%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO269^5 : 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 : n012.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 08:42:40 AM UTC 2026
% Result : Theorem 43.02s 7.41s
% Output : CNFRefutation 43.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 59 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 730 ( 43 ~; 60 |; 22 &; 599 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 157 ( 157 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 1 con; 0-3 aty)
% Number of variables : 237 ( 164 ^; 67 !; 6 ?; 237 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
epred1_0: $i > $o ).
thf(decl_24,type,
esk1_2: ( ( $i > $i ) > $i > $o ) > ( ( $i > $i ) > $i > $o ) > $i ).
thf(decl_25,type,
esk2_2: ( ( $i > $i ) > $i > $o ) > ( ( $i > $i ) > $i > $o ) > $i > $i ).
thf(decl_26,type,
esk3_2: ( ( $i > $i ) > $i > $o ) > ( ( $i > $i ) > $i > $o ) > $i > $i ).
thf(decl_27,type,
esk4_2: ( ( $i > $i ) > $i > $o ) > ( ( $i > $i ) > $i > $o ) > $i ).
thf(decl_28,type,
esk5_2: ( ( $i > $i ) > $i > $o ) > ( ( $i > $i ) > $i > $o ) > $i ).
thf(decl_590,type,
esk563_1: ( ( $i > $i ) > $i > $o ) > $i ).
thf(cTHM112D,conjecture,
! [X1: $i > $o] :
? [X2: ( $i > $i ) > $i > $o,X3: ( $i > $i ) > $i > $o] :
( ! [X4: $i] :
( ( X2
@ ^ [X5: $i] : X5
@ X4 )
| ( X3
@ ^ [X5: $i] : X5
@ X4 ) )
& ! [X6: $i > $i,X7: $i > $i] :
( ( ! [X4: $i] :
( ( X2 @ X6 @ X4 )
| ( X3 @ X6 @ X4 ) )
& ! [X4: $i] :
( ( X2 @ X6 @ X4 )
| ( X3 @ X6 @ X4 ) )
& ! [X4: $i] :
( ( X2 @ X7 @ X4 )
| ( X3 @ X7 @ X4 ) ) )
=> ( ! [X4: $i] :
( ( X2
@ ^ [X5: $i] : ( X6 @ ( X7 @ X5 ) )
@ X4 )
| ( X3
@ ^ [X5: $i] : ( X6 @ ( X7 @ X5 ) )
@ X4 ) )
& ! [X8: $i] :
( ( X1 @ X8 )
=> ( X1 @ ( X6 @ X8 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.DaB3eTfUBT/E---3.1_349342.p',cTHM112D) ).
thf(c_0_1,negated_conjecture,
~ ! [X1: $i > $o] :
? [X2: ( $i > $i ) > $i > $o,X3: ( $i > $i ) > $i > $o] :
( ! [X4: $i] :
( ( X2
@ ^ [X5: $i] : X5
@ X4 )
| ( X3
@ ^ [X5: $i] : X5
@ X4 ) )
& ! [X6: $i > $i,X7: $i > $i] :
( ( ! [X4: $i] :
( ( X2 @ X6 @ X4 )
| ( X3 @ X6 @ X4 ) )
& ! [X4: $i] :
( ( X2 @ X6 @ X4 )
| ( X3 @ X6 @ X4 ) )
& ! [X4: $i] :
( ( X2 @ X7 @ X4 )
| ( X3 @ X7 @ X4 ) ) )
=> ( ! [X4: $i] :
( ( X2
@ ^ [X5: $i] : ( X6 @ ( X7 @ X5 ) )
@ X4 )
| ( X3
@ ^ [X5: $i] : ( X6 @ ( X7 @ X5 ) )
@ X4 ) )
& ! [X8: $i] :
( ( X1 @ X8 )
=> ( X1 @ ( X6 @ X8 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM112D]) ).
