%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM925+8 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:56:58 PM UTC 2026
% Result : Theorem 130.74s 20.28s
% Output : CNFRefutation 130.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 40
% Syntax : Number of formulae : 167 ( 126 unt; 0 def)
% Number of atoms : 225 ( 165 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 120 ( 62 ~; 49 |; 2 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 36 ( 36 usr; 17 con; 0-4 aty)
% Number of variables : 191 ( 8 sgn 88 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(help_fNot_1_1_U,axiom,
! [X230] :
( ~ hBOOL(X230)
| ~ hBOOL(hAPP(bool,bool,fNot,X230)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
fof(tsy_c_hAPP_arg2,axiom,
! [X1,X2,X4,X5] : hAPP(X1,X2,X4,ti(X1,X5)) = hAPP(X1,X2,X4,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).
fof(help_COMBI_1_1_U,axiom,
! [X1,X230] : hAPP(X1,X1,combi(X1),X230) = ti(X1,X230),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
fof(help_If_3_1_T,axiom,
! [X230] :
( ti(bool,X230) = fFalse
| ti(bool,X230) = fTrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
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/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
fof(fact_2924_succ__pred,axiom,
! [X11] : hAPP(int,int,succ,hAPP(int,int,pred,X11)) = ti(int,X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/sandbox2/benchmark/theBenchmark.p',fact_123_number__of__is__id) ).
fof(help_fTrue_1_1_U,axiom,
hBOOL(fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
fof(fact_3592_number__of__real__def,axiom,
! [X11] : hAPP(int,real,number_number_of(real),X11) = hAPP(int,real,ring_1_of_int(real),X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3592_number__of__real__def) ).
fof(fact_3352_floor__real__of__int,axiom,
! [X16] : hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),X16)) = ti(int,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3352_floor__real__of__int) ).
fof(fact_2146_iszero__def,axiom,
! [X1] :
( semiring_1(X1)
=> ! [X30] :
( hBOOL(hAPP(X1,bool,iszero(X1),X30))
<=> ti(X1,X30) = zero_zero(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2146_iszero__def) ).
fof(help_fNot_2_1_U,axiom,
! [X230] :
( hBOOL(hAPP(bool,bool,fNot,X230))
| hBOOL(X230) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
fof(fact_3367_real__of__int__minus,axiom,
! [X11] : hAPP(int,real,real_1(int),hAPP(int,int,uminus_uminus(int),X11)) = hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3367_real__of__int__minus) ).
fof(fact_3614_real__eq__of__int,axiom,
real_1(int) = ring_1_of_int(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3614_real__eq__of__int) ).
fof(fact_2079_mult__Min,axiom,
! [X21] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),min),X21) = hAPP(int,int,uminus_uminus(int),X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2079_mult__Min) ).
fof(fact_71_rel__simps_I38_J,axiom,
! [X14] :
( pls = hAPP(int,int,bit0,X14)
<=> pls = ti(int,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_rel__simps_I38_J) ).
fof(fact_2063_minus__numeral__code_I5_J,axiom,
! [X9] : hAPP(int,int,uminus_uminus(int),hAPP(int,int,number_number_of(int),X9)) = hAPP(int,int,number_number_of(int),hAPP(int,int,uminus_uminus(int),X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2063_minus__numeral__code_I5_J) ).
fof(fact_3398_floor__minus__real__of__int,axiom,
! [X16] : hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X16))) = hAPP(int,int,uminus_uminus(int),X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3398_floor__minus__real__of__int) ).
fof(help_fFalse_1_1_U,axiom,
~ hBOOL(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
fof(fact_1586_not__neg__0,axiom,
~ hBOOL(hAPP(int,bool,nat_neg,zero_zero(int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1586_not__neg__0) ).
fof(fact_742_diff__bin__simps_I1_J,axiom,
! [X21] : hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X21),pls) = ti(int,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_742_diff__bin__simps_I1_J) ).
fof(fact_76_Pls__def,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Pls__def) ).
fof(arity_Int_Oint___Rings_Osemiring__1,axiom,
semiring_1(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
fof(fact_3593_int__number__of__def,axiom,
! [X9] : hAPP(int,int,number_number_of(int),X9) = hAPP(int,int,ring_1_of_int(int),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3593_int__number__of__def) ).
fof(fact_168_field__power__not__zero,axiom,
! [X1] :
( ring_11004092258visors(X1)
=> ! [X16,X37] :
( ti(X1,X37) != zero_zero(X1)
=> hAPP(nat,X1,hAPP(X1,fun(nat,X1),power_power(X1),X37),X16) != zero_zero(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_field__power__not__zero) ).
