%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM926^3 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:17:13 AM UTC 2026
% Result : Theorem 2.41s 0.80s
% Output : CNFRefutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 52 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 53 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 511 ( 21 ~; 12 |; 4 &; 470 @)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 10 con; 0-2 aty)
% Number of variables : 54 ( 0 ^; 46 !; 8 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
int: $tType ).
thf(decl_sort2,type,
nat: $tType ).
thf(decl_28,type,
one_one_int: int ).
thf(decl_31,type,
plus_plus_int: int > int > int ).
thf(decl_34,type,
times_times_int: int > int > int ).
thf(decl_37,type,
zero_zero_int: int ).
thf(decl_45,type,
bit0: int > int ).
thf(decl_46,type,
bit1: int > int ).
thf(decl_48,type,
pls: int ).
thf(decl_49,type,
number_number_of_int: int > int ).
thf(decl_50,type,
number_number_of_nat: int > nat ).
thf(decl_52,type,
ord_less_int: int > int > $o ).
thf(decl_55,type,
ord_less_eq_int: int > int > $o ).
thf(decl_58,type,
power_power_int: int > nat > int ).
thf(decl_75,type,
m: int ).
thf(decl_78,type,
t: int ).
thf(decl_80,type,
esk1_0: int ).
thf(decl_81,type,
esk2_0: int ).
thf(decl_82,type,
esk3_0: int ).
thf(decl_83,type,
esk4_0: int ).
thf(fact_265_semiring__norm_I110_J,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zkIK4X9Qk3/E---3.1_729466.p',fact_265_semiring__norm_I110_J) ).
thf(fact_358_Pls__def,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/tmp/tmp.zkIK4X9Qk3/E---3.1_729466.p',fact_358_Pls__def) ).
thf(conj_0,conjecture,
? [X1: int,X2: int] :
( ( plus_plus_int @ ( power_power_int @ X1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ X2 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ),
file('/export/starexec/sandbox2/tmp/tmp.zkIK4X9Qk3/E---3.1_729466.p',conj_0) ).
thf(fact_32_one__add__one__is__two,axiom,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zkIK4X9Qk3/E---3.1_729466.p',fact_32_one__add__one__is__two) ).
thf(fact_144_number__of__is__id,axiom,
! [X29: int] :
( ( number_number_of_int @ X29 )
= X29 ),
file('/export/starexec/sandbox2/tmp/tmp.zkIK4X9Qk3/E---3.1_729466.p',fact_144_number__of__is__id) ).
thf(fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X12: int] :
( ( times_times_int @ X12 @ X12 )
= ( power_power_int @ X12 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zkIK4X9Qk3/E---3.1_729466.p',fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(fact_269_double__number__of__Bit0,axiom,
! [X338: int] :
( ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ ( number_number_of_int @ X338 ) )
= ( number_number_of_int @ ( bit0 @ X338 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zkIK4X9Qk3/E---3.1_729466.p',fact_269_double__number__of__Bit0) ).
thf(fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X193: int,X194: int] :
( ( plus_plus_int @ X193 @ X194 )
= ( plus_plus_int @ X194 @ X193 ) ),
file('/export/starexec/sandbox2/tmp/tmp.zkIK4X9Qk3/E---3.1_729466.p',fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
( ( t = one_one_int )
=> ? [X1: int,X2: int] :
( ( plus_plus_int @ ( power_power_int @ X1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ X2 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zkIK4X9Qk3/E---3.1_729466.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
thf(fact_37_zless__le,axiom,
! [X26: int,X25: int] :
( ( ord_less_int @ X26 @ X25 )
<=> ( ( ord_less_eq_int @ X26 @ X25 )
& ( X26 != X25 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zkIK4X9Qk3/E---3.1_729466.p',fact_37_zless__le) ).
thf(fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
( ( ord_less_int @ one_one_int @ t )
=> ? [X1: int,X2: int] :
( ( plus_plus_int @ ( power_power_int @ X1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ X2 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zkIK4X9Qk3/E---3.1_729466.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
thf(fact_106_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [X118: int,X119: int,X120: int] :
( ( times_times_int @ X118 @ ( times_times_int @ X119 @ X120 ) )
= ( times_times_int @ ( times_times_int @ X118 @ X119 ) @ X120 ) ),
file('/export/starexec/sandbox2/tmp/tmp.zkIK4X9Qk3/E---3.1_729466.p',fact_106_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(fact_0_tpos,axiom,
ord_less_eq_int @ one_one_int @ t,
file('/export/starexec/sandbox2/tmp/tmp.zkIK4X9Qk3/E---3.1_729466.p',fact_0_tpos) ).