thf(c_0_2,negated_conjecture,
~ ! [X1: $i > $o] :
? [X2: ( $i > $i ) > $i > $o,X3: ( $i > $i ) > $i > $o] :
( ! [X4: $i] :
( ( X2
@ ^ [Z0: $i] : Z0
@ X4 )
| ( X3
@ ^ [Z0: $i] : Z0
@ X4 ) )
& ! [X6: $i > $i,X7: $i > $i] :
( ( ! [X4: $i] :
( ( X2 @ X6 @ X4 )
| ( X3 @ X6 @ X4 ) )
& ! [X4: $i] :
( ( X2 @ X7 @ X4 )
| ( X3 @ X7 @ X4 ) ) )
=> ( ! [X4: $i] :
( ( X2
@ ^ [Z0: $i] : ( X6 @ ( X7 @ Z0 ) )
@ X4 )
| ( X3
@ ^ [Z0: $i] : ( X6 @ ( X7 @ Z0 ) )
@ X4 ) )
& ! [X8: $i] :
( ( X1 @ X8 )
=> ( X1 @ ( X6 @ X8 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_1])]) ).
thf(c_0_3,negated_conjecture,
! [X21: ( $i > $i ) > $i > $o,X22: ( $i > $i ) > $i > $o,X26: $i,X27: $i] :
( ( ( X21 @ ( esk2_2 @ X21 @ X22 ) @ X26 )
| ( X22 @ ( esk2_2 @ X21 @ X22 ) @ X26 )
| ~ ( X21
@ ^ [Z0: $i] : Z0
@ ( esk1_2 @ X21 @ X22 ) ) )
& ( ( X21 @ ( esk3_2 @ X21 @ X22 ) @ X27 )
| ( X22 @ ( esk3_2 @ X21 @ X22 ) @ X27 )
| ~ ( X21
@ ^ [Z0: $i] : Z0
@ ( esk1_2 @ X21 @ X22 ) ) )
& ( ( epred1_0 @ ( esk5_2 @ X21 @ X22 ) )
| ~ ( X21
@ ^ [Z0: $i] : ( esk2_2 @ X21 @ X22 @ ( esk3_2 @ X21 @ X22 @ Z0 ) )
@ ( esk4_2 @ X21 @ X22 ) )
| ~ ( X21
@ ^ [Z0: $i] : Z0
@ ( esk1_2 @ X21 @ X22 ) ) )
& ( ~ ( epred1_0 @ ( esk2_2 @ X21 @ X22 @ ( esk5_2 @ X21 @ X22 ) ) )
| ~ ( X21
@ ^ [Z0: $i] : ( esk2_2 @ X21 @ X22 @ ( esk3_2 @ X21 @ X22 @ Z0 ) )
@ ( esk4_2 @ X21 @ X22 ) )
| ~ ( X21
@ ^ [Z0: $i] : Z0
@ ( esk1_2 @ X21 @ X22 ) ) )
& ( ( epred1_0 @ ( esk5_2 @ X21 @ X22 ) )
| ~ ( X22
@ ^ [Z0: $i] : ( esk2_2 @ X21 @ X22 @ ( esk3_2 @ X21 @ X22 @ Z0 ) )
@ ( esk4_2 @ X21 @ X22 ) )
| ~ ( X21
@ ^ [Z0: $i] : Z0
@ ( esk1_2 @ X21 @ X22 ) ) )
& ( ~ ( epred1_0 @ ( esk2_2 @ X21 @ X22 @ ( esk5_2 @ X21 @ X22 ) ) )
| ~ ( X22
@ ^ [Z0: $i] : ( esk2_2 @ X21 @ X22 @ ( esk3_2 @ X21 @ X22 @ Z0 ) )
@ ( esk4_2 @ X21 @ X22 ) )
| ~ ( X21
@ ^ [Z0: $i] : Z0
@ ( esk1_2 @ X21 @ X22 ) ) )
& ( ( X21 @ ( esk2_2 @ X21 @ X22 ) @ X26 )
| ( X22 @ ( esk2_2 @ X21 @ X22 ) @ X26 )
| ~ ( X22
@ ^ [Z0: $i] : Z0
@ ( esk1_2 @ X21 @ X22 ) ) )
& ( ( X21 @ ( esk3_2 @ X21 @ X22 ) @ X27 )
| ( X22 @ ( esk3_2 @ X21 @ X22 ) @ X27 )
| ~ ( X22
@ ^ [Z0: $i] : Z0
@ ( esk1_2 @ X21 @ X22 ) ) )
& ( ( epred1_0 @ ( esk5_2 @ X21 @ X22 ) )
| ~ ( X21
@ ^ [Z0: $i] : ( esk2_2 @ X21 @ X22 @ ( esk3_2 @ X21 @ X22 @ Z0 ) )
@ ( esk4_2 @ X21 @ X22 ) )
| ~ ( X22
@ ^ [Z0: $i] : Z0
@ ( esk1_2 @ X21 @ X22 ) ) )
& ( ~ ( epred1_0 @ ( esk2_2 @ X21 @ X22 @ ( esk5_2 @ X21 @ X22 ) ) )