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/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_2926_pred__Bit1,axiom,
! [X21] : hAPP(int,int,pred,hAPP(int,int,bit1,X21)) = hAPP(int,int,bit0,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2926_pred__Bit1) ).
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/sandbox2/benchmark/theBenchmark.p',fact_1004_nat__number__of__def) ).
fof(fact_4285_card__atLeastZeroLessThan__int,axiom,
! [X80] : hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),X80)) = hAPP(int,nat,nat_1,X80),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4285_card__atLeastZeroLessThan__int) ).
fof(fact_2092_neg__zminus__int,axiom,
! [X16] : hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X16))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2092_neg__zminus__int) ).
fof(fact_367_zmult__commute,axiom,
! [X17,X9] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X17),X9) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X9),X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_zmult__commute) ).
fof(fact_398_mult__Pls,axiom,
! [X9] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),X9) = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_398_mult__Pls) ).
fof(fact_3596_of__int__int__eq,axiom,
! [X16] : hAPP(int,int,ring_1_of_int(int),hAPP(nat,int,semiring_1_of_nat(int),X16)) = hAPP(nat,int,semiring_1_of_nat(int),X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3596_of__int__int__eq) ).
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/sandbox2/benchmark/theBenchmark.p',fact_37_one__is__num__one) ).
fof(fact_72_Bit0__Pls,axiom,
hAPP(int,int,bit0,pls) = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Bit0__Pls) ).
fof(fact_284_succ__Pls,axiom,
hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_succ__Pls) ).
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/sandbox2/benchmark/theBenchmark.p',fact_1450_int__Suc) ).
fof(fact_4286_card__atLeastLessThan__int,axiom,
! [X14,X80] : hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),X14),X80)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X80),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4286_card__atLeastLessThan__int) ).
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/sandbox2/benchmark/theBenchmark.p',fact_21_int__power) ).
fof(arity_Int_Oint___Rings_Oring__1__no__zero__divisors,axiom,
ring_11004092258visors(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
fof(c_0_40,plain,
! [X230] :
( ~ hBOOL(X230)
| ~ hBOOL(hAPP(bool,bool,fNot,X230)) ),
inference(fof_simplification,[status(thm)],[help_fNot_1_1_U]) ).
fof(c_0_41,plain,
! [X386,X387,X388,X389] : hAPP(X386,X387,X388,ti(X386,X389)) = hAPP(X386,X387,X388,X389),
inference(variable_rename,[status(thm)],[tsy_c_hAPP_arg2]) ).
fof(c_0_42,plain,
! [X13894,X13895] : hAPP(X13894,X13894,combi(X13894),X13895) = ti(X13894,X13895),
inference(variable_rename,[status(thm)],[help_COMBI_1_1_U]) ).
fof(c_0_43,plain,
! [X13880] :
( ~ hBOOL(X13880)
| ~ hBOOL(hAPP(bool,bool,fNot,X13880)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_40])]) ).
cnf(c_0_44,plain,
hAPP(X1,X2,X3,ti(X1,X4)) = hAPP(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_45,plain,
hAPP(X1,X1,combi(X1),X2) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_46,plain,
! [X13876] :
( ti(bool,X13876) = fFalse
| ti(bool,X13876) = fTrue ),
inference(variable_rename,[status(thm)],[help_If_3_1_T]) ).
fof(c_0_47,plain,
! [X390,X391,X392,X393] : ti(X390,hAPP(X391,X390,X392,X393)) = hAPP(X391,X390,X392,X393),
inference(variable_rename,[status(thm)],[tsy_c_hAPP_res]) ).
cnf(c_0_48,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_49,plain,
hAPP(X1,X2,X3,hAPP(X1,X1,combi(X1),X4)) = hAPP(X1,X2,X3,X4),
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,plain,
( ti(bool,X1) = fFalse
| ti(bool,X1) = fTrue ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_51,plain,
! [X7308] : hAPP(int,int,succ,hAPP(int,int,pred,X7308)) = ti(int,X7308),
inference(variable_rename,[status(thm)],[fact_2924_succ__pred]) ).
