TSTP Solution File: NUM924+7 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : NUM924+7 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n012.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 : 600s
% DateTime : Mon Jul 18 09:37:45 EDT 2022
% Result : Theorem 0.37s 2.55s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 25
% Syntax : Number of formulae : 94 ( 88 unt; 0 def)
% Number of atoms : 106 ( 70 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 27 ( 15 ~; 8 |; 0 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 8 con; 0-4 aty)
% Number of variables : 73 ( 0 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',conj_0) ).
fof(fact_132_Bit0__def,axiom,
! [X15] : bit0(X15) = hAPP(int,int,plus_plus(int,X15),X15),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_132_Bit0__def) ).
fof(fact_130_add__Pls,axiom,
! [X15] : hAPP(int,int,plus_plus(int,pls),X15) = ti(int,X15),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_130_add__Pls) ).
fof(fact_22_number__of__is__id,axiom,
! [X15] : number_number_of(int,X15) = ti(int,X15),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_22_number__of__is__id) ).
fof(tsy_c_Int_OBit1_res,hypothesis,
! [X4] : ti(int,bit1(X4)) = bit1(X4),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',tsy_c_Int_OBit1_res) ).
fof(fact_751__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096,axiom,
twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) = hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_751__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096) ).
fof(tsy_c_Int_OBit0_arg1,hypothesis,
! [X4] : bit0(ti(int,X4)) = bit0(X4),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',tsy_c_Int_OBit0_arg1) ).
fof(fact_67_plus__numeral__code_I9_J,axiom,
! [X13,X12] : hAPP(int,int,plus_plus(int,number_number_of(int,X13)),number_number_of(int,X12)) = number_number_of(int,hAPP(int,int,plus_plus(int,X13),X12)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_67_plus__numeral__code_I9_J) ).
fof(fact_466__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096,axiom,
hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_466__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
fof(fact_61_nat__1__add__1,axiom,
hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_61_nat__1__add__1) ).
fof(tsy_c_Int_OBit1_arg1,hypothesis,
! [X4] : bit1(ti(int,X4)) = bit1(X4),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',tsy_c_Int_OBit1_arg1) ).
fof(fact_3_t,axiom,
hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)) = hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_3_t) ).
fof(fact_162_add__Bit0__Bit1,axiom,
! [X15,X32] : hAPP(int,int,plus_plus(int,bit0(X15)),bit1(X32)) = bit1(hAPP(int,int,plus_plus(int,X15),X32)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_162_add__Bit0__Bit1) ).
fof(fact_173_semiring__norm_I110_J,axiom,
! [X3] :
( number_ring(X3)
=> one_one(X3) = number_number_of(X3,bit1(pls)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_173_semiring__norm_I110_J) ).
fof(fact_111_one__is__num__one,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_111_one__is__num__one) ).
fof(fact_98_zadd__commute,axiom,
! [X16,X12] : hAPP(int,int,plus_plus(int,X16),X12) = hAPP(int,int,plus_plus(int,X12),X16),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_98_zadd__commute) ).
fof(tsy_c_Int_OMin_res,axiom,
ti(int,min) = min,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',tsy_c_Int_OMin_res) ).
fof(fact_6_p0,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_6_p0) ).
fof(fact_122_Pls__def,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_122_Pls__def) ).
fof(fact_23_zmult__commute,axiom,
! [X16,X12] : hAPP(int,int,times_times(int,X16),X12) = hAPP(int,int,times_times(int,X12),X16),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_23_zmult__commute) ).
fof(fact_97_zadd__left__commute,axiom,
! [X6,X7,X16] : hAPP(int,int,plus_plus(int,X6),hAPP(int,int,plus_plus(int,X7),X16)) = hAPP(int,int,plus_plus(int,X7),hAPP(int,int,plus_plus(int,X6),X16)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_97_zadd__left__commute) ).
