPC : TH0_THM_EQU_NAR
% 0.33/0.49
% 0.33/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.33/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.33/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.33/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 thf(a_type,type,
% 0.33/0.49 a: $tType ).
% 0.33/0.49
% 0.33/0.49 thf(cEQP_1B_pme,conjecture,
% 0.33/0.49 ! [Xx: a > $o,Xy: a > $o] :
% 0.33/0.49 ( ? [Xs: a > a] :
% 0.33/0.49 ( ! [Xx0: a] :
% 0.33/0.49 ( ( Xx @ Xx0 )
% 0.33/0.49 => ( Xy @ ( Xs @ Xx0 ) ) )
% 0.33/0.49 & ! [Xy0: a] :
% 0.33/0.49 ( ( Xy @ Xy0 )
% 0.33/0.49 => ? [Xy_38: a] :
% 0.33/0.49 ( ( ^ [Xx0: a] :
% 0.33/0.49 ( ( Xx @ Xx0 )
% 0.33/0.49 & ( Xy0
% 0.33/0.49 = ( Xs @ Xx0 ) ) ) )
% 0.33/0.49 = ( ^ [Xx: a,Xy: a] : ( Xx = Xy )
% 0.33/0.49 @ Xy_38 ) ) ) )
% 0.33/0.49 => ? [Xs: a > a] :
% 0.33/0.49 ( ! [Xx0: a] :
% 0.33/0.49 ( ( Xy @ Xx0 )
% 0.33/0.49 => ( Xx @ ( Xs @ Xx0 ) ) )
% 0.33/0.49 & ! [Xy0: a] :
% 0.33/0.49 ( ( Xx @ Xy0 )
% 0.33/0.49 => ? [Xy_39: a] :
% 0.33/0.49 ( ( ^ [Xx0: a] :
% 0.33/0.49 ( ( Xy @ Xx0 )
% 0.33/0.49 & ( Xy0
% 0.33/0.49 = ( Xs @ Xx0 ) ) ) )
% 0.33/0.49 = ( ^ [Xx: a,Xy: a] : ( Xx = Xy )
% 0.33/0.49 @ Xy_39 ) ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 ------------------------
% 1.48/1.25 ---- Embedded in THF ---
% 1.48/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.25 %%% Generated on Tue Feb 24 12:40:13 EST 2026
% 1.48/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.25 %%% Logic specification used:
% 1.48/1.25 %%% thf(spec, logic, $$dhol).
% 1.48/1.25
% 1.48/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.i5qrV6Zz6N/DTF2DTF6063.p
% See solution above
% 1.48/1.25 ------------------------
% 1.48/1.26 ---- Cleaned THF ---
% 1.48/1.26 thf(a_type,type,
% 1.48/1.26 a: $tType ).
% 1.48/1.26
% 1.48/1.26 thf(cEQP_1B_pme,conjecture,
% 1.48/1.26 ! [Xx: a > $o,Xy: a > $o] :
% 1.48/1.26 ( ? [Xs: a > a] :
% 1.48/1.26 ( ! [Xx0: a] :
% 1.48/1.26 ( ( Xx @ Xx0 )
% 1.48/1.26 => ( Xy @ ( Xs @ Xx0 ) ) )
% 1.48/1.26 & ! [Xy0: a] :
% 1.48/1.26 ( ( Xy @ Xy0 )
% 1.48/1.26 => ? [Xy_38: a] :
% 1.48/1.26 ( ( ^ [Xx0: a] :
% 1.48/1.26 ( ( Xx @ Xx0 )
% 1.48/1.26 & ( Xy0
% 1.48/1.26 = ( Xs @ Xx0 ) ) ) )
% 1.48/1.26 = ( ^ [Xx: a,Xy: a] : ( Xx = Xy )
% 1.48/1.26 @ Xy_38 ) ) ) )
% 1.48/1.26 => ? [Xs: a > a] :
% 1.48/1.26 ( ! [Xx0: a] :
% 1.48/1.26 ( ( Xy @ Xx0 )
% 1.48/1.26 => ( Xx @ ( Xs @ Xx0 ) ) )
% 1.48/1.26 & ! [Xy0: a] :
% 1.48/1.26 ( ( Xx @ Xy0 )
% 1.48/1.26 => ? [Xy_39: a] :
% 1.48/1.26 ( ( ^ [Xx0: a] :
% 1.48/1.26 ( ( Xy @ Xx0 )
% 1.48/1.26 & ( Xy0
% 1.48/1.26 = ( Xs @ Xx0 ) ) ) )
% 1.48/1.26 = ( ^ [Xx: a,Xy: a] : ( Xx = Xy )
% 1.48/1.26 @ Xy_39 ) ) ) ) ) ).
% 1.48/1.26 ------------------------
% 1.48/1.27 % (6175)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6063 for (3000ds/183Mi)
% 1.48/1.28 % (6181)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6063 for (3000ds/18Mi)
% 1.48/1.28 % (6178)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6063 for (3000ds/2Mi)
% 1.48/1.28 % (6179)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_6063 for (3000ds/2Mi)
% 1.48/1.28 % (6180)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_6063 for (3000ds/275Mi)
% 1.48/1.28 % (6177)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_6063 for (3000ds/27Mi)
% 1.48/1.28 % (6178)Instruction limit reached!
% 1.48/1.28 % (6178)------------------------------
% 1.48/1.28 % (6178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (6178)Termination reason: Unknown
% 1.48/1.28 % (6178)Termination phase: Preprocessing 3
% 1.48/1.28 % (6179)Instruction limit reached!
% 1.48/1.28 % (6179)------------------------------
% 1.48/1.28 % (6179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (6179)Termination reason: Unknown
% 1.48/1.28 % (6179)Termination phase: Property scanning
% 1.48/1.28
% 1.48/1.28 % (6179)Memory used [KB]: 895
% 1.48/1.28 % (6179)Time elapsed: 0.003 s
% 1.48/1.28 % (6179)Instructions burned: 2 (million)
% 1.48/1.28 % (6179)------------------------------
% 1.48/1.28 % (6179)------------------------------
% 1.48/1.28
% 1.48/1.28 % (6178)Memory used [KB]: 1023
% 1.48/1.28 % (6178)Time elapsed: 0.003 s
% 1.48/1.28 % (6178)Instructions burned: 2 (million)
% 1.48/1.28 % (6178)------------------------------
% 1.48/1.28 % (6178)------------------------------
% 1.48/1.28 % (6176)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_6063 for (3000ds/4Mi)
% 1.48/1.28 % (6176)Instruction limit reached!
% 1.48/1.28 % (6176)------------------------------
% 1.48/1.28 % (6176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (6176)Termination reason: Unknown
% 1.48/1.28 % (6176)Termination phase: Saturation
% 1.48/1.28
% 1.48/1.28 % (6176)Memory used [KB]: 5500
% 1.48/1.28 % (6176)Time elapsed: 0.005 s
% 1.48/1.28 % (6176)Instructions burned: 4 (million)
% 1.48/1.28 % (6176)------------------------------
% 1.48/1.28 % (6176)------------------------------
% 1.48/1.29 % (6181)Instruction limit reached!
% 1.48/1.29 % (6181)------------------------------
% 1.48/1.29 % (6181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (6181)Termination reason: Unknown
% 1.48/1.29 % (6181)Termination phase: Saturation
% 1.48/1.29
% 1.48/1.29 % (6181)Memory used [KB]: 5628
% 1.48/1.29 % (6181)Time elapsed: 0.012 s
% 1.48/1.29 % (6181)Instructions burned: 18 (million)
% 1.48/1.29 % (6181)------------------------------
% 1.48/1.29 % (6181)------------------------------
% 1.48/1.29 % (6177)Instruction limit reached!
% 1.48/1.29 % (6177)------------------------------
% 1.48/1.29 % (6177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (6177)Termination reason: Unknown
% 1.48/1.29 % (6177)Termination phase: Saturation
% 1.48/1.29
% 1.48/1.29 % (6177)Memory used [KB]: 5628
% 1.48/1.29 % (6177)Time elapsed: 0.018 s
% 1.48/1.29 % (6177)Instructions burned: 27 (million)
% 1.48/1.29 % (6177)------------------------------
% 1.48/1.29 % (6177)------------------------------
% 1.59/1.30 % (6182)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6063 for (2999ds/3Mi)
% 1.59/1.30 % (6183)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_6063 for (2999ds/37Mi)
% 1.59/1.30 % (6182)Instruction limit reached!
% 1.59/1.30 % (6182)------------------------------
% 1.59/1.30 % (6182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.30 % (6182)Termination reason: Unknown
% 1.59/1.30 % (6182)Termination phase: Saturation
% 1.59/1.30
% 1.59/1.30 % (6182)Memory used [KB]: 5500
% 1.59/1.30 % (6182)Time elapsed: 0.004 s
% 1.59/1.30 % (6182)Instructions burned: 3 (million)
% 1.59/1.30 % (6182)------------------------------
% 1.59/1.30 % (6182)------------------------------
% 1.59/1.31 % (6185)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_6063 for (2999ds/3Mi)
% 1.59/1.31 % (6184)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_6063 for (2999ds/15Mi)
% 1.59/1.31 % (6185)Instruction limit reached!
% 1.59/1.31 % (6185)------------------------------
% 1.59/1.31 % (6185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.31 % (6185)Termination reason: Unknown
% 1.59/1.31 % (6185)Termination phase: Saturation
% 1.59/1.31
% 1.59/1.31 % (6185)Memory used [KB]: 5500
% 1.59/1.31 % (6185)Time elapsed: 0.004 s
% 1.59/1.31 % (6185)Instructions burned: 3 (million)
% 1.59/1.31 % (6185)------------------------------
% 1.59/1.31 % (6185)------------------------------
% 1.59/1.32 % (6184)Instruction limit reached!
% 1.59/1.32 % (6184)------------------------------
% 1.59/1.32 % (6184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (6184)Termination reason: Unknown
% 1.59/1.32 % (6184)Termination phase: Saturation
% 1.59/1.32
% 1.59/1.32 % (6184)Memory used [KB]: 5628
% 1.59/1.32 % (6184)Time elapsed: 0.011 s
% 1.59/1.32 % (6184)Instructions burned: 16 (million)
% 1.59/1.32 % (6184)------------------------------
% 1.59/1.32 % (6184)------------------------------
% 1.59/1.32 % (6187)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_6063 for (2999ds/7Mi)
% 1.59/1.32 % (6183)Instruction limit reached!
% 1.59/1.32 % (6183)------------------------------
% 1.59/1.32 % (6183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (6183)Termination reason: Unknown
% 1.59/1.32 % (6183)Termination phase: Saturation
% 1.59/1.32
% 1.59/1.32 % (6183)Memory used [KB]: 5884
% 1.59/1.32 % (6183)Time elapsed: 0.021 s
% 1.59/1.32 % (6183)Instructions burned: 38 (million)
% 1.59/1.32 % (6183)------------------------------
% 1.59/1.32 % (6183)------------------------------
% 1.59/1.32 % (6187)Instruction limit reached!
