%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP149^1 : 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 : n016.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 08:04:30 AM UTC 2026
% Result : Theorem 166.18s 24.99s
% Output : CNFRefutation 166.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 62 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 104 ( 41 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 603 ( 35 ~; 24 |; 12 &; 526 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 9 con; 0-2 aty)
% Number of variables : 94 ( 4 ^; 86 !; 4 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
real: $tType ).
thf(decl_sort2,type,
set_a: $tType ).
thf(decl_sort3,type,
a: $tType ).
thf(decl_24,type,
elemen49976720ball_a: a > real > set_a ).
thf(decl_29,type,
minus_minus_a: a > a > a ).
thf(decl_30,type,
uminus_uminus_a_a: ( a > a ) > a > a ).
thf(decl_31,type,
uminus_uminus_real: real > real ).
thf(decl_34,type,
uminus_uminus_a: a > a ).
thf(decl_35,type,
zero_zero_real: real ).
thf(decl_36,type,
zero_zero_a: a ).
thf(decl_39,type,
inner_1173012732nner_a: a > a > real ).
thf(decl_44,type,
ord_less_real: real > real > $o ).
thf(decl_50,type,
ord_less_eq_real: real > real > $o ).
thf(decl_61,type,
poinca659159244_rot_a: a > a ).
thf(decl_77,type,
member_a: a > set_a > $o ).
thf(decl_78,type,
x: set_a ).
thf(decl_79,type,
a2: a ).
thf(decl_80,type,
b: a ).
thf(decl_81,type,
d: real ).
thf(decl_82,type,
f: a > a ).
thf(decl_85,type,
x2: a ).
thf(decl_87,type,
esk1_2: real > real > a ).
thf(decl_97,type,
esk11_0: a ).
thf(fact_225_uminus__apply,axiom,
( uminus_uminus_a_a
= ( ^ [X234: a > a,X29: a] : ( uminus_uminus_a @ ( X234 @ X29 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rD2iJHzmGc/E---3.1_841684.p',fact_225_uminus__apply) ).
thf(fact_203_diff__0,axiom,
! [X16: a] :
( ( minus_minus_a @ zero_zero_a @ X16 )
= ( uminus_uminus_a @ X16 ) ),
file('/export/starexec/sandbox2/tmp/tmp.rD2iJHzmGc/E---3.1_841684.p',fact_203_diff__0) ).
thf(conj_0,conjecture,
? [X124: real] :
( ( ord_less_real @ zero_zero_real @ X124 )
& ? [X437: real] :
( ( ord_less_real @ zero_zero_real @ X437 )
& ! [X107: a] :
( ( member_a @ X107 @ ( elemen49976720ball_a @ x2 @ X124 ) )
=> ( ord_less_eq_real @ X437 @ ( inner_1173012732nner_a @ ( f @ X107 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rD2iJHzmGc/E---3.1_841684.p',conj_0) ).
thf(fact_77_inner__commute,axiom,
( inner_1173012732nner_a
= ( ^ [X29: a,X56: a] : ( inner_1173012732nner_a @ X56 @ X29 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rD2iJHzmGc/E---3.1_841684.p',fact_77_inner__commute) ).
thf(fact_228_rot__diff__commute,axiom,
! [X17: a,X16: a] :
( ( poinca659159244_rot_a @ ( minus_minus_a @ X17 @ X16 ) )
= ( uminus_uminus_a @ ( poinca659159244_rot_a @ ( minus_minus_a @ X16 @ X17 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rD2iJHzmGc/E---3.1_841684.p',fact_228_rot__diff__commute) ).
thf(fact_156_add_Oinverse__inverse,axiom,
! [X16: a] :
( ( uminus_uminus_a @ ( uminus_uminus_a @ X16 ) )
= X16 ),
file('/export/starexec/sandbox2/tmp/tmp.rD2iJHzmGc/E---3.1_841684.p',fact_156_add_Oinverse__inverse) ).
thf(fact_182_minus__diff__eq,axiom,
! [X16: a,X17: a] :
( ( uminus_uminus_a @ ( minus_minus_a @ X16 @ X17 ) )
= ( minus_minus_a @ X17 @ X16 ) ),
file('/export/starexec/sandbox2/tmp/tmp.rD2iJHzmGc/E---3.1_841684.p',fact_182_minus__diff__eq) ).
