%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV293^5 : 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 : n015.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 08:35:20 AM UTC 2026
% Result : Theorem 0.11s 0.28s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 4
% Syntax : Number of formulae : 89 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 265 ( 152 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 487 ( 99 ~; 134 |; 16 &; 233 @)
% ( 2 <=>; 0 =>; 0 <=; 3 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 110 ( 22 ^; 66 !; 22 ?; 110 :)
% 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_1: $i > $o ).
thf(decl_27,type,
esk2_1: $i > $i ).
thf(decl_28,type,
esk3_0: $i ).
thf(decl_29,type,
esk4_0: $i ).
thf(decl_30,type,
esk3_1: $i > $i ).
thf(decl_31,type,
esk4_1: $i > $i ).
thf(cZERO_def,axiom,
( cZERO
= ( ^ [X1: $i > $o] :
~ ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.36NxkqKM8M/E---3.1_3666659.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.36NxkqKM8M/E---3.1_3666659.p',cSUCC_def) ).
thf(cX6101_pme,conjecture,
( cONE
= ( ^ [X5: $i > $o] :
? [X6: $i] :
( X5
= ( ^ [X2: $i,X6: $i] : ( X2 = X6 )
@ X6 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.36NxkqKM8M/E---3.1_3666659.p',cX6101_pme) ).
thf(cONE_def,axiom,
( cONE
= ( ^ [Z0: $i > $o] :
? [X8: $i] :
( ( Z0 @ X8 )
& ~ ? [X7: $i] :
( ( X7 != X8 )
& ( Z0 @ X7 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.36NxkqKM8M/E---3.1_3666659.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,
( cONE
!= ( ^ [X5: $i > $o] :
? [X6: $i] :
( X5
= ( ^ [X2: $i,X6: $i] : ( X2 = X6 )
@ X6 ) ) ) ),
inference(assume_negation,[status(cth)],[cX6101_pme]) ).
thf(c_0_7,axiom,
( cONE
= ( ^ [Z0: $i > $o] :
? [X8: $i] :
( ( Z0 @ X8 )
& ~ ? [X7: $i] :
( ( X7 != X8 )
& ( Z0 @ X7 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[cONE_def,c_0_4]),c_0_5]) ).
thf(c_0_8,negated_conjecture,
( ( ^ [Z0: $i > $o] :
? [X9: $i] :
( ( Z0 @ X9 )
& ~ ? [X10: $i] :
( ( X10 != X9 )
& ( Z0 @ X10 ) ) ) )
!= ( ^ [Z0: $i > $o] :
? [X6: $i] :
( Z0
= ( $eq @ X6 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_6]),c_0_7])])]) ).
thf(c_0_9,negated_conjecture,
( ( ^ [Z0: $i > $o] :
? [X9: $i] :
( ( Z0 @ X9 )
& ~ ? [X10: $i] :
( ( X10 != X9 )
& ( Z0 @ X10 ) ) ) )
!= ( ^ [Z0: $i > $o] :
? [X6: $i] :
( Z0
= ( $eq @ X6 ) ) ) ),
inference(fof_nnf,[status(thm)],[c_0_8]) ).
thf(c_0_10,negated_conjecture,
( ( ^ [Z0: $i > $o] :
? [X32: $i] :
( ( Z0 @ X32 )
& ~ ? [X33: $i] :
( ( X33 != X32 )
& ( Z0 @ X33 ) ) ) )
!= ( ^ [Z0: $i > $o] :
? [X34: $i] :
( Z0
= ( $eq @ X34 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_11,negated_conjecture,
( ? [X35: $i] :
( ( esk1_1 @ X35 )
& ~ ? [X36: $i] :
( ( X36 != X35 )
& ( esk1_1 @ X36 ) ) )
<~> ? [X37: $i] :
( esk1_1
= ( $eq @ X37 ) ) ),
inference(neg_ext,[status(thm)],[c_0_10]) ).
