%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP026^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:04:08 AM UTC 2026
% Result : Theorem 2.81s 0.66s
% Output : CNFRefutation 2.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 19
% Syntax : Number of formulae : 75 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 143 ( 31 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 468 ( 63 ~; 45 |; 4 &; 337 @)
% ( 5 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 105 ( 0 ^; 105 !; 0 ?; 105 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
set_a: $tType ).
thf(decl_sort2,type,
a: $tType ).
thf(decl_sort3,type,
nat: $tType ).
thf(decl_84,type,
minus_minus_nat: nat > nat > nat ).
thf(decl_88,type,
zero_zero_nat: nat ).
thf(decl_89,type,
suc: nat > nat ).
thf(decl_95,type,
ord_less_nat: nat > nat > $o ).
thf(decl_97,type,
ord_less_eq_nat: nat > nat > $o ).
thf(decl_113,type,
member_a: a > set_a > $o ).
thf(decl_116,type,
h1: set_a ).
thf(decl_120,type,
g: nat > a ).
thf(decl_121,type,
h2: a ).
thf(decl_122,type,
m2: nat ).
thf(decl_125,type,
xa: nat ).
thf(fact_76_less__nat__zero__code,axiom,
! [X8: nat] :
~ ( ord_less_nat @ X8 @ zero_zero_nat ),
file('/export/starexec/sandbox2/tmp/tmp.zIHU0thtgI/E---3.1_1082832.p',fact_76_less__nat__zero__code) ).
thf(fact_196_not__less__eq,axiom,
! [X234: nat,X8: nat] :
( ~ ( ord_less_nat @ X234 @ X8 )
<=> ( ord_less_nat @ X8 @ ( suc @ X234 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zIHU0thtgI/E---3.1_1082832.p',fact_196_not__less__eq) ).
thf(fact_252_diff__less__mono,axiom,
! [X291: nat,X168: nat,X248: nat] :
( ( ord_less_nat @ X291 @ X168 )
=> ( ( ord_less_eq_nat @ X248 @ X291 )
=> ( ord_less_nat @ ( minus_minus_nat @ X291 @ X248 ) @ ( minus_minus_nat @ X168 @ X248 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zIHU0thtgI/E---3.1_1082832.p',fact_252_diff__less__mono) ).
thf(fact_54_diff__is__0__eq,axiom,
! [X71: nat,X8: nat] :
( ( ( minus_minus_nat @ X71 @ X8 )
= zero_zero_nat )
<=> ( ord_less_eq_nat @ X71 @ X8 ) ),
file('/export/starexec/sandbox2/tmp/tmp.zIHU0thtgI/E---3.1_1082832.p',fact_54_diff__is__0__eq) ).
thf(fact_254_diff__less__Suc,axiom,
! [X293: nat,X8: nat] : ( ord_less_nat @ ( minus_minus_nat @ X293 @ X8 ) @ ( suc @ X293 ) ),
file('/export/starexec/sandbox2/tmp/tmp.zIHU0thtgI/E---3.1_1082832.p',fact_254_diff__less__Suc) ).
thf(conj_21,conjecture,
member_a @ ( g @ xa ) @ h1,
file('/export/starexec/sandbox2/tmp/tmp.zIHU0thtgI/E---3.1_1082832.p',conj_21) ).
thf(fact_222_less__imp__diff__less,axiom,
! [X173: nat,X104: nat,X8: nat] :
( ( ord_less_nat @ X173 @ X104 )
=> ( ord_less_nat @ ( minus_minus_nat @ X173 @ X8 ) @ X104 ) ),
file('/export/starexec/sandbox2/tmp/tmp.zIHU0thtgI/E---3.1_1082832.p',fact_222_less__imp__diff__less) ).
thf(fact_183_le__neq__implies__less,axiom,
! [X219: nat,X8: nat] :
( ( ord_less_eq_nat @ X219 @ X8 )
=> ( ( X219 != X8 )
=> ( ord_less_nat @ X219 @ X8 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zIHU0thtgI/E---3.1_1082832.p',fact_183_le__neq__implies__less) ).
