%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV210^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:35:12 AM UTC 2026
% Result : Theorem 0.21s 0.37s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 1
% Syntax : Number of formulae : 86 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 552 ( 345 equ; 0 cnn)
% Maximal formula atoms : 165 ( 6 avg)
% Number of connectives : 2147 ( 122 ~; 395 |; 130 &;1464 @)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 75 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 169 ( 169 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 7 con; 0-3 aty)
% Number of variables : 220 ( 0 ^; 166 !; 54 ?; 220 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
a: $tType ).
thf(decl_23,type,
v: a ).
thf(decl_24,type,
u: a ).
thf(decl_25,type,
cP: a > a > a ).
thf(decl_26,type,
y: a ).
thf(decl_27,type,
x: a ).
thf(decl_28,type,
cZ: a ).
thf(decl_29,type,
esk1_1: ( a > $o ) > a ).
thf(decl_30,type,
esk2_1: ( a > $o ) > a ).
thf(decl_31,type,
esk3_1: ( a > a > a > $o ) > a ).
thf(decl_32,type,
esk4_1: ( a > a > a > $o ) > a ).
thf(decl_33,type,
esk5_1: ( a > a > a > $o ) > a ).
thf(decl_34,type,
esk6_1: ( a > a > a > $o ) > a ).
thf(decl_35,type,
esk7_1: ( a > a > a > $o ) > a ).
thf(decl_36,type,
esk8_1: ( a > a > a > $o ) > a ).
thf(decl_37,type,
esk9_1: ( a > a > a > $o ) > a ).
thf(decl_38,type,
esk10_1: ( a > a > a > $o ) > a ).
thf(decl_39,type,
esk11_1: ( a > a > a > $o ) > a ).
thf(decl_40,type,
esk12_1: ( a > a > a > $o ) > a ).
thf(decl_41,type,
esk13_1: ( a > a > a > $o ) > a ).
thf(decl_42,type,
esk14_1: ( a > a > a > $o ) > a ).
thf(decl_43,type,
esk15_1: ( a > a > a > $o ) > a ).
thf(decl_44,type,
esk16_1: ( a > a > a > $o ) > a ).
thf(decl_45,type,
esk17_1: ( a > a > a > $o ) > a ).
thf(decl_46,type,
esk18_1: ( a > a > a > $o ) > a ).
thf(decl_47,type,
esk19_1: ( a > a > a > $o ) > a ).
thf(decl_48,type,
esk20_1: ( a > a > a > $o ) > a ).
thf(decl_49,type,
epred1_0: a > a > a > $o ).
thf(cS_LEM1E_pme,conjecture,
( ( ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
!= cZ )
& ! [X1: a,X2: a,X3: a,X4: a] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ( ( X1 = X2 )
& ( X3 = X4 ) ) )
& ! [X5: a > $o] :
( ( ( X5 @ cZ )
& ! [X1: a,X2: a] :
( ( ( X5 @ X1 )
& ( X5 @ X2 ) )
=> ( X5 @ ( cP @ X1 @ X2 ) ) ) )
=> ! [X1: a] : ( X5 @ X1 ) ) )
=> ( ! [X6: a > a > a > $o] :
( ( $true
& ! [X7: a,X8: a,X9: a] :
( ( ( ( X7 = cZ )
& ( X8 = X9 ) )
| ( ( X8 = cZ )
& ( X7 = X9 ) )
| ? [X10: a,X11: a,X12: a,X13: a,X14: a,X15: a] :
( ( X7
= ( cP @ X10 @ X11 ) )
& ( X8
= ( cP @ X12 @ X13 ) )
& ( X9
= ( cP @ X14 @ X15 ) )
& ( X6 @ X10 @ X12 @ X14 )
& ( X6 @ X11 @ X13 @ X15 ) ) )
=> ( X6 @ X7 @ X8 @ X9 ) ) )
=> ( X6 @ x @ u @ u ) )
=> ( ! [X6: a > a > a > $o] :
( ( $true
& ! [X7: a,X8: a,X9: a] :
( ( ( ( X7 = cZ )
& ( X8 = X9 ) )
| ( ( X8 = cZ )
& ( X7 = X9 ) )
| ? [X10: a,X11: a,X12: a,X13: a,X14: a,X15: a] :
( ( X7
= ( cP @ X10 @ X11 ) )
& ( X8
= ( cP @ X12 @ X13 ) )
& ( X9
= ( cP @ X14 @ X15 ) )
& ( X6 @ X10 @ X12 @ X14 )
& ( X6 @ X11 @ X13 @ X15 ) ) )
=> ( X6 @ X7 @ X8 @ X9 ) ) )
=> ( X6 @ y @ v @ v ) )
=> ! [X6: a > a > a > $o] :
( ( $true
& ! [X7: a,X8: a,X9: a] :
( ( ( ( X7 = cZ )
& ( X8 = X9 ) )
| ( ( X8 = cZ )
& ( X7 = X9 ) )
| ? [X10: a,X11: a,X12: a,X13: a,X14: a,X15: a] :
( ( X7
= ( cP @ X10 @ X11 ) )
& ( X8
= ( cP @ X12 @ X13 ) )
& ( X9
= ( cP @ X14 @ X15 ) )
& ( X6 @ X10 @ X12 @ X14 )
& ( X6 @ X11 @ X13 @ X15 ) ) )
=> ( X6 @ X7 @ X8 @ X9 ) ) )
=> ( X6 @ ( cP @ x @ y ) @ ( cP @ u @ v ) @ ( cP @ u @ v ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.c6kLyUOAKY/E---3.1_911251.p',cS_LEM1E_pme) ).
thf(c_0_1,negated_conjecture,
~ ( ( ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
!= cZ )
& ! [X1: a,X2: a,X3: a,X4: a] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ( ( X1 = X2 )
& ( X3 = X4 ) ) )
& ! [X5: a > $o] :
( ( ( X5 @ cZ )
& ! [X1: a,X2: a] :
( ( ( X5 @ X1 )
& ( X5 @ X2 ) )
=> ( X5 @ ( cP @ X1 @ X2 ) ) ) )
=> ! [X1: a] : ( X5 @ X1 ) ) )
=> ( ! [X6: a > a > a > $o] :
( ( $true
& ! [X7: a,X8: a,X9: a] :
( ( ( ( X7 = cZ )
& ( X8 = X9 ) )
| ( ( X8 = cZ )
& ( X7 = X9 ) )
| ? [X10: a,X11: a,X12: a,X13: a,X14: a,X15: a] :
( ( X7
= ( cP @ X10 @ X11 ) )
& ( X8
= ( cP @ X12 @ X13 ) )
& ( X9
= ( cP @ X14 @ X15 ) )
& ( X6 @ X10 @ X12 @ X14 )
& ( X6 @ X11 @ X13 @ X15 ) ) )
=> ( X6 @ X7 @ X8 @ X9 ) ) )
=> ( X6 @ x @ u @ u ) )
=> ( ! [X6: a > a > a > $o] :
( ( $true
& ! [X7: a,X8: a,X9: a] :
( ( ( ( X7 = cZ )
& ( X8 = X9 ) )
| ( ( X8 = cZ )
& ( X7 = X9 ) )
| ? [X10: a,X11: a,X12: a,X13: a,X14: a,X15: a] :
( ( X7
= ( cP @ X10 @ X11 ) )
& ( X8
= ( cP @ X12 @ X13 ) )
& ( X9
= ( cP @ X14 @ X15 ) )
& ( X6 @ X10 @ X12 @ X14 )
& ( X6 @ X11 @ X13 @ X15 ) ) )
=> ( X6 @ X7 @ X8 @ X9 ) ) )
=> ( X6 @ y @ v @ v ) )
=> ! [X6: a > a > a > $o] :
( ( $true
& ! [X7: a,X8: a,X9: a] :
( ( ( ( X7 = cZ )
& ( X8 = X9 ) )
| ( ( X8 = cZ )
& ( X7 = X9 ) )
| ? [X10: a,X11: a,X12: a,X13: a,X14: a,X15: a] :
( ( X7
= ( cP @ X10 @ X11 ) )
& ( X8
= ( cP @ X12 @ X13 ) )
& ( X9
= ( cP @ X14 @ X15 ) )
& ( X6 @ X10 @ X12 @ X14 )
& ( X6 @ X11 @ X13 @ X15 ) ) )
=> ( X6 @ X7 @ X8 @ X9 ) ) )
=> ( X6 @ ( cP @ x @ y ) @ ( cP @ u @ v ) @ ( cP @ u @ v ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cS_LEM1E_pme]) ).
