%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV100^5 : 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 : n011.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 08:34:52 AM UTC 2026
% Result : Theorem 1.09s 0.43s
% Output : CNFRefutation 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 1
% Syntax : Number of formulae : 53 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 618 ( 95 equ; 0 cnn)
% Maximal formula atoms : 104 ( 11 avg)
% Number of connectives : 1512 ( 234 ~; 191 |; 52 &;1028 @)
% ( 1 <=>; 3 =>; 0 <=; 3 <~>)
% Maximal formula depth : 23 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 510 ( 510 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 700 ( 561 ^; 133 !; 6 ?; 700 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
p: $o ).
thf(decl_24,type,
epred1_2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(decl_25,type,
epred2_2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(decl_26,type,
epred3_2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(decl_27,type,
esk1_2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(decl_28,type,
epred4_2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(decl_29,type,
esk2_2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(decl_49,type,
esk24_1: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(decl_79,type,
esk54_0: $i ).
thf(cTHM120F_pme,conjecture,
? [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X3: $i > $o,X4: $i > $o,X5: $i > $o] :
( ( ! [X6: $i] :
( ( X2 @ X3 @ X4 @ X6 )
| ( X1 @ X3 @ X4 @ X6 ) )
& ! [X6: $i] :
( ( X2 @ X4 @ X5 @ X6 )
| ( X1 @ X4 @ X5 @ X6 ) ) )
=> ! [X6: $i] :
( ( X2 @ X3 @ X5 @ X6 )
| ( X1 @ X3 @ X5 @ X6 ) ) )
& ! [X3: $i > $o,X6: $i] :
( ( X2 @ X3 @ X3 @ X6 )
| ( X1 @ X3 @ X3 @ X6 ) )
& ~ ! [X6: $i] :
( ( X2
@ ^ [X7: $i] :
( p
| ~ p )
@ ^ [X8: $i] :
( p
& ~ p )
@ X6 )
| ( X1
@ ^ [X9: $i] :
( p
| ~ p )
@ ^ [X10: $i] :
( p
& ~ p )
@ X6 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LRCQD3gCGs/E---3.1_199869.p',cTHM120F_pme) ).
thf(c_0_1,negated_conjecture,
~ ? [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X3: $i > $o,X4: $i > $o,X5: $i > $o] :
( ( ! [X6: $i] :
( ( X2 @ X3 @ X4 @ X6 )
| ( X1 @ X3 @ X4 @ X6 ) )
& ! [X6: $i] :
( ( X2 @ X4 @ X5 @ X6 )
| ( X1 @ X4 @ X5 @ X6 ) ) )
=> ! [X6: $i] :
( ( X2 @ X3 @ X5 @ X6 )
| ( X1 @ X3 @ X5 @ X6 ) ) )
& ! [X3: $i > $o,X6: $i] :
( ( X2 @ X3 @ X3 @ X6 )
| ( X1 @ X3 @ X3 @ X6 ) )
& ~ ! [X6: $i] :
( ( X2
@ ^ [X7: $i] :
( p
| ~ p )
@ ^ [X8: $i] :
( p
& ~ p )
@ X6 )
| ( X1
@ ^ [X9: $i] :
( p
| ~ p )
@ ^ [X10: $i] :
( p
& ~ p )
@ X6 ) ) ),
inference(assume_negation,[status(cth)],[cTHM120F_pme]) ).
