TSTP Solution File: NUM926+5 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM926+5 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n010.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 10:41:38 EDT 2023
% Result : Theorem 0.21s 0.61s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 41
% Syntax : Number of formulae : 62 ( 20 unt; 33 typ; 0 def)
% Number of atoms : 45 ( 29 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 33 ( 17 ~; 10 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 22 >; 12 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 11 con; 0-3 aty)
% Number of variables : 37 ( 6 sgn; 16 !; 8 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
semiring_1: $i > $o ).
tff(decl_23,type,
one_one: $i > $i ).
tff(decl_24,type,
ti: ( $i * $i ) > $i ).
tff(decl_25,type,
comm_semiring_1: $i > $o ).
tff(decl_26,type,
plus_plus: ( $i * $i * $i ) > $i ).
tff(decl_27,type,
monoid_mult: $i > $o ).
tff(decl_28,type,
times_times: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
undefined: $i > $i ).
tff(decl_30,type,
int: $i ).
tff(decl_31,type,
zprime: $i > $o ).
tff(decl_32,type,
bit0: $i > $i ).
tff(decl_33,type,
bit1: $i > $i ).
tff(decl_34,type,
pls: $i ).
tff(decl_35,type,
number: $i > $o ).
tff(decl_36,type,
number_number_of: ( $i * $i ) > $i ).
tff(decl_37,type,
linorder: $i > $o ).
tff(decl_38,type,
ord_less: ( $i * $i * $i ) > $o ).
tff(decl_39,type,
ord_less_eq: ( $i * $i * $i ) > $o ).
tff(decl_40,type,
power_power: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
nat: $i ).
tff(decl_42,type,
twoSqu33214720sum2sq: $i > $o ).
tff(decl_43,type,
m: $i ).
tff(decl_44,type,
s: $i ).
tff(decl_45,type,
t: $i ).
tff(decl_46,type,
number_semiring: $i > $o ).
tff(decl_47,type,
number_ring: $i > $o ).
tff(decl_48,type,
linordered_idom: $i > $o ).
tff(decl_49,type,
ring_char_0: $i > $o ).
tff(decl_50,type,
esk1_0: $i ).
tff(decl_51,type,
esk2_0: $i ).
tff(decl_52,type,
esk3_0: $i ).
tff(decl_53,type,
esk4_0: $i ).
tff(decl_54,type,
esk5_0: $i ).
fof(conj_0,conjecture,
? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,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/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_86_number__of__is__id,axiom,
! [X18] : number_number_of(int,X18) = X18,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_number__of__is__id) ).
fof(fact_89_zadd__commute,axiom,
! [X15,X11] : plus_plus(int,X15,X11) = plus_plus(int,X11,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_zadd__commute) ).
fof(fact_85_zmult__commute,axiom,
! [X15,X11] : times_times(int,X15,X11) = times_times(int,X11,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_zmult__commute) ).
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)
=> ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,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/sandbox/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_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)
=> ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,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/sandbox/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_22_zless__le,axiom,
! [X16,X17] :
( ord_less(int,X16,X17)
<=> ( ord_less_eq(int,X16,X17)
& X16 != X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_zless__le) ).
fof(fact_0_tpos,axiom,
ord_less_eq(int,one_one(int),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tpos) ).
fof(c_0_8,negated_conjecture,
~ ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,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_9,negated_conjecture,
! [X308,X309] : plus_plus(int,power_power(int,X308,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X309,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_8])]) ).
fof(c_0_10,plain,
! [X285] : number_number_of(int,X285) = X285,
inference(variable_rename,[status(thm)],[fact_86_number__of__is__id]) ).
fof(c_0_11,plain,
! [X292,X293] : plus_plus(int,X292,X293) = plus_plus(int,X293,X292),
inference(variable_rename,[status(thm)],[fact_89_zadd__commute]) ).
cnf(c_0_12,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_9]) ).
cnf(c_0_13,plain,
number_number_of(int,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
plus_plus(int,X1,X2) = plus_plus(int,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,plain,
! [X283,X284] : times_times(int,X283,X284) = times_times(int,X284,X283),
inference(variable_rename,[status(thm)],[fact_85_zmult__commute]) ).
fof(c_0_16,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_17,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,bit0(bit0(bit1(pls))),m)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_18,plain,
times_times(int,X1,X2) = times_times(int,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,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_20,plain,
! [X126,X127] :
( ( ord_less_eq(int,X126,X127)
| ~ ord_less(int,X126,X127) )
& ( X126 != X127
| ~ ord_less(int,X126,X127) )
& ( ~ ord_less_eq(int,X126,X127)
| X126 = X127
| ord_less(int,X126,X127) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_22_zless__le])])]) ).
cnf(c_0_21,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_16]) ).
cnf(c_0_22,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)],[c_0_17,c_0_18]) ).
cnf(c_0_23,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_19]) ).
cnf(c_0_24,plain,
( X1 = X2
| ord_less(int,X1,X2)
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
ord_less_eq(int,one_one(int),t),
inference(split_conjunct,[status(thm)],[fact_0_tpos]) ).
cnf(c_0_26,plain,
one_one(int) != t,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_13]),c_0_18]),c_0_14]),c_0_22]) ).
cnf(c_0_27,plain,
~ ord_less(int,one_one(int),t),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_13]),c_0_18]),c_0_14]),c_0_22]) ).
cnf(c_0_28,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM926+5 : TPTP v8.1.2. Released v5.3.0.
% 0.14/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 16:23:50 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 0.21/0.61 % Version : CSE_E---1.5
% 0.21/0.61 % Problem : theBenchmark.p
% 0.21/0.61 % Proof found
% 0.21/0.61 % SZS status Theorem for theBenchmark.p
% 0.21/0.61 % SZS output start Proof
% See solution above
% 0.21/0.61 % Total time : 0.021000 s
% 0.21/0.61 % SZS output end Proof
% 0.21/0.61 % Total time : 0.027000 s
%------------------------------------------------------------------------------