%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV300^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:35:21 AM UTC 2026
% Result : Theorem 0.26s 0.37s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 4
% Syntax : Number of formulae : 60 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 219 ( 111 equ; 0 cnn)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 445 ( 67 ~; 128 |; 18 &; 224 @)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 97 ( 16 ^; 68 !; 13 ?; 97 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
cONE: ( $i > $o ) > $o ).
thf(decl_24,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(decl_25,type,
cZERO: ( $i > $o ) > $o ).
thf(decl_26,type,
esk1_2: ( $i > $i ) > ( $i > $i ) > $i ).
thf(decl_27,type,
epred1_0: $i > $o ).
thf(decl_28,type,
esk2_1: $i > $i ).
thf(decl_29,type,
esk3_1: $i > $i ).
thf(decl_30,type,
esk4_0: $i ).
thf(decl_31,type,
esk5_0: $i ).
thf(cZERO_def,axiom,
( cZERO
= ( ^ [X1: $i > $o] :
~ ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qxZbZUeVZU/E---3.1_2256587.p',cZERO_def) ).
thf(cSUCC_def,axiom,
( cSUCC
= ( ^ [X3: ( $i > $o ) > $o,X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ( X3
@ ^ [X4: $i] :
( ( X4 != X2 )
& ( X1 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qxZbZUeVZU/E---3.1_2256587.p',cSUCC_def) ).
thf(cX6101_EXT_pme,conjecture,
( ! [X5: $i > $i,X6: $i > $i] :
( ! [X2: $i] :
( ( X5 @ X2 )
= ( X6 @ X2 ) )
=> ( X5 = X6 ) )
=> ( cONE
= ( ^ [X7: $i > $o] :
? [X8: $i] :
( X7
= ( ^ [X2: $i,X8: $i] : ( X2 = X8 )
@ X8 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qxZbZUeVZU/E---3.1_2256587.p',cX6101_EXT_pme) ).
thf(cONE_def,axiom,
( cONE
= ( ^ [Z0: $i > $o] :
? [X13: $i] :
( ( Z0 @ X13 )
& ~ ? [X12: $i] :
( ( X12 != X13 )
& ( Z0 @ X12 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qxZbZUeVZU/E---3.1_2256587.p',cONE_def) ).
thf(c_0_4,plain,
( cZERO
= ( ^ [Z0: $i > $o] :
~ ? [X2: $i] : ( Z0 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[cZERO_def]) ).
thf(c_0_5,plain,
( cSUCC
= ( ^ [Z0: ( $i > $o ) > $o,Z1: $i > $o] :
? [X2: $i] :
( ( Z1 @ X2 )
& ( Z0
@ ^ [Z2: $i] :
( ( Z2 != X2 )
& ( Z1 @ Z2 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cSUCC_def]) ).
thf(c_0_6,negated_conjecture,
~ ( ! [X5: $i > $i,X6: $i > $i] :
( ! [X2: $i] :
( ( X5 @ X2 )
= ( X6 @ X2 ) )
=> ( X5 = X6 ) )
=> ( cONE
= ( ^ [X7: $i > $o] :
? [X8: $i] :
( X7
= ( ^ [X2: $i,X8: $i] : ( X2 = X8 )
@ X8 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cX6101_EXT_pme]) ).
thf(c_0_7,axiom,
( cONE
= ( ^ [Z0: $i > $o] :
? [X13: $i] :
( ( Z0 @ X13 )
& ~ ? [X12: $i] :
( ( X12 != X13 )
& ( Z0 @ X12 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[cONE_def,c_0_4]),c_0_5]) ).
thf(c_0_8,negated_conjecture,
~ ( ! [X5: $i > $i,X6: $i > $i] :
( ! [X2: $i] :
( ( X5 @ X2 )
= ( X6 @ X2 ) )
=> ( X5 = X6 ) )
=> ! [X16: $i > $o] :
( ? [X14: $i] :
( ( X16 @ X14 )
& ~ ? [X15: $i] :
( ( X15 != X14 )
& ( X16 @ X15 ) ) )
<=> ? [X8: $i] :
! [X17: $i] :
( ( X16 @ X17 )
<=> ( X8 = X17 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_6]),c_0_7])])]) ).