thf(c_0_2,negated_conjecture,
~ ? [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X3: $i > $o,X4: $i > $o,X5: $i > $o] :
( ( ! [X6: $i] :
( ( X2 @ X3 @ X4 @ X6 )
| ( X1 @ X3 @ X4 @ X6 ) )
& ! [X6: $i] :
( ( X2 @ X4 @ X5 @ X6 )
| ( X1 @ X4 @ X5 @ X6 ) ) )
=> ! [X6: $i] :
( ( X2 @ X3 @ X5 @ X6 )
| ( X1 @ X3 @ X5 @ X6 ) ) )
& ! [X3: $i > $o,X6: $i] :
( ( X2 @ X3 @ X3 @ X6 )
| ( X1 @ X3 @ X3 @ X6 ) )
& ~ ! [X6: $i] :
( ( X2
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X6 )
| ( X1
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X6 ) ) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
thf(c_0_3,negated_conjecture,
! [X22: ( $i > $o ) > ( $i > $o ) > $i > $o,X23: ( $i > $o ) > ( $i > $o ) > $i > $o,X27: $i,X28: $i,X32: $i] :
( ( ~ ( X23 @ ( epred4_2 @ X22 @ X23 ) @ ( epred4_2 @ X22 @ X23 ) @ ( esk2_2 @ X22 @ X23 ) )
| ( X23 @ ( epred1_2 @ X22 @ X23 ) @ ( epred2_2 @ X22 @ X23 ) @ X27 )
| ( X22 @ ( epred1_2 @ X22 @ X23 ) @ ( epred2_2 @ X22 @ X23 ) @ X27 )
| ( X23
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X32 )
| ( X22
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X32 ) )
& ( ~ ( X22 @ ( epred4_2 @ X22 @ X23 ) @ ( epred4_2 @ X22 @ X23 ) @ ( esk2_2 @ X22 @ X23 ) )
| ( X23 @ ( epred1_2 @ X22 @ X23 ) @ ( epred2_2 @ X22 @ X23 ) @ X27 )
| ( X22 @ ( epred1_2 @ X22 @ X23 ) @ ( epred2_2 @ X22 @ X23 ) @ X27 )
| ( X23
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X32 )
| ( X22
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X32 ) )
& ( ~ ( X23 @ ( epred4_2 @ X22 @ X23 ) @ ( epred4_2 @ X22 @ X23 ) @ ( esk2_2 @ X22 @ X23 ) )
| ( X23 @ ( epred2_2 @ X22 @ X23 ) @ ( epred3_2 @ X22 @ X23 ) @ X28 )
| ( X22 @ ( epred2_2 @ X22 @ X23 ) @ ( epred3_2 @ X22 @ X23 ) @ X28 )
| ( X23
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X32 )
| ( X22
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X32 ) )
& ( ~ ( X22 @ ( epred4_2 @ X22 @ X23 ) @ ( epred4_2 @ X22 @ X23 ) @ ( esk2_2 @ X22 @ X23 ) )
| ( X23 @ ( epred2_2 @ X22 @ X23 ) @ ( epred3_2 @ X22 @ X23 ) @ X28 )
| ( X22 @ ( epred2_2 @ X22 @ X23 ) @ ( epred3_2 @ X22 @ X23 ) @ X28 )
| ( X23
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X32 )
| ( X22
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X32 ) )
& ( ~ ( X23 @ ( epred4_2 @ X22 @ X23 ) @ ( epred4_2 @ X22 @ X23 ) @ ( esk2_2 @ X22 @ X23 ) )
| ~ ( X23 @ ( epred1_2 @ X22 @ X23 ) @ ( epred3_2 @ X22 @ X23 ) @ ( esk1_2 @ X22 @ X23 ) )
| ( X23
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X32 )
| ( X22
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X32 ) )
& ( ~ ( X22 @ ( epred4_2 @ X22 @ X23 ) @ ( epred4_2 @ X22 @ X23 ) @ ( esk2_2 @ X22 @ X23 ) )
| ~ ( X23 @ ( epred1_2 @ X22 @ X23 ) @ ( epred3_2 @ X22 @ X23 ) @ ( esk1_2 @ X22 @ X23 ) )
| ( X23
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X32 )
| ( X22
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X32 ) )
& ( ~ ( X23 @ ( epred4_2 @ X22 @ X23 ) @ ( epred4_2 @ X22 @ X23 ) @ ( esk2_2 @ X22 @ X23 ) )
| ~ ( X22 @ ( epred1_2 @ X22 @ X23 ) @ ( epred3_2 @ X22 @ X23 ) @ ( esk1_2 @ X22 @ X23 ) )
| ( X23
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X32 )
| ( X22
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X32 ) )
& ( ~ ( X22 @ ( epred4_2 @ X22 @ X23 ) @ ( epred4_2 @ X22 @ X23 ) @ ( esk2_2 @ X22 @ X23 ) )
| ~ ( X22 @ ( epred1_2 @ X22 @ X23 ) @ ( epred3_2 @ X22 @ X23 ) @ ( esk1_2 @ X22 @ X23 ) )
| ( X23
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X32 )
| ( X22
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X32 ) ) ),
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: $i,X6: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1 @ ( epred1_2 @ X2 @ X1 ) @ ( epred2_2 @ X2 @ X1 ) @ X6 )
| ( X2 @ ( epred1_2 @ X2 @ X1 ) @ ( epred2_2 @ X2 @ X1 ) @ X6 )
| ( X1
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X7 )
| ( X2
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X7 )
| ~ ( X1 @ ( epred4_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ ( esk2_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X7: $i,X6: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1 @ ( epred1_2 @ X2 @ X1 ) @ ( epred2_2 @ X2 @ X1 ) @ X6 )
| ( X2 @ ( epred1_2 @ X2 @ X1 ) @ ( epred2_2 @ X2 @ X1 ) @ X6 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 )
| ~ ( X1 @ ( epred4_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ ( esk2_2 @ X2 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_4]) ).
