TSTP Solution File: NUM925+8 by E---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : NUM925+8 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n028.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 18:58:01 EDT 2023
% Result : Theorem 72.59s 12.23s
% Output : CNFRefutation 72.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 29
% Syntax : Number of formulae : 88 ( 80 unt; 0 def)
% Number of atoms : 135 ( 85 equ)
% Maximal formula atoms : 19 ( 1 avg)
% Number of connectives : 84 ( 37 ~; 33 |; 8 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 12 con; 0-4 aty)
% Number of variables : 65 ( 2 sgn; 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_2924_succ__pred,axiom,
! [X11] : hAPP(int,int,succ,hAPP(int,int,pred,X11)) = ti(int,X11),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_2924_succ__pred) ).
fof(fact_123_number__of__is__id,axiom,
! [X21] : hAPP(int,int,number_number_of(int),X21) = ti(int,X21),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_123_number__of__is__id) ).
fof(fact_1006_transfer__nat__int__numerals_I2_J,axiom,
one_one(nat) = hAPP(int,nat,nat_1,one_one(int)),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_1006_transfer__nat__int__numerals_I2_J) ).
fof(fact_1382_One__nat__def,axiom,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_1382_One__nat__def) ).
fof(fact_998_transfer__nat__int__numerals_I1_J,axiom,
zero_zero(nat) = hAPP(int,nat,nat_1,zero_zero(int)),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_998_transfer__nat__int__numerals_I1_J) ).
fof(fact_76_Pls__def,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_76_Pls__def) ).
fof(fact_2926_pred__Bit1,axiom,
! [X21] : hAPP(int,int,pred,hAPP(int,int,bit1,X21)) = hAPP(int,int,bit0,X21),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_2926_pred__Bit1) ).
fof(fact_37_one__is__num__one,axiom,
one_one(int) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_37_one__is__num__one) ).
fof(fact_72_Bit0__Pls,axiom,
hAPP(int,int,bit0,pls) = pls,
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_72_Bit0__Pls) ).
fof(fact_284_succ__Pls,axiom,
hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_284_succ__Pls) ).
fof(fact_1004_nat__number__of__def,axiom,
! [X10] : hAPP(int,nat,number_number_of(nat),X10) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),X10)),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_1004_nat__number__of__def) ).
fof(conj_0,conjecture,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',conj_0) ).
fof(fact_1484_semiring__norm_I115_J,axiom,
hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_1484_semiring__norm_I115_J) ).
fof(fact_1450_int__Suc,axiom,
! [X15] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X15)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),X15)),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_1450_int__Suc) ).
fof(fact_2925_pred__Bit0,axiom,
! [X21] : hAPP(int,int,pred,hAPP(int,int,bit0,X21)) = hAPP(int,int,bit1,hAPP(int,int,pred,X21)),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_2925_pred__Bit0) ).
fof(fact_285_succ__Bit1,axiom,
! [X21] : hAPP(int,int,succ,hAPP(int,int,bit1,X21)) = hAPP(int,int,bit0,hAPP(int,int,succ,X21)),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_285_succ__Bit1) ).
fof(fact_1503_nat__2,axiom,
hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_1503_nat__2) ).
fof(fact_534_not__less__iff__gr__or__eq,axiom,
! [X1] :
( linorder(X1)
=> ! [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6))
| ti(X1,X6) = ti(X1,X7) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_534_not__less__iff__gr__or__eq) ).
fof(fact_188_power__eq__0__iff,axiom,
! [X1] :
( ( power(X1)
& mult_zero(X1)
& no_zero_divisors(X1)
& zero_neq_one(X1) )
=> ! [X8,X18] :
( hAPP(nat,X1,hAPP(X1,fun(nat,X1),power_power(X1),X8),X18) = zero_zero(X1)
<=> ( ti(X1,X8) = zero_zero(X1)
& X18 != zero_zero(nat) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_188_power__eq__0__iff) ).