| ~ ( X21
@ ^ [Z0: $i] : ( esk2_2 @ X21 @ X22 @ ( esk3_2 @ X21 @ X22 @ Z0 ) )
@ ( esk4_2 @ X21 @ X22 ) )
| ~ ( X22
@ ^ [Z0: $i] : Z0
@ ( esk1_2 @ X21 @ X22 ) ) )
& ( ( epred1_0 @ ( esk5_2 @ X21 @ X22 ) )
| ~ ( X22
@ ^ [Z0: $i] : ( esk2_2 @ X21 @ X22 @ ( esk3_2 @ X21 @ X22 @ Z0 ) )
@ ( esk4_2 @ X21 @ X22 ) )
| ~ ( X22
@ ^ [Z0: $i] : Z0
@ ( esk1_2 @ X21 @ X22 ) ) )
& ( ~ ( epred1_0 @ ( esk2_2 @ X21 @ X22 @ ( esk5_2 @ X21 @ X22 ) ) )
| ~ ( X22
@ ^ [Z0: $i] : ( esk2_2 @ X21 @ X22 @ ( esk3_2 @ X21 @ X22 @ Z0 ) )
@ ( esk4_2 @ X21 @ X22 ) )
| ~ ( X22
@ ^ [Z0: $i] : Z0
@ ( esk1_2 @ X21 @ 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,
! [X2: ( $i > $i ) > $i > $o,X4: $i,X3: ( $i > $i ) > $i > $o] :
( ( X2 @ ( esk2_2 @ X2 @ X3 ) @ X4 )
| ( X3 @ ( esk2_2 @ X2 @ X3 ) @ X4 )
| ~ ( X3
@ ^ [Z0: $i] : Z0
@ ( esk1_2 @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X2: ( $i > $i ) > $i > $o,X3: ( $i > $i ) > $i > $o] :
( ~ ( epred1_0 @ ( esk2_2 @ X2 @ X3 @ ( esk5_2 @ X2 @ X3 ) ) )
| ~ ( X3
@ ^ [Z0: $i] : ( esk2_2 @ X2 @ X3 @ ( esk3_2 @ X2 @ X3 @ Z0 ) )
@ ( esk4_2 @ X2 @ X3 ) )
| ~ ( X3
@ ^ [Z0: $i] : Z0
@ ( esk1_2 @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_6,negated_conjecture,
! [X2: ( $i > $i ) > $i > $o,X4: $i] :
( ( ( esk2_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( Z0
= ( ^ [Z2: $i] : Z2 ) ) )
= ( ^ [Z0: $i] : Z0 ) )
| ( X2
@ ( esk2_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( Z0
= ( ^ [Z2: $i] : Z2 ) ) )
@ X4 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_4]) ).
thf(c_0_7,negated_conjecture,
! [X2: ( $i > $i ) > $i > $o,X3: ( $i > $i ) > $i > $o] :
( ( epred1_0 @ ( esk5_2 @ X2 @ X3 ) )
| ~ ( X3
@ ^ [Z0: $i] : ( esk2_2 @ X2 @ X3 @ ( esk3_2 @ X2 @ X3 @ Z0 ) )
@ ( esk4_2 @ X2 @ X3 ) )
| ~ ( X3
@ ^ [Z0: $i] : Z0
@ ( esk1_2 @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_8,negated_conjecture,
! [X2: ( $i > $i ) > $i > $o,X37: ( $i > $i ) > $i > $i > $i,X38: ( $i > $i ) > $i > $i > $i] :
( ( ( X37
@ ^ [Z0: $i] :
( esk2_2 @ X2
@ ^ [Z1: $i > $i,Z2: $i] :
( ( X37 @ Z1 @ Z2 )
= ( X38 @ Z1 @ Z2 ) )
@ ( esk3_2 @ X2
@ ^ [Z1: $i > $i,Z2: $i] :
( ( X37 @ Z1 @ Z2 )
= ( X38 @ Z1 @ Z2 ) )
@ Z0 ) )
@ ( esk4_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( ( X37 @ Z0 @ Z1 )
= ( X38 @ Z0 @ Z1 ) ) ) )
!= ( X38
@ ^ [Z0: $i] :
( esk2_2 @ X2
@ ^ [Z1: $i > $i,Z2: $i] :
( ( X37 @ Z1 @ Z2 )
= ( X38 @ Z1 @ Z2 ) )
