%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM681^4 : 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 : n010.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 08:16:48 AM UTC 2026
% Result : Theorem 0.61s 0.44s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of formulae : 81 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 209 ( 73 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 698 ( 51 ~; 47 |; 6 &; 569 @)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 136 ( 59 ^; 77 !; 0 ?; 136 :)
% 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_78,type,
e_is: $i > $i > $i > $o ).
thf(decl_124,type,
nat: $i ).
thf(decl_125,type,
n_is: $i > $i > $o ).
thf(decl_131,type,
n_1: $i ).
thf(decl_143,type,
n_pl: $i > $i > $i ).
thf(decl_156,type,
esk1_0: $i ).
thf(decl_157,type,
esk2_0: $i ).
thf(decl_158,type,
esk3_0: $i ).
thf(decl_171,type,
epred5_1: $i > $i > $o ).
thf(decl_174,type,
epred8_2: $i > $i > $i > $o ).
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.102bVFH1Jy/E---3.1_2793365.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.102bVFH1Jy/E---3.1_2793365.p',def_is_of) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.102bVFH1Jy/E---3.1_2793365.p',def_e_is) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.102bVFH1Jy/E---3.1_2793365.p',def_n_is) ).
thf(satz20b,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X297: $i] : ( in @ X297 @ nat )
@ ^ [X298: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( n_is @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X298 @ X4 ) )
=> ( n_is @ X1 @ X298 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.102bVFH1Jy/E---3.1_2793365.p',satz20b) ).
thf(satz4f,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X189: $i] : ( in @ X189 @ nat )
@ ^ [X190: $i] : ( n_is @ ( ordsucc @ ( n_pl @ X1 @ X190 ) ) @ ( n_pl @ X1 @ ( ordsucc @ X190 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.102bVFH1Jy/E---3.1_2793365.p',satz4f) ).
thf(satz4h,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X191: $i] : ( in @ X191 @ nat )
@ ^ [X192: $i] : ( n_is @ ( ordsucc @ ( n_pl @ X1 @ X192 ) ) @ ( n_pl @ ( ordsucc @ X1 ) @ X192 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.102bVFH1Jy/E---3.1_2793365.p',satz4h) ).
thf(satz4g,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ ( ordsucc @ X1 ) @ ( n_pl @ n_1 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.102bVFH1Jy/E---3.1_2793365.p',satz4g) ).
thf(satz5,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X194: $i] : ( in @ X194 @ nat )
@ ^ [X195: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] : ( n_is @ ( n_pl @ ( n_pl @ X1 @ X195 ) @ X4 ) @ ( n_pl @ X1 @ ( n_pl @ X195 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.102bVFH1Jy/E---3.1_2793365.p',satz5) ).
thf(n_1_p,axiom,
( is_of @ n_1
@ ^ [X1: $i] : ( in @ X1 @ nat ) ),
file('/export/starexec/sandbox/tmp/tmp.102bVFH1Jy/E---3.1_2793365.p',n_1_p) ).
thf(satz6,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X197: $i] : ( in @ X197 @ nat )
@ ^ [X198: $i] : ( n_is @ ( n_pl @ X1 @ X198 ) @ ( n_pl @ X198 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.102bVFH1Jy/E---3.1_2793365.p',satz6) ).
thf(satz8a,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X205: $i] : ( in @ X205 @ nat )
@ ^ [X206: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( n_is @ ( n_pl @ X1 @ X206 ) @ ( n_pl @ X1 @ X4 ) )
=> ( n_is @ X206 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.102bVFH1Jy/E---3.1_2793365.p',satz8a) ).
thf(ordsucc_inj,axiom,
! [X1: $i,X43: $i] :
( ( ( ordsucc @ X1 )
= ( ordsucc @ X43 ) )
=> ( X1 = X43 ) ),
file('/export/starexec/sandbox/tmp/tmp.102bVFH1Jy/E---3.1_2793365.p',ordsucc_inj) ).
thf(c_0_13,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_14,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_15,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_16,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_15]) ).
thf(c_0_18,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X297: $i] : ( in @ X297 @ nat )
@ ^ [X298: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( n_is @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X298 @ X4 ) )
=> ( n_is @ X1 @ X298 ) ) ) ) ),
inference(assume_negation,[status(cth)],[satz20b]) ).
