%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM924+8 : 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 : n001.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 01:51:01 PM UTC 2026
% Result : Theorem 15.61s 4.03s
% Output : CNFRefutation 15.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 20
% Syntax : Number of formulae : 69 ( 69 unt; 0 def)
% Number of atoms : 69 ( 58 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 12 con; 0-4 aty)
% Number of variables : 45 ( 1 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_22_number__of__is__id,axiom,
! [X15] : hAPP(int,int,number_number_of(int),X15) = ti(int,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_number__of__is__id) ).
fof(fact_2143_zminus__zminus,axiom,
! [X16] : hAPP(int,int,uminus_uminus(int),hAPP(int,int,uminus_uminus(int),X16)) = ti(int,X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2143_zminus__zminus) ).
fof(tsy_c_Int_OMin_res,axiom,
ti(int,min_1) = min_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OMin_res) ).
fof(fact_99_zadd__commute,axiom,
! [X16,X12] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X16),X12) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X12),X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_zadd__commute) ).
fof(conj_0,conjecture,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_2160_mult__Min,axiom,
! [X15] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),min_1),X15) = hAPP(int,int,uminus_uminus(int),X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2160_mult__Min) ).
fof(fact_65_zmult__1__right,axiom,
! [X16] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X16),one_one(int)) = ti(int,X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_zmult__1__right) ).
fof(tsy_c_hAPP_res,axiom,
! [X3,X1,X4,X5] : ti(X3,hAPP(X1,X3,X4,X5)) = hAPP(X1,X3,X4,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
fof(fact_1316_transfer__int__nat__numerals_I2_J,axiom,
one_one(int) = hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1316_transfer__int__nat__numerals_I2_J) ).
fof(fact_1330_One__nat__def,axiom,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1330_One__nat__def) ).
fof(fact_23_zmult__commute,axiom,
! [X16,X12] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X16),X12) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X12),X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_zmult__commute) ).
fof(fact_467__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096,axiom,
hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,number_number_of(int),min_1)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_467__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
fof(fact_1427_semiring__norm_I115_J,axiom,
hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1427_semiring__norm_I115_J) ).
fof(fact_2164_minus__Min,axiom,
hAPP(int,int,uminus_uminus(int),min_1) = hAPP(int,int,bit1,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2164_minus__Min) ).
fof(fact_1228_nat__int,axiom,
! [X45] : hAPP(int,nat,nat_1,hAPP(nat,int,semiring_1_of_nat(int),X45)) = X45,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1228_nat__int) ).
fof(fact_1291_transfer__int__nat__numerals_I1_J,axiom,
zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1291_transfer__int__nat__numerals_I1_J) ).
fof(fact_123_Pls__def,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_Pls__def) ).
fof(fact_3_t,axiom,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_t) ).
fof(fact_62_mult__Pls,axiom,
! [X12] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),X12) = pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_mult__Pls) ).
fof(fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
fof(c_0_20,plain,
! [X347] : hAPP(int,int,number_number_of(int),X347) = ti(int,X347),
inference(variable_rename,[status(thm)],[fact_22_number__of__is__id]) ).
fof(c_0_21,plain,
! [X1457] : hAPP(int,int,uminus_uminus(int),hAPP(int,int,uminus_uminus(int),X1457)) = ti(int,X1457),
inference(variable_rename,[status(thm)],[fact_2143_zminus__zminus]) ).
cnf(c_0_22,plain,
ti(int,min_1) = min_1,
inference(split_conjunct,[status(thm)],[tsy_c_Int_OMin_res]) ).
cnf(c_0_23,plain,
hAPP(int,int,number_number_of(int),X1) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_24,plain,
! [X588,X589] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X588),X589) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X589),X588),
inference(variable_rename,[status(thm)],[fact_99_zadd__commute]) ).
fof(c_0_25,negated_conjecture,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int))),
inference(assume_negation,[status(cth)],[conj_0]) ).
