%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM638^4 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 08:17:16 AM UTC 2026
% Result : Theorem 0.08s 0.20s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 70 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 332 ( 109 equ; 0 cnn)
% Maximal formula atoms : 44 ( 4 avg)
% Number of connectives : 601 ( 125 ~; 84 |; 17 &; 269 @)
% ( 0 <=>; 106 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 7 con; 0-3 aty)
% Number of variables : 138 ( 90 ^; 48 !; 0 ?; 138 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
is_of: $i > ( $i > $o ) > $o ).
thf(decl_24,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_26,type,
in: $i > $i > $o ).
thf(decl_48,type,
ordsucc: $i > $i ).
thf(decl_62,type,
imp: $o > $o > $o ).
thf(decl_63,type,
d_not: $o > $o ).
thf(decl_66,type,
l_ec: $o > $o > $o ).
thf(decl_67,type,
d_and: $o > $o > $o ).
thf(decl_72,type,
non: $i > ( $i > $o ) > $i > $o ).
thf(decl_73,type,
l_some: $i > ( $i > $o ) > $o ).
thf(decl_78,type,
e_is: $i > $i > $i > $o ).
thf(decl_79,type,
amone: $i > ( $i > $o ) > $o ).
thf(decl_80,type,
one: $i > ( $i > $o ) > $o ).
thf(decl_124,type,
nat: $i ).
thf(decl_125,type,
n_is: $i > $i > $o ).
thf(decl_126,type,
nis: $i > $i > $o ).
thf(decl_128,type,
n_some: ( $i > $o ) > $o ).
thf(decl_130,type,
n_one: ( $i > $o ) > $o ).
thf(decl_131,type,
n_1: $i ).
thf(decl_137,type,
esk1_0: $i ).
thf(decl_138,type,
esk2_0: $i ).
thf(decl_139,type,
esk3_0: $i ).
thf(decl_140,type,
esk4_1: $i > $i ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yPjxPvr7Lc/E---3.1_19448.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yPjxPvr7Lc/E---3.1_19448.p',def_imp) ).
thf(def_all_of,axiom,
( all_of
= ( ^ [X3: $i > $o,X2: $i > $o] :
! [X4: $i] :
( ( is_of @ X4 @ X3 )
=> ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yPjxPvr7Lc/E---3.1_19448.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yPjxPvr7Lc/E---3.1_19448.p',def_is_of) ).
thf(def_non,axiom,
( non
= ( ^ [X1: $i,X2: $i > $o,X4: $i] : ( d_not @ ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yPjxPvr7Lc/E---3.1_19448.p',def_non) ).
thf(def_l_ec,axiom,
( l_ec
= ( ^ [X79: $o,X80: $o] : ( imp @ X79 @ ( d_not @ X80 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yPjxPvr7Lc/E---3.1_19448.p',def_l_ec) ).
thf(def_amone,axiom,
( amone
= ( ^ [X1: $i,X2: $i > $o] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ X1 )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ X1 )
@ ^ [X13: $i] :
( ( X2 @ X4 )
=> ( ( X2 @ X13 )
=> ( e_is @ X1 @ X4 @ X13 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yPjxPvr7Lc/E---3.1_19448.p',def_amone) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yPjxPvr7Lc/E---3.1_19448.p',def_e_is) ).
thf(def_l_some,axiom,
( l_some
= ( ^ [X1: $i,X2: $i > $o] :
( d_not
@ ( all_of
@ ^ [X4: $i] : ( in @ X4 @ X1 )
@ ( non @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yPjxPvr7Lc/E---3.1_19448.p',def_l_some) ).
thf(def_d_and,axiom,
( d_and
= ( ^ [X81: $o,X82: $o] : ( d_not @ ( l_ec @ X81 @ X82 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yPjxPvr7Lc/E---3.1_19448.p',def_d_and) ).
thf(def_one,axiom,
( one
= ( ^ [X1: $i,X2: $i > $o] : ( d_and @ ( amone @ X1 @ X2 ) @ ( l_some @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yPjxPvr7Lc/E---3.1_19448.p',def_one) ).