thf(c_0_12,negated_conjecture,
( ( ( $eq @ esk4_0 )
= esk1_1 )
| ( esk1_1 @ esk3_0 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_11]) ).
thf(c_0_13,negated_conjecture,
! [X20: $i] :
( ( ( esk4_0 = X20 )
<=> ( esk1_1 @ X20 ) )
| ( esk1_1 @ esk3_0 ) ),
inference(arg_cong,[status(thm)],[c_0_12]) ).
thf(c_0_14,negated_conjecture,
! [X4: $i,X2: $i] :
( ( esk1_1 @ ( esk2_1 @ X2 ) )
| ( ( $eq @ X4 )
!= esk1_1 )
| ~ ( esk1_1 @ X2 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_11]) ).
thf(c_0_15,negated_conjecture,
! [X2: $i] :
( ( ( $eq @ esk4_0 )
= esk1_1 )
| ( X2 = esk3_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_11]) ).
thf(c_0_16,negated_conjecture,
! [X2: $i] :
( ( esk4_0 = X2 )
| ( esk1_1 @ esk3_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_13]) ).
thf(c_0_17,negated_conjecture,
! [X2: $i] :
( ( esk1_1 @ ( esk2_1 @ X2 ) )
| ( esk1_1 @ esk3_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_12]) ).
thf(c_0_18,negated_conjecture,
! [X24: $i,X2: $i] :
( ( ( esk4_0 = X24 )
<=> ( esk1_1 @ X24 ) )
| ( X2 = esk3_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(arg_cong,[status(thm)],[c_0_15]) ).
thf(c_0_19,negated_conjecture,
! [X2: $i,X4: $i] :
( ( ( $eq @ X2 )
!= esk1_1 )
| ( ( esk2_1 @ X4 )
!= X4 )
| ~ ( esk1_1 @ X4 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_11]) ).
thf(c_0_20,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ X2 )
= esk4_0 )
| ( esk1_1 @ esk3_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_21,negated_conjecture,
! [X4: $i,X2: $i] :
( ( esk1_1 @ ( esk2_1 @ X2 ) )
| ( ( X4
= ( esk4_1 @ X4 ) )
<~> ( esk1_1 @ ( esk4_1 @ X4 ) ) )
| ~ ( esk1_1 @ X2 ) ),
inference(neg_ext,[status(thm)],[c_0_14]) ).
thf(c_0_22,negated_conjecture,
! [X4: $i,X2: $i] :
( ( X2 = esk3_0 )
| ( esk4_0 = X4 )
| ~ ( esk1_1 @ X4 )
| ~ ( esk1_1 @ X2 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_18]) ).
thf(c_0_23,negated_conjecture,
! [X4: $i,X2: $i] :
( ( X2 = esk3_0 )
| ( esk1_1 @ ( esk2_1 @ X4 ) )
| ~ ( esk1_1 @ X4 )
| ~ ( esk1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_24,negated_conjecture,
! [X2: $i] :
( ( esk1_1 @ esk3_0 )
| ( ( esk2_1 @ X2 )
!= X2 )
| ~ ( esk1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_12]) ).
thf(c_0_25,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ ( esk2_1 @ X2 ) )
= esk4_0 )
| ( esk1_1 @ esk3_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
thf(c_0_26,negated_conjecture,
! [X2: $i,X4: $i] :
( ( ( esk4_1 @ X2 )
= X2 )
| ( esk1_1 @ ( esk2_1 @ X4 ) )
| ( esk1_1 @ ( esk4_1 @ X2 ) )
| ~ ( esk1_1 @ X4 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_21]) ).
thf(c_0_27,negated_conjecture,
! [X4: $i,X2: $i] :
( ( ( esk2_1 @ X2 )
= esk4_0 )
| ( X4 = esk3_0 )
| ~ ( esk1_1 @ X4 )
| ~ ( esk1_1 @ X2 ) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23])]) ).
thf(c_0_28,negated_conjecture,
! [X2: $i] :
( ( esk1_1 @ esk3_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_17]),c_0_20]) ).
