%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV101^5 : 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 : n017.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 1.74s 0.50s
% Output : CNFRefutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 1
% Syntax : Number of formulae : 54 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 623 ( 94 equ; 0 cnn)
% Maximal formula atoms : 104 ( 11 avg)
% Number of connectives : 1535 ( 235 ~; 193 |; 52 &;1048 @)
% ( 1 <=>; 3 =>; 0 <=; 3 <~>)
% Maximal formula depth : 22 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 519 ( 519 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 711 ( 569 ^; 136 !; 6 ?; 711 :)
% 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,
esk1_2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(decl_26,type,
epred2_2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(decl_27,type,
epred3_2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
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_54,type,
esk29_1: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(decl_71,type,
esk46_0: $i ).
thf(cTHM120E_pme,conjecture,
? [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X3: $i > $o,X4: $i] :
( ( X2 @ X3 @ X3 @ X4 )
| ( X1 @ X3 @ X3 @ X4 ) )
& ! [X3: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( ! [X4: $i] :
( ( X2 @ X3 @ X5 @ X4 )
| ( X1 @ X3 @ X5 @ X4 ) )
& ! [X4: $i] :
( ( X2 @ X5 @ X6 @ X4 )
| ( X1 @ X5 @ X6 @ X4 ) ) )
=> ! [X4: $i] :
( ( X2 @ X3 @ X6 @ X4 )
| ( X1 @ X3 @ X6 @ X4 ) ) )
& ~ ! [X4: $i] :
( ( X2
@ ^ [X7: $i] :
( p
| ~ p )
@ ^ [X8: $i] :
( p
& ~ p )
@ X4 )
| ( X1
@ ^ [X9: $i] :
( p
| ~ p )
@ ^ [X10: $i] :
( p
& ~ p )
@ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.jKDcaqTMRx/E---3.1_443265.p',cTHM120E_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] :
( ( X2 @ X3 @ X3 @ X4 )
| ( X1 @ X3 @ X3 @ X4 ) )
& ! [X3: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( ! [X4: $i] :
( ( X2 @ X3 @ X5 @ X4 )
| ( X1 @ X3 @ X5 @ X4 ) )
& ! [X4: $i] :
( ( X2 @ X5 @ X6 @ X4 )
| ( X1 @ X5 @ X6 @ X4 ) ) )
=> ! [X4: $i] :
( ( X2 @ X3 @ X6 @ X4 )
| ( X1 @ X3 @ X6 @ X4 ) ) )
& ~ ! [X4: $i] :
( ( X2
@ ^ [X7: $i] :
( p
| ~ p )
@ ^ [X8: $i] :
( p
& ~ p )
@ X4 )
| ( X1
@ ^ [X9: $i] :
( p
| ~ p )
@ ^ [X10: $i] :
( p
& ~ p )
@ X4 ) ) ),
inference(assume_negation,[status(cth)],[cTHM120E_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] :
( ( X2 @ X3 @ X3 @ X4 )
| ( X1 @ X3 @ X3 @ X4 ) )
& ! [X3: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( ! [X4: $i] :
( ( X2 @ X3 @ X5 @ X4 )
| ( X1 @ X3 @ X5 @ X4 ) )
& ! [X4: $i] :
( ( X2 @ X5 @ X6 @ X4 )
| ( X1 @ X5 @ X6 @ X4 ) ) )
=> ! [X4: $i] :
( ( X2 @ X3 @ X6 @ X4 )
| ( X1 @ X3 @ X6 @ X4 ) ) )