thf(c_0_19,plain,
! [X376: $i] :
( ( in @ X376 @ nat )
=> ! [X375: $i] :
( ( in @ X375 @ nat )
=> ( ( ordsucc @ ( n_pl @ X376 @ X375 ) )
= ( n_pl @ X376 @ ( ordsucc @ X375 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz4f]),c_0_16]),c_0_17]) ).
thf(c_0_20,negated_conjecture,
~ ! [X368: $i] :
( ( in @ X368 @ nat )
=> ! [X367: $i] :
( ( in @ X367 @ nat )
=> ! [X366: $i] :
( ( in @ X366 @ nat )
=> ( ( ( n_pl @ X368 @ X366 )
= ( n_pl @ X367 @ X366 ) )
=> ( X368 = X367 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_18]),c_0_16]),c_0_17]) ).
thf(c_0_21,plain,
! [X910: $i,X911: $i] :
( ( ~ ( epred5_1 @ X911 @ X910 )
| ( X911
= ( ordsucc @ X910 ) ) )
& ( ( X911
!= ( ordsucc @ X910 ) )
| ( epred5_1 @ X911 @ X910 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])]) ).
thf(c_0_22,plain,
! [X536: $i,X537: $i] :
( ~ ( in @ X536 @ nat )
| ~ ( in @ X537 @ nat )
| ( ( ordsucc @ ( n_pl @ X536 @ X537 ) )
= ( n_pl @ X536 @ ( ordsucc @ X537 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
thf(c_0_23,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( in @ esk3_0 @ nat )
& ( ( n_pl @ esk1_0 @ esk3_0 )
= ( n_pl @ esk2_0 @ esk3_0 ) )
& ( esk1_0 != esk2_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
thf(c_0_24,plain,
! [X1: $i,X4: $i] :
( ( epred5_1 @ X1 @ X4 )
| ( X1
!= ( ordsucc @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_25,plain,
! [X1: $i,X4: $i] :
( ( ( ordsucc @ ( n_pl @ X1 @ X4 ) )
= ( n_pl @ X1 @ ( ordsucc @ X4 ) ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_26,negated_conjecture,
( ( n_pl @ esk1_0 @ esk3_0 )
= ( n_pl @ esk2_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_27,negated_conjecture,
in @ esk3_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_28,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_29,plain,
! [X378: $i] :
( ( in @ X378 @ nat )
=> ! [X377: $i] :
( ( in @ X377 @ nat )
=> ( ( ordsucc @ ( n_pl @ X378 @ X377 ) )
= ( n_pl @ ( ordsucc @ X378 ) @ X377 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz4h]),c_0_16]),c_0_17]) ).
thf(c_0_30,plain,
! [X1: $i] : ( epred5_1 @ ( ordsucc @ X1 ) @ X1 ),
inference(er,[status(thm)],[c_0_24]) ).
thf(c_0_31,negated_conjecture,
( ( ordsucc @ ( n_pl @ esk1_0 @ esk3_0 ) )
= ( n_pl @ esk2_0 @ ( ordsucc @ esk3_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]) ).
thf(c_0_32,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_33,plain,
! [X396: $i] :
( ( in @ X396 @ nat )
=> ( ( ordsucc @ X396 )
= ( n_pl @ n_1 @ X396 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz4g]),c_0_16]),c_0_17]) ).
thf(c_0_34,plain,
! [X538: $i,X539: $i] :
( ~ ( in @ X538 @ nat )
| ~ ( in @ X539 @ nat )
| ( ( ordsucc @ ( n_pl @ X538 @ X539 ) )
= ( n_pl @ ( ordsucc @ X538 ) @ X539 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])]) ).
thf(c_0_35,plain,
epred5_1 @ ( n_pl @ esk2_0 @ ( ordsucc @ esk3_0 ) ) @ ( n_pl @ esk1_0 @ esk3_0 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_36,negated_conjecture,
( ( n_pl @ esk2_0 @ ( ordsucc @ esk3_0 ) )
= ( n_pl @ esk1_0 @ ( ordsucc @ esk3_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_31]),c_0_27]),c_0_32])]) ).