fof(fact_21_int__power,axiom,
! [X15,X16] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X15),X16)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),X15)),X16),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_21_int__power) ).
fof(tsy_c_hAPP_res,axiom,
! [X2,X1,X4,X5] : ti(X2,hAPP(X1,X2,X4,X5)) = hAPP(X1,X2,X4,X5),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',tsy_c_hAPP_res) ).
fof(fact_0_n1pos,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_0_n1pos) ).
fof(arity_Int_Oint___Rings_Ozero__neq__one,axiom,
zero_neq_one(int),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
fof(arity_Int_Oint___Rings_Omult__zero,axiom,
mult_zero(int),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',arity_Int_Oint___Rings_Omult__zero) ).
fof(arity_Int_Oint___Rings_Ono__zero__divisors,axiom,
no_zero_divisors(int),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
fof(arity_Int_Oint___Power_Opower,axiom,
power(int),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',arity_Int_Oint___Power_Opower) ).
fof(fact_2928_pred__Pls,axiom,
hAPP(int,int,pred,pls) = min,
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_2928_pred__Pls) ).
fof(fact_686_succ__Min,axiom,
hAPP(int,int,succ,min) = pls,
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',fact_686_succ__Min) ).
fof(arity_Int_Oint___Orderings_Olinorder,axiom,
linorder(int),
file('/export/starexec/sandbox/tmp/tmp.yznxZscYT9/E---3.1_17648.p',arity_Int_Oint___Orderings_Olinorder) ).
fof(c_0_29,plain,
! [X9861] : hAPP(int,int,succ,hAPP(int,int,pred,X9861)) = ti(int,X9861),
inference(variable_rename,[status(thm)],[fact_2924_succ__pred]) ).
fof(c_0_30,plain,
! [X561] : hAPP(int,int,number_number_of(int),X561) = ti(int,X561),
inference(variable_rename,[status(thm)],[fact_123_number__of__is__id]) ).
cnf(c_0_31,plain,
one_one(nat) = hAPP(int,nat,nat_1,one_one(int)),
inference(split_conjunct,[status(thm)],[fact_1006_transfer__nat__int__numerals_I2_J]) ).
cnf(c_0_32,plain,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
inference(split_conjunct,[status(thm)],[fact_1382_One__nat__def]) ).
cnf(c_0_33,plain,
zero_zero(nat) = hAPP(int,nat,nat_1,zero_zero(int)),
inference(split_conjunct,[status(thm)],[fact_998_transfer__nat__int__numerals_I1_J]) ).
cnf(c_0_34,plain,
pls = zero_zero(int),
inference(split_conjunct,[status(thm)],[fact_76_Pls__def]) ).
cnf(c_0_35,plain,
hAPP(int,int,succ,hAPP(int,int,pred,X1)) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
hAPP(int,int,number_number_of(int),X1) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_37,plain,
! [X9863] : hAPP(int,int,pred,hAPP(int,int,bit1,X9863)) = hAPP(int,int,bit0,X9863),
inference(variable_rename,[status(thm)],[fact_2926_pred__Bit1]) ).
cnf(c_0_38,plain,
hAPP(int,nat,nat_1,one_one(int)) = hAPP(nat,nat,suc,zero_zero(nat)),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,plain,
zero_zero(nat) = hAPP(int,nat,nat_1,pls),
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,plain,
one_one(int) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)),
inference(split_conjunct,[status(thm)],[fact_37_one__is__num__one]) ).
cnf(c_0_41,plain,
hAPP(int,int,number_number_of(int),X1) = hAPP(int,int,succ,hAPP(int,int,pred,X1)),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,plain,
hAPP(int,int,pred,hAPP(int,int,bit1,X1)) = hAPP(int,int,bit0,X1),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,plain,
hAPP(int,int,bit0,pls) = pls,
inference(split_conjunct,[status(thm)],[fact_72_Bit0__Pls]) ).
cnf(c_0_44,plain,
hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
inference(split_conjunct,[status(thm)],[fact_284_succ__Pls]) ).