thf(fact_42_diff__zero,axiom,
! [X16: a] :
( ( minus_minus_a @ X16 @ zero_zero_a )
= X16 ),
file('/export/starexec/sandbox2/tmp/tmp.rD2iJHzmGc/E---3.1_841684.p',fact_42_diff__zero) ).
thf(fact_11__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062s_O_A_092_060lbrakk_062s_A_092_060in_062_Acball_Ax_Ad_059_A_092_060forall_062x_092_060in_062cball_Ax_Ad_O_Af_As_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_A_092_060le_062_Af_Ax_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
~ ! [X4: a] :
( ( member_a @ X4 @ ( elemen49976720ball_a @ x2 @ d ) )
=> ~ ! [X3: a] :
( ( member_a @ X3 @ ( elemen49976720ball_a @ x2 @ d ) )
=> ( ord_less_eq_real @ ( inner_1173012732nner_a @ ( f @ X4 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) @ ( inner_1173012732nner_a @ ( f @ X3 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rD2iJHzmGc/E---3.1_841684.p',fact_11__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062s_O_A_092_060lbrakk_062s_A_092_060in_062_Acball_Ax_Ad_059_A_092_060forall_062x_092_060in_062cball_Ax_Ad_O_Af_As_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_A_092_060le_062_Af_Ax_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(fact_8_d_I2_J,axiom,
! [X2: a] :
( ( member_a @ X2 @ ( elemen49976720ball_a @ x2 @ d ) )
=> ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ X2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
& ( member_a @ X2 @ x )
& ( ( f @ X2 )
!= zero_zero_a ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rD2iJHzmGc/E---3.1_841684.p',fact_8_d_I2_J) ).
thf(fact_185_inner__minus__left,axiom,
! [X1: a,X2: a] :
( ( inner_1173012732nner_a @ ( uminus_uminus_a @ X1 ) @ X2 )
= ( uminus_uminus_real @ ( inner_1173012732nner_a @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rD2iJHzmGc/E---3.1_841684.p',fact_185_inner__minus__left) ).
thf(fact_187_inner__minus__right,axiom,
! [X1: a,X2: a] :
( ( inner_1173012732nner_a @ X1 @ ( uminus_uminus_a @ X2 ) )
= ( uminus_uminus_real @ ( inner_1173012732nner_a @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rD2iJHzmGc/E---3.1_841684.p',fact_187_inner__minus__right) ).
thf(fact_0_d_I1_J,axiom,
ord_less_real @ zero_zero_real @ d,
file('/export/starexec/sandbox2/tmp/tmp.rD2iJHzmGc/E---3.1_841684.p',fact_0_d_I1_J) ).
thf(c_0_13,plain,
! [X1094: a > a,X1095: a] :
( ( uminus_uminus_a_a @ X1094 @ X1095 )
= ( uminus_uminus_a @ ( X1094 @ X1095 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_225_uminus__apply])]) ).
thf(c_0_14,plain,
! [X1698: a > a,X1699: a] :
( ( uminus_uminus_a_a @ X1698 @ X1699 )
= ( uminus_uminus_a @ ( X1698 @ X1699 ) ) ),
inference(variable_rename,[status(thm)],[c_0_13]) ).
thf(c_0_15,plain,
! [X1329: a] :
( ( minus_minus_a @ zero_zero_a @ X1329 )
= ( uminus_uminus_a @ X1329 ) ),
inference(variable_rename,[status(thm)],[fact_203_diff__0]) ).
thf(c_0_16,negated_conjecture,
~ ? [X124: real] :
( ( ord_less_real @ zero_zero_real @ X124 )
& ? [X437: real] :
( ( ord_less_real @ zero_zero_real @ X437 )
& ! [X107: a] :
( ( member_a @ X107 @ ( elemen49976720ball_a @ x2 @ X124 ) )
=> ( ord_less_eq_real @ X437 @ ( inner_1173012732nner_a @ ( f @ X107 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_17,plain,
! [X1056: a,X1057: a] :
( ( inner_1173012732nner_a @ X1056 @ X1057 )
= ( inner_1173012732nner_a @ X1057 @ X1056 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_77_inner__commute])]) ).
