TSTP Solution File: NUM926+6 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM926+6 : TPTP v8.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n005.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 : Tue May 21 01:17:57 EDT 2024
% Result : Theorem 3.06s 0.88s
% Output : CNFRefutation 3.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 22
% Syntax : Number of formulae : 87 ( 71 unt; 0 def)
% Number of atoms : 112 ( 86 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 48 ( 23 ~; 16 |; 4 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-3 aty)
% Number of variables : 97 ( 7 sgn 50 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_123_add__Pls__right,axiom,
! [X19] : plus_plus(int,X19,pls) = ti(int,X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_add__Pls__right) ).
fof(fact_86_number__of__is__id,axiom,
! [X19] : number_number_of(int,X19) = ti(int,X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_number__of__is__id) ).
fof(conj_0,conjecture,
? [X5,X6] : plus_plus(int,power_power(int,X5,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X6,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(tsy_c_Int_OBit0_arg1,hypothesis,
! [X1] : bit0(ti(int,X1)) = bit0(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OBit0_arg1) ).
fof(fact_126_Bit0__def,axiom,
! [X19] : bit0(X19) = plus_plus(int,X19,X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_Bit0__def) ).
fof(tsy_c_Int_OBit1_res,hypothesis,
! [X1] : ti(int,bit1(X1)) = bit1(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OBit1_res) ).
fof(fact_151_Bit1__def,axiom,
! [X19] : bit1(X19) = plus_plus(int,plus_plus(int,one_one(int),X19),X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_Bit1__def) ).
fof(tsy_v_m_res,hypothesis,
ti(int,m) = m,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_m_res) ).
fof(fact_124_add__Pls,axiom,
! [X19] : plus_plus(int,pls,X19) = ti(int,X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_add__Pls) ).
fof(fact_89_zadd__commute,axiom,
! [X16,X12] : plus_plus(int,X16,X12) = plus_plus(int,X12,X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_zadd__commute) ).
fof(fact_128_zmult__1,axiom,
! [X16] : times_times(int,one_one(int),X16) = ti(int,X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_zmult__1) ).
fof(fact_22_zless__le,axiom,
! [X17,X18] :
( ord_less(int,X17,X18)
<=> ( ord_less_eq(int,X17,X18)
& ti(int,X17) != ti(int,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_zless__le) ).
fof(tsy_c_Groups_Oone__class_Oone_0_res,axiom,
! [X3] :
( zero_neq_one(X3)
=> ti(X3,one_one(X3)) = one_one(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oone__class_Oone_0_res) ).
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)
=> ? [X5,X6] : plus_plus(int,power_power(int,X5,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X6,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_87_zadd__assoc,axiom,
! [X40,X41,X42] : plus_plus(int,plus_plus(int,X40,X41),X42) = plus_plus(int,X40,plus_plus(int,X41,X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_zadd__assoc) ).
fof(fact_88_zadd__left__commute,axiom,
! [X9,X10,X16] : plus_plus(int,X9,plus_plus(int,X10,X16)) = plus_plus(int,X10,plus_plus(int,X9,X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_zadd__left__commute) ).
fof(fact_130_zadd__zmult__distrib,axiom,
! [X40,X41,X12] : times_times(int,plus_plus(int,X40,X41),X12) = plus_plus(int,times_times(int,X40,X12),times_times(int,X41,X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_zadd__zmult__distrib) ).
fof(fact_121_mult__Pls,axiom,
! [X12] : times_times(int,pls,X12) = pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_mult__Pls) ).
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)
=> ? [X5,X6] : plus_plus(int,power_power(int,X5,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X6,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(arity_Int_Oint___Rings_Ozero__neq__one,axiom,
zero_neq_one(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
fof(tsy_v_t_____res,axiom,
ti(int,t) = t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_t_____res) ).