thf(c_0_13,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(split_conjunct,[status(thm)],[fact_265_semiring__norm_I110_J]) ).
thf(c_0_14,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_358_Pls__def]) ).
thf(c_0_15,negated_conjecture,
~ ? [X1: int,X2: int] :
( ( plus_plus_int @ ( power_power_int @ X1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ X2 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_16,plain,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(split_conjunct,[status(thm)],[fact_32_one__add__one__is__two]) ).
thf(c_0_17,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ zero_zero_int ) ) ),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_18,plain,
! [X4636: int] :
( ( number_number_of_int @ X4636 )
= X4636 ),
inference(variable_rename,[status(thm)],[fact_144_number__of__is__id]) ).
thf(c_0_19,negated_conjecture,
! [X6958: int,X6959: int] :
( ( plus_plus_int @ ( power_power_int @ X6958 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ X6959 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
thf(c_0_20,plain,
! [X4360: int] :
( ( times_times_int @ X4360 @ X4360 )
= ( power_power_int @ X4360 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(variable_rename,[status(thm)],[fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J]) ).
thf(c_0_21,plain,
! [X4860: int] :
( ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ ( number_number_of_int @ X4860 ) )
= ( number_number_of_int @ ( bit0 @ X4860 ) ) ),
inference(variable_rename,[status(thm)],[fact_269_double__number__of__Bit0]) ).
thf(c_0_22,plain,
( ( number_number_of_int @ ( bit0 @ ( bit1 @ zero_zero_int ) ) )
= ( plus_plus_int @ ( number_number_of_int @ ( bit1 @ zero_zero_int ) ) @ ( number_number_of_int @ ( bit1 @ zero_zero_int ) ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17]),c_0_14]) ).
thf(c_0_23,plain,
! [X1: int] :
( ( number_number_of_int @ X1 )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_24,negated_conjecture,
! [X1: int,X2: int] :
( ( plus_plus_int @ ( power_power_int @ X1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ X2 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_25,plain,
! [X1: int] :
( ( times_times_int @ X1 @ X1 )
= ( power_power_int @ X1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_26,plain,
! [X1: int] :
( ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ ( number_number_of_int @ X1 ) )
= ( number_number_of_int @ ( bit0 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_27,plain,
( ( plus_plus_int @ ( bit1 @ zero_zero_int ) @ ( bit1 @ zero_zero_int ) )
= ( bit0 @ ( bit1 @ zero_zero_int ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_23]),c_0_23]) ).
thf(c_0_28,negated_conjecture,
! [X1: int,X2: int] :
( ( plus_plus_int @ ( power_power_int @ X1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ zero_zero_int ) ) ) ) @ ( power_power_int @ X2 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ zero_zero_int ) ) ) ) )
!= ( plus_plus_int @ ( times_times_int @ ( bit0 @ ( bit0 @ ( bit1 @ zero_zero_int ) ) ) @ m ) @ ( bit1 @ zero_zero_int ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_14]),c_0_14]),c_0_14]),c_0_23]),c_0_17]),c_0_23]) ).
thf(c_0_29,plain,
! [X1: int] :
( ( power_power_int @ X1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ zero_zero_int ) ) ) )
= ( times_times_int @ X1 @ X1 ) ),
inference(rw,[status(thm)],[c_0_25,c_0_14]) ).
thf(c_0_30,plain,
! [X1: int] :
( ( times_times_int @ ( bit0 @ ( bit1 @ zero_zero_int ) ) @ X1 )
= ( bit0 @ X1 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_17]),c_0_23]),c_0_17]),c_0_23]),c_0_27]),c_0_23]),c_0_23]) ).
thf(c_0_31,plain,
! [X4611: int,X4612: int] :
( ( plus_plus_int @ X4611 @ X4612 )
= ( plus_plus_int @ X4612 @ X4611 ) ),
inference(variable_rename,[status(thm)],[fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).
thf(c_0_32,plain,
( ( t != one_one_int )
| ( ( plus_plus_int @ ( power_power_int @ esk1_0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ esk2_0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06])])])]) ).