fof(c_0_52,plain,
! [X585] : hAPP(int,int,number_number_of(int),X585) = ti(int,X585),
inference(variable_rename,[status(thm)],[fact_123_number__of__is__id]) ).
cnf(c_0_53,plain,
ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_54,plain,
( ~ hBOOL(hAPP(bool,bool,fNot,X1))
| ~ hBOOL(hAPP(bool,bool,combi(bool),X1)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_55,plain,
( hAPP(bool,bool,combi(bool),X1) = fTrue
| hAPP(bool,bool,combi(bool),X1) = fFalse ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_45]),c_0_45]) ).
cnf(c_0_56,plain,
hBOOL(fTrue),
inference(split_conjunct,[status(thm)],[help_fTrue_1_1_U]) ).
fof(c_0_57,plain,
! [X9074] : hAPP(int,real,number_number_of(real),X9074) = hAPP(int,real,ring_1_of_int(real),X9074),
inference(variable_rename,[status(thm)],[fact_3592_number__of__real__def]) ).
fof(c_0_58,plain,
! [X8395] : hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),X8395)) = ti(int,X8395),
inference(variable_rename,[status(thm)],[fact_3352_floor__real__of__int]) ).
cnf(c_0_59,plain,
hAPP(int,int,succ,hAPP(int,int,pred,X1)) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_60,plain,
hAPP(int,int,number_number_of(int),X1) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_61,plain,
! [X5675,X5676] :
( ( ~ semiring_1(X5675)
| hBOOL(hAPP(X5675,bool,iszero(X5675),X5676))
| ti(X5675,X5676) != zero_zero(X5675) )
& ( ~ semiring_1(X5675)
| ti(X5675,X5676) = zero_zero(X5675)
| ~ hBOOL(hAPP(X5675,bool,iszero(X5675),X5676)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2146_iszero__def])])])])]) ).
cnf(c_0_62,plain,
hAPP(X1,X1,combi(X1),hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
inference(rw,[status(thm)],[c_0_53,c_0_45]) ).
cnf(c_0_63,plain,
( ~ hBOOL(hAPP(bool,bool,fNot,X1))
| hAPP(bool,bool,combi(bool),X1) = fFalse ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56])]) ).
fof(c_0_64,plain,
! [X13881] :
( hBOOL(hAPP(bool,bool,fNot,X13881))
| hBOOL(X13881) ),
inference(variable_rename,[status(thm)],[help_fNot_2_1_U]) ).
fof(c_0_65,plain,
! [X8424] : hAPP(int,real,real_1(int),hAPP(int,int,uminus_uminus(int),X8424)) = hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X8424)),
inference(variable_rename,[status(thm)],[fact_3367_real__of__int__minus]) ).
cnf(c_0_66,plain,
hAPP(int,real,number_number_of(real),X1) = hAPP(int,real,ring_1_of_int(real),X1),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_67,plain,
real_1(int) = ring_1_of_int(real),
inference(split_conjunct,[status(thm)],[fact_3614_real__eq__of__int]) ).
fof(c_0_68,plain,
! [X5545] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),min),X5545) = hAPP(int,int,uminus_uminus(int),X5545),
inference(variable_rename,[status(thm)],[fact_2079_mult__Min]) ).
cnf(c_0_69,plain,
hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),X1)) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_70,plain,
hAPP(int,int,succ,hAPP(int,int,pred,X1)) = hAPP(int,int,combi(int),X1),
inference(rw,[status(thm)],[c_0_59,c_0_45]) ).
cnf(c_0_71,plain,
hAPP(int,int,number_number_of(int),X1) = hAPP(int,int,combi(int),X1),
inference(rw,[status(thm)],[c_0_60,c_0_45]) ).
fof(c_0_72,plain,
! [X498] :
( ( pls = hAPP(int,int,bit0,X498)
| pls != ti(int,X498) )
& ( pls = ti(int,X498)
| pls != hAPP(int,int,bit0,X498) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_71_rel__simps_I38_J])])]) ).