& ~ ! [X4: $i] :
( ( X2
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X4 )
| ( X1
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X4 ) ) ),
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,X29: $i,X30: $i,X32: $i] :
( ( ( X23 @ ( epred2_2 @ X22 @ X23 ) @ ( epred3_2 @ X22 @ X23 ) @ X29 )
| ( X22 @ ( epred2_2 @ X22 @ X23 ) @ ( epred3_2 @ X22 @ X23 ) @ X29 )
| ~ ( X23 @ ( epred1_2 @ X22 @ X23 ) @ ( epred1_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 @ ( epred3_2 @ X22 @ X23 ) @ ( epred4_2 @ X22 @ X23 ) @ X30 )
| ( X22 @ ( epred3_2 @ X22 @ X23 ) @ ( epred4_2 @ X22 @ X23 ) @ X30 )
| ~ ( X23 @ ( epred1_2 @ X22 @ X23 ) @ ( epred1_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 @ ( epred2_2 @ X22 @ X23 ) @ ( epred4_2 @ X22 @ X23 ) @ ( esk2_2 @ X22 @ X23 ) )
| ~ ( X23 @ ( epred1_2 @ X22 @ X23 ) @ ( epred1_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 @ ( epred2_2 @ X22 @ X23 ) @ ( epred4_2 @ X22 @ X23 ) @ ( esk2_2 @ X22 @ X23 ) )
| ~ ( X23 @ ( epred1_2 @ X22 @ X23 ) @ ( epred1_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 @ ( epred2_2 @ X22 @ X23 ) @ ( epred3_2 @ X22 @ X23 ) @ X29 )
| ( X22 @ ( epred2_2 @ X22 @ X23 ) @ ( epred3_2 @ X22 @ X23 ) @ X29 )
| ~ ( X22 @ ( epred1_2 @ X22 @ X23 ) @ ( epred1_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 @ ( epred3_2 @ X22 @ X23 ) @ ( epred4_2 @ X22 @ X23 ) @ X30 )
| ( X22 @ ( epred3_2 @ X22 @ X23 ) @ ( epred4_2 @ X22 @ X23 ) @ X30 )
| ~ ( X22 @ ( epred1_2 @ X22 @ X23 ) @ ( epred1_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 @ ( epred2_2 @ X22 @ X23 ) @ ( epred4_2 @ X22 @ X23 ) @ ( esk2_2 @ X22 @ X23 ) )
| ~ ( X22 @ ( epred1_2 @ X22 @ X23 ) @ ( epred1_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 @ ( epred2_2 @ X22 @ X23 ) @ ( epred4_2 @ X22 @ X23 ) @ ( esk2_2 @ X22 @ X23 ) )
| ~ ( X22 @ ( epred1_2 @ X22 @ X23 ) @ ( epred1_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,X4: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1 @ ( epred2_2 @ X2 @ X1 ) @ ( epred3_2 @ X2 @ X1 ) @ X4 )
| ( X2 @ ( epred2_2 @ X2 @ X1 ) @ ( epred3_2 @ X2 @ X1 ) @ X4 )
| ( X1
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X7 )
| ( X2
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X7 )
| ~ ( X2 @ ( epred1_2 @ X2 @ X1 ) @ ( epred1_2 @ X2 @ X1 ) @ ( esk1_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X7: $i,X4: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1 @ ( epred2_2 @ X2 @ X1 ) @ ( epred3_2 @ X2 @ X1 ) @ X4 )
| ( X2 @ ( epred2_2 @ X2 @ X1 ) @ ( epred3_2 @ X2 @ X1 ) @ X4 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 )
| ~ ( X2 @ ( epred1_2 @ X2 @ X1 ) @ ( epred1_2 @ X2 @ X1 ) @ ( esk1_2 @ X2 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_4]) ).