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_22,plain,
! [X484] : plus_plus(int,X484,pls) = ti(int,X484),
inference(variable_rename,[status(thm)],[fact_123_add__Pls__right]) ).
fof(c_0_23,plain,
! [X407] : number_number_of(int,X407) = ti(int,X407),
inference(variable_rename,[status(thm)],[fact_86_number__of__is__id]) ).
fof(c_0_24,negated_conjecture,
~ ? [X5,X6] : plus_plus(int,power_power(int,X5,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X6,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_25,hypothesis,
! [X163] : bit0(ti(int,X163)) = bit0(X163),
inference(variable_rename,[status(thm)],[tsy_c_Int_OBit0_arg1]) ).
fof(c_0_26,plain,
! [X488] : bit0(X488) = plus_plus(int,X488,X488),
inference(variable_rename,[status(thm)],[fact_126_Bit0__def]) ).
fof(c_0_27,hypothesis,
! [X166] : ti(int,bit1(X166)) = bit1(X166),
inference(variable_rename,[status(thm)],[tsy_c_Int_OBit1_res]) ).
fof(c_0_28,plain,
! [X552] : bit1(X552) = plus_plus(int,plus_plus(int,one_one(int),X552),X552),
inference(variable_rename,[status(thm)],[fact_151_Bit1__def]) ).
cnf(c_0_29,plain,
plus_plus(int,X1,pls) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
number_number_of(int,X1) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,hypothesis,
ti(int,m) = m,
inference(split_conjunct,[status(thm)],[tsy_v_m_res]) ).
fof(c_0_32,plain,
! [X485] : plus_plus(int,pls,X485) = ti(int,X485),
inference(variable_rename,[status(thm)],[fact_124_add__Pls]) ).
fof(c_0_33,negated_conjecture,
! [X1371,X1372] : plus_plus(int,power_power(int,X1371,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1372,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_24])])]) ).
cnf(c_0_34,hypothesis,
bit0(ti(int,X1)) = bit0(X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,plain,
bit0(X1) = plus_plus(int,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,hypothesis,
ti(int,bit1(X1)) = bit1(X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,plain,
bit1(X1) = plus_plus(int,plus_plus(int,one_one(int),X1),X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_38,plain,
! [X414,X415] : plus_plus(int,X414,X415) = plus_plus(int,X415,X414),
inference(variable_rename,[status(thm)],[fact_89_zadd__commute]) ).
cnf(c_0_39,plain,
number_number_of(int,X1) = plus_plus(int,X1,pls),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_40,plain,
! [X490] : times_times(int,one_one(int),X490) = ti(int,X490),
inference(variable_rename,[status(thm)],[fact_128_zmult__1]) ).
cnf(c_0_41,hypothesis,
number_number_of(int,m) = m,
inference(rw,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_42,plain,
plus_plus(int,pls,X1) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_43,plain,
! [X17,X18] :
( ord_less(int,X17,X18)
<=> ( ord_less_eq(int,X17,X18)
& ti(int,X17) != ti(int,X18) ) ),
inference(fof_simplification,[status(thm)],[fact_22_zless__le]) ).
fof(c_0_44,plain,
! [X83] :
( ~ zero_neq_one(X83)
| ti(X83,one_one(X83)) = one_one(X83) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oone__class_Oone_0_res])])]) ).
fof(c_0_45,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])])])]) ).
cnf(c_0_46,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_33]) ).
cnf(c_0_47,hypothesis,
plus_plus(int,ti(int,X1),ti(int,X1)) = plus_plus(int,X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_35]) ).
fof(c_0_48,plain,
! [X408,X409,X410] : plus_plus(int,plus_plus(int,X408,X409),X410) = plus_plus(int,X408,plus_plus(int,X409,X410)),
inference(variable_rename,[status(thm)],[fact_87_zadd__assoc]) ).
fof(c_0_49,plain,
! [X411,X412,X413] : plus_plus(int,X411,plus_plus(int,X412,X413)) = plus_plus(int,X412,plus_plus(int,X411,X413)),
inference(variable_rename,[status(thm)],[fact_88_zadd__left__commute]) ).
cnf(c_0_50,hypothesis,
ti(int,plus_plus(int,plus_plus(int,one_one(int),X1),X1)) = plus_plus(int,plus_plus(int,one_one(int),X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_37]) ).