% 1.59/1.32 % (6187)------------------------------
% 1.59/1.32 % (6187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (6187)Termination reason: Unknown
% 1.59/1.32 % (6187)Termination phase: Saturation
% 1.59/1.32
% 1.59/1.32 % (6187)Memory used [KB]: 1023
% 1.59/1.32 % (6187)Time elapsed: 0.007 s
% 1.59/1.32 % (6187)Instructions burned: 8 (million)
% 1.59/1.32 % (6187)------------------------------
% 1.59/1.32 % (6187)------------------------------
% 1.59/1.32 % (6186)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_6063 for (2999ds/1041Mi)
% 1.59/1.33 % (6188)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_6063 for (2999ds/16Mi)
% 1.59/1.33 % (6175)Instruction limit reached!
% 1.59/1.33 % (6175)------------------------------
% 1.59/1.33 % (6175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.33 % (6175)Termination reason: Unknown
% 1.59/1.33 % (6175)Termination phase: Saturation
% 1.59/1.33
% 1.59/1.33 % (6175)Memory used [KB]: 5884
% 1.59/1.33 % (6175)Time elapsed: 0.056 s
% 1.59/1.33 % (6175)Instructions burned: 183 (million)
% 1.59/1.33 % (6175)------------------------------
% 1.59/1.33 % (6175)------------------------------
% 1.59/1.33 % (6189)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_6063 for (2999ds/3Mi)
% 1.59/1.33 % (6190)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_6063 for (2999ds/3Mi)
% 1.59/1.33 % (6189)Instruction limit reached!
% 1.59/1.33 % (6189)------------------------------
% 1.59/1.33 % (6189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.33 % (6189)Termination reason: Unknown
% 1.59/1.33 % (6189)Termination phase: Twee Goal Transformation
% 1.59/1.33
% 1.59/1.33 % (6189)Memory used [KB]: 1023
% 1.59/1.33 % (6189)Time elapsed: 0.004 s
% 1.59/1.33 % (6189)Instructions burned: 3 (million)
% 1.59/1.33 % (6189)------------------------------
% 1.59/1.33 % (6189)------------------------------
% 1.59/1.34 % (6190)Instruction limit reached!
% 1.59/1.34 % (6190)------------------------------
% 1.59/1.34 % (6190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.34 % (6190)Termination reason: Unknown
% 1.59/1.34 % (6190)Termination phase: Property scanning
% 1.59/1.34
% 1.59/1.34 % (6190)Memory used [KB]: 1023
% 1.59/1.34 % (6190)Time elapsed: 0.003 s
% 1.59/1.34 % (6190)Instructions burned: 3 (million)
% 1.59/1.34 % (6190)------------------------------
% 1.59/1.34 % (6190)------------------------------
% 1.59/1.34 % (6188)Instruction limit reached!
% 1.59/1.34 % (6188)------------------------------
% 1.59/1.34 % (6188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.34 % (6188)Termination reason: Unknown
% 1.59/1.34 % (6188)Termination phase: Saturation
% 1.59/1.34
% 1.59/1.34 % (6188)Memory used [KB]: 5628
% 1.59/1.34 % (6188)Time elapsed: 0.011 s
% 1.59/1.34 % (6188)Instructions burned: 17 (million)
% 1.59/1.34 % (6188)------------------------------
% 1.59/1.34 % (6188)------------------------------
% 1.59/1.34 % (6191)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_6063 for (2999ds/7Mi)
% 1.59/1.34 % (6192)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_6063 for (2999ds/3Mi)
% 1.59/1.34 % (6192)Instruction limit reached!
% 1.59/1.34 % (6192)------------------------------
% 1.59/1.34 % (6192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.34 % (6192)Termination reason: Unknown
% 1.59/1.34 % (6192)Termination phase: Saturation
% 1.59/1.34
% 1.59/1.34 % (6192)Memory used [KB]: 5500
% 1.59/1.34 % (6192)Time elapsed: 0.003 s
% 1.59/1.34 % (6192)Instructions burned: 5 (million)
% 1.59/1.34 % (6192)------------------------------
% 1.59/1.34 % (6192)------------------------------
% 1.59/1.34 % (6191)Instruction limit reached!
% 1.59/1.34 % (6191)------------------------------
% 1.59/1.34 % (6191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.34 % (6191)Termination reason: Unknown
% 1.59/1.34 % (6191)Termination phase: Saturation
% 1.59/1.34
% 1.59/1.34 % (6191)Memory used [KB]: 5500
% 1.59/1.34 % (6191)Time elapsed: 0.006 s
% 1.59/1.34 % (6191)Instructions burned: 7 (million)
% 1.59/1.34 % (6191)------------------------------
% 1.59/1.34 % (6191)------------------------------
% 1.59/1.35 % (6196)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_6063 for (2999ds/6Mi)
% 1.59/1.35 % (6196)Instruction limit reached!
% 1.59/1.35 % (6196)------------------------------
% 1.59/1.35 % (6196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (6196)Termination reason: Unknown
% 1.59/1.35 % (6196)Termination phase: Saturation
% 1.59/1.35
% 1.59/1.35 % (6196)Memory used [KB]: 5500
% 1.59/1.35 % (6196)Time elapsed: 0.004 s
% 1.59/1.35 % (6196)Instructions burned: 6 (million)
% 1.59/1.35 % (6196)------------------------------
% 1.59/1.35 % (6196)------------------------------
% 1.59/1.35 % (6195)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_6063 for (2999ds/710Mi)
% 1.59/1.35 % (6193)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_6063 for (2999ds/4Mi)
% 1.59/1.35 % (6194)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_6063 for (2999ds/18Mi)
% 1.59/1.35 % (6193)Instruction limit reached!
% 1.59/1.35 % (6193)------------------------------
% 1.59/1.35 % (6193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (6193)Termination reason: Unknown
% 1.59/1.35 % (6193)Termination phase: Saturation
% 1.59/1.35
% 1.59/1.35 % (6193)Memory used [KB]: 5500
% 1.59/1.35 % (6193)Time elapsed: 0.005 s
% 1.59/1.35 % (6193)Instructions burned: 4 (million)
% 1.59/1.35 % (6193)------------------------------
% 1.59/1.35 % (6193)------------------------------
% 1.59/1.36 % (6197)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_6063 for (2999ds/902Mi)
% 1.59/1.36 % (6198)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_6063 for (2999ds/21Mi)
% 1.59/1.36 % (6194)Instruction limit reached!
% 1.59/1.36 % (6194)------------------------------
% 1.59/1.36 % (6194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.36 % (6194)Termination reason: Unknown
% 1.59/1.36 % (6194)Termination phase: Saturation
% 1.59/1.36
% 1.59/1.36 % (6194)Memory used [KB]: 5628
% 1.59/1.36 % (6194)Time elapsed: 0.012 s
% 1.59/1.36 % (6194)Instructions burned: 19 (million)
% 1.59/1.36 % (6194)------------------------------
% 1.59/1.36 % (6194)------------------------------
% 1.59/1.37 % (6198)Instruction limit reached!
% 1.59/1.37 % (6198)------------------------------
% 1.59/1.37 % (6198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.37 % (6198)Termination reason: Unknown
% 1.59/1.37 % (6198)Termination phase: Saturation
% 1.59/1.37
% 1.59/1.37 % (6198)Memory used [KB]: 5628
% 1.59/1.37 % (6198)Time elapsed: 0.009 s
% 1.59/1.37 % (6198)Instructions burned: 21 (million)
% 1.59/1.37 % (6198)------------------------------
% 1.59/1.37 % (6198)------------------------------
% 1.59/1.37 % (6199)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_6063 for (2999ds/5Mi)
% 1.59/1.38 % (6199)Instruction limit reached!
% 1.59/1.38 % (6199)------------------------------
% 1.59/1.38 % (6199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.38 % (6199)Termination reason: Unknown
% 1.59/1.38 % (6199)Termination phase: Saturation
% 1.59/1.38
% 1.59/1.38 % (6199)Memory used [KB]: 5500
% 1.59/1.38 % (6199)Time elapsed: 0.005 s
% 1.59/1.38 % (6199)Instructions burned: 6 (million)
% 1.59/1.38 % (6199)------------------------------
% 1.59/1.38 % (6199)------------------------------
% 1.59/1.38 % (6201)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_6063 for (2999ds/377Mi)
% 1.59/1.38 % (6200)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_6063 for (2999ds/6Mi)
% 1.59/1.39 % (6200)Instruction limit reached!
% 1.59/1.39 % (6200)------------------------------
% 1.59/1.39 % (6200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.39 % (6200)Termination reason: Unknown
% 1.59/1.39 % (6200)Termination phase: Saturation
% 1.59/1.39
% 1.59/1.39 % (6200)Memory used [KB]: 5500
% 1.59/1.39 % (6200)Time elapsed: 0.006 s
% 1.59/1.39 % (6200)Instructions burned: 7 (million)
% 1.59/1.39 % (6200)------------------------------
% 1.59/1.39 % (6200)------------------------------
% 1.59/1.40 % (6202)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_6063 for (2998ds/779Mi)
% 1.59/1.41 % (6203)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_6063 for (2998ds/19Mi)
% 1.59/1.42 % (6203)Instruction limit reached!
% 1.59/1.42 % (6203)------------------------------
% 1.59/1.42 % (6203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.42 % (6203)Termination reason: Unknown
% 1.59/1.42 % (6203)Termination phase: Saturation
% 1.59/1.42
% 1.59/1.42 % (6203)Memory used [KB]: 5628
% 1.59/1.42 % (6203)Time elapsed: 0.012 s
% 1.59/1.42 % (6203)Instructions burned: 19 (million)
% 1.59/1.42 % (6203)------------------------------
% 1.59/1.42 % (6203)------------------------------
% 1.59/1.42 % (6180)Instruction limit reached!
% 1.59/1.42 % (6180)------------------------------
% 1.59/1.42 % (6180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.42 % (6180)Termination reason: Unknown
% 1.59/1.42 % (6180)Termination phase: Saturation
% 1.59/1.42
% 1.59/1.42 % (6180)Memory used [KB]: 6012
% 1.59/1.42 % (6180)Time elapsed: 0.143 s
% 1.59/1.42 % (6180)Instructions burned: 276 (million)
% 1.59/1.42 % (6180)------------------------------
% 1.59/1.42 % (6180)------------------------------
% 1.59/1.43 % (6204)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_6063 for (2998ds/879Mi)
% 1.59/1.44 % (6205)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_6063 for (2998ds/17Mi)
% 1.59/1.45 % (6205)Instruction limit reached!
% 1.59/1.45 % (6205)------------------------------
% 1.59/1.45 % (6205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.45 % (6205)Termination reason: Unknown
% 1.59/1.45 % (6205)Termination phase: Saturation
% 1.59/1.45
% 1.59/1.45 % (6205)Memory used [KB]: 5500
% 1.59/1.45 % (6205)Time elapsed: 0.012 s
% 1.59/1.45 % (6205)Instructions burned: 17 (million)
% 1.59/1.45 % (6205)------------------------------
% 1.59/1.45 % (6205)------------------------------
% 1.59/1.47 % (6206)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_6063 for (2998ds/3Mi)
% 1.59/1.47 % (6206)Instruction limit reached!