fof(arity_Int_Oint___Int_Onumber__ring,axiom,
number_ring(int),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
fof(fact_384_mult__neg__pos,axiom,
! [X3] :
( linord20386208strict(X3)
=> ! [X36,X10] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X10),zero_zero(X3)))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X36))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,times_times(X3,X10),X36)),zero_zero(X3))) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_384_mult__neg__pos) ).
fof(fact_0__096t_A_060_A0_096,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),t),zero_zero(int))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_0__096t_A_060_A0_096) ).
fof(arity_Int_Oint___Rings_Olinordered__semiring__strict,axiom,
linord20386208strict(int),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semiring__strict) ).
fof(c_0_25,negated_conjecture,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int))),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_26,plain,
! [X16] : bit0(X16) = hAPP(int,int,plus_plus(int,X16),X16),
inference(variable_rename,[status(thm)],[fact_132_Bit0__def]) ).
fof(c_0_27,plain,
! [X16] : hAPP(int,int,plus_plus(int,pls),X16) = ti(int,X16),
inference(variable_rename,[status(thm)],[fact_130_add__Pls]) ).
fof(c_0_28,plain,
! [X16] : number_number_of(int,X16) = ti(int,X16),
inference(variable_rename,[status(thm)],[fact_22_number__of__is__id]) ).
fof(c_0_29,hypothesis,
! [X5] : ti(int,bit1(X5)) = bit1(X5),
inference(variable_rename,[status(thm)],[tsy_c_Int_OBit1_res]) ).
fof(c_0_30,negated_conjecture,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int))),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) = hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t),
inference(split_conjunct,[status(thm)],[fact_751__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096]) ).
cnf(c_0_32,plain,
bit0(X1) = hAPP(int,int,plus_plus(int,X1),X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
hAPP(int,int,plus_plus(int,pls),X1) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
number_number_of(int,X1) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_35,hypothesis,
! [X5] : bit0(ti(int,X5)) = bit0(X5),
inference(variable_rename,[status(thm)],[tsy_c_Int_OBit0_arg1]) ).
fof(c_0_36,plain,
! [X14,X15] : hAPP(int,int,plus_plus(int,number_number_of(int,X14)),number_number_of(int,X15)) = number_number_of(int,hAPP(int,int,plus_plus(int,X14),X15)),
inference(variable_rename,[status(thm)],[fact_67_plus__numeral__code_I9_J]) ).
cnf(c_0_37,hypothesis,
ti(int,bit1(X1)) = bit1(X1),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,plain,
hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)),
inference(split_conjunct,[status(thm)],[fact_466__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096]) ).
cnf(c_0_39,plain,
hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
inference(split_conjunct,[status(thm)],[fact_61_nat__1__add__1]) ).
fof(c_0_40,hypothesis,
! [X5] : bit1(ti(int,X5)) = bit1(X5),
inference(variable_rename,[status(thm)],[tsy_c_Int_OBit1_arg1]) ).
cnf(c_0_41,negated_conjecture,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int))),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_42,plain,
hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)) = hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t),
inference(split_conjunct,[status(thm)],[fact_3_t]) ).
cnf(c_0_43,plain,
twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) = hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))),hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))))),m)),one_one(int))),t),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_32]) ).
cnf(c_0_44,plain,
number_number_of(int,X1) = hAPP(int,int,plus_plus(int,pls),X1),
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_45,hypothesis,
bit0(ti(int,X1)) = bit0(X1),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_46,plain,
hAPP(int,int,plus_plus(int,number_number_of(int,X1)),number_number_of(int,X2)) = number_number_of(int,hAPP(int,int,plus_plus(int,X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_47,plain,
! [X33,X34] : hAPP(int,int,plus_plus(int,bit0(X33)),bit1(X34)) = bit1(hAPP(int,int,plus_plus(int,X33),X34)),
inference(variable_rename,[status(thm)],[fact_162_add__Bit0__Bit1]) ).