thf(c_0_2,negated_conjecture,
~ ( ( ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
!= cZ )
& ! [X1: a,X2: a,X3: a,X4: a] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ( ( X1 = X2 )
& ( X3 = X4 ) ) )
& ! [X5: a > $o] :
( ( ( X5 @ cZ )
& ! [X1: a,X2: a] :
( ( ( X5 @ X1 )
& ( X5 @ X2 ) )
=> ( X5 @ ( cP @ X1 @ X2 ) ) ) )
=> ! [X1: a] : ( X5 @ X1 ) ) )
=> ( ! [X6: a > a > a > $o] :
( ( $true
& ! [X7: a,X8: a,X9: a] :
( ( ( ( X7 = cZ )
& ( X8 = X9 ) )
| ( ( X8 = cZ )
& ( X7 = X9 ) )
| ? [X10: a,X11: a,X12: a,X13: a,X14: a,X15: a] :
( ( X7
= ( cP @ X10 @ X11 ) )
& ( X8
= ( cP @ X12 @ X13 ) )
& ( X9
= ( cP @ X14 @ X15 ) )
& ( X6 @ X10 @ X12 @ X14 )
& ( X6 @ X11 @ X13 @ X15 ) ) )
=> ( X6 @ X7 @ X8 @ X9 ) ) )
=> ( X6 @ x @ u @ u ) )
=> ( ! [X6: a > a > a > $o] :
( ( $true
& ! [X7: a,X8: a,X9: a] :
( ( ( ( X7 = cZ )
& ( X8 = X9 ) )
| ( ( X8 = cZ )
& ( X7 = X9 ) )
| ? [X10: a,X11: a,X12: a,X13: a,X14: a,X15: a] :
( ( X7
= ( cP @ X10 @ X11 ) )
& ( X8
= ( cP @ X12 @ X13 ) )
& ( X9
= ( cP @ X14 @ X15 ) )
& ( X6 @ X10 @ X12 @ X14 )
& ( X6 @ X11 @ X13 @ X15 ) ) )
=> ( X6 @ X7 @ X8 @ X9 ) ) )
=> ( X6 @ y @ v @ v ) )
=> ! [X6: a > a > a > $o] :
( ( $true
& ! [X7: a,X8: a,X9: a] :
( ( ( ( X7 = cZ )
& ( X8 = X9 ) )
| ( ( X8 = cZ )
& ( X7 = X9 ) )
| ? [X10: a,X11: a,X12: a,X13: a,X14: a,X15: a] :
( ( X7
= ( cP @ X10 @ X11 ) )
& ( X8
= ( cP @ X12 @ X13 ) )
& ( X9
= ( cP @ X14 @ X15 ) )
& ( X6 @ X10 @ X12 @ X14 )
& ( X6 @ X11 @ X13 @ X15 ) ) )
=> ( X6 @ X7 @ X8 @ X9 ) ) )
=> ( X6 @ ( cP @ x @ y ) @ ( cP @ u @ v ) @ ( cP @ u @ v ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
thf(c_0_3,negated_conjecture,
! [X56: a,X57: a,X58: a,X59: a,X60: a,X61: a,X62: a > $o,X65: a,X66: a > a > a > $o,X76: a > a > a > $o,X87: a,X88: a,X89: a,X90: a,X91: a,X92: a,X93: a,X94: a,X95: a] :
( ( ( cP @ X56 @ X57 )
!= cZ )
& ( ( X58 = X59 )
| ( ( cP @ X58 @ X60 )
!= ( cP @ X59 @ X61 ) ) )
& ( ( X60 = X61 )
| ( ( cP @ X58 @ X60 )
!= ( cP @ X59 @ X61 ) ) )
& ( ( X62 @ ( esk1_1 @ X62 ) )
| ~ ( X62 @ cZ )
| ( X62 @ X65 ) )
& ( ( X62 @ ( esk2_1 @ X62 ) )
| ~ ( X62 @ cZ )
| ( X62 @ X65 ) )
& ( ~ ( X62 @ ( cP @ ( esk1_1 @ X62 ) @ ( esk2_1 @ X62 ) ) )
| ~ ( X62 @ cZ )
| ( X62 @ X65 ) )
& ( ( ( esk3_1 @ X66 )
= ( cP @ ( esk6_1 @ X66 ) @ ( esk7_1 @ X66 ) ) )
| ( ( esk4_1 @ X66 )
= cZ )
| ( ( esk3_1 @ X66 )
= cZ )
| ~ $true
| ( X66 @ x @ u @ u ) )
& ( ( ( esk4_1 @ X66 )
= ( cP @ ( esk8_1 @ X66 ) @ ( esk9_1 @ X66 ) ) )
| ( ( esk4_1 @ X66 )
= cZ )
| ( ( esk3_1 @ X66 )
= cZ )
| ~ $true
| ( X66 @ x @ u @ u ) )
& ( ( ( esk5_1 @ X66 )
= ( cP @ ( esk10_1 @ X66 ) @ ( esk11_1 @ X66 ) ) )
| ( ( esk4_1 @ X66 )
= cZ )
| ( ( esk3_1 @ X66 )
= cZ )
| ~ $true
| ( X66 @ x @ u @ u ) )
& ( ( X66 @ ( esk6_1 @ X66 ) @ ( esk8_1 @ X66 ) @ ( esk10_1 @ X66 ) )
| ( ( esk4_1 @ X66 )
= cZ )
| ( ( esk3_1 @ X66 )
= cZ )
| ~ $true
| ( X66 @ x @ u @ u ) )
& ( ( X66 @ ( esk7_1 @ X66 ) @ ( esk9_1 @ X66 ) @ ( esk11_1 @ X66 ) )
| ( ( esk4_1 @ X66 )
= cZ )
| ( ( esk3_1 @ X66 )
= cZ )
| ~ $true
| ( X66 @ x @ u @ u ) )
& ( ( ( esk3_1 @ X66 )
= ( cP @ ( esk6_1 @ X66 ) @ ( esk7_1 @ X66 ) ) )
| ( ( esk3_1 @ X66 )
= ( esk5_1 @ X66 ) )
| ( ( esk3_1 @ X66 )
= cZ )
| ~ $true
| ( X66 @ x @ u @ u ) )
& ( ( ( esk4_1 @ X66 )
= ( cP @ ( esk8_1 @ X66 ) @ ( esk9_1 @ X66 ) ) )
| ( ( esk3_1 @ X66 )
= ( esk5_1 @ X66 ) )
| ( ( esk3_1 @ X66 )
= cZ )
| ~ $true
| ( X66 @ x @ u @ u ) )
& ( ( ( esk5_1 @ X66 )
= ( cP @ ( esk10_1 @ X66 ) @ ( esk11_1 @ X66 ) ) )
| ( ( esk3_1 @ X66 )
= ( esk5_1 @ X66 ) )
| ( ( esk3_1 @ X66 )
= cZ )
| ~ $true
| ( X66 @ x @ u @ u ) )
& ( ( X66 @ ( esk6_1 @ X66 ) @ ( esk8_1 @ X66 ) @ ( esk10_1 @ X66 ) )