thf(c_0_37,plain,
! [X557: $i] :
( ~ ( in @ X557 @ nat )
| ( ( ordsucc @ X557 )
= ( n_pl @ n_1 @ X557 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])]) ).
thf(c_0_38,plain,
! [X1: $i,X4: $i] :
( ( ( ordsucc @ ( n_pl @ X1 @ X4 ) )
= ( n_pl @ ( ordsucc @ X1 ) @ X4 ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_39,plain,
epred5_1 @ ( n_pl @ esk1_0 @ ( ordsucc @ esk3_0 ) ) @ ( n_pl @ esk1_0 @ esk3_0 ),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_40,plain,
! [X1: $i] :
( ( ( ordsucc @ X1 )
= ( n_pl @ n_1 @ X1 ) )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_41,negated_conjecture,
( ( n_pl @ ( ordsucc @ esk2_0 ) @ esk3_0 )
= ( n_pl @ esk1_0 @ ( ordsucc @ esk3_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_26]),c_0_31]),c_0_36]),c_0_27]),c_0_28])]) ).
thf(c_0_42,plain,
! [X1: $i,X4: $i] :
( ( X1
= ( ordsucc @ X4 ) )
| ~ ( epred5_1 @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_43,plain,
epred5_1 @ ( n_pl @ esk1_0 @ ( n_pl @ n_1 @ esk3_0 ) ) @ ( n_pl @ esk1_0 @ esk3_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_27])]) ).
thf(c_0_44,plain,
! [X381: $i] :
( ( in @ X381 @ nat )
=> ! [X380: $i] :
( ( in @ X380 @ nat )
=> ! [X379: $i] :
( ( in @ X379 @ nat )
=> ( ( n_pl @ ( n_pl @ X381 @ X380 ) @ X379 )
= ( n_pl @ X381 @ ( n_pl @ X380 @ X379 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz5]),c_0_16]),c_0_17]) ).
thf(c_0_45,negated_conjecture,
( ( n_pl @ ( n_pl @ n_1 @ esk2_0 ) @ esk3_0 )
= ( n_pl @ esk1_0 @ ( ordsucc @ esk3_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_40]),c_0_28])]) ).
thf(c_0_46,plain,
( ( n_pl @ esk1_0 @ ( ordsucc @ esk3_0 ) )
= ( n_pl @ esk1_0 @ ( n_pl @ n_1 @ esk3_0 ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_31]),c_0_36]) ).
thf(c_0_47,plain,
! [X540: $i,X541: $i,X542: $i] :
( ~ ( in @ X540 @ nat )
| ~ ( in @ X541 @ nat )
| ~ ( in @ X542 @ nat )
| ( ( n_pl @ ( n_pl @ X540 @ X541 ) @ X542 )
= ( n_pl @ X540 @ ( n_pl @ X541 @ X542 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])]) ).
thf(c_0_48,plain,
in @ n_1 @ nat,
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[n_1_p]),c_0_14]) ).
thf(c_0_49,plain,
! [X383: $i] :
( ( in @ X383 @ nat )
=> ! [X382: $i] :
( ( in @ X382 @ nat )
=> ( ( n_pl @ X383 @ X382 )
= ( n_pl @ X382 @ X383 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz6]),c_0_16]),c_0_17]) ).
thf(c_0_50,plain,
! [X903: $i,X904: $i,X905: $i] :
( ( ~ ( epred8_2 @ X905 @ X904 @ X903 )
| ( X904
= ( n_pl @ X905 @ X903 ) ) )
& ( ( X904
!= ( n_pl @ X905 @ X903 ) )
| ( epred8_2 @ X905 @ X904 @ X903 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])]) ).
thf(c_0_51,negated_conjecture,
( ( ordsucc @ ( n_pl @ esk1_0 @ esk3_0 ) )
= ( n_pl @ esk1_0 @ ( ordsucc @ esk3_0 ) ) ),
inference(rw,[status(thm)],[c_0_31,c_0_36]) ).
