TSTP Solution File: NUM925+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM925+2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n019.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 : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 10:41:28 EDT 2023
% Result : Theorem 0.19s 0.70s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 82
% Syntax : Number of formulae : 109 ( 30 unt; 72 typ; 0 def)
% Number of atoms : 50 ( 37 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 27 ( 14 ~; 8 |; 3 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 83 ( 50 >; 33 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 70 ( 70 usr; 22 con; 0-3 aty)
% Number of variables : 31 ( 2 sgn; 18 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
fFalse: $i ).
tff(decl_23,type,
is_bool: $i > $o ).
tff(decl_24,type,
fTrue: $i ).
tff(decl_25,type,
hAPP_int_bool: ( $i * $i ) > $i ).
tff(decl_26,type,
hAPP_nat_bool: ( $i * $i ) > $i ).
tff(decl_27,type,
hAPP_real_bool: ( $i * $i ) > $i ).
tff(decl_28,type,
ord_less_int: $i ).
tff(decl_29,type,
zero_zero_int: $i ).
tff(decl_30,type,
hAPP_i1948725293t_bool: ( $i * $i ) > $i ).
tff(decl_31,type,
one_one_int: $i ).
tff(decl_32,type,
plus_plus_int: $i > $i ).
tff(decl_33,type,
semiri1621563631at_int: $i ).
tff(decl_34,type,
n: $i ).
tff(decl_35,type,
hAPP_nat_int: ( $i * $i ) > $i ).
tff(decl_36,type,
hAPP_int_int: ( $i * $i ) > $i ).
tff(decl_37,type,
hBOOL: $i > $o ).
tff(decl_38,type,
t: $i ).
tff(decl_39,type,
power_power_int: $i > $i ).
tff(decl_40,type,
pls: $i ).
tff(decl_41,type,
bit1: $i > $i ).
tff(decl_42,type,
bit0: $i > $i ).
tff(decl_43,type,
number_number_of_nat: $i > $i ).
tff(decl_44,type,
power_power_real: $i > $i ).
tff(decl_45,type,
hAPP_nat_real: ( $i * $i ) > $i ).
tff(decl_46,type,
plus_plus_real: $i > $i ).
tff(decl_47,type,
hAPP_real_real: ( $i * $i ) > $i ).
tff(decl_48,type,
zero_zero_real: $i ).
tff(decl_49,type,
one_one_nat: $i ).
tff(decl_50,type,
power_power_nat: $i > $i ).
tff(decl_51,type,
hAPP_nat_nat: ( $i * $i ) > $i ).
tff(decl_52,type,
one_one_real: $i ).
tff(decl_53,type,
zero_zero_nat: $i ).
tff(decl_54,type,
number_number_of_int: $i > $i ).
tff(decl_55,type,
number267125858f_real: $i > $i ).
tff(decl_56,type,
plus_plus_nat: $i > $i ).
tff(decl_57,type,
ord_less_nat: $i ).
tff(decl_58,type,
hAPP_n1699378549t_bool: ( $i * $i ) > $i ).
tff(decl_59,type,
ord_less_real: $i ).
tff(decl_60,type,
hAPP_r1134773055l_bool: ( $i * $i ) > $i ).
tff(decl_61,type,
semiri984289939at_nat: $i ).
tff(decl_62,type,
semiri132038758t_real: $i ).
tff(decl_63,type,
m1: $i ).
tff(decl_64,type,
tn: $i ).
tff(decl_65,type,
if_nat: ( $i * $i ) > $i ).
tff(decl_66,type,
ord_less_eq_int: $i ).
tff(decl_67,type,
succ: $i > $i ).
tff(decl_68,type,
ord_less_eq_real: $i ).
tff(decl_69,type,
ord_less_eq_nat: $i ).
tff(decl_70,type,
sqrt: $i > $i ).
tff(decl_71,type,
times_times_int: ( $i * $i ) > $i ).
tff(decl_72,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_73,type,
esk2_1: $i > $i ).
tff(decl_74,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_75,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_76,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_77,type,
esk6_1: $i > $i ).
tff(decl_78,type,
esk7_1: $i > $i ).
tff(decl_79,type,
esk8_1: $i > $i ).
tff(decl_80,type,
esk9_1: $i > $i ).
tff(decl_81,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_82,type,
esk11_1: $i > $i ).
tff(decl_83,type,
esk12_1: $i > $i ).
tff(decl_84,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_85,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_86,type,
esk15_1: $i > $i ).
tff(decl_87,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_88,type,
esk17_3: ( $i * $i * $i ) > $i ).
tff(decl_89,type,
esk18_3: ( $i * $i * $i ) > $i ).
tff(decl_90,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_91,type,
esk20_3: ( $i * $i * $i ) > $i ).
tff(decl_92,type,
esk21_3: ( $i * $i * $i ) > $i ).
tff(decl_93,type,
esk22_2: ( $i * $i ) > $i ).