@ ( esk3_2 @ X2
@ ^ [Z1: $i > $i,Z2: $i] :
( ( X37 @ Z1 @ Z2 )
= ( X38 @ Z1 @ Z2 ) )
@ Z0 ) )
@ ( esk4_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( ( X37 @ Z0 @ Z1 )
= ( X38 @ Z0 @ Z1 ) ) ) ) )
| ( ( X37
@ ^ [Z0: $i] : Z0
@ ( esk1_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( ( X37 @ Z0 @ Z1 )
= ( X38 @ Z0 @ Z1 ) ) ) )
!= ( X38
@ ^ [Z0: $i] : Z0
@ ( esk1_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( ( X37 @ Z0 @ Z1 )
= ( X38 @ Z0 @ Z1 ) ) ) ) )
| ~ ( epred1_0
@ ( esk2_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( ( X37 @ Z0 @ Z1 )
= ( X38 @ Z0 @ Z1 ) )
@ ( esk5_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( ( X37 @ Z0 @ Z1 )
= ( X38 @ Z0 @ Z1 ) ) ) ) ) ),
inference(primitive_enumeration,[status(thm)],[inference(cn,[status(thm)],[]),c_0_5]) ).
thf(c_0_9,negated_conjecture,
! [X2: ( $i > $i ) > $i > $o,X4: $i,X5: $i] :
( ( ( esk2_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( Z0
= ( ^ [Z2: $i] : Z2 ) )
@ X4 )
= X4 )
| ( X2
@ ( esk2_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( Z0
= ( ^ [Z2: $i] : Z2 ) ) )
@ X5 ) ),
inference(arg_cong,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
! [X2: ( $i > $i ) > $i > $o,X37: ( $i > $i ) > $i > $i > $i,X38: ( $i > $i ) > $i > $i > $i] :
( ( epred1_0
@ ( esk5_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( ( X37 @ Z0 @ Z1 )
= ( X38 @ Z0 @ Z1 ) ) ) )
| ( ( X37
@ ^ [Z0: $i] :
( esk2_2 @ X2
@ ^ [Z1: $i > $i,Z2: $i] :
( ( X37 @ Z1 @ Z2 )
= ( X38 @ Z1 @ Z2 ) )
@ ( esk3_2 @ X2
@ ^ [Z1: $i > $i,Z2: $i] :
( ( X37 @ Z1 @ Z2 )
= ( X38 @ Z1 @ Z2 ) )
@ Z0 ) )
@ ( esk4_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( ( X37 @ Z0 @ Z1 )
= ( X38 @ Z0 @ Z1 ) ) ) )
!= ( X38
@ ^ [Z0: $i] :
( esk2_2 @ X2
@ ^ [Z1: $i > $i,Z2: $i] :
( ( X37 @ Z1 @ Z2 )
= ( X38 @ Z1 @ Z2 ) )
@ ( esk3_2 @ X2
@ ^ [Z1: $i > $i,Z2: $i] :
( ( X37 @ Z1 @ Z2 )
= ( X38 @ Z1 @ Z2 ) )
@ Z0 ) )
@ ( esk4_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( ( X37 @ Z0 @ Z1 )
= ( X38 @ Z0 @ Z1 ) ) ) ) )
| ( ( X37
@ ^ [Z0: $i] : Z0
@ ( esk1_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( ( X37 @ Z0 @ Z1 )
= ( X38 @ Z0 @ Z1 ) ) ) )
!= ( X38
@ ^ [Z0: $i] : Z0
@ ( esk1_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( ( X37 @ Z0 @ Z1 )
= ( X38 @ Z0 @ Z1 ) ) ) ) ) ),
inference(primitive_enumeration,[status(thm)],[inference(cn,[status(thm)],[]),c_0_7]) ).
