%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM924+3 : TPTP v9.2.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n009.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 04:58:51 PM UTC 2026
% Result : Theorem 2.18s 2.11s
% Output : CNFRefutation 2.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 53 ( 53 unt; 0 def)
% Number of atoms : 53 ( 41 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 18 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 8 con; 0-2 aty)
% Number of variables : 38 ( 1 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_182_Bit0__def,axiom,
! [X13] : bit0(X13) = hAPP_int_int(plus_plus_int(X13),X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_Bit0__def) ).
fof(fact_236_Bit1__def,axiom,
! [X13] : bit1(X13) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X13)),X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_Bit1__def) ).
fof(conj_0,conjecture,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_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/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_87_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/sandbox2/benchmark/theBenchmark.p',fact_87_nat__1__add__1) ).
fof(fact_134_zadd__commute,axiom,
! [X14,X12] : hAPP_int_int(plus_plus_int(X14),X12) = hAPP_int_int(plus_plus_int(X12),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_zadd__commute) ).
fof(fact_285_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X96] : hAPP_int_int(times_times_int(X96),X96) = hAPP_nat_int(power_power_int(X96),number_number_of_nat(bit0(bit1(pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
fof(fact_172_Pls__def,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_Pls__def) ).
fof(fact_415_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [X188] : hAPP_int_int(plus_plus_int(X188),X188) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X188),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_1068__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096,axiom,
twoSqu1241645765sum2sq(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/sandbox2/benchmark/theBenchmark.p',fact_1068__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096) ).
fof(fact_95_zadd__zmult__distrib2,axiom,
! [X12,X18,X19] : hAPP_int_int(times_times_int(X12),hAPP_int_int(plus_plus_int(X18),X19)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X12),X18)),hAPP_int_int(times_times_int(X12),X19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_zadd__zmult__distrib2) ).
fof(fact_35_zmult__commute,axiom,
! [X14,X12] : hAPP_int_int(times_times_int(X14),X12) = hAPP_int_int(times_times_int(X12),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_zmult__commute) ).
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/sandbox2/benchmark/theBenchmark.p',fact_3_t) ).
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(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)),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)),zero_zero_int))),
file('/export/starexec/sandbox2/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(fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [X159] : hAPP_int_int(times_times_int(X159),zero_zero_int) = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(c_0_14,plain,
! [X3350] : bit0(X3350) = hAPP_int_int(plus_plus_int(X3350),X3350),
inference(variable_rename,[status(thm)],[fact_182_Bit0__def]) ).
fof(c_0_15,plain,
! [X3411] : bit1(X3411) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X3411)),X3411),
inference(variable_rename,[status(thm)],[fact_236_Bit1__def]) ).
fof(c_0_16,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_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)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_17,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_87_nat__1__add__1]) ).
cnf(c_0_18,plain,
bit0(X1) = hAPP_int_int(plus_plus_int(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
bit1(X1) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,plain,
! [X3279,X3280] : hAPP_int_int(plus_plus_int(X3279),X3280) = hAPP_int_int(plus_plus_int(X3280),X3279),
inference(variable_rename,[status(thm)],[fact_134_zadd__commute]) ).
cnf(c_0_21,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_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_16]) ).
fof(c_0_22,plain,
! [X3458] : hAPP_int_int(times_times_int(X3458),X3458) = hAPP_nat_int(power_power_int(X3458),number_number_of_nat(bit0(bit1(pls)))),
inference(variable_rename,[status(thm)],[fact_285_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J]) ).
cnf(c_0_23,plain,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_19]) ).
cnf(c_0_24,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_172_Pls__def]) ).
cnf(c_0_25,plain,
hAPP_int_int(plus_plus_int(X1),X2) = hAPP_int_int(plus_plus_int(X2),X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_26,plain,
! [X3779] : hAPP_int_int(plus_plus_int(X3779),X3779) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X3779),
inference(variable_rename,[status(thm)],[fact_415_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J]) ).
cnf(c_0_27,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_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(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),one_one_int)),zero_zero_int)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_18]),c_0_19]),c_0_19]) ).
cnf(c_0_28,plain,
twoSqu1241645765sum2sq(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_1068__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096]) ).
fof(c_0_29,plain,
! [X3201,X3202,X3203] : hAPP_int_int(times_times_int(X3201),hAPP_int_int(plus_plus_int(X3202),X3203)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3201),X3202)),hAPP_int_int(times_times_int(X3201),X3203)),
inference(variable_rename,[status(thm)],[fact_95_zadd__zmult__distrib2]) ).