thf(c_0_33,plain,
! [X26: int,X25: int] :
( ( ord_less_int @ X26 @ X25 )
<=> ( ( ord_less_eq_int @ X26 @ X25 )
& ( X26 != X25 ) ) ),
inference(fof_simplification,[status(thm)],[fact_37_zless__le]) ).
thf(c_0_34,plain,
( ~ ( ord_less_int @ one_one_int @ t )
| ( ( plus_plus_int @ ( power_power_int @ esk3_0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ esk4_0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06])])])]) ).
thf(c_0_35,negated_conjecture,
! [X1: int,X2: int] :
( ( plus_plus_int @ ( times_times_int @ X1 @ X1 ) @ ( times_times_int @ X2 @ X2 ) )
!= ( plus_plus_int @ ( times_times_int @ ( times_times_int @ ( bit0 @ ( bit1 @ zero_zero_int ) ) @ ( bit0 @ ( bit1 @ zero_zero_int ) ) ) @ m ) @ ( bit1 @ zero_zero_int ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_29]),c_0_30]) ).
thf(c_0_36,plain,
! [X2: int,X1: int] :
( ( plus_plus_int @ X1 @ X2 )
= ( plus_plus_int @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_37,plain,
( ( ( plus_plus_int @ ( power_power_int @ esk1_0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ esk2_0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
| ( t != one_one_int ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_38,plain,
! [X4536: int,X4537: int,X4538: int] :
( ( times_times_int @ X4536 @ ( times_times_int @ X4537 @ X4538 ) )
= ( times_times_int @ ( times_times_int @ X4536 @ X4537 ) @ X4538 ) ),
inference(variable_rename,[status(thm)],[fact_106_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J]) ).
thf(c_0_39,plain,
! [X4380: int,X4381: int] :
( ( ( ord_less_eq_int @ X4380 @ X4381 )
| ~ ( ord_less_int @ X4380 @ X4381 ) )
& ( ( X4380 != X4381 )
| ~ ( ord_less_int @ X4380 @ X4381 ) )
& ( ~ ( ord_less_eq_int @ X4380 @ X4381 )
| ( X4380 = X4381 )
| ( ord_less_int @ X4380 @ X4381 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])])]) ).
thf(c_0_40,plain,
ord_less_eq_int @ one_one_int @ t,
inference(split_conjunct,[status(thm)],[fact_0_tpos]) ).
thf(c_0_41,plain,
( ( ( plus_plus_int @ ( power_power_int @ esk3_0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ esk4_0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
| ~ ( ord_less_int @ one_one_int @ t ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_42,negated_conjecture,
! [X1: int,X2: int] :
( ( plus_plus_int @ ( times_times_int @ X1 @ X1 ) @ ( times_times_int @ X2 @ X2 ) )
!= ( plus_plus_int @ ( bit1 @ zero_zero_int ) @ ( times_times_int @ ( times_times_int @ ( bit0 @ ( bit1 @ zero_zero_int ) ) @ ( bit0 @ ( bit1 @ zero_zero_int ) ) ) @ m ) ) ),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_43,plain,
( ( ( plus_plus_int @ ( times_times_int @ esk1_0 @ esk1_0 ) @ ( times_times_int @ esk2_0 @ esk2_0 ) )
= ( plus_plus_int @ ( bit1 @ zero_zero_int ) @ ( times_times_int @ ( times_times_int @ ( bit0 @ ( bit1 @ zero_zero_int ) ) @ ( bit0 @ ( bit1 @ zero_zero_int ) ) ) @ m ) ) )
| ( t
!= ( bit1 @ zero_zero_int ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_14]),c_0_29]),c_0_14]),c_0_29]),c_0_14]),c_0_30]),c_0_23]),c_0_17]),c_0_23]),c_0_36]),c_0_17]),c_0_23]) ).
thf(c_0_44,plain,
! [X1: int,X2: int,X3: int] :
( ( times_times_int @ X1 @ ( times_times_int @ X2 @ X3 ) )
= ( times_times_int @ ( times_times_int @ X1 @ X2 ) @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_45,plain,
! [X1: int,X2: int] :
( ( X1 = X2 )
| ( ord_less_int @ X1 @ X2 )
| ~ ( ord_less_eq_int @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_46,plain,
ord_less_eq_int @ ( bit1 @ zero_zero_int ) @ t,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_17]),c_0_23]) ).
