TSTP Solution File: SEV100^5 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEV100^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 04:07:35 EDT 2024
% Result : Theorem 0.80s 0.60s
% Output : CNFRefutation 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 61 ( 6 unt; 9 typ; 0 def)
% Number of atoms : 610 ( 95 equ; 0 cnn)
% Maximal formula atoms : 104 ( 11 avg)
% Number of connectives : 1463 ( 228 ~; 184 |; 47 &; 998 @)
% ( 1 <=>; 2 =>; 0 <=; 3 <~>)
% Maximal formula depth : 22 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 578 ( 578 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 685 ( 557 ^ 124 !; 4 ?; 685 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
p: $o ).
thf(decl_23,type,
epred1_2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(decl_24,type,
epred2_2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(decl_25,type,
epred3_2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(decl_26,type,
esk1_2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(decl_27,type,
epred4_2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(decl_28,type,
esk2_2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(decl_48,type,
esk22_1: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(decl_78,type,
esk52_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/sandbox/benchmark/theBenchmark.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
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X6 )
| ( X1
@ ^ [Z0: $i] :
( p
| ~ p )
@ ^ [Z0: $i] :
( p
& ~ p )
@ X6 ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[cTHM120F_pme])]) ).
thf(c_0_2,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_1])])])])])]) ).
thf(c_0_3,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_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] : $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_3]) ).
thf(c_0_5,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_4]) ).
thf(c_0_6,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_2]) ).
thf(c_0_7,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_5])]) ).
thf(c_0_8,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_6]) ).
thf(c_0_9,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_7]) ).
thf(c_0_10,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_8]) ).
thf(c_0_11,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_9])]) ).
thf(c_0_12,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_10]) ).
thf(c_0_13,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_11,c_0_12])])]) ).
thf(c_0_14,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_2]) ).
thf(c_0_15,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_13])]) ).
thf(c_0_16,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_2]) ).
thf(c_0_17,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_14]) ).
thf(c_0_18,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
@ esk52_0 ) ),
inference(neg_ext,[status(thm)],[c_0_15]) ).
thf(c_0_19,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_16]) ).
thf(c_0_20,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_17]) ).
thf(c_0_21,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_18,c_0_12])]) ).
thf(c_0_22,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_19]) ).
thf(c_0_23,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
@ ( esk22_1 @ X1 ) ) ),
inference(neg_ext,[status(thm)],[c_0_20]) ).
thf(c_0_24,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_21])]) ).
thf(c_0_25,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_8]) ).
thf(c_0_26,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_22])])]) ).
thf(c_0_27,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_23,c_0_24])]) ).
thf(c_0_28,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_25])])]) ).
thf(c_0_29,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_26,c_0_27])])]) ).
thf(c_0_30,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_28,c_0_27])])]) ).
thf(c_0_31,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_2]) ).
thf(c_0_32,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_29])]) ).
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 )
= ( ^ [Z0: $i] : $true ) ) ),
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_30])]) ).
thf(c_0_34,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_2]) ).
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] : $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_31]) ).
thf(c_0_36,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_32,c_0_33]) ).
thf(c_0_37,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_34]) ).
thf(c_0_38,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_35]) ).
thf(c_0_39,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_36]),c_0_24]) ).
thf(c_0_40,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_37]) ).
thf(c_0_41,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_2]) ).
thf(c_0_42,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_38,c_0_39])])]) ).
thf(c_0_43,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_40])])]) ).
thf(c_0_44,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_41]) ).
thf(c_0_45,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_42])]) ).
thf(c_0_46,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_43,c_0_42])])]) ).
thf(c_0_47,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_44]) ).
thf(c_0_48,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_7,c_0_45])])]) ).
thf(c_0_49,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_46])]) ).
thf(c_0_50,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_47,c_0_48])])]),c_0_49]) ).
thf(c_0_51,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_50])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEV100^5 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.13 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun May 19 19:14:38 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.19/0.46 Running higher-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.80/0.60 # Version: 3.1.0-ho
% 0.80/0.60 # Preprocessing class: HSMSSMSSSSMNHHA.
% 0.80/0.60 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.80/0.60 # Starting ehoh_best4_fo with 1200s (4) cores
% 0.80/0.60 # Starting ehoh_best_nonlift_rwall with 600s (2) cores
% 0.80/0.60 # Starting lpo1_lambda_fix with 300s (1) cores
% 0.80/0.60 # Starting full_lambda_9 with 300s (1) cores
% 0.80/0.60 # ehoh_best4_fo with pid 11892 completed with status 0
% 0.80/0.60 # Result found by ehoh_best4_fo
% 0.80/0.60 # Preprocessing class: HSMSSMSSSSMNHHA.
% 0.80/0.60 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.80/0.60 # Starting ehoh_best4_fo with 1200s (4) cores
% 0.80/0.60 # No SInE strategy applied
% 0.80/0.60 # Search class: HGUNF-FFMF22-MHHFFMBN
% 0.80/0.60 # partial match(1): HGUNF-FFMF22-SHHFFMBN
% 0.80/0.60 # Scheduled 6 strats onto 4 cores with 1200 seconds (1200 total)
% 0.80/0.60 # Starting ehoh_best_nonlift with 649s (1) cores
% 0.80/0.60 # Starting ehoh_best4_fo with 121s (1) cores
% 0.80/0.60 # Starting sh2l with 109s (1) cores
% 0.80/0.60 # Starting lpo1_def_fix with 109s (1) cores
% 0.80/0.60 # ehoh_best4_fo with pid 11898 completed with status 0
% 0.80/0.60 # Result found by ehoh_best4_fo
% 0.80/0.60 # Preprocessing class: HSMSSMSSSSMNHHA.