cnf(c_0_26,plain,
hAPP(int,int,uminus_uminus(int),hAPP(int,int,uminus_uminus(int),X1)) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_27,plain,
! [X1735] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),min_1),X1735) = hAPP(int,int,uminus_uminus(int),X1735),
inference(variable_rename,[status(thm)],[fact_2160_mult__Min]) ).
fof(c_0_28,plain,
! [X352] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X352),one_one(int)) = ti(int,X352),
inference(variable_rename,[status(thm)],[fact_65_zmult__1__right]) ).
fof(c_0_29,plain,
! [X343,X344,X345,X346] : ti(X343,hAPP(X344,X343,X345,X346)) = hAPP(X344,X343,X345,X346),
inference(variable_rename,[status(thm)],[tsy_c_hAPP_res]) ).
cnf(c_0_30,plain,
one_one(int) = hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)),
inference(split_conjunct,[status(thm)],[fact_1316_transfer__int__nat__numerals_I2_J]) ).
cnf(c_0_31,plain,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
inference(split_conjunct,[status(thm)],[fact_1330_One__nat__def]) ).
fof(c_0_32,plain,
! [X920,X921] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X920),X921) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X921),X920),
inference(variable_rename,[status(thm)],[fact_23_zmult__commute]) ).
cnf(c_0_33,plain,
hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,number_number_of(int),min_1)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)),
inference(split_conjunct,[status(thm)],[fact_467__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096]) ).
cnf(c_0_34,plain,
hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
inference(split_conjunct,[status(thm)],[fact_1427_semiring__norm_I115_J]) ).
cnf(c_0_35,plain,
hAPP(int,int,number_number_of(int),min_1) = min_1,
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_36,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_24]) ).
fof(c_0_37,negated_conjecture,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int))),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
cnf(c_0_38,plain,
hAPP(int,int,uminus_uminus(int),hAPP(int,int,uminus_uminus(int),X1)) = hAPP(int,int,number_number_of(int),X1),
inference(rw,[status(thm)],[c_0_26,c_0_23]) ).
cnf(c_0_39,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),min_1),X1) = hAPP(int,int,uminus_uminus(int),X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_40,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),one_one(int)) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_41,plain,
hAPP(int,int,uminus_uminus(int),min_1) = hAPP(int,int,bit1,pls),
inference(split_conjunct,[status(thm)],[fact_2164_minus__Min]) ).
cnf(c_0_42,plain,
ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_43,plain,
hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,zero_zero(nat))) = one_one(int),
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_44,plain,
! [X2560] : hAPP(int,nat,nat_1,hAPP(nat,int,semiring_1_of_nat(int),X2560)) = X2560,
inference(variable_rename,[status(thm)],[fact_1228_nat__int]) ).
cnf(c_0_45,plain,
zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)),
inference(split_conjunct,[status(thm)],[fact_1291_transfer__int__nat__numerals_I1_J]) ).
cnf(c_0_46,plain,
pls = zero_zero(int),
inference(split_conjunct,[status(thm)],[fact_123_Pls__def]) ).
cnf(c_0_47,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t),
inference(split_conjunct,[status(thm)],[fact_3_t]) ).
cnf(c_0_48,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_32]) ).
cnf(c_0_49,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))),min_1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_34]),c_0_36]) ).
fof(c_0_50,plain,
! [X432] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),X432) = pls,
inference(variable_rename,[status(thm)],[fact_62_mult__Pls]) ).
fof(c_0_51,negated_conjecture,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int))),
inference(fof_nnf,[status(thm)],[c_0_37]) ).
cnf(c_0_52,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),min_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),min_1),X1)) = hAPP(int,int,number_number_of(int),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_39]) ).
cnf(c_0_53,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),one_one(int)) = hAPP(int,int,number_number_of(int),X1),
inference(rw,[status(thm)],[c_0_40,c_0_23]) ).
cnf(c_0_54,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),min_1),min_1) = hAPP(int,int,bit1,pls),
inference(rw,[status(thm)],[c_0_41,c_0_39]) ).
cnf(c_0_55,plain,
hAPP(int,int,number_number_of(int),one_one(int)) = one_one(int),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_23]) ).