thf(fact_184_less__or__eq__imp__le,axiom,
! [X220: nat,X8: nat] :
( ( ( ord_less_nat @ X220 @ X8 )
| ( X220 = X8 ) )
=> ( ord_less_eq_nat @ X220 @ X8 ) ),
file('/export/starexec/sandbox2/tmp/tmp.zIHU0thtgI/E---3.1_1082832.p',fact_184_less__or__eq__imp__le) ).
thf(fact_158_not__less__eq__eq,axiom,
! [X198: nat,X8: nat] :
( ~ ( ord_less_eq_nat @ X198 @ X8 )
<=> ( ord_less_eq_nat @ ( suc @ X8 ) @ X198 ) ),
file('/export/starexec/sandbox2/tmp/tmp.zIHU0thtgI/E---3.1_1082832.p',fact_158_not__less__eq__eq) ).
thf(fact_78_diff__diff__cancel,axiom,
! [X102: nat,X8: nat] :
( ( ord_less_eq_nat @ X102 @ X8 )
=> ( ( minus_minus_nat @ X8 @ ( minus_minus_nat @ X8 @ X102 ) )
= X102 ) ),
file('/export/starexec/sandbox2/tmp/tmp.zIHU0thtgI/E---3.1_1082832.p',fact_78_diff__diff__cancel) ).
thf(conj_1,hypothesis,
! [X401: nat] :
( ( ord_less_eq_nat @ X401 @ m2 )
=> ! [X170: nat] :
( ( ord_less_eq_nat @ X170 @ m2 )
=> ( ( ( g @ X401 )
= ( g @ X170 ) )
=> ( X401 = X170 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zIHU0thtgI/E---3.1_1082832.p',conj_1) ).
thf(conj_19,hypothesis,
ord_less_eq_nat @ xa @ ( minus_minus_nat @ m2 @ ( suc @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/tmp/tmp.zIHU0thtgI/E---3.1_1082832.p',conj_19) ).
thf(conj_3,hypothesis,
( ( g @ m2 )
= h2 ),
file('/export/starexec/sandbox2/tmp/tmp.zIHU0thtgI/E---3.1_1082832.p',conj_3) ).
thf(conj_20,hypothesis,
( ( ( g @ xa )
= h2 )
| ( member_a @ ( g @ xa ) @ h1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.zIHU0thtgI/E---3.1_1082832.p',conj_20) ).
thf(fact_143_less__irrefl__nat,axiom,
! [X8: nat] :
~ ( ord_less_nat @ X8 @ X8 ),
file('/export/starexec/sandbox2/tmp/tmp.zIHU0thtgI/E---3.1_1082832.p',fact_143_less__irrefl__nat) ).
thf(fact_256_diff__less,axiom,
! [X8: nat,X295: nat] :
( ( ord_less_nat @ zero_zero_nat @ X8 )
=> ( ( ord_less_nat @ zero_zero_nat @ X295 )
=> ( ord_less_nat @ ( minus_minus_nat @ X295 @ X8 ) @ X295 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zIHU0thtgI/E---3.1_1082832.p',fact_256_diff__less) ).
thf(fact_92_zero__less__Suc,axiom,
! [X8: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ X8 ) ),
file('/export/starexec/sandbox2/tmp/tmp.zIHU0thtgI/E---3.1_1082832.p',fact_92_zero__less__Suc) ).
thf(conj_16,hypothesis,
ord_less_nat @ zero_zero_nat @ m2,
file('/export/starexec/sandbox2/tmp/tmp.zIHU0thtgI/E---3.1_1082832.p',conj_16) ).
thf(c_0_19,plain,
! [X8: nat] :
~ ( ord_less_nat @ X8 @ zero_zero_nat ),
inference(fof_simplification,[status(thm)],[fact_76_less__nat__zero__code]) ).