% 0.80/0.60 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.80/0.60 # Starting ehoh_best4_fo with 1200s (4) cores
% 0.80/0.60 # No SInE strategy applied
% 0.80/0.60 # Search class: HGUNF-FFMF22-MHHFFMBN
% 0.80/0.60 # partial match(1): HGUNF-FFMF22-SHHFFMBN
% 0.80/0.60 # Scheduled 6 strats onto 4 cores with 1200 seconds (1200 total)
% 0.80/0.60 # Starting ehoh_best_nonlift with 649s (1) cores
% 0.80/0.60 # Starting ehoh_best4_fo with 121s (1) cores
% 0.80/0.60 # Preprocessing time : 0.001 s
% 0.80/0.60 # Presaturation interreduction done
% 0.80/0.60
% 0.80/0.60 # Proof found!
% 0.80/0.60 # SZS status Theorem
% 0.80/0.60 # SZS output start CNFRefutation
% See solution above
% 0.80/0.60 # Parsed axioms : 2
% 0.80/0.60 # Removed by relevancy pruning/SinE : 0
% 0.80/0.60 # Initial clauses : 9
% 0.80/0.60 # Removed in clause preprocessing : 1
% 0.80/0.60 # Initial clauses in saturation : 8
% 0.80/0.60 # Processed clauses : 382
% 0.80/0.60 # ...of these trivial : 21
% 0.80/0.60 # ...subsumed : 38
% 0.80/0.60 # ...remaining for further processing : 323
% 0.80/0.60 # Other redundant clauses eliminated : 8
% 0.80/0.60 # Clauses deleted for lack of memory : 0
% 0.80/0.60 # Backward-subsumed : 72
% 0.80/0.60 # Backward-rewritten : 153
% 0.80/0.60 # Generated clauses : 670
% 0.80/0.60 # ...of the previous two non-redundant : 584
% 0.80/0.60 # ...aggressively subsumed : 0
% 0.80/0.60 # Contextual simplify-reflections : 10
% 0.80/0.60 # Paramodulations : 217
% 0.80/0.60 # Factorizations : 0
% 0.80/0.60 # NegExts : 62
% 0.80/0.60 # Equation resolutions : 8
% 0.80/0.60 # Disequality decompositions : 0
% 0.80/0.60 # Total rewrite steps : 304
% 0.80/0.60 # ...of those cached : 274
% 0.80/0.60 # Propositional unsat checks : 0
% 0.80/0.60 # Propositional check models : 0
% 0.80/0.60 # Propositional check unsatisfiable : 0
% 0.80/0.60 # Propositional clauses : 0
% 0.80/0.60 # Propositional clauses after purity: 0
% 0.80/0.60 # Propositional unsat core size : 0
% 0.80/0.60 # Propositional preprocessing time : 0.000
% 0.80/0.60 # Propositional encoding time : 0.000
% 0.80/0.60 # Propositional solver time : 0.000
% 0.80/0.60 # Success case prop preproc time : 0.000
% 0.80/0.60 # Success case prop encoding time : 0.000
% 0.80/0.60 # Success case prop solver time : 0.000
% 0.80/0.60 # Current number of processed clauses : 42
% 0.80/0.60 # Positive orientable unit clauses : 15
% 0.80/0.60 # Positive unorientable unit clauses: 0
% 0.80/0.60 # Negative unit clauses : 5
% 0.80/0.60 # Non-unit-clauses : 22
% 0.80/0.60 # Current number of unprocessed clauses: 62
% 0.80/0.60 # ...number of literals in the above : 251
% 0.80/0.60 # Current number of archived formulas : 0
% 0.80/0.60 # Current number of archived clauses : 281
% 0.80/0.60 # Clause-clause subsumption calls (NU) : 6045
% 0.80/0.60 # Rec. Clause-clause subsumption calls : 2876
% 0.80/0.60 # Non-unit clause-clause subsumptions : 95
% 0.80/0.60 # Unit Clause-clause subsumption calls : 277
% 0.80/0.60 # Rewrite failures with RHS unbound : 0
% 0.80/0.60 # BW rewrite match attempts : 136
% 0.80/0.60 # BW rewrite match successes : 13
% 0.80/0.60 # Condensation attempts : 0
% 0.80/0.60 # Condensation successes : 0
% 0.80/0.60 # Termbank termtop insertions : 230610
% 0.80/0.60 # Search garbage collected termcells : 267
% 0.80/0.60
% 0.80/0.60 # -------------------------------------------------
% 0.80/0.60 # User time : 0.105 s
% 0.80/0.60 # System time : 0.008 s
% 0.80/0.60 # Total time : 0.113 s
% 0.80/0.60 # Maximum resident set size: 1856 pages
% 0.80/0.60
% 0.80/0.60 # -------------------------------------------------
% 0.80/0.60 # User time : 0.412 s
% 0.80/0.60 # System time : 0.022 s
% 0.80/0.60 # Total time : 0.434 s
% 0.80/0.60 # Maximum resident set size: 1732 pages
% 0.80/0.60 % E---3.1 exiting
% 0.80/0.60 % E exiting
%------------------------------------------------------------------------------