thf(c_0_18,plain,
! [X1275: a,X1276: a] :
( ( poinca659159244_rot_a @ ( minus_minus_a @ X1275 @ X1276 ) )
= ( uminus_uminus_a @ ( poinca659159244_rot_a @ ( minus_minus_a @ X1276 @ X1275 ) ) ) ),
inference(variable_rename,[status(thm)],[fact_228_rot__diff__commute]) ).
thf(c_0_19,plain,
! [X234: a > a,X1: a] :
( ( uminus_uminus_a_a @ X234 @ X1 )
= ( uminus_uminus_a @ ( X234 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_20,plain,
! [X1: a] :
( ( minus_minus_a @ zero_zero_a @ X1 )
= ( uminus_uminus_a @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_21,plain,
! [X1702: a] :
( ( uminus_uminus_a @ ( uminus_uminus_a @ X1702 ) )
= X1702 ),
inference(variable_rename,[status(thm)],[fact_156_add_Oinverse__inverse]) ).
thf(c_0_22,plain,
! [X1327: a,X1328: a] :
( ( uminus_uminus_a @ ( minus_minus_a @ X1327 @ X1328 ) )
= ( minus_minus_a @ X1328 @ X1327 ) ),
inference(variable_rename,[status(thm)],[fact_182_minus__diff__eq]) ).
thf(c_0_23,negated_conjecture,
! [X1098: real,X1099: real] :
( ( ( member_a @ ( esk1_2 @ X1098 @ X1099 ) @ ( elemen49976720ball_a @ x2 @ X1098 ) )
| ~ ( ord_less_real @ zero_zero_real @ X1099 )
| ~ ( ord_less_real @ zero_zero_real @ X1098 ) )
& ( ~ ( ord_less_eq_real @ X1099 @ ( inner_1173012732nner_a @ ( f @ ( esk1_2 @ X1098 @ X1099 ) ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
| ~ ( ord_less_real @ zero_zero_real @ X1099 )
| ~ ( ord_less_real @ zero_zero_real @ X1098 ) ) ),
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_16])])])])])]) ).
thf(c_0_24,plain,
! [X1256: a,X1257: a] :
( ( inner_1173012732nner_a @ X1256 @ X1257 )
= ( inner_1173012732nner_a @ X1257 @ X1256 ) ),
inference(variable_rename,[status(thm)],[c_0_17]) ).
thf(c_0_25,plain,
! [X2: a,X1: a] :
( ( poinca659159244_rot_a @ ( minus_minus_a @ X1 @ X2 ) )
= ( uminus_uminus_a @ ( poinca659159244_rot_a @ ( minus_minus_a @ X2 @ X1 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_26,plain,
! [X234: a > a,X1: a] :
( ( uminus_uminus_a_a @ X234 @ X1 )
= ( minus_minus_a @ zero_zero_a @ ( X234 @ X1 ) ) ),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_27,plain,
! [X1: a] :
( ( uminus_uminus_a @ ( uminus_uminus_a @ X1 ) )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_28,plain,
! [X1283: a] :
( ( minus_minus_a @ X1283 @ zero_zero_a )
= X1283 ),
inference(variable_rename,[status(thm)],[fact_42_diff__zero]) ).
thf(c_0_29,plain,
! [X2: a,X1: a] :
( ( uminus_uminus_a @ ( minus_minus_a @ X1 @ X2 ) )
= ( minus_minus_a @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_30,plain,
! [X1335: a] :
( ( member_a @ esk11_0 @ ( elemen49976720ball_a @ x2 @ d ) )
& ( ~ ( member_a @ X1335 @ ( elemen49976720ball_a @ x2 @ d ) )
| ( ord_less_eq_real @ ( inner_1173012732nner_a @ ( f @ esk11_0 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) @ ( inner_1173012732nner_a @ ( f @ X1335 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_11__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062s_O_A_092_060lbrakk_062s_A_092_060in_062_Acball_Ax_Ad_059_A_092_060forall_062x_092_060in_062cball_Ax_Ad_O_Af_As_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_A_092_060le_062_Af_Ax_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062])])])])]) ).
