%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM924+3 : 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 : n007.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 01:50:59 PM UTC 2026
% Result : Theorem 2.68s 0.91s
% Output : CNFRefutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 45 ( 45 unt; 0 def)
% Number of atoms : 45 ( 32 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 ( 4 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 7 con; 0-2 aty)
% Number of variables : 40 ( 2 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_182_Bit0__def,axiom,
! [X13] : bit0(X13) = hAPP_int_int(plus_plus_int(X13),X13),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_236_Bit1__def) ).
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/sandbox/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_339_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [X140,X141,X142] : hAPP_int_int(plus_plus_int(X140),hAPP_int_int(plus_plus_int(X141),X142)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X140),X141)),X142),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
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/sandbox/benchmark/theBenchmark.p',fact_134_zadd__commute) ).
fof(fact_133_zadd__left__commute,axiom,
! [X3,X4,X14] : hAPP_int_int(plus_plus_int(X3),hAPP_int_int(plus_plus_int(X4),X14)) = hAPP_int_int(plus_plus_int(X4),hAPP_int_int(plus_plus_int(X3),X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_zadd__left__commute) ).
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/sandbox/benchmark/theBenchmark.p',fact_35_zmult__commute) ).
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/sandbox/benchmark/theBenchmark.p',fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_3_t,axiom,
hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t),
file('/export/starexec/sandbox/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/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(fact_172_Pls__def,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_Pls__def) ).
fof(c_0_12,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(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_13,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)],[c_0_12]) ).
fof(c_0_14,plain,
! [X747] : bit0(X747) = hAPP_int_int(plus_plus_int(X747),X747),
inference(variable_rename,[status(thm)],[fact_182_Bit0__def]) ).
fof(c_0_15,plain,
! [X808] : bit1(X808) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X808)),X808),
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_nnf,[status(thm)],[c_0_13]) ).
cnf(c_0_17,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]) ).
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,
! [X1004,X1005,X1006] : hAPP_int_int(plus_plus_int(X1004),hAPP_int_int(plus_plus_int(X1005),X1006)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1004),X1005)),X1006),
inference(variable_rename,[status(thm)],[fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).
fof(c_0_21,plain,
! [X676,X677] : hAPP_int_int(plus_plus_int(X676),X677) = hAPP_int_int(plus_plus_int(X677),X676),
inference(variable_rename,[status(thm)],[fact_134_zadd__commute]) ).
fof(c_0_22,plain,
! [X673,X674,X675] : hAPP_int_int(plus_plus_int(X673),hAPP_int_int(plus_plus_int(X674),X675)) = hAPP_int_int(plus_plus_int(X674),hAPP_int_int(plus_plus_int(X673),X675)),
inference(variable_rename,[status(thm)],[fact_133_zadd__left__commute]) ).
fof(c_0_23,plain,
! [X494,X495] : hAPP_int_int(times_times_int(X494),X495) = hAPP_int_int(times_times_int(X495),X494),
inference(variable_rename,[status(thm)],[fact_35_zmult__commute]) ).
fof(c_0_24,plain,
! [X1064] : hAPP_int_int(times_times_int(X1064),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_25,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]) ).
cnf(c_0_26,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_27,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_17,c_0_18]),c_0_18]),c_0_19]),c_0_19]),c_0_19]),c_0_19]) ).
cnf(c_0_28,plain,
hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),X3),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,plain,
hAPP_int_int(plus_plus_int(X1),X2) = hAPP_int_int(plus_plus_int(X2),X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,plain,
hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3)) = hAPP_int_int(plus_plus_int(X2),hAPP_int_int(plus_plus_int(X1),X3)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,plain,
hAPP_int_int(times_times_int(X1),X2) = hAPP_int_int(times_times_int(X2),X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,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_33,plain,
hAPP_int_int(times_times_int(X1),zero_zero_int) = zero_zero_int,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_172_Pls__def]) ).
cnf(c_0_35,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_25,c_0_18]),c_0_19]),c_0_19]) ).
cnf(c_0_36,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_26,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_37,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(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_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)],[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_27,c_0_28]),c_0_29]),c_0_29]),c_0_29]),c_0_28]),c_0_30]),c_0_30]),c_0_30]),c_0_28]),c_0_29]),c_0_29]),c_0_29]),c_0_28]),c_0_30]),c_0_30]),c_0_30]),c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_31]),c_0_29]),c_0_31]) ).