thf(c_0_52,negated_conjecture,
( ( n_pl @ ( n_pl @ n_1 @ esk2_0 ) @ esk3_0 )
= ( n_pl @ esk1_0 @ ( n_pl @ n_1 @ esk3_0 ) ) ),
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
thf(c_0_53,plain,
! [X1: $i,X4: $i,X5: $i] :
( ( ( n_pl @ ( n_pl @ X1 @ X4 ) @ X5 )
= ( n_pl @ X1 @ ( n_pl @ X4 @ X5 ) ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_54,plain,
in @ n_1 @ nat,
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_55,plain,
! [X543: $i,X544: $i] :
( ~ ( in @ X543 @ nat )
| ~ ( in @ X544 @ nat )
| ( ( n_pl @ X543 @ X544 )
= ( n_pl @ X544 @ X543 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])]) ).
thf(c_0_56,plain,
! [X1: $i,X4: $i,X5: $i] :
( ( epred8_2 @ X4 @ X1 @ X5 )
| ( X1
!= ( n_pl @ X4 @ X5 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_57,negated_conjecture,
( ( ordsucc @ ( n_pl @ esk1_0 @ esk3_0 ) )
= ( n_pl @ esk1_0 @ ( n_pl @ n_1 @ esk3_0 ) ) ),
inference(rw,[status(thm)],[c_0_51,c_0_46]) ).
thf(c_0_58,negated_conjecture,
( ( n_pl @ esk1_0 @ ( n_pl @ n_1 @ esk3_0 ) )
= ( n_pl @ n_1 @ ( n_pl @ esk1_0 @ esk3_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_26]),c_0_27]),c_0_28]),c_0_54])]) ).
thf(c_0_59,plain,
! [X1: $i,X4: $i] :
( ( ( n_pl @ X1 @ X4 )
= ( n_pl @ X4 @ X1 ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
thf(c_0_60,plain,
! [X1: $i,X4: $i] : ( epred8_2 @ X1 @ ( n_pl @ X1 @ X4 ) @ X4 ),
inference(er,[status(thm)],[c_0_56]) ).
thf(c_0_61,negated_conjecture,
( ( ordsucc @ ( n_pl @ esk1_0 @ esk3_0 ) )
= ( n_pl @ n_1 @ ( n_pl @ esk1_0 @ esk3_0 ) ) ),
inference(rw,[status(thm)],[c_0_57,c_0_58]) ).
thf(c_0_62,plain,
! [X1: $i,X4: $i] :
( ( ( ordsucc @ ( n_pl @ X1 @ X4 ) )
= ( n_pl @ X4 @ ( ordsucc @ X1 ) ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(spm,[status(thm)],[c_0_25,c_0_59]) ).
thf(c_0_63,plain,
! [X386: $i] :
( ( in @ X386 @ nat )
=> ! [X385: $i] :
( ( in @ X385 @ nat )
=> ! [X384: $i] :
( ( in @ X384 @ nat )
=> ( ( ( n_pl @ X386 @ X385 )
= ( n_pl @ X386 @ X384 ) )
=> ( X385 = X384 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz8a]),c_0_16]),c_0_17]) ).
thf(c_0_64,plain,
! [X1: $i,X4: $i] :
( ( epred8_2 @ X1 @ ( n_pl @ X4 @ X1 ) @ X4 )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(spm,[status(thm)],[c_0_60,c_0_59]) ).
thf(c_0_65,plain,
! [X620: $i,X621: $i] :
( ( ( ordsucc @ X620 )
!= ( ordsucc @ X621 ) )
| ( X620 = X621 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ordsucc_inj])])]) ).
thf(c_0_66,plain,
! [X4: $i,X1: $i] :
( ( epred5_1 @ ( n_pl @ X1 @ ( ordsucc @ X4 ) ) @ ( n_pl @ X1 @ X4 ) )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(spm,[status(thm)],[c_0_30,c_0_25]) ).
thf(c_0_67,negated_conjecture,
( ( n_pl @ esk3_0 @ ( ordsucc @ esk1_0 ) )
= ( n_pl @ n_1 @ ( n_pl @ esk1_0 @ esk3_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_32]),c_0_27])]) ).
thf(c_0_68,plain,
! [X545: $i,X546: $i,X547: $i] :
( ~ ( in @ X545 @ nat )
| ~ ( in @ X546 @ nat )
| ~ ( in @ X547 @ nat )
| ( ( n_pl @ X545 @ X546 )
!= ( n_pl @ X545 @ X547 ) )
| ( X546 = X547 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_63])])])]) ).