thf(c_0_29,negated_conjecture,
! [X2: $i,X4: $i] :
( ( ( esk4_1 @ X2 )
= esk3_0 )
| ( ( esk4_1 @ X2 )
= X2 )
| ( esk1_1 @ ( esk2_1 @ X4 ) )
| ~ ( esk1_1 @ X4 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_26]),c_0_14]) ).
thf(c_0_30,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ esk3_0 )
= esk4_0 )
| ( X2 = esk3_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28])]) ).
thf(c_0_31,negated_conjecture,
! [X2: $i] :
( ( ( esk4_1 @ esk3_0 )
= esk3_0 )
| ( esk1_1 @ ( esk2_1 @ X2 ) )
| ~ ( esk1_1 @ X2 ) ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_29])]) ).
thf(c_0_32,negated_conjecture,
! [X2: $i] :
( ( ( esk4_1 @ esk3_0 )
= esk3_0 )
| ( ( esk2_1 @ esk3_0 )
= esk4_0 )
| ( ( esk2_1 @ X2 )
= esk3_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_33,negated_conjecture,
( ( esk1_1 @ esk3_0 )
| ( esk1_1 @ esk4_0 ) ),
inference(er,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_13])]) ).
thf(c_0_34,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ esk3_0 )
= esk3_0 )
| ( ( esk2_1 @ esk3_0 )
= esk4_0 )
| ( ( esk4_1 @ esk3_0 )
= esk3_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_32,c_0_28]) ).
thf(c_0_35,negated_conjecture,
( ( ( esk2_1 @ esk3_0 )
= esk3_0 )
| ( ( esk2_1 @ esk3_0 )
= esk4_0 )
| ( ( esk4_1 @ esk3_0 )
= esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
thf(c_0_36,negated_conjecture,
! [X4: $i,X2: $i] :
( ( X2 = esk3_0 )
| ( ( esk2_1 @ X4 )
!= X4 )
| ~ ( esk1_1 @ X4 )
| ~ ( esk1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
thf(c_0_37,negated_conjecture,
( ( ( esk4_1 @ esk3_0 )
= esk3_0 )
| ( ( esk2_1 @ esk3_0 )
= esk4_0 )
| ( esk3_0 != esk4_0 ) ),
inference(ef,[status(thm)],[c_0_35]) ).
thf(c_0_38,negated_conjecture,
! [X2: $i] :
( ( esk3_0 = esk4_0 )
| ( X2 = esk3_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_28])]) ).
thf(c_0_39,negated_conjecture,
! [X2: $i] :
( ( ( esk4_1 @ esk3_0 )
= esk3_0 )
| ( X2 = esk3_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_28]),c_0_38]) ).
thf(c_0_40,negated_conjecture,
! [X2: $i] :
( ( ( esk4_1 @ esk3_0 )
= esk3_0 )
| ( ( esk2_1 @ X2 )
= esk3_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_39,c_0_31]) ).
thf(c_0_41,negated_conjecture,
! [X2: $i,X4: $i] :
( ( ( X2
= ( esk3_1 @ X2 ) )
<~> ( esk1_1 @ ( esk3_1 @ X2 ) ) )
| ( ( esk2_1 @ X4 )
!= X4 )
| ~ ( esk1_1 @ X4 ) ),
inference(neg_ext,[status(thm)],[c_0_19]) ).
thf(c_0_42,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ esk3_0 )
= esk3_0 )
| ( ( esk4_1 @ esk3_0 )
= esk3_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_28]) ).
thf(c_0_43,negated_conjecture,
( ( ( esk2_1 @ esk3_0 )
= esk3_0 )
| ( ( esk4_1 @ esk3_0 )
= esk3_0 )
| ( esk1_1 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_33]) ).
thf(c_0_44,negated_conjecture,
! [X2: $i,X4: $i] :
( ( ( esk3_1 @ X2 )
= X2 )
| ( esk1_1 @ ( esk3_1 @ X2 ) )
| ( ( esk2_1 @ X4 )
!= X4 )
| ~ ( esk1_1 @ X4 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_41]) ).