fof(c_0_30,plain,
! [X3097,X3098] : hAPP_int_int(times_times_int(X3097),X3098) = hAPP_int_int(times_times_int(X3098),X3097),
inference(variable_rename,[status(thm)],[fact_35_zmult__commute]) ).
cnf(c_0_31,plain,
hAPP_int_int(times_times_int(X1),X1) = hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,plain,
number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(zero_zero_int),hAPP_int_int(plus_plus_int(zero_zero_int),one_one_int))),hAPP_int_int(plus_plus_int(zero_zero_int),hAPP_int_int(plus_plus_int(zero_zero_int),one_one_int)))) = hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat),
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_23,c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_24]),c_0_25]) ).
cnf(c_0_33,plain,
hAPP_int_int(plus_plus_int(X1),X1) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_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(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),zero_zero_int)),zero_zero_int))))),one_one_int)),zero_zero_int)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_24]),c_0_24]),c_0_24]),c_0_24]) ).
cnf(c_0_35,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_36,plain,
twoSqu1241645765sum2sq(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(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t),
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_28,c_0_18]),c_0_18]),c_0_19]),c_0_19]),c_0_19]),c_0_19]) ).
cnf(c_0_37,plain,
hAPP_int_int(times_times_int(X1),hAPP_int_int(plus_plus_int(X2),X3)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1),X2)),hAPP_int_int(times_times_int(X1),X3)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,plain,
hAPP_int_int(times_times_int(X1),X2) = hAPP_int_int(times_times_int(X2),X1),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,plain,
hAPP_int_int(times_times_int(X1),X1) = hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_18]),c_0_19]),c_0_19]) ).
cnf(c_0_40,plain,
number_number_of_nat(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(plus_plus_int(zero_zero_int),hAPP_int_int(plus_plus_int(zero_zero_int),one_one_int)))) = hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_41,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(zero_zero_int),hAPP_int_int(plus_plus_int(zero_zero_int),one_one_int))),hAPP_int_int(plus_plus_int(zero_zero_int),hAPP_int_int(plus_plus_int(zero_zero_int),one_one_int))))))),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_34,c_0_25]),c_0_25]),c_0_25]),c_0_25]),c_0_25]) ).
cnf(c_0_42,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_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)),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)),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_43,plain,
hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),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(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t),
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_35,c_0_18]),c_0_18]),c_0_18]),c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_19]) ).
cnf(c_0_44,plain,
hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),number_number_of_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),hAPP_int_int(plus_plus_int(zero_zero_int),hAPP_int_int(plus_plus_int(zero_zero_int),one_one_int)))))))) = twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)),
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)],[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_36,c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_33]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_33]),c_0_37]),c_0_33]),c_0_38]),c_0_25]),c_0_38]) ).
cnf(c_0_45,plain,
hAPP_int_int(times_times_int(X1),X1) = hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),
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_39,c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_33]),c_0_40]) ).
fof(c_0_46,plain,
! [X3667] : hAPP_int_int(times_times_int(X3667),zero_zero_int) = zero_zero_int,
inference(variable_rename,[status(thm)],[fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J]) ).
cnf(c_0_47,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(power_power_int(s),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)))),zero_zero_int)),
inference(rw,[status(thm)],[c_0_41,c_0_32]) ).
cnf(c_0_48,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_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(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t)),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(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),zero_zero_int))),
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_42,c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_19]) ).
cnf(c_0_49,plain,
twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)) = hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(s),s)),
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)],[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)],[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_43,c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_33]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_33]),c_0_37]),c_0_33]),c_0_38]),c_0_25]),c_0_38]),c_0_44]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_33]),c_0_40]),c_0_45]),c_0_25]) ).
cnf(c_0_50,plain,
hAPP_int_int(times_times_int(X1),zero_zero_int) = zero_zero_int,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_51,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(s),s))),zero_zero_int)),
inference(rw,[status(thm)],[c_0_47,c_0_45]) ).
cnf(c_0_52,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)],[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)],[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)],[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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_33]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_33]),c_0_37]),c_0_33]),c_0_38]),c_0_25]),c_0_38]),c_0_44]),c_0_49]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_33]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_24]),c_0_25]),c_0_33]),c_0_37]),c_0_33]),c_0_38]),c_0_25]),c_0_50]),c_0_51]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM924+3 : TPTP v9.2.1. Released v5.3.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n009.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:17:56 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.18/2.11 % Version : CSE_E---1.7
% 2.18/2.11 % Problem : theBenchmark.p
% 2.18/2.11 % SZS status Theorem for theBenchmark.p
% 2.18/2.11 % SZS output start CNFRefutation
% See solution above
% 2.18/2.11 % Total time : 1.588s
%------------------------------------------------------------------------------