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CSE_E---1.7.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : NUM924+4 : TPTP v9.2.1. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n013.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  : 300s
% DateTime : Tue May  5 04:58:52 PM UTC 2026

% Result   : Theorem 5.22s 4.46s
% Output   : CNFRefutation 5.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   48 (  48 unt;   0 def)
%            Number of atoms       :   48 (  38 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    5 (   5   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :   13 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   21 (  21 usr;  14 con; 0-2 aty)
%            Number of variables   :   37 (   1 sgn  22   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_199_zadd__commute,axiom,
    ! [X15,X13] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X15),X13) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X13),X15),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_zadd__commute) ).

fof(fact_434_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
    ! [X97] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X97),X97) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X97),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_434_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).

fof(fact_270_double__number__of__Bit0,axiom,
    ! [X70] : 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),one_one_int)),hAPP_int_int(number_number_of_int,X70)) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,X70)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_double__number__of__Bit0) ).

fof(fact_266_Bit0__def,axiom,
    ! [X14] : hAPP_int_int(bit0,X14) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X14),X14),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_Bit0__def) ).

fof(fact_691_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
    ! [X189] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X189),X189) = 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),one_one_int)),X189),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

fof(fact_126_mult__Bit0,axiom,
    ! [X14,X42] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(bit0,X14)),X42) = hAPP_int_int(bit0,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X14),X42)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_mult__Bit0) ).

fof(conj_0,conjecture,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_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_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_256_Pls__def,axiom,
    pls = zero_zero_int,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_Pls__def) ).

fof(fact_54_zmult__commute,axiom,
    ! [X15,X13] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X15),X13) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X13),X15),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_zmult__commute) ).

fof(fact_590_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
    ! [X160] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X160),zero_zero_int) = zero_zero_int,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_590_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).

fof(fact_243_one__is__num__one,axiom,
    one_one_int = hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_one__is__num__one) ).

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_i1948725293t_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_13,plain,
    ! [X2313,X2314] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2313),X2314) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2314),X2313),
    inference(variable_rename,[status(thm)],[fact_199_zadd__commute]) ).

fof(c_0_14,plain,
    ! [X2143] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X2143),X2143) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X2143),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
    inference(variable_rename,[status(thm)],[fact_434_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J]) ).

fof(c_0_15,plain,
    ! [X2756] : 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),one_one_int)),hAPP_int_int(number_number_of_int,X2756)) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,X2756)),
    inference(variable_rename,[status(thm)],[fact_270_double__number__of__Bit0]) ).

fof(c_0_16,plain,
    ! [X2321] : hAPP_int_int(bit0,X2321) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2321),X2321),
    inference(variable_rename,[status(thm)],[fact_266_Bit0__def]) ).

fof(c_0_17,plain,
    ! [X2049] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2049),X2049) = 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),one_one_int)),X2049),
    inference(variable_rename,[status(thm)],[fact_691_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J]) ).

fof(c_0_18,plain,
    ! [X2678,X2679] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(bit0,X2678)),X2679) = hAPP_int_int(bit0,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X2678),X2679)),
    inference(variable_rename,[status(thm)],[fact_126_mult__Bit0]) ).

fof(c_0_19,negated_conjecture,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_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)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

cnf(c_0_20,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_21,plain,
    pls = zero_zero_int,
    inference(split_conjunct,[status(thm)],[fact_256_Pls__def]) ).

cnf(c_0_22,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_13]) ).

fof(c_0_23,plain,
    ! [X2672,X2673] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X2672),X2673) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X2673),X2672),
    inference(variable_rename,[status(thm)],[fact_54_zmult__commute]) ).

cnf(c_0_24,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_14]) ).

cnf(c_0_25,plain,
    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),one_one_int)),hAPP_int_int(number_number_of_int,X1)) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,X1)),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_26,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_16]) ).

cnf(c_0_27,plain,
    hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X1) = 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),one_one_int)),X1),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_28,plain,
    hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(bit0,X1)),X2) = hAPP_int_int(bit0,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X2)),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_29,negated_conjecture,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_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_19]) ).

fof(c_0_30,plain,
    ! [X2707] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X2707),zero_zero_int) = zero_zero_int,
    inference(variable_rename,[status(thm)],[fact_590_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J]) ).

cnf(c_0_31,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_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int))))) = 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_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,zero_zero_int))))),m))),t),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_21]),c_0_22]) ).

cnf(c_0_32,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_23]) ).

cnf(c_0_33,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,zero_zero_int)))),
    inference(rw,[status(thm)],[c_0_24,c_0_21]) ).

cnf(c_0_34,plain,
    hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(bit0,one_one_int)),hAPP_int_int(number_number_of_int,X1)) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,X1)),
    inference(rw,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_35,plain,
    hAPP_int_int(bit0,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),X1)) = hAPP_int_int(bit0,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_26]),c_0_26]),c_0_28]) ).

cnf(c_0_36,plain,
    one_one_int = hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)),
    inference(split_conjunct,[status(thm)],[fact_243_one__is__num__one]) ).

cnf(c_0_37,negated_conjecture,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_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,zero_zero_int))))),one_one_int)),zero_zero_int)),
    inference(rw,[status(thm)],[c_0_29,c_0_21]) ).

cnf(c_0_38,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_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_39,plain,
    hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),zero_zero_int) = zero_zero_int,
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_40,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,zero_zero_int))))))) = 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,s),s)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_32]),c_0_33]) ).

cnf(c_0_41,plain,
    hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,X1)) = hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_28]),c_0_35]) ).

cnf(c_0_42,plain,
    hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,zero_zero_int)) = one_one_int,
    inference(rw,[status(thm)],[c_0_36,c_0_21]) ).

cnf(c_0_43,negated_conjecture,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,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,zero_zero_int)))))))),zero_zero_int)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_22]),c_0_31]),c_0_32]),c_0_32]) ).

cnf(c_0_44,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_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,one_one_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,zero_zero_int))))),m))),t)),zero_zero_int)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_21]),c_0_22]),c_0_21]),c_0_22]),c_0_39]) ).

cnf(c_0_45,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(bit0,hAPP_int_int(bit0,one_one_int))))) = 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,s),s)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_41]),c_0_42]) ).

cnf(c_0_46,negated_conjecture,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,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,s),s))),zero_zero_int)),
    inference(rw,[status(thm)],[c_0_43,c_0_40]) ).

cnf(c_0_47,plain,
    $false,
    inference(sr,[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_44,c_0_32]),c_0_32]),c_0_41]),c_0_41]),c_0_42]),c_0_45]),c_0_46]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : NUM924+4 : TPTP v9.2.1. Released v5.3.0.
% 0.11/0.13  % Command    : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.34  % Computer : n013.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue May  5 01:17:56 EDT 2026
% 0.14/0.34  % CPUTime    : 
% 0.18/0.35  % start to proof: theBenchmark
% 5.22/4.46  % Version  : CSE_E---1.7
% 5.22/4.46  % Problem  : theBenchmark.p
% 5.22/4.46  % SZS status Theorem for theBenchmark.p
% 5.22/4.46  % SZS output start CNFRefutation
% See solution above
% 5.22/4.47  % Total time : 3.604s
%------------------------------------------------------------------------------