thf(c_0_11,plain,
! [X4: $i,X2: ( $i > $i ) > $i > $o,X37: ( $i > $i ) > $i > $i > $i,X38: ( $i > $i ) > $i > $i > $i] :
( ( X2
@ ( esk2_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( Z0
= ( ^ [Z2: $i] : Z2 ) ) )
@ X4 )
| ( ( X37
@ ^ [Z0: $i] :
( esk2_2 @ X2
@ ^ [Z1: $i > $i,Z2: $i] :
( ( X37 @ Z1 @ Z2 )
= ( X38 @ Z1 @ Z2 ) )
@ ( esk3_2 @ X2
@ ^ [Z1: $i > $i,Z2: $i] :
( ( X37 @ Z1 @ Z2 )
= ( X38 @ Z1 @ Z2 ) )
@ Z0 ) )
@ ( esk4_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( ( X37 @ Z0 @ Z1 )
= ( X38 @ Z0 @ Z1 ) ) ) )
!= ( X38
@ ^ [Z0: $i] :
( esk2_2 @ X2
@ ^ [Z1: $i > $i,Z2: $i] :
( ( X37 @ Z1 @ Z2 )
= ( X38 @ Z1 @ Z2 ) )
@ ( esk3_2 @ X2
@ ^ [Z1: $i > $i,Z2: $i] :
( ( X37 @ Z1 @ Z2 )
= ( X38 @ Z1 @ Z2 ) )
@ Z0 ) )
@ ( esk4_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( ( X37 @ Z0 @ Z1 )
= ( X38 @ Z0 @ Z1 ) ) ) ) )
| ( ( X37
@ ^ [Z0: $i] : Z0
@ ( esk1_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( ( X37 @ Z0 @ Z1 )
= ( X38 @ Z0 @ Z1 ) ) ) )
!= ( X38
@ ^ [Z0: $i] : Z0
@ ( esk1_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( ( X37 @ Z0 @ Z1 )
= ( X38 @ Z0 @ Z1 ) ) ) ) )
| ( ( ^ [Z0: $i > $i,Z1: $i] :
( ( X37 @ Z0 @ Z1 )
= ( X38 @ Z0 @ Z1 ) ) )
!= ( ^ [Z0: $i > $i,Z1: $i] :
( Z0
= ( ^ [Z2: $i] : Z2 ) ) ) ) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_8,c_0_9])])]),c_0_10]) ).
thf(c_0_12,negated_conjecture,
! [X2: ( $i > $i ) > $i > $o,X4: $i,X3: ( $i > $i ) > $i > $o] :
( ( X2 @ ( esk3_2 @ X2 @ X3 ) @ X4 )
| ( X3 @ ( esk3_2 @ X2 @ X3 ) @ X4 )
| ~ ( X3
@ ^ [Z0: $i] : Z0
@ ( esk1_2 @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_13,plain,
! [X4: $i,X2: ( $i > $i ) > $i > $o] :
( ( X2
@ ( esk2_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( Z0
= ( ^ [Z2: $i] : Z2 ) ) )
@ X4 )
| ( ( ^ [Z0: $i] :
( esk2_2 @ X2
@ ^ [Z1: $i > $i,Z2: $i] :
( Z1
= ( ^ [Z3: $i] : Z3 ) )
@ ( esk3_2 @ X2
@ ^ [Z1: $i > $i,Z2: $i] :
( Z1
= ( ^ [Z3: $i] : Z3 ) )
@ Z0 ) ) )
!= ( ^ [Z0: $i] : Z0 ) ) ),
inference(er,[status(thm)],[c_0_11]) ).
thf(c_0_14,negated_conjecture,
! [X2: ( $i > $i ) > $i > $o,X4: $i] :
( ( ( esk3_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( Z0
= ( ^ [Z2: $i] : Z2 ) ) )
= ( ^ [Z0: $i] : Z0 ) )
| ( X2
@ ( esk3_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( Z0
= ( ^ [Z2: $i] : Z2 ) ) )
@ X4 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_12]) ).
thf(c_0_15,plain,
! [X4: $i,X2: ( $i > $i ) > $i > $o] :
( ( X2
@ ( esk2_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( Z0
= ( ^ [Z2: $i] : Z2 ) ) )
@ X4 )
| ( ( esk2_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( Z0
= ( ^ [Z2: $i] : Z2 ) )
@ ( esk3_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( Z0
= ( ^ [Z2: $i] : Z2 ) )
@ ( esk563_1 @ X2 ) ) )
!= ( esk563_1 @ X2 ) ) ),
inference(neg_ext,[status(thm)],[c_0_13]) ).
