%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEV064^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:35:54 AM UTC 2026
% Result : Theorem 1.12s 0.45s
% Output : CNFRefutation 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 25 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 245 ( 32 equ; 0 cnn)
% Maximal formula atoms : 72 ( 9 avg)
% Number of connectives : 845 ( 106 ~; 90 |; 16 &; 629 @)
% ( 0 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 22 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 235 ( 235 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 294 ( 208 ^; 80 !; 6 ?; 294 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
epred1_2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(decl_24,type,
esk1_2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
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,
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(cTHM120C_pme,conjecture,
? [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ! [X3: $i] :
( ( X2
@ ^ [X4: $i] : $true
@ ^ [X4: $i] : ~ $true
@ X3 )
| ( X1
@ ^ [X4: $i] : $true
@ ^ [X4: $i] : ~ $true
@ X3 ) )
& ! [X5: $i > $o,X3: $i] :
( ( X2 @ X5 @ X5 @ X3 )
| ( X1 @ X5 @ X5 @ X3 ) )
& ! [X6: $i > $o,X7: $i > $o,X8: $i > $o] :
( ( ! [X3: $i] :
( ( X2 @ X6 @ X7 @ X3 )
| ( X1 @ X6 @ X7 @ X3 ) )
& ! [X3: $i] :
( ( X2 @ X7 @ X8 @ X3 )
| ( X1 @ X7 @ X8 @ X3 ) ) )
=> ! [X3: $i] :
( ( X2 @ X6 @ X8 @ X3 )
| ( X1 @ X6 @ X8 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2aXy7rfTPK/E---3.1_3477653.p',cTHM120C_pme) ).
thf(c_0_1,negated_conjecture,
~ ? [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ! [X3: $i] :
( ( X2
@ ^ [X4: $i] : $true
@ ^ [X4: $i] : ~ $true
@ X3 )
| ( X1
@ ^ [X4: $i] : $true
@ ^ [X4: $i] : ~ $true
@ X3 ) )
& ! [X5: $i > $o,X3: $i] :
( ( X2 @ X5 @ X5 @ X3 )
| ( X1 @ X5 @ X5 @ X3 ) )
& ! [X6: $i > $o,X7: $i > $o,X8: $i > $o] :
( ( ! [X3: $i] :
( ( X2 @ X6 @ X7 @ X3 )
| ( X1 @ X6 @ X7 @ X3 ) )
& ! [X3: $i] :
( ( X2 @ X7 @ X8 @ X3 )
| ( X1 @ X7 @ X8 @ X3 ) ) )
=> ! [X3: $i] :
( ( X2 @ X6 @ X8 @ X3 )
| ( X1 @ X6 @ X8 @ X3 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM120C_pme]) ).
thf(c_0_2,negated_conjecture,
~ ? [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ! [X3: $i] :
( ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X3 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X3 ) )
& ! [X5: $i > $o,X3: $i] :
( ( X2 @ X5 @ X5 @ X3 )
| ( X1 @ X5 @ X5 @ X3 ) )
& ! [X6: $i > $o,X7: $i > $o,X8: $i > $o] :
( ( ! [X3: $i] :
( ( X2 @ X6 @ X7 @ X3 )
| ( X1 @ X6 @ X7 @ X3 ) )
& ! [X3: $i] :
( ( X2 @ X7 @ X8 @ X3 )
| ( X1 @ X7 @ X8 @ X3 ) ) )
=> ! [X3: $i] :
( ( X2 @ X6 @ X8 @ X3 )
| ( X1 @ X6 @ X8 @ X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
thf(c_0_3,negated_conjecture,
! [X20: ( $i > $o ) > ( $i > $o ) > $i > $o,X21: ( $i > $o ) > ( $i > $o ) > $i > $o,X22: $i,X28: $i,X29: $i] :
( ( ( X21 @ ( epred2_2 @ X20 @ X21 ) @ ( epred3_2 @ X20 @ X21 ) @ X28 )
| ( X20 @ ( epred2_2 @ X20 @ X21 ) @ ( epred3_2 @ X20 @ X21 ) @ X28 )
| ~ ( X21 @ ( epred1_2 @ X20 @ X21 ) @ ( epred1_2 @ X20 @ X21 ) @ ( esk1_2 @ X20 @ X21 ) )
| ( X21
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X22 )
| ( X20
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X22 ) )
& ( ( X21 @ ( epred3_2 @ X20 @ X21 ) @ ( epred4_2 @ X20 @ X21 ) @ X29 )
| ( X20 @ ( epred3_2 @ X20 @ X21 ) @ ( epred4_2 @ X20 @ X21 ) @ X29 )
| ~ ( X21 @ ( epred1_2 @ X20 @ X21 ) @ ( epred1_2 @ X20 @ X21 ) @ ( esk1_2 @ X20 @ X21 ) )
| ( X21
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X22 )
| ( X20
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X22 ) )
& ( ~ ( X21 @ ( epred2_2 @ X20 @ X21 ) @ ( epred4_2 @ X20 @ X21 ) @ ( esk2_2 @ X20 @ X21 ) )
| ~ ( X21 @ ( epred1_2 @ X20 @ X21 ) @ ( epred1_2 @ X20 @ X21 ) @ ( esk1_2 @ X20 @ X21 ) )
| ( X21
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X22 )
| ( X20
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X22 ) )
& ( ~ ( X20 @ ( epred2_2 @ X20 @ X21 ) @ ( epred4_2 @ X20 @ X21 ) @ ( esk2_2 @ X20 @ X21 ) )
| ~ ( X21 @ ( epred1_2 @ X20 @ X21 ) @ ( epred1_2 @ X20 @ X21 ) @ ( esk1_2 @ X20 @ X21 ) )
| ( X21
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X22 )