cnf(c_0_73,plain,
( ~ semiring_1(X1)
| ~ hBOOL(hAPP(X1,bool,iszero(X1),X2))
| ti(X1,X2) = zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_74,plain,
( ~ hBOOL(hAPP(bool,bool,fNot,hAPP(X1,bool,X2,X3)))
| hAPP(X1,bool,X2,X3) = fFalse ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_75,plain,
( hBOOL(hAPP(bool,bool,fNot,X1))
| hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
fof(c_0_76,plain,
! [X5517] : hAPP(int,int,uminus_uminus(int),hAPP(int,int,number_number_of(int),X5517)) = hAPP(int,int,number_number_of(int),hAPP(int,int,uminus_uminus(int),X5517)),
inference(variable_rename,[status(thm)],[fact_2063_minus__numeral__code_I5_J]) ).
fof(c_0_77,plain,
! [X8489] : hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X8489))) = hAPP(int,int,uminus_uminus(int),X8489),
inference(variable_rename,[status(thm)],[fact_3398_floor__minus__real__of__int]) ).
cnf(c_0_78,plain,
hAPP(int,real,real_1(int),hAPP(int,int,uminus_uminus(int),X1)) = hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X1)),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_79,plain,
hAPP(int,real,real_1(int),X1) = hAPP(int,real,number_number_of(real),X1),
inference(rw,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_80,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),min),X1) = hAPP(int,int,uminus_uminus(int),X1),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_81,plain,
hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),X1)) = hAPP(int,int,combi(int),X1),
inference(rw,[status(thm)],[c_0_69,c_0_45]) ).
cnf(c_0_82,plain,
hAPP(int,int,number_number_of(int),X1) = hAPP(int,int,succ,hAPP(int,int,pred,X1)),
inference(rw,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_83,plain,
( ~ semiring_1(X1)
| ti(X1,X2) != zero_zero(X1)
| hBOOL(hAPP(X1,bool,iszero(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_84,plain,
( pls != hAPP(int,int,bit0,X1)
| pls = ti(int,X1) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_85,plain,
( ~ hBOOL(hAPP(X1,bool,iszero(X1),X2))
| ~ semiring_1(X1)
| hAPP(X1,X1,combi(X1),X2) = zero_zero(X1) ),
inference(rw,[status(thm)],[c_0_73,c_0_45]) ).
cnf(c_0_86,plain,
( hBOOL(hAPP(X1,bool,X2,X3))
| hAPP(X1,bool,X2,X3) = fFalse ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
fof(c_0_87,plain,
~ hBOOL(fFalse),
inference(fof_simplification,[status(thm)],[help_fFalse_1_1_U]) ).
fof(c_0_88,plain,
~ hBOOL(hAPP(int,bool,nat_neg,zero_zero(int))),
inference(fof_simplification,[status(thm)],[fact_1586_not__neg__0]) ).
fof(c_0_89,plain,
! [X2216] : hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X2216),pls) = ti(int,X2216),
inference(variable_rename,[status(thm)],[fact_742_diff__bin__simps_I1_J]) ).
cnf(c_0_90,plain,
hAPP(int,int,uminus_uminus(int),hAPP(int,int,number_number_of(int),X1)) = hAPP(int,int,number_number_of(int),hAPP(int,int,uminus_uminus(int),X1)),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_91,plain,
hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X1))) = hAPP(int,int,uminus_uminus(int),X1),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_92,plain,
hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),X1)) = hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),min),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_79]),c_0_80]),c_0_79]) ).
cnf(c_0_93,plain,
hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,number_number_of(real),X1)) = hAPP(int,int,succ,hAPP(int,int,pred,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_79]),c_0_71]),c_0_82]) ).
cnf(c_0_94,plain,
( ~ semiring_1(X1)
| hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
| hBOOL(hAPP(X1,bool,iszero(X1),X2)) ),
inference(rw,[status(thm)],[c_0_83,c_0_45]) ).
cnf(c_0_95,plain,
( pls != hAPP(int,int,bit0,X1)
| pls = hAPP(int,int,combi(int),X1) ),
inference(rw,[status(thm)],[c_0_84,c_0_45]) ).
cnf(c_0_96,plain,
pls = zero_zero(int),
inference(split_conjunct,[status(thm)],[fact_76_Pls__def]) ).
cnf(c_0_97,plain,
semiring_1(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Osemiring__1]) ).