thf(c_0_9,negated_conjecture,
! [X18: $i > $i,X19: $i > $i,X22: $i,X24: $i,X27: $i,X29: $i] :
( ( ( ( X18 @ ( esk1_2 @ X18 @ X19 ) )
!= ( X19 @ ( esk1_2 @ X18 @ X19 ) ) )
| ( X18 = X19 ) )
& ( ~ ( epred1_0 @ ( esk3_1 @ X24 ) )
| ( X24
!= ( esk3_1 @ X24 ) )
| ( ( esk2_1 @ X22 )
!= X22 )
| ~ ( epred1_0 @ X22 ) )
& ( ( epred1_0 @ ( esk3_1 @ X24 ) )
| ( X24
= ( esk3_1 @ X24 ) )
| ( ( esk2_1 @ X22 )
!= X22 )
| ~ ( epred1_0 @ X22 ) )
& ( ~ ( epred1_0 @ ( esk3_1 @ X24 ) )
| ( X24
!= ( esk3_1 @ X24 ) )
| ( epred1_0 @ ( esk2_1 @ X22 ) )
| ~ ( epred1_0 @ X22 ) )
& ( ( epred1_0 @ ( esk3_1 @ X24 ) )
| ( X24
= ( esk3_1 @ X24 ) )
| ( epred1_0 @ ( esk2_1 @ X22 ) )
| ~ ( epred1_0 @ X22 ) )
& ( ~ ( epred1_0 @ X29 )
| ( esk5_0 = X29 )
| ( epred1_0 @ esk4_0 ) )
& ( ( esk5_0 != X29 )
| ( epred1_0 @ X29 )
| ( epred1_0 @ esk4_0 ) )
& ( ~ ( epred1_0 @ X29 )
| ( esk5_0 = X29 )
| ( X27 = esk4_0 )
| ~ ( epred1_0 @ X27 ) )
& ( ( esk5_0 != X29 )
| ( epred1_0 @ X29 )
| ( X27 = esk4_0 )
| ~ ( epred1_0 @ X27 ) ) ),
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_8])])])])])]) ).
thf(c_0_10,negated_conjecture,
! [X2: $i] :
( ( epred1_0 @ X2 )
| ( epred1_0 @ esk4_0 )
| ( esk5_0 != X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X2: $i,X4: $i] :
( ( epred1_0 @ X2 )
| ( X4 = esk4_0 )
| ( esk5_0 != X2 )
| ~ ( epred1_0 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
! [X2: $i,X4: $i] :
( ( epred1_0 @ ( esk3_1 @ X2 ) )
| ( X2
= ( esk3_1 @ X2 ) )
| ( epred1_0 @ ( esk2_1 @ X4 ) )
| ~ ( epred1_0 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,negated_conjecture,
( ( epred1_0 @ esk5_0 )
| ( epred1_0 @ esk4_0 ) ),
inference(er,[status(thm)],[c_0_10]) ).
thf(c_0_14,negated_conjecture,
! [X2: $i] :
( ( X2 = esk4_0 )
| ( epred1_0 @ esk5_0 )
| ~ ( epred1_0 @ X2 ) ),
inference(er,[status(thm)],[c_0_11]) ).
thf(c_0_15,negated_conjecture,
! [X2: $i] :
( ( ( esk3_1 @ X2 )
= X2 )
| ( epred1_0 @ ( esk2_1 @ esk4_0 ) )
| ( epred1_0 @ ( esk3_1 @ X2 ) )
| ( epred1_0 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_16,negated_conjecture,
! [X2: $i] :
( ( ( esk3_1 @ X2 )
= esk4_0 )
| ( ( esk3_1 @ X2 )
= X2 )
| ( epred1_0 @ ( esk2_1 @ esk4_0 ) )
| ( epred1_0 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_17,negated_conjecture,
( ( ( esk3_1 @ esk4_0 )
= esk4_0 )
| ( epred1_0 @ ( esk2_1 @ esk4_0 ) )
| ( epred1_0 @ esk5_0 ) ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_16])]) ).
