TSTP Solution File: NUM926_3 by E-SAT---3.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : NUM926_3 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:08:56 EDT 2023
% Result : Theorem 674.20s 87.65s
% Output : CNFRefutation 674.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 34
% Syntax : Number of formulae : 67 ( 34 unt; 22 typ; 0 def)
% Number of atoms : 63 ( 46 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 37 ( 19 ~; 12 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 16 ( 12 >; 4 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 10 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn; 46 !; 8 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_30,type,
one_one_int: int ).
tff(decl_33,type,
plus_plus_int: int > fun_int_int ).
tff(decl_36,type,
times_times_int: int > fun_int_int ).
tff(decl_47,type,
bit0: int > int ).
tff(decl_48,type,
bit1: int > int ).
tff(decl_50,type,
pls: int ).
tff(decl_51,type,
number_number_of_int: int > int ).
tff(decl_52,type,
number_number_of_nat: int > nat ).
tff(decl_54,type,
ord_less_int: fun_int_fun_int_bool ).
tff(decl_57,type,
ord_less_eq_int: fun_int_fun_int_bool ).
tff(decl_60,type,
power_power_int: int > fun_nat_int ).
tff(decl_79,type,
hAPP_int_bool: ( fun_int_bool * int ) > bool ).
tff(decl_80,type,
hAPP_int_int: ( fun_int_int * int ) > int ).
tff(decl_82,type,
hAPP_i1948725293t_bool: ( fun_int_fun_int_bool * int ) > fun_int_bool ).
tff(decl_84,type,
hAPP_nat_int: ( fun_nat_int * nat ) > int ).
tff(decl_91,type,
hBOOL: bool > $o ).
tff(decl_93,type,
m: int ).
tff(decl_96,type,
t: int ).
tff(decl_98,type,
esk1_0: int ).
tff(decl_99,type,
esk2_0: int ).
tff(decl_100,type,
esk3_0: int ).
tff(decl_101,type,
esk4_0: int ).
tff(conj_0,conjecture,
? [X1: int,X2: int] : ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) ),
file('/export/starexec/sandbox/tmp/tmp.y5C2oAaE4y/E---3.1_20192.p',conj_0) ).
tff(fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X12: int] : ( hAPP_int_int(times_times_int(X12),X12) = hAPP_nat_int(power_power_int(X12),number_number_of_nat(bit0(bit1(pls)))) ),
file('/export/starexec/sandbox/tmp/tmp.y5C2oAaE4y/E---3.1_20192.p',fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
tff(fact_206_Bit0__def,axiom,
! [X31: int] : ( bit0(X31) = hAPP_int_int(plus_plus_int(X31),X31) ),
file('/export/starexec/sandbox/tmp/tmp.y5C2oAaE4y/E---3.1_20192.p',fact_206_Bit0__def) ).
tff(fact_253_Bit1__def,axiom,
! [X31: int] : ( bit1(X31) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X31)),X31) ),
file('/export/starexec/sandbox/tmp/tmp.y5C2oAaE4y/E---3.1_20192.p',fact_253_Bit1__def) ).
tff(fact_144_number__of__is__id,axiom,
! [X31: int] : ( number_number_of_int(X31) = X31 ),
file('/export/starexec/sandbox/tmp/tmp.y5C2oAaE4y/E---3.1_20192.p',fact_144_number__of__is__id) ).
tff(fact_203_add__Pls__right,axiom,
! [X31: int] : ( hAPP_int_int(plus_plus_int(X31),pls) = X31 ),
file('/export/starexec/sandbox/tmp/tmp.y5C2oAaE4y/E---3.1_20192.p',fact_203_add__Pls__right) ).
tff(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] : ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) ) ),
file('/export/starexec/sandbox/tmp/tmp.y5C2oAaE4y/E---3.1_20192.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) ).
tff(fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [X172: int,X173: int,X174: int] : ( hAPP_int_int(plus_plus_int(X172),hAPP_int_int(plus_plus_int(X173),X174)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X172),X173)),X174) ),
file('/export/starexec/sandbox/tmp/tmp.y5C2oAaE4y/E---3.1_20192.p',fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
tff(fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X190: int,X191: int] : ( hAPP_int_int(plus_plus_int(X190),X191) = hAPP_int_int(plus_plus_int(X191),X190) ),
file('/export/starexec/sandbox/tmp/tmp.y5C2oAaE4y/E---3.1_20192.p',fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
tff(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,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
=> ? [X1: int,X2: int] : ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) ) ),
file('/export/starexec/sandbox/tmp/tmp.y5C2oAaE4y/E---3.1_20192.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) ).