cnf(c_0_98,plain,
( ~ semiring_1(X1)
| hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
| hAPP(X1,bool,iszero(X1),X2) = fFalse ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
fof(c_0_99,plain,
~ hBOOL(fFalse),
inference(fof_nnf,[status(thm)],[c_0_87]) ).
fof(c_0_100,plain,
~ hBOOL(hAPP(int,bool,nat_neg,zero_zero(int))),
inference(fof_nnf,[status(thm)],[c_0_88]) ).
cnf(c_0_101,plain,
( pls != ti(int,X1)
| pls = hAPP(int,int,bit0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
fof(c_0_102,plain,
! [X9075] : hAPP(int,int,number_number_of(int),X9075) = hAPP(int,int,ring_1_of_int(int),X9075),
inference(variable_rename,[status(thm)],[fact_3593_int__number__of__def]) ).
fof(c_0_103,plain,
! [X1] :
( ring_11004092258visors(X1)
=> ! [X16,X37] :
( ti(X1,X37) != zero_zero(X1)
=> hAPP(nat,X1,hAPP(X1,fun(nat,X1),power_power(X1),X37),X16) != zero_zero(X1) ) ),
inference(fof_simplification,[status(thm)],[fact_168_field__power__not__zero]) ).
fof(c_0_104,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(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_105,plain,
! [X7310] : hAPP(int,int,pred,hAPP(int,int,bit1,X7310)) = hAPP(int,int,bit0,X7310),
inference(variable_rename,[status(thm)],[fact_2926_pred__Bit1]) ).
fof(c_0_106,plain,
! [X2961] : hAPP(int,nat,number_number_of(nat),X2961) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),X2961)),
inference(variable_rename,[status(thm)],[fact_1004_nat__number__of__def]) ).
fof(c_0_107,plain,
! [X11051] : hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),X11051)) = hAPP(int,nat,nat_1,X11051),
inference(variable_rename,[status(thm)],[fact_4285_card__atLeastZeroLessThan__int]) ).
cnf(c_0_108,plain,
hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X1),pls) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
fof(c_0_109,plain,
! [X5565] : hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X5565))))),
inference(variable_rename,[status(thm)],[fact_2092_neg__zminus__int]) ).
cnf(c_0_110,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),min),hAPP(int,int,succ,hAPP(int,int,pred,X1))) = hAPP(int,int,succ,hAPP(int,int,pred,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),min),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_82]),c_0_80]),c_0_80]),c_0_82]) ).
cnf(c_0_111,plain,
hAPP(int,int,succ,hAPP(int,int,pred,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),min),X1))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),min),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_79]),c_0_92]),c_0_93]),c_0_80]) ).
cnf(c_0_112,plain,
( hAPP(int,int,bit0,X1) != pls
| hBOOL(hAPP(int,bool,iszero(int),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96]),c_0_97])]) ).
cnf(c_0_113,plain,
( hAPP(int,bool,iszero(int),X1) = fFalse
| hAPP(int,int,succ,hAPP(int,int,pred,X1)) = pls ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_97]),c_0_71]),c_0_82]),c_0_96]) ).
cnf(c_0_114,plain,
~ hBOOL(fFalse),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
fof(c_0_115,plain,
! [X1196,X1197] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1196),X1197) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1197),X1196),
inference(variable_rename,[status(thm)],[fact_367_zmult__commute]) ).
fof(c_0_116,plain,
! [X1287] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),X1287) = pls,
inference(variable_rename,[status(thm)],[fact_398_mult__Pls]) ).
cnf(c_0_117,plain,
~ hBOOL(hAPP(int,bool,nat_neg,zero_zero(int))),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_118,plain,
( pls != hAPP(int,int,combi(int),X1)
| pls = hAPP(int,int,bit0,X1) ),
inference(rw,[status(thm)],[c_0_101,c_0_45]) ).
fof(c_0_119,plain,
! [X9079] : hAPP(int,int,ring_1_of_int(int),hAPP(nat,int,semiring_1_of_nat(int),X9079)) = hAPP(nat,int,semiring_1_of_nat(int),X9079),
inference(variable_rename,[status(thm)],[fact_3596_of__int__int__eq]) ).
cnf(c_0_120,plain,
hAPP(int,int,number_number_of(int),X1) = hAPP(int,int,ring_1_of_int(int),X1),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
fof(c_0_121,plain,
! [X681,X682,X683] :
( hAPP(nat,X681,hAPP(X681,fun(nat,X681),power_power(X681),X683),X682) != zero_zero(X681)
| ti(X681,X683) = zero_zero(X681)
| ~ ring_11004092258visors(X681) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_103])])])]) ).