| ( X20
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X22 ) )
& ( ( X21 @ ( epred2_2 @ X20 @ X21 ) @ ( epred3_2 @ X20 @ X21 ) @ X28 )
| ( X20 @ ( epred2_2 @ X20 @ X21 ) @ ( epred3_2 @ X20 @ X21 ) @ X28 )
| ~ ( X20 @ ( epred1_2 @ X20 @ X21 ) @ ( epred1_2 @ X20 @ X21 ) @ ( esk1_2 @ X20 @ X21 ) )
| ( X21
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X22 )
| ( X20
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X22 ) )
& ( ( X21 @ ( epred3_2 @ X20 @ X21 ) @ ( epred4_2 @ X20 @ X21 ) @ X29 )
| ( X20 @ ( epred3_2 @ X20 @ X21 ) @ ( epred4_2 @ X20 @ X21 ) @ X29 )
| ~ ( X20 @ ( epred1_2 @ X20 @ X21 ) @ ( epred1_2 @ X20 @ X21 ) @ ( esk1_2 @ X20 @ X21 ) )
| ( X21
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X22 )
| ( X20
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X22 ) )
& ( ~ ( X21 @ ( epred2_2 @ X20 @ X21 ) @ ( epred4_2 @ X20 @ X21 ) @ ( esk2_2 @ X20 @ X21 ) )
| ~ ( X20 @ ( epred1_2 @ X20 @ X21 ) @ ( epred1_2 @ X20 @ X21 ) @ ( esk1_2 @ X20 @ X21 ) )
| ( X21
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X22 )
| ( X20
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X22 ) )
& ( ~ ( X20 @ ( epred2_2 @ X20 @ X21 ) @ ( epred4_2 @ X20 @ X21 ) @ ( esk2_2 @ X20 @ X21 ) )
| ~ ( X20 @ ( epred1_2 @ X20 @ X21 ) @ ( epred1_2 @ X20 @ X21 ) @ ( esk1_2 @ X20 @ X21 ) )
| ( X21
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X22 )
| ( X20
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X22 ) ) ),
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,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X3: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X3 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X3 )
| ~ ( 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_5,negated_conjecture,
! [X4: $i,X3: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1 @ ( epred3_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ X3 )
| ( X2 @ ( epred3_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ X3 )
| ( 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 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_6,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X3: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X3 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X3 )
| ~ ( 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_4]) ).
thf(c_0_7,negated_conjecture,
! [X4: $i,X3: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1 @ ( epred3_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ X3 )
| ( X2 @ ( epred3_2 @ X2 @ X1 ) @ ( epred4_2 @ X2 @ X1 ) @ X3 )
| ( 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 ) ) ),
inference(cn,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
! [X4: $i,X3: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1 @ ( epred2_2 @ X2 @ X1 ) @ ( epred3_2 @ X2 @ X1 ) @ X3 )
| ( X2 @ ( epred2_2 @ X2 @ X1 ) @ ( epred3_2 @ X2 @ X1 ) @ X3 )
| ( 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 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_9,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X3: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X3 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X3 )
| ~ ( 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_10,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X3: $i] :
( ( ( esk1_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : ( Z2 != X3 ) )
= X3 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X3 )
| ~ ( X1
@ ( epred2_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : ( Z2 != X3 ) )
@ ( epred4_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : ( Z2 != X3 ) )
@ ( esk2_2 @ X1
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : ( Z2 != X3 ) ) ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_6]) ).
thf(c_0_11,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X3: $i,X4: $i] :
( ( ( epred4_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
@ ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1 )
@ ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1 )
@ X3 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 ) ),
inference(primitive_enumeration,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[])]),c_0_7]) ).