thf(c_0_20,plain,
! [X234: nat,X8: nat] :
( ~ ( ord_less_nat @ X234 @ X8 )
<=> ( ord_less_nat @ X8 @ ( suc @ X234 ) ) ),
inference(fof_simplification,[status(thm)],[fact_196_not__less__eq]) ).
thf(c_0_21,plain,
! [X1240: nat,X1241: nat,X1242: nat] :
( ~ ( ord_less_nat @ X1240 @ X1241 )
| ~ ( ord_less_eq_nat @ X1242 @ X1240 )
| ( ord_less_nat @ ( minus_minus_nat @ X1240 @ X1242 ) @ ( minus_minus_nat @ X1241 @ X1242 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_252_diff__less__mono])])]) ).
thf(c_0_22,plain,
! [X1189: nat,X1190: nat] :
( ( ( ( minus_minus_nat @ X1189 @ X1190 )
!= zero_zero_nat )
| ( ord_less_eq_nat @ X1189 @ X1190 ) )
& ( ~ ( ord_less_eq_nat @ X1189 @ X1190 )
| ( ( minus_minus_nat @ X1189 @ X1190 )
= zero_zero_nat ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_54_diff__is__0__eq])])]) ).
thf(c_0_23,plain,
! [X1082: nat] :
~ ( ord_less_nat @ X1082 @ zero_zero_nat ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_19])]) ).
thf(c_0_24,plain,
! [X1022: nat,X1023: nat] :
( ( ( ord_less_nat @ X1022 @ X1023 )
| ( ord_less_nat @ X1023 @ ( suc @ X1022 ) ) )
& ( ~ ( ord_less_nat @ X1023 @ ( suc @ X1022 ) )
| ~ ( ord_less_nat @ X1022 @ X1023 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
thf(c_0_25,plain,
! [X1246: nat,X1247: nat] : ( ord_less_nat @ ( minus_minus_nat @ X1246 @ X1247 ) @ ( suc @ X1246 ) ),
inference(variable_rename,[status(thm)],[fact_254_diff__less__Suc]) ).
thf(c_0_26,plain,
! [X12: nat,X11: nat,X8: nat] :
( ( ord_less_nat @ ( minus_minus_nat @ X8 @ X12 ) @ ( minus_minus_nat @ X11 @ X12 ) )
| ~ ( ord_less_nat @ X8 @ X11 )
| ~ ( ord_less_eq_nat @ X12 @ X8 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_27,plain,
! [X8: nat,X11: nat] :
( ( ( minus_minus_nat @ X8 @ X11 )
= zero_zero_nat )
| ~ ( ord_less_eq_nat @ X8 @ X11 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_28,plain,
! [X8: nat] :
~ ( ord_less_nat @ X8 @ zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_29,negated_conjecture,
~ ( member_a @ ( g @ xa ) @ h1 ),
inference(assume_negation,[status(cth)],[conj_21]) ).
thf(c_0_30,plain,
! [X11: nat,X8: nat] :
( ~ ( ord_less_nat @ X8 @ ( suc @ X11 ) )
| ~ ( ord_less_nat @ X11 @ X8 ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_31,plain,
! [X11: nat,X8: nat] : ( ord_less_nat @ ( minus_minus_nat @ X8 @ X11 ) @ ( suc @ X8 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_32,plain,
! [X1232: nat,X1233: nat,X1234: nat] :
( ~ ( ord_less_nat @ X1232 @ X1233 )
| ( ord_less_nat @ ( minus_minus_nat @ X1232 @ X1234 ) @ X1233 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_222_less__imp__diff__less])])]) ).
thf(c_0_33,plain,
! [X219: nat,X8: nat] :
( ( ord_less_eq_nat @ X219 @ X8 )
=> ( ( X219 != X8 )
=> ( ord_less_nat @ X219 @ X8 ) ) ),
inference(fof_simplification,[status(thm)],[fact_183_le__neq__implies__less]) ).