fof(c_0_45,plain,
! [X3049] : hAPP(int,nat,number_number_of(nat),X3049) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),X3049)),
inference(variable_rename,[status(thm)],[fact_1004_nat__number__of__def]) ).
fof(c_0_46,negated_conjecture,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_47,plain,
hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
inference(split_conjunct,[status(thm)],[fact_1484_semiring__norm_I115_J]) ).
cnf(c_0_48,plain,
hAPP(int,nat,nat_1,one_one(int)) = hAPP(nat,nat,suc,hAPP(int,nat,nat_1,pls)),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_49,plain,
one_one(int) = hAPP(int,int,bit1,pls),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43]),c_0_44]) ).
fof(c_0_50,plain,
! [X1354] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X1354)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),X1354)),
inference(variable_rename,[status(thm)],[fact_1450_int__Suc]) ).
cnf(c_0_51,plain,
hAPP(int,nat,number_number_of(nat),X1) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),X1)),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_52,plain,
! [X9862] : hAPP(int,int,pred,hAPP(int,int,bit0,X9862)) = hAPP(int,int,bit1,hAPP(int,int,pred,X9862)),
inference(variable_rename,[status(thm)],[fact_2925_pred__Bit0]) ).
fof(c_0_53,plain,
! [X9932] : hAPP(int,int,succ,hAPP(int,int,bit1,X9932)) = hAPP(int,int,bit0,hAPP(int,int,succ,X9932)),
inference(variable_rename,[status(thm)],[fact_285_succ__Bit1]) ).
cnf(c_0_54,negated_conjecture,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_55,plain,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(int,nat,nat_1,pls))),
inference(rw,[status(thm)],[c_0_47,c_0_39]) ).
cnf(c_0_56,plain,
hAPP(nat,nat,suc,hAPP(int,nat,nat_1,pls)) = hAPP(int,nat,nat_1,hAPP(int,int,bit1,pls)),
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_57,plain,
hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X1)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),X1)),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_58,plain,
hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))),
inference(split_conjunct,[status(thm)],[fact_1503_nat__2]) ).
cnf(c_0_59,plain,
hAPP(int,nat,number_number_of(nat),X1) = hAPP(int,nat,nat_1,hAPP(int,int,succ,hAPP(int,int,pred,X1))),
inference(rw,[status(thm)],[c_0_51,c_0_41]) ).
cnf(c_0_60,plain,
hAPP(int,int,pred,hAPP(int,int,bit0,X1)) = hAPP(int,int,bit1,hAPP(int,int,pred,X1)),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_61,plain,
hAPP(int,int,succ,hAPP(int,int,bit1,X1)) = hAPP(int,int,bit0,hAPP(int,int,succ,X1)),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
fof(c_0_62,plain,
! [X1] :
( linorder(X1)
=> ! [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6))
| ti(X1,X6) = ti(X1,X7) ) ) ),
inference(fof_simplification,[status(thm)],[fact_534_not__less__iff__gr__or__eq]) ).
fof(c_0_63,plain,
! [X11679,X11680,X11681] :
( ( ti(X11679,X11680) = zero_zero(X11679)
| hAPP(nat,X11679,hAPP(X11679,fun(nat,X11679),power_power(X11679),X11680),X11681) != zero_zero(X11679)
| ~ power(X11679)
| ~ mult_zero(X11679)
| ~ no_zero_divisors(X11679)
| ~ zero_neq_one(X11679) )
& ( X11681 != zero_zero(nat)
| hAPP(nat,X11679,hAPP(X11679,fun(nat,X11679),power_power(X11679),X11680),X11681) != zero_zero(X11679)
| ~ power(X11679)
| ~ mult_zero(X11679)
| ~ no_zero_divisors(X11679)
| ~ zero_neq_one(X11679) )
& ( ti(X11679,X11680) != zero_zero(X11679)
| X11681 = zero_zero(nat)
| hAPP(nat,X11679,hAPP(X11679,fun(nat,X11679),power_power(X11679),X11680),X11681) = zero_zero(X11679)
| ~ power(X11679)
| ~ mult_zero(X11679)
| ~ no_zero_divisors(X11679)
| ~ zero_neq_one(X11679) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_188_power__eq__0__iff])])])]) ).