thf(c_0_69,plain,
! [X1: $i,X4: $i,X5: $i] :
( ( X4
= ( n_pl @ X1 @ X5 ) )
| ~ ( epred8_2 @ X1 @ X4 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_70,negated_conjecture,
epred8_2 @ esk3_0 @ ( n_pl @ esk1_0 @ esk3_0 ) @ esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_26]),c_0_27]),c_0_28])]) ).
thf(c_0_71,plain,
! [X1: $i,X4: $i] :
( ( X1 = X4 )
| ( ( ordsucc @ X1 )
!= ( ordsucc @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
thf(c_0_72,plain,
epred5_1 @ ( n_pl @ n_1 @ ( n_pl @ esk1_0 @ esk3_0 ) ) @ ( n_pl @ esk3_0 @ esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_32]),c_0_27])]) ).
thf(c_0_73,plain,
! [X1: $i,X4: $i,X5: $i] :
( ( X4 = X5 )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat )
| ( ( n_pl @ X1 @ X4 )
!= ( n_pl @ X1 @ X5 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
thf(c_0_74,plain,
( ( n_pl @ esk3_0 @ esk2_0 )
= ( n_pl @ esk1_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
thf(c_0_75,negated_conjecture,
! [X1: $i] :
( ( ( n_pl @ esk1_0 @ esk3_0 )
= X1 )
| ( ( n_pl @ n_1 @ ( n_pl @ esk1_0 @ esk3_0 ) )
!= ( ordsucc @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_71,c_0_61]) ).
thf(c_0_76,plain,
( ( ordsucc @ ( n_pl @ esk3_0 @ esk1_0 ) )
= ( n_pl @ n_1 @ ( n_pl @ esk1_0 @ esk3_0 ) ) ),
inference(spm,[status(thm)],[c_0_42,c_0_72]) ).
thf(c_0_77,plain,
! [X1: $i] :
( ( esk2_0 = X1 )
| ( ( n_pl @ esk3_0 @ X1 )
!= ( n_pl @ esk1_0 @ esk3_0 ) )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_28]),c_0_27])]) ).
thf(c_0_78,negated_conjecture,
( ( n_pl @ esk3_0 @ esk1_0 )
= ( n_pl @ esk1_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
thf(c_0_79,negated_conjecture,
esk1_0 != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_80,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_32])]),c_0_79]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM681^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n010.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 12:38:03 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.06/0.26 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.102bVFH1Jy/E---3.1_2793365.p
% 0.61/0.44 % Version: 3.5.1-ho
% 0.61/0.44 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.61/0.44 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.61/0.44 % Starting lpo1_fix with 900s (3) cores
% 0.61/0.44 % Starting full_lambda_9 with 300s (1) cores
% 0.61/0.44 % Starting almost_fo_4 with 300s (1) cores
% 0.61/0.44 % Starting new_ho_9 with 300s (1) cores
% 0.61/0.44 % Starting pre_casc_4 with 300s (1) cores
% 0.61/0.44 % Starting ho_unfolding_6 with 300s (1) cores
% 0.61/0.44 % full_lambda_9 with pid 2793379 completed with status 0
% 0.61/0.44 % Result found by full_lambda_9
% 0.61/0.44 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.61/0.44 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.61/0.44 % Starting lpo1_fix with 900s (3) cores
% 0.61/0.44 % Starting full_lambda_9 with 300s (1) cores
% 0.61/0.44 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.61/0.44 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.61/0.44 % Search class: HGHSM-FSLM32-DHSMMSBN
% 0.61/0.44 % partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.61/0.44 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.61/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.61/0.44 % SubtermCWHack with pid 2793385 completed with status 0
% 0.61/0.44 % Result found by SubtermCWHack
% 0.61/0.44 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.61/0.44 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.61/0.44 % Starting lpo1_fix with 900s (3) cores
% 0.61/0.44 % Starting full_lambda_9 with 300s (1) cores
% 0.61/0.44 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.61/0.44 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.61/0.44 % Search class: HGHSM-FSLM32-DHSMMSBN
% 0.61/0.44 % partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.61/0.44 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.61/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.61/0.44 % Preprocessing time : 0.003 s
% 0.61/0.44
% 0.61/0.44 % Proof found!