thf(c_0_45,negated_conjecture,
( ( ( esk4_1 @ esk3_0 )
= esk3_0 )
| ( ( esk2_1 @ esk3_0 )
= esk3_0 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_46,negated_conjecture,
! [X2: $i] :
( ( ( esk4_1 @ esk3_0 )
= esk3_0 )
| ( ( esk3_1 @ X2 )
= X2 )
| ( esk1_1 @ ( esk3_1 @ X2 ) )
| ~ ( esk1_1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_47,negated_conjecture,
! [X2: $i] :
( ( ( esk4_1 @ esk3_0 )
= esk3_0 )
| ( ( esk3_1 @ X2 )
= esk3_0 )
| ( ( esk3_1 @ X2 )
= X2 )
| ~ ( esk1_1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_39,c_0_46]) ).
thf(c_0_48,negated_conjecture,
! [X2: $i,X4: $i] :
( ( ( esk4_1 @ esk3_0 )
= esk3_0 )
| ( ( esk3_1 @ X2 )
= esk3_0 )
| ( ( esk3_1 @ X2 )
= X2 )
| ~ ( esk1_1 @ X4 ) ),
inference(spm,[status(thm)],[c_0_47,c_0_28]) ).
thf(c_0_49,negated_conjecture,
! [X2: $i] :
( ( ( esk3_1 @ esk3_0 )
= esk3_0 )
| ( ( esk4_1 @ esk3_0 )
= esk3_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_48])]) ).
thf(c_0_50,negated_conjecture,
! [X2: $i,X4: $i] :
( ( ( esk3_1 @ X2 )
!= X2 )
| ( ( esk2_1 @ X4 )
!= X4 )
| ~ ( esk1_1 @ ( esk3_1 @ X2 ) )
| ~ ( esk1_1 @ X4 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_41]) ).
thf(c_0_51,negated_conjecture,
( ( ( esk4_1 @ esk3_0 )
= esk3_0 )
| ( ( esk3_1 @ esk3_0 )
= esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_33]),c_0_49]) ).
thf(c_0_52,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ ( esk2_1 @ X2 ) )
= esk3_0 )
| ( ( esk4_1 @ esk3_0 )
= esk3_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_31]) ).
thf(c_0_53,negated_conjecture,
! [X2: $i] :
( ( ( esk4_1 @ esk3_0 )
= esk3_0 )
| ( ( esk2_1 @ X2 )
!= X2 )
| ~ ( esk1_1 @ X2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_28]) ).
thf(c_0_54,negated_conjecture,
( ( ( esk4_1 @ esk3_0 )
= esk3_0 )
| ( ( esk2_1 @ esk4_0 )
= esk3_0 )
| ( esk3_0 != esk4_0 )
| ~ ( esk1_1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_52,c_0_37]) ).
thf(c_0_55,negated_conjecture,
( ( ( esk4_1 @ esk3_0 )
= esk3_0 )
| ( esk1_1 @ esk4_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_33]),c_0_45]) ).
thf(c_0_56,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ esk4_0 )
= esk3_0 )
| ( ( esk4_1 @ esk3_0 )
= esk3_0 )
| ( esk3_0 != esk4_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_54,c_0_28]) ).
thf(c_0_57,negated_conjecture,
( ( ( esk4_1 @ esk3_0 )
= esk3_0 )
| ( ( esk2_1 @ esk4_0 )
!= esk4_0 ) ),
inference(spm,[status(thm)],[c_0_53,c_0_55]) ).
thf(c_0_58,negated_conjecture,
( ( ( esk4_1 @ esk3_0 )
= esk3_0 )
| ( ( esk2_1 @ esk4_0 )
= esk3_0 )
| ( esk3_0 != esk4_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_33]),c_0_40]) ).