% 1.59/1.47 % (6206)------------------------------
% 1.59/1.47 % (6206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.47 % (6206)Termination reason: Unknown
% 1.59/1.47 % (6206)Termination phase: Property scanning
% 1.59/1.47
% 1.59/1.47 % (6206)Memory used [KB]: 1023
% 1.59/1.47 % (6206)Time elapsed: 0.004 s
% 1.59/1.47 % (6206)Instructions burned: 3 (million)
% 1.59/1.47 % (6206)------------------------------
% 1.59/1.47 % (6206)------------------------------
% 1.59/1.49 % (6207)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_6063 for (2998ds/30Mi)
% 1.59/1.50 % (6201)Instruction limit reached!
% 1.59/1.50 % (6201)------------------------------
% 1.59/1.50 % (6201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.50 % (6201)Termination reason: Unknown
% 1.59/1.50 % (6201)Termination phase: Saturation
% 1.59/1.50
% 1.59/1.50 % (6201)Memory used [KB]: 6268
% 1.59/1.50 % (6201)Time elapsed: 0.119 s
% 1.59/1.50 % (6201)Instructions burned: 378 (million)
% 1.59/1.50 % (6201)------------------------------
% 1.59/1.50 % (6201)------------------------------
% 1.59/1.51 % (6207)Instruction limit reached!
% 1.59/1.51 % (6207)------------------------------
% 1.59/1.51 % (6207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.51 % (6207)Termination reason: Unknown
% 1.59/1.51 % (6207)Termination phase: Saturation
% 1.59/1.51
% 1.59/1.51 % (6207)Memory used [KB]: 5628
% 1.59/1.51 % (6207)Time elapsed: 0.019 s
% 1.59/1.51 % (6207)Instructions burned: 31 (million)
% 1.59/1.51 % (6207)------------------------------
% 1.59/1.51 % (6207)------------------------------
% 1.59/1.51 % (6208)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_6063 for (2997ds/127Mi)
% 1.59/1.52 % (6209)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_6063 for (2997ds/100Mi)
% 1.59/1.54 % (6208)Instruction limit reached!
% 1.59/1.54 % (6208)------------------------------
% 1.59/1.54 % (6208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.54 % (6208)Termination reason: Unknown
% 1.59/1.54 % (6208)Termination phase: Saturation
% 1.59/1.54
% 1.59/1.54 % (6208)Memory used [KB]: 6652
% 1.59/1.54 % (6208)Time elapsed: 0.036 s
% 1.59/1.54 % (6208)Instructions burned: 128 (million)
% 1.59/1.54 % (6208)------------------------------
% 1.59/1.54 % (6208)------------------------------
% 1.59/1.55 % (6210)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_6063 for (2997ds/3Mi)
% 1.59/1.55 % (6210)Instruction limit reached!
% 1.59/1.55 % (6210)------------------------------
% 1.59/1.55 % (6210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.55 % (6210)Termination reason: Unknown
% 1.59/1.55 % (6210)Termination phase: Saturation
% 1.59/1.55
% 1.59/1.55 % (6210)Memory used [KB]: 5500
% 1.59/1.55 % (6210)Time elapsed: 0.004 s
% 1.59/1.55 % (6210)Instructions burned: 5 (million)
% 1.59/1.55 % (6210)------------------------------
% 1.59/1.55 % (6210)------------------------------
% 1.59/1.56 % (6211)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_6063 for (2997ds/20Mi)
% 1.59/1.57 % (6209)Instruction limit reached!
% 1.59/1.57 % (6209)------------------------------
% 1.59/1.57 % (6209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.57 % (6209)Termination reason: Unknown
% 1.59/1.57 % (6209)Termination phase: Saturation
% 1.59/1.57
% 1.59/1.57 % (6209)Memory used [KB]: 5884
% 1.59/1.57 % (6209)Time elapsed: 0.070 s
% 1.59/1.57 % (6209)Instructions burned: 102 (million)
% 1.59/1.57 % (6209)------------------------------
% 1.59/1.57 % (6209)------------------------------
% 1.59/1.57 % (6211)Instruction limit reached!
% 1.59/1.57 % (6211)------------------------------
% 1.59/1.57 % (6211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.57 % (6211)Termination reason: Unknown
% 1.59/1.57 % (6211)Termination phase: Saturation
% 1.59/1.57
% 1.59/1.57 % (6211)Memory used [KB]: 5628
% 1.59/1.57 % (6211)Time elapsed: 0.032 s
% 1.59/1.57 % (6211)Instructions burned: 20 (million)
% 1.59/1.57 % (6211)------------------------------
% 1.59/1.57 % (6211)------------------------------
% 1.59/1.58 % (6212)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_6063 for (2997ds/86Mi)
% 1.59/1.58 % (6213)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_6063 for (2997ds/107Mi)
% 1.59/1.61 % (6212)Instruction limit reached!
% 1.59/1.61 % (6212)------------------------------
% 1.59/1.61 % (6212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.61 % (6212)Termination reason: Unknown
% 1.59/1.61 % (6212)Termination phase: Saturation
% 1.59/1.61
% 1.59/1.61 % (6212)Memory used [KB]: 5756
% 1.59/1.61 % (6212)Time elapsed: 0.050 s
% 1.59/1.61 % (6212)Instructions burned: 87 (million)
% 1.59/1.61 % (6212)------------------------------
% 1.59/1.61 % (6212)------------------------------
% 1.59/1.62 % (6214)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_6063 for (2996ds/39Mi)
% 1.59/1.62 % (6213)Instruction limit reached!
% 1.59/1.62 % (6213)------------------------------
% 1.59/1.62 % (6213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.62 % (6213)Termination reason: Unknown
% 1.59/1.62 % (6213)Termination phase: Saturation
% 1.59/1.62
% 1.59/1.62 % (6213)Memory used [KB]: 5884
% 1.59/1.62 % (6213)Time elapsed: 0.062 s
% 1.59/1.62 % (6213)Instructions burned: 109 (million)
% 1.59/1.62 % (6213)------------------------------
% 1.59/1.62 % (6213)------------------------------
% 1.59/1.62 % (6204)First to succeed.
% 1.59/1.63 % (6204)Refutation found. Thanks to Tanya!
% 1.59/1.63 % SZS status Theorem for DTF2THF_6063
% 1.59/1.63 % SZS output start Proof for DTF2THF_6063
% 1.59/1.63 thf(type_def_5, type, a: $tType).
% 1.59/1.63 thf(func_def_0, type, a: $tType).
% 1.59/1.63 thf(func_def_9, type, sK0: a > $o).
% 1.59/1.63 thf(func_def_10, type, sK1: a > $o).
% 1.59/1.63 thf(func_def_11, type, sK2: (a > a) > a).
% 1.59/1.63 thf(func_def_12, type, sK3: (a > a) > a).
% 1.59/1.63 thf(func_def_13, type, sK4: a > a).
% 1.59/1.63 thf(func_def_14, type, sK5: a > a).
% 1.59/1.63 thf(func_def_16, type, ph7: !>[X0: $tType]:(X0)).
% 1.59/1.63 thf(func_def_17, type, sK8: a > (a > a) > a).
% 1.59/1.63 thf(func_def_18, type, sK9: a > (a > a) > a).
% 1.59/1.63 thf(f1008,plain,(
% 1.59/1.63 $false),
% 1.59/1.63 inference(avatar_sat_refutation,[status(thm)],[f719,f723,f1007])).
% 1.59/1.63 thf(f1007,plain,(
% 1.59/1.63 spl6_5 | ~spl6_23),
% 1.59/1.63 inference(avatar_contradiction_clause,[status(thm)],[f1006])).
% 1.59/1.63 thf(f1006,plain,(
% 1.59/1.63 $false | (spl6_5 | ~spl6_23)),
% 1.59/1.63 inference(trivial_inequality_removal,[status(thm)],[f1005])).
% 1.59/1.63 thf(f1005,plain,(
% 1.59/1.63 ($true = $false) | (spl6_5 | ~spl6_23)),
% 1.59/1.63 inference(backward_demodulation,[status(thm)],[f72,f1004])).
% 1.59/1.63 thf(f1004,plain,(
% 1.59/1.63 ((sK0 @ (sK4 @ (sK2 @ sK5))) = $false) | (spl6_5 | ~spl6_23)),
% 1.59/1.63 inference(subsumption_resolution,[status(thm)],[f1003,f117])).
% 1.59/1.63 thf(f117,plain,(
% 1.59/1.63 ($true != (sK0 @ (sK3 @ sK5))) | spl6_5),
% 1.59/1.63 inference(avatar_component_clause,[status(thm)],[f116])).
% 1.59/1.63 thf(f116,definition,(
% 1.59/1.63 spl6_5 <=> ($true = (sK0 @ (sK3 @ sK5)))),
% 1.59/1.63 introduced(definition,[new_symbols(naming,[spl6_5])],[avatar_definition])).
% 1.59/1.63 thf(f1003,plain,(
% 1.59/1.63 ((sK0 @ (sK4 @ (sK2 @ sK5))) = $false) | ($true = (sK0 @ (sK3 @ sK5))) | (spl6_5 | ~spl6_23)),
% 1.59/1.63 inference(subsumption_resolution,[status(thm)],[f1002,f382])).
% 1.59/1.63 thf(f382,plain,(
% 1.59/1.63 ((sK2 @ sK5) = (sK5 @ (sK4 @ (sK2 @ sK5))))),
% 1.59/1.63 inference(trivial_inequality_removal,[status(thm)],[f381])).
% 1.59/1.63 thf(f381,plain,(
% 1.59/1.63 ((sK2 @ sK5) = (sK5 @ (sK4 @ (sK2 @ sK5)))) | ($true = $false)),
% 1.59/1.63 inference(forward_demodulation,[status(thm)],[f371,f70])).
% 1.59/1.63 thf(f70,plain,(
% 1.59/1.63 ((sK1 @ (sK2 @ sK5)) = $true)),
% 1.59/1.63 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.59/1.63 thf(f69,plain,(
% 1.59/1.63 ($true != $true) | ((sK1 @ (sK2 @ sK5)) = $true)),
% 1.59/1.63 inference(duplicate_literal_removal,[status(thm)],[f66])).
% 1.59/1.63 thf(f66,plain,(
% 1.59/1.63 ((sK1 @ (sK2 @ sK5)) = $true) | ($true != $true) | ((sK1 @ (sK2 @ sK5)) = $true)),
% 1.59/1.63 inference(superposition,[status(thm)],[f18,f63])).
% 1.59/1.63 thf(f63,plain,(
% 1.59/1.63 ( ! [X0 : a > a] : (($true = (sK1 @ (sK5 @ (sK3 @ X0)))) | ((sK1 @ (sK2 @ X0)) = $true)) )),
% 1.59/1.63 inference(equality_resolution,[status(thm)],[f62])).