thf(c_0_16,negated_conjecture,
! [X2: ( $i > $i ) > $i > $o,X4: $i,X5: $i] :
( ( ( esk3_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( Z0
= ( ^ [Z2: $i] : Z2 ) )
@ X4 )
= X4 )
| ( X2
@ ( esk3_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( Z0
= ( ^ [Z2: $i] : Z2 ) ) )
@ X5 ) ),
inference(arg_cong,[status(thm)],[c_0_14]) ).
thf(c_0_17,negated_conjecture,
! [X2: ( $i > $i ) > $i > $o,X4: $i,X5: $i] :
( ( X2
@ ( esk3_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( Z0
= ( ^ [Z2: $i] : Z2 ) ) )
@ X4 )
| ( X2
@ ( esk2_2 @ X2
@ ^ [Z0: $i > $i,Z1: $i] :
( Z0
= ( ^ [Z2: $i] : Z2 ) ) )
@ X5 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_9]) ).
thf(c_0_18,negated_conjecture,
$false,
inference(flex_resolve,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_6])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYO269^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.12 % Computer : n012.cluster.edu
% 0.00/0.12 % Model : x86_64 x86_64
% 0.00/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.12 % Memory : 8046.5625MB
% 0.00/0.12 % OS : Linux 6.8.0-71-generic
% 0.00/0.12 % CPULimit : 300
% 0.00/0.12 % WCLimit : 300
% 0.00/0.12 % DateTime : Tue Sep 29 16:41:48 UTC 2026
% 0.00/0.12 % CPUTime :
% 0.00/0.12 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.16 Running higher-order theorem proving
% 0.11/0.17 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.DaB3eTfUBT/E---3.1_349342.p
% 43.02/7.41 % Version: 3.5.1-ho
% 43.02/7.41 % Preprocessing class: HSSSSMSSSSMNHHA.
% 43.02/7.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 43.02/7.41 % Starting post_as_ho5 with 1500s (5) cores
% 43.02/7.41 % Starting sh2lt with 300s (1) cores
% 43.02/7.41 % Starting ehoh_best8_lambda with 300s (1) cores
% 43.02/7.41 % Starting post_as_ho10 with 300s (1) cores
% 43.02/7.41 % ehoh_best8_lambda with pid 349357 completed with status 0
% 43.02/7.41 % Result found by ehoh_best8_lambda
% 43.02/7.41 % Preprocessing class: HSSSSMSSSSMNHHA.
% 43.02/7.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 43.02/7.41 % Starting post_as_ho5 with 1500s (5) cores
% 43.02/7.41 % Starting sh2lt with 300s (1) cores
% 43.02/7.41 % Starting ehoh_best8_lambda with 300s (1) cores
% 43.02/7.41 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = Auto)
% 43.02/7.41 % No SInE strategy applied
% 43.02/7.41 % Search class: HGHNF-FFMF22-MHHFFMBN
% 43.02/7.41 % partial match(1): HGHNF-FFMF22-SHHFFMBN
% 43.02/7.41 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 43.02/7.41 % Starting SubtermCWHack with 28s (1) cores
% 43.02/7.41 % SubtermCWHack with pid 349360 completed with status 10
% 43.02/7.41 % Starting ehoh_best8_lambda with 31s (1) cores
% 43.02/7.41 % ehoh_best8_lambda with pid 349368 completed with status 0
% 43.02/7.41 % Result found by ehoh_best8_lambda
% 43.02/7.41 % Preprocessing class: HSSSSMSSSSMNHHA.
% 43.02/7.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 43.02/7.41 % Starting post_as_ho5 with 1500s (5) cores
% 43.02/7.41 % Starting sh2lt with 300s (1) cores
% 43.02/7.41 % Starting ehoh_best8_lambda with 300s (1) cores
% 43.02/7.41 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = Auto)
% 43.02/7.41 % No SInE strategy applied
% 43.02/7.41 % Search class: HGHNF-FFMF22-MHHFFMBN
% 43.02/7.41 % partial match(1): HGHNF-FFMF22-SHHFFMBN
% 43.02/7.41 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 43.02/7.41 % Starting SubtermCWHack with 28s (1) cores
% 43.02/7.41 % SubtermCWHack with pid 349360 completed with status 10
% 43.02/7.41 % Starting ehoh_best8_lambda with 31s (1) cores
% 43.02/7.41 % Preprocessing time : 0.001 s
% 43.02/7.41 % Presaturation interreduction done
% 43.02/7.41
% 43.02/7.41 % Proof found!