fof(c_0_122,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)],[c_0_104]) ).
cnf(c_0_123,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_124,plain,
hAPP(int,int,pred,hAPP(int,int,bit1,X1)) = hAPP(int,int,bit0,X1),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_125,plain,
hAPP(int,int,bit0,pls) = pls,
inference(split_conjunct,[status(thm)],[fact_72_Bit0__Pls]) ).
cnf(c_0_126,plain,
hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
inference(split_conjunct,[status(thm)],[fact_284_succ__Pls]) ).
cnf(c_0_127,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_106]) ).
fof(c_0_128,plain,
! [X4003] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X4003)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),X4003)),
inference(variable_rename,[status(thm)],[fact_1450_int__Suc]) ).
cnf(c_0_129,plain,
hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),X1)) = hAPP(int,nat,nat_1,X1),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
fof(c_0_130,plain,
! [X11052,X11053] : hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),X11052),X11053)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X11053),X11052)),
inference(variable_rename,[status(thm)],[fact_4286_card__atLeastLessThan__int]) ).
cnf(c_0_131,plain,
hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X1),pls) = hAPP(int,int,combi(int),X1),
inference(rw,[status(thm)],[c_0_108,c_0_45]) ).
cnf(c_0_132,plain,
hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X1))))),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_133,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),min),hAPP(int,int,succ,hAPP(int,int,pred,X1))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),min),X1),
inference(rw,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_134,plain,
( hAPP(int,int,bit0,X1) != pls
| hAPP(int,int,succ,hAPP(int,int,pred,X1)) = pls ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_114]) ).
cnf(c_0_135,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X2) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X2),X1),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_136,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),X1) = pls,
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_137,plain,
~ hBOOL(hAPP(int,bool,nat_neg,pls)),
inference(rw,[status(thm)],[c_0_117,c_0_96]) ).
cnf(c_0_138,plain,
( hAPP(int,int,number_number_of(int),X1) != pls
| hAPP(int,int,bit0,X1) = pls ),
inference(rw,[status(thm)],[c_0_118,c_0_71]) ).
cnf(c_0_139,plain,
hAPP(int,int,ring_1_of_int(int),hAPP(nat,int,semiring_1_of_nat(int),X1)) = hAPP(nat,int,semiring_1_of_nat(int),X1),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_140,plain,
hAPP(int,int,ring_1_of_int(int),X1) = hAPP(int,int,succ,hAPP(int,int,pred,X1)),
inference(rw,[status(thm)],[c_0_120,c_0_82]) ).
cnf(c_0_141,plain,
( hAPP(nat,X1,hAPP(X1,fun(nat,X1),power_power(X1),X2),X3) != zero_zero(X1)
| ~ ring_11004092258visors(X1)
| ti(X1,X2) = zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
fof(c_0_142,plain,
! [X425,X426] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X425),X426)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),X425)),X426),
inference(variable_rename,[status(thm)],[fact_21_int__power]) ).
cnf(c_0_143,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_122]) ).
cnf(c_0_144,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_123,c_0_82]),c_0_124]),c_0_125]),c_0_126]) ).
cnf(c_0_145,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_127,c_0_82]) ).
cnf(c_0_146,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_128]) ).
cnf(c_0_147,plain,
hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),pls),X1)) = hAPP(int,nat,nat_1,X1),
inference(rw,[status(thm)],[c_0_129,c_0_96]) ).
cnf(c_0_148,plain,
hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),X1),X2)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X2),X1)),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_149,plain,
hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X1),pls) = hAPP(int,int,succ,hAPP(int,int,pred,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_131,c_0_71]),c_0_82]) ).
cnf(c_0_150,plain,
hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),min),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X1))))),
inference(rw,[status(thm)],[c_0_132,c_0_80]) ).
cnf(c_0_151,plain,
( hAPP(int,int,bit0,X1) != pls
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),min),X1) = pls ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_135]),c_0_136]) ).
cnf(c_0_152,plain,
hAPP(int,bool,nat_neg,pls) = fFalse,
inference(spm,[status(thm)],[c_0_137,c_0_86]) ).