thf(c_0_31,plain,
! [X2: a] :
( ( member_a @ X2 @ ( elemen49976720ball_a @ x2 @ d ) )
=> ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ X2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
& ( member_a @ X2 @ x )
& ( ( f @ X2 )
!= zero_zero_a ) ) ),
inference(fof_simplification,[status(thm)],[fact_8_d_I2_J]) ).
thf(c_0_32,negated_conjecture,
! [X5: real,X7: real] :
( ~ ( ord_less_eq_real @ X5 @ ( inner_1173012732nner_a @ ( f @ ( esk1_2 @ X7 @ X5 ) ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
| ~ ( ord_less_real @ zero_zero_real @ X5 )
| ~ ( ord_less_real @ zero_zero_real @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_33,plain,
! [X2: a,X1: a] :
( ( inner_1173012732nner_a @ X1 @ X2 )
= ( inner_1173012732nner_a @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_34,plain,
! [X2: a,X1: a] :
( ( poinca659159244_rot_a @ ( minus_minus_a @ X1 @ X2 ) )
= ( uminus_uminus_a_a @ poinca659159244_rot_a @ ( minus_minus_a @ X2 @ X1 ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_20]),c_0_26]) ).
thf(c_0_35,plain,
! [X1: a] :
( ( minus_minus_a @ zero_zero_a @ ( minus_minus_a @ zero_zero_a @ X1 ) )
= X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_20]),c_0_20]) ).
thf(c_0_36,plain,
! [X1: a] :
( ( minus_minus_a @ X1 @ zero_zero_a )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_37,plain,
! [X2: a,X1: a] :
( ( minus_minus_a @ zero_zero_a @ ( minus_minus_a @ X1 @ X2 ) )
= ( minus_minus_a @ X2 @ X1 ) ),
inference(rw,[status(thm)],[c_0_29,c_0_20]) ).
thf(c_0_38,plain,
! [X1267: a,X1268: a] :
( ( inner_1173012732nner_a @ ( uminus_uminus_a @ X1267 ) @ X1268 )
= ( uminus_uminus_real @ ( inner_1173012732nner_a @ X1267 @ X1268 ) ) ),
inference(variable_rename,[status(thm)],[fact_185_inner__minus__left]) ).
thf(c_0_39,plain,
! [X1: a] :
( ( ord_less_eq_real @ ( inner_1173012732nner_a @ ( f @ esk11_0 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) @ ( inner_1173012732nner_a @ ( f @ X1 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
| ~ ( member_a @ X1 @ ( elemen49976720ball_a @ x2 @ d ) ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_40,plain,
! [X1269: a,X1270: a] :
( ( inner_1173012732nner_a @ X1269 @ ( uminus_uminus_a @ X1270 ) )
= ( uminus_uminus_real @ ( inner_1173012732nner_a @ X1269 @ X1270 ) ) ),
inference(variable_rename,[status(thm)],[fact_187_inner__minus__right]) ).
thf(c_0_41,plain,
! [X1333: a] :
( ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ X1333 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
| ~ ( member_a @ X1333 @ ( elemen49976720ball_a @ x2 @ d ) ) )
& ( ( member_a @ X1333 @ x )
| ~ ( member_a @ X1333 @ ( elemen49976720ball_a @ x2 @ d ) ) )
& ( ( ( f @ X1333 )
!= zero_zero_a )
| ~ ( member_a @ X1333 @ ( elemen49976720ball_a @ x2 @ d ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])]) ).
thf(c_0_42,negated_conjecture,
! [X7: real,X5: real] :
( ~ ( ord_less_eq_real @ X5 @ ( inner_1173012732nner_a @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) @ ( f @ ( esk1_2 @ X7 @ X5 ) ) ) )
| ~ ( ord_less_real @ zero_zero_real @ X7 )
| ~ ( ord_less_real @ zero_zero_real @ X5 ) ),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_43,plain,
! [X1: a] :
( ( poinca659159244_rot_a @ X1 )
= ( uminus_uminus_a_a @ poinca659159244_rot_a @ ( minus_minus_a @ zero_zero_a @ X1 ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
thf(c_0_44,plain,
! [X234: a > a,X1: a] :
( ( minus_minus_a @ zero_zero_a @ ( uminus_uminus_a_a @ X234 @ X1 ) )
= ( X234 @ X1 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_26]),c_0_36]) ).