cnf(c_0_38,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_32,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_39,plain,
hAPP_int_int(times_times_int(X1),pls) = pls,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_34]) ).
cnf(c_0_40,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)),pls)),
inference(rw,[status(thm)],[c_0_35,c_0_34]) ).
cnf(c_0_41,plain,
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(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_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)],[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_28]),c_0_29]),c_0_29]),c_0_29]),c_0_28]),c_0_30]),c_0_30]),c_0_30]),c_0_28]),c_0_29]),c_0_29]),c_0_29]),c_0_28]),c_0_30]),c_0_30]),c_0_30]),c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_31]),c_0_29]),c_0_31]),c_0_37]),c_0_29]),c_0_28]),c_0_29]),c_0_29]),c_0_29]),c_0_28]),c_0_30]),c_0_30]),c_0_30]) ).
cnf(c_0_42,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),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)],[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)],[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_38,c_0_28]),c_0_29]),c_0_29]),c_0_29]),c_0_28]),c_0_30]),c_0_30]),c_0_30]),c_0_28]),c_0_29]),c_0_29]),c_0_29]),c_0_28]),c_0_30]),c_0_30]),c_0_30]),c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_31]),c_0_29]),c_0_31]),c_0_37]),c_0_28]),c_0_29]),c_0_29]),c_0_29]),c_0_28]),c_0_30]),c_0_30]),c_0_30]),c_0_28]),c_0_29]),c_0_29]),c_0_29]),c_0_28]),c_0_30]),c_0_30]),c_0_30]),c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_31]),c_0_29]),c_0_34]),c_0_39]) ).
cnf(c_0_43,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),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)],[inference(rw,[status(thm)],[c_0_40,c_0_29]),c_0_28]),c_0_29]),c_0_29]),c_0_29]),c_0_28]),c_0_30]),c_0_30]),c_0_30]),c_0_41]) ).
cnf(c_0_44,plain,
$false,
inference(sr,[status(thm)],[c_0_42,c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM924+3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 03:14:35 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 2.68/0.91 % Version: 3.5.1
% 2.68/0.91 % Preprocessing class: FMLSSMSMSSSNFFN.
% 2.68/0.91 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.68/0.91 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 2.68/0.91 % Starting new_bool_3 with 600s (2) cores
% 2.68/0.91 % Starting new_bool_1 with 600s (2) cores
% 2.68/0.91 % Starting sh5l with 300s (1) cores
% 2.68/0.91 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 48184 completed with status 0
% 2.68/0.91 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 2.68/0.91 % Preprocessing class: FMLSSMSMSSSNFFN.
% 2.68/0.91 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.68/0.91 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 2.68/0.91 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.68/0.91 % No SInE strategy applied
% 2.68/0.91 % Search class: FGHSM-SMLM31-DFFFFFNN
% 2.68/0.91 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 2.68/0.91 % Starting SubtermCWHack with 82s (1) cores
% 2.68/0.91 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 91s (1) cores
% 2.68/0.91 % Starting SAT001_MinMin_p005000_rr_RG with 89s (1) cores
% 2.68/0.91 % SAT001_MinMin_p005000_rr_RG with pid 48212 completed with status 0
% 2.68/0.91 % Result found by SAT001_MinMin_p005000_rr_RG
% 2.68/0.91 % Preprocessing class: FMLSSMSMSSSNFFN.
% 2.68/0.91 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.68/0.91 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 2.68/0.91 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.68/0.91 % No SInE strategy applied
% 2.68/0.91 % Search class: FGHSM-SMLM31-DFFFFFNN
% 2.68/0.91 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 2.68/0.91 % Starting SubtermCWHack with 82s (1) cores
% 2.68/0.91 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 91s (1) cores
% 2.68/0.91 % Starting SAT001_MinMin_p005000_rr_RG with 89s (1) cores
% 2.68/0.91 % Preprocessing time : 0.030 s
% 2.68/0.91 % Presaturation interreduction done
% 2.68/0.91
% 2.68/0.91 % Proof found!
