%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM925+4 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 01:51:02 PM UTC 2026
% Result : Theorem 2.04s 1.12s
% Output : CNFRefutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 20
% Syntax : Number of formulae : 85 ( 60 unt; 0 def)
% Number of atoms : 134 ( 71 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 94 ( 45 ~; 32 |; 5 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 13 con; 0-2 aty)
% Number of variables : 94 ( 13 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_279_number__of__is__id,axiom,
! [X22] :
( is_int(X22)
=> hAPP_int_int(number_number_of_int,X22) = X22 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_number__of__is__id) ).
fof(gsy_c_hAPP_000tc__Int__Oint_000tc__Int__Oint,hypothesis,
! [X1,X2] :
( is_int(X2)
=> is_int(hAPP_int_int(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Int__Oint_000tc__Int__Oint) ).
fof(fact_158_zadd__0,axiom,
! [X18] :
( is_int(X18)
=> hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),X18) = X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_zadd__0) ).
fof(fact_51_semiring__norm_I110_J,axiom,
one_one_int = hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_semiring__norm_I110_J) ).
fof(fact_151_Pls__def,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_Pls__def) ).
fof(gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint,hypothesis,
is_int(zero_zero_int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint) ).
fof(fact_102_zadd__commute,axiom,
! [X18,X15] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X18),X15) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X15),X18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_zadd__commute) ).
fof(fact_201_Bit1__def,axiom,
! [X22] : hAPP_int_int(bit1,X22) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X22)),X22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_Bit1__def) ).
fof(fact_1883_mult__2__right,axiom,
! [X558] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X558),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X558),X558),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1883_mult__2__right) ).
fof(gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint,hypothesis,
is_int(one_one_int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint) ).
fof(fact_156_Bit0__def,axiom,
! [X22] : hAPP_int_int(bit0,X22) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X22),X22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_Bit0__def) ).
fof(fact_101_zadd__left__commute,axiom,
! [X9,X11,X18] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X9),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X11),X18)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X11),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X9),X18)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_zadd__left__commute) ).
fof(fact_114_rel__simps_I4_J,axiom,
! [X12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(bit0,X12)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_rel__simps_I4_J) ).
fof(fact_907_add__0__iff,axiom,
! [X83,X6] :
( ( is_int(X6)
& is_int(X83) )
=> ( X83 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X83),X6)
<=> X6 = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_907_add__0__iff) ).
fof(fact_1856_order__less__irrefl,axiom,
! [X543] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X543),X543)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1856_order__less__irrefl) ).
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(semiri1621563631at_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/benchmark/theBenchmark.p',conj_0) ).
fof(fact_1907_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X563] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X563),X563) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X563),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1907_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint,hypothesis,
! [X1,X2] : is_int(hAPP_nat_int(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint) ).
fof(fact_1130_no__zero__divisors,axiom,
! [X292,X293] :
( ( is_int(X293)
& is_int(X292) )
=> ( X293 != zero_zero_int
=> ( X292 != zero_zero_int
=> hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X293),X292) != zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1130_no__zero__divisors) ).
fof(fact_0_n1pos,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).
fof(c_0_20,plain,
! [X904] :
( hAPP_int_int(number_number_of_int,X904) = X904
| ~ is_int(X904) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_279_number__of__is__id])])]) ).
fof(c_0_21,hypothesis,
! [X875,X876] :
( is_int(hAPP_int_int(X875,X876))
| ~ is_int(X876) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Int__Oint_000tc__Int__Oint])])]) ).
cnf(c_0_22,plain,
( ~ is_int(X1)
| hAPP_int_int(number_number_of_int,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,hypothesis,
( ~ is_int(X1)
| is_int(hAPP_int_int(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_24,plain,
! [X897] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),X897) = X897
| ~ is_int(X897) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_158_zadd__0])])]) ).
cnf(c_0_25,plain,
one_one_int = hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)),
inference(split_conjunct,[status(thm)],[fact_51_semiring__norm_I110_J]) ).
cnf(c_0_26,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_151_Pls__def]) ).
cnf(c_0_27,hypothesis,
( ~ is_int(X2)
| hAPP_int_int(number_number_of_int,hAPP_int_int(X1,X2)) = hAPP_int_int(X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,hypothesis,
is_int(zero_zero_int),
inference(split_conjunct,[status(thm)],[gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint]) ).
fof(c_0_29,plain,
! [X1346,X1347] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1346),X1347) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1347),X1346),
inference(variable_rename,[status(thm)],[fact_102_zadd__commute]) ).