thf(c_0_34,plain,
! [X979: nat,X980: nat] :
( ( ~ ( ord_less_nat @ X979 @ X980 )
| ( ord_less_eq_nat @ X979 @ X980 ) )
& ( ( X979 != X980 )
| ( ord_less_eq_nat @ X979 @ X980 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_184_less__or__eq__imp__le])])])]) ).
thf(c_0_35,plain,
! [X8: nat,X11: nat,X12: nat] :
( ~ ( ord_less_nat @ X8 @ X11 )
| ~ ( ord_less_eq_nat @ X12 @ X8 )
| ~ ( ord_less_eq_nat @ X11 @ X12 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
thf(c_0_36,plain,
! [X198: nat,X8: nat] :
( ~ ( ord_less_eq_nat @ X198 @ X8 )
<=> ( ord_less_eq_nat @ ( suc @ X8 ) @ X198 ) ),
inference(fof_simplification,[status(thm)],[fact_158_not__less__eq__eq]) ).
thf(c_0_37,negated_conjecture,
~ ( member_a @ ( g @ xa ) @ h1 ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
thf(c_0_38,plain,
! [X8: nat,X11: nat] :
~ ( ord_less_nat @ X8 @ ( minus_minus_nat @ X8 @ X11 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_39,plain,
! [X8: nat,X12: nat,X11: nat] :
( ( ord_less_nat @ ( minus_minus_nat @ X8 @ X12 ) @ X11 )
| ~ ( ord_less_nat @ X8 @ X11 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_40,plain,
! [X1193: nat,X1194: nat] :
( ~ ( ord_less_eq_nat @ X1193 @ X1194 )
| ( ( minus_minus_nat @ X1194 @ ( minus_minus_nat @ X1194 @ X1193 ) )
= X1193 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_78_diff__diff__cancel])])]) ).
thf(c_0_41,plain,
! [X977: nat,X978: nat] :
( ~ ( ord_less_eq_nat @ X977 @ X978 )
| ( X977 = X978 )
| ( ord_less_nat @ X977 @ X978 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])]) ).
thf(c_0_42,hypothesis,
! [X839: nat,X840: nat] :
( ~ ( ord_less_eq_nat @ X839 @ m2 )
| ~ ( ord_less_eq_nat @ X840 @ m2 )
| ( ( g @ X839 )
!= ( g @ X840 ) )
| ( X839 = X840 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_1])])])]) ).
thf(c_0_43,plain,
! [X8: nat,X11: nat] :
( ( ord_less_eq_nat @ X8 @ X11 )
| ( X8 != X11 ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_44,plain,
! [X12: nat,X11: nat,X8: nat] :
( ~ ( ord_less_eq_nat @ X8 @ ( minus_minus_nat @ X11 @ X12 ) )
| ~ ( ord_less_eq_nat @ ( suc @ X11 ) @ X8 ) ),
inference(spm,[status(thm)],[c_0_35,c_0_31]) ).
thf(c_0_45,hypothesis,
ord_less_eq_nat @ xa @ ( minus_minus_nat @ m2 @ ( suc @ zero_zero_nat ) ),
inference(split_conjunct,[status(thm)],[conj_19]) ).
thf(c_0_46,plain,
! [X1282: nat,X1283: nat] :
( ( ( ord_less_eq_nat @ X1282 @ X1283 )
| ( ord_less_eq_nat @ ( suc @ X1283 ) @ X1282 ) )
& ( ~ ( ord_less_eq_nat @ ( suc @ X1283 ) @ X1282 )
| ~ ( ord_less_eq_nat @ X1282 @ X1283 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])]) ).
thf(c_0_47,negated_conjecture,
~ ( member_a @ ( g @ xa ) @ h1 ),
inference(fof_nnf,[status(thm)],[c_0_37]) ).