% 1.59/1.63 thf(f62,plain,(
% 1.59/1.63 ( ! [X0 : a > a,X1 : a] : (((sK5 @ (sK3 @ X0)) != X1) | ($true = (sK1 @ X1)) | ((sK1 @ (sK2 @ X0)) = $true)) )),
% 1.59/1.63 inference(equality_proxy_clausification,[status(thm)],[f58])).
% 1.59/1.63 thf(f58,plain,(
% 1.59/1.63 ( ! [X0 : a > a,X1 : a] : (($false = ((sK5 @ (sK3 @ X0)) = X1)) | ($true = (sK1 @ X1)) | ((sK1 @ (sK2 @ X0)) = $true)) )),
% 1.59/1.63 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.59/1.63 thf(f53,plain,(
% 1.59/1.63 ( ! [X0 : a > a,X1 : a] : (((((sK4 @ X1) = (sK3 @ X0)) & (sK1 @ X1)) = $true) | ($false = ((sK5 @ (sK3 @ X0)) = X1)) | ((sK1 @ (sK2 @ X0)) = $true)) )),
% 1.59/1.63 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.59/1.63 thf(f52,plain,(
% 1.59/1.63 ( ! [X0 : a > a,X1 : a] : (((((sK4 @ X1) = (sK3 @ X0)) & (sK1 @ X1)) = ((sK5 @ (sK3 @ X0)) = X1)) | ((sK1 @ (sK2 @ X0)) = $true)) )),
% 1.59/1.63 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.59/1.63 thf(f51,plain,(
% 1.59/1.63 ( ! [X0 : a > a,X1 : a] : ((((^[Y0 : a]: (((sK4 @ Y0) = (sK3 @ X0)) & (sK1 @ Y0))) @ X1) = ((sK5 @ (sK3 @ X0)) = X1)) | ((sK1 @ (sK2 @ X0)) = $true)) )),
% 1.59/1.63 inference(argument_congruence,[status(thm)],[f25])).
% 1.59/1.63 thf(f25,plain,(
% 1.59/1.63 ( ! [X0 : a > a] : (((^[Y0 : a]: (((sK4 @ Y0) = (sK3 @ X0)) & (sK1 @ Y0))) = (= @ (sK5 @ (sK3 @ X0)))) | ((sK1 @ (sK2 @ X0)) = $true)) )),
% 1.59/1.63 inference(trivial_inequality_removal,[status(thm)],[f24])).
% 1.59/1.63 thf(f24,plain,(
% 1.59/1.63 ( ! [X0 : a > a] : (((^[Y0 : a]: (((sK4 @ Y0) = (sK3 @ X0)) & (sK1 @ Y0))) = (= @ (sK5 @ (sK3 @ X0)))) | ((sK1 @ (sK2 @ X0)) = $true) | ($true != $true)) )),
% 1.59/1.63 inference(superposition,[status(thm)],[f23,f17])).
% 1.59/1.63 thf(f17,plain,(
% 1.59/1.63 ( ! [X2 : a > a] : (($true = (sK0 @ (sK3 @ X2))) | ((sK1 @ (sK2 @ X2)) = $true)) )),
% 1.59/1.63 inference(cnf_transformation,[status(thm)],[f14])).
% 1.59/1.63 thf(f14,plain,(
% 1.59/1.63 ! [X2 : a > a] : ((! [X4 : a] : (((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X4) != (^[Y0 : a]: (((X2 @ Y0) = (sK2 @ X2)) & (sK0 @ Y0)))) & ((sK1 @ (sK2 @ X2)) = $true)) | (((sK1 @ (X2 @ (sK3 @ X2))) != $true) & ($true = (sK0 @ (sK3 @ X2))))) & (! [X7 : a] : ((((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ (sK5 @ X7)) = (^[Y0 : a]: (((sK4 @ Y0) = X7) & (sK1 @ Y0)))) | ((sK0 @ X7) != $true)) & ! [X9 : a] : (((sK1 @ X9) != $true) | ($true = (sK0 @ (sK4 @ X9)))))),
% 1.59/1.63 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f13,f12,f11,f10,f9])).
% 1.59/1.63 thf(f9,plain,(
% 1.59/1.63 ? [X0 : a > $o,X1 : a > $o] : (! [X2 : a > a] : (? [X3 : a] : (! [X4 : a] : ((^[Y0 : a]: (((X2 @ Y0) = X3) & (X0 @ Y0))) != ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X4)) & ((X1 @ X3) = $true)) | ? [X5 : a] : (($true != (X1 @ (X2 @ X5))) & ((X0 @ X5) = $true))) & ? [X6 : a > a] : (! [X7 : a] : (? [X8 : a] : ((^[Y0 : a]: (((X6 @ Y0) = X7) & (X1 @ Y0))) = ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X8)) | ($true != (X0 @ X7))) & ! [X9 : a] : (((X1 @ X9) != $true) | ((X0 @ (X6 @ X9)) = $true)))) => (! [X2 : a > a] : (? [X3 : a] : (! [X4 : a] : (((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X4) != (^[Y0 : a]: (((X2 @ Y0) = X3) & (sK0 @ Y0)))) & ((sK1 @ X3) = $true)) | ? [X5 : a] : (((sK1 @ (X2 @ X5)) != $true) & ($true = (sK0 @ X5)))) & ? [X6 : a > a] : (! [X7 : a] : (? [X8 : a] : ((^[Y0 : a]: (((X6 @ Y0) = X7) & (sK1 @ Y0))) = ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X8)) | ((sK0 @ X7) != $true)) & ! [X9 : a] : (((sK1 @ X9) != $true) | ($true = (sK0 @ (X6 @ X9))))))),
% 1.59/1.63 introduced(definition,[],[choice_axiom])).
% 1.59/1.63 thf(f10,plain,(
% 1.59/1.63 ! [X2 : a > a] : (? [X3 : a] : (! [X4 : a] : (((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X4) != (^[Y0 : a]: (((X2 @ Y0) = X3) & (sK0 @ Y0)))) & ((sK1 @ X3) = $true)) => (! [X4 : a] : (((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X4) != (^[Y0 : a]: (((X2 @ Y0) = (sK2 @ X2)) & (sK0 @ Y0)))) & ((sK1 @ (sK2 @ X2)) = $true)))),
% 1.59/1.63 introduced(definition,[],[choice_axiom])).
% 1.59/1.63 thf(f11,plain,(
% 1.59/1.63 ! [X2 : a > a] : (? [X5 : a] : (((sK1 @ (X2 @ X5)) != $true) & ($true = (sK0 @ X5))) => (((sK1 @ (X2 @ (sK3 @ X2))) != $true) & ($true = (sK0 @ (sK3 @ X2)))))),
% 1.59/1.63 introduced(definition,[],[choice_axiom])).
% 1.59/1.63 thf(f12,plain,(
% 1.59/1.63 ? [X6 : a > a] : (! [X7 : a] : (? [X8 : a] : ((^[Y0 : a]: (((X6 @ Y0) = X7) & (sK1 @ Y0))) = ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X8)) | ((sK0 @ X7) != $true)) & ! [X9 : a] : (((sK1 @ X9) != $true) | ($true = (sK0 @ (X6 @ X9))))) => (! [X7 : a] : (? [X8 : a] : ((^[Y0 : a]: (((sK4 @ Y0) = X7) & (sK1 @ Y0))) = ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X8)) | ((sK0 @ X7) != $true)) & ! [X9 : a] : (((sK1 @ X9) != $true) | ($true = (sK0 @ (sK4 @ X9)))))),
% 1.59/1.63 introduced(definition,[],[choice_axiom])).
% 1.59/1.63 thf(f13,plain,(
% 1.59/1.63 ! [X7 : a] : (? [X8 : a] : ((^[Y0 : a]: (((sK4 @ Y0) = X7) & (sK1 @ Y0))) = ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X8)) => (((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ (sK5 @ X7)) = (^[Y0 : a]: (((sK4 @ Y0) = X7) & (sK1 @ Y0)))))),
% 1.59/1.63 introduced(definition,[],[choice_axiom])).
% 1.59/1.63 thf(f8,plain,(
% 1.59/1.63 ? [X0 : a > $o,X1 : a > $o] : (! [X2 : a > a] : (? [X3 : a] : (! [X4 : a] : ((^[Y0 : a]: (((X2 @ Y0) = X3) & (X0 @ Y0))) != ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X4)) & ((X1 @ X3) = $true)) | ? [X5 : a] : (($true != (X1 @ (X2 @ X5))) & ((X0 @ X5) = $true))) & ? [X6 : a > a] : (! [X7 : a] : (? [X8 : a] : ((^[Y0 : a]: (((X6 @ Y0) = X7) & (X1 @ Y0))) = ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X8)) | ($true != (X0 @ X7))) & ! [X9 : a] : (((X1 @ X9) != $true) | ((X0 @ (X6 @ X9)) = $true))))),
% 1.59/1.63 inference(rectify,[status(thm)],[f7])).
% 1.59/1.63 thf(f7,plain,(
% 1.59/1.63 ? [X0 : a > $o,X1 : a > $o] : (! [X6 : a > a] : (? [X7 : a] : (! [X8 : a] : ((^[Y0 : a]: (((X6 @ Y0) = X7) & (X0 @ Y0))) != ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X8)) & ((X1 @ X7) = $true)) | ? [X9 : a] : (($true != (X1 @ (X6 @ X9))) & ((X0 @ X9) = $true))) & ? [X2 : a > a] : (! [X4 : a] : (? [X5 : a] : ((^[Y0 : a]: (((X2 @ Y0) = X4) & (X1 @ Y0))) = ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X5)) | ((X0 @ X4) != $true)) & ! [X3 : a] : (((X1 @ X3) != $true) | ((X0 @ (X2 @ X3)) = $true))))),
% 1.59/1.63 inference(ennf_transformation,[status(thm)],[f6])).
% 1.59/1.63 thf(f6,plain,(
% 1.59/1.63 ~! [X0 : a > $o,X1 : a > $o] : (? [X2 : a > a] : (! [X4 : a] : (((X0 @ X4) = $true) => ? [X5 : a] : ((^[Y0 : a]: (((X2 @ Y0) = X4) & (X1 @ Y0))) = ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X5))) & ! [X3 : a] : (((X1 @ X3) = $true) => ((X0 @ (X2 @ X3)) = $true))) => ? [X6 : a > a] : (! [X9 : a] : (((X0 @ X9) = $true) => ($true = (X1 @ (X6 @ X9)))) & ! [X7 : a] : (((X1 @ X7) = $true) => ? [X8 : a] : ((^[Y0 : a]: (((X6 @ Y0) = X7) & (X0 @ Y0))) = ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X8)))))),
% 1.59/1.63 inference(rectify,[status(thm)],[f5])).