cnf(c_0_51,plain,
plus_plus(int,X1,X2) = plus_plus(int,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_52,plain,
ti(int,X1) = plus_plus(int,X1,pls),
inference(rw,[status(thm)],[c_0_30,c_0_39]) ).
fof(c_0_53,plain,
! [X493,X494,X495] : times_times(int,plus_plus(int,X493,X494),X495) = plus_plus(int,times_times(int,X493,X495),times_times(int,X494,X495)),
inference(variable_rename,[status(thm)],[fact_130_zadd__zmult__distrib]) ).
fof(c_0_54,plain,
! [X481] : times_times(int,pls,X481) = pls,
inference(variable_rename,[status(thm)],[fact_121_mult__Pls]) ).
cnf(c_0_55,plain,
times_times(int,one_one(int),X1) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_56,hypothesis,
plus_plus(int,m,pls) = m,
inference(rw,[status(thm)],[c_0_41,c_0_39]) ).
cnf(c_0_57,plain,
plus_plus(int,X1,pls) = plus_plus(int,pls,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_30]),c_0_39]) ).
fof(c_0_58,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])])])]) ).
fof(c_0_59,plain,
! [X248,X249] :
( ( ord_less_eq(int,X248,X249)
| ~ ord_less(int,X248,X249) )
& ( ti(int,X248) != ti(int,X249)
| ~ ord_less(int,X248,X249) )
& ( ~ ord_less_eq(int,X248,X249)
| ti(int,X248) = ti(int,X249)
| ord_less(int,X248,X249) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])]) ).
cnf(c_0_60,plain,
( ti(X1,one_one(X1)) = one_one(X1)
| ~ zero_neq_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_61,plain,
zero_neq_one(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Ozero__neq__one]) ).
cnf(c_0_62,plain,
ti(int,t) = t,
inference(split_conjunct,[status(thm)],[tsy_v_t_____res]) ).
cnf(c_0_63,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_45]) ).
cnf(c_0_64,negated_conjecture,
plus_plus(int,power_power(int,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(int,X2,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))) != plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(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)],[c_0_46,c_0_35]),c_0_35]),c_0_35]),c_0_35]),c_0_37]),c_0_37]),c_0_37]),c_0_37]),c_0_37]),c_0_37]),c_0_37]),c_0_37]) ).
cnf(c_0_65,hypothesis,
plus_plus(int,plus_plus(int,X1,pls),plus_plus(int,X1,pls)) = plus_plus(int,X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_30]),c_0_39]),c_0_30]),c_0_39]) ).
cnf(c_0_66,plain,
plus_plus(int,plus_plus(int,X1,X2),X3) = plus_plus(int,X1,plus_plus(int,X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_67,plain,
plus_plus(int,X1,plus_plus(int,X2,X3)) = plus_plus(int,X2,plus_plus(int,X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_68,hypothesis,
plus_plus(int,pls,plus_plus(int,X1,plus_plus(int,one_one(int),X1))) = plus_plus(int,X1,plus_plus(int,one_one(int),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_51]),c_0_51]) ).
cnf(c_0_69,plain,
times_times(int,plus_plus(int,X1,X2),X3) = plus_plus(int,times_times(int,X1,X3),times_times(int,X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_70,plain,
times_times(int,pls,X1) = pls,
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_71,plain,
times_times(int,one_one(int),X1) = plus_plus(int,X1,pls),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_30]),c_0_39]) ).
cnf(c_0_72,hypothesis,
plus_plus(int,pls,m) = m,
inference(rw,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_73,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_58]) ).
cnf(c_0_74,plain,
( ti(int,X1) = ti(int,X2)
| ord_less(int,X1,X2)
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_75,plain,
ti(int,one_one(int)) = one_one(int),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_76,plain,
number_number_of(int,t) = t,
inference(rw,[status(thm)],[c_0_62,c_0_30]) ).