thf(c_0_47,plain,
~ ( ord_less_int @ ( bit1 @ zero_zero_int ) @ t ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_14]),c_0_29]),c_0_14]),c_0_29]),c_0_14]),c_0_30]),c_0_23]),c_0_17]),c_0_23]),c_0_36]),c_0_17]),c_0_23]),c_0_42]) ).
thf(c_0_48,plain,
( ( ( plus_plus_int @ ( times_times_int @ esk1_0 @ esk1_0 ) @ ( times_times_int @ esk2_0 @ esk2_0 ) )
= ( plus_plus_int @ ( bit1 @ zero_zero_int ) @ ( times_times_int @ ( bit0 @ ( bit1 @ zero_zero_int ) ) @ ( times_times_int @ ( bit0 @ ( bit1 @ zero_zero_int ) ) @ m ) ) ) )
| ( t
!= ( bit1 @ zero_zero_int ) ) ),
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
thf(c_0_49,plain,
( t
= ( bit1 @ zero_zero_int ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
thf(c_0_50,negated_conjecture,
! [X1: int,X2: int] :
( ( plus_plus_int @ ( times_times_int @ X1 @ X1 ) @ ( times_times_int @ X2 @ X2 ) )
!= ( plus_plus_int @ ( bit1 @ zero_zero_int ) @ ( times_times_int @ ( bit0 @ ( bit1 @ zero_zero_int ) ) @ ( times_times_int @ ( bit0 @ ( bit1 @ zero_zero_int ) ) @ m ) ) ) ),
inference(rw,[status(thm)],[c_0_42,c_0_44]) ).
thf(c_0_51,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]),c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM926^3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n019.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 13:06:03 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.23/0.29 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.zkIK4X9Qk3/E---3.1_729466.p
% 2.41/0.80 % Version: 3.5.1-ho
% 2.41/0.80 % Preprocessing class: HMLSSMSMSSSNSFA.
% 2.41/0.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.41/0.80 % Starting sh3 with 1500s (5) cores
% 2.41/0.80 % Starting lpo1_def_fix with 300s (1) cores
% 2.41/0.80 % Starting lpo8_s with 300s (1) cores
% 2.41/0.80 % Starting lpo1_lambda_fix with 300s (1) cores
% 2.41/0.80 % sh3 with pid 729479 completed with status 0
% 2.41/0.80 % Result found by sh3
% 2.41/0.80 % Preprocessing class: HMLSSMSMSSSNSFA.
% 2.41/0.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.41/0.80 % Starting sh3 with 1500s (5) cores
% 2.41/0.80 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.41/0.80 % No SInE strategy applied
% 2.41/0.80 % Search class: HGHSM-SSLM32-DSFFFFBN
% 2.41/0.80 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 2.41/0.80 % Starting SubtermCWHack with 151s (1) cores
% 2.41/0.80 % Starting sh3 with 750s (1) cores
% 2.41/0.80 % Starting lpo1_def_fix with 188s (1) cores
% 2.41/0.80 % Starting lpo8_s with 188s (1) cores
% 2.41/0.80 % Starting lpo1_lambda_fix with 188s (1) cores
% 2.41/0.80 % lpo8_s with pid 729489 completed with status 0
% 2.41/0.80 % Result found by lpo8_s
% 2.41/0.80 % Preprocessing class: HMLSSMSMSSSNSFA.
% 2.41/0.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.41/0.80 % Starting sh3 with 1500s (5) cores
% 2.41/0.80 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.41/0.80 % No SInE strategy applied
% 2.41/0.80 % Search class: HGHSM-SSLM32-DSFFFFBN
% 2.41/0.80 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 2.41/0.80 % Starting SubtermCWHack with 151s (1) cores
% 2.41/0.80 % Starting sh3 with 750s (1) cores
% 2.41/0.80 % Starting lpo1_def_fix with 188s (1) cores
% 2.41/0.80 % Starting lpo8_s with 188s (1) cores
% 2.41/0.80 % Preprocessing time : 0.017 s
% 2.41/0.80 % Presaturation interreduction done
% 2.41/0.80
% 2.41/0.80 % Proof found!