% 1.59/1.63 thf(f5,plain,(
% 1.59/1.63 ~! [X0 : a > $o,X1 : a > $o] : (? [X2 : a > a] : (! [X4 : a] : (((X0 @ X4) = $true) => ? [X5 : a] : ((^[Y0 : a]: (((X2 @ Y0) = X4) & (X1 @ Y0))) = ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X5))) & ! [X3 : a] : (((X1 @ X3) = $true) => ((X0 @ (X2 @ X3)) = $true))) => ? [X9 : a > a] : (! [X10 : a] : (($true = (X1 @ X10)) => ? [X11 : a] : (((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X11) = (^[Y0 : a]: (((X9 @ Y0) = X10) & (X0 @ Y0))))) & ! [X15 : a] : (($true = (X0 @ X15)) => ($true = (X1 @ (X9 @ X15))))))),
% 1.59/1.63 inference(fool_elimination,[status(thm)],[f4])).
% 1.59/1.63 thf(f4,plain,(
% 1.59/1.63 ~! [X0 : a > $o,X1 : a > $o] : (? [X2 : a > a] : (! [X3 : a] : ((X1 @ X3) => (X0 @ (X2 @ X3))) & ! [X4 : a] : ((X0 @ X4) => ? [X5 : a] : ((^[X6 : a] : ((X1 @ X6) & ((X2 @ X6) = X4))) = ((^[X7 : a, X8 : a] : ((X7 = X8))) @ X5)))) => ? [X9 : a > a] : (! [X10 : a] : ((X1 @ X10) => ? [X11 : a] : ((^[X12 : a] : ((X0 @ X12) & ((X9 @ X12) = X10))) = ((^[X13 : a, X14 : a] : ((X13 = X14))) @ X11))) & ! [X15 : a] : ((X0 @ X15) => (X1 @ (X9 @ X15)))))),
% 1.59/1.63 inference(rectify,[status(thm)],[f2])).
% 1.59/1.63 thf(f2,negated_conjecture,(
% 1.59/1.63 ~! [X1 : a > $o,X0 : a > $o] : (? [X2 : a > a] : (! [X3 : a] : ((X0 @ X3) => (X1 @ (X2 @ X3))) & ! [X4 : a] : ((X1 @ X4) => ? [X5 : a] : ((^[X3 : a] : ((X0 @ X3) & ((X2 @ X3) = X4))) = ((^[X0 : a, X1 : a] : ((X0 = X1))) @ X5)))) => ? [X2 : a > a] : (! [X4 : a] : ((X0 @ X4) => ? [X6 : a] : ((^[X3 : a] : ((X1 @ X3) & ((X2 @ X3) = X4))) = ((^[X0 : a, X1 : a] : ((X0 = X1))) @ X6))) & ! [X3 : a] : ((X1 @ X3) => (X0 @ (X2 @ X3)))))),
% 1.59/1.63 inference(negated_conjecture,[status(cth)],[f1])).
% 1.59/1.63 thf(f1,conjecture,(
% 1.59/1.63 ! [X1 : a > $o,X0 : a > $o] : (? [X2 : a > a] : (! [X3 : a] : ((X0 @ X3) => (X1 @ (X2 @ X3))) & ! [X4 : a] : ((X1 @ X4) => ? [X5 : a] : ((^[X3 : a] : ((X0 @ X3) & ((X2 @ X3) = X4))) = ((^[X0 : a, X1 : a] : ((X0 = X1))) @ X5)))) => ? [X2 : a > a] : (! [X4 : a] : ((X0 @ X4) => ? [X6 : a] : ((^[X3 : a] : ((X1 @ X3) & ((X2 @ X3) = X4))) = ((^[X0 : a, X1 : a] : ((X0 = X1))) @ X6))) & ! [X3 : a] : ((X1 @ X3) => (X0 @ (X2 @ X3)))))),
% 1.59/1.63 file('/export/starexec/sandbox/tmp/tmp.i5qrV6Zz6N/DTF2THF_6063.p',cEQP_1B_pme)).
% 1.59/1.63 thf(f23,plain,(
% 1.59/1.63 ( ! [X7 : a] : (((sK0 @ X7) != $true) | ((= @ (sK5 @ X7)) = (^[Y0 : a]: (((sK4 @ Y0) = X7) & (sK1 @ Y0))))) )),
% 1.59/1.63 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.59/1.63 thf(f16,plain,(
% 1.59/1.63 ( ! [X7 : a] : (((sK0 @ X7) != $true) | (((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ (sK5 @ X7)) = (^[Y0 : a]: (((sK4 @ Y0) = X7) & (sK1 @ Y0))))) )),
% 1.59/1.63 inference(cnf_transformation,[status(thm)],[f14])).
% 1.59/1.63 thf(f18,plain,(
% 1.59/1.63 ( ! [X2 : a > a] : (((sK1 @ (X2 @ (sK3 @ X2))) != $true) | ((sK1 @ (sK2 @ X2)) = $true)) )),
% 1.59/1.63 inference(cnf_transformation,[status(thm)],[f14])).
% 1.59/1.63 thf(f371,plain,(
% 1.59/1.63 ((sK2 @ sK5) = (sK5 @ (sK4 @ (sK2 @ sK5)))) | ((sK1 @ (sK2 @ sK5)) = $false)),
% 1.59/1.63 inference(equality_resolution,[status(thm)],[f178])).
% 1.59/1.63 thf(f178,plain,(
% 1.59/1.63 ( ! [X1 : a] : (((sK4 @ (sK2 @ sK5)) != (sK4 @ X1)) | ((sK5 @ (sK4 @ (sK2 @ sK5))) = X1) | ($false = (sK1 @ X1))) )),
% 1.59/1.63 inference(equality_proxy_clausification,[status(thm)],[f177])).
% 1.59/1.63 thf(f177,plain,(
% 1.59/1.63 ( ! [X1 : a] : (((sK5 @ (sK4 @ (sK2 @ sK5))) = X1) | (((sK4 @ X1) = (sK4 @ (sK2 @ sK5))) = $false) | ($false = (sK1 @ X1))) )),
% 1.59/1.63 inference(equality_proxy_clausification,[status(thm)],[f176])).
% 1.59/1.63 thf(f176,plain,(
% 1.59/1.63 ( ! [X1 : a] : (($false = (sK1 @ X1)) | ($true = ((sK5 @ (sK4 @ (sK2 @ sK5))) = X1)) | (((sK4 @ X1) = (sK4 @ (sK2 @ sK5))) = $false)) )),
% 1.59/1.63 inference(binary_proxy_clausification,[status(thm)],[f175])).
% 1.59/1.63 thf(f175,plain,(
% 1.59/1.63 ( ! [X1 : a] : (((((sK4 @ X1) = (sK4 @ (sK2 @ sK5))) & (sK1 @ X1)) = $false) | ($true = ((sK5 @ (sK4 @ (sK2 @ sK5))) = X1))) )),
% 1.59/1.63 inference(binary_proxy_clausification,[status(thm)],[f173])).
% 1.59/1.63 thf(f173,plain,(
% 1.59/1.63 ( ! [X1 : a] : (((((sK4 @ X1) = (sK4 @ (sK2 @ sK5))) & (sK1 @ X1)) = ((sK5 @ (sK4 @ (sK2 @ sK5))) = X1))) )),
% 1.59/1.63 inference(beta_eta_normalization,[status(thm)],[f172])).
% 1.59/1.63 thf(f172,plain,(
% 1.59/1.63 ( ! [X1 : a] : ((((^[Y0 : a]: (((sK4 @ Y0) = (sK4 @ (sK2 @ sK5))) & (sK1 @ Y0))) @ X1) = ((sK5 @ (sK4 @ (sK2 @ sK5))) = X1))) )),
% 1.59/1.63 inference(argument_congruence,[status(thm)],[f74])).
% 1.59/1.63 thf(f74,plain,(
% 1.59/1.63 ((^[Y0 : a]: (((sK4 @ Y0) = (sK4 @ (sK2 @ sK5))) & (sK1 @ Y0))) = (= @ (sK5 @ (sK4 @ (sK2 @ sK5)))))),
% 1.59/1.63 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.59/1.63 thf(f73,plain,(
% 1.59/1.63 ($true != $true) | ((^[Y0 : a]: (((sK4 @ Y0) = (sK4 @ (sK2 @ sK5))) & (sK1 @ Y0))) = (= @ (sK5 @ (sK4 @ (sK2 @ sK5)))))),
% 1.59/1.63 inference(superposition,[status(thm)],[f23,f72])).
% 1.59/1.63 thf(f1002,plain,(
% 1.59/1.63 ((sK2 @ sK5) != (sK5 @ (sK4 @ (sK2 @ sK5)))) | ($true = (sK0 @ (sK3 @ sK5))) | ((sK0 @ (sK4 @ (sK2 @ sK5))) = $false) | (spl6_5 | ~spl6_23)),
% 1.59/1.63 inference(trivial_inequality_removal,[status(thm)],[f968])).
% 1.59/1.63 thf(f968,plain,(
% 1.59/1.63 ((sK0 @ (sK4 @ (sK2 @ sK5))) = $false) | ((sK2 @ sK5) != (sK5 @ (sK4 @ (sK2 @ sK5)))) | ((sK4 @ (sK2 @ sK5)) != (sK4 @ (sK2 @ sK5))) | ($true = (sK0 @ (sK3 @ sK5))) | (spl6_5 | ~spl6_23)),
% 1.59/1.63 inference(superposition,[status(thm)],[f32,f967])).
% 1.59/1.63 thf(f967,plain,(
% 1.59/1.63 ((sK8 @ (sK4 @ (sK2 @ sK5)) @ sK5) = (sK4 @ (sK2 @ sK5))) | (spl6_5 | ~spl6_23)),
% 1.59/1.63 inference(equality_resolution,[status(thm)],[f888])).
% 1.59/1.63 thf(f888,plain,(
% 1.59/1.63 ( ! [X0 : a] : (((sK4 @ (sK2 @ sK5)) != X0) | ((sK8 @ X0 @ sK5) = X0)) ) | (spl6_5 | ~spl6_23)),
% 1.59/1.63 inference(trivial_inequality_removal,[status(thm)],[f887])).
% 1.59/1.63 thf(f887,plain,(
% 1.59/1.63 ( ! [X0 : a] : (((sK4 @ (sK2 @ sK5)) != X0) | ($true = $false) | ((sK8 @ X0 @ sK5) = X0)) ) | (spl6_5 | ~spl6_23)),
% 1.59/1.63 inference(forward_demodulation,[status(thm)],[f886,f72])).
% 1.59/1.63 thf(f886,plain,(
% 1.59/1.63 ( ! [X0 : a] : (((sK8 @ X0 @ sK5) = X0) | ((sK4 @ (sK2 @ sK5)) != X0) | ((sK0 @ (sK4 @ (sK2 @ sK5))) = $false)) ) | (spl6_5 | ~spl6_23)),
% 1.59/1.63 inference(subsumption_resolution,[status(thm)],[f885,f117])).