cnf(c_0_77,plain,
( plus_plus(int,power_power(int,esk1_0,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(int,esk2_0,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))) = plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(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)],[c_0_63,c_0_35]),c_0_35]),c_0_35]),c_0_35]),c_0_37]),c_0_37]),c_0_37]),c_0_37]),c_0_37]),c_0_37]),c_0_37]),c_0_37]) ).
cnf(c_0_78,negated_conjecture,
plus_plus(int,power_power(int,X1,number_number_of(nat,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,one_one(int),one_one(int)))))),power_power(int,X2,number_number_of(nat,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,one_one(int),one_one(int))))))) != plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,one_one(int),plus_plus(int,m,plus_plus(int,m,plus_plus(int,m,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)],[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)],[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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65]),c_0_57]),c_0_57]),c_0_66]),c_0_67]),c_0_65]),c_0_57]),c_0_57]),c_0_66]),c_0_67]),c_0_65]),c_0_57]),c_0_57]),c_0_66]),c_0_67]),c_0_65]),c_0_57]),c_0_57]),c_0_66]),c_0_67]),c_0_66]),c_0_66]),c_0_66]),c_0_67]),c_0_67]),c_0_68]),c_0_68]),c_0_39]),c_0_66]),c_0_66]),c_0_66]),c_0_66]),c_0_66]),c_0_57]),c_0_67]),c_0_67]),c_0_68]),c_0_69]),c_0_70]),c_0_69]),c_0_70]),c_0_69]),c_0_71]),c_0_57]),c_0_72]),c_0_69]),c_0_71]),c_0_57]),c_0_72]),c_0_69]),c_0_71]),c_0_57]),c_0_72]),c_0_71]),c_0_57]),c_0_72]),c_0_66]),c_0_66]),c_0_66]),c_0_66]),c_0_66]),c_0_51]),c_0_67]),c_0_67]),c_0_67]) ).
cnf(c_0_79,plain,
( plus_plus(int,power_power(int,esk3_0,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(int,esk4_0,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))) = plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int))
| ~ 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)],[c_0_73,c_0_35]),c_0_35]),c_0_35]),c_0_35]),c_0_37]),c_0_37]),c_0_37]),c_0_37]),c_0_37]),c_0_37]),c_0_37]),c_0_37]) ).
cnf(c_0_80,plain,
( plus_plus(int,X1,pls) = plus_plus(int,X2,pls)
| ord_less(int,X1,X2)
| ~ ord_less_eq(int,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_30]),c_0_39]),c_0_52]) ).
cnf(c_0_81,plain,
ord_less_eq(int,one_one(int),t),
inference(split_conjunct,[status(thm)],[fact_0_tpos]) ).
cnf(c_0_82,plain,
plus_plus(int,pls,one_one(int)) = one_one(int),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_52]),c_0_57]) ).
cnf(c_0_83,plain,
plus_plus(int,pls,t) = t,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_39]),c_0_57]) ).
cnf(c_0_84,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)],[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)],[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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_65]),c_0_57]),c_0_57]),c_0_66]),c_0_67]),c_0_65]),c_0_57]),c_0_57]),c_0_66]),c_0_67]),c_0_65]),c_0_57]),c_0_57]),c_0_66]),c_0_67]),c_0_65]),c_0_57]),c_0_57]),c_0_66]),c_0_67]),c_0_66]),c_0_66]),c_0_66]),c_0_67]),c_0_67]),c_0_68]),c_0_68]),c_0_39]),c_0_66]),c_0_66]),c_0_66]),c_0_66]),c_0_66]),c_0_57]),c_0_67]),c_0_67]),c_0_68]),c_0_69]),c_0_70]),c_0_69]),c_0_70]),c_0_69]),c_0_71]),c_0_57]),c_0_72]),c_0_69]),c_0_71]),c_0_57]),c_0_72]),c_0_69]),c_0_71]),c_0_57]),c_0_72]),c_0_71]),c_0_57]),c_0_72]),c_0_66]),c_0_66]),c_0_66]),c_0_66]),c_0_66]),c_0_51]),c_0_67]),c_0_67]),c_0_67]),c_0_78]) ).