fof(c_0_48,plain,
! [X4] :
( ~ number_ring(X4)
| one_one(X4) = number_number_of(X4,bit1(pls)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_173_semiring__norm_I110_J])]) ).
cnf(c_0_49,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(split_conjunct,[status(thm)],[fact_111_one__is__num__one]) ).
cnf(c_0_50,hypothesis,
number_number_of(int,bit1(X1)) = bit1(X1),
inference(rw,[status(thm)],[c_0_37,c_0_34]) ).
cnf(c_0_51,plain,
hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))))),number_number_of(int,min)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))))),one_one(int)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_32]),c_0_32]) ).
cnf(c_0_52,plain,
hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) = number_number_of(nat,hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))),
inference(rw,[status(thm)],[c_0_39,c_0_32]) ).
fof(c_0_53,plain,
! [X17,X18] : hAPP(int,int,plus_plus(int,X17),X18) = hAPP(int,int,plus_plus(int,X18),X17),
inference(variable_rename,[status(thm)],[fact_98_zadd__commute]) ).
cnf(c_0_54,plain,
ti(int,min) = min,
inference(split_conjunct,[status(thm)],[tsy_c_Int_OMin_res]) ).
cnf(c_0_55,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))),
inference(split_conjunct,[status(thm)],[fact_6_p0]) ).
cnf(c_0_56,hypothesis,
bit1(ti(int,X1)) = bit1(X1),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_57,negated_conjecture,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))))),one_one(int))),zero_zero(int))),
inference(rw,[status(thm)],[c_0_41,c_0_32]) ).
cnf(c_0_58,plain,
pls = zero_zero(int),
inference(split_conjunct,[status(thm)],[fact_122_Pls__def]) ).
cnf(c_0_59,plain,
hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))))),one_one(int)) = hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))),hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))))),m)),one_one(int))),t),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_32]),c_0_32]),c_0_32]) ).
cnf(c_0_60,plain,
hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))),hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))))),m)),one_one(int))),t) = twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
fof(c_0_61,plain,
! [X17,X18] : hAPP(int,int,times_times(int,X17),X18) = hAPP(int,int,times_times(int,X18),X17),
inference(variable_rename,[status(thm)],[fact_23_zmult__commute]) ).
cnf(c_0_62,hypothesis,
hAPP(int,int,plus_plus(int,ti(int,X1)),ti(int,X1)) = hAPP(int,int,plus_plus(int,X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_32]),c_0_32]) ).
cnf(c_0_63,plain,
hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,pls),X1)),hAPP(int,int,plus_plus(int,pls),X2)) = hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_44]),c_0_44]),c_0_44]) ).
fof(c_0_64,plain,
! [X17,X18,X19] : hAPP(int,int,plus_plus(int,X17),hAPP(int,int,plus_plus(int,X18),X19)) = hAPP(int,int,plus_plus(int,X18),hAPP(int,int,plus_plus(int,X17),X19)),
inference(variable_rename,[status(thm)],[fact_97_zadd__left__commute]) ).
cnf(c_0_65,plain,
hAPP(int,int,plus_plus(int,bit0(X1)),bit1(X2)) = bit1(hAPP(int,int,plus_plus(int,X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_66,plain,
( one_one(X1) = number_number_of(X1,bit1(pls))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_67,plain,
number_ring(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Int_Onumber__ring]) ).
cnf(c_0_68,plain,
one_one(int) = bit1(pls),
inference(rw,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_69,plain,
hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))),hAPP(int,int,plus_plus(int,pls),min)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))),one_one(int)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52]),c_0_44]),c_0_52]) ).
cnf(c_0_70,plain,
hAPP(int,int,plus_plus(int,X1),X2) = hAPP(int,int,plus_plus(int,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_71,plain,
hAPP(int,int,plus_plus(int,pls),min) = min,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_34]),c_0_44]) ).