thf(c_0_12,negated_conjecture,
! [X4: $i,X3: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1 @ ( epred2_2 @ X2 @ X1 ) @ ( epred3_2 @ X2 @ X1 ) @ X3 )
| ( X2 @ ( epred2_2 @ X2 @ X1 ) @ ( epred3_2 @ X2 @ X1 ) @ X3 )
| ( 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 ) ) ),
inference(cn,[status(thm)],[c_0_8]) ).
thf(c_0_13,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X3: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X3 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X3 )
| ~ ( 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_9]) ).
thf(c_0_14,negated_conjecture,
! [X3: $i] :
( ( ( esk1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : ( Z2 != X3 ) )
= X3 )
| ( ( ^ [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] : ( Z2 != X3 ) )
!= ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : ( Z2 != X3 ) ) ) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11])])])])]) ).
thf(c_0_15,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X3: $i,X4: $i] :
( ( ( epred3_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ X1 )
= ( epred2_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 )
@ X3 )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X4 ) ),
inference(primitive_enumeration,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[])]),c_0_12]) ).
thf(c_0_16,plain,
! [X3: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X3 )
| ( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X3 )
<~> ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X3 ) )
| ~ ( 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_13]) ).
thf(c_0_17,negated_conjecture,
! [X3: $i] :
( ( ( esk1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : ( Z2 != X3 ) )
= X3 )
| ( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) ) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15])])])]) ).
thf(c_0_18,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X3: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X3 )
| ( X2
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true
@ X3 )
| ~ ( 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_16])])]) ).
thf(c_0_19,negated_conjecture,
! [X3: $i] :
( ( esk1_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : ( Z2 != X3 ) )
= X3 ),
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_17])]) ).
thf(c_0_20,plain,
! [X3: $i] :
( ( ( ^ [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] : ( Z2 != X3 ) )
!= ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : ( Z2 != X3 ) ) ) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19])])])]) ).
thf(c_0_21,plain,
! [X3: $i] :
( ( epred4_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : ( Z2 != X3 ) )
!= ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : ( Z2 != X3 ) ) ),
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_20])]) ).
thf(c_0_22,negated_conjecture,
! [X3: $i] :
( ( ( ^ [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] : ( Z2 != X3 ) )
!= ( epred2_2
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : Z0
@ ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] : ( Z2 != X3 ) ) ) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_11])])])]) ).
thf(c_0_23,negated_conjecture,
( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_15])])])]) ).
thf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV064^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n007.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 15:04:11 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 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/tmp/tmp.2aXy7rfTPK/E---3.1_3477653.p
% 1.12/0.45 % Version: 3.5.1-ho
% 1.12/0.45 % Preprocessing class: HSSSSMSSSSMNHHA.
% 1.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.12/0.45 % Starting post_as_ho5 with 1500s (5) cores
% 1.12/0.45 % Starting sh2lt with 300s (1) cores
% 1.12/0.45 % Starting ehoh_best8_lambda with 300s (1) cores
% 1.12/0.45 % Starting post_as_ho10 with 300s (1) cores
% 1.12/0.45 % post_as_ho5 with pid 3477687 completed with status 0
% 1.12/0.45 % Result found by post_as_ho5
% 1.12/0.45 % Preprocessing class: HSSSSMSSSSMNHHA.
% 1.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.12/0.45 % Starting post_as_ho5 with 1500s (5) cores
% 1.12/0.45 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 1.12/0.45 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 1.12/0.45 % Search class: HGUNF-FFMF22-SHHFFMBN
% 1.12/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.12/0.45 % Starting SubtermCWHack with 136s (1) cores
% 1.12/0.45 % Starting post_as_ho5 with 151s (1) cores
% 1.12/0.45 % Starting sh2lt with 136s (1) cores
% 1.12/0.45 % Starting sh2l with 136s (1) cores
% 1.12/0.45 % Starting lpo1_def_fix with 136s (1) cores
% 1.12/0.45 % SubtermCWHack with pid 3477692 completed with status 10
% 1.12/0.45 % Starting ehoh_best3_rw with 136s (1) cores
% 1.12/0.45 % sh2l with pid 3477695 completed with status 0
% 1.12/0.45 % Result found by sh2l
% 1.12/0.45 % Preprocessing class: HSSSSMSSSSMNHHA.