cnf(c_0_30,plain,
( ~ is_int(X1)
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_31,plain,
! [X1027] : hAPP_int_int(bit1,X1027) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1027)),X1027),
inference(variable_rename,[status(thm)],[fact_201_Bit1__def]) ).
fof(c_0_32,plain,
! [X1752] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1752),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1752),X1752),
inference(variable_rename,[status(thm)],[fact_1883_mult__2__right]) ).
cnf(c_0_33,plain,
hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,zero_zero_int)) = one_one_int,
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,hypothesis,
hAPP_int_int(number_number_of_int,hAPP_int_int(X1,zero_zero_int)) = hAPP_int_int(X1,zero_zero_int),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,hypothesis,
is_int(one_one_int),
inference(split_conjunct,[status(thm)],[gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint]) ).
fof(c_0_36,plain,
! [X1350] : hAPP_int_int(bit0,X1350) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1350),X1350),
inference(variable_rename,[status(thm)],[fact_156_Bit0__def]) ).
cnf(c_0_37,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,hypothesis,
( ~ is_int(X2)
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),hAPP_int_int(X1,X2)) = hAPP_int_int(X1,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_23]) ).
cnf(c_0_39,plain,
hAPP_int_int(bit1,X1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_40,plain,
! [X1343,X1344,X1345] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1343),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1344),X1345)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1344),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1343),X1345)),
inference(variable_rename,[status(thm)],[fact_101_zadd__left__commute]) ).
cnf(c_0_41,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X1),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,plain,
hAPP_int_int(bit1,zero_zero_int) = one_one_int,
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_43,hypothesis,
hAPP_int_int(number_number_of_int,hAPP_int_int(X1,one_one_int)) = hAPP_int_int(X1,one_one_int),
inference(spm,[status(thm)],[c_0_27,c_0_35]) ).
cnf(c_0_44,plain,
hAPP_int_int(bit0,X1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X1),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,hypothesis,
( ~ is_int(X1)
| is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)) ),
inference(spm,[status(thm)],[c_0_23,c_0_37]) ).
cnf(c_0_46,hypothesis,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),hAPP_int_int(X1,one_one_int)) = hAPP_int_int(X1,one_one_int),
inference(spm,[status(thm)],[c_0_38,c_0_35]) ).
cnf(c_0_47,hypothesis,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),hAPP_int_int(X1,zero_zero_int)) = hAPP_int_int(X1,zero_zero_int),
inference(spm,[status(thm)],[c_0_38,c_0_28]) ).
fof(c_0_48,plain,
! [X1080] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(bit0,X1080)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1080)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1080))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(bit0,X1080))) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_114_rel__simps_I4_J])])]) ).
fof(c_0_49,plain,
! [X930,X931] :
( ( ~ is_int(X931)
| ~ is_int(X930)
| X930 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X930),X931)
| X931 != zero_zero_int )
& ( ~ is_int(X931)
| ~ is_int(X930)
| X931 = zero_zero_int
| X930 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X930),X931) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_907_add__0__iff])])])]) ).
cnf(c_0_50,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)) = hAPP_int_int(bit1,X1),
inference(rw,[status(thm)],[c_0_39,c_0_37]) ).
cnf(c_0_51,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X3)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X3)),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_52,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),hAPP_int_int(bit0,one_one_int)) = hAPP_int_int(bit0,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_26]),c_0_42]),c_0_43]),c_0_44]) ).
cnf(c_0_53,hypothesis,
is_int(hAPP_int_int(X1,one_one_int)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_28])]) ).
fof(c_0_54,plain,
! [X543] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X543),X543)),
inference(fof_simplification,[status(thm)],[fact_1856_order__less__irrefl]) ).
fof(c_0_55,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(semiri1621563631at_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_56,plain,
! [X1205] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1205),X1205) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X1205),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
inference(variable_rename,[status(thm)],[fact_1907_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J]) ).
cnf(c_0_57,hypothesis,
is_int(hAPP_int_int(X1,zero_zero_int)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_47]),c_0_28])]) ).
fof(c_0_58,hypothesis,
! [X877,X878] : is_int(hAPP_nat_int(X877,X878)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint]) ).
cnf(c_0_59,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(bit0,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_60,plain,
( ~ is_int(X2)
| ~ is_int(X1)
| X1 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)
| X2 = zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_61,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(bit0,X1)) = hAPP_int_int(bit1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_44]) ).
cnf(c_0_62,hypothesis,
is_int(hAPP_int_int(bit0,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_52]),c_0_53])]) ).