| ( ( esk3_1 @ X66 )
= ( esk5_1 @ X66 ) )
| ( ( esk3_1 @ X66 )
= cZ )
| ~ $true
| ( X66 @ x @ u @ u ) )
& ( ( X66 @ ( esk7_1 @ X66 ) @ ( esk9_1 @ X66 ) @ ( esk11_1 @ X66 ) )
| ( ( esk3_1 @ X66 )
= ( esk5_1 @ X66 ) )
| ( ( esk3_1 @ X66 )
= cZ )
| ~ $true
| ( X66 @ x @ u @ u ) )
& ( ( ( esk3_1 @ X66 )
= ( cP @ ( esk6_1 @ X66 ) @ ( esk7_1 @ X66 ) ) )
| ( ( esk4_1 @ X66 )
= cZ )
| ( ( esk4_1 @ X66 )
= ( esk5_1 @ X66 ) )
| ~ $true
| ( X66 @ x @ u @ u ) )
& ( ( ( esk4_1 @ X66 )
= ( cP @ ( esk8_1 @ X66 ) @ ( esk9_1 @ X66 ) ) )
| ( ( esk4_1 @ X66 )
= cZ )
| ( ( esk4_1 @ X66 )
= ( esk5_1 @ X66 ) )
| ~ $true
| ( X66 @ x @ u @ u ) )
& ( ( ( esk5_1 @ X66 )
= ( cP @ ( esk10_1 @ X66 ) @ ( esk11_1 @ X66 ) ) )
| ( ( esk4_1 @ X66 )
= cZ )
| ( ( esk4_1 @ X66 )
= ( esk5_1 @ X66 ) )
| ~ $true
| ( X66 @ x @ u @ u ) )
& ( ( X66 @ ( esk6_1 @ X66 ) @ ( esk8_1 @ X66 ) @ ( esk10_1 @ X66 ) )
| ( ( esk4_1 @ X66 )
= cZ )
| ( ( esk4_1 @ X66 )
= ( esk5_1 @ X66 ) )
| ~ $true
| ( X66 @ x @ u @ u ) )
& ( ( X66 @ ( esk7_1 @ X66 ) @ ( esk9_1 @ X66 ) @ ( esk11_1 @ X66 ) )
| ( ( esk4_1 @ X66 )
= cZ )
| ( ( esk4_1 @ X66 )
= ( esk5_1 @ X66 ) )
| ~ $true
| ( X66 @ x @ u @ u ) )
& ( ( ( esk3_1 @ X66 )
= ( cP @ ( esk6_1 @ X66 ) @ ( esk7_1 @ X66 ) ) )
| ( ( esk3_1 @ X66 )
= ( esk5_1 @ X66 ) )
| ( ( esk4_1 @ X66 )
= ( esk5_1 @ X66 ) )
| ~ $true
| ( X66 @ x @ u @ u ) )
& ( ( ( esk4_1 @ X66 )
= ( cP @ ( esk8_1 @ X66 ) @ ( esk9_1 @ X66 ) ) )
| ( ( esk3_1 @ X66 )
= ( esk5_1 @ X66 ) )
| ( ( esk4_1 @ X66 )
= ( esk5_1 @ X66 ) )
| ~ $true
| ( X66 @ x @ u @ u ) )
& ( ( ( esk5_1 @ X66 )
= ( cP @ ( esk10_1 @ X66 ) @ ( esk11_1 @ X66 ) ) )
| ( ( esk3_1 @ X66 )
= ( esk5_1 @ X66 ) )
| ( ( esk4_1 @ X66 )
= ( esk5_1 @ X66 ) )
| ~ $true
| ( X66 @ x @ u @ u ) )
& ( ( X66 @ ( esk6_1 @ X66 ) @ ( esk8_1 @ X66 ) @ ( esk10_1 @ X66 ) )
| ( ( esk3_1 @ X66 )
= ( esk5_1 @ X66 ) )
| ( ( esk4_1 @ X66 )
= ( esk5_1 @ X66 ) )
| ~ $true
| ( X66 @ x @ u @ u ) )
& ( ( X66 @ ( esk7_1 @ X66 ) @ ( esk9_1 @ X66 ) @ ( esk11_1 @ X66 ) )
| ( ( esk3_1 @ X66 )
= ( esk5_1 @ X66 ) )
| ( ( esk4_1 @ X66 )
= ( esk5_1 @ X66 ) )
| ~ $true
| ( X66 @ x @ u @ u ) )
& ( ~ ( X66 @ ( esk3_1 @ X66 ) @ ( esk4_1 @ X66 ) @ ( esk5_1 @ X66 ) )
| ~ $true
| ( X66 @ x @ u @ u ) )
& ( ( ( esk12_1 @ X76 )
= ( cP @ ( esk15_1 @ X76 ) @ ( esk16_1 @ X76 ) ) )
| ( ( esk13_1 @ X76 )
= cZ )
| ( ( esk12_1 @ X76 )
= cZ )
| ~ $true
| ( X76 @ y @ v @ v ) )
& ( ( ( esk13_1 @ X76 )
= ( cP @ ( esk17_1 @ X76 ) @ ( esk18_1 @ X76 ) ) )
| ( ( esk13_1 @ X76 )
= cZ )
| ( ( esk12_1 @ X76 )
= cZ )
| ~ $true
| ( X76 @ y @ v @ v ) )
& ( ( ( esk14_1 @ X76 )
= ( cP @ ( esk19_1 @ X76 ) @ ( esk20_1 @ X76 ) ) )
| ( ( esk13_1 @ X76 )
= cZ )
| ( ( esk12_1 @ X76 )
= cZ )
| ~ $true
| ( X76 @ y @ v @ v ) )
& ( ( X76 @ ( esk15_1 @ X76 ) @ ( esk17_1 @ X76 ) @ ( esk19_1 @ X76 ) )
| ( ( esk13_1 @ X76 )
= cZ )
| ( ( esk12_1 @ X76 )
= cZ )
| ~ $true
| ( X76 @ y @ v @ v ) )
& ( ( X76 @ ( esk16_1 @ X76 ) @ ( esk18_1 @ X76 ) @ ( esk20_1 @ X76 ) )
| ( ( esk13_1 @ X76 )
= cZ )
| ( ( esk12_1 @ X76 )
= cZ )
| ~ $true
| ( X76 @ y @ v @ v ) )
& ( ( ( esk12_1 @ X76 )
= ( cP @ ( esk15_1 @ X76 ) @ ( esk16_1 @ X76 ) ) )
| ( ( esk12_1 @ X76 )
= ( esk14_1 @ X76 ) )
| ( ( esk12_1 @ X76 )
= cZ )
| ~ $true
| ( X76 @ y @ v @ v ) )
& ( ( ( esk13_1 @ X76 )
= ( cP @ ( esk17_1 @ X76 ) @ ( esk18_1 @ X76 ) ) )
| ( ( esk12_1 @ X76 )
= ( esk14_1 @ X76 ) )
| ( ( esk12_1 @ X76 )
= cZ )
| ~ $true
| ( X76 @ y @ v @ v ) )
& ( ( ( esk14_1 @ X76 )
= ( cP @ ( esk19_1 @ X76 ) @ ( esk20_1 @ X76 ) ) )
| ( ( esk12_1 @ X76 )
= ( esk14_1 @ X76 ) )
| ( ( esk12_1 @ X76 )
= cZ )
| ~ $true
| ( X76 @ y @ v @ v ) )