thf(c_0_45,plain,
! [X1: a,X2: a] :
( ( inner_1173012732nner_a @ ( uminus_uminus_a @ X1 ) @ X2 )
= ( uminus_uminus_real @ ( inner_1173012732nner_a @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_46,plain,
! [X1: a] :
( ( ord_less_eq_real @ ( inner_1173012732nner_a @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) @ ( f @ esk11_0 ) ) @ ( inner_1173012732nner_a @ ( f @ X1 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
| ~ ( member_a @ X1 @ ( elemen49976720ball_a @ x2 @ d ) ) ),
inference(rw,[status(thm)],[c_0_39,c_0_33]) ).
thf(c_0_47,plain,
! [X1: a,X2: a] :
( ( inner_1173012732nner_a @ X1 @ ( uminus_uminus_a @ X2 ) )
= ( uminus_uminus_real @ ( inner_1173012732nner_a @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_48,plain,
! [X1: a] :
( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ X1 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
| ~ ( member_a @ X1 @ ( elemen49976720ball_a @ x2 @ d ) ) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_49,negated_conjecture,
! [X7: real,X5: real] :
( ~ ( ord_less_eq_real @ X5 @ ( inner_1173012732nner_a @ ( uminus_uminus_a_a @ poinca659159244_rot_a @ ( minus_minus_a @ zero_zero_a @ ( minus_minus_a @ a2 @ b ) ) ) @ ( f @ ( esk1_2 @ X7 @ X5 ) ) ) )
| ~ ( ord_less_real @ zero_zero_real @ X7 )
| ~ ( ord_less_real @ zero_zero_real @ X5 ) ),
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_50,plain,
! [X1: a] :
( ( uminus_uminus_a_a @ poinca659159244_rot_a @ ( minus_minus_a @ zero_zero_a @ X1 ) )
= ( minus_minus_a @ zero_zero_a @ ( uminus_uminus_a_a @ poinca659159244_rot_a @ X1 ) ) ),
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
thf(c_0_51,plain,
! [X1: a,X2: a] :
( ( inner_1173012732nner_a @ ( minus_minus_a @ zero_zero_a @ X1 ) @ X2 )
= ( uminus_uminus_real @ ( inner_1173012732nner_a @ X1 @ X2 ) ) ),
inference(rw,[status(thm)],[c_0_45,c_0_20]) ).
thf(c_0_52,plain,
! [X1: a] :
( ( ord_less_eq_real @ ( inner_1173012732nner_a @ ( uminus_uminus_a_a @ poinca659159244_rot_a @ ( minus_minus_a @ zero_zero_a @ ( minus_minus_a @ a2 @ b ) ) ) @ ( f @ esk11_0 ) ) @ ( inner_1173012732nner_a @ ( f @ X1 ) @ ( uminus_uminus_a_a @ poinca659159244_rot_a @ ( minus_minus_a @ zero_zero_a @ ( minus_minus_a @ a2 @ b ) ) ) ) )
| ~ ( member_a @ X1 @ ( elemen49976720ball_a @ x2 @ d ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_43]),c_0_43]) ).
thf(c_0_53,negated_conjecture,
! [X7: real,X5: real] :
( ( member_a @ ( esk1_2 @ X5 @ X7 ) @ ( elemen49976720ball_a @ x2 @ X5 ) )
| ~ ( ord_less_real @ zero_zero_real @ X7 )
| ~ ( ord_less_real @ zero_zero_real @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_54,plain,
ord_less_real @ zero_zero_real @ d,
inference(split_conjunct,[status(thm)],[fact_0_d_I1_J]) ).
thf(c_0_55,plain,
! [X1: a,X2: a] :
( ( inner_1173012732nner_a @ X1 @ ( minus_minus_a @ zero_zero_a @ X2 ) )
= ( uminus_uminus_real @ ( inner_1173012732nner_a @ X1 @ X2 ) ) ),
inference(rw,[status(thm)],[c_0_47,c_0_20]) ).
thf(c_0_56,plain,
! [X1: a] :
( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ X1 ) @ ( uminus_uminus_a_a @ poinca659159244_rot_a @ ( minus_minus_a @ zero_zero_a @ ( minus_minus_a @ a2 @ b ) ) ) ) )
| ~ ( member_a @ X1 @ ( elemen49976720ball_a @ x2 @ d ) ) ),
inference(rw,[status(thm)],[c_0_48,c_0_43]) ).