% 1.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.12/0.45 % Starting post_as_ho5 with 1500s (5) cores
% 1.12/0.45 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 1.12/0.45 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 1.12/0.45 % Search class: HGUNF-FFMF22-SHHFFMBN
% 1.12/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.12/0.45 % Starting SubtermCWHack with 136s (1) cores
% 1.12/0.45 % Starting post_as_ho5 with 151s (1) cores
% 1.12/0.45 % Starting sh2lt with 136s (1) cores
% 1.12/0.45 % Starting sh2l with 136s (1) cores
% 1.12/0.45 % Preprocessing time : 0.001 s
% 1.12/0.45 % Presaturation interreduction done
% 1.12/0.45
% 1.12/0.45 % Proof found!
% 1.12/0.45 % SZS status Theorem
% 1.12/0.45 % SZS output start CNFRefutation
% See solution above
% 1.12/0.45 % Parsed axioms : 1
% 1.12/0.45 % Removed by relevancy pruning/SinE : 0
% 1.12/0.45 % Initial clauses : 8
% 1.12/0.45 % Removed in clause preprocessing : 0
% 1.12/0.45 % Initial clauses in saturation : 8
% 1.12/0.45 % Processed clauses : 484
% 1.12/0.45 % ...of these trivial : 8
% 1.12/0.45 % ...subsumed : 91
% 1.12/0.45 % ...remaining for further processing : 385
% 1.12/0.45 % Other redundant clauses eliminated : 130
% 1.12/0.45 % Clauses deleted for lack of memory : 0
% 1.12/0.45 % Backward-subsumed : 100
% 1.12/0.45 % Backward-rewritten : 159
% 1.12/0.45 % Generated clauses : 3193
% 1.12/0.45 % ...of the previous two non-redundant : 2564
% 1.12/0.45 % ...aggressively subsumed : 0
% 1.12/0.45 % Contextual simplify-reflections : 5
% 1.12/0.45 % Paramodulations : 2575
% 1.12/0.45 % Factorizations : 4
% 1.12/0.45 % NegExts : 79
% 1.12/0.45 % Equation resolutions : 130
% 1.12/0.45 % Disequality decompositions : 0
% 1.12/0.45 % Total rewrite steps : 332
% 1.12/0.45 % ...of those cached : 308
% 1.12/0.45 % Propositional unsat checks : 0
% 1.12/0.45 % Propositional check models : 0
% 1.12/0.45 % Propositional check unsatisfiable : 0
% 1.12/0.45 % Propositional clauses : 0
% 1.12/0.45 % Propositional clauses after purity: 0
% 1.12/0.45 % Propositional unsat core size : 0
% 1.12/0.45 % Propositional preprocessing time : 0.000
% 1.12/0.45 % Propositional encoding time : 0.000
% 1.12/0.45 % Propositional solver time : 0.000
% 1.12/0.45 % Success case prop preproc time : 0.000
% 1.12/0.45 % Success case prop encoding time : 0.000
% 1.12/0.45 % Success case prop solver time : 0.000
% 1.12/0.45 % Current number of processed clauses : 62
% 1.12/0.45 % Positive orientable unit clauses : 11
% 1.12/0.45 % Positive unorientable unit clauses: 7
% 1.12/0.45 % Negative unit clauses : 9
% 1.12/0.45 % Non-unit-clauses : 35
% 1.12/0.45 % Current number of unprocessed clauses: 1896
% 1.12/0.45 % ...number of literals in the above : 8089
% 1.12/0.45 % Current number of archived formulas : 0
% 1.12/0.45 % Current number of archived clauses : 323
% 1.12/0.45 % Clause-clause subsumption calls (NU) : 5038
% 1.12/0.45 % Rec. Clause-clause subsumption calls : 2745
% 1.12/0.45 % Non-unit clause-clause subsumptions : 131
% 1.12/0.45 % Unit Clause-clause subsumption calls : 1075
% 1.12/0.45 % Rewrite failures with RHS unbound : 0
% 1.12/0.45 % BW rewrite match attempts : 2681
% 1.12/0.45 % BW rewrite match successes : 625
% 1.12/0.45 % Condensation attempts : 0
% 1.12/0.45 % Condensation successes : 0
% 1.12/0.45 % Termbank termtop insertions : 685319
% 1.12/0.45 % Search garbage collected termcells : 255
% 1.12/0.45
% 1.12/0.45 % -------------------------------------------------
% 1.12/0.45 % User time : 0.183 s
% 1.12/0.45 % System time : 0.006 s
% 1.12/0.45 % Total time : 0.189 s
% 1.12/0.45 % Maximum resident set size: 3636 pages
% 1.12/0.45
% 1.12/0.45 % -------------------------------------------------
% 1.12/0.45 % User time : 0.873 s
% 1.12/0.45 % System time : 0.043 s
% 1.12/0.45 % Total time : 0.916 s
% 1.12/0.45 % Maximum resident set size: 4608 pages
% 1.12/0.45 % E exiting
%------------------------------------------------------------------------------