thf(c_0_6,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: $i,X7: $i] :
( ( ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1 )
= ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1 ) )
| ( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) )
| ( X1
@ ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1 )
@ ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1 )
@ X4 )
| ( 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,
! [X4: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X4 )
| ( X2
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X4 )
| ~ ( X1 @ ( epred2_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ ( esk2_2 @ X2 @ X1 ) )
| ~ ( X1 @ ( epred1_2 @ X2 @ X1 ) @ ( epred1_2 @ X2 @ X1 ) @ ( esk1_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_8,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: $i,X7: $i] :
( ( ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1 )
= ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1 ) )
| ( X1
@ ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1 )
@ ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1 )
@ X4 )
| ( 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,
! [X4: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 )
| ~ ( X1 @ ( epred1_2 @ X2 @ X1 ) @ ( epred1_2 @ X2 @ X1 ) @ ( esk1_2 @ X2 @ X1 ) )
| ~ ( X1 @ ( epred2_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ ( esk2_2 @ X2 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: $i,X291: $i,X7: $i] :
( ( ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1
@ X291 )
<=> ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1
@ X291 ) )
| ( X1
@ ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1 )
@ ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1 )
@ X4 )
| ( 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,X4: $i] :
( ( ( epred2_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( ^ [Z0: $i] : $true ) )
| ( ( epred1_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( ^ [Z0: $i] : $true ) )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_9]) ).
thf(c_0_12,negated_conjecture,
! [X4: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i,X7: $i] :
( ( X1
@ ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1 )
@ ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1 )
@ X4 )
| ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1
@ X7 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X8 )
| ~ ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1
@ 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,X4: $i,X7: $i] :
( ( ( epred1_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( ^ [Z0: $i] : $true ) )
| ( epred2_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ X4 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 ) ),
inference(arg_cong,[status(thm)],[c_0_11]) ).
thf(c_0_14,negated_conjecture,
! [X4: $i] :
( ( ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( ^ [Z0: $i] : $true ) )
| ( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) )
| ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ X4 )
| ( ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
!= ( ^ [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,
! [X7: $i,X4: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1 @ ( epred3_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ X4 )
| ( X2 @ ( epred3_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ X4 )
| ( X1
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X7 )
| ( X2
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X7 )
| ~ ( X1 @ ( epred1_2 @ X2 @ X1 ) @ ( epred1_2 @ X2 @ X1 ) @ ( esk1_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_16,negated_conjecture,
! [X4: $i] :
( ( ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( ^ [Z0: $i] : $true ) )
| ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ X4 )
| ( ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
!= ( ^ [Z0: $i] : $true ) ) ),
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_14])]) ).
thf(c_0_17,negated_conjecture,
! [X7: $i,X4: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1 @ ( epred3_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ X4 )
| ( X2 @ ( epred3_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ X4 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 )
| ~ ( X1 @ ( epred1_2 @ X2 @ X1 ) @ ( epred1_2 @ X2 @ X1 ) @ ( esk1_2 @ X2 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_15]) ).
thf(c_0_18,negated_conjecture,
! [X4: $i] :
( ( ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( ^ [Z0: $i] : $true ) )
| ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ X4 )
| ~ ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ esk46_0 ) ),
inference(neg_ext,[status(thm)],[c_0_16]) ).
thf(c_0_19,negated_conjecture,
! [X4: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X4 )
| ( X2
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X4 )
| ~ ( X1 @ ( epred2_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ ( esk2_2 @ X2 @ X1 ) )
| ~ ( X2 @ ( epred1_2 @ X2 @ X1 ) @ ( epred1_2 @ X2 @ X1 ) @ ( esk1_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_20,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X2
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X4 )
| ( X1
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X4 )
| ~ ( X1 @ ( epred2_2 @ X1 @ X2 ) @ ( epred4_2 @ X1 @ X2 ) @ ( esk2_2 @ X1 @ X2 ) )
| ~ ( X2 @ ( epred1_2 @ X1 @ X2 ) @ ( epred1_2 @ X1 @ X2 ) @ ( esk1_2 @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_21,negated_conjecture,
! [X7: $i,X4: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( epred1_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( ^ [Z0: $i] : $true ) )
| ( X1
@ ( epred3_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
@ ( epred4_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
@ X4 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 )
| ( ( epred3_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
!= ( ^ [Z0: $i] : $true ) ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_17]) ).
thf(c_0_22,negated_conjecture,
! [X4: $i] :
( ( ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( ^ [Z0: $i] : $true ) )
| ( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) )
| ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ X4 ) ),
inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_13])]) ).