thf(c_0_48,plain,
! [X8: nat,X11: nat,X12: nat] :
~ ( ord_less_nat @ X8 @ ( minus_minus_nat @ ( minus_minus_nat @ X8 @ X11 ) @ X12 ) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
thf(c_0_49,plain,
! [X8: nat,X11: nat] :
( ( ( minus_minus_nat @ X11 @ ( minus_minus_nat @ X11 @ X8 ) )
= X8 )
| ~ ( ord_less_eq_nat @ X8 @ X11 ) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_50,plain,
! [X8: nat,X11: nat] :
( ( X8 = X11 )
| ( ord_less_nat @ X8 @ X11 )
| ~ ( ord_less_eq_nat @ X8 @ X11 ) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_51,hypothesis,
! [X8: nat,X11: nat] :
( ( X8 = X11 )
| ~ ( ord_less_eq_nat @ X8 @ m2 )
| ~ ( ord_less_eq_nat @ X11 @ m2 )
| ( ( g @ X8 )
!= ( g @ X11 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_52,plain,
! [X8: nat] : ( ord_less_eq_nat @ X8 @ X8 ),
inference(er,[status(thm)],[c_0_43]) ).
thf(c_0_53,hypothesis,
( ( g @ m2 )
= h2 ),
inference(split_conjunct,[status(thm)],[conj_3]) ).
thf(c_0_54,hypothesis,
~ ( ord_less_eq_nat @ ( suc @ m2 ) @ xa ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_55,plain,
! [X11: nat,X8: nat] :
( ( ord_less_eq_nat @ X8 @ X11 )
| ( ord_less_eq_nat @ ( suc @ X11 ) @ X8 ) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_56,hypothesis,
( ( ( g @ xa )
= h2 )
| ( member_a @ ( g @ xa ) @ h1 ) ),
inference(split_conjunct,[status(thm)],[conj_20]) ).
thf(c_0_57,negated_conjecture,
~ ( member_a @ ( g @ xa ) @ h1 ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_58,plain,
! [X12: nat,X11: nat,X8: nat] :
( ~ ( ord_less_nat @ X8 @ ( minus_minus_nat @ X11 @ X12 ) )
| ~ ( ord_less_eq_nat @ X11 @ X8 ) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
thf(c_0_59,hypothesis,
( ( ( minus_minus_nat @ m2 @ ( suc @ zero_zero_nat ) )
= xa )
| ( ord_less_nat @ xa @ ( minus_minus_nat @ m2 @ ( suc @ zero_zero_nat ) ) ) ),
inference(spm,[status(thm)],[c_0_50,c_0_45]) ).
thf(c_0_60,hypothesis,
! [X8: nat] :
( ( X8 = m2 )
| ( ( g @ X8 )
!= h2 )
| ~ ( ord_less_eq_nat @ X8 @ m2 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
thf(c_0_61,hypothesis,
ord_less_eq_nat @ xa @ m2,
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
thf(c_0_62,hypothesis,
( ( g @ xa )
= h2 ),
inference(sr,[status(thm)],[c_0_56,c_0_57]) ).
thf(c_0_63,plain,
! [X8: nat] :
~ ( ord_less_nat @ X8 @ X8 ),
inference(fof_simplification,[status(thm)],[fact_143_less__irrefl__nat]) ).
thf(c_0_64,plain,
! [X1250: nat,X1251: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ X1250 )
| ~ ( ord_less_nat @ zero_zero_nat @ X1251 )
| ( ord_less_nat @ ( minus_minus_nat @ X1251 @ X1250 ) @ X1251 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_256_diff__less])])]) ).
thf(c_0_65,hypothesis,
( ( ( minus_minus_nat @ m2 @ ( suc @ zero_zero_nat ) )
= xa )
| ~ ( ord_less_eq_nat @ m2 @ xa ) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
thf(c_0_66,hypothesis,
xa = m2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62])]) ).
thf(c_0_67,plain,
! [X1084: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ X1084 ) ),
inference(variable_rename,[status(thm)],[fact_92_zero__less__Suc]) ).
thf(c_0_68,plain,
! [X964: nat] :
~ ( ord_less_nat @ X964 @ X964 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_63])]) ).