% 1.59/1.63 thf(f885,plain,(
% 1.59/1.63 ( ! [X0 : a] : (((sK0 @ (sK4 @ (sK2 @ sK5))) = $false) | ((sK4 @ (sK2 @ sK5)) != X0) | ((sK8 @ X0 @ sK5) = X0) | ($true = (sK0 @ (sK3 @ sK5)))) ) | ~spl6_23),
% 1.59/1.63 inference(subsumption_resolution,[status(thm)],[f821,f382])).
% 1.59/1.63 thf(f821,plain,(
% 1.59/1.63 ( ! [X0 : a] : (((sK2 @ sK5) != (sK5 @ (sK4 @ (sK2 @ sK5)))) | ((sK4 @ (sK2 @ sK5)) != X0) | ((sK8 @ X0 @ sK5) = X0) | ((sK0 @ (sK4 @ (sK2 @ sK5))) = $false) | ($true = (sK0 @ (sK3 @ sK5)))) ) | ~spl6_23),
% 1.59/1.63 inference(superposition,[status(thm)],[f32,f722])).
% 1.59/1.63 thf(f722,plain,(
% 1.59/1.63 ( ! [X0 : a] : (((sK4 @ (sK2 @ sK5)) = (sK8 @ X0 @ sK5)) | ((sK8 @ X0 @ sK5) = X0)) ) | ~spl6_23),
% 1.59/1.63 inference(avatar_component_clause,[status(thm)],[f721])).
% 1.59/1.63 thf(f721,definition,(
% 1.59/1.63 spl6_23 <=> ! [X0 : a] : (((sK8 @ X0 @ sK5) = X0) | ((sK4 @ (sK2 @ sK5)) = (sK8 @ X0 @ sK5)))),
% 1.59/1.63 introduced(definition,[new_symbols(naming,[spl6_23])],[avatar_definition])).
% 1.59/1.63 thf(f32,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (((X2 @ (sK8 @ X4 @ X2)) != (sK2 @ X2)) | ((sK8 @ X4 @ X2) != X4) | ($true = (sK0 @ (sK3 @ X2))) | ((sK0 @ (sK8 @ X4 @ X2)) = $false)) )),
% 1.59/1.63 inference(equality_proxy_clausification,[status(thm)],[f31])).
% 1.59/1.63 thf(f31,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (((sK8 @ X4 @ X2) != X4) | ((sK0 @ (sK8 @ X4 @ X2)) = $false) | (((X2 @ (sK8 @ X4 @ X2)) = (sK2 @ X2)) = $false) | ($true = (sK0 @ (sK3 @ X2)))) )),
% 1.59/1.63 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.59/1.63 thf(f30,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (((sK8 @ X4 @ X2) != X4) | ($true = (sK0 @ (sK3 @ X2))) | ($false = (((X2 @ (sK8 @ X4 @ X2)) = (sK2 @ X2)) & (sK0 @ (sK8 @ X4 @ X2))))) )),
% 1.59/1.63 inference(equality_proxy_clausification,[status(thm)],[f29])).
% 1.59/1.63 thf(f29,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (($false = (X4 = (sK8 @ X4 @ X2))) | ($false = (((X2 @ (sK8 @ X4 @ X2)) = (sK2 @ X2)) & (sK0 @ (sK8 @ X4 @ X2)))) | ($true = (sK0 @ (sK3 @ X2)))) )),
% 1.59/1.63 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.59/1.63 thf(f27,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (($true = (sK0 @ (sK3 @ X2))) | ((((X2 @ (sK8 @ X4 @ X2)) = (sK2 @ X2)) & (sK0 @ (sK8 @ X4 @ X2))) != (X4 = (sK8 @ X4 @ X2)))) )),
% 1.59/1.63 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.59/1.63 thf(f26,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : ((((^[Y0 : a]: (((X2 @ Y0) = (sK2 @ X2)) & (sK0 @ Y0))) @ (sK8 @ X4 @ X2)) != (X4 = (sK8 @ X4 @ X2))) | ($true = (sK0 @ (sK3 @ X2)))) )),
% 1.59/1.63 inference(negative_extensionality,[status(thm)],[f22])).
% 1.59/1.63 thf(f22,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (((^[Y0 : a]: (((X2 @ Y0) = (sK2 @ X2)) & (sK0 @ Y0))) != (= @ X4)) | ($true = (sK0 @ (sK3 @ X2)))) )),
% 1.59/1.63 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.59/1.63 thf(f19,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (($true = (sK0 @ (sK3 @ X2))) | (((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X4) != (^[Y0 : a]: (((X2 @ Y0) = (sK2 @ X2)) & (sK0 @ Y0))))) )),
% 1.59/1.63 inference(cnf_transformation,[status(thm)],[f14])).
% 1.59/1.63 thf(f72,plain,(
% 1.59/1.63 ((sK0 @ (sK4 @ (sK2 @ sK5))) = $true)),
% 1.59/1.63 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.59/1.63 thf(f71,plain,(
% 1.59/1.63 ($true != $true) | ((sK0 @ (sK4 @ (sK2 @ sK5))) = $true)),
% 1.59/1.63 inference(superposition,[status(thm)],[f15,f70])).
% 1.59/1.63 thf(f15,plain,(
% 1.59/1.63 ( ! [X9 : a] : (((sK1 @ X9) != $true) | ($true = (sK0 @ (sK4 @ X9)))) )),
% 1.59/1.63 inference(cnf_transformation,[status(thm)],[f14])).
% 1.59/1.63 thf(f723,plain,(
% 1.59/1.63 spl6_5 | spl6_23),
% 1.59/1.63 inference(avatar_split_clause,[status(thm)],[f168,f721,f116])).
% 1.59/1.63 thf(f168,plain,(
% 1.59/1.63 ( ! [X0 : a] : (((sK8 @ X0 @ sK5) = X0) | ($true = (sK0 @ (sK3 @ sK5))) | ((sK4 @ (sK2 @ sK5)) = (sK8 @ X0 @ sK5))) )),
% 1.59/1.63 inference(duplicate_literal_removal,[status(thm)],[f165])).
% 1.59/1.63 thf(f165,plain,(
% 1.59/1.63 ( ! [X0 : a] : (((sK8 @ X0 @ sK5) = X0) | ($true = (sK0 @ (sK3 @ sK5))) | ((sK8 @ X0 @ sK5) = X0) | ($true = (sK0 @ (sK3 @ sK5))) | ((sK4 @ (sK2 @ sK5)) = (sK8 @ X0 @ sK5))) )),
% 1.59/1.63 inference(superposition,[status(thm)],[f134,f36])).
% 1.59/1.63 thf(f36,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (((X2 @ (sK8 @ X4 @ X2)) = (sK2 @ X2)) | ($true = (sK0 @ (sK3 @ X2))) | ((sK8 @ X4 @ X2) = X4)) )),
% 1.59/1.63 inference(equality_proxy_clausification,[status(thm)],[f35])).
% 1.59/1.63 thf(f35,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (($true = (sK0 @ (sK3 @ X2))) | (((X2 @ (sK8 @ X4 @ X2)) = (sK2 @ X2)) = $true) | ((sK8 @ X4 @ X2) = X4)) )),
% 1.59/1.63 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.59/1.63 thf(f33,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (((sK8 @ X4 @ X2) = X4) | ($true = (((X2 @ (sK8 @ X4 @ X2)) = (sK2 @ X2)) & (sK0 @ (sK8 @ X4 @ X2)))) | ($true = (sK0 @ (sK3 @ X2)))) )),
% 1.59/1.63 inference(equality_proxy_clausification,[status(thm)],[f28])).
% 1.59/1.63 thf(f28,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (($true = (sK0 @ (sK3 @ X2))) | ($true = (X4 = (sK8 @ X4 @ X2))) | ($true = (((X2 @ (sK8 @ X4 @ X2)) = (sK2 @ X2)) & (sK0 @ (sK8 @ X4 @ X2))))) )),
% 1.59/1.63 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.59/1.63 thf(f134,plain,(
% 1.59/1.63 ( ! [X0 : a,X1 : a > a] : (((sK8 @ X0 @ X1) = (sK4 @ (sK5 @ (sK8 @ X0 @ X1)))) | ((sK8 @ X0 @ X1) = X0) | ((sK0 @ (sK3 @ X1)) = $true)) )),
% 1.59/1.63 inference(equality_resolution,[status(thm)],[f101])).
% 1.59/1.63 thf(f101,plain,(
% 1.59/1.63 ( ! [X2 : a,X0 : a,X1 : a > a] : (((sK5 @ (sK8 @ X0 @ X1)) != X2) | ((sK4 @ X2) = (sK8 @ X0 @ X1)) | ((sK8 @ X0 @ X1) = X0) | ((sK0 @ (sK3 @ X1)) = $true)) )),
% 1.59/1.63 inference(equality_proxy_clausification,[status(thm)],[f100])).
% 1.59/1.63 thf(f100,plain,(
% 1.59/1.63 ( ! [X2 : a,X0 : a,X1 : a > a] : (($true = ((sK4 @ X2) = (sK8 @ X0 @ X1))) | ((sK8 @ X0 @ X1) = X0) | ((sK0 @ (sK3 @ X1)) = $true) | ((sK5 @ (sK8 @ X0 @ X1)) != X2)) )),
% 1.59/1.63 inference(equality_proxy_clausification,[status(thm)],[f99])).
% 1.59/1.63 thf(f99,plain,(
% 1.59/1.63 ( ! [X2 : a,X0 : a,X1 : a > a] : ((((sK5 @ (sK8 @ X0 @ X1)) = X2) = $false) | ($true = ((sK4 @ X2) = (sK8 @ X0 @ X1))) | ((sK8 @ X0 @ X1) = X0) | ((sK0 @ (sK3 @ X1)) = $true)) )),
% 1.59/1.63 inference(binary_proxy_clausification,[status(thm)],[f97])).
% 1.59/1.63 thf(f97,plain,(
% 1.59/1.63 ( ! [X2 : a,X0 : a,X1 : a > a] : (((sK0 @ (sK3 @ X1)) = $true) | ((sK8 @ X0 @ X1) = X0) | ((((sK4 @ X2) = (sK8 @ X0 @ X1)) & (sK1 @ X2)) = $true) | (((sK5 @ (sK8 @ X0 @ X1)) = X2) = $false)) )),
% 1.59/1.63 inference(binary_proxy_clausification,[status(thm)],[f95])).
% 1.59/1.63 thf(f95,plain,(
% 1.59/1.63 ( ! [X2 : a,X0 : a,X1 : a > a] : (((sK0 @ (sK3 @ X1)) = $true) | (((sK5 @ (sK8 @ X0 @ X1)) = X2) = (((sK4 @ X2) = (sK8 @ X0 @ X1)) & (sK1 @ X2))) | ((sK8 @ X0 @ X1) = X0)) )),
% 1.59/1.63 inference(beta_eta_normalization,[status(thm)],[f94])).