thf(c_0_57,plain,
member_a @ esk11_0 @ ( elemen49976720ball_a @ x2 @ d ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_58,negated_conjecture,
! [X7: real,X5: real] :
( ~ ( ord_less_eq_real @ X5 @ ( uminus_uminus_real @ ( inner_1173012732nner_a @ ( uminus_uminus_a_a @ poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) @ ( f @ ( esk1_2 @ X7 @ X5 ) ) ) ) )
| ~ ( ord_less_real @ zero_zero_real @ X7 )
| ~ ( ord_less_real @ zero_zero_real @ X5 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
thf(c_0_59,negated_conjecture,
! [X5: real] :
( ( ord_less_eq_real @ ( uminus_uminus_real @ ( inner_1173012732nner_a @ ( uminus_uminus_a_a @ poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) @ ( f @ esk11_0 ) ) ) @ ( uminus_uminus_real @ ( inner_1173012732nner_a @ ( uminus_uminus_a_a @ poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) @ ( f @ ( esk1_2 @ d @ X5 ) ) ) ) )
| ~ ( ord_less_real @ zero_zero_real @ X5 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54])]),c_0_50]),c_0_51]),c_0_50]),c_0_55]),c_0_33]) ).
thf(c_0_60,plain,
ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( inner_1173012732nner_a @ ( uminus_uminus_a_a @ poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) @ ( f @ esk11_0 ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_50]),c_0_55]),c_0_33]) ).
thf(c_0_61,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_54]),c_0_60])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP149^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n016.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 20:07:01 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.21/0.27 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.rD2iJHzmGc/E---3.1_841684.p
% 166.18/24.99 % Version: 3.5.1-ho
% 166.18/24.99 % Preprocessing class: HSLSSMSMSSMNHFA.
% 166.18/24.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 166.18/24.99 % Starting new_ho_3 with 1500s (5) cores
% 166.18/24.99 % Starting sh7 with 300s (1) cores
% 166.18/24.99 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 166.18/24.99 % Starting pre_casc_7 with 300s (1) cores
% 166.18/24.99 % new_ho_3 with pid 841697 completed with status 0
% 166.18/24.99 % Result found by new_ho_3
% 166.18/24.99 % Preprocessing class: HSLSSMSMSSMNHFA.
% 166.18/24.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 166.18/24.99 % Starting new_ho_3 with 1500s (5) cores
% 166.18/24.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,4,20000,1.0,true))
% 166.18/24.99 % SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 166.18/24.99 % Search class: HGHSM-FSLM31-MHFFFFBN
% 166.18/24.99 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 166.18/24.99 % Starting SubtermCWHack with 136s (1) cores
% 166.18/24.99 % Starting new_ho_3 with 151s (1) cores
% 166.18/24.99 % Starting full_lambda_5 with 136s (1) cores
% 166.18/24.99 % Starting almost_fo_3 with 136s (1) cores
% 166.18/24.99 % Starting ehoh_best4_fo with 136s (1) cores
% 166.18/24.99 % full_lambda_5 with pid 841704 completed with status 0
% 166.18/24.99 % Result found by full_lambda_5
% 166.18/24.99 % Preprocessing class: HSLSSMSMSSMNHFA.
% 166.18/24.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 166.18/24.99 % Starting new_ho_3 with 1500s (5) cores
% 166.18/24.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,4,20000,1.0,true))
% 166.18/24.99 % SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 166.18/24.99 % Search class: HGHSM-FSLM31-MHFFFFBN
% 166.18/24.99 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 166.18/24.99 % Starting SubtermCWHack with 136s (1) cores
% 166.18/24.99 % Starting new_ho_3 with 151s (1) cores
% 166.18/24.99 % Starting full_lambda_5 with 136s (1) cores
% 166.18/24.99 % Preprocessing time : 0.009 s
% 166.18/24.99 % Presaturation interreduction done
% 166.18/24.99
% 166.18/24.99 % Proof found!