thf(c_0_23,negated_conjecture,
! [X4: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 )
| ~ ( X2 @ ( epred1_2 @ X2 @ X1 ) @ ( epred1_2 @ X2 @ X1 ) @ ( esk1_2 @ X2 @ X1 ) )
| ~ ( X1 @ ( epred2_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ ( esk2_2 @ X2 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_19]) ).
thf(c_0_24,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 )
| ~ ( X2 @ ( epred1_2 @ X1 @ X2 ) @ ( epred1_2 @ X1 @ X2 ) @ ( esk1_2 @ X1 @ X2 ) )
| ~ ( X1 @ ( epred2_2 @ X1 @ X2 ) @ ( epred4_2 @ X1 @ X2 ) @ ( esk2_2 @ X1 @ X2 ) ) ),
inference(cn,[status(thm)],[c_0_20]) ).
thf(c_0_25,negated_conjecture,
! [X7: $i,X4: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( epred1_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( ^ [Z0: $i] : $true ) )
| ( X1
@ ( epred3_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
@ ( epred4_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
@ X4 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 )
| ~ ( epred3_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ ( esk29_1 @ X1 ) ) ),
inference(neg_ext,[status(thm)],[c_0_21]) ).
thf(c_0_26,negated_conjecture,
! [X4: $i] :
( ( ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( ^ [Z0: $i] : $true ) )
| ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) )
@ X4 ) ),
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_22])]) ).
thf(c_0_27,negated_conjecture,
! [X4: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 )
| ~ ( X1
@ ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1 )
@ ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1 )
@ ( esk2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1 ) ) ),
inference(primitive_enumeration,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[])]),c_0_23]) ).
thf(c_0_28,negated_conjecture,
! [X4: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( epred1_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( ^ [Z0: $i] : $true ) )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 )
| ~ ( X1
@ ( epred2_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
@ ( epred4_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
@ ( esk2_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) ) ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_24]) ).
thf(c_0_29,negated_conjecture,
( ( ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) ) )
| ( ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( ^ [Z0: $i] : $true ) )
| ( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) ) ),
inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26])]) ).
thf(c_0_30,negated_conjecture,
! [X4: $i,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 )
| ~ ( X1
@ ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1 )
@ ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1 )
@ ( esk2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1 ) ) ),
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_27])]) ).
thf(c_0_31,negated_conjecture,
( ( ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( ^ [Z0: $i] : $true ) )
| ( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) )
| ( ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
!= ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) ) ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29])])]) ).
thf(c_0_32,negated_conjecture,
( ( ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( ^ [Z0: $i] : $true ) )
| ( ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( ^ [Z0: $i] : $true ) )
| ( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_29])])]) ).
thf(c_0_33,negated_conjecture,
( ( ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( ^ [Z0: $i] : $true ) )
| ( ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
!= ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) ) ) ),
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_31])]) ).
thf(c_0_34,negated_conjecture,
( ( ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( ^ [Z0: $i] : $true ) )
| ( ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( ^ [Z0: $i] : $true ) ) ),
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_32])]) ).
thf(c_0_35,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X2
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X4 )
| ( X1
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X4 )
| ~ ( X1 @ ( epred2_2 @ X1 @ X2 ) @ ( epred4_2 @ X1 @ X2 ) @ ( esk2_2 @ X1 @ X2 ) )
| ~ ( X1 @ ( epred1_2 @ X1 @ X2 ) @ ( epred1_2 @ X1 @ X2 ) @ ( esk1_2 @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_36,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 )
| ( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 )
<~> ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 ) )
| ~ ( X1 @ ( epred1_2 @ X1 @ X2 ) @ ( epred1_2 @ X1 @ X2 ) @ ( esk1_2 @ X1 @ X2 ) )
| ~ ( X2 @ ( epred2_2 @ X1 @ X2 ) @ ( epred4_2 @ X1 @ X2 ) @ ( esk2_2 @ X1 @ X2 ) ) ),
inference(ext_eqfact,[status(thm)],[c_0_23]) ).