fof(c_0_64,plain,
! [X1222,X1223] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X1222),X1223)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),X1222)),X1223),
inference(variable_rename,[status(thm)],[fact_21_int__power]) ).
fof(c_0_65,plain,
! [X2121,X2122,X2123,X2124] : ti(X2121,hAPP(X2122,X2121,X2123,X2124)) = hAPP(X2122,X2121,X2123,X2124),
inference(variable_rename,[status(thm)],[tsy_c_hAPP_res]) ).
cnf(c_0_66,negated_conjecture,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(nat,nat,suc,hAPP(int,nat,nat_1,hAPP(int,int,bit1,pls)))) = pls,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_49]),c_0_55]),c_0_56]),c_0_34]) ).
cnf(c_0_67,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(nat,int,semiring_1_of_nat(int),X1)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X1)),
inference(rw,[status(thm)],[c_0_57,c_0_49]) ).
cnf(c_0_68,plain,
hAPP(nat,nat,suc,hAPP(int,nat,nat_1,hAPP(int,int,bit1,pls))) = hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_58,c_0_51]),c_0_59]),c_0_60]),c_0_42]),c_0_43]),c_0_61]),c_0_44]),c_0_39]),c_0_56]) ).
fof(c_0_69,plain,
! [X11323,X11324,X11325] :
( ( hBOOL(hAPP(X11323,bool,hAPP(X11323,fun(X11323,bool),ord_less(X11323),X11324),X11325))
| hBOOL(hAPP(X11323,bool,hAPP(X11323,fun(X11323,bool),ord_less(X11323),X11325),X11324))
| ti(X11323,X11324) = ti(X11323,X11325)
| ~ linorder(X11323) )
& ( ~ hBOOL(hAPP(X11323,bool,hAPP(X11323,fun(X11323,bool),ord_less(X11323),X11325),X11324))
| ~ hBOOL(hAPP(X11323,bool,hAPP(X11323,fun(X11323,bool),ord_less(X11323),X11324),X11325))
| ~ linorder(X11323) )
& ( ti(X11323,X11324) != ti(X11323,X11325)
| ~ hBOOL(hAPP(X11323,bool,hAPP(X11323,fun(X11323,bool),ord_less(X11323),X11324),X11325))
| ~ linorder(X11323) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])])])]) ).
cnf(c_0_70,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(split_conjunct,[status(thm)],[fact_0_n1pos]) ).
cnf(c_0_71,plain,
( ti(X1,X2) = zero_zero(X1)
| hAPP(nat,X1,hAPP(X1,fun(nat,X1),power_power(X1),X2),X3) != zero_zero(X1)
| ~ power(X1)
| ~ mult_zero(X1)
| ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_72,plain,
hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X1),X2)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),X2),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_73,plain,
ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_74,plain,
zero_neq_one(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Ozero__neq__one]) ).
cnf(c_0_75,plain,
mult_zero(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Omult__zero]) ).
cnf(c_0_76,plain,
no_zero_divisors(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Ono__zero__divisors]) ).
cnf(c_0_77,plain,
power(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Power_Opower]) ).
cnf(c_0_78,negated_conjecture,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = pls,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).
cnf(c_0_79,plain,
( ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_80,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_34]),c_0_49]),c_0_67]) ).
cnf(c_0_81,plain,
hAPP(int,int,pred,pls) = min,
inference(split_conjunct,[status(thm)],[fact_2928_pred__Pls]) ).
cnf(c_0_82,plain,
hAPP(int,int,succ,min) = pls,
inference(split_conjunct,[status(thm)],[fact_686_succ__Min]) ).