thf(c_0_59,negated_conjecture,
( ( ( esk4_1 @ esk3_0 )
= esk3_0 )
| ( esk3_0 != esk4_0 ) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
thf(c_0_60,negated_conjecture,
! [X4: $i,X2: $i] :
( ( esk1_1 @ ( esk2_1 @ X2 ) )
| ( ( esk4_1 @ X4 )
!= X4 )
| ~ ( esk1_1 @ ( esk4_1 @ X4 ) )
| ~ ( esk1_1 @ X2 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_21]) ).
thf(c_0_61,negated_conjecture,
( ( esk4_1 @ esk3_0 )
= esk3_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_55]),c_0_59]) ).
thf(c_0_62,negated_conjecture,
! [X2: $i] :
( ( esk1_1 @ ( esk2_1 @ X2 ) )
| ~ ( esk1_1 @ X2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_28]) ).
thf(c_0_63,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ esk3_0 )
= esk4_0 )
| ( ( esk2_1 @ X2 )
= esk3_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_62]) ).
thf(c_0_64,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ esk3_0 )
= esk3_0 )
| ( ( esk2_1 @ esk3_0 )
= esk4_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_63,c_0_28]) ).
thf(c_0_65,negated_conjecture,
( ( ( esk2_1 @ esk3_0 )
= esk3_0 )
| ( ( esk2_1 @ esk3_0 )
= esk4_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_33]),c_0_64]) ).
thf(c_0_66,negated_conjecture,
( ( ( esk2_1 @ esk3_0 )
= esk4_0 )
| ( esk3_0 != esk4_0 ) ),
inference(ef,[status(thm)],[c_0_65]) ).
thf(c_0_67,negated_conjecture,
! [X2: $i] :
( ( X2 = esk3_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_66]),c_0_28]),c_0_38]) ).
thf(c_0_68,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ X2 )
= esk3_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_67,c_0_62]) ).
thf(c_0_69,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ esk3_0 )
= esk3_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_68,c_0_28]) ).
thf(c_0_70,negated_conjecture,
( ( ( esk2_1 @ esk3_0 )
= esk3_0 )
| ( esk1_1 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_68,c_0_33]) ).
thf(c_0_71,negated_conjecture,
( ( esk2_1 @ esk3_0 )
= esk3_0 ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
thf(c_0_72,negated_conjecture,
! [X2: $i] :
( ( ( esk3_1 @ X2 )
= X2 )
| ( esk1_1 @ ( esk3_1 @ X2 ) )
| ~ ( esk1_1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_71]) ).
thf(c_0_73,negated_conjecture,
! [X2: $i] :
( ( ( esk3_1 @ X2 )
= esk3_0 )
| ( ( esk3_1 @ X2 )
= X2 )
| ~ ( esk1_1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_67,c_0_72]) ).
thf(c_0_74,negated_conjecture,
! [X2: $i] :
( ( ( esk3_1 @ X2 )
= esk3_0 )
| ( ( esk3_1 @ X2 )
= X2 )
| ( esk1_1 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_73,c_0_33]) ).
thf(c_0_75,negated_conjecture,
( ( ( esk3_1 @ esk3_0 )
= esk3_0 )
| ( esk1_1 @ esk4_0 ) ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_74])]) ).
thf(c_0_76,negated_conjecture,
( ( ( esk3_1 @ esk3_0 )
= esk3_0 )
| ( esk3_0 = esk4_0 ) ),
inference(spm,[status(thm)],[c_0_67,c_0_75]) ).
thf(c_0_77,negated_conjecture,
! [X2: $i] :
( ( esk3_0 = esk4_0 )
| ( ( esk2_1 @ X2 )
!= X2 )
| ~ ( esk1_1 @ X2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_76]),c_0_28]) ).
thf(c_0_78,negated_conjecture,
esk3_0 = esk4_0,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_33]),c_0_71])]),c_0_67]) ).
thf(c_0_79,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ ( esk2_1 @ X2 ) )
= esk3_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_68,c_0_62]) ).