tff(fact_37_zless__le,axiom,
! [X27: int,X28: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X27),X28))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X27),X28))
& ( X27 != X28 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.y5C2oAaE4y/E---3.1_20192.p',fact_37_zless__le) ).
tff(fact_0_tpos,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
file('/export/starexec/sandbox/tmp/tmp.y5C2oAaE4y/E---3.1_20192.p',fact_0_tpos) ).
tff(c_0_12,negated_conjecture,
~ ? [X1: int,X2: int] : ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
tff(c_0_13,plain,
! [X1661: int] : ( hAPP_int_int(times_times_int(X1661),X1661) = hAPP_nat_int(power_power_int(X1661),number_number_of_nat(bit0(bit1(pls)))) ),
inference(variable_rename,[status(thm)],[fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J]) ).
tff(c_0_14,plain,
! [X2057: int] : ( bit0(X2057) = hAPP_int_int(plus_plus_int(X2057),X2057) ),
inference(variable_rename,[status(thm)],[fact_206_Bit0__def]) ).
tff(c_0_15,plain,
! [X2152: int] : ( bit1(X2152) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X2152)),X2152) ),
inference(variable_rename,[status(thm)],[fact_253_Bit1__def]) ).
tff(c_0_16,negated_conjecture,
! [X4274: int,X4275: int] : ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X4274),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X4275),number_number_of_nat(bit0(bit1(pls))))) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).
tff(c_0_17,plain,
! [X1937: int] : ( number_number_of_int(X1937) = X1937 ),
inference(variable_rename,[status(thm)],[fact_144_number__of__is__id]) ).
tcf(c_0_18,plain,
! [X1: int] : hAPP_int_int(times_times_int(X1),X1) = hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tcf(c_0_19,plain,
! [X1: int] : bit0(X1) = hAPP_int_int(plus_plus_int(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
tcf(c_0_20,plain,
! [X1: int] : bit1(X1) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
tff(c_0_21,plain,
! [X2053: int] : ( hAPP_int_int(plus_plus_int(X2053),pls) = X2053 ),
inference(variable_rename,[status(thm)],[fact_203_add__Pls__right]) ).
tff(c_0_22,plain,
( ( t != one_one_int )
| ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(esk1_0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(esk2_0),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) ) ),
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])])]) ).
tcf(c_0_23,negated_conjecture,
! [X1: int,X2: int] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
tcf(c_0_24,plain,
! [X1: int] : number_number_of_int(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
tcf(c_0_25,plain,
! [X1: int] : hAPP_int_int(times_times_int(X1),X1) = hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_20]) ).
tcf(c_0_26,plain,
! [X1: int] : hAPP_int_int(plus_plus_int(X1),pls) = X1,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
tff(c_0_27,plain,
! [X1894: int,X1895: int,X1896: int] : ( hAPP_int_int(plus_plus_int(X1894),hAPP_int_int(plus_plus_int(X1895),X1896)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1894),X1895)),X1896) ),
inference(variable_rename,[status(thm)],[fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).
tff(c_0_28,plain,
! [X1912: int,X1913: int] : ( hAPP_int_int(plus_plus_int(X1912),X1913) = hAPP_int_int(plus_plus_int(X1913),X1912) ),
inference(variable_rename,[status(thm)],[fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).
tff(c_0_29,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
| ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(esk3_0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(esk4_0),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) ) ),
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])])]) ).
tcf(c_0_30,plain,
( ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(esk1_0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(esk2_0),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_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_22]) ).
tcf(c_0_31,negated_conjecture,
! [X1: int,X2: int] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),m)),one_one_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)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_20]),c_0_20]),c_0_20]),c_0_20]),c_0_20]),c_0_20]),c_0_20]),c_0_20]) ).
tcf(c_0_32,plain,
! [X1: int] : hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),one_one_int))) = hAPP_int_int(times_times_int(X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_26]),c_0_26]),c_0_26]) ).