thf(def_nis,axiom,
( nis
= ( ^ [X1: $i,X165: $i] : ( d_not @ ( n_is @ X1 @ X165 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yPjxPvr7Lc/E---3.1_19448.p',def_nis) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yPjxPvr7Lc/E---3.1_19448.p',def_n_is) ).
thf(satz3a,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( ( nis @ X1 @ n_1 )
=> ( n_one
@ ^ [X176: $i] : ( n_is @ X1 @ ( ordsucc @ X176 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yPjxPvr7Lc/E---3.1_19448.p',satz3a) ).
thf(def_n_one,axiom,
( n_one
= ( ^ [Z0: $i > $o] :
( ( ! [X323: $i] :
( ( in @ X323 @ nat )
=> ! [X324: $i] :
( ( in @ X324 @ nat )
=> ( ( Z0 @ X323 )
=> ( ( Z0 @ X324 )
=> ( X323 = X324 ) ) ) ) )
=> ( ( ! [X325: $i] :
( ( in @ X325 @ nat )
=> ( ( Z0 @ X325 )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yPjxPvr7Lc/E---3.1_19448.p',def_n_one) ).
thf(def_n_some,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X322: $i] :
( ( in @ X322 @ nat )
=> ( ( Z0 @ X322 )
=> ~ $true ) )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yPjxPvr7Lc/E---3.1_19448.p',def_n_some) ).
thf(satz3,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( ( nis @ X1 @ n_1 )
=> ( n_some
@ ^ [X175: $i] : ( n_is @ X1 @ ( ordsucc @ X175 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yPjxPvr7Lc/E---3.1_19448.p',satz3) ).
thf(ordsucc_inj,axiom,
! [X1: $i,X43: $i] :
( ( ( ordsucc @ X1 )
= ( ordsucc @ X43 ) )
=> ( X1 = X43 ) ),
file('/export/starexec/sandbox/tmp/tmp.yPjxPvr7Lc/E---3.1_19448.p',ordsucc_inj) ).
thf(c_0_18,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_19,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_20,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_all_of]) ).
thf(c_0_21,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_22,plain,
( non
= ( ^ [Z0: $i,Z1: $i > $o,Z2: $i] :
( ( Z1 @ Z2 )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_non]) ).
thf(c_0_23,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_24,plain,
( l_ec
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> ( Z1
=> ~ $true ) ) ) ),
inference(fof_simplification,[status(thm)],[def_l_ec]) ).
thf(c_0_25,plain,
( amone
= ( ^ [Z0: $i,Z1: $i > $o] :
! [X314: $i] :
( ( in @ X314 @ Z0 )
=> ! [X313: $i] :
( ( in @ X313 @ Z0 )
=> ( ( Z1 @ X314 )
=> ( ( Z1 @ X313 )
=> ( X314 = X313 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_amone]) ).
thf(c_0_26,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_27,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_28,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X312: $i] :
( ( in @ X312 @ Z0 )
=> ( ( Z1 @ X312 )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_l_some]) ).
thf(c_0_29,plain,
( non
= ( ^ [Z0: $i,Z1: $i > $o,Z2: $i] :
( ( Z1 @ Z2 )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_30,plain,
( d_and
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ( Z1
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_and]) ).
thf(c_0_31,plain,
( l_ec
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> ( Z1
=> ~ $true ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_24,c_0_19]),c_0_23]) ).
thf(c_0_32,plain,
( one
= ( ^ [Z0: $i,Z1: $i > $o] :
( ( ! [X315: $i] :
( ( in @ X315 @ Z0 )
=> ! [X316: $i] :
( ( in @ X316 @ Z0 )
=> ( ( Z1 @ X315 )
=> ( ( Z1 @ X316 )
=> ( X315 = X316 ) ) ) ) )
=> ( ( ! [X317: $i] :
( ( in @ X317 @ Z0 )
=> ( ( Z1 @ X317 )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_one]) ).