thf(c_0_69,plain,
! [X8: nat,X11: nat] :
( ( ord_less_nat @ ( minus_minus_nat @ X11 @ X8 ) @ X11 )
| ~ ( ord_less_nat @ zero_zero_nat @ X8 )
| ~ ( ord_less_nat @ zero_zero_nat @ X11 ) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
thf(c_0_70,hypothesis,
( ( minus_minus_nat @ m2 @ ( suc @ zero_zero_nat ) )
= m2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66]),c_0_66]),c_0_52])]) ).
thf(c_0_71,hypothesis,
ord_less_nat @ zero_zero_nat @ m2,
inference(split_conjunct,[status(thm)],[conj_16]) ).
thf(c_0_72,plain,
! [X8: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ X8 ) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
thf(c_0_73,plain,
! [X8: nat] :
~ ( ord_less_nat @ X8 @ X8 ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
thf(c_0_74,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]),c_0_72])]),c_0_73]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP026^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n026.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 19:40:57 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.21/0.30 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.zIHU0thtgI/E---3.1_1082832.p
% 2.81/0.66 % Version: 3.5.1-ho
% 2.81/0.66 % Preprocessing class: HSLMSMSMSSLNHSA.
% 2.81/0.66 % Scheduled 7 strats onto 8 cores with 300 seconds (2400 total)
% 2.81/0.66 % Starting new_bool_8 with 600s (2) cores
% 2.81/0.66 % Starting new_ho_3 with 300s (1) cores
% 2.81/0.66 % Starting additional_ho_3 with 300s (1) cores
% 2.81/0.66 % Starting full_lambda_10 with 300s (1) cores
% 2.81/0.66 % Starting ehoh_best with 300s (1) cores
% 2.81/0.66 % Starting sh2lt with 300s (1) cores
% 2.81/0.66 % Starting full_lambda_4 with 300s (1) cores
% 2.81/0.66 % new_bool_8 with pid 1082899 completed with status 0
% 2.81/0.66 % Result found by new_bool_8
% 2.81/0.66 % Preprocessing class: HSLMSMSMSSLNHSA.
% 2.81/0.66 % Scheduled 7 strats onto 8 cores with 300 seconds (2400 total)
% 2.81/0.66 % Starting new_bool_8 with 600s (2) cores
% 2.81/0.66 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1,,2,20000,1.0))
% 2.81/0.66 % SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 2.81/0.66 % Search class: HGHSM-FSLM31-MHSFFSBN
% 2.81/0.66 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 2.81/0.66 % Starting SubtermCWHack with 55s (1) cores
% 2.81/0.66 % Starting new_bool_8 with 61s (1) cores
% 2.81/0.66 % new_bool_8 with pid 1082907 completed with status 0
% 2.81/0.66 % Result found by new_bool_8
% 2.81/0.66 % Preprocessing class: HSLMSMSMSSLNHSA.
% 2.81/0.66 % Scheduled 7 strats onto 8 cores with 300 seconds (2400 total)
% 2.81/0.66 % Starting new_bool_8 with 600s (2) cores
% 2.81/0.66 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1,,2,20000,1.0))
% 2.81/0.66 % SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 2.81/0.66 % Search class: HGHSM-FSLM31-MHSFFSBN
% 2.81/0.66 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 2.81/0.66 % Starting SubtermCWHack with 55s (1) cores
% 2.81/0.66 % Starting new_bool_8 with 61s (1) cores
% 2.81/0.66 % Preprocessing time : 0.007 s
% 2.81/0.66 % Presaturation interreduction done
% 2.81/0.66
% 2.81/0.66 % Proof found!