thf(c_0_18,negated_conjecture,
! [X2: $i,X4: $i] :
( ( epred1_0 @ ( esk3_1 @ X2 ) )
| ( X2
= ( esk3_1 @ X2 ) )
| ( ( esk2_1 @ X4 )
!= X4 )
| ~ ( epred1_0 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_19,negated_conjecture,
( ( ( esk3_1 @ esk4_0 )
= esk4_0 )
| ( ( esk2_1 @ esk4_0 )
= esk4_0 )
| ( epred1_0 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
thf(c_0_20,negated_conjecture,
! [X2: $i] :
( ( ( esk3_1 @ esk4_0 )
= esk4_0 )
| ( ( esk3_1 @ X2 )
= X2 )
| ( epred1_0 @ ( esk3_1 @ X2 ) )
| ( epred1_0 @ esk5_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_13]) ).
thf(c_0_21,negated_conjecture,
! [X2: $i] :
( ( ( esk3_1 @ esk4_0 )
= esk4_0 )
| ( ( esk3_1 @ X2 )
= esk4_0 )
| ( ( esk3_1 @ X2 )
= X2 )
| ( epred1_0 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_20]) ).
thf(c_0_22,negated_conjecture,
! [X2: $i,X4: $i] :
( ( epred1_0 @ ( esk2_1 @ X4 ) )
| ~ ( epred1_0 @ ( esk3_1 @ X2 ) )
| ( X2
!= ( esk3_1 @ X2 ) )
| ~ ( epred1_0 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_23,negated_conjecture,
( ( ( esk3_1 @ esk4_0 )
= esk4_0 )
| ( epred1_0 @ esk5_0 ) ),
inference(ef,[status(thm)],[c_0_21]) ).
thf(c_0_24,negated_conjecture,
! [X2: $i,X4: $i] :
( ~ ( epred1_0 @ ( esk3_1 @ X2 ) )
| ( X2
!= ( esk3_1 @ X2 ) )
| ( ( esk2_1 @ X4 )
!= X4 )
| ~ ( epred1_0 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_25,negated_conjecture,
! [X2: $i] :
( ( epred1_0 @ ( esk2_1 @ X2 ) )
| ( epred1_0 @ esk5_0 )
| ~ ( epred1_0 @ X2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_13]) ).
thf(c_0_26,negated_conjecture,
! [X2: $i] :
( ( epred1_0 @ esk5_0 )
| ( ( esk2_1 @ X2 )
!= X2 )
| ~ ( epred1_0 @ X2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_23]),c_0_13]) ).
thf(c_0_27,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ X2 )
= esk4_0 )
| ( epred1_0 @ esk5_0 )
| ~ ( epred1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_25]) ).
thf(c_0_28,negated_conjecture,
epred1_0 @ esk5_0,
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27])]),c_0_13]) ).
thf(c_0_29,negated_conjecture,
! [X2: $i] :
( ( esk5_0 = X2 )
| ( epred1_0 @ esk4_0 )
| ~ ( epred1_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_30,negated_conjecture,
! [X2: $i] :
( ( ( esk3_1 @ X2 )
= X2 )
| ( epred1_0 @ ( esk2_1 @ esk5_0 ) )
| ( epred1_0 @ ( esk3_1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_12,c_0_28]) ).
thf(c_0_31,negated_conjecture,
! [X2: $i] :
( ( ( esk3_1 @ X2 )
= esk5_0 )
| ( ( esk3_1 @ X2 )
= X2 )
| ( epred1_0 @ ( esk2_1 @ esk5_0 ) )
| ( epred1_0 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_32,negated_conjecture,
( ( ( esk3_1 @ esk5_0 )
= esk5_0 )
| ( epred1_0 @ ( esk2_1 @ esk5_0 ) )
| ( epred1_0 @ esk4_0 ) ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_31])]) ).
thf(c_0_33,negated_conjecture,
( ( ( esk3_1 @ esk5_0 )
= esk5_0 )
| ( ( esk2_1 @ esk5_0 )
= esk5_0 )
| ( epred1_0 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_29,c_0_32]) ).
thf(c_0_34,negated_conjecture,
! [X2: $i] :
( ( ( esk3_1 @ esk5_0 )
= esk5_0 )
| ( ( esk3_1 @ X2 )
= X2 )
| ( epred1_0 @ ( esk3_1 @ X2 ) )
| ( epred1_0 @ esk4_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_33]),c_0_28])]) ).
thf(c_0_35,negated_conjecture,
! [X2: $i] :
( ( ( esk3_1 @ esk5_0 )
= esk5_0 )
| ( ( esk3_1 @ X2 )
= esk5_0 )
| ( ( esk3_1 @ X2 )
= X2 )
| ( epred1_0 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_29,c_0_34]) ).