thf(c_0_6,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X7: $i] :
( ( ( epred1_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
= ( epred2_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 ) )
| ( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) )
| ( X1
@ ( epred1_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
@ ( epred2_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
@ X6 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 ) ),
inference(primitive_enumeration,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[])]),c_0_5]) ).
thf(c_0_7,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X2
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X6 )
| ( X1
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X6 )
| ~ ( X1 @ ( epred4_2 @ X1 @ X2 ) @ ( epred4_2 @ X1 @ X2 ) @ ( esk2_2 @ X1 @ X2 ) )
| ~ ( X1 @ ( epred1_2 @ X1 @ X2 ) @ ( epred3_2 @ X1 @ X2 ) @ ( esk1_2 @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_8,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X7: $i] :
( ( ( epred1_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
= ( epred2_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 ) )
| ( X1
@ ( epred1_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
@ ( epred2_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
@ X6 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 ) ),
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_6])]) ).
thf(c_0_9,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 )
| ~ ( X1 @ ( epred1_2 @ X1 @ X2 ) @ ( epred3_2 @ X1 @ X2 ) @ ( esk1_2 @ X1 @ X2 ) )
| ~ ( X1 @ ( epred4_2 @ X1 @ X2 ) @ ( epred4_2 @ X1 @ X2 ) @ ( esk2_2 @ X1 @ X2 ) ) ),
inference(cn,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X310: $i,X7: $i] :
( ( ( epred1_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X310 )
<=> ( epred2_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X310 ) )
| ( X1
@ ( epred1_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
@ ( epred2_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
@ X6 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 ) ),
inference(arg_cong,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ X1 )
= ( ^ [Z0: $i] : $true ) )
| ( ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ X1 )
= ( ^ [Z0: $i] : $true ) )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_9]) ).
thf(c_0_12,negated_conjecture,
! [X6: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i,X7: $i] :
( ( X1
@ ( epred1_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
@ ( epred2_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
@ X6 )
| ( epred2_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X7 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X8 )
| ~ ( epred1_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X7 ) ),
inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_10])]) ).
thf(c_0_13,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X7: $i] :
( ( ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ X1 )
= ( ^ [Z0: $i] : $true ) )
| ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ X1
@ X6 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 ) ),
inference(arg_cong,[status(thm)],[c_0_11]) ).
thf(c_0_14,negated_conjecture,
! [X6: $i] :
( ( ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
= ( ^ [Z0: $i] : $true ) )
| ( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) )
| ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X6 )
| ( ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
!= ( ^ [Z0: $i] : $true ) ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13])])]) ).
thf(c_0_15,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X7: $i,X6: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X2 @ ( epred2_2 @ X1 @ X2 ) @ ( epred3_2 @ X1 @ X2 ) @ X6 )
| ( X1 @ ( epred2_2 @ X1 @ X2 ) @ ( epred3_2 @ X1 @ X2 ) @ X6 )
| ( X2
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X7 )
| ( X1
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X7 )
| ~ ( X1 @ ( epred4_2 @ X1 @ X2 ) @ ( epred4_2 @ X1 @ X2 ) @ ( esk2_2 @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_16,negated_conjecture,
! [X6: $i] :
( ( ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
= ( ^ [Z0: $i] : $true ) )
| ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X6 )
| ( ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
!= ( ^ [Z0: $i] : $true ) ) ),
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_14])]) ).