thf(c_0_80,negated_conjecture,
esk1_1 @ esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_78])]) ).
thf(c_0_81,negated_conjecture,
( ( ( esk2_1 @ esk4_0 )
= esk3_0 )
| ( esk3_0 != esk4_0 )
| ~ ( esk1_1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_79,c_0_66]) ).
thf(c_0_82,negated_conjecture,
! [X2: $i] :
( ( ( esk3_1 @ X2 )
= esk4_0 )
| ( ( esk3_1 @ X2 )
= X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_78]),c_0_78]),c_0_80])]) ).
thf(c_0_83,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ esk4_0 )
= esk3_0 )
| ( esk3_0 != esk4_0 )
| ~ ( esk1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_81,c_0_28]) ).
thf(c_0_84,negated_conjecture,
( ( esk3_1 @ esk4_0 )
= esk4_0 ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_82])]) ).
thf(c_0_85,negated_conjecture,
( ( ( esk2_1 @ esk4_0 )
= esk3_0 )
| ( esk3_0 != esk4_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_33]),c_0_68]) ).
thf(c_0_86,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ X2 )
!= X2 )
| ~ ( esk1_1 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_84]),c_0_80])]) ).
thf(c_0_87,negated_conjecture,
( ( esk2_1 @ esk4_0 )
= esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_78]),c_0_78])]) ).
thf(c_0_88,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_80]),c_0_87])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV293^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n015.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 15:35:03 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 Running higher-order theorem proving
% 0.11/0.24 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.36NxkqKM8M/E---3.1_3666659.p
% 0.11/0.28 % Version: 3.5.1-ho
% 0.11/0.28 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.11/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.28 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.11/0.28 % Starting sh5l with 300s (1) cores
% 0.11/0.28 % Starting full_lambda_10 with 300s (1) cores
% 0.11/0.28 % Starting full_lambda_6 with 300s (1) cores
% 0.11/0.28 % ehoh_best_nonlift_nonlambdatoforall with pid 3666672 completed with status 0
% 0.11/0.28 % Result found by ehoh_best_nonlift_nonlambdatoforall
% 0.11/0.28 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.11/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.28 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.11/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.28 % No SInE strategy applied
% 0.11/0.28 % Search class: HUUPF-FFSF00-DHHFMFNN
% 0.11/0.28 % partial match(3): HUHPF-FFSF00-SHHFFFNN
% 0.11/0.28 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.28 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.28 % Starting ehoh_best_nonlift_nonlambdatoforall with 151s (1) cores
% 0.11/0.28 % Starting sh5l with 136s (1) cores
% 0.11/0.28 % Starting new_bool_1 with 136s (1) cores
% 0.11/0.28 % Starting new_bool_2 with 136s (1) cores
% 0.11/0.28 % SubtermCWHack with pid 3666677 completed with status 10
% 0.11/0.28 % Starting new_bool_9 with 136s (1) cores
% 0.11/0.28 % sh5l with pid 3666681 completed with status 0
% 0.11/0.28 % Result found by sh5l
% 0.11/0.28 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.11/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.28 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.11/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.28 % No SInE strategy applied
% 0.11/0.28 % Search class: HUUPF-FFSF00-DHHFMFNN
% 0.11/0.28 % partial match(3): HUHPF-FFSF00-SHHFFFNN
% 0.11/0.28 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.28 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.28 % Starting ehoh_best_nonlift_nonlambdatoforall with 151s (1) cores
% 0.11/0.28 % Starting sh5l with 136s (1) cores
% 0.11/0.28 % Preprocessing time : 0.001 s
% 0.11/0.28 % Presaturation interreduction done
% 0.11/0.28
% 0.11/0.28 % Proof found!