thf(c_0_37,negated_conjecture,
( ( ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( ^ [Z0: $i] : $true ) )
| ( ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
!= ( ^ [Z0: $i] : $true ) ) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
thf(c_0_38,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 )
| ~ ( X1 @ ( epred1_2 @ X1 @ X2 ) @ ( epred1_2 @ X1 @ X2 ) @ ( esk1_2 @ X1 @ X2 ) )
| ~ ( X1 @ ( epred2_2 @ X1 @ X2 ) @ ( epred4_2 @ X1 @ X2 ) @ ( esk2_2 @ X1 @ X2 ) ) ),
inference(cn,[status(thm)],[c_0_35]) ).
thf(c_0_39,plain,
! [X4: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 )
| ~ ( X2 @ ( epred1_2 @ X2 @ X1 ) @ ( epred1_2 @ X2 @ X1 ) @ ( esk1_2 @ X2 @ X1 ) )
| ~ ( X1 @ ( epred2_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_36])])]) ).
thf(c_0_40,negated_conjecture,
( ( epred1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( ^ [Z0: $i] : $true ) ),
inference(csr,[status(thm)],[inference(neg_ext,[status(thm)],[c_0_37]),c_0_26]) ).
thf(c_0_41,negated_conjecture,
! [X7: $i,X4: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1 @ ( epred3_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ X4 )
| ( X2 @ ( epred3_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ X4 )
| ( X1
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X7 )
| ( X2
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X7 )
| ~ ( X2 @ ( epred1_2 @ X2 @ X1 ) @ ( epred1_2 @ X2 @ X1 ) @ ( esk1_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_42,plain,
! [X4: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 )
| ( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 )
<~> ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 ) )
| ~ ( X2 @ ( epred1_2 @ X2 @ X1 ) @ ( epred1_2 @ X2 @ X1 ) @ ( esk1_2 @ X2 @ X1 ) )
| ~ ( X2 @ ( epred2_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ ( esk2_2 @ X2 @ X1 ) ) ),
inference(ext_eqfact,[status(thm)],[c_0_38]) ).
thf(c_0_43,plain,
( ( ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( ^ [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,negated_conjecture,
! [X7: $i,X4: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1 @ ( epred3_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ X4 )
| ( X2 @ ( epred3_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ X4 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 )
| ~ ( X2 @ ( epred1_2 @ X2 @ X1 ) @ ( epred1_2 @ X2 @ X1 ) @ ( esk1_2 @ X2 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_41]) ).
thf(c_0_45,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 )
| ~ ( X1 @ ( epred1_2 @ X1 @ X2 ) @ ( epred1_2 @ X1 @ X2 ) @ ( esk1_2 @ X1 @ X2 ) )
| ~ ( X1 @ ( epred2_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_42])])]) ).
thf(c_0_46,plain,
( ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( ^ [Z0: $i] : $true ) ),
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_43])]) ).
thf(c_0_47,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X7: $i,X4: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X2 @ ( epred3_2 @ X1 @ X2 ) @ ( epred4_2 @ X1 @ X2 ) @ X4 )
| ( X1 @ ( epred3_2 @ X1 @ X2 ) @ ( epred4_2 @ X1 @ X2 ) @ X4 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 )
| ( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 )
<~> ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 ) )
| ~ ( X1 @ ( epred1_2 @ X1 @ X2 ) @ ( epred1_2 @ X1 @ X2 ) @ ( esk1_2 @ X1 @ X2 ) ) ),
inference(ext_eqfact,[status(thm)],[c_0_44]) ).
thf(c_0_48,plain,
( ( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) )
| ( ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
!= ( ^ [Z0: $i] : $true ) ) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_40])])]),c_0_46]) ).