thf(c_0_36,negated_conjecture,
( ( ( esk3_1 @ esk5_0 )
= esk5_0 )
| ( epred1_0 @ esk4_0 ) ),
inference(ef,[status(thm)],[c_0_35]) ).
thf(c_0_37,negated_conjecture,
! [X2: $i] :
( ( epred1_0 @ ( esk2_1 @ X2 ) )
| ( epred1_0 @ esk4_0 )
| ~ ( epred1_0 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_36]),c_0_28])]) ).
thf(c_0_38,negated_conjecture,
! [X2: $i,X4: $i] :
( ( esk5_0 = X2 )
| ( X4 = esk4_0 )
| ~ ( epred1_0 @ X2 )
| ~ ( epred1_0 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_39,negated_conjecture,
! [X2: $i] :
( ( epred1_0 @ esk4_0 )
| ( ( esk2_1 @ X2 )
!= X2 )
| ~ ( epred1_0 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_36]),c_0_28])]) ).
thf(c_0_40,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ X2 )
= esk5_0 )
| ( epred1_0 @ esk4_0 )
| ~ ( epred1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_29,c_0_37]) ).
thf(c_0_41,negated_conjecture,
! [X2: $i] :
( ( esk4_0 = esk5_0 )
| ( esk5_0 = X2 )
| ~ ( epred1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_38,c_0_28]) ).
thf(c_0_42,negated_conjecture,
epred1_0 @ esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40])]),c_0_28])]) ).
thf(c_0_43,negated_conjecture,
esk4_0 = esk5_0,
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
thf(c_0_44,negated_conjecture,
! [X2: $i,X4: $i] :
( ( X2 = esk5_0 )
| ( esk5_0 = X4 )
| ~ ( epred1_0 @ X2 )
| ~ ( epred1_0 @ X4 ) ),
inference(rw,[status(thm)],[c_0_38,c_0_43]) ).
thf(c_0_45,negated_conjecture,
! [X2: $i,X4: $i] :
( ( ( esk2_1 @ esk5_0 )
= esk5_0 )
| ( ( esk3_1 @ X2 )
= X2 )
| ( esk5_0 = X4 )
| ( epred1_0 @ ( esk3_1 @ X2 ) )
| ~ ( epred1_0 @ X4 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_30]) ).
thf(c_0_46,negated_conjecture,
! [X2: $i,X4: $i] :
( ( ( esk2_1 @ esk5_0 )
= esk5_0 )
| ( ( esk3_1 @ X2 )
= X2 )
| ( ( esk3_1 @ X4 )
= X4 )
| ( epred1_0 @ ( esk3_1 @ X2 ) )
| ( epred1_0 @ ( esk3_1 @ X4 ) ) ),
inference(spm,[status(thm)],[c_0_45,c_0_30]) ).
thf(c_0_47,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ esk5_0 )
= esk5_0 )
| ( ( esk3_1 @ X2 )
= X2 )
| ( epred1_0 @ ( esk3_1 @ X2 ) ) ),
inference(ef,[status(thm)],[c_0_46]) ).
thf(c_0_48,negated_conjecture,
! [X2: $i,X4: $i] :
( ( ( esk3_1 @ X2 )
= X2 )
| ( ( esk3_1 @ X4 )
= X4 )
| ( epred1_0 @ ( esk3_1 @ X2 ) )
| ( epred1_0 @ ( esk3_1 @ X4 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_47]),c_0_28])]) ).
thf(c_0_49,negated_conjecture,
! [X2: $i] :
( ( ( esk3_1 @ X2 )
= X2 )
| ( epred1_0 @ ( esk3_1 @ X2 ) ) ),
inference(ef,[status(thm)],[c_0_48]) ).
thf(c_0_50,negated_conjecture,
! [X2: $i,X4: $i] :
( ( ( esk3_1 @ X2 )
= esk5_0 )
| ( ( esk3_1 @ X2 )
= X2 )
| ( esk5_0 = X4 )
| ~ ( epred1_0 @ X4 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_49]) ).
thf(c_0_51,negated_conjecture,
! [X2: $i,X4: $i] :
( ( ( esk3_1 @ X2 )
= esk5_0 )
| ( ( esk3_1 @ X4 )
= esk5_0 )
| ( ( esk3_1 @ X2 )
= X2 )
| ( ( esk3_1 @ X4 )
= X4 ) ),
inference(spm,[status(thm)],[c_0_50,c_0_49]) ).