% 0.11/0.28 % SZS status Theorem
% 0.11/0.28 % SZS output start CNFRefutation
% See solution above
% 0.11/0.28 % Parsed axioms : 7
% 0.11/0.28 % Removed by relevancy pruning/SinE : 0
% 0.11/0.28 % Initial clauses : 4
% 0.11/0.28 % Removed in clause preprocessing : 3
% 0.11/0.28 % Initial clauses in saturation : 1
% 0.11/0.28 % Processed clauses : 184
% 0.11/0.28 % ...of these trivial : 10
% 0.11/0.28 % ...subsumed : 70
% 0.11/0.28 % ...remaining for further processing : 104
% 0.11/0.28 % Other redundant clauses eliminated : 19
% 0.11/0.28 % Clauses deleted for lack of memory : 0
% 0.11/0.28 % Backward-subsumed : 51
% 0.11/0.28 % Backward-rewritten : 35
% 0.11/0.28 % Generated clauses : 563
% 0.11/0.28 % ...of the previous two non-redundant : 508
% 0.11/0.28 % ...aggressively subsumed : 0
% 0.11/0.28 % Contextual simplify-reflections : 20
% 0.11/0.28 % Paramodulations : 509
% 0.11/0.28 % Factorizations : 14
% 0.11/0.28 % NegExts : 3
% 0.11/0.28 % Equation resolutions : 19
% 0.11/0.28 % Disequality decompositions : 0
% 0.11/0.28 % Total rewrite steps : 70
% 0.11/0.28 % ...of those cached : 64
% 0.11/0.28 % Propositional unsat checks : 0
% 0.11/0.28 % Propositional check models : 0
% 0.11/0.28 % Propositional check unsatisfiable : 0
% 0.11/0.28 % Propositional clauses : 0
% 0.11/0.28 % Propositional clauses after purity: 0
% 0.11/0.28 % Propositional unsat core size : 0
% 0.11/0.28 % Propositional preprocessing time : 0.000
% 0.11/0.28 % Propositional encoding time : 0.000
% 0.11/0.28 % Propositional solver time : 0.000
% 0.11/0.28 % Success case prop preproc time : 0.000
% 0.11/0.28 % Success case prop encoding time : 0.000
% 0.11/0.28 % Success case prop solver time : 0.000
% 0.11/0.28 % Current number of processed clauses : 12
% 0.11/0.28 % Positive orientable unit clauses : 5
% 0.11/0.28 % Positive unorientable unit clauses: 0
% 0.11/0.28 % Negative unit clauses : 1
% 0.11/0.28 % Non-unit-clauses : 6
% 0.11/0.28 % Current number of unprocessed clauses: 25
% 0.11/0.28 % ...number of literals in the above : 104
% 0.11/0.28 % Current number of archived formulas : 0
% 0.11/0.28 % Current number of archived clauses : 92
% 0.11/0.28 % Clause-clause subsumption calls (NU) : 2409
% 0.11/0.28 % Rec. Clause-clause subsumption calls : 1336
% 0.11/0.28 % Non-unit clause-clause subsumptions : 144
% 0.11/0.28 % Unit Clause-clause subsumption calls : 46
% 0.11/0.28 % Rewrite failures with RHS unbound : 0
% 0.11/0.28 % BW rewrite match attempts : 5
% 0.11/0.28 % BW rewrite match successes : 5
% 0.11/0.28 % Condensation attempts : 185
% 0.11/0.28 % Condensation successes : 6
% 0.11/0.28 % Termbank termtop insertions : 22272
% 0.11/0.28 % Search garbage collected termcells : 84
% 0.11/0.28
% 0.11/0.28 % -------------------------------------------------
% 0.11/0.28 % User time : 0.026 s
% 0.11/0.28 % System time : 0.003 s
% 0.11/0.28 % Total time : 0.029 s
% 0.11/0.28 % Maximum resident set size: 3636 pages
% 0.11/0.28
% 0.11/0.28 % -------------------------------------------------
% 0.11/0.28 % User time : 0.099 s
% 0.11/0.28 % System time : 0.014 s
% 0.11/0.28 % Total time : 0.113 s
% 0.11/0.28 % Maximum resident set size: 4864 pages
% 0.11/0.28 % E exiting
%------------------------------------------------------------------------------