cnf(c_0_85,plain,
~ 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)],[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)],[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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_65]),c_0_57]),c_0_57]),c_0_66]),c_0_67]),c_0_65]),c_0_57]),c_0_57]),c_0_66]),c_0_67]),c_0_65]),c_0_57]),c_0_57]),c_0_66]),c_0_67]),c_0_65]),c_0_57]),c_0_57]),c_0_66]),c_0_67]),c_0_66]),c_0_66]),c_0_66]),c_0_67]),c_0_67]),c_0_68]),c_0_68]),c_0_39]),c_0_66]),c_0_66]),c_0_66]),c_0_66]),c_0_66]),c_0_57]),c_0_67]),c_0_67]),c_0_68]),c_0_69]),c_0_70]),c_0_69]),c_0_70]),c_0_69]),c_0_71]),c_0_57]),c_0_72]),c_0_69]),c_0_71]),c_0_57]),c_0_72]),c_0_69]),c_0_71]),c_0_57]),c_0_72]),c_0_71]),c_0_57]),c_0_72]),c_0_66]),c_0_66]),c_0_66]),c_0_66]),c_0_66]),c_0_51]),c_0_67]),c_0_67]),c_0_67]),c_0_78]) ).
cnf(c_0_86,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_57]),c_0_82]),c_0_57]),c_0_83]),c_0_84]),c_0_85]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : NUM926+6 : TPTP v8.2.0. Released v5.3.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon May 20 07:07:22 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.17/0.45 Running first-order theorem proving
% 0.17/0.45 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.06/0.88 # Version: 3.1.0
% 3.06/0.88 # Preprocessing class: FSLSSMSMSSSNFFN.
% 3.06/0.88 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.06/0.88 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 3.06/0.88 # Starting new_bool_3 with 300s (1) cores
% 3.06/0.88 # Starting new_bool_1 with 300s (1) cores
% 3.06/0.88 # Starting sh5l with 300s (1) cores
% 3.06/0.88 # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 6976 completed with status 0
% 3.06/0.88 # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 3.06/0.88 # Preprocessing class: FSLSSMSMSSSNFFN.
% 3.06/0.88 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.06/0.88 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 3.06/0.88 # No SInE strategy applied
% 3.06/0.88 # Search class: FGHSM-FSLM32-DFFFFFNN
% 3.06/0.88 # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 3.06/0.88 # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 113s (1) cores
% 3.06/0.88 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 3.06/0.88 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 113s (1) cores
% 3.06/0.88 # Starting U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 3.06/0.88 # Starting G-E--_208_B07_F1_AE_CS_SP_PS_S5PRR_S0Y with 113s (1) cores
% 3.06/0.88 # G-E--_208_B07_F1_AE_CS_SP_PS_S5PRR_S0Y with pid 6987 completed with status 0
% 3.06/0.88 # Result found by G-E--_208_B07_F1_AE_CS_SP_PS_S5PRR_S0Y
% 3.06/0.88 # Preprocessing class: FSLSSMSMSSSNFFN.
% 3.06/0.88 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.06/0.88 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 3.06/0.88 # No SInE strategy applied
% 3.06/0.88 # Search class: FGHSM-FSLM32-DFFFFFNN
% 3.06/0.88 # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 3.06/0.88 # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 113s (1) cores
% 3.06/0.88 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 3.06/0.88 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 113s (1) cores
% 3.06/0.88 # Starting U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 3.06/0.88 # Starting G-E--_208_B07_F1_AE_CS_SP_PS_S5PRR_S0Y with 113s (1) cores
% 3.06/0.88 # Preprocessing time : 0.011 s
% 3.06/0.88 # Presaturation interreduction done
% 3.06/0.88
% 3.06/0.88 # Proof found!