& ( ( X76 @ ( esk15_1 @ X76 ) @ ( esk17_1 @ X76 ) @ ( esk19_1 @ X76 ) )
| ( ( esk12_1 @ X76 )
= ( esk14_1 @ X76 ) )
| ( ( esk12_1 @ X76 )
= cZ )
| ~ $true
| ( X76 @ y @ v @ v ) )
& ( ( X76 @ ( esk16_1 @ X76 ) @ ( esk18_1 @ X76 ) @ ( esk20_1 @ X76 ) )
| ( ( esk12_1 @ X76 )
= ( esk14_1 @ X76 ) )
| ( ( esk12_1 @ X76 )
= cZ )
| ~ $true
| ( X76 @ y @ v @ v ) )
& ( ( ( esk12_1 @ X76 )
= ( cP @ ( esk15_1 @ X76 ) @ ( esk16_1 @ X76 ) ) )
| ( ( esk13_1 @ X76 )
= cZ )
| ( ( esk13_1 @ X76 )
= ( esk14_1 @ X76 ) )
| ~ $true
| ( X76 @ y @ v @ v ) )
& ( ( ( esk13_1 @ X76 )
= ( cP @ ( esk17_1 @ X76 ) @ ( esk18_1 @ X76 ) ) )
| ( ( esk13_1 @ X76 )
= cZ )
| ( ( esk13_1 @ X76 )
= ( esk14_1 @ X76 ) )
| ~ $true
| ( X76 @ y @ v @ v ) )
& ( ( ( esk14_1 @ X76 )
= ( cP @ ( esk19_1 @ X76 ) @ ( esk20_1 @ X76 ) ) )
| ( ( esk13_1 @ X76 )
= cZ )
| ( ( esk13_1 @ X76 )
= ( esk14_1 @ X76 ) )
| ~ $true
| ( X76 @ y @ v @ v ) )
& ( ( X76 @ ( esk15_1 @ X76 ) @ ( esk17_1 @ X76 ) @ ( esk19_1 @ X76 ) )
| ( ( esk13_1 @ X76 )
= cZ )
| ( ( esk13_1 @ X76 )
= ( esk14_1 @ X76 ) )
| ~ $true
| ( X76 @ y @ v @ v ) )
& ( ( X76 @ ( esk16_1 @ X76 ) @ ( esk18_1 @ X76 ) @ ( esk20_1 @ X76 ) )
| ( ( esk13_1 @ X76 )
= cZ )
| ( ( esk13_1 @ X76 )
= ( esk14_1 @ X76 ) )
| ~ $true
| ( X76 @ y @ v @ v ) )
& ( ( ( esk12_1 @ X76 )
= ( cP @ ( esk15_1 @ X76 ) @ ( esk16_1 @ X76 ) ) )
| ( ( esk12_1 @ X76 )
= ( esk14_1 @ X76 ) )
| ( ( esk13_1 @ X76 )
= ( esk14_1 @ X76 ) )
| ~ $true
| ( X76 @ y @ v @ v ) )
& ( ( ( esk13_1 @ X76 )
= ( cP @ ( esk17_1 @ X76 ) @ ( esk18_1 @ X76 ) ) )
| ( ( esk12_1 @ X76 )
= ( esk14_1 @ X76 ) )
| ( ( esk13_1 @ X76 )
= ( esk14_1 @ X76 ) )
| ~ $true
| ( X76 @ y @ v @ v ) )
& ( ( ( esk14_1 @ X76 )
= ( cP @ ( esk19_1 @ X76 ) @ ( esk20_1 @ X76 ) ) )
| ( ( esk12_1 @ X76 )
= ( esk14_1 @ X76 ) )
| ( ( esk13_1 @ X76 )
= ( esk14_1 @ X76 ) )
| ~ $true
| ( X76 @ y @ v @ v ) )
& ( ( X76 @ ( esk15_1 @ X76 ) @ ( esk17_1 @ X76 ) @ ( esk19_1 @ X76 ) )
| ( ( esk12_1 @ X76 )
= ( esk14_1 @ X76 ) )
| ( ( esk13_1 @ X76 )
= ( esk14_1 @ X76 ) )
| ~ $true
| ( X76 @ y @ v @ v ) )
& ( ( X76 @ ( esk16_1 @ X76 ) @ ( esk18_1 @ X76 ) @ ( esk20_1 @ X76 ) )
| ( ( esk12_1 @ X76 )
= ( esk14_1 @ X76 ) )
| ( ( esk13_1 @ X76 )
= ( esk14_1 @ X76 ) )
| ~ $true
| ( X76 @ y @ v @ v ) )
& ( ~ ( X76 @ ( esk12_1 @ X76 ) @ ( esk13_1 @ X76 ) @ ( esk14_1 @ X76 ) )
| ~ $true
| ( X76 @ y @ v @ v ) )
& $true
& ( ( X87 != cZ )
| ( X88 != X89 )
| ( epred1_0 @ X87 @ X88 @ X89 ) )
& ( ( X88 != cZ )
| ( X87 != X89 )
| ( epred1_0 @ X87 @ X88 @ X89 ) )
& ( ( X87
!= ( cP @ X90 @ X91 ) )
| ( X88
!= ( cP @ X92 @ X93 ) )
| ( X89
!= ( cP @ X94 @ X95 ) )
| ~ ( epred1_0 @ X90 @ X92 @ X94 )
| ~ ( epred1_0 @ X91 @ X93 @ X95 )
| ( epred1_0 @ X87 @ X88 @ X89 ) )
& ~ ( epred1_0 @ ( cP @ x @ y ) @ ( cP @ u @ v ) @ ( cP @ u @ v ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])])])]) ).
thf(c_0_4,negated_conjecture,
! [X7: a,X1: a,X2: a,X4: a,X3: a,X9: a,X8: a,X10: a,X11: a] :
( ( epred1_0 @ X1 @ X4 @ X9 )
| ( X1
!= ( cP @ X2 @ X3 ) )
| ( X4
!= ( cP @ X7 @ X8 ) )
| ( X9
!= ( cP @ X10 @ X11 ) )
| ~ ( epred1_0 @ X2 @ X7 @ X10 )
| ~ ( epred1_0 @ X3 @ X8 @ X11 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk4_1 @ X6 )
= ( cP @ ( esk8_1 @ X6 ) @ ( esk9_1 @ X6 ) ) )
| ( ( esk4_1 @ X6 )
= cZ )
| ( ( esk3_1 @ X6 )
= cZ )
| ( X6 @ x @ u @ u )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_6,negated_conjecture,
! [X2: a,X8: a,X4: a,X3: a,X1: a,X7: a] :
( ( epred1_0 @ ( cP @ X1 @ X2 ) @ ( cP @ X3 @ X4 ) @ ( cP @ X7 @ X8 ) )
| ~ ( epred1_0 @ X2 @ X4 @ X8 )
| ~ ( epred1_0 @ X1 @ X3 @ X7 ) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_4])])]) ).