cnf(c_0_83,plain,
linorder(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Orderings_Olinorder]) ).
cnf(c_0_84,plain,
( hAPP(nat,int,semiring_1_of_nat(int),X1) = pls
| hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X1),X2)) != pls ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]),c_0_34]),c_0_34]),c_0_74]),c_0_75]),c_0_76]),c_0_77])]) ).
cnf(c_0_85,negated_conjecture,
hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = pls,
inference(rw,[status(thm)],[c_0_78,c_0_72]) ).
cnf(c_0_86,plain,
hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n)) != pls,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_36]),c_0_41]),c_0_81]),c_0_82]),c_0_73]),c_0_83])]) ).
cnf(c_0_87,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 1.29/1.30 % Problem : NUM925+8 : TPTP v8.1.2. Released v5.3.0.
% 1.29/1.31 % Command : run_E %s %d THM
% 1.31/1.51 % Computer : n028.cluster.edu
% 1.31/1.51 % Model : x86_64 x86_64
% 1.31/1.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 1.31/1.51 % Memory : 8042.1875MB
% 1.31/1.51 % OS : Linux 3.10.0-693.el7.x86_64
% 1.31/1.51 % CPULimit : 2400
% 1.31/1.51 % WCLimit : 300
% 1.31/1.51 % DateTime : Mon Oct 2 15:20:23 EDT 2023
% 1.31/1.51 % CPUTime :
% 2.56/2.81 Running first-order theorem proving
% 2.56/2.81 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/tmp/tmp.yznxZscYT9/E---3.1_17648.p
% 72.59/12.23 # Version: 3.1pre001
% 72.59/12.23 # Preprocessing class: FMLMSMSLSSSNFFN.
% 72.59/12.23 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 72.59/12.23 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 72.59/12.23 # Starting new_bool_3 with 600s (2) cores
% 72.59/12.23 # Starting new_bool_1 with 600s (2) cores
% 72.59/12.23 # Starting sh5l with 300s (1) cores
% 72.59/12.23 # sh5l with pid 17729 completed with status 0
% 72.59/12.23 # Result found by sh5l
% 72.59/12.23 # Preprocessing class: FMLMSMSLSSSNFFN.
% 72.59/12.23 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 72.59/12.23 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 72.59/12.23 # Starting new_bool_3 with 600s (2) cores
% 72.59/12.23 # Starting new_bool_1 with 600s (2) cores
% 72.59/12.23 # Starting sh5l with 300s (1) cores
% 72.59/12.23 # SinE strategy is gf500_gu_R04_F100_L20000
% 72.59/12.23 # Search class: FGHSM-SMLM33-DFFFFFNN
% 72.59/12.23 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 72.59/12.23 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 72.59/12.23 # SAT001_MinMin_p005000_rr with pid 17735 completed with status 0
% 72.59/12.23 # Result found by SAT001_MinMin_p005000_rr
% 72.59/12.23 # Preprocessing class: FMLMSMSLSSSNFFN.
% 72.59/12.23 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 72.59/12.23 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 72.59/12.23 # Starting new_bool_3 with 600s (2) cores
% 72.59/12.23 # Starting new_bool_1 with 600s (2) cores
% 72.59/12.23 # Starting sh5l with 300s (1) cores
% 72.59/12.23 # SinE strategy is gf500_gu_R04_F100_L20000
% 72.59/12.23 # Search class: FGHSM-SMLM33-DFFFFFNN
% 72.59/12.23 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 72.59/12.23 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 72.59/12.23 # Preprocessing time : 0.188 s
% 72.59/12.23 # Presaturation interreduction done
% 72.59/12.23
% 72.59/12.23 # Proof found!