thf(c_0_17,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X2
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X6 )
| ( X1
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X6 )
| ~ ( X1 @ ( epred4_2 @ X1 @ X2 ) @ ( epred4_2 @ X1 @ X2 ) @ ( esk2_2 @ X1 @ X2 ) )
| ~ ( X2 @ ( epred1_2 @ X1 @ X2 ) @ ( epred3_2 @ X1 @ X2 ) @ ( esk1_2 @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_18,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X7: $i,X6: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1 @ ( epred2_2 @ X1 @ X2 ) @ ( epred3_2 @ X1 @ X2 ) @ X6 )
| ( X2 @ ( epred2_2 @ X1 @ X2 ) @ ( epred3_2 @ X1 @ X2 ) @ X6 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 )
| ~ ( X1 @ ( epred4_2 @ X1 @ X2 ) @ ( epred4_2 @ X1 @ X2 ) @ ( esk2_2 @ X1 @ X2 ) ) ),
inference(cn,[status(thm)],[c_0_15]) ).
thf(c_0_19,negated_conjecture,
! [X6: $i] :
( ( ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
= ( ^ [Z0: $i] : $true ) )
| ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X6 )
| ~ ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ esk54_0 ) ),
inference(neg_ext,[status(thm)],[c_0_16]) ).
thf(c_0_20,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 )
| ~ ( X2 @ ( epred1_2 @ X1 @ X2 ) @ ( epred3_2 @ X1 @ X2 ) @ ( esk1_2 @ X1 @ X2 ) )
| ~ ( X1 @ ( epred4_2 @ X1 @ X2 ) @ ( epred4_2 @ X1 @ X2 ) @ ( esk2_2 @ X1 @ X2 ) ) ),
inference(cn,[status(thm)],[c_0_17]) ).
thf(c_0_21,negated_conjecture,
! [X7: $i,X6: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ X1 )
= ( ^ [Z0: $i] : $true ) )
| ( X1
@ ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ X1 )
@ ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ X1 )
@ X6 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 )
| ( ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ X1 )
!= ( ^ [Z0: $i] : $true ) ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_18]) ).
thf(c_0_22,negated_conjecture,
! [X6: $i] :
( ( ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
= ( ^ [Z0: $i] : $true ) )
| ( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) )
| ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X6 ) ),
inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_13])]) ).
thf(c_0_23,plain,
! [X6: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 )
| ( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 )
<~> ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 ) )
| ~ ( X1 @ ( epred1_2 @ X2 @ X1 ) @ ( epred3_2 @ X2 @ X1 ) @ ( esk1_2 @ X2 @ X1 ) )
| ~ ( X2 @ ( epred4_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ ( esk2_2 @ X2 @ X1 ) ) ),
inference(ext_eqfact,[status(thm)],[c_0_20]) ).
thf(c_0_24,negated_conjecture,
! [X7: $i,X6: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ X1 )
= ( ^ [Z0: $i] : $true ) )
| ( X1
@ ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ X1 )
@ ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ X1 )
@ X6 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 )
| ~ ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ X1
@ ( esk24_1 @ X1 ) ) ),
inference(neg_ext,[status(thm)],[c_0_21]) ).
thf(c_0_25,negated_conjecture,
! [X6: $i] :
( ( ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
= ( ^ [Z0: $i] : $true ) )
| ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X6 ) ),
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_22])]) ).
thf(c_0_26,plain,
! [X6: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 )
| ( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 )
<~> ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 ) )
| ~ ( X2 @ ( epred1_2 @ X2 @ X1 ) @ ( epred3_2 @ X2 @ X1 ) @ ( esk1_2 @ X2 @ X1 ) )
| ~ ( X2 @ ( epred4_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ ( esk2_2 @ X2 @ X1 ) ) ),
inference(ext_eqfact,[status(thm)],[c_0_9]) ).
thf(c_0_27,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 )
| ~ ( X2 @ ( epred1_2 @ X1 @ X2 ) @ ( epred3_2 @ X1 @ X2 ) @ ( esk1_2 @ X1 @ X2 ) )
| ~ ( X1 @ ( epred4_2 @ X1 @ X2 ) @ ( epred4_2 @ X1 @ X2 ) @ ( esk2_2 @ X1 @ X2 ) ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_23])])]) ).
thf(c_0_28,negated_conjecture,
( ( ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
= ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 ) )
| ( ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
= ( ^ [Z0: $i] : $true ) )
| ( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) ) ),
inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25])]) ).