thf(c_0_7,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk3_1 @ X6 )
= cZ )
| ( ( esk4_1 @ X6 )
= cZ )
| ( ( esk4_1 @ X6 )
= ( cP @ ( esk8_1 @ X6 ) @ ( esk9_1 @ X6 ) ) )
| ( X6 @ x @ u @ u ) ),
inference(cn,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
! [X6: a > a > a > $o] :
( ( X6 @ ( esk7_1 @ X6 ) @ ( esk9_1 @ X6 ) @ ( esk11_1 @ X6 ) )
| ( ( esk4_1 @ X6 )
= cZ )
| ( ( esk3_1 @ X6 )
= cZ )
| ( X6 @ x @ u @ u )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_9,negated_conjecture,
! [X6: a > a > a > $o,X2: a,X1: a,X4: a,X3: a] :
( ( ( esk4_1 @ X6 )
= cZ )
| ( ( esk3_1 @ X6 )
= cZ )
| ( epred1_0 @ ( cP @ X1 @ X2 ) @ ( esk4_1 @ X6 ) @ ( cP @ X3 @ X4 ) )
| ( X6 @ x @ u @ u )
| ~ ( epred1_0 @ X2 @ ( esk9_1 @ X6 ) @ X4 )
| ~ ( epred1_0 @ X1 @ ( esk8_1 @ X6 ) @ X3 ) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk3_1 @ X6 )
= cZ )
| ( ( esk4_1 @ X6 )
= cZ )
| ( X6 @ x @ u @ u )
| ( X6 @ ( esk7_1 @ X6 ) @ ( esk9_1 @ X6 ) @ ( esk11_1 @ X6 ) ) ),
inference(cn,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
! [X6: a > a > a > $o] :
( ( X6 @ ( esk6_1 @ X6 ) @ ( esk8_1 @ X6 ) @ ( esk10_1 @ X6 ) )
| ( ( esk4_1 @ X6 )
= cZ )
| ( ( esk3_1 @ X6 )
= cZ )
| ( X6 @ x @ u @ u )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_12,negated_conjecture,
! [X1: a,X2: a] :
( ( ( esk3_1 @ epred1_0 )
= cZ )
| ( ( esk4_1 @ epred1_0 )
= cZ )
| ( epred1_0 @ ( cP @ X1 @ ( esk7_1 @ epred1_0 ) ) @ ( esk4_1 @ epred1_0 ) @ ( cP @ X2 @ ( esk11_1 @ epred1_0 ) ) )
| ( epred1_0 @ x @ u @ u )
| ~ ( epred1_0 @ X1 @ ( esk8_1 @ epred1_0 ) @ X2 ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_13,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk3_1 @ X6 )
= cZ )
| ( ( esk4_1 @ X6 )
= cZ )
| ( X6 @ x @ u @ u )
| ( X6 @ ( esk6_1 @ X6 ) @ ( esk8_1 @ X6 ) @ ( esk10_1 @ X6 ) ) ),
inference(cn,[status(thm)],[c_0_11]) ).
thf(c_0_14,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk5_1 @ X6 )
= ( cP @ ( esk10_1 @ X6 ) @ ( esk11_1 @ X6 ) ) )
| ( ( esk4_1 @ X6 )
= cZ )
| ( ( esk3_1 @ X6 )
= cZ )
| ( X6 @ x @ u @ u )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_15,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk3_1 @ X6 )
= ( cP @ ( esk6_1 @ X6 ) @ ( esk7_1 @ X6 ) ) )
| ( ( esk4_1 @ X6 )
= cZ )
| ( ( esk4_1 @ X6 )
= ( esk5_1 @ X6 ) )
| ( X6 @ x @ u @ u )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_16,negated_conjecture,
( ( ( esk4_1 @ epred1_0 )
= cZ )
| ( ( esk3_1 @ epred1_0 )
= cZ )
| ( epred1_0 @ ( cP @ ( esk6_1 @ epred1_0 ) @ ( esk7_1 @ epred1_0 ) ) @ ( esk4_1 @ epred1_0 ) @ ( cP @ ( esk10_1 @ epred1_0 ) @ ( esk11_1 @ epred1_0 ) ) )
| ( epred1_0 @ x @ u @ u ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_17,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk3_1 @ X6 )
= cZ )
| ( ( esk4_1 @ X6 )
= cZ )
| ( ( esk5_1 @ X6 )
= ( cP @ ( esk10_1 @ X6 ) @ ( esk11_1 @ X6 ) ) )
| ( X6 @ x @ u @ u ) ),
inference(cn,[status(thm)],[c_0_14]) ).
thf(c_0_18,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk3_1 @ X6 )
= ( cP @ ( esk6_1 @ X6 ) @ ( esk7_1 @ X6 ) ) )
| ( ( esk4_1 @ X6 )
= cZ )
| ( ( esk3_1 @ X6 )
= cZ )
| ( X6 @ x @ u @ u )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_19,negated_conjecture,
! [X6: a > a > a > $o] :
( ( X6 @ x @ u @ u )
| ~ ( X6 @ ( esk3_1 @ X6 ) @ ( esk4_1 @ X6 ) @ ( esk5_1 @ X6 ) )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_20,negated_conjecture,
! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
!= cZ ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_21,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk4_1 @ X6 )
= cZ )
| ( ( esk5_1 @ X6 )
= ( esk4_1 @ X6 ) )
| ( ( esk3_1 @ X6 )
= ( cP @ ( esk6_1 @ X6 ) @ ( esk7_1 @ X6 ) ) )
| ( X6 @ x @ u @ u ) ),
inference(cn,[status(thm)],[c_0_15]) ).
thf(c_0_22,negated_conjecture,
( ( ( esk3_1 @ epred1_0 )
= cZ )
| ( ( esk4_1 @ epred1_0 )
= cZ )
| ( epred1_0 @ ( cP @ ( esk6_1 @ epred1_0 ) @ ( esk7_1 @ epred1_0 ) ) @ ( esk4_1 @ epred1_0 ) @ ( esk5_1 @ epred1_0 ) )
| ( epred1_0 @ x @ u @ u ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_23,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk3_1 @ X6 )
= cZ )
| ( ( esk4_1 @ X6 )
= cZ )
| ( ( esk3_1 @ X6 )
= ( cP @ ( esk6_1 @ X6 ) @ ( esk7_1 @ X6 ) ) )
| ( X6 @ x @ u @ u ) ),
inference(cn,[status(thm)],[c_0_18]) ).
thf(c_0_24,negated_conjecture,
! [X6: a > a > a > $o] :
( ( X6 @ x @ u @ u )
| ~ ( X6 @ ( esk3_1 @ X6 ) @ ( esk4_1 @ X6 ) @ ( esk5_1 @ X6 ) ) ),
inference(cn,[status(thm)],[c_0_19]) ).
thf(c_0_25,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk5_1 @ X6 )
= ( esk4_1 @ X6 ) )
| ( ( esk4_1 @ X6 )
= cZ )
| ( X6 @ x @ u @ u )
| ( ( esk3_1 @ X6 )
!= cZ ) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_26,negated_conjecture,
( ( ( esk4_1 @ epred1_0 )
= cZ )
| ( ( esk3_1 @ epred1_0 )
= cZ )
| ( epred1_0 @ x @ u @ u ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
thf(c_0_27,negated_conjecture,
( ( ( esk5_1 @ epred1_0 )
= ( esk4_1 @ epred1_0 ) )
| ( ( esk4_1 @ epred1_0 )
= cZ )
| ( epred1_0 @ x @ u @ u ) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_28,negated_conjecture,
! [X1: a,X2: a,X3: a] :
( ( epred1_0 @ X1 @ X2 @ X3 )
| ( X1 != cZ )
| ( X2 != X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_29,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk4_1 @ X6 )
= ( cP @ ( esk8_1 @ X6 ) @ ( esk9_1 @ X6 ) ) )
| ( ( esk3_1 @ X6 )
= ( esk5_1 @ X6 ) )
| ( ( esk3_1 @ X6 )
= cZ )
| ( X6 @ x @ u @ u )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_30,negated_conjecture,
( ( ( esk4_1 @ epred1_0 )
= cZ )
| ( epred1_0 @ x @ u @ u )
| ~ ( epred1_0 @ ( esk3_1 @ epred1_0 ) @ ( esk4_1 @ epred1_0 ) @ ( esk4_1 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_24,c_0_27]) ).
thf(c_0_31,negated_conjecture,
! [X1: a] : ( epred1_0 @ cZ @ X1 @ X1 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_28])]) ).