cnf(c_0_153,plain,
( hAPP(int,int,succ,hAPP(int,int,pred,X1)) != pls
| hAPP(int,int,bit0,X1) = pls ),
inference(rw,[status(thm)],[c_0_138,c_0_82]) ).
cnf(c_0_154,plain,
hAPP(int,int,succ,hAPP(int,int,pred,hAPP(nat,int,semiring_1_of_nat(int),X1))) = hAPP(nat,int,semiring_1_of_nat(int),X1),
inference(rw,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_155,plain,
( ~ ring_11004092258visors(X1)
| hAPP(nat,X1,hAPP(X1,fun(nat,X1),power_power(X1),X2),X3) != zero_zero(X1)
| hAPP(X1,X1,combi(X1),X2) = zero_zero(X1) ),
inference(rw,[status(thm)],[c_0_141,c_0_45]) ).
cnf(c_0_156,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_142]) ).
cnf(c_0_157,plain,
ring_11004092258visors(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Oring__1__no__zero__divisors]) ).
cnf(c_0_158,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(int,nat,nat_1,hAPP(int,int,succ,hAPP(int,int,pred,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = pls,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_143,c_0_144]),c_0_145]),c_0_96]) ).
cnf(c_0_159,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_146,c_0_144]) ).
cnf(c_0_160,plain,
hAPP(int,nat,nat_1,hAPP(int,int,succ,hAPP(int,int,pred,X1))) = hAPP(int,nat,nat_1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_147,c_0_148]),c_0_149]) ).
cnf(c_0_161,plain,
hAPP(int,int,bit0,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X1))) != pls,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_152]),c_0_114]) ).
cnf(c_0_162,plain,
( hAPP(nat,int,semiring_1_of_nat(int),X1) != pls
| hAPP(int,int,bit0,hAPP(nat,int,semiring_1_of_nat(int),X1)) = pls ),
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_163,plain,
( hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X1),X2)) != pls
| hAPP(nat,int,semiring_1_of_nat(int),X1) = pls ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_62]),c_0_96]),c_0_96]),c_0_157])]) ).
cnf(c_0_164,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_158,c_0_159]),c_0_160]),c_0_156]) ).
cnf(c_0_165,plain,
hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X1)) != pls,
inference(spm,[status(thm)],[c_0_161,c_0_162]) ).
cnf(c_0_166,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_165]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925+8 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n003.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 03:19:45 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 130.74/20.28 % Version: 3.5.1
% 130.74/20.28 % Preprocessing class: FMLMSMSLSSSNFFN.
% 130.74/20.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 130.74/20.28 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 130.74/20.28 % Starting new_bool_3 with 600s (2) cores
% 130.74/20.28 % Starting new_bool_1 with 600s (2) cores
% 130.74/20.28 % Starting sh5l with 300s (1) cores
% 130.74/20.28 % G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 3289442 completed with status 0
% 130.74/20.28 % Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 130.74/20.28 % Preprocessing class: FMLMSMSLSSSNFFN.
% 130.74/20.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 130.74/20.28 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 130.74/20.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 130.74/20.28 % No SInE strategy applied
% 130.74/20.28 % Search class: FGHSM-SMLM33-DFFFFFNN
% 130.74/20.28 % Scheduled 7 strats onto 3 cores with 899 seconds (899 total)
% 130.74/20.28 % Starting SubtermCWHack with 81s (1) cores
% 130.74/20.28 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 90s (1) cores
% 130.74/20.28 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 81s (1) cores
% 130.74/20.28 % G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 3289452 completed with status 0
% 130.74/20.28 % Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 130.74/20.28 % Preprocessing class: FMLMSMSLSSSNFFN.
% 130.74/20.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 130.74/20.28 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 130.74/20.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 130.74/20.28 % No SInE strategy applied
% 130.74/20.28 % Search class: FGHSM-SMLM33-DFFFFFNN
% 130.74/20.28 % Scheduled 7 strats onto 3 cores with 899 seconds (899 total)
% 130.74/20.28 % Starting SubtermCWHack with 81s (1) cores
% 130.74/20.28 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 90s (1) cores
% 130.74/20.28 % Preprocessing time : 0.447 s
% 130.74/20.28 % Presaturation interreduction done
% 130.74/20.28
% 130.74/20.28 % Proof found!