% 0.61/0.44 % SZS status Theorem
% 0.61/0.44 % SZS output start CNFRefutation
% See solution above
% 0.61/0.44 % Parsed axioms : 384
% 0.61/0.44 % Removed by relevancy pruning/SinE : 264
% 0.61/0.44 % Initial clauses : 325
% 0.61/0.44 % Removed in clause preprocessing : 171
% 0.61/0.44 % Initial clauses in saturation : 154
% 0.61/0.44 % Processed clauses : 1670
% 0.61/0.44 % ...of these trivial : 52
% 0.61/0.44 % ...subsumed : 786
% 0.61/0.44 % ...remaining for further processing : 832
% 0.61/0.44 % Other redundant clauses eliminated : 86
% 0.61/0.44 % Clauses deleted for lack of memory : 0
% 0.61/0.44 % Backward-subsumed : 2
% 0.61/0.44 % Backward-rewritten : 65
% 0.61/0.44 % Generated clauses : 6678
% 0.61/0.44 % ...of the previous two non-redundant : 6211
% 0.61/0.44 % ...aggressively subsumed : 0
% 0.61/0.44 % Contextual simplify-reflections : 2
% 0.61/0.44 % Paramodulations : 6574
% 0.61/0.44 % Factorizations : 2
% 0.61/0.44 % NegExts : 0
% 0.61/0.44 % Equation resolutions : 92
% 0.61/0.44 % Disequality decompositions : 0
% 0.61/0.44 % Total rewrite steps : 3289
% 0.61/0.44 % ...of those cached : 3180
% 0.61/0.44 % Propositional unsat checks : 0
% 0.61/0.44 % Propositional check models : 0
% 0.61/0.44 % Propositional check unsatisfiable : 0
% 0.61/0.44 % Propositional clauses : 0
% 0.61/0.44 % Propositional clauses after purity: 0
% 0.61/0.44 % Propositional unsat core size : 0
% 0.61/0.44 % Propositional preprocessing time : 0.000
% 0.61/0.44 % Propositional encoding time : 0.000
% 0.61/0.44 % Propositional solver time : 0.000
% 0.61/0.44 % Success case prop preproc time : 0.000
% 0.61/0.44 % Success case prop encoding time : 0.000
% 0.61/0.44 % Success case prop solver time : 0.000
% 0.61/0.44 % Current number of processed clauses : 753
% 0.61/0.44 % Positive orientable unit clauses : 80
% 0.61/0.44 % Positive unorientable unit clauses: 0
% 0.61/0.44 % Negative unit clauses : 387
% 0.61/0.44 % Non-unit-clauses : 286
% 0.61/0.44 % Current number of unprocessed clauses: 4594
% 0.61/0.44 % ...number of literals in the above : 14019
% 0.61/0.44 % Current number of archived formulas : 0
% 0.61/0.44 % Current number of archived clauses : 67
% 0.61/0.44 % Clause-clause subsumption calls (NU) : 12989
% 0.61/0.44 % Rec. Clause-clause subsumption calls : 8804
% 0.61/0.44 % Non-unit clause-clause subsumptions : 479
% 0.61/0.44 % Unit Clause-clause subsumption calls : 40995
% 0.61/0.44 % Rewrite failures with RHS unbound : 0
% 0.61/0.44 % BW rewrite match attempts : 48
% 0.61/0.44 % BW rewrite match successes : 8
% 0.61/0.44 % Condensation attempts : 0
% 0.61/0.44 % Condensation successes : 0
% 0.61/0.44 % Termbank termtop insertions : 149195
% 0.61/0.44 % Search garbage collected termcells : 14854
% 0.61/0.44
% 0.61/0.44 % -------------------------------------------------
% 0.61/0.44 % User time : 0.129 s
% 0.61/0.44 % System time : 0.013 s
% 0.61/0.44 % Total time : 0.142 s
% 0.61/0.44 % Maximum resident set size: 6304 pages
% 0.61/0.44
% 0.61/0.44 % -------------------------------------------------
% 0.61/0.44 % User time : 0.139 s
% 0.61/0.44 % System time : 0.019 s
% 0.61/0.44 % Total time : 0.158 s
% 0.61/0.44 % Maximum resident set size: 5376 pages
% 0.61/0.44 % E exiting
%------------------------------------------------------------------------------