fof(c_0_63,plain,
! [X1668] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1668),X1668)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_54])]) ).
fof(c_0_64,plain,
! [X292,X293] :
( ( is_int(X293)
& is_int(X292) )
=> ( X293 != zero_zero_int
=> ( X292 != zero_zero_int
=> hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X293),X292) != zero_zero_int ) ) ),
inference(fof_simplification,[status(thm)],[fact_1130_no__zero__divisors]) ).
fof(c_0_65,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(semiri1621563631at_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_55]) ).
cnf(c_0_66,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X1) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_67,hypothesis,
is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),X1)),
inference(spm,[status(thm)],[c_0_57,c_0_37]) ).
cnf(c_0_68,hypothesis,
is_int(hAPP_nat_int(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_69,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(bit0,X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_26]),c_0_26]) ).
cnf(c_0_70,plain,
( hAPP_int_int(bit1,X1) != one_one_int
| hAPP_int_int(bit0,X1) = zero_zero_int ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),c_0_35])]) ).
cnf(c_0_71,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
fof(c_0_72,plain,
! [X946,X947] :
( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X947),X946) != zero_zero_int
| X946 = zero_zero_int
| X947 = zero_zero_int
| ~ is_int(X947)
| ~ is_int(X946) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])]) ).
cnf(c_0_73,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(semiri1621563631at_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_65]) ).
cnf(c_0_74,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X1) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_26]),c_0_42]) ).
cnf(c_0_75,hypothesis,
is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),X2))),
inference(spm,[status(thm)],[c_0_67,c_0_51]) ).
cnf(c_0_76,hypothesis,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),hAPP_nat_int(X1,X2)) = hAPP_nat_int(X1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_68]) ).
cnf(c_0_77,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| hAPP_int_int(bit1,X1) != one_one_int ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).
cnf(c_0_78,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(split_conjunct,[status(thm)],[fact_0_n1pos]) ).
cnf(c_0_79,plain,
( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X2),X1) != zero_zero_int
| ~ is_int(X2)
| ~ is_int(X1)
| X1 = zero_zero_int
| X2 = zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_80,negated_conjecture,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) = zero_zero_int,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_26]),c_0_42]),c_0_74]) ).
cnf(c_0_81,hypothesis,
is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_nat_int(X2,X3))),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_82,plain,
hAPP_int_int(bit1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) != one_one_int,
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_83,negated_conjecture,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81])]) ).
cnf(c_0_84,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_83]),c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925+4 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 % Computer : n009.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Mon Sep 21 03:17:28 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.45 Running first-order theorem proving
% 0.11/0.45 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.04/1.12 % Version: 3.5.1
% 2.04/1.12 % Preprocessing class: FMLLSMLLSSSNFFN.
% 2.04/1.12 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.04/1.12 % Starting new_bool_3 with 900s (3) cores
% 2.04/1.12 % Starting new_bool_1 with 900s (3) cores
% 2.04/1.12 % Starting sh5l with 300s (1) cores
% 2.04/1.12 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 2.04/1.12 % G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with pid 722043 completed with status 0
% 2.04/1.12 % Result found by G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y
% 2.04/1.12 % Preprocessing class: FMLLSMLLSSSNFFN.
% 2.04/1.12 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.04/1.12 % Starting new_bool_3 with 900s (3) cores
% 2.04/1.12 % Starting new_bool_1 with 900s (3) cores
% 2.04/1.12 % Starting sh5l with 300s (1) cores
% 2.04/1.12 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 2.04/1.12 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.04/1.12 % SinE strategy is gf120_h_gu_RUU_F100_L00500
% 2.04/1.12 % Search class: FGHSM-FSLM31-DFFFFFNN
% 2.04/1.12 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 2.04/1.12 % Starting SubtermCWHack with 28s (1) cores
% 2.04/1.12 % SubtermCWHack with pid 722045 completed with status 0
% 2.04/1.12 % Result found by SubtermCWHack
% 2.04/1.12 % Preprocessing class: FMLLSMLLSSSNFFN.
% 2.04/1.12 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.04/1.12 % Starting new_bool_3 with 900s (3) cores
% 2.04/1.12 % Starting new_bool_1 with 900s (3) cores
% 2.04/1.12 % Starting sh5l with 300s (1) cores
% 2.04/1.12 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 2.04/1.12 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.04/1.12 % SinE strategy is gf120_h_gu_RUU_F100_L00500
% 2.04/1.12 % Search class: FGHSM-FSLM31-DFFFFFNN
% 2.04/1.12 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 2.04/1.12 % Starting SubtermCWHack with 28s (1) cores
% 2.04/1.12 % Preprocessing time : 0.017 s
% 2.04/1.12
% 2.04/1.12 % Proof found!