thf(c_0_32,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk3_1 @ X6 )
= cZ )
| ( ( esk5_1 @ X6 )
= ( esk3_1 @ X6 ) )
| ( ( esk4_1 @ X6 )
= ( cP @ ( esk8_1 @ X6 ) @ ( esk9_1 @ X6 ) ) )
| ( X6 @ x @ u @ u ) ),
inference(cn,[status(thm)],[c_0_29]) ).
thf(c_0_33,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk4_1 @ X6 )
= ( cP @ ( esk8_1 @ X6 ) @ ( esk9_1 @ X6 ) ) )
| ( ( esk3_1 @ X6 )
= ( esk5_1 @ X6 ) )
| ( ( esk4_1 @ X6 )
= ( esk5_1 @ X6 ) )
| ( X6 @ x @ u @ u )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_34,negated_conjecture,
( ( ( esk4_1 @ epred1_0 )
= cZ )
| ( epred1_0 @ x @ u @ u ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_26]),c_0_31])]) ).
thf(c_0_35,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk5_1 @ X6 )
= ( esk3_1 @ X6 ) )
| ( ( esk3_1 @ X6 )
= cZ )
| ( X6 @ x @ u @ u )
| ( ( esk4_1 @ X6 )
!= cZ ) ),
inference(spm,[status(thm)],[c_0_20,c_0_32]) ).
thf(c_0_36,negated_conjecture,
! [X1: a,X2: a,X3: a] :
( ( epred1_0 @ X2 @ X1 @ X3 )
| ( X1 != cZ )
| ( X2 != X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_37,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk5_1 @ X6 )
= ( esk3_1 @ X6 ) )
| ( ( esk5_1 @ X6 )
= ( esk4_1 @ X6 ) )
| ( ( esk4_1 @ X6 )
= ( cP @ ( esk8_1 @ X6 ) @ ( esk9_1 @ X6 ) ) )
| ( X6 @ x @ u @ u ) ),
inference(cn,[status(thm)],[c_0_33]) ).
thf(c_0_38,negated_conjecture,
( ( epred1_0 @ x @ u @ u )
| ~ ( epred1_0 @ ( esk3_1 @ epred1_0 ) @ cZ @ ( esk5_1 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_24,c_0_34]) ).
thf(c_0_39,negated_conjecture,
( ( ( esk5_1 @ epred1_0 )
= ( esk3_1 @ epred1_0 ) )
| ( ( esk3_1 @ epred1_0 )
= cZ )
| ( epred1_0 @ x @ u @ u ) ),
inference(spm,[status(thm)],[c_0_35,c_0_34]) ).
thf(c_0_40,negated_conjecture,
! [X1: a] : ( epred1_0 @ X1 @ cZ @ X1 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_36])]) ).
thf(c_0_41,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk5_1 @ X6 )
= ( esk4_1 @ X6 ) )
| ( ( esk5_1 @ X6 )
= ( esk3_1 @ X6 ) )
| ( X6 @ x @ u @ u )
| ( ( esk4_1 @ X6 )
!= cZ ) ),
inference(spm,[status(thm)],[c_0_20,c_0_37]) ).
thf(c_0_42,negated_conjecture,
( ( ( esk3_1 @ epred1_0 )
= cZ )
| ( epred1_0 @ x @ u @ u ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
thf(c_0_43,negated_conjecture,
( ( ( esk5_1 @ epred1_0 )
= ( esk3_1 @ epred1_0 ) )
| ( ( esk5_1 @ epred1_0 )
= cZ )
| ( epred1_0 @ x @ u @ u ) ),
inference(spm,[status(thm)],[c_0_41,c_0_34]) ).
thf(c_0_44,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk12_1 @ X6 )
= ( cP @ ( esk15_1 @ X6 ) @ ( esk16_1 @ X6 ) ) )
| ( ( esk13_1 @ X6 )
= cZ )
| ( ( esk12_1 @ X6 )
= cZ )
| ( X6 @ y @ v @ v )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_45,negated_conjecture,
~ ( epred1_0 @ ( cP @ x @ y ) @ ( cP @ u @ v ) @ ( cP @ u @ v ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_46,negated_conjecture,
( ( epred1_0 @ x @ u @ u )
| ~ ( epred1_0 @ cZ @ cZ @ ( esk5_1 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_38,c_0_42]) ).
thf(c_0_47,negated_conjecture,
( ( ( esk5_1 @ epred1_0 )
= cZ )
| ( epred1_0 @ x @ u @ u ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_43]),c_0_40])]) ).
thf(c_0_48,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk12_1 @ X6 )
= cZ )
| ( ( esk13_1 @ X6 )
= cZ )
| ( ( esk12_1 @ X6 )
= ( cP @ ( esk15_1 @ X6 ) @ ( esk16_1 @ X6 ) ) )
| ( X6 @ y @ v @ v ) ),
inference(cn,[status(thm)],[c_0_44]) ).
thf(c_0_49,negated_conjecture,
! [X6: a > a > a > $o] :
( ( X6 @ ( esk16_1 @ X6 ) @ ( esk18_1 @ X6 ) @ ( esk20_1 @ X6 ) )
| ( ( esk13_1 @ X6 )
= cZ )
| ( ( esk12_1 @ X6 )
= cZ )
| ( X6 @ y @ v @ v )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_50,negated_conjecture,
( ~ ( epred1_0 @ y @ v @ v )
| ~ ( epred1_0 @ x @ u @ u ) ),
inference(spm,[status(thm)],[c_0_45,c_0_6]) ).
thf(c_0_51,negated_conjecture,
epred1_0 @ x @ u @ u,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_40])]) ).
thf(c_0_52,negated_conjecture,
! [X6: a > a > a > $o,X1: a,X2: a,X4: a,X3: a] :
( ( ( esk13_1 @ X6 )
= cZ )
| ( ( esk12_1 @ X6 )
= cZ )
| ( epred1_0 @ ( esk12_1 @ X6 ) @ ( cP @ X1 @ X2 ) @ ( cP @ X3 @ X4 ) )
| ( X6 @ y @ v @ v )
| ~ ( epred1_0 @ ( esk16_1 @ X6 ) @ X2 @ X4 )
| ~ ( epred1_0 @ ( esk15_1 @ X6 ) @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_6,c_0_48]) ).
thf(c_0_53,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk12_1 @ X6 )
= cZ )
| ( ( esk13_1 @ X6 )
= cZ )
| ( X6 @ y @ v @ v )
| ( X6 @ ( esk16_1 @ X6 ) @ ( esk18_1 @ X6 ) @ ( esk20_1 @ X6 ) ) ),
inference(cn,[status(thm)],[c_0_49]) ).
thf(c_0_54,negated_conjecture,
~ ( epred1_0 @ y @ v @ v ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51])]) ).
thf(c_0_55,negated_conjecture,
! [X6: a > a > a > $o] :
( ( X6 @ ( esk15_1 @ X6 ) @ ( esk17_1 @ X6 ) @ ( esk19_1 @ X6 ) )
| ( ( esk13_1 @ X6 )
= cZ )
| ( ( esk12_1 @ X6 )
= cZ )
| ( X6 @ y @ v @ v )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_56,negated_conjecture,
! [X1: a,X2: a] :
( ( ( esk12_1 @ epred1_0 )
= cZ )
| ( ( esk13_1 @ epred1_0 )
= cZ )
| ( epred1_0 @ ( esk12_1 @ epred1_0 ) @ ( cP @ X1 @ ( esk18_1 @ epred1_0 ) ) @ ( cP @ X2 @ ( esk20_1 @ epred1_0 ) ) )
| ~ ( epred1_0 @ ( esk15_1 @ epred1_0 ) @ X1 @ X2 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).