% 2.81/0.66 % SZS status Theorem
% 2.81/0.66 % SZS output start CNFRefutation
% See solution above
% 2.81/0.66 % Parsed axioms : 493
% 2.81/0.66 % Removed by relevancy pruning/SinE : 295
% 2.81/0.66 % Initial clauses : 329
% 2.81/0.66 % Removed in clause preprocessing : 4
% 2.81/0.66 % Initial clauses in saturation : 325
% 2.81/0.66 % Processed clauses : 1844
% 2.81/0.66 % ...of these trivial : 36
% 2.81/0.66 % ...subsumed : 920
% 2.81/0.66 % ...remaining for further processing : 888
% 2.81/0.66 % Other redundant clauses eliminated : 85
% 2.81/0.66 % Clauses deleted for lack of memory : 0
% 2.81/0.66 % Backward-subsumed : 15
% 2.81/0.66 % Backward-rewritten : 56
% 2.81/0.66 % Generated clauses : 9384
% 2.81/0.66 % ...of the previous two non-redundant : 8626
% 2.81/0.66 % ...aggressively subsumed : 0
% 2.81/0.66 % Contextual simplify-reflections : 1
% 2.81/0.66 % Paramodulations : 9268
% 2.81/0.66 % Factorizations : 6
% 2.81/0.66 % NegExts : 0
% 2.81/0.66 % Equation resolutions : 89
% 2.81/0.66 % Disequality decompositions : 0
% 2.81/0.66 % Total rewrite steps : 2091
% 2.81/0.66 % ...of those cached : 1757
% 2.81/0.66 % Propositional unsat checks : 0
% 2.81/0.66 % Propositional check models : 0
% 2.81/0.66 % Propositional check unsatisfiable : 0
% 2.81/0.66 % Propositional clauses : 0
% 2.81/0.66 % Propositional clauses after purity: 0
% 2.81/0.66 % Propositional unsat core size : 0
% 2.81/0.66 % Propositional preprocessing time : 0.000
% 2.81/0.66 % Propositional encoding time : 0.000
% 2.81/0.66 % Propositional solver time : 0.000
% 2.81/0.66 % Success case prop preproc time : 0.000
% 2.81/0.66 % Success case prop encoding time : 0.000
% 2.81/0.66 % Success case prop solver time : 0.000
% 2.81/0.66 % Current number of processed clauses : 537
% 2.81/0.66 % Positive orientable unit clauses : 70
% 2.81/0.66 % Positive unorientable unit clauses: 5
% 2.81/0.66 % Negative unit clauses : 27
% 2.81/0.66 % Non-unit-clauses : 435
% 2.81/0.66 % Current number of unprocessed clauses: 7273
% 2.81/0.66 % ...number of literals in the above : 23428
% 2.81/0.66 % Current number of archived formulas : 0
% 2.81/0.66 % Current number of archived clauses : 321
% 2.81/0.66 % Clause-clause subsumption calls (NU) : 28123
% 2.81/0.66 % Rec. Clause-clause subsumption calls : 20763
% 2.81/0.66 % Non-unit clause-clause subsumptions : 450
% 2.81/0.66 % Unit Clause-clause subsumption calls : 834
% 2.81/0.66 % Rewrite failures with RHS unbound : 36
% 2.81/0.66 % BW rewrite match attempts : 71
% 2.81/0.66 % BW rewrite match successes : 20
% 2.81/0.66 % Condensation attempts : 0
% 2.81/0.66 % Condensation successes : 0
% 2.81/0.66 % Termbank termtop insertions : 151342
% 2.81/0.66 % Search garbage collected termcells : 9387
% 2.81/0.66
% 2.81/0.66 % -------------------------------------------------
% 2.81/0.66 % User time : 0.280 s
% 2.81/0.66 % System time : 0.019 s
% 2.81/0.66 % Total time : 0.300 s
% 2.81/0.66 % Maximum resident set size: 5804 pages
% 2.81/0.66
% 2.81/0.66 % -------------------------------------------------
% 2.81/0.66 % User time : 0.554 s
% 2.81/0.66 % System time : 0.043 s
% 2.81/0.66 % Total time : 0.598 s
% 2.81/0.66 % Maximum resident set size: 5632 pages
% 2.81/0.66 % E exiting
%------------------------------------------------------------------------------