% 130.74/20.28 % SZS status Theorem
% 130.74/20.28 % SZS output start CNFRefutation
% See solution above
% 130.74/20.28 % Parsed axioms : 5747
% 130.74/20.28 % Removed by relevancy pruning/SinE : 0
% 130.74/20.28 % Initial clauses : 8678
% 130.74/20.28 % Removed in clause preprocessing : 213
% 130.74/20.28 % Initial clauses in saturation : 8465
% 130.74/20.28 % Processed clauses : 15780
% 130.74/20.28 % ...of these trivial : 413
% 130.74/20.28 % ...subsumed : 4992
% 130.74/20.28 % ...remaining for further processing : 10375
% 130.74/20.28 % Other redundant clauses eliminated : 388
% 130.74/20.28 % Clauses deleted for lack of memory : 0
% 130.74/20.28 % Backward-subsumed : 196
% 130.74/20.28 % Backward-rewritten : 389
% 130.74/20.28 % Generated clauses : 16892
% 130.74/20.28 % ...of the previous two non-redundant : 13565
% 130.74/20.28 % ...aggressively subsumed : 0
% 130.74/20.28 % Contextual simplify-reflections : 26
% 130.74/20.28 % Paramodulations : 16509
% 130.74/20.28 % Factorizations : 5
% 130.74/20.28 % NegExts : 0
% 130.74/20.28 % Equation resolutions : 399
% 130.74/20.28 % Disequality decompositions : 0
% 130.74/20.28 % Total rewrite steps : 32404
% 130.74/20.28 % ...of those cached : 29051
% 130.74/20.28 % Propositional unsat checks : 3
% 130.74/20.28 % Propositional check models : 2
% 130.74/20.28 % Propositional check unsatisfiable : 0
% 130.74/20.28 % Propositional clauses : 0
% 130.74/20.28 % Propositional clauses after purity: 0
% 130.74/20.28 % Propositional unsat core size : 0
% 130.74/20.28 % Propositional preprocessing time : 0.000
% 130.74/20.28 % Propositional encoding time : 0.288
% 130.74/20.28 % Propositional solver time : 0.129
% 130.74/20.28 % Success case prop preproc time : 0.000
% 130.74/20.28 % Success case prop encoding time : 0.000
% 130.74/20.28 % Success case prop solver time : 0.000
% 130.74/20.28 % Current number of processed clauses : 2270
% 130.74/20.28 % Positive orientable unit clauses : 1298
% 130.74/20.28 % Positive unorientable unit clauses: 0
% 130.74/20.28 % Negative unit clauses : 159
% 130.74/20.28 % Non-unit-clauses : 813
% 130.74/20.28 % Current number of unprocessed clauses: 13194
% 130.74/20.28 % ...number of literals in the above : 33062
% 130.74/20.28 % Current number of archived formulas : 0
% 130.74/20.28 % Current number of archived clauses : 7800
% 130.74/20.28 % Clause-clause subsumption calls (NU) : 8365030
% 130.74/20.28 % Rec. Clause-clause subsumption calls : 1647673
% 130.74/20.28 % Non-unit clause-clause subsumptions : 2136
% 130.74/20.28 % Unit Clause-clause subsumption calls : 6874
% 130.74/20.28 % Rewrite failures with RHS unbound : 0
% 130.74/20.28 % BW rewrite match attempts : 339386
% 130.74/20.28 % BW rewrite match successes : 633
% 130.74/20.28 % Condensation attempts : 0
% 130.74/20.28 % Condensation successes : 0
% 130.74/20.28 % Termbank termtop insertions : 3311639
% 130.74/20.28 % Search garbage collected termcells : 114441
% 130.74/20.28
% 130.74/20.28 % -------------------------------------------------
% 130.74/20.28 % User time : 18.753 s
% 130.74/20.28 % System time : 0.309 s
% 130.74/20.28 % Total time : 19.062 s
% 130.74/20.28 % Maximum resident set size: 45296 pages
% 130.74/20.28
% 130.74/20.28 % -------------------------------------------------
% 130.74/20.28 % User time : 53.374 s
% 130.74/20.28 % System time : 1.008 s
% 130.74/20.28 % Total time : 54.382 s
% 130.74/20.28 % Maximum resident set size: 12800 pages
% 130.74/20.28 % E exiting
%------------------------------------------------------------------------------