% 72.59/12.23 # SZS status Theorem
% 72.59/12.23 # SZS output start CNFRefutation
% See solution above
% 72.59/12.23 # Parsed axioms : 5747
% 72.59/12.23 # Removed by relevancy pruning/SinE : 584
% 72.59/12.23 # Initial clauses : 7950
% 72.59/12.23 # Removed in clause preprocessing : 208
% 72.59/12.23 # Initial clauses in saturation : 7742
% 72.59/12.23 # Processed clauses : 20915
% 72.59/12.23 # ...of these trivial : 503
% 72.59/12.23 # ...subsumed : 9895
% 72.59/12.23 # ...remaining for further processing : 10517
% 72.59/12.23 # Other redundant clauses eliminated : 470
% 72.59/12.23 # Clauses deleted for lack of memory : 0
% 72.59/12.23 # Backward-subsumed : 206
% 72.59/12.23 # Backward-rewritten : 369
% 72.59/12.23 # Generated clauses : 47924
% 72.59/12.23 # ...of the previous two non-redundant : 39610
% 72.59/12.23 # ...aggressively subsumed : 0
% 72.59/12.23 # Contextual simplify-reflections : 37
% 72.59/12.23 # Paramodulations : 47456
% 72.59/12.23 # Factorizations : 3
% 72.59/12.23 # NegExts : 0
% 72.59/12.23 # Equation resolutions : 486
% 72.59/12.23 # Total rewrite steps : 74293
% 72.59/12.23 # Propositional unsat checks : 3
% 72.59/12.23 # Propositional check models : 2
% 72.59/12.23 # Propositional check unsatisfiable : 0
% 72.59/12.23 # Propositional clauses : 0
% 72.59/12.23 # Propositional clauses after purity: 0
% 72.59/12.23 # Propositional unsat core size : 0
% 72.59/12.23 # Propositional preprocessing time : 0.000
% 72.59/12.23 # Propositional encoding time : 0.151
% 72.59/12.23 # Propositional solver time : 0.045
% 72.59/12.23 # Success case prop preproc time : 0.000
% 72.59/12.23 # Success case prop encoding time : 0.000
% 72.59/12.23 # Success case prop solver time : 0.000
% 72.59/12.23 # Current number of processed clauses : 3103
% 72.59/12.23 # Positive orientable unit clauses : 1633
% 72.59/12.23 # Positive unorientable unit clauses: 44
% 72.59/12.23 # Negative unit clauses : 266
% 72.59/12.23 # Non-unit-clauses : 1160
% 72.59/12.23 # Current number of unprocessed clauses: 32681
% 72.59/12.23 # ...number of literals in the above : 61921
% 72.59/12.23 # Current number of archived formulas : 0
% 72.59/12.23 # Current number of archived clauses : 7112
% 72.59/12.23 # Clause-clause subsumption calls (NU) : 7398865
% 72.59/12.23 # Rec. Clause-clause subsumption calls : 1406062
% 72.59/12.23 # Non-unit clause-clause subsumptions : 3561
% 72.59/12.23 # Unit Clause-clause subsumption calls : 10979
% 72.59/12.23 # Rewrite failures with RHS unbound : 4
% 72.59/12.23 # BW rewrite match attempts : 412041
% 72.59/12.23 # BW rewrite match successes : 1266
% 72.59/12.23 # Condensation attempts : 0
% 72.59/12.23 # Condensation successes : 0
% 72.59/12.23 # Termbank termtop insertions : 5474266
% 72.59/12.23
% 72.59/12.23 # -------------------------------------------------
% 72.59/12.23 # User time : 8.802 s
% 72.59/12.23 # System time : 0.169 s
% 72.59/12.23 # Total time : 8.971 s
% 72.59/12.23 # Maximum resident set size: 40616 pages
% 72.59/12.23
% 72.59/12.23 # -------------------------------------------------
% 72.59/12.23 # User time : 9.000 s
% 72.59/12.23 # System time : 0.185 s
% 72.59/12.23 # Total time : 9.185 s
% 72.59/12.23 # Maximum resident set size: 9936 pages
% 72.59/12.23 % E---3.1 exiting
% 72.59/12.23 % E---3.1 exiting
%------------------------------------------------------------------------------