thf(c_0_33,plain,
( amone
= ( ^ [Z0: $i,Z1: $i > $o] :
! [X314: $i] :
( ( in @ X314 @ Z0 )
=> ! [X313: $i] :
( ( in @ X313 @ Z0 )
=> ( ( Z1 @ X314 )
=> ( ( Z1 @ X313 )
=> ( X314 = X313 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
thf(c_0_34,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X312: $i] :
( ( in @ X312 @ Z0 )
=> ( ( Z1 @ X312 )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_28,c_0_29]),c_0_23]),c_0_27]) ).
thf(c_0_35,plain,
( d_and
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ( Z1
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_30,c_0_31]),c_0_23]) ).
thf(c_0_36,plain,
( nis
= ( ^ [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_nis]) ).
thf(c_0_37,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_26]) ).
thf(c_0_38,plain,
( one
= ( ^ [Z0: $i,Z1: $i > $o] :
( ( ! [X315: $i] :
( ( in @ X315 @ Z0 )
=> ! [X316: $i] :
( ( in @ X316 @ Z0 )
=> ( ( Z1 @ X315 )
=> ( ( Z1 @ X316 )
=> ( X315 = X316 ) ) ) ) )
=> ( ( ! [X317: $i] :
( ( in @ X317 @ Z0 )
=> ( ( Z1 @ X317 )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35]) ).
thf(c_0_39,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( ( nis @ X1 @ n_1 )
=> ( n_one
@ ^ [X176: $i] : ( n_is @ X1 @ ( ordsucc @ X176 ) ) ) ) ),
inference(assume_negation,[status(cth)],[satz3a]) ).
thf(c_0_40,plain,
( nis
= ( ^ [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_36,c_0_23]),c_0_37]) ).
thf(c_0_41,axiom,
( n_one
= ( ^ [Z0: $i > $o] :
( ( ! [X323: $i] :
( ( in @ X323 @ nat )
=> ! [X324: $i] :
( ( in @ X324 @ nat )
=> ( ( Z0 @ X323 )
=> ( ( Z0 @ X324 )
=> ( X323 = X324 ) ) ) ) )
=> ( ( ! [X325: $i] :
( ( in @ X325 @ nat )
=> ( ( Z0 @ X325 )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[def_n_one,c_0_38]) ).
thf(c_0_42,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X322: $i] :
( ( in @ X322 @ nat )
=> ( ( Z0 @ X322 )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[def_n_some,c_0_34]) ).
thf(c_0_43,negated_conjecture,
~ ! [X330: $i] :
( ( in @ X330 @ nat )
=> ( ( ( X330 = n_1 )
=> ~ $true )
=> ( ( ! [X327: $i] :
( ( in @ X327 @ nat )
=> ! [X328: $i] :
( ( in @ X328 @ nat )
=> ( ( X330
= ( ordsucc @ X327 ) )
=> ( ( X330
= ( ordsucc @ X328 ) )
=> ( X327 = X328 ) ) ) ) )
=> ( ( ! [X329: $i] :
( ( in @ X329 @ nat )
=> ( ( X330
= ( ordsucc @ X329 ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_39]),c_0_40]),c_0_37]),c_0_41]),c_0_27]) ).
thf(c_0_44,plain,
! [X340: $i] :
( ( in @ X340 @ nat )
=> ( ( ( X340 = n_1 )
=> ~ $true )
=> ( ! [X339: $i] :
( ( in @ X339 @ nat )
=> ( ( X340
= ( ordsucc @ X339 ) )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz3]),c_0_42]),c_0_40]),c_0_37]),c_0_27]) ).