% 1.59/1.63 thf(f94,plain,(
% 1.59/1.63 ( ! [X2 : a,X0 : a,X1 : a > a] : ((((^[Y0 : a]: (((sK4 @ Y0) = (sK8 @ X0 @ X1)) & (sK1 @ Y0))) @ X2) = ((sK5 @ (sK8 @ X0 @ X1)) = X2)) | ((sK0 @ (sK3 @ X1)) = $true) | ((sK8 @ X0 @ X1) = X0)) )),
% 1.59/1.63 inference(argument_congruence,[status(thm)],[f38])).
% 1.59/1.63 thf(f38,plain,(
% 1.59/1.63 ( ! [X0 : a,X1 : a > a] : (((^[Y0 : a]: (((sK4 @ Y0) = (sK8 @ X0 @ X1)) & (sK1 @ Y0))) = (= @ (sK5 @ (sK8 @ X0 @ X1)))) | ((sK0 @ (sK3 @ X1)) = $true) | ((sK8 @ X0 @ X1) = X0)) )),
% 1.59/1.63 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.59/1.63 thf(f37,plain,(
% 1.59/1.63 ( ! [X0 : a,X1 : a > a] : (($true != $true) | ((sK8 @ X0 @ X1) = X0) | ((sK0 @ (sK3 @ X1)) = $true) | ((^[Y0 : a]: (((sK4 @ Y0) = (sK8 @ X0 @ X1)) & (sK1 @ Y0))) = (= @ (sK5 @ (sK8 @ X0 @ X1))))) )),
% 1.59/1.63 inference(superposition,[status(thm)],[f23,f34])).
% 1.59/1.63 thf(f34,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (((sK0 @ (sK8 @ X4 @ X2)) = $true) | ($true = (sK0 @ (sK3 @ X2))) | ((sK8 @ X4 @ X2) = X4)) )),
% 1.59/1.63 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.59/1.63 thf(f719,plain,(
% 1.59/1.63 ~spl6_5),
% 1.59/1.63 inference(avatar_contradiction_clause,[status(thm)],[f718])).
% 1.59/1.63 thf(f718,plain,(
% 1.59/1.63 $false | ~spl6_5),
% 1.59/1.63 inference(trivial_inequality_removal,[status(thm)],[f717])).
% 1.59/1.63 thf(f717,plain,(
% 1.59/1.63 ($true = $false) | ~spl6_5),
% 1.59/1.63 inference(backward_demodulation,[status(thm)],[f72,f716])).
% 1.59/1.63 thf(f716,plain,(
% 1.59/1.63 ((sK0 @ (sK4 @ (sK2 @ sK5))) = $false) | ~spl6_5),
% 1.59/1.63 inference(subsumption_resolution,[status(thm)],[f715,f382])).
% 1.59/1.63 thf(f715,plain,(
% 1.59/1.63 ((sK2 @ sK5) != (sK5 @ (sK4 @ (sK2 @ sK5)))) | ((sK0 @ (sK4 @ (sK2 @ sK5))) = $false) | ~spl6_5),
% 1.59/1.63 inference(subsumption_resolution,[status(thm)],[f714,f311])).
% 1.59/1.63 thf(f311,plain,(
% 1.59/1.63 ($true = (sK1 @ (sK5 @ (sK3 @ sK5)))) | ~spl6_5),
% 1.59/1.63 inference(equality_resolution,[status(thm)],[f305])).
% 1.59/1.63 thf(f305,plain,(
% 1.59/1.63 ( ! [X1 : a] : (((sK5 @ (sK3 @ sK5)) != X1) | ($true = (sK1 @ X1))) ) | ~spl6_5),
% 1.59/1.63 inference(binary_proxy_clausification,[status(thm)],[f304])).
% 1.59/1.63 thf(f304,plain,(
% 1.59/1.63 ( ! [X1 : a] : (($true = (((sK4 @ X1) = (sK3 @ sK5)) & (sK1 @ X1))) | ((sK5 @ (sK3 @ sK5)) != X1)) ) | ~spl6_5),
% 1.59/1.63 inference(equality_proxy_clausification,[status(thm)],[f303])).
% 1.59/1.63 thf(f303,plain,(
% 1.59/1.63 ( ! [X1 : a] : ((((sK5 @ (sK3 @ sK5)) = X1) = $false) | ($true = (((sK4 @ X1) = (sK3 @ sK5)) & (sK1 @ X1)))) ) | ~spl6_5),
% 1.59/1.63 inference(binary_proxy_clausification,[status(thm)],[f301])).
% 1.59/1.63 thf(f301,plain,(
% 1.59/1.63 ( ! [X1 : a] : ((((sK5 @ (sK3 @ sK5)) = X1) = (((sK4 @ X1) = (sK3 @ sK5)) & (sK1 @ X1)))) ) | ~spl6_5),
% 1.59/1.63 inference(beta_eta_normalization,[status(thm)],[f300])).
% 1.59/1.63 thf(f300,plain,(
% 1.59/1.63 ( ! [X1 : a] : ((((^[Y0 : a]: (((sK4 @ Y0) = (sK3 @ sK5)) & (sK1 @ Y0))) @ X1) = ((sK5 @ (sK3 @ sK5)) = X1))) ) | ~spl6_5),
% 1.59/1.63 inference(argument_congruence,[status(thm)],[f141])).
% 1.59/1.63 thf(f141,plain,(
% 1.59/1.63 ((^[Y0 : a]: (((sK4 @ Y0) = (sK3 @ sK5)) & (sK1 @ Y0))) = (= @ (sK5 @ (sK3 @ sK5)))) | ~spl6_5),
% 1.59/1.63 inference(trivial_inequality_removal,[status(thm)],[f140])).
% 1.59/1.63 thf(f140,plain,(
% 1.59/1.63 ((^[Y0 : a]: (((sK4 @ Y0) = (sK3 @ sK5)) & (sK1 @ Y0))) = (= @ (sK5 @ (sK3 @ sK5)))) | ($true != $true) | ~spl6_5),
% 1.59/1.63 inference(superposition,[status(thm)],[f23,f118])).
% 1.59/1.63 thf(f118,plain,(
% 1.59/1.63 ($true = (sK0 @ (sK3 @ sK5))) | ~spl6_5),
% 1.59/1.63 inference(avatar_component_clause,[status(thm)],[f116])).
% 1.59/1.63 thf(f714,plain,(
% 1.59/1.63 ($true != (sK1 @ (sK5 @ (sK3 @ sK5)))) | ((sK2 @ sK5) != (sK5 @ (sK4 @ (sK2 @ sK5)))) | ((sK0 @ (sK4 @ (sK2 @ sK5))) = $false) | ~spl6_5),
% 1.59/1.63 inference(trivial_inequality_removal,[status(thm)],[f707])).
% 1.59/1.63 thf(f707,plain,(
% 1.59/1.63 ((sK0 @ (sK4 @ (sK2 @ sK5))) = $false) | ((sK2 @ sK5) != (sK5 @ (sK4 @ (sK2 @ sK5)))) | ((sK4 @ (sK2 @ sK5)) != (sK4 @ (sK2 @ sK5))) | ($true != (sK1 @ (sK5 @ (sK3 @ sK5)))) | ~spl6_5),
% 1.59/1.63 inference(superposition,[status(thm)],[f45,f700])).
% 1.59/1.63 thf(f700,plain,(
% 1.59/1.63 ((sK4 @ (sK2 @ sK5)) = (sK9 @ (sK4 @ (sK2 @ sK5)) @ sK5)) | ~spl6_5),
% 1.59/1.63 inference(equality_resolution,[status(thm)],[f693])).
% 1.59/1.63 thf(f693,plain,(
% 1.59/1.63 ( ! [X0 : a] : (((sK4 @ (sK2 @ sK5)) != X0) | ((sK9 @ X0 @ sK5) = X0)) ) | ~spl6_5),
% 1.59/1.63 inference(trivial_inequality_removal,[status(thm)],[f692])).
% 1.59/1.63 thf(f692,plain,(
% 1.59/1.63 ( ! [X0 : a] : (((sK9 @ X0 @ sK5) = X0) | ($true = $false) | ((sK4 @ (sK2 @ sK5)) != X0)) ) | ~spl6_5),
% 1.59/1.63 inference(forward_demodulation,[status(thm)],[f691,f72])).
% 1.59/1.63 thf(f691,plain,(
% 1.59/1.63 ( ! [X0 : a] : (((sK0 @ (sK4 @ (sK2 @ sK5))) = $false) | ((sK4 @ (sK2 @ sK5)) != X0) | ((sK9 @ X0 @ sK5) = X0)) ) | ~spl6_5),
% 1.59/1.63 inference(subsumption_resolution,[status(thm)],[f690,f382])).
% 1.59/1.63 thf(f690,plain,(
% 1.59/1.63 ( ! [X0 : a] : (((sK2 @ sK5) != (sK5 @ (sK4 @ (sK2 @ sK5)))) | ((sK9 @ X0 @ sK5) = X0) | ((sK4 @ (sK2 @ sK5)) != X0) | ((sK0 @ (sK4 @ (sK2 @ sK5))) = $false)) ) | ~spl6_5),
% 1.59/1.63 inference(subsumption_resolution,[status(thm)],[f681,f311])).
% 1.59/1.63 thf(f681,plain,(
% 1.59/1.63 ( ! [X0 : a] : (((sK9 @ X0 @ sK5) = X0) | ((sK4 @ (sK2 @ sK5)) != X0) | ($true != (sK1 @ (sK5 @ (sK3 @ sK5)))) | ((sK2 @ sK5) != (sK5 @ (sK4 @ (sK2 @ sK5)))) | ((sK0 @ (sK4 @ (sK2 @ sK5))) = $false)) ) | ~spl6_5),
% 1.59/1.63 inference(superposition,[status(thm)],[f45,f676])).
% 1.59/1.63 thf(f676,plain,(
% 1.59/1.63 ( ! [X0 : a] : (((sK4 @ (sK2 @ sK5)) = (sK9 @ X0 @ sK5)) | ((sK9 @ X0 @ sK5) = X0)) ) | ~spl6_5),
% 1.59/1.63 inference(equality_resolution,[status(thm)],[f671])).
% 1.59/1.63 thf(f671,plain,(
% 1.59/1.63 ( ! [X0 : a,X1 : a] : (((sK2 @ sK5) != X1) | ((sK9 @ X0 @ sK5) = (sK4 @ X1)) | ((sK9 @ X0 @ sK5) = X0)) ) | ~spl6_5),
% 1.59/1.63 inference(duplicate_literal_removal,[status(thm)],[f669])).
% 1.59/1.63 thf(f669,plain,(
% 1.59/1.63 ( ! [X0 : a,X1 : a] : (((sK9 @ X0 @ sK5) = (sK4 @ X1)) | ((sK9 @ X0 @ sK5) = X0) | ((sK9 @ X0 @ sK5) = X0) | ((sK2 @ sK5) != X1)) ) | ~spl6_5),
% 1.59/1.63 inference(superposition,[status(thm)],[f581,f317])).