% 3.06/0.88 # SZS status Theorem
% 3.06/0.88 # SZS output start CNFRefutation
% See solution above
% 3.06/0.88 # Parsed axioms : 653
% 3.06/0.88 # Removed by relevancy pruning/SinE : 0
% 3.06/0.88 # Initial clauses : 854
% 3.06/0.88 # Removed in clause preprocessing : 8
% 3.06/0.88 # Initial clauses in saturation : 846
% 3.06/0.88 # Processed clauses : 4230
% 3.06/0.88 # ...of these trivial : 68
% 3.06/0.88 # ...subsumed : 2382
% 3.06/0.88 # ...remaining for further processing : 1780
% 3.06/0.88 # Other redundant clauses eliminated : 6
% 3.06/0.88 # Clauses deleted for lack of memory : 0
% 3.06/0.88 # Backward-subsumed : 57
% 3.06/0.88 # Backward-rewritten : 109
% 3.06/0.88 # Generated clauses : 9766
% 3.06/0.88 # ...of the previous two non-redundant : 8195
% 3.06/0.88 # ...aggressively subsumed : 0
% 3.06/0.88 # Contextual simplify-reflections : 1
% 3.06/0.88 # Paramodulations : 9738
% 3.06/0.88 # Factorizations : 7
% 3.06/0.88 # NegExts : 0
% 3.06/0.88 # Equation resolutions : 21
% 3.06/0.88 # Disequality decompositions : 0
% 3.06/0.88 # Total rewrite steps : 44304
% 3.06/0.88 # ...of those cached : 41311
% 3.06/0.88 # Propositional unsat checks : 0
% 3.06/0.88 # Propositional check models : 0
% 3.06/0.88 # Propositional check unsatisfiable : 0
% 3.06/0.88 # Propositional clauses : 0
% 3.06/0.88 # Propositional clauses after purity: 0
% 3.06/0.88 # Propositional unsat core size : 0
% 3.06/0.88 # Propositional preprocessing time : 0.000
% 3.06/0.88 # Propositional encoding time : 0.000
% 3.06/0.88 # Propositional solver time : 0.000
% 3.06/0.88 # Success case prop preproc time : 0.000
% 3.06/0.88 # Success case prop encoding time : 0.000
% 3.06/0.88 # Success case prop solver time : 0.000
% 3.06/0.88 # Current number of processed clauses : 868
% 3.06/0.88 # Positive orientable unit clauses : 257
% 3.06/0.88 # Positive unorientable unit clauses: 7
% 3.06/0.88 # Negative unit clauses : 139
% 3.06/0.88 # Non-unit-clauses : 465
% 3.06/0.88 # Current number of unprocessed clauses: 5511
% 3.06/0.88 # ...number of literals in the above : 10511
% 3.06/0.88 # Current number of archived formulas : 0
% 3.06/0.88 # Current number of archived clauses : 910
% 3.06/0.88 # Clause-clause subsumption calls (NU) : 64961
% 3.06/0.88 # Rec. Clause-clause subsumption calls : 38631
% 3.06/0.88 # Non-unit clause-clause subsumptions : 665
% 3.06/0.88 # Unit Clause-clause subsumption calls : 4004
% 3.06/0.88 # Rewrite failures with RHS unbound : 0
% 3.06/0.88 # BW rewrite match attempts : 2302
% 3.06/0.88 # BW rewrite match successes : 347
% 3.06/0.88 # Condensation attempts : 0
% 3.06/0.88 # Condensation successes : 0
% 3.06/0.88 # Termbank termtop insertions : 359339
% 3.06/0.88 # Search garbage collected termcells : 9671
% 3.06/0.88
% 3.06/0.88 # -------------------------------------------------
% 3.06/0.88 # User time : 0.363 s
% 3.06/0.88 # System time : 0.021 s
% 3.06/0.88 # Total time : 0.384 s
% 3.06/0.88 # Maximum resident set size: 5120 pages
% 3.06/0.88
% 3.06/0.88 # -------------------------------------------------
% 3.06/0.88 # User time : 1.732 s
% 3.06/0.88 # System time : 0.069 s
% 3.06/0.88 # Total time : 1.801 s
% 3.06/0.88 # Maximum resident set size: 2452 pages
% 3.06/0.88 % E---3.1 exiting
% 3.06/0.88 % E exiting
%------------------------------------------------------------------------------