thf(c_0_52,negated_conjecture,
( ( esk3_1 @ esk5_0 )
= esk5_0 ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_51])]) ).
thf(c_0_53,negated_conjecture,
! [X2: $i] :
( ( epred1_0 @ ( esk2_1 @ X2 ) )
| ~ ( epred1_0 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_52]),c_0_28])]) ).
thf(c_0_54,negated_conjecture,
! [X4: $i,X2: $i] :
( ( ( esk2_1 @ X2 )
= esk5_0 )
| ( esk5_0 = X4 )
| ~ ( epred1_0 @ X4 )
| ~ ( epred1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_53]) ).
thf(c_0_55,negated_conjecture,
! [X4: $i,X2: $i] :
( ( ( esk2_1 @ X2 )
= esk5_0 )
| ( ( esk2_1 @ X4 )
= esk5_0 )
| ~ ( epred1_0 @ X4 )
| ~ ( epred1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_54,c_0_53]) ).
thf(c_0_56,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ esk5_0 )
= esk5_0 )
| ( ( esk2_1 @ X2 )
= esk5_0 )
| ~ ( epred1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_55,c_0_28]) ).
thf(c_0_57,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ X2 )
!= X2 )
| ~ ( epred1_0 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_52]),c_0_28])]) ).
thf(c_0_58,negated_conjecture,
( ( esk2_1 @ esk5_0 )
= esk5_0 ),
inference(spm,[status(thm)],[c_0_56,c_0_28]) ).
thf(c_0_59,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV300^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 % Computer : n013.cluster.edu
% 0.11/0.24 % Model : x86_64 x86_64
% 0.11/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.24 % Memory : 8046.5625MB
% 0.11/0.24 % OS : Linux 6.8.0-71-generic
% 0.11/0.24 % CPULimit : 300
% 0.11/0.24 % WCLimit : 300
% 0.11/0.24 % DateTime : Tue Sep 29 15:31:51 UTC 2026
% 0.11/0.24 % CPUTime :
% 0.11/0.24 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.31 Running higher-order theorem proving
% 0.26/0.32 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.qxZbZUeVZU/E---3.1_2256587.p
% 0.26/0.37 % Version: 3.5.1-ho
% 0.26/0.37 % Preprocessing class: HSSSSMSSSLSNHHA.
% 0.26/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.37 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.26/0.37 % Starting sh3l with 300s (1) cores
% 0.26/0.37 % Starting lpo6_lambda_fix with 300s (1) cores
% 0.26/0.37 % Starting full_lambda_8 with 300s (1) cores
% 0.26/0.37 % lpo6_lambda_fix with pid 2256602 completed with status 0
% 0.26/0.37 % Result found by lpo6_lambda_fix
% 0.26/0.37 % Preprocessing class: HSSSSMSSSLSNHHA.
% 0.26/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.37 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.26/0.37 % Starting sh3l with 300s (1) cores
% 0.26/0.37 % Starting lpo6_lambda_fix with 300s (1) cores
% 0.26/0.37 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.26/0.37 % No SInE strategy applied
% 0.26/0.37 % Search class: HGHSF-FFSF21-SHHFMSNN
% 0.26/0.37 % partial match(2): HGHSF-FFSF21-SHHFMMBN
% 0.26/0.37 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.37 % Starting SubtermCWHack with 28s (1) cores
% 0.26/0.37 % SubtermCWHack with pid 2256609 completed with status 0
% 0.26/0.37 % Result found by SubtermCWHack
% 0.26/0.37 % Preprocessing class: HSSSSMSSSLSNHHA.
% 0.26/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.37 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.26/0.37 % Starting sh3l with 300s (1) cores
% 0.26/0.37 % Starting lpo6_lambda_fix with 300s (1) cores
% 0.26/0.37 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.26/0.37 % No SInE strategy applied
% 0.26/0.37 % Search class: HGHSF-FFSF21-SHHFMSNN
% 0.26/0.37 % partial match(2): HGHSF-FFSF21-SHHFMMBN
% 0.26/0.37 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.37 % Starting SubtermCWHack with 28s (1) cores
% 0.26/0.37 % Preprocessing time : 0.002 s
% 0.26/0.37
% 0.26/0.37 % Proof found!