cnf(c_0_72,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))),hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))))),m)),one_one(int)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_32]),c_0_32]) ).
cnf(c_0_73,hypothesis,
bit1(number_number_of(int,X1)) = bit1(X1),
inference(rw,[status(thm)],[c_0_56,c_0_34]) ).
cnf(c_0_74,negated_conjecture,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))),one_one(int))),pls)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_52]),c_0_58]) ).
fof(c_0_75,plain,
! [X37,X38,X39] :
( ~ linord20386208strict(X37)
| ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),X39),zero_zero(X37)))
| ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),zero_zero(X37)),X38))
| hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),hAPP(X37,X37,times_times(X37,X39),X38)),zero_zero(X37))) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_384_mult__neg__pos])])])])]) ).
cnf(c_0_76,plain,
twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))),one_one(int)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_44]),c_0_60]),c_0_52]) ).
cnf(c_0_77,plain,
hAPP(int,int,times_times(int,X1),X2) = hAPP(int,int,times_times(int,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_78,hypothesis,
hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,X1),X1)) = hAPP(int,int,plus_plus(int,X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_34]),c_0_44]),c_0_34]),c_0_44]),c_0_63]) ).
cnf(c_0_79,plain,
hAPP(int,int,plus_plus(int,X1),hAPP(int,int,plus_plus(int,X2),X3)) = hAPP(int,int,plus_plus(int,X2),hAPP(int,int,plus_plus(int,X1),X3)),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_80,plain,
hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,X1),X1)),bit1(X2)) = bit1(hAPP(int,int,plus_plus(int,X1),X2)),
inference(rw,[status(thm)],[c_0_65,c_0_32]) ).
cnf(c_0_81,plain,
hAPP(int,int,plus_plus(int,pls),bit1(pls)) = bit1(pls),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_44]),c_0_67])]),c_0_68]) ).
cnf(c_0_82,plain,
hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))) = hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))),min),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70]),c_0_71]),c_0_68]) ).
cnf(c_0_83,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),t),zero_zero(int))),
inference(split_conjunct,[status(thm)],[fact_0__096t_A_060_A0_096]) ).
cnf(c_0_84,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))),hAPP(int,int,plus_plus(int,bit1(pls)),bit1(pls))))),m)),one_one(int)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_58]),c_0_44]) ).
cnf(c_0_85,hypothesis,
bit1(hAPP(int,int,plus_plus(int,pls),X1)) = bit1(X1),
inference(rw,[status(thm)],[c_0_73,c_0_44]) ).
cnf(c_0_86,negated_conjecture,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))))),pls)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_70]),c_0_68]) ).
cnf(c_0_87,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,times_times(X1,X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_88,plain,
hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),hAPP(int,int,plus_plus(int,bit1(pls)),bit1(bit1(pls)))))) = hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))),min),
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_60,c_0_76]),c_0_70]),c_0_68]),c_0_77]),c_0_78]),c_0_79]),c_0_80]),c_0_70]),c_0_81]),c_0_77]),c_0_70]),c_0_68]),c_0_82]) ).
cnf(c_0_89,plain,
linord20386208strict(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Olinordered__semiring__strict]) ).
cnf(c_0_90,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),t),pls)),
inference(rw,[status(thm)],[c_0_83,c_0_58]) ).
cnf(c_0_91,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),hAPP(int,int,plus_plus(int,bit1(pls)),bit1(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)],[c_0_84,c_0_70]),c_0_68]),c_0_77]),c_0_78]),c_0_79]),c_0_80]),c_0_70]),c_0_85]) ).
cnf(c_0_92,negated_conjecture,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))),min)),pls)),
inference(rw,[status(thm)],[c_0_86,c_0_82]) ).
cnf(c_0_93,plain,
$false,
inference(sr,[status(thm)],[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_87,c_0_88]),c_0_58]),c_0_89]),c_0_58]),c_0_90]),c_0_58]),c_0_91])]),c_0_92]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM924+7 : TPTP v8.1.0. Released v5.3.0.