thf(c_0_49,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X7: $i,X4: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1 @ ( epred3_2 @ X1 @ X2 ) @ ( epred4_2 @ X1 @ X2 ) @ X4 )
| ( X2 @ ( epred3_2 @ X1 @ X2 ) @ ( epred4_2 @ X1 @ X2 ) @ X4 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X7 )
| ~ ( X1 @ ( epred1_2 @ X1 @ X2 ) @ ( epred1_2 @ X1 @ X2 ) @ ( esk1_2 @ X1 @ X2 ) ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_47])])]) ).
thf(c_0_50,negated_conjecture,
( ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
= ( ^ [Z0: $i] : $true ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_46])])]) ).
thf(c_0_51,plain,
( ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( Z0
!= ( ^ [Z3: $i] : $true ) ) )
!= ( ^ [Z0: $i] : $true ) ),
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_48])]) ).
thf(c_0_52,plain,
( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_40])])]),c_0_50]),c_0_50])]),c_0_51]) ).
thf(c_0_53,plain,
$false,
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_52])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV101^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n017.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 15:05:52 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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.jKDcaqTMRx/E---3.1_443265.p
% 1.74/0.50 % Version: 3.5.1-ho
% 1.74/0.50 % Preprocessing class: HSMSSMSSSSMNHHA.
% 1.74/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.74/0.50 % Starting ehoh_best4_fo with 1200s (4) cores
% 1.74/0.50 % Starting ehoh_best_nonlift_rwall with 600s (2) cores
% 1.74/0.50 % Starting lpo1_lambda_fix with 300s (1) cores
% 1.74/0.50 % Starting full_lambda_9 with 300s (1) cores
% 1.74/0.50 % ehoh_best4_fo with pid 443278 completed with status 0
% 1.74/0.50 % Result found by ehoh_best4_fo
% 1.74/0.50 % Preprocessing class: HSMSSMSSSSMNHHA.
% 1.74/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.74/0.50 % Starting ehoh_best4_fo with 1200s (4) cores
% 1.74/0.50 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.74/0.50 % No SInE strategy applied
% 1.74/0.50 % Search class: HGUNF-FFMF22-MHHFFMBN
% 1.74/0.50 % partial match(1): HGUNF-FFMF22-SHHFFMBN
% 1.74/0.50 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 1.74/0.50 % Starting SubtermCWHack with 109s (1) cores
% 1.74/0.50 % Starting ehoh_best4_fo with 121s (1) cores
% 1.74/0.50 % Starting sh2lt with 109s (1) cores
% 1.74/0.50 % Starting sh2l with 109s (1) cores
% 1.74/0.50 % SubtermCWHack with pid 443282 completed with status 10
% 1.74/0.50 % Starting lpo1_def_fix with 109s (1) cores
% 1.74/0.50 % ehoh_best4_fo with pid 443285 completed with status 0
% 1.74/0.50 % Result found by ehoh_best4_fo
% 1.74/0.50 % Preprocessing class: HSMSSMSSSSMNHHA.
% 1.74/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.74/0.50 % Starting ehoh_best4_fo with 1200s (4) cores
% 1.74/0.50 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.74/0.50 % No SInE strategy applied
% 1.74/0.50 % Search class: HGUNF-FFMF22-MHHFFMBN
% 1.74/0.50 % partial match(1): HGUNF-FFMF22-SHHFFMBN
% 1.74/0.50 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 1.74/0.50 % Starting SubtermCWHack with 109s (1) cores
% 1.74/0.50 % Starting ehoh_best4_fo with 121s (1) cores
% 1.74/0.50 % Preprocessing time : 0.001 s
% 1.74/0.50 % Presaturation interreduction done
% 1.74/0.50
% 1.74/0.50 % Proof found!