tcf(c_0_33,plain,
! [X1: int,X2: int,X3: int] : hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),X3),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
tcf(c_0_34,plain,
! [X2: int,X1: int] : hAPP_int_int(plus_plus_int(X1),X2) = hAPP_int_int(plus_plus_int(X2),X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
tcf(c_0_35,plain,
( ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(esk3_0),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(esk4_0),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
tff(c_0_36,plain,
! [X1681: int,X1682: int] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1681),X1682))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1681),X1682)) )
& ( ( X1681 != X1682 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1681),X1682)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1681),X1682))
| ( X1681 = X1682 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1681),X1682)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_37_zless__le])])]) ).
tcf(c_0_37,plain,
( ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(esk1_0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(esk2_0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),m)),one_one_int) )
| ( t != one_one_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)],[inference(rw,[status(thm)],[c_0_30,c_0_24]),c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_20]),c_0_20]),c_0_20]),c_0_20]),c_0_20]),c_0_20]),c_0_20]),c_0_20]) ).
tcf(c_0_38,negated_conjecture,
! [X1: int,X2: int] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X1)),hAPP_int_int(times_times_int(X2),X2)) != hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))),m)),
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)],[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_31,c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_32]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_32]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_33]),c_0_34]) ).
tcf(c_0_39,plain,
( ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(esk3_0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),hAPP_nat_int(power_power_int(esk4_0),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),m)),one_one_int) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
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)],[inference(rw,[status(thm)],[c_0_35,c_0_24]),c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_20]),c_0_20]),c_0_20]),c_0_20]),c_0_20]),c_0_20]),c_0_20]),c_0_20]) ).
tcf(c_0_40,plain,
! [X1: int,X2: int] :
( ( X1 = X2 )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
tcf(c_0_41,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
inference(split_conjunct,[status(thm)],[fact_0_tpos]) ).
tcf(c_0_42,plain,
t != one_one_int,
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)],[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_26]),c_0_26]),c_0_26]),c_0_26]),c_0_32]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_32]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_33]),c_0_34]),c_0_38]) ).
tcf(c_0_43,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_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)],[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_39,c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_32]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_32]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_33]),c_0_34]),c_0_38]) ).
cnf(c_0_44,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM926_3 : TPTP v8.1.2. Released v5.3.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n004.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 2400
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon Oct 2 14:26:30 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.16/0.59 Running first-order model finding
% 0.16/0.59 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.y5C2oAaE4y/E---3.1_20192.p
% 674.20/87.65 # Version: 3.1pre001
% 674.20/87.65 # Preprocessing class: FMLSSMSMSSSNFFN.
% 674.20/87.65 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 674.20/87.65 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 674.20/87.65 # Starting new_bool_3 with 600s (2) cores
% 674.20/87.65 # Starting new_bool_1 with 600s (2) cores
% 674.20/87.65 # Starting sh5l with 300s (1) cores
% 674.20/87.65 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 20269 completed with status 0
% 674.20/87.65 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 674.20/87.65 # Preprocessing class: FMLSSMSMSSSNFFN.
% 674.20/87.65 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 674.20/87.65 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 674.20/87.65 # No SInE strategy applied
% 674.20/87.65 # Search class: FGHSM-SSLM31-DFFFFFNN
% 674.20/87.65 # Scheduled 6 strats onto 3 cores with 900 seconds (900 total)
% 674.20/87.65 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 487s (1) cores
% 674.20/87.65 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 91s (1) cores
% 674.20/87.65 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 82s (1) cores
% 674.20/87.65 # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 20280 completed with status 7
% 674.20/87.65 # Starting G-E--_208_B07AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 82s (1) cores
% 674.20/87.65 # G-E--_208_B07AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 20298 completed with status 0
% 674.20/87.65 # Result found by G-E--_208_B07AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 674.20/87.65 # Preprocessing class: FMLSSMSMSSSNFFN.
% 674.20/87.65 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 674.20/87.65 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 674.20/87.65 # No SInE strategy applied
% 674.20/87.65 # Search class: FGHSM-SSLM31-DFFFFFNN
% 674.20/87.65 # Scheduled 6 strats onto 3 cores with 900 seconds (900 total)
% 674.20/87.65 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 487s (1) cores
% 674.20/87.65 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 91s (1) cores
% 674.20/87.65 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 82s (1) cores
% 674.20/87.65 # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 20280 completed with status 7
% 674.20/87.65 # Starting G-E--_208_B07AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 82s (1) cores
% 674.20/87.65 # Preprocessing time : 0.016 s
% 674.20/87.65 # Presaturation interreduction done
% 674.20/87.65
% 674.20/87.65 # Proof found!