thf(c_0_57,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk12_1 @ X6 )
= cZ )
| ( ( esk13_1 @ X6 )
= cZ )
| ( X6 @ y @ v @ v )
| ( X6 @ ( esk15_1 @ X6 ) @ ( esk17_1 @ X6 ) @ ( esk19_1 @ X6 ) ) ),
inference(cn,[status(thm)],[c_0_55]) ).
thf(c_0_58,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk14_1 @ X6 )
= ( cP @ ( esk19_1 @ X6 ) @ ( esk20_1 @ X6 ) ) )
| ( ( esk13_1 @ X6 )
= cZ )
| ( ( esk12_1 @ X6 )
= cZ )
| ( X6 @ y @ v @ v )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_59,negated_conjecture,
( ( ( esk13_1 @ epred1_0 )
= cZ )
| ( ( esk12_1 @ epred1_0 )
= cZ )
| ( epred1_0 @ ( esk12_1 @ epred1_0 ) @ ( cP @ ( esk17_1 @ epred1_0 ) @ ( esk18_1 @ epred1_0 ) ) @ ( cP @ ( esk19_1 @ epred1_0 ) @ ( esk20_1 @ epred1_0 ) ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_54]) ).
thf(c_0_60,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk12_1 @ X6 )
= cZ )
| ( ( esk13_1 @ X6 )
= cZ )
| ( ( esk14_1 @ X6 )
= ( cP @ ( esk19_1 @ X6 ) @ ( esk20_1 @ X6 ) ) )
| ( X6 @ y @ v @ v ) ),
inference(cn,[status(thm)],[c_0_58]) ).
thf(c_0_61,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk13_1 @ X6 )
= ( cP @ ( esk17_1 @ X6 ) @ ( esk18_1 @ X6 ) ) )
| ( ( esk13_1 @ X6 )
= cZ )
| ( ( esk12_1 @ X6 )
= cZ )
| ( X6 @ y @ v @ v )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_62,negated_conjecture,
! [X6: a > a > a > $o] :
( ( X6 @ y @ v @ v )
| ~ ( X6 @ ( esk12_1 @ X6 ) @ ( esk13_1 @ X6 ) @ ( esk14_1 @ X6 ) )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_63,negated_conjecture,
( ( ( esk12_1 @ epred1_0 )
= cZ )
| ( ( esk13_1 @ epred1_0 )
= cZ )
| ( epred1_0 @ ( esk12_1 @ epred1_0 ) @ ( cP @ ( esk17_1 @ epred1_0 ) @ ( esk18_1 @ epred1_0 ) ) @ ( esk14_1 @ epred1_0 ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_54]) ).
thf(c_0_64,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk12_1 @ X6 )
= cZ )
| ( ( esk13_1 @ X6 )
= cZ )
| ( ( esk13_1 @ X6 )
= ( cP @ ( esk17_1 @ X6 ) @ ( esk18_1 @ X6 ) ) )
| ( X6 @ y @ v @ v ) ),
inference(cn,[status(thm)],[c_0_61]) ).
thf(c_0_65,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk13_1 @ X6 )
= ( cP @ ( esk17_1 @ X6 ) @ ( esk18_1 @ X6 ) ) )
| ( ( esk12_1 @ X6 )
= ( esk14_1 @ X6 ) )
| ( ( esk12_1 @ X6 )
= cZ )
| ( X6 @ y @ v @ v )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_66,negated_conjecture,
! [X6: a > a > a > $o] :
( ( X6 @ y @ v @ v )
| ~ ( X6 @ ( esk12_1 @ X6 ) @ ( esk13_1 @ X6 ) @ ( esk14_1 @ X6 ) ) ),
inference(cn,[status(thm)],[c_0_62]) ).
thf(c_0_67,negated_conjecture,
( ( ( esk13_1 @ epred1_0 )
= cZ )
| ( ( esk12_1 @ epred1_0 )
= cZ )
| ( epred1_0 @ ( esk12_1 @ epred1_0 ) @ ( esk13_1 @ epred1_0 ) @ ( esk14_1 @ epred1_0 ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_54]) ).
thf(c_0_68,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk12_1 @ X6 )
= cZ )
| ( ( esk14_1 @ X6 )
= ( esk12_1 @ X6 ) )
| ( ( esk13_1 @ X6 )
= ( cP @ ( esk17_1 @ X6 ) @ ( esk18_1 @ X6 ) ) )
| ( X6 @ y @ v @ v ) ),
inference(cn,[status(thm)],[c_0_65]) ).
thf(c_0_69,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk12_1 @ X6 )
= ( cP @ ( esk15_1 @ X6 ) @ ( esk16_1 @ X6 ) ) )
| ( ( esk13_1 @ X6 )
= cZ )
| ( ( esk13_1 @ X6 )
= ( esk14_1 @ X6 ) )
| ( X6 @ y @ v @ v )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_70,negated_conjecture,
( ( ( esk12_1 @ epred1_0 )
= cZ )
| ( ( esk13_1 @ epred1_0 )
= cZ ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_54]) ).
thf(c_0_71,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk14_1 @ X6 )
= ( esk12_1 @ X6 ) )
| ( ( esk12_1 @ X6 )
= cZ )
| ( X6 @ y @ v @ v )
| ( ( esk13_1 @ X6 )
!= cZ ) ),
inference(spm,[status(thm)],[c_0_20,c_0_68]) ).
thf(c_0_72,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk13_1 @ X6 )
= cZ )
| ( ( esk14_1 @ X6 )
= ( esk13_1 @ X6 ) )
| ( ( esk12_1 @ X6 )
= ( cP @ ( esk15_1 @ X6 ) @ ( esk16_1 @ X6 ) ) )
| ( X6 @ y @ v @ v ) ),
inference(cn,[status(thm)],[c_0_69]) ).
thf(c_0_73,negated_conjecture,
( ( ( esk12_1 @ epred1_0 )
= cZ )
| ~ ( epred1_0 @ ( esk12_1 @ epred1_0 ) @ cZ @ ( esk14_1 @ epred1_0 ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_70]),c_0_54]) ).
thf(c_0_74,negated_conjecture,
( ( ( esk14_1 @ epred1_0 )
= ( esk12_1 @ epred1_0 ) )
| ( ( esk12_1 @ epred1_0 )
= cZ ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_70]),c_0_54]) ).
thf(c_0_75,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk14_1 @ X6 )
= ( esk13_1 @ X6 ) )
| ( ( esk13_1 @ X6 )
= cZ )
| ( X6 @ y @ v @ v )
| ( ( esk12_1 @ X6 )
!= cZ ) ),
inference(spm,[status(thm)],[c_0_20,c_0_72]) ).
thf(c_0_76,negated_conjecture,
( ( esk12_1 @ epred1_0 )
= cZ ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_40])]) ).
thf(c_0_77,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk13_1 @ X6 )
= ( cP @ ( esk17_1 @ X6 ) @ ( esk18_1 @ X6 ) ) )
| ( ( esk12_1 @ X6 )
= ( esk14_1 @ X6 ) )
| ( ( esk13_1 @ X6 )
= ( esk14_1 @ X6 ) )
| ( X6 @ y @ v @ v )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_78,negated_conjecture,
( ( ( esk14_1 @ epred1_0 )
= ( esk13_1 @ epred1_0 ) )
| ( ( esk13_1 @ epred1_0 )
= cZ ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_54]) ).
thf(c_0_79,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk14_1 @ X6 )
= ( esk12_1 @ X6 ) )
| ( ( esk14_1 @ X6 )
= ( esk13_1 @ X6 ) )
| ( ( esk13_1 @ X6 )
= ( cP @ ( esk17_1 @ X6 ) @ ( esk18_1 @ X6 ) ) )
| ( X6 @ y @ v @ v ) ),
inference(cn,[status(thm)],[c_0_77]) ).