% 0.11/0.13 % Command : run_ET %s %d
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jul 5 15:20:30 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.37/2.55 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.37/2.55 # Preprocessing time : 0.178 s
% 0.37/2.55
% 0.37/2.55 # Proof found!
% 0.37/2.55 # SZS status Theorem
% 0.37/2.55 # SZS output start CNFRefutation
% See solution above
% 0.37/2.56 # Proof object total steps : 94
% 0.37/2.56 # Proof object clause steps : 54
% 0.37/2.56 # Proof object formula steps : 40
% 0.37/2.56 # Proof object conjectures : 8
% 0.37/2.56 # Proof object clause conjectures : 5
% 0.37/2.56 # Proof object formula conjectures : 3
% 0.37/2.56 # Proof object initial clauses used : 25
% 0.37/2.56 # Proof object initial formulas used : 25
% 0.37/2.56 # Proof object generating inferences : 2
% 0.37/2.56 # Proof object simplifying inferences : 79
% 0.37/2.56 # Training examples: 0 positive, 0 negative
% 0.37/2.56 # Parsed axioms : 1255
% 0.37/2.56 # Removed by relevancy pruning/SinE : 0
% 0.37/2.56 # Initial clauses : 1736
% 0.37/2.56 # Removed in clause preprocessing : 85
% 0.37/2.56 # Initial clauses in saturation : 1651
% 0.37/2.56 # Processed clauses : 1746
% 0.37/2.56 # ...of these trivial : 20
% 0.37/2.56 # ...subsumed : 240
% 0.37/2.56 # ...remaining for further processing : 1486
% 0.37/2.56 # Other redundant clauses eliminated : 61
% 0.37/2.56 # Clauses deleted for lack of memory : 0
% 0.37/2.56 # Backward-subsumed : 5
% 0.37/2.56 # Backward-rewritten : 196
% 0.37/2.56 # Generated clauses : 72221
% 0.37/2.56 # ...of the previous two non-trivial : 67350
% 0.37/2.56 # Contextual simplify-reflections : 31
% 0.37/2.56 # Paramodulations : 72123
% 0.37/2.56 # Factorizations : 14
% 0.37/2.56 # Equation resolutions : 84
% 0.37/2.56 # Current number of processed clauses : 1269
% 0.37/2.56 # Positive orientable unit clauses : 326
% 0.37/2.56 # Positive unorientable unit clauses: 20
% 0.37/2.56 # Negative unit clauses : 16
% 0.37/2.56 # Non-unit-clauses : 907
% 0.37/2.56 # Current number of unprocessed clauses: 61671
% 0.37/2.56 # ...number of literals in the above : 196722
% 0.37/2.56 # Current number of archived formulas : 0
% 0.37/2.56 # Current number of archived clauses : 204
% 0.37/2.56 # Clause-clause subsumption calls (NU) : 110641
% 0.37/2.56 # Rec. Clause-clause subsumption calls : 52989
% 0.37/2.56 # Non-unit clause-clause subsumptions : 230
% 0.37/2.56 # Unit Clause-clause subsumption calls : 1445
% 0.37/2.56 # Rewrite failures with RHS unbound : 0
% 0.37/2.56 # BW rewrite match attempts : 22540
% 0.37/2.56 # BW rewrite match successes : 697
% 0.37/2.56 # Condensation attempts : 0
% 0.37/2.56 # Condensation successes : 0
% 0.37/2.56 # Termbank termtop insertions : 3650347
% 0.37/2.56
% 0.37/2.56 # -------------------------------------------------
% 0.37/2.56 # User time : 1.388 s
% 0.37/2.56 # System time : 0.047 s
% 0.37/2.56 # Total time : 1.435 s
% 0.37/2.56 # Maximum resident set size: 77332 pages
%------------------------------------------------------------------------------