% 2.04/1.12 % SZS status Theorem
% 2.04/1.12 % SZS output start CNFRefutation
% See solution above
% 2.04/1.13 % Parsed axioms : 5487
% 2.04/1.13 % Removed by relevancy pruning/SinE : 4986
% 2.04/1.13 % Initial clauses : 706
% 2.04/1.13 % Removed in clause preprocessing : 42
% 2.04/1.13 % Initial clauses in saturation : 664
% 2.04/1.13 % Processed clauses : 2797
% 2.04/1.13 % ...of these trivial : 268
% 2.04/1.13 % ...subsumed : 1611
% 2.04/1.13 % ...remaining for further processing : 918
% 2.04/1.13 % Other redundant clauses eliminated : 67
% 2.04/1.13 % Clauses deleted for lack of memory : 0
% 2.04/1.13 % Backward-subsumed : 81
% 2.04/1.13 % Backward-rewritten : 158
% 2.04/1.13 % Generated clauses : 19511
% 2.04/1.13 % ...of the previous two non-redundant : 13162
% 2.04/1.13 % ...aggressively subsumed : 0
% 2.04/1.13 % Contextual simplify-reflections : 4
% 2.04/1.13 % Paramodulations : 19443
% 2.04/1.13 % Factorizations : 2
% 2.04/1.13 % NegExts : 0
% 2.04/1.13 % Equation resolutions : 69
% 2.04/1.13 % Disequality decompositions : 0
% 2.04/1.13 % Total rewrite steps : 11918
% 2.04/1.13 % ...of those cached : 10186
% 2.04/1.13 % Propositional unsat checks : 0
% 2.04/1.13 % Propositional check models : 0
% 2.04/1.13 % Propositional check unsatisfiable : 0
% 2.04/1.13 % Propositional clauses : 0
% 2.04/1.13 % Propositional clauses after purity: 0
% 2.04/1.13 % Propositional unsat core size : 0
% 2.04/1.13 % Propositional preprocessing time : 0.000
% 2.04/1.13 % Propositional encoding time : 0.000
% 2.04/1.13 % Propositional solver time : 0.000
% 2.04/1.13 % Success case prop preproc time : 0.000
% 2.04/1.13 % Success case prop encoding time : 0.000
% 2.04/1.13 % Success case prop solver time : 0.000
% 2.04/1.13 % Current number of processed clauses : 643
% 2.04/1.13 % Positive orientable unit clauses : 328
% 2.04/1.13 % Positive unorientable unit clauses: 8
% 2.04/1.13 % Negative unit clauses : 68
% 2.04/1.13 % Non-unit-clauses : 239
% 2.04/1.13 % Current number of unprocessed clauses: 10668
% 2.04/1.13 % ...number of literals in the above : 22139
% 2.04/1.13 % Current number of archived formulas : 0
% 2.04/1.13 % Current number of archived clauses : 239
% 2.04/1.13 % Clause-clause subsumption calls (NU) : 8342
% 2.04/1.13 % Rec. Clause-clause subsumption calls : 5080
% 2.04/1.13 % Non-unit clause-clause subsumptions : 358
% 2.04/1.13 % Unit Clause-clause subsumption calls : 3145
% 2.04/1.13 % Rewrite failures with RHS unbound : 0
% 2.04/1.13 % BW rewrite match attempts : 3975
% 2.04/1.13 % BW rewrite match successes : 192
% 2.04/1.13 % Condensation attempts : 0
% 2.04/1.13 % Condensation successes : 0
% 2.04/1.13 % Termbank termtop insertions : 458974
% 2.04/1.13 % Search garbage collected termcells : 55632
% 2.04/1.13
% 2.04/1.13 % -------------------------------------------------
% 2.04/1.13 % User time : 0.327 s
% 2.04/1.13 % System time : 0.041 s
% 2.04/1.13 % Total time : 0.368 s
% 2.04/1.13 % Maximum resident set size: 14344 pages
% 2.04/1.13
% 2.04/1.13 % -------------------------------------------------
% 2.04/1.13 % User time : 0.564 s
% 2.04/1.13 % System time : 0.062 s
% 2.04/1.13 % Total time : 0.626 s
% 2.04/1.13 % Maximum resident set size: 13312 pages
% 2.04/1.13 % E exiting
%------------------------------------------------------------------------------