thf(c_0_29,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 )
| ~ ( X1 @ ( epred1_2 @ X1 @ X2 ) @ ( epred3_2 @ X1 @ X2 ) @ ( esk1_2 @ X1 @ X2 ) )
| ~ ( X1 @ ( epred4_2 @ X1 @ X2 ) @ ( epred4_2 @ X1 @ X2 ) @ ( esk2_2 @ X1 @ X2 ) ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_26])])]) ).
thf(c_0_30,plain,
( ( ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
= ( ^ [Z0: $i] : $true ) )
| ( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) )
| ( ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
!= ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 ) ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28])])]) ).
thf(c_0_31,plain,
( ( ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
= ( ^ [Z0: $i] : $true ) )
| ( ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
= ( ^ [Z0: $i] : $true ) )
| ( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_28])])]) ).
thf(c_0_32,negated_conjecture,
! [X6: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X6 )
| ( X2
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X6 )
| ~ ( X1 @ ( epred4_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ ( esk2_2 @ X2 @ X1 ) )
| ~ ( X2 @ ( epred1_2 @ X2 @ X1 ) @ ( epred3_2 @ X2 @ X1 ) @ ( esk1_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_33,plain,
( ( ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
= ( ^ [Z0: $i] : $true ) )
| ( ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
!= ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 ) ) ),
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_30])]) ).
thf(c_0_34,plain,
( ( ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
= ( ^ [Z0: $i] : $true ) )
| ( ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
= ( ^ [Z0: $i] : $true ) ) ),
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_31])]) ).
thf(c_0_35,negated_conjecture,
! [X6: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X6 )
| ( X2
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X6 )
| ~ ( X1 @ ( epred4_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ ( esk2_2 @ X2 @ X1 ) )
| ~ ( X1 @ ( epred1_2 @ X2 @ X1 ) @ ( epred3_2 @ X2 @ X1 ) @ ( esk1_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_36,negated_conjecture,
! [X6: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 )
| ~ ( X2 @ ( epred1_2 @ X2 @ X1 ) @ ( epred3_2 @ X2 @ X1 ) @ ( esk1_2 @ X2 @ X1 ) )
| ~ ( X1 @ ( epred4_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ ( esk2_2 @ X2 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_32]) ).
thf(c_0_37,plain,
( ( ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
= ( ^ [Z0: $i] : $true ) )
| ( ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
!= ( ^ [Z0: $i] : $true ) ) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
thf(c_0_38,negated_conjecture,
! [X6: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 )
| ~ ( X1 @ ( epred1_2 @ X2 @ X1 ) @ ( epred3_2 @ X2 @ X1 ) @ ( esk1_2 @ X2 @ X1 ) )
| ~ ( X1 @ ( epred4_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ ( esk2_2 @ X2 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_35]) ).
thf(c_0_39,negated_conjecture,
! [X6: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ X1 )
= ( ^ [Z0: $i] : $true ) )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 )
| ~ ( X1
@ ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ X1 )
@ ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ X1 )
@ ( esk2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ X1 ) ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_36]) ).
thf(c_0_40,plain,
( ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
= ( ^ [Z0: $i] : $true ) ),
inference(csr,[status(thm)],[inference(neg_ext,[status(thm)],[c_0_37]),c_0_25]) ).
thf(c_0_41,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 )
| ( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 )
<~> ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 ) )
| ~ ( X2 @ ( epred1_2 @ X1 @ X2 ) @ ( epred3_2 @ X1 @ X2 ) @ ( esk1_2 @ X1 @ X2 ) )
| ~ ( X2 @ ( epred4_2 @ X1 @ X2 ) @ ( epred4_2 @ X1 @ X2 ) @ ( esk2_2 @ X1 @ X2 ) ) ),
inference(ext_eqfact,[status(thm)],[c_0_38]) ).
thf(c_0_42,negated_conjecture,
! [X7: $i,X6: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1 @ ( epred2_2 @ X2 @ X1 ) @ ( epred3_2 @ X2 @ X1 ) @ X6 )
| ( X2 @ ( epred2_2 @ X2 @ X1 ) @ ( epred3_2 @ X2 @ X1 ) @ X6 )
| ( X1
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X7 )
| ( X2
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X7 )
| ~ ( X1 @ ( epred4_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ ( esk2_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_43,negated_conjecture,
( ( ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
= ( ^ [Z0: $i] : $true ) )
| ( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40])])]) ).