% 166.18/24.99 % SZS status Theorem
% 166.18/24.99 % SZS output start CNFRefutation
% See solution above
% 166.18/24.99 % Parsed axioms : 424
% 166.18/24.99 % Removed by relevancy pruning/SinE : 102
% 166.18/24.99 % Initial clauses : 530
% 166.18/24.99 % Removed in clause preprocessing : 13
% 166.18/24.99 % Initial clauses in saturation : 517
% 166.18/24.99 % Processed clauses : 56788
% 166.18/24.99 % ...of these trivial : 662
% 166.18/24.99 % ...subsumed : 48600
% 166.18/24.99 % ...remaining for further processing : 7526
% 166.18/24.99 % Other redundant clauses eliminated : 2478
% 166.18/24.99 % Clauses deleted for lack of memory : 0
% 166.18/24.99 % Backward-subsumed : 239
% 166.18/24.99 % Backward-rewritten : 280
% 166.18/24.99 % Generated clauses : 802749
% 166.18/24.99 % ...of the previous two non-redundant : 746502
% 166.18/24.99 % ...aggressively subsumed : 0
% 166.18/24.99 % Contextual simplify-reflections : 54
% 166.18/24.99 % Paramodulations : 799951
% 166.18/24.99 % Factorizations : 22
% 166.18/24.99 % NegExts : 52
% 166.18/24.99 % Equation resolutions : 2556
% 166.18/24.99 % Disequality decompositions : 0
% 166.18/24.99 % Total rewrite steps : 1197467
% 166.18/24.99 % ...of those cached : 1141541
% 166.18/24.99 % Propositional unsat checks : 1
% 166.18/24.99 % Propositional check models : 0
% 166.18/24.99 % Propositional check unsatisfiable : 0
% 166.18/24.99 % Propositional clauses : 0
% 166.18/24.99 % Propositional clauses after purity: 0
% 166.18/24.99 % Propositional unsat core size : 0
% 166.18/24.99 % Propositional preprocessing time : 0.000
% 166.18/24.99 % Propositional encoding time : 0.539
% 166.18/24.99 % Propositional solver time : 0.133
% 166.18/24.99 % Success case prop preproc time : 0.000
% 166.18/24.99 % Success case prop encoding time : 0.000
% 166.18/24.99 % Success case prop solver time : 0.000
% 166.18/24.99 % Current number of processed clauses : 6602
% 166.18/24.99 % Positive orientable unit clauses : 278
% 166.18/24.99 % Positive unorientable unit clauses: 71
% 166.18/24.99 % Negative unit clauses : 421
% 166.18/24.99 % Non-unit-clauses : 5832
% 166.18/24.99 % Current number of unprocessed clauses: 687323
% 166.18/24.99 % ...number of literals in the above : 2393633
% 166.18/24.99 % Current number of archived formulas : 0
% 166.18/24.99 % Current number of archived clauses : 872
% 166.18/24.99 % Clause-clause subsumption calls (NU) : 6620582
% 166.18/24.99 % Rec. Clause-clause subsumption calls : 3963926
% 166.18/24.99 % Non-unit clause-clause subsumptions : 25473
% 166.18/24.99 % Unit Clause-clause subsumption calls : 78407
% 166.18/24.99 % Rewrite failures with RHS unbound : 2557
% 166.18/24.99 % BW rewrite match attempts : 9424
% 166.18/24.99 % BW rewrite match successes : 2118
% 166.18/24.99 % Condensation attempts : 0
% 166.18/24.99 % Condensation successes : 0
% 166.18/24.99 % Termbank termtop insertions : 38048440
% 166.18/24.99 % Search garbage collected termcells : 9502
% 166.18/24.99
% 166.18/24.99 % -------------------------------------------------
% 166.18/24.99 % User time : 22.788 s
% 166.18/24.99 % System time : 0.532 s
% 166.18/24.99 % Total time : 23.320 s
% 166.18/24.99 % Maximum resident set size: 5880 pages
% 166.18/24.99
% 166.18/24.99 % -------------------------------------------------
% 166.18/24.99 % User time : 115.724 s
% 166.18/24.99 % System time : 2.945 s
% 166.18/24.99 % Total time : 118.669 s
% 166.18/24.99 % Maximum resident set size: 5632 pages
% 166.18/24.99 % E exiting
%------------------------------------------------------------------------------