fof(fact_176_number__of__is__id,axiom,
! [X21] : number_number_of_int(X21) = X21,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_number__of__is__id) ).
fof(conj_0,conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_568_succ__Bit0,axiom,
! [X21] : succ(bit0(X21)) = bit1(X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_568_succ__Bit0) ).
fof(fact_103_Bit0__def,axiom,
! [X21] : bit0(X21) = hAPP_int_int(plus_plus_int(X21),X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_Bit0__def) ).
fof(fact_573_succ__def,axiom,
! [X21] : succ(X21) = hAPP_int_int(plus_plus_int(X21),one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_573_succ__def) ).
fof(fact_105_zadd__0,axiom,
! [X17] : hAPP_int_int(plus_plus_int(zero_zero_int),X17) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_zadd__0) ).
fof(fact_35_zero__is__num__zero,axiom,
zero_zero_int = number_number_of_int(pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_zero__is__num__zero) ).
fof(fact_231_field__power__not__zero,axiom,
! [X64,X65] :
( X65 != zero_zero_int
=> hAPP_nat_int(power_power_int(X65),X64) != zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_field__power__not__zero) ).
fof(fact_447_zless__le,axiom,
! [X30,X25] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X30),X25))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X30),X25))
& X30 != X25 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_zless__le) ).
fof(fact_0_n1pos,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
fof(c_0_10,plain,
! [X485] : number_number_of_int(X485) = X485,
inference(variable_rename,[status(thm)],[fact_176_number__of__is__id]) ).
fof(c_0_11,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(c_0_12,plain,
! [X1283] : succ(bit0(X1283)) = bit1(X1283),
inference(variable_rename,[status(thm)],[fact_568_succ__Bit0]) ).
fof(c_0_13,plain,
! [X398] : bit0(X398) = hAPP_int_int(plus_plus_int(X398),X398),
inference(variable_rename,[status(thm)],[fact_103_Bit0__def]) ).
fof(c_0_14,plain,
! [X1291] : succ(X1291) = hAPP_int_int(plus_plus_int(X1291),one_one_int),
inference(variable_rename,[status(thm)],[fact_573_succ__def]) ).
fof(c_0_15,plain,
! [X400] : hAPP_int_int(plus_plus_int(zero_zero_int),X400) = X400,
inference(variable_rename,[status(thm)],[fact_105_zadd__0]) ).
cnf(c_0_16,plain,
zero_zero_int = number_number_of_int(pls),
inference(split_conjunct,[status(thm)],[fact_35_zero__is__num__zero]) ).
cnf(c_0_17,plain,
number_number_of_int(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_18,plain,
! [X586,X587] :
( X587 = zero_zero_int
| hAPP_nat_int(power_power_int(X587),X586) != zero_zero_int ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_231_field__power__not__zero])]) ).
cnf(c_0_19,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,plain,
succ(bit0(X1)) = bit1(X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,plain,
bit0(X1) = hAPP_int_int(plus_plus_int(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
succ(X1) = hAPP_int_int(plus_plus_int(X1),one_one_int),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
hAPP_int_int(plus_plus_int(zero_zero_int),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
pls = zero_zero_int,
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_25,plain,
( X1 = zero_zero_int
| hAPP_nat_int(power_power_int(X1),X2) != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)))) = zero_zero_int,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_21]),c_0_22]),c_0_22]) ).
cnf(c_0_27,plain,
hAPP_int_int(plus_plus_int(pls),X1) = X1,
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_28,plain,
! [X1038,X1039] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1038),X1039))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1038),X1039)) )
& ( X1038 != X1039
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1038),X1039)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1038),X1039))
| X1038 = X1039
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1038),X1039)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_447_zless__le])])]) ).
cnf(c_0_29,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(split_conjunct,[status(thm)],[fact_0_n1pos]) ).
cnf(c_0_30,plain,
( X1 = pls
| hAPP_nat_int(power_power_int(X1),X2) != pls ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_24]),c_0_24]) ).
cnf(c_0_31,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),one_one_int))) = pls,
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_27]),c_0_27]),c_0_27]),c_0_27]),c_0_24]) ).
cnf(c_0_32,plain,
( X1 != X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(rw,[status(thm)],[c_0_29,c_0_24]) ).
cnf(c_0_34,negated_conjecture,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = pls,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1)),
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_36,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM925+2 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.33 % Computer : n019.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Fri Aug 25 13:32:58 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.70 % Version : CSE_E---1.5
% 0.19/0.70 % Problem : theBenchmark.p
% 0.19/0.70 % Proof found
% 0.19/0.70 % SZS status Theorem for theBenchmark.p
% 0.19/0.70 % SZS output start Proof
% See solution above
% 0.19/0.71 % Total time : 0.105000 s
% 0.19/0.71 % SZS output end Proof
% 0.19/0.71 % Total time : 0.129000 s
%------------------------------------------------------------------------------