% 1.59/1.63 thf(f317,plain,(
% 1.59/1.63 ( ! [X0 : a] : (((sK2 @ sK5) = (sK5 @ (sK9 @ X0 @ sK5))) | ((sK9 @ X0 @ sK5) = X0)) ) | ~spl6_5),
% 1.59/1.63 inference(trivial_inequality_removal,[status(thm)],[f313])).
% 1.59/1.63 thf(f313,plain,(
% 1.59/1.63 ( ! [X0 : a] : (((sK2 @ sK5) = (sK5 @ (sK9 @ X0 @ sK5))) | ((sK9 @ X0 @ sK5) = X0) | ($true != $true)) ) | ~spl6_5),
% 1.59/1.63 inference(superposition,[status(thm)],[f49,f311])).
% 1.59/1.63 thf(f49,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (((sK1 @ (X2 @ (sK3 @ X2))) != $true) | ((X2 @ (sK9 @ X4 @ X2)) = (sK2 @ X2)) | ((sK9 @ X4 @ X2) = X4)) )),
% 1.59/1.63 inference(equality_proxy_clausification,[status(thm)],[f48])).
% 1.59/1.63 thf(f48,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (((X4 = (sK9 @ X4 @ X2)) = $true) | ((X2 @ (sK9 @ X4 @ X2)) = (sK2 @ X2)) | ((sK1 @ (X2 @ (sK3 @ X2))) != $true)) )),
% 1.59/1.63 inference(equality_proxy_clausification,[status(thm)],[f47])).
% 1.59/1.63 thf(f47,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (($true = ((X2 @ (sK9 @ X4 @ X2)) = (sK2 @ X2))) | ((X4 = (sK9 @ X4 @ X2)) = $true) | ((sK1 @ (X2 @ (sK3 @ X2))) != $true)) )),
% 1.59/1.63 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.59/1.63 thf(f41,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (((sK1 @ (X2 @ (sK3 @ X2))) != $true) | ($true = (((X2 @ (sK9 @ X4 @ X2)) = (sK2 @ X2)) & (sK0 @ (sK9 @ X4 @ X2)))) | ((X4 = (sK9 @ X4 @ X2)) = $true)) )),
% 1.59/1.63 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.59/1.63 thf(f40,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (((X4 = (sK9 @ X4 @ X2)) != (((X2 @ (sK9 @ X4 @ X2)) = (sK2 @ X2)) & (sK0 @ (sK9 @ X4 @ X2)))) | ((sK1 @ (X2 @ (sK3 @ X2))) != $true)) )),
% 1.59/1.63 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.59/1.63 thf(f39,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (((X4 = (sK9 @ X4 @ X2)) != ((^[Y0 : a]: (((X2 @ Y0) = (sK2 @ X2)) & (sK0 @ Y0))) @ (sK9 @ X4 @ X2))) | ((sK1 @ (X2 @ (sK3 @ X2))) != $true)) )),
% 1.59/1.63 inference(negative_extensionality,[status(thm)],[f21])).
% 1.59/1.63 thf(f21,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (((^[Y0 : a]: (((X2 @ Y0) = (sK2 @ X2)) & (sK0 @ Y0))) != (= @ X4)) | ((sK1 @ (X2 @ (sK3 @ X2))) != $true)) )),
% 1.59/1.63 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.59/1.63 thf(f20,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : ((((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X4) != (^[Y0 : a]: (((X2 @ Y0) = (sK2 @ X2)) & (sK0 @ Y0)))) | ((sK1 @ (X2 @ (sK3 @ X2))) != $true)) )),
% 1.59/1.63 inference(cnf_transformation,[status(thm)],[f14])).
% 1.59/1.63 thf(f581,plain,(
% 1.59/1.63 ( ! [X0 : a,X1 : a] : (((sK5 @ (sK9 @ X0 @ sK5)) != X1) | ((sK9 @ X0 @ sK5) = (sK4 @ X1)) | ((sK9 @ X0 @ sK5) = X0)) ) | ~spl6_5),
% 1.59/1.63 inference(equality_proxy_clausification,[status(thm)],[f580])).
% 1.59/1.63 thf(f580,plain,(
% 1.59/1.63 ( ! [X0 : a,X1 : a] : (($true = ((sK4 @ X1) = (sK9 @ X0 @ sK5))) | ((sK9 @ X0 @ sK5) = X0) | ((sK5 @ (sK9 @ X0 @ sK5)) != X1)) ) | ~spl6_5),
% 1.59/1.63 inference(binary_proxy_clausification,[status(thm)],[f578])).
% 1.59/1.63 thf(f578,plain,(
% 1.59/1.63 ( ! [X0 : a,X1 : a] : (((sK9 @ X0 @ sK5) = X0) | ((sK5 @ (sK9 @ X0 @ sK5)) != X1) | ($true = (((sK4 @ X1) = (sK9 @ X0 @ sK5)) & (sK1 @ X1)))) ) | ~spl6_5),
% 1.59/1.63 inference(equality_proxy_clausification,[status(thm)],[f577])).
% 1.59/1.63 thf(f577,plain,(
% 1.59/1.63 ( ! [X0 : a,X1 : a] : ((((sK5 @ (sK9 @ X0 @ sK5)) = X1) = $false) | ($true = (((sK4 @ X1) = (sK9 @ X0 @ sK5)) & (sK1 @ X1))) | ((sK9 @ X0 @ sK5) = X0)) ) | ~spl6_5),
% 1.59/1.63 inference(binary_proxy_clausification,[status(thm)],[f575])).
% 1.59/1.63 thf(f575,plain,(
% 1.59/1.63 ( ! [X0 : a,X1 : a] : (((sK9 @ X0 @ sK5) = X0) | (((sK5 @ (sK9 @ X0 @ sK5)) = X1) = (((sK4 @ X1) = (sK9 @ X0 @ sK5)) & (sK1 @ X1)))) ) | ~spl6_5),
% 1.59/1.63 inference(beta_eta_normalization,[status(thm)],[f574])).
% 1.59/1.63 thf(f574,plain,(
% 1.59/1.63 ( ! [X0 : a,X1 : a] : ((((sK5 @ (sK9 @ X0 @ sK5)) = X1) = ((^[Y0 : a]: (((sK4 @ Y0) = (sK9 @ X0 @ sK5)) & (sK1 @ Y0))) @ X1)) | ((sK9 @ X0 @ sK5) = X0)) ) | ~spl6_5),
% 1.59/1.63 inference(argument_congruence,[status(thm)],[f471])).
% 1.59/1.63 thf(f471,plain,(
% 1.59/1.63 ( ! [X0 : a] : (((= @ (sK5 @ (sK9 @ X0 @ sK5))) = (^[Y0 : a]: (((sK4 @ Y0) = (sK9 @ X0 @ sK5)) & (sK1 @ Y0)))) | ((sK9 @ X0 @ sK5) = X0)) ) | ~spl6_5),
% 1.59/1.63 inference(trivial_inequality_removal,[status(thm)],[f470])).
% 1.59/1.63 thf(f470,plain,(
% 1.59/1.63 ( ! [X0 : a] : (($true != $true) | ((= @ (sK5 @ (sK9 @ X0 @ sK5))) = (^[Y0 : a]: (((sK4 @ Y0) = (sK9 @ X0 @ sK5)) & (sK1 @ Y0)))) | ((sK9 @ X0 @ sK5) = X0)) ) | ~spl6_5),
% 1.59/1.63 inference(superposition,[status(thm)],[f23,f318])).
% 1.59/1.63 thf(f318,plain,(
% 1.59/1.63 ( ! [X0 : a] : (((sK0 @ (sK9 @ X0 @ sK5)) = $true) | ((sK9 @ X0 @ sK5) = X0)) ) | ~spl6_5),
% 1.59/1.63 inference(trivial_inequality_removal,[status(thm)],[f314])).
% 1.59/1.63 thf(f314,plain,(
% 1.59/1.63 ( ! [X0 : a] : (((sK0 @ (sK9 @ X0 @ sK5)) = $true) | ($true != $true) | ((sK9 @ X0 @ sK5) = X0)) ) | ~spl6_5),
% 1.59/1.63 inference(superposition,[status(thm)],[f50,f311])).
% 1.59/1.63 thf(f50,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (((sK1 @ (X2 @ (sK3 @ X2))) != $true) | ($true = (sK0 @ (sK9 @ X4 @ X2))) | ((sK9 @ X4 @ X2) = X4)) )),
% 1.59/1.63 inference(equality_proxy_clausification,[status(thm)],[f46])).
% 1.59/1.63 thf(f46,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (((sK1 @ (X2 @ (sK3 @ X2))) != $true) | ((X4 = (sK9 @ X4 @ X2)) = $true) | ($true = (sK0 @ (sK9 @ X4 @ X2)))) )),
% 1.59/1.63 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.59/1.63 thf(f45,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (((X2 @ (sK9 @ X4 @ X2)) != (sK2 @ X2)) | ((sK9 @ X4 @ X2) != X4) | ($false = (sK0 @ (sK9 @ X4 @ X2))) | ((sK1 @ (X2 @ (sK3 @ X2))) != $true)) )),
% 1.59/1.63 inference(equality_proxy_clausification,[status(thm)],[f44])).
% 1.59/1.63 thf(f44,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (($false = ((X2 @ (sK9 @ X4 @ X2)) = (sK2 @ X2))) | ((sK1 @ (X2 @ (sK3 @ X2))) != $true) | ($false = (sK0 @ (sK9 @ X4 @ X2))) | ((sK9 @ X4 @ X2) != X4)) )),
% 1.59/1.63 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.59/1.63 thf(f43,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (((sK9 @ X4 @ X2) != X4) | ((sK1 @ (X2 @ (sK3 @ X2))) != $true) | ($false = (((X2 @ (sK9 @ X4 @ X2)) = (sK2 @ X2)) & (sK0 @ (sK9 @ X4 @ X2))))) )),
% 1.59/1.63 inference(equality_proxy_clausification,[status(thm)],[f42])).
% 1.59/1.63 thf(f42,plain,(
% 1.59/1.63 ( ! [X2 : a > a,X4 : a] : (((X4 = (sK9 @ X4 @ X2)) = $false) | ((sK1 @ (X2 @ (sK3 @ X2))) != $true) | ($false = (((X2 @ (sK9 @ X4 @ X2)) = (sK2 @ X2)) & (sK0 @ (sK9 @ X4 @ X2))))) )),
% 1.59/1.63 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.59/1.63 % SZS output end Proof for DTF2THF_6063
% 1.59/1.63 % (6204)------------------------------
% 1.59/1.63 % (6204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.63 % (6204)Termination reason: Refutation
% 1.59/1.63
% 1.59/1.63 % (6204)Memory used [KB]: 6268
% 1.59/1.63 % (6204)Time elapsed: 0.192 s
% 1.59/1.63 % (6204)Instructions burned: 322 (million)
% 1.59/1.63 % (6204)------------------------------
% 1.59/1.63 % (6204)------------------------------
% 1.59/1.63 % (6174)Success in time 0.369 s
%------------------------------------------------------------------------------