thf(c_0_45,negated_conjecture,
! [X394: $i] :
( ( in @ esk1_0 @ nat )
& ( ( esk1_0 != n_1 )
| ~ $true )
& ( ~ ( in @ X394 @ nat )
| ( esk1_0
!= ( ordsucc @ X394 ) )
| ~ $true
| ~ $true
| ( in @ esk2_0 @ nat ) )
& ( $true
| ~ $true
| ( in @ esk2_0 @ nat ) )
& ( ~ ( in @ X394 @ nat )
| ( esk1_0
!= ( ordsucc @ X394 ) )
| ~ $true
| ~ $true
| ( in @ esk3_0 @ nat ) )
& ( $true
| ~ $true
| ( in @ esk3_0 @ nat ) )
& ( ~ ( in @ X394 @ nat )
| ( esk1_0
!= ( ordsucc @ X394 ) )
| ~ $true
| ~ $true
| ( esk1_0
= ( ordsucc @ esk2_0 ) ) )
& ( $true
| ~ $true
| ( esk1_0
= ( ordsucc @ esk2_0 ) ) )
& ( ~ ( in @ X394 @ nat )
| ( esk1_0
!= ( ordsucc @ X394 ) )
| ~ $true
| ~ $true
| ( esk1_0
= ( ordsucc @ esk3_0 ) ) )
& ( $true
| ~ $true
| ( esk1_0
= ( ordsucc @ esk3_0 ) ) )
& ( ~ ( in @ X394 @ nat )
| ( esk1_0
!= ( ordsucc @ X394 ) )
| ~ $true
| ~ $true
| ( esk2_0 != esk3_0 ) )
& ( $true
| ~ $true
| ( esk2_0 != esk3_0 ) )
& $true ),
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_43])])])])])]) ).
thf(c_0_46,plain,
! [X410: $i] :
( ( ( in @ ( esk4_1 @ X410 ) @ nat )
| ~ $true
| ( X410 = n_1 )
| ~ ( in @ X410 @ nat ) )
& ( ( X410
= ( ordsucc @ ( esk4_1 @ X410 ) ) )
| ~ $true
| ( X410 = n_1 )
| ~ ( in @ X410 @ nat ) )
& ( $true
| ~ $true
| ( X410 = n_1 )
| ~ ( in @ X410 @ nat ) )
& ( ( in @ ( esk4_1 @ X410 ) @ nat )
| ~ $true
| $true
| ~ ( in @ X410 @ nat ) )
& ( ( X410
= ( ordsucc @ ( esk4_1 @ X410 ) ) )
| ~ $true
| $true
| ~ ( in @ X410 @ nat ) )
& ( $true
| ~ $true
| $true
| ~ ( in @ X410 @ nat ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])])]) ).
thf(c_0_47,negated_conjecture,
! [X1: $i] :
( ( esk1_0
= ( ordsucc @ esk2_0 ) )
| ~ ( in @ X1 @ nat )
| ( esk1_0
!= ( ordsucc @ X1 ) )
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_48,plain,
! [X1: $i] :
( ( X1
= ( ordsucc @ ( esk4_1 @ X1 ) ) )
| ( X1 = n_1 )
| ~ $true
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_49,negated_conjecture,
( ( esk1_0 != n_1 )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_50,negated_conjecture,
! [X1: $i] :
( ( esk1_0
= ( ordsucc @ esk2_0 ) )
| ( esk1_0
!= ( ordsucc @ X1 ) )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_47]) ).
thf(c_0_51,plain,
! [X1: $i] :
( ( X1 = n_1 )
| ( X1
= ( ordsucc @ ( esk4_1 @ X1 ) ) )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_48]) ).
thf(c_0_52,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_53,negated_conjecture,
esk1_0 != n_1,
inference(cn,[status(thm)],[c_0_49]) ).
thf(c_0_54,plain,
! [X1: $i] :
( ( in @ ( esk4_1 @ X1 ) @ nat )
| ( X1 = n_1 )
| ~ $true
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_55,negated_conjecture,
! [X1: $i] :
( ( esk1_0
= ( ordsucc @ esk3_0 ) )
| ~ ( in @ X1 @ nat )
| ( esk1_0
!= ( ordsucc @ X1 ) )
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_56,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1 @ nat )
| ( esk1_0
!= ( ordsucc @ X1 ) )
| ~ $true
| ~ $true
| ( esk2_0 != esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_57,plain,
! [X413: $i,X414: $i] :
( ( ( ordsucc @ X413 )
!= ( ordsucc @ X414 ) )
| ( X413 = X414 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ordsucc_inj])])]) ).