% 2.41/0.80 % SZS status Theorem
% 2.41/0.80 % SZS output start CNFRefutation
% See solution above
% 2.41/0.80 % Parsed axioms : 1259
% 2.41/0.80 % Removed by relevancy pruning/SinE : 0
% 2.41/0.80 % Initial clauses : 1789
% 2.41/0.80 % Removed in clause preprocessing : 150
% 2.41/0.80 % Initial clauses in saturation : 1639
% 2.41/0.80 % Processed clauses : 4351
% 2.41/0.80 % ...of these trivial : 208
% 2.41/0.80 % ...subsumed : 1928
% 2.41/0.80 % ...remaining for further processing : 2214
% 2.41/0.80 % Other redundant clauses eliminated : 199
% 2.41/0.80 % Clauses deleted for lack of memory : 0
% 2.41/0.80 % Backward-subsumed : 90
% 2.41/0.80 % Backward-rewritten : 88
% 2.41/0.80 % Generated clauses : 9411
% 2.41/0.80 % ...of the previous two non-redundant : 8049
% 2.41/0.80 % ...aggressively subsumed : 0
% 2.41/0.80 % Contextual simplify-reflections : 3
% 2.41/0.80 % Paramodulations : 8935
% 2.41/0.80 % Factorizations : 2
% 2.41/0.80 % NegExts : 150
% 2.41/0.80 % Equation resolutions : 212
% 2.41/0.80 % Disequality decompositions : 0
% 2.41/0.80 % Total rewrite steps : 8753
% 2.41/0.80 % ...of those cached : 6983
% 2.41/0.80 % Propositional unsat checks : 0
% 2.41/0.80 % Propositional check models : 0
% 2.41/0.80 % Propositional check unsatisfiable : 0
% 2.41/0.80 % Propositional clauses : 0
% 2.41/0.80 % Propositional clauses after purity: 0
% 2.41/0.80 % Propositional unsat core size : 0
% 2.41/0.80 % Propositional preprocessing time : 0.000
% 2.41/0.80 % Propositional encoding time : 0.000
% 2.41/0.80 % Propositional solver time : 0.000
% 2.41/0.80 % Success case prop preproc time : 0.000
% 2.41/0.80 % Success case prop encoding time : 0.000
% 2.41/0.80 % Success case prop solver time : 0.000
% 2.41/0.80 % Current number of processed clauses : 838
% 2.41/0.80 % Positive orientable unit clauses : 250
% 2.41/0.80 % Positive unorientable unit clauses: 24
% 2.41/0.80 % Negative unit clauses : 205
% 2.41/0.80 % Non-unit-clauses : 359
% 2.41/0.80 % Current number of unprocessed clauses: 6213
% 2.41/0.80 % ...number of literals in the above : 10418
% 2.41/0.80 % Current number of archived formulas : 0
% 2.41/0.80 % Current number of archived clauses : 1244
% 2.41/0.80 % Clause-clause subsumption calls (NU) : 175015
% 2.41/0.80 % Rec. Clause-clause subsumption calls : 112117
% 2.41/0.80 % Non-unit clause-clause subsumptions : 509
% 2.41/0.80 % Unit Clause-clause subsumption calls : 19810
% 2.41/0.80 % Rewrite failures with RHS unbound : 0
% 2.41/0.80 % BW rewrite match attempts : 625
% 2.41/0.80 % BW rewrite match successes : 401
% 2.41/0.80 % Condensation attempts : 4352
% 2.41/0.80 % Condensation successes : 30
% 2.41/0.80 % Termbank termtop insertions : 294340
% 2.41/0.80 % Search garbage collected termcells : 29960
% 2.41/0.80
% 2.41/0.80 % -------------------------------------------------
% 2.41/0.80 % User time : 0.421 s
% 2.41/0.80 % System time : 0.023 s
% 2.41/0.80 % Total time : 0.444 s
% 2.41/0.80 % Maximum resident set size: 11664 pages
% 2.41/0.80
% 2.41/0.80 % -------------------------------------------------
% 2.41/0.80 % User time : 1.420 s
% 2.41/0.80 % System time : 0.108 s
% 2.41/0.80 % Total time : 1.528 s
% 2.41/0.80 % Maximum resident set size: 6912 pages
% 2.41/0.80 % E exiting
%------------------------------------------------------------------------------