% 674.20/87.65 # SZS status Theorem
% 674.20/87.65 # SZS output start CNFRefutation
% See solution above
% 674.20/87.65 # Parsed axioms : 1299
% 674.20/87.65 # Removed by relevancy pruning/SinE : 0
% 674.20/87.65 # Initial clauses : 1826
% 674.20/87.65 # Removed in clause preprocessing : 209
% 674.20/87.65 # Initial clauses in saturation : 1617
% 674.20/87.65 # Processed clauses : 4417
% 674.20/87.65 # ...of these trivial : 170
% 674.20/87.65 # ...subsumed : 2398
% 674.20/87.65 # ...remaining for further processing : 1849
% 674.20/87.65 # Other redundant clauses eliminated : 226
% 674.20/87.65 # Clauses deleted for lack of memory : 0
% 674.20/87.65 # Backward-subsumed : 26
% 674.20/87.65 # Backward-rewritten : 74
% 674.20/87.65 # Generated clauses : 12284
% 674.20/87.65 # ...of the previous two non-redundant : 10854
% 674.20/87.65 # ...aggressively subsumed : 0
% 674.20/87.65 # Contextual simplify-reflections : 3
% 674.20/87.65 # Paramodulations : 12068
% 674.20/87.65 # Factorizations : 2
% 674.20/87.65 # NegExts : 0
% 674.20/87.65 # Equation resolutions : 235
% 674.20/87.65 # Total rewrite steps : 20386
% 674.20/87.65 # Propositional unsat checks : 0
% 674.20/87.65 # Propositional check models : 0
% 674.20/87.65 # Propositional check unsatisfiable : 0
% 674.20/87.65 # Propositional clauses : 0
% 674.20/87.65 # Propositional clauses after purity: 0
% 674.20/87.65 # Propositional unsat core size : 0
% 674.20/87.65 # Propositional preprocessing time : 0.000
% 674.20/87.65 # Propositional encoding time : 0.000
% 674.20/87.65 # Propositional solver time : 0.000
% 674.20/87.65 # Success case prop preproc time : 0.000
% 674.20/87.65 # Success case prop encoding time : 0.000
% 674.20/87.65 # Success case prop solver time : 0.000
% 674.20/87.65 # Current number of processed clauses : 601
% 674.20/87.65 # Positive orientable unit clauses : 206
% 674.20/87.65 # Positive unorientable unit clauses: 51
% 674.20/87.65 # Negative unit clauses : 184
% 674.20/87.65 # Non-unit-clauses : 160
% 674.20/87.65 # Current number of unprocessed clauses: 9005
% 674.20/87.65 # ...number of literals in the above : 12183
% 674.20/87.65 # Current number of archived formulas : 0
% 674.20/87.65 # Current number of archived clauses : 1122
% 674.20/87.65 # Clause-clause subsumption calls (NU) : 74167
% 674.20/87.65 # Rec. Clause-clause subsumption calls : 39308
% 674.20/87.65 # Non-unit clause-clause subsumptions : 469
% 674.20/87.65 # Unit Clause-clause subsumption calls : 4744
% 674.20/87.65 # Rewrite failures with RHS unbound : 0
% 674.20/87.65 # BW rewrite match attempts : 2162
% 674.20/87.65 # BW rewrite match successes : 608
% 674.20/87.65 # Condensation attempts : 0
% 674.20/87.65 # Condensation successes : 0
% 674.20/87.65 # Termbank termtop insertions : 461132
% 674.20/87.65
% 674.20/87.65 # -------------------------------------------------
% 674.20/87.65 # User time : 80.962 s
% 674.20/87.65 # System time : 1.791 s
% 674.20/87.65 # Total time : 82.754 s
% 674.20/87.65 # Maximum resident set size: 10068 pages
% 674.20/87.65
% 674.20/87.65 # -------------------------------------------------
% 674.20/87.65 # User time : 246.804 s
% 674.20/87.65 # System time : 5.456 s
% 674.20/87.65 # Total time : 252.260 s
% 674.20/87.65 # Maximum resident set size: 4344 pages
% 674.20/87.65 % E---3.1 exiting
%------------------------------------------------------------------------------