thf(c_0_58,negated_conjecture,
( ( ( ordsucc @ esk2_0 )
= esk1_0 )
| ~ ( in @ ( esk4_1 @ esk1_0 ) @ nat ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51])]),c_0_52])]),c_0_53]) ).
thf(c_0_59,plain,
! [X1: $i] :
( ( X1 = n_1 )
| ( in @ ( esk4_1 @ X1 ) @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_54]) ).
thf(c_0_60,negated_conjecture,
! [X1: $i] :
( ( esk1_0
= ( ordsucc @ esk3_0 ) )
| ( esk1_0
!= ( ordsucc @ X1 ) )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_55]) ).
thf(c_0_61,negated_conjecture,
! [X1: $i] :
( ( esk3_0 != esk2_0 )
| ( esk1_0
!= ( ordsucc @ X1 ) )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_56]) ).
thf(c_0_62,plain,
! [X1: $i,X4: $i] :
( ( X1 = X4 )
| ( ( ordsucc @ X1 )
!= ( ordsucc @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
thf(c_0_63,negated_conjecture,
( ( ordsucc @ esk2_0 )
= esk1_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_52])]),c_0_53]) ).
thf(c_0_64,negated_conjecture,
( ( ( ordsucc @ esk3_0 )
= esk1_0 )
| ~ ( in @ ( esk4_1 @ esk1_0 ) @ nat ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_51])]),c_0_52])]),c_0_53]) ).
thf(c_0_65,negated_conjecture,
( ( esk3_0 != esk2_0 )
| ~ ( in @ ( esk4_1 @ esk1_0 ) @ nat ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_51])]),c_0_52])]),c_0_53]) ).
thf(c_0_66,negated_conjecture,
! [X1: $i] :
( ( esk2_0 = X1 )
| ( ( ordsucc @ X1 )
!= esk1_0 ) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
thf(c_0_67,negated_conjecture,
( ( ordsucc @ esk3_0 )
= esk1_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_59]),c_0_52])]),c_0_53]) ).
thf(c_0_68,negated_conjecture,
esk3_0 != esk2_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_59]),c_0_52])]),c_0_53]) ).
thf(c_0_69,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM638^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 12:21:01 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.14 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.yPjxPvr7Lc/E---3.1_19448.p
% 0.08/0.20 % Version: 3.5.1-ho
% 0.08/0.20 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.08/0.20 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.20 % Starting lpo1_fix with 900s (3) cores
% 0.08/0.20 % Starting full_lambda_9 with 300s (1) cores
% 0.08/0.20 % Starting almost_fo_4 with 300s (1) cores
% 0.08/0.20 % Starting new_ho_9 with 300s (1) cores
% 0.08/0.20 % Starting pre_casc_4 with 300s (1) cores
% 0.08/0.20 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.20 % full_lambda_9 with pid 19481 completed with status 0
% 0.08/0.20 % Result found by full_lambda_9
% 0.08/0.20 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.08/0.20 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.20 % Starting lpo1_fix with 900s (3) cores
% 0.08/0.20 % Starting full_lambda_9 with 300s (1) cores
% 0.08/0.20 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.08/0.20 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.08/0.20 % Search class: HGHSM-FSLM32-DHSMMSBN
% 0.08/0.20 % partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.08/0.20 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.20 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.20 % SubtermCWHack with pid 19492 completed with status 0
% 0.08/0.20 % Result found by SubtermCWHack
% 0.08/0.20 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.08/0.20 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.20 % Starting lpo1_fix with 900s (3) cores
% 0.08/0.20 % Starting full_lambda_9 with 300s (1) cores
% 0.08/0.20 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.08/0.20 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.08/0.20 % Search class: HGHSM-FSLM32-DHSMMSBN
% 0.08/0.20 % partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.08/0.20 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.20 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.20 % Preprocessing time : 0.004 s
% 0.08/0.20
% 0.08/0.20 % Proof found!