% 43.02/7.41 % SZS status Theorem
% 43.02/7.41 % SZS output start CNFRefutation
% See solution above
% 43.02/7.41 % Parsed axioms : 1
% 43.02/7.41 % Removed by relevancy pruning/SinE : 0
% 43.02/7.41 % Initial clauses : 12
% 43.02/7.41 % Removed in clause preprocessing : 0
% 43.02/7.41 % Initial clauses in saturation : 12
% 43.02/7.41 % Processed clauses : 8757
% 43.02/7.41 % ...of these trivial : 14
% 43.02/7.41 % ...subsumed : 7238
% 43.02/7.41 % ...remaining for further processing : 1504
% 43.02/7.41 % Other redundant clauses eliminated : 12944
% 43.02/7.41 % Clauses deleted for lack of memory : 0
% 43.02/7.41 % Backward-subsumed : 14
% 43.02/7.41 % Backward-rewritten : 0
% 43.02/7.41 % Generated clauses : 70217
% 43.02/7.41 % ...of the previous two non-redundant : 56746
% 43.02/7.41 % ...aggressively subsumed : 0
% 43.02/7.41 % Contextual simplify-reflections : 5
% 43.02/7.41 % Paramodulations : 55800
% 43.02/7.41 % Factorizations : 30
% 43.02/7.41 % NegExts : 562
% 43.02/7.41 % Equation resolutions : 13028
% 43.02/7.41 % Disequality decompositions : 0
% 43.02/7.41 % Total rewrite steps : 70
% 43.02/7.41 % ...of those cached : 66
% 43.02/7.41 % Propositional unsat checks : 0
% 43.02/7.41 % Propositional check models : 0
% 43.02/7.41 % Propositional check unsatisfiable : 0
% 43.02/7.41 % Propositional clauses : 0
% 43.02/7.41 % Propositional clauses after purity: 0
% 43.02/7.41 % Propositional unsat core size : 0
% 43.02/7.41 % Propositional preprocessing time : 0.000
% 43.02/7.41 % Propositional encoding time : 0.000
% 43.02/7.41 % Propositional solver time : 0.000
% 43.02/7.41 % Success case prop preproc time : 0.000
% 43.02/7.41 % Success case prop encoding time : 0.000
% 43.02/7.41 % Success case prop solver time : 0.000
% 43.02/7.41 % Current number of processed clauses : 1386
% 43.02/7.41 % Positive orientable unit clauses : 2
% 43.02/7.41 % Positive unorientable unit clauses: 0
% 43.02/7.41 % Negative unit clauses : 6
% 43.02/7.41 % Non-unit-clauses : 1378
% 43.02/7.41 % Current number of unprocessed clauses: 48011
% 43.02/7.41 % ...number of literals in the above : 261548
% 43.02/7.41 % Current number of archived formulas : 0
% 43.02/7.41 % Current number of archived clauses : 118
% 43.02/7.41 % Clause-clause subsumption calls (NU) : 393955
% 43.02/7.41 % Rec. Clause-clause subsumption calls : 122341
% 43.02/7.41 % Non-unit clause-clause subsumptions : 6921
% 43.02/7.41 % Unit Clause-clause subsumption calls : 57
% 43.02/7.41 % Rewrite failures with RHS unbound : 0
% 43.02/7.41 % BW rewrite match attempts : 0
% 43.02/7.41 % BW rewrite match successes : 0
% 43.02/7.41 % Condensation attempts : 0
% 43.02/7.41 % Condensation successes : 0
% 43.02/7.41 % Termbank termtop insertions : 57065911
% 43.02/7.41 % Search garbage collected termcells : 320
% 43.02/7.41
% 43.02/7.41 % -------------------------------------------------
% 43.02/7.41 % User time : 7.070 s
% 43.02/7.41 % System time : 0.035 s
% 43.02/7.41 % Total time : 7.105 s
% 43.02/7.41 % Maximum resident set size: 3640 pages
% 43.02/7.41
% 43.02/7.41 % -------------------------------------------------
% 43.02/7.41 % User time : 7.072 s
% 43.02/7.41 % System time : 0.038 s
% 43.02/7.41 % Total time : 7.110 s
% 43.02/7.41 % Maximum resident set size: 4864 pages
% 43.02/7.41 % E exiting
%------------------------------------------------------------------------------