thf(c_0_80,negated_conjecture,
~ ( epred1_0 @ cZ @ ( esk13_1 @ epred1_0 ) @ ( esk14_1 @ epred1_0 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_76]),c_0_54]) ).
thf(c_0_81,negated_conjecture,
( ( esk13_1 @ epred1_0 )
= cZ ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_78]),c_0_76]),c_0_31])]),c_0_54]) ).
thf(c_0_82,negated_conjecture,
! [X6: a > a > a > $o] :
( ( ( esk14_1 @ X6 )
= ( esk13_1 @ X6 ) )
| ( ( esk14_1 @ X6 )
= ( esk12_1 @ X6 ) )
| ( X6 @ y @ v @ v )
| ( ( esk13_1 @ X6 )
!= cZ ) ),
inference(spm,[status(thm)],[c_0_20,c_0_79]) ).
thf(c_0_83,negated_conjecture,
~ ( epred1_0 @ cZ @ cZ @ ( esk14_1 @ epred1_0 ) ),
inference(rw,[status(thm)],[c_0_80,c_0_81]) ).
thf(c_0_84,negated_conjecture,
( ( esk14_1 @ epred1_0 )
= cZ ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_81]),c_0_76])]),c_0_54]) ).
thf(c_0_85,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_84]),c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV210^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n019.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 15:21:32 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.23 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.c6kLyUOAKY/E---3.1_911251.p
% 0.21/0.37 % Version: 3.5.1-ho
% 0.21/0.37 % Preprocessing class: HSMSSMSSSSSNSSA.
% 0.21/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.37 % Starting post_as_ho1 with 1500s (5) cores
% 0.21/0.37 % Starting post_as_ho12 with 300s (1) cores
% 0.21/0.37 % Starting new_ho_3 with 300s (1) cores
% 0.21/0.37 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.21/0.37 % post_as_ho1 with pid 911264 completed with status 0
% 0.21/0.37 % Result found by post_as_ho1
% 0.21/0.37 % Preprocessing class: HSMSSMSSSSSNSSA.
% 0.21/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.37 % Starting post_as_ho1 with 1500s (5) cores
% 0.21/0.37 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.37 % No SInE strategy applied
% 0.21/0.37 % Search class: HGUSF-FFMF21-SSSFFMBN
% 0.21/0.37 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.37 % Starting SubtermCWHack with 136s (1) cores
% 0.21/0.37 % Starting post_as_ho1 with 151s (1) cores
% 0.21/0.37 % Starting lpo8_s with 145s (1) cores
% 0.21/0.37 % Starting sh2lt with 145s (1) cores
% 0.21/0.37 % Starting full_lambda_9 with 145s (1) cores
% 0.21/0.37 % post_as_ho1 with pid 911270 completed with status 0
% 0.21/0.37 % Result found by post_as_ho1
% 0.21/0.37 % Preprocessing class: HSMSSMSSSSSNSSA.
% 0.21/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.37 % Starting post_as_ho1 with 1500s (5) cores
% 0.21/0.37 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.37 % No SInE strategy applied
% 0.21/0.37 % Search class: HGUSF-FFMF21-SSSFFMBN
% 0.21/0.37 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.37 % Starting SubtermCWHack with 136s (1) cores
% 0.21/0.37 % Starting post_as_ho1 with 151s (1) cores
% 0.21/0.37 % Preprocessing time : 0.002 s
% 0.21/0.37 % Presaturation interreduction done
% 0.21/0.37
% 0.21/0.37 % Proof found!
% 0.21/0.37 % SZS status Theorem
% 0.21/0.37 % SZS output start CNFRefutation
% See solution above
% 0.21/0.37 % Parsed axioms : 8
% 0.21/0.37 % Removed by relevancy pruning/SinE : 0
% 0.21/0.37 % Initial clauses : 60
% 0.21/0.37 % Removed in clause preprocessing : 8
% 0.21/0.37 % Initial clauses in saturation : 52
% 0.21/0.37 % Processed clauses : 276
% 0.21/0.37 % ...of these trivial : 5
% 0.21/0.37 % ...subsumed : 51
% 0.21/0.37 % ...remaining for further processing : 220
% 0.21/0.37 % Other redundant clauses eliminated : 7
% 0.21/0.37 % Clauses deleted for lack of memory : 0
% 0.21/0.37 % Backward-subsumed : 16
% 0.21/0.37 % Backward-rewritten : 13
% 0.21/0.37 % Generated clauses : 1584
% 0.21/0.37 % ...of the previous two non-redundant : 1539
% 0.21/0.37 % ...aggressively subsumed : 0
% 0.21/0.37 % Contextual simplify-reflections : 1
% 0.21/0.37 % Paramodulations : 1574
% 0.21/0.37 % Factorizations : 5
% 0.21/0.37 % NegExts : 0
% 0.21/0.37 % Equation resolutions : 9
% 0.21/0.37 % Disequality decompositions : 0
% 0.21/0.37 % Total rewrite steps : 59
% 0.21/0.37 % ...of those cached : 48
% 0.21/0.37 % Propositional unsat checks : 0
% 0.21/0.37 % Propositional check models : 0
% 0.21/0.37 % Propositional check unsatisfiable : 0
% 0.21/0.37 % Propositional clauses : 0
% 0.21/0.37 % Propositional clauses after purity: 0
% 0.21/0.37 % Propositional unsat core size : 0
% 0.21/0.37 % Propositional preprocessing time : 0.000
% 0.21/0.37 % Propositional encoding time : 0.000
% 0.21/0.37 % Propositional solver time : 0.000
% 0.21/0.37 % Success case prop preproc time : 0.000
% 0.21/0.37 % Success case prop encoding time : 0.000
% 0.21/0.37 % Success case prop solver time : 0.000
% 0.21/0.37 % Current number of processed clauses : 136
% 0.21/0.37 % Positive orientable unit clauses : 8
% 0.21/0.37 % Positive unorientable unit clauses: 0
% 0.21/0.37 % Negative unit clauses : 3
% 0.21/0.37 % Non-unit-clauses : 125
% 0.21/0.37 % Current number of unprocessed clauses: 1307
% 0.21/0.37 % ...number of literals in the above : 10116
% 0.21/0.37 % Current number of archived formulas : 0
% 0.21/0.37 % Current number of archived clauses : 81
% 0.21/0.37 % Clause-clause subsumption calls (NU) : 1260
% 0.21/0.37 % Rec. Clause-clause subsumption calls : 137
% 0.21/0.37 % Non-unit clause-clause subsumptions : 66
% 0.21/0.37 % Unit Clause-clause subsumption calls : 102
% 0.21/0.37 % Rewrite failures with RHS unbound : 0
% 0.21/0.37 % BW rewrite match attempts : 9
% 0.21/0.37 % BW rewrite match successes : 6
% 0.21/0.37 % Condensation attempts : 0
% 0.21/0.37 % Condensation successes : 0
% 0.21/0.37 % Termbank termtop insertions : 36900
% 0.21/0.37 % Search garbage collected termcells : 1154
% 0.21/0.37
% 0.21/0.37 % -------------------------------------------------
% 0.21/0.37 % User time : 0.053 s
% 0.21/0.37 % System time : 0.003 s
% 0.21/0.37 % Total time : 0.056 s
% 0.21/0.37 % Maximum resident set size: 3904 pages
% 0.21/0.37
% 0.21/0.37 % -------------------------------------------------
% 0.21/0.37 % User time : 0.401 s
% 0.21/0.37 % System time : 0.017 s
% 0.21/0.37 % Total time : 0.418 s
% 0.21/0.37 % Maximum resident set size: 4864 pages
% 0.21/0.37 % E exiting
%------------------------------------------------------------------------------