thf(c_0_44,plain,
! [X6: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X6 )
| ~ ( X1 @ ( epred1_2 @ X2 @ X1 ) @ ( epred3_2 @ X2 @ X1 ) @ ( esk1_2 @ X2 @ X1 ) )
| ~ ( X1 @ ( epred4_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ ( esk2_2 @ X2 @ X1 ) ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_41])])]) ).
thf(c_0_45,negated_conjecture,
! [X7: $i,X6: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1 @ ( epred2_2 @ X2 @ X1 ) @ ( epred3_2 @ X2 @ X1 ) @ X6 )
| ( X2 @ ( epred2_2 @ X2 @ X1 ) @ ( epred3_2 @ X2 @ X1 ) @ X6 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 )
| ~ ( X1 @ ( epred4_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ ( esk2_2 @ X2 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_42]) ).
thf(c_0_46,negated_conjecture,
( ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
= ( ^ [Z0: $i] : $true ) ),
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_43])]) ).
thf(c_0_47,plain,
( ( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) )
| ( ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
!= ( ^ [Z0: $i] : $true ) ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_43])])]) ).
thf(c_0_48,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X7: $i] :
( ( ( epred3_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
= ( epred2_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 ) )
| ( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) )
| ( X1
@ ( epred2_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
@ ( epred3_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
@ X6 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 ) ),
inference(primitive_enumeration,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[])]),c_0_45]) ).
thf(c_0_49,negated_conjecture,
( ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
= ( ^ [Z0: $i] : $true ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_46])])]) ).
thf(c_0_50,plain,
( ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0 )
!= ( ^ [Z0: $i] : $true ) ),
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_47])]) ).
thf(c_0_51,negated_conjecture,
( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49])])]),c_0_50]) ).
thf(c_0_52,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_51])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV100^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n011.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 15:10:16 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.22 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.LRCQD3gCGs/E---3.1_199869.p
% 1.09/0.43 % Version: 3.5.1-ho
% 1.09/0.43 % Preprocessing class: HSMSSMSSSSMNHHA.
% 1.09/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.09/0.43 % Starting ehoh_best4_fo with 1200s (4) cores
% 1.09/0.43 % Starting ehoh_best_nonlift_rwall with 600s (2) cores
% 1.09/0.43 % Starting lpo1_lambda_fix with 300s (1) cores
% 1.09/0.43 % Starting full_lambda_9 with 300s (1) cores
% 1.09/0.43 % ehoh_best4_fo with pid 199898 completed with status 0
% 1.09/0.43 % Result found by ehoh_best4_fo
% 1.09/0.43 % Preprocessing class: HSMSSMSSSSMNHHA.
% 1.09/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.09/0.43 % Starting ehoh_best4_fo with 1200s (4) cores
% 1.09/0.43 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.09/0.43 % No SInE strategy applied
% 1.09/0.43 % Search class: HGUNF-FFMF22-MHHFFMBN
% 1.09/0.43 % partial match(1): HGUNF-FFMF22-SHHFFMBN
% 1.09/0.43 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 1.09/0.43 % Starting SubtermCWHack with 109s (1) cores
% 1.09/0.43 % Starting ehoh_best4_fo with 121s (1) cores
% 1.09/0.43 % Starting sh2lt with 109s (1) cores
% 1.09/0.43 % Starting sh2l with 109s (1) cores
% 1.09/0.43 % SubtermCWHack with pid 199903 completed with status 10
% 1.09/0.43 % Starting lpo1_def_fix with 109s (1) cores
% 1.09/0.43 % ehoh_best4_fo with pid 199905 completed with status 0
% 1.09/0.43 % Result found by ehoh_best4_fo
% 1.09/0.43 % Preprocessing class: HSMSSMSSSSMNHHA.
% 1.09/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.09/0.43 % Starting ehoh_best4_fo with 1200s (4) cores
% 1.09/0.43 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.09/0.43 % No SInE strategy applied
% 1.09/0.43 % Search class: HGUNF-FFMF22-MHHFFMBN
% 1.09/0.43 % partial match(1): HGUNF-FFMF22-SHHFFMBN
% 1.09/0.43 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 1.09/0.43 % Starting SubtermCWHack with 109s (1) cores
% 1.09/0.43 % Starting ehoh_best4_fo with 121s (1) cores
% 1.09/0.43 % Preprocessing time : 0.001 s
% 1.09/0.43 % Presaturation interreduction done
% 1.09/0.43
% 1.09/0.43 % Proof found!