cnf(c_0_56,plain,
hAPP(int,nat,nat_1,hAPP(nat,int,semiring_1_of_nat(int),X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_57,plain,
hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)) = pls,
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_58,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)))),
inference(split_conjunct,[status(thm)],[fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096]) ).
cnf(c_0_59,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))),min_1),
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_47,c_0_48]),c_0_36]),c_0_48]),c_0_34]),c_0_36]),c_0_49]) ).
cnf(c_0_60,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),X1) = pls,
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_61,negated_conjecture,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int))),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_62,plain,
one_one(int) = hAPP(int,int,bit1,pls),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_35]),c_0_54]),c_0_55]) ).
cnf(c_0_63,plain,
zero_zero(nat) = hAPP(int,nat,nat_1,pls),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_64,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))),min_1)),pls)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_48]),c_0_36]),c_0_48]),c_0_59]),c_0_48]),c_0_36]),c_0_46]),c_0_48]),c_0_60]) ).
cnf(c_0_65,negated_conjecture,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))),one_one(int))),pls)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_34]),c_0_46]) ).
cnf(c_0_66,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(int,nat,nat_1,pls))))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(int,nat,nat_1,pls))))),min_1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_62]),c_0_63]),c_0_63]) ).
cnf(c_0_67,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(int,nat,nat_1,pls))))),min_1)),pls)),
inference(rw,[status(thm)],[c_0_64,c_0_63]) ).
cnf(c_0_68,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_36]),c_0_62]),c_0_63]),c_0_66]),c_0_67])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM924+8 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.46 % Computer : n001.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.47 % DateTime : Mon Sep 21 03:22:28 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.53 Running first-order theorem proving
% 0.24/0.53 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
% 15.61/4.03 % Version: 3.5.1
% 15.61/4.03 % Preprocessing class: FMLMSMSLSSSNFFN.
% 15.61/4.03 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.61/4.03 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 15.61/4.03 % Starting new_bool_3 with 600s (2) cores
% 15.61/4.03 % Starting new_bool_1 with 600s (2) cores
% 15.61/4.03 % Starting sh5l with 300s (1) cores
% 15.61/4.03 % new_bool_3 with pid 2076204 completed with status 0
% 15.61/4.03 % Result found by new_bool_3
% 15.61/4.03 % Preprocessing class: FMLMSMSLSSSNFFN.
% 15.61/4.03 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.61/4.03 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 15.61/4.03 % Starting new_bool_3 with 600s (2) cores
% 15.61/4.03 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 15.61/4.03 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 15.61/4.03 % Search class: FGHSM-SMLM32-DFFFFFNN
% 15.61/4.03 % Scheduled 13 strats onto 2 cores with 600 seconds (600 total)
% 15.61/4.03 % Starting SubtermCWHack with 55s (1) cores
% 15.61/4.03 % Starting new_bool_3 with 61s (1) cores
% 15.61/4.03 % new_bool_3 with pid 2076208 completed with status 0
% 15.61/4.03 % Result found by new_bool_3
% 15.61/4.03 % Preprocessing class: FMLMSMSLSSSNFFN.
% 15.61/4.03 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.61/4.03 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 15.61/4.03 % Starting new_bool_3 with 600s (2) cores
% 15.61/4.03 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 15.61/4.03 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 15.61/4.03 % Search class: FGHSM-SMLM32-DFFFFFNN
% 15.61/4.03 % Scheduled 13 strats onto 2 cores with 600 seconds (600 total)
% 15.61/4.03 % Starting SubtermCWHack with 55s (1) cores
% 15.61/4.03 % Starting new_bool_3 with 61s (1) cores
% 15.61/4.03 % Preprocessing time : 0.113 s
% 15.61/4.03 % Presaturation interreduction done
% 15.61/4.03
% 15.61/4.03 % Proof found!