% 0.08/0.20 % SZS status Theorem
% 0.08/0.20 % SZS output start CNFRefutation
% See solution above
% 0.08/0.20 % Parsed axioms : 291
% 0.08/0.20 % Removed by relevancy pruning/SinE : 162
% 0.08/0.20 % Initial clauses : 198
% 0.08/0.20 % Removed in clause preprocessing : 27
% 0.08/0.20 % Initial clauses in saturation : 171
% 0.08/0.20 % Processed clauses : 174
% 0.08/0.20 % ...of these trivial : 19
% 0.08/0.20 % ...subsumed : 18
% 0.08/0.20 % ...remaining for further processing : 137
% 0.08/0.20 % Other redundant clauses eliminated : 21
% 0.08/0.20 % Clauses deleted for lack of memory : 0
% 0.08/0.20 % Backward-subsumed : 2
% 0.08/0.20 % Backward-rewritten : 8
% 0.08/0.20 % Generated clauses : 208
% 0.08/0.20 % ...of the previous two non-redundant : 161
% 0.08/0.20 % ...aggressively subsumed : 0
% 0.08/0.20 % Contextual simplify-reflections : 1
% 0.08/0.20 % Paramodulations : 132
% 0.08/0.20 % Factorizations : 0
% 0.08/0.20 % NegExts : 0
% 0.08/0.20 % Equation resolutions : 22
% 0.08/0.20 % Disequality decompositions : 0
% 0.08/0.20 % Total rewrite steps : 69
% 0.08/0.20 % ...of those cached : 36
% 0.08/0.20 % Propositional unsat checks : 0
% 0.08/0.20 % Propositional check models : 0
% 0.08/0.20 % Propositional check unsatisfiable : 0
% 0.08/0.20 % Propositional clauses : 0
% 0.08/0.20 % Propositional clauses after purity: 0
% 0.08/0.20 % Propositional unsat core size : 0
% 0.08/0.20 % Propositional preprocessing time : 0.000
% 0.08/0.20 % Propositional encoding time : 0.000
% 0.08/0.20 % Propositional solver time : 0.000
% 0.08/0.20 % Success case prop preproc time : 0.000
% 0.08/0.20 % Success case prop encoding time : 0.000
% 0.08/0.20 % Success case prop solver time : 0.000
% 0.08/0.20 % Current number of processed clauses : 125
% 0.08/0.20 % Positive orientable unit clauses : 72
% 0.08/0.20 % Positive unorientable unit clauses: 2
% 0.08/0.20 % Negative unit clauses : 10
% 0.08/0.20 % Non-unit-clauses : 41
% 0.08/0.20 % Current number of unprocessed clauses: 157
% 0.08/0.20 % ...number of literals in the above : 467
% 0.08/0.20 % Current number of archived formulas : 0
% 0.08/0.20 % Current number of archived clauses : 10
% 0.08/0.20 % Clause-clause subsumption calls (NU) : 482
% 0.08/0.20 % Rec. Clause-clause subsumption calls : 447
% 0.08/0.20 % Non-unit clause-clause subsumptions : 10
% 0.08/0.20 % Unit Clause-clause subsumption calls : 292
% 0.08/0.20 % Rewrite failures with RHS unbound : 0
% 0.08/0.20 % BW rewrite match attempts : 44
% 0.08/0.20 % BW rewrite match successes : 4
% 0.08/0.20 % Condensation attempts : 0
% 0.08/0.20 % Condensation successes : 0
% 0.08/0.20 % Termbank termtop insertions : 23504
% 0.08/0.20 % Search garbage collected termcells : 7217
% 0.08/0.20
% 0.08/0.20 % -------------------------------------------------
% 0.08/0.20 % User time : 0.023 s
% 0.08/0.20 % System time : 0.007 s
% 0.08/0.20 % Total time : 0.030 s
% 0.08/0.20 % Maximum resident set size: 5048 pages
% 0.08/0.20
% 0.08/0.20 % -------------------------------------------------
% 0.08/0.20 % User time : 0.026 s
% 0.08/0.20 % System time : 0.011 s
% 0.08/0.20 % Total time : 0.037 s
% 0.08/0.20 % Maximum resident set size: 4864 pages
% 0.08/0.20 % E exiting
%------------------------------------------------------------------------------