TSTP Solution File: NUM926+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM926+1 : 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 : n020.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 10:41:35 EDT 2023
% Result : Theorem 0.18s 0.64s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 36
% Syntax : Number of formulae : 66 ( 21 unt; 27 typ; 0 def)
% Number of atoms : 62 ( 34 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 22 ~; 16 |; 1 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 16 >; 10 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 11 con; 0-2 aty)
% Number of variables : 47 ( 6 sgn; 22 !; 8 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
one_one_int: $i ).
tff(decl_23,type,
t: $i ).
tff(decl_24,type,
ord_less_eq_int: ( $i * $i ) > $o ).
tff(decl_25,type,
pls: $i ).
tff(decl_26,type,
bit1: $i > $i ).
tff(decl_27,type,
bit0: $i > $i ).
tff(decl_28,type,
number_number_of_nat: $i > $i ).
tff(decl_29,type,
power_power_int: ( $i * $i ) > $i ).
tff(decl_30,type,
plus_plus_int: ( $i * $i ) > $i ).
tff(decl_31,type,
number_number_of_int: $i > $i ).
tff(decl_32,type,
m: $i ).
tff(decl_33,type,
times_times_int: ( $i * $i ) > $i ).
tff(decl_34,type,
ord_less_int: ( $i * $i ) > $o ).
tff(decl_35,type,
zprime: $i > $o ).
tff(decl_36,type,
s: $i ).
tff(decl_37,type,
twoSqu526106917sum2sq: $i > $o ).
tff(decl_38,type,
plus_plus_nat: ( $i * $i ) > $i ).
tff(decl_39,type,
power_power_nat: ( $i * $i ) > $i ).
tff(decl_40,type,
times_times_nat: ( $i * $i ) > $i ).
tff(decl_41,type,
one_one_nat: $i ).
tff(decl_42,type,
ord_less_eq_nat: ( $i * $i ) > $o ).
tff(decl_43,type,
ord_less_nat: ( $i * $i ) > $o ).
tff(decl_44,type,
esk1_0: $i ).
tff(decl_45,type,
esk2_0: $i ).
tff(decl_46,type,
esk3_0: $i ).
tff(decl_47,type,
esk4_0: $i ).
tff(decl_48,type,
esk5_0: $i ).
fof(conj_0,conjecture,
? [X1,X2] : 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/benchmark/theBenchmark.p',conj_0) ).
fof(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,X2] : 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/benchmark/theBenchmark.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) ).
fof(fact_111_number__of__is__id,axiom,
! [X21] : number_number_of_int(X21) = X21,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_number__of__is__id) ).
fof(fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X82,X83] : plus_plus_int(X82,X83) = plus_plus_int(X83,X82),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X64,X65] : times_times_int(X64,X65) = times_times_int(X65,X64),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_38_le__number__of__eq__not__less,axiom,
! [X28,X18] :
( ord_less_eq_int(number_number_of_int(X28),number_number_of_int(X18))
<=> ~ ord_less_int(number_number_of_int(X18),number_number_of_int(X28)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_le__number__of__eq__not__less) ).
fof(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,X2] : 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/benchmark/theBenchmark.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) ).
fof(fact_31_zle__antisym,axiom,
! [X16,X15] :
( ord_less_eq_int(X16,X15)
=> ( ord_less_eq_int(X15,X16)
=> X16 = X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_zle__antisym) ).
fof(fact_0_tpos,axiom,
ord_less_eq_int(one_one_int,t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_tpos) ).
fof(c_0_9,negated_conjecture,
~ ? [X1,X2] : 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]) ).
fof(c_0_10,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(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])])]) ).
fof(c_0_11,plain,
! [X308] : number_number_of_int(X308) = X308,
inference(variable_rename,[status(thm)],[fact_111_number__of__is__id]) ).
fof(c_0_12,negated_conjecture,
! [X329,X330] : plus_plus_int(power_power_int(X329,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X330,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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).
cnf(c_0_13,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_10]) ).