% 1.74/0.50 % SZS status Theorem
% 1.74/0.50 % SZS output start CNFRefutation
% See solution above
% 1.74/0.50 % Parsed axioms : 2
% 1.74/0.50 % Removed by relevancy pruning/SinE : 0
% 1.74/0.50 % Initial clauses : 9
% 1.74/0.50 % Removed in clause preprocessing : 1
% 1.74/0.50 % Initial clauses in saturation : 8
% 1.74/0.50 % Processed clauses : 362
% 1.74/0.50 % ...of these trivial : 21
% 1.74/0.50 % ...subsumed : 33
% 1.74/0.50 % ...remaining for further processing : 308
% 1.74/0.50 % Other redundant clauses eliminated : 8
% 1.74/0.50 % Clauses deleted for lack of memory : 0
% 1.74/0.50 % Backward-subsumed : 72
% 1.74/0.50 % Backward-rewritten : 142
% 1.74/0.50 % Generated clauses : 582
% 1.74/0.50 % ...of the previous two non-redundant : 543
% 1.74/0.50 % ...aggressively subsumed : 0
% 1.74/0.50 % Contextual simplify-reflections : 5
% 1.74/0.50 % Paramodulations : 147
% 1.74/0.50 % Factorizations : 0
% 1.74/0.50 % NegExts : 56
% 1.74/0.50 % Equation resolutions : 8
% 1.74/0.50 % Disequality decompositions : 0
% 1.74/0.50 % Total rewrite steps : 261
% 1.74/0.50 % ...of those cached : 231
% 1.74/0.50 % Propositional unsat checks : 0
% 1.74/0.50 % Propositional check models : 0
% 1.74/0.50 % Propositional check unsatisfiable : 0
% 1.74/0.50 % Propositional clauses : 0
% 1.74/0.50 % Propositional clauses after purity: 0
% 1.74/0.50 % Propositional unsat core size : 0
% 1.74/0.50 % Propositional preprocessing time : 0.000
% 1.74/0.50 % Propositional encoding time : 0.000
% 1.74/0.50 % Propositional solver time : 0.000
% 1.74/0.50 % Success case prop preproc time : 0.000
% 1.74/0.50 % Success case prop encoding time : 0.000
% 1.74/0.50 % Success case prop solver time : 0.000
% 1.74/0.50 % Current number of processed clauses : 40
% 1.74/0.50 % Positive orientable unit clauses : 15
% 1.74/0.50 % Positive unorientable unit clauses: 0
% 1.74/0.50 % Negative unit clauses : 5
% 1.74/0.50 % Non-unit-clauses : 20
% 1.74/0.50 % Current number of unprocessed clauses: 58
% 1.74/0.50 % ...number of literals in the above : 237
% 1.74/0.50 % Current number of archived formulas : 0
% 1.74/0.50 % Current number of archived clauses : 268
% 1.74/0.50 % Clause-clause subsumption calls (NU) : 4630
% 1.74/0.50 % Rec. Clause-clause subsumption calls : 2154
% 1.74/0.50 % Non-unit clause-clause subsumptions : 88
% 1.74/0.50 % Unit Clause-clause subsumption calls : 492
% 1.74/0.50 % Rewrite failures with RHS unbound : 0
% 1.74/0.50 % BW rewrite match attempts : 136
% 1.74/0.50 % BW rewrite match successes : 13
% 1.74/0.50 % Condensation attempts : 0
% 1.74/0.50 % Condensation successes : 0
% 1.74/0.50 % Termbank termtop insertions : 215689
% 1.74/0.50 % Search garbage collected termcells : 266
% 1.74/0.50
% 1.74/0.50 % -------------------------------------------------
% 1.74/0.50 % User time : 0.208 s
% 1.74/0.50 % System time : 0.007 s
% 1.74/0.50 % Total time : 0.215 s
% 1.74/0.50 % Maximum resident set size: 3640 pages
% 1.74/0.50
% 1.74/0.50 % -------------------------------------------------
% 1.74/0.50 % User time : 0.812 s
% 1.74/0.50 % System time : 0.027 s
% 1.74/0.50 % Total time : 0.839 s
% 1.74/0.50 % Maximum resident set size: 4864 pages
% 1.74/0.50 % E exiting
%------------------------------------------------------------------------------