% 15.61/4.03 % SZS status Theorem
% 15.61/4.03 % SZS output start CNFRefutation
% See solution above
% 15.61/4.03 % Parsed axioms : 5738
% 15.61/4.03 % Removed by relevancy pruning/SinE : 4366
% 15.61/4.03 % Initial clauses : 2237
% 15.61/4.03 % Removed in clause preprocessing : 83
% 15.61/4.03 % Initial clauses in saturation : 2154
% 15.61/4.03 % Processed clauses : 6122
% 15.61/4.03 % ...of these trivial : 400
% 15.61/4.03 % ...subsumed : 2297
% 15.61/4.03 % ...remaining for further processing : 3424
% 15.61/4.03 % Other redundant clauses eliminated : 257
% 15.61/4.03 % Clauses deleted for lack of memory : 0
% 15.61/4.03 % Backward-subsumed : 47
% 15.61/4.03 % Backward-rewritten : 181
% 15.61/4.03 % Generated clauses : 15415
% 15.61/4.03 % ...of the previous two non-redundant : 12380
% 15.61/4.03 % ...aggressively subsumed : 0
% 15.61/4.03 % Contextual simplify-reflections : 4
% 15.61/4.03 % Paramodulations : 15159
% 15.61/4.03 % Factorizations : 0
% 15.61/4.03 % NegExts : 0
% 15.61/4.03 % Equation resolutions : 269
% 15.61/4.03 % Disequality decompositions : 0
% 15.61/4.03 % Total rewrite steps : 15062
% 15.61/4.03 % ...of those cached : 12224
% 15.61/4.03 % Propositional unsat checks : 0
% 15.61/4.03 % Propositional check models : 0
% 15.61/4.03 % Propositional check unsatisfiable : 0
% 15.61/4.03 % Propositional clauses : 0
% 15.61/4.03 % Propositional clauses after purity: 0
% 15.61/4.03 % Propositional unsat core size : 0
% 15.61/4.03 % Propositional preprocessing time : 0.000
% 15.61/4.03 % Propositional encoding time : 0.000
% 15.61/4.03 % Propositional solver time : 0.000
% 15.61/4.03 % Success case prop preproc time : 0.000
% 15.61/4.03 % Success case prop encoding time : 0.000
% 15.61/4.03 % Success case prop solver time : 0.000
% 15.61/4.03 % Current number of processed clauses : 1216
% 15.61/4.03 % Positive orientable unit clauses : 680
% 15.61/4.03 % Positive unorientable unit clauses: 21
% 15.61/4.03 % Negative unit clauses : 158
% 15.61/4.03 % Non-unit-clauses : 357
% 15.61/4.03 % Current number of unprocessed clauses: 10073
% 15.61/4.03 % ...number of literals in the above : 15482
% 15.61/4.03 % Current number of archived formulas : 0
% 15.61/4.03 % Current number of archived clauses : 1995
% 15.61/4.03 % Clause-clause subsumption calls (NU) : 299744
% 15.61/4.03 % Rec. Clause-clause subsumption calls : 122116
% 15.61/4.03 % Non-unit clause-clause subsumptions : 1438
% 15.61/4.03 % Unit Clause-clause subsumption calls : 3677
% 15.61/4.03 % Rewrite failures with RHS unbound : 0
% 15.61/4.03 % BW rewrite match attempts : 120597
% 15.61/4.03 % BW rewrite match successes : 598
% 15.61/4.03 % Condensation attempts : 0
% 15.61/4.03 % Condensation successes : 0
% 15.61/4.03 % Termbank termtop insertions : 1825171
% 15.61/4.03 % Search garbage collected termcells : 63838
% 15.61/4.03
% 15.61/4.03 % -------------------------------------------------
% 15.61/4.03 % User time : 2.555 s
% 15.61/4.03 % System time : 0.106 s
% 15.61/4.03 % Total time : 2.662 s
% 15.61/4.03 % Maximum resident set size: 17120 pages
% 15.61/4.03
% 15.61/4.03 % -------------------------------------------------
% 15.61/4.03 % User time : 5.651 s
% 15.61/4.03 % System time : 0.221 s
% 15.61/4.03 % Total time : 5.871 s
% 15.61/4.03 % Maximum resident set size: 12800 pages
% 15.61/4.03 % E exiting
%------------------------------------------------------------------------------