% 1.09/0.43 % SZS status Theorem
% 1.09/0.43 % SZS output start CNFRefutation
% See solution above
% 1.09/0.43 % Parsed axioms : 2
% 1.09/0.43 % Removed by relevancy pruning/SinE : 0
% 1.09/0.43 % Initial clauses : 9
% 1.09/0.43 % Removed in clause preprocessing : 1
% 1.09/0.43 % Initial clauses in saturation : 8
% 1.09/0.43 % Processed clauses : 382
% 1.09/0.43 % ...of these trivial : 21
% 1.09/0.43 % ...subsumed : 38
% 1.09/0.43 % ...remaining for further processing : 323
% 1.09/0.43 % Other redundant clauses eliminated : 8
% 1.09/0.43 % Clauses deleted for lack of memory : 0
% 1.09/0.43 % Backward-subsumed : 72
% 1.09/0.43 % Backward-rewritten : 153
% 1.09/0.43 % Generated clauses : 670
% 1.09/0.43 % ...of the previous two non-redundant : 584
% 1.09/0.43 % ...aggressively subsumed : 0
% 1.09/0.43 % Contextual simplify-reflections : 10
% 1.09/0.43 % Paramodulations : 217
% 1.09/0.43 % Factorizations : 0
% 1.09/0.43 % NegExts : 62
% 1.09/0.43 % Equation resolutions : 8
% 1.09/0.43 % Disequality decompositions : 0
% 1.09/0.43 % Total rewrite steps : 304
% 1.09/0.43 % ...of those cached : 274
% 1.09/0.43 % Propositional unsat checks : 0
% 1.09/0.43 % Propositional check models : 0
% 1.09/0.43 % Propositional check unsatisfiable : 0
% 1.09/0.43 % Propositional clauses : 0
% 1.09/0.43 % Propositional clauses after purity: 0
% 1.09/0.43 % Propositional unsat core size : 0
% 1.09/0.43 % Propositional preprocessing time : 0.000
% 1.09/0.43 % Propositional encoding time : 0.000
% 1.09/0.43 % Propositional solver time : 0.000
% 1.09/0.43 % Success case prop preproc time : 0.000
% 1.09/0.43 % Success case prop encoding time : 0.000
% 1.09/0.43 % Success case prop solver time : 0.000
% 1.09/0.43 % Current number of processed clauses : 42
% 1.09/0.43 % Positive orientable unit clauses : 15
% 1.09/0.43 % Positive unorientable unit clauses: 0
% 1.09/0.43 % Negative unit clauses : 5
% 1.09/0.43 % Non-unit-clauses : 22
% 1.09/0.43 % Current number of unprocessed clauses: 62
% 1.09/0.43 % ...number of literals in the above : 251
% 1.09/0.43 % Current number of archived formulas : 0
% 1.09/0.43 % Current number of archived clauses : 281
% 1.09/0.43 % Clause-clause subsumption calls (NU) : 4778
% 1.09/0.43 % Rec. Clause-clause subsumption calls : 2166
% 1.09/0.43 % Non-unit clause-clause subsumptions : 95
% 1.09/0.43 % Unit Clause-clause subsumption calls : 202
% 1.09/0.43 % Rewrite failures with RHS unbound : 0
% 1.09/0.43 % BW rewrite match attempts : 136
% 1.09/0.43 % BW rewrite match successes : 13
% 1.09/0.43 % Condensation attempts : 0
% 1.09/0.43 % Condensation successes : 0
% 1.09/0.43 % Termbank termtop insertions : 223017
% 1.09/0.43 % Search garbage collected termcells : 266
% 1.09/0.43
% 1.09/0.43 % -------------------------------------------------
% 1.09/0.43 % User time : 0.084 s
% 1.09/0.43 % System time : 0.008 s
% 1.09/0.43 % Total time : 0.092 s
% 1.09/0.43 % Maximum resident set size: 3640 pages
% 1.09/0.43
% 1.09/0.43 % -------------------------------------------------
% 1.09/0.43 % User time : 0.483 s
% 1.09/0.43 % System time : 0.028 s
% 1.09/0.43 % Total time : 0.511 s
% 1.09/0.43 % Maximum resident set size: 4864 pages
% 1.09/0.43 % E exiting
%------------------------------------------------------------------------------