cnf(c_0_14,plain,
number_number_of_int(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,plain,
! [X289,X290] : plus_plus_int(X289,X290) = plus_plus_int(X290,X289),
inference(variable_rename,[status(thm)],[fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).
cnf(c_0_16,negated_conjecture,
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_12]) ).
fof(c_0_17,plain,
! [X253,X254] : times_times_int(X253,X254) = times_times_int(X254,X253),
inference(variable_rename,[status(thm)],[fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J]) ).
fof(c_0_18,plain,
! [X28,X18] :
( ord_less_eq_int(number_number_of_int(X28),number_number_of_int(X18))
<=> ~ ord_less_int(number_number_of_int(X18),number_number_of_int(X28)) ),
inference(fof_simplification,[status(thm)],[fact_38_le__number__of__eq__not__less]) ).
cnf(c_0_19,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(bit0(bit0(bit1(pls))),m),one_one_int)
| ~ ord_less_int(one_one_int,t) ),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
plus_plus_int(X1,X2) = plus_plus_int(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
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(bit0(bit0(bit1(pls))),m),one_one_int),
inference(rw,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_22,plain,
times_times_int(X1,X2) = times_times_int(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_23,plain,
! [X138,X139] :
( ( ~ ord_less_eq_int(number_number_of_int(X138),number_number_of_int(X139))
| ~ ord_less_int(number_number_of_int(X139),number_number_of_int(X138)) )
& ( ord_less_int(number_number_of_int(X139),number_number_of_int(X138))
| ord_less_eq_int(number_number_of_int(X138),number_number_of_int(X139)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])]) ).
fof(c_0_24,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(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])])]) ).
cnf(c_0_25,plain,
( plus_plus_int(one_one_int,times_times_int(bit0(bit0(bit1(pls))),m)) = 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)))))
| ~ ord_less_int(one_one_int,t) ),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,negated_conjecture,
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(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_20]),c_0_22]) ).
cnf(c_0_27,plain,
( ord_less_int(number_number_of_int(X1),number_number_of_int(X2))
| ord_less_eq_int(number_number_of_int(X2),number_number_of_int(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,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_24]) ).
fof(c_0_29,plain,
! [X123,X124] :
( ~ ord_less_eq_int(X123,X124)
| ~ ord_less_eq_int(X124,X123)
| X123 = X124 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_31_zle__antisym])]) ).
cnf(c_0_30,plain,
~ ord_less_int(one_one_int,t),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_22]),c_0_26]) ).
cnf(c_0_31,plain,
( ord_less_eq_int(X2,X1)
| ord_less_int(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_14]),c_0_14]),c_0_14]),c_0_14]) ).
cnf(c_0_32,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(bit0(bit0(bit1(pls))),m),one_one_int)
| t != one_one_int ),
inference(rw,[status(thm)],[c_0_28,c_0_14]) ).
cnf(c_0_33,plain,
( X1 = X2
| ~ ord_less_eq_int(X1,X2)
| ~ ord_less_eq_int(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,plain,
ord_less_eq_int(t,one_one_int),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
ord_less_eq_int(one_one_int,t),
inference(split_conjunct,[status(thm)],[fact_0_tpos]) ).
cnf(c_0_36,plain,
( plus_plus_int(one_one_int,times_times_int(bit0(bit0(bit1(pls))),m)) = 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)))))
| t != one_one_int ),
inference(rw,[status(thm)],[c_0_32,c_0_20]) ).
cnf(c_0_37,plain,
t = one_one_int,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
cnf(c_0_38,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_22]),c_0_37])]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM926+1 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Aug 25 09:29:00 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.18/0.61 start to proof: theBenchmark
% 0.18/0.64 % Version : CSE_E---1.5
% 0.18/0.64 % Problem : theBenchmark.p
% 0.18/0.64 % Proof found
% 0.18/0.64 % SZS status Theorem for theBenchmark.p
% 0.18/0.64 % SZS output start Proof
% See solution above
% 0.18/0.65 % Total time : 0.024000 s
% 0.18/0.65 % SZS output end Proof
% 0.18/0.65 % Total time : 0.029000 s
%------------------------------------------------------------------------------