% 0.26/0.37 % SZS status Theorem
% 0.26/0.37 % SZS output start CNFRefutation
% See solution above
% 0.26/0.37 % Parsed axioms : 7
% 0.26/0.37 % Removed by relevancy pruning/SinE : 0
% 0.26/0.37 % Initial clauses : 12
% 0.26/0.37 % Removed in clause preprocessing : 3
% 0.26/0.37 % Initial clauses in saturation : 9
% 0.26/0.37 % Processed clauses : 116
% 0.26/0.37 % ...of these trivial : 3
% 0.26/0.37 % ...subsumed : 36
% 0.26/0.37 % ...remaining for further processing : 77
% 0.26/0.37 % Other redundant clauses eliminated : 64
% 0.26/0.37 % Clauses deleted for lack of memory : 0
% 0.26/0.37 % Backward-subsumed : 31
% 0.26/0.37 % Backward-rewritten : 31
% 0.26/0.37 % Generated clauses : 623
% 0.26/0.37 % ...of the previous two non-redundant : 438
% 0.26/0.37 % ...aggressively subsumed : 0
% 0.26/0.37 % Contextual simplify-reflections : 4
% 0.26/0.37 % Paramodulations : 499
% 0.26/0.37 % Factorizations : 56
% 0.26/0.37 % NegExts : 0
% 0.26/0.37 % Equation resolutions : 66
% 0.26/0.37 % Disequality decompositions : 0
% 0.26/0.37 % Total rewrite steps : 169
% 0.26/0.37 % ...of those cached : 164
% 0.26/0.37 % Propositional unsat checks : 0
% 0.26/0.37 % Propositional check models : 0
% 0.26/0.37 % Propositional check unsatisfiable : 0
% 0.26/0.37 % Propositional clauses : 0
% 0.26/0.37 % Propositional clauses after purity: 0
% 0.26/0.37 % Propositional unsat core size : 0
% 0.26/0.37 % Propositional preprocessing time : 0.000
% 0.26/0.37 % Propositional encoding time : 0.000
% 0.26/0.37 % Propositional solver time : 0.000
% 0.26/0.37 % Success case prop preproc time : 0.000
% 0.26/0.37 % Success case prop encoding time : 0.000
% 0.26/0.37 % Success case prop solver time : 0.000
% 0.26/0.37 % Current number of processed clauses : 13
% 0.26/0.37 % Positive orientable unit clauses : 4
% 0.26/0.37 % Positive unorientable unit clauses: 0
% 0.26/0.37 % Negative unit clauses : 0
% 0.26/0.37 % Non-unit-clauses : 9
% 0.26/0.37 % Current number of unprocessed clauses: 92
% 0.26/0.37 % ...number of literals in the above : 517
% 0.26/0.37 % Current number of archived formulas : 0
% 0.26/0.37 % Current number of archived clauses : 62
% 0.26/0.37 % Clause-clause subsumption calls (NU) : 276
% 0.26/0.37 % Rec. Clause-clause subsumption calls : 127
% 0.26/0.37 % Non-unit clause-clause subsumptions : 71
% 0.26/0.37 % Unit Clause-clause subsumption calls : 13
% 0.26/0.37 % Rewrite failures with RHS unbound : 0
% 0.26/0.37 % BW rewrite match attempts : 5
% 0.26/0.37 % BW rewrite match successes : 5
% 0.26/0.37 % Condensation attempts : 0
% 0.26/0.37 % Condensation successes : 0
% 0.26/0.37 % Termbank termtop insertions : 9330
% 0.26/0.37 % Search garbage collected termcells : 397
% 0.26/0.37
% 0.26/0.37 % -------------------------------------------------
% 0.26/0.37 % User time : 0.027 s
% 0.26/0.37 % System time : 0.006 s
% 0.26/0.37 % Total time : 0.033 s
% 0.26/0.37 % Maximum resident set size: 3640 pages
% 0.26/0.37
% 0.26/0.37 % -------------------------------------------------
% 0.26/0.37 % User time : 0.028 s
% 0.26/0.37 % System time : 0.012 s
% 0.26/0.37 % Total time : 0.040 s
% 0.26/0.37 % Maximum resident set size: 4608 pages
% 0.26/0.37 % E exiting
%------------------------------------------------------------------------------