% 2.68/0.91 % SZS status Theorem
% 2.68/0.91 % SZS output start CNFRefutation
% See solution above
% 2.68/0.91 % Parsed axioms : 1230
% 2.68/0.91 % Removed by relevancy pruning/SinE : 0
% 2.68/0.91 % Initial clauses : 1824
% 2.68/0.91 % Removed in clause preprocessing : 95
% 2.68/0.91 % Initial clauses in saturation : 1729
% 2.68/0.91 % Processed clauses : 2004
% 2.68/0.91 % ...of these trivial : 122
% 2.68/0.91 % ...subsumed : 374
% 2.68/0.91 % ...remaining for further processing : 1507
% 2.68/0.91 % Other redundant clauses eliminated : 157
% 2.68/0.91 % Clauses deleted for lack of memory : 0
% 2.68/0.91 % Backward-subsumed : 6
% 2.68/0.91 % Backward-rewritten : 19
% 2.68/0.91 % Generated clauses : 331
% 2.68/0.91 % ...of the previous two non-redundant : 202
% 2.68/0.91 % ...aggressively subsumed : 0
% 2.68/0.91 % Contextual simplify-reflections : 4
% 2.68/0.91 % Paramodulations : 193
% 2.68/0.91 % Factorizations : 0
% 2.68/0.91 % NegExts : 0
% 2.68/0.91 % Equation resolutions : 159
% 2.68/0.91 % Disequality decompositions : 0
% 2.68/0.91 % Total rewrite steps : 4366
% 2.68/0.91 % ...of those cached : 4055
% 2.68/0.91 % Propositional unsat checks : 0
% 2.68/0.91 % Propositional check models : 0
% 2.68/0.91 % Propositional check unsatisfiable : 0
% 2.68/0.91 % Propositional clauses : 0
% 2.68/0.91 % Propositional clauses after purity: 0
% 2.68/0.91 % Propositional unsat core size : 0
% 2.68/0.91 % Propositional preprocessing time : 0.000
% 2.68/0.91 % Propositional encoding time : 0.000
% 2.68/0.91 % Propositional solver time : 0.000
% 2.68/0.91 % Success case prop preproc time : 0.000
% 2.68/0.91 % Success case prop encoding time : 0.000
% 2.68/0.91 % Success case prop solver time : 0.000
% 2.68/0.91 % Current number of processed clauses : 160
% 2.68/0.91 % Positive orientable unit clauses : 92
% 2.68/0.91 % Positive unorientable unit clauses: 0
% 2.68/0.91 % Negative unit clauses : 27
% 2.68/0.91 % Non-unit-clauses : 41
% 2.68/0.91 % Current number of unprocessed clauses: 1119
% 2.68/0.91 % ...number of literals in the above : 2911
% 2.68/0.91 % Current number of archived formulas : 0
% 2.68/0.91 % Current number of archived clauses : 1222
% 2.68/0.91 % Clause-clause subsumption calls (NU) : 148494
% 2.68/0.91 % Rec. Clause-clause subsumption calls : 60049
% 2.68/0.91 % Non-unit clause-clause subsumptions : 268
% 2.68/0.91 % Unit Clause-clause subsumption calls : 906
% 2.68/0.91 % Rewrite failures with RHS unbound : 0
% 2.68/0.91 % BW rewrite match attempts : 1698
% 2.68/0.91 % BW rewrite match successes : 182
% 2.68/0.91 % Condensation attempts : 0
% 2.68/0.91 % Condensation successes : 0
% 2.68/0.91 % Termbank termtop insertions : 215699
% 2.68/0.91 % Search garbage collected termcells : 19779
% 2.68/0.91
% 2.68/0.91 % -------------------------------------------------
% 2.68/0.91 % User time : 0.371 s
% 2.68/0.91 % System time : 0.027 s
% 2.68/0.91 % Total time : 0.398 s
% 2.68/0.91 % Maximum resident set size: 11340 pages
% 2.68/0.91
% 2.68/0.91 % -------------------------------------------------
% 2.68/0.91 % User time : 0.912 s
% 2.68/0.91 % System time : 0.091 s
% 2.68/0.91 % Total time : 1.003 s
% 2.68/0.91 % Maximum resident set size: 6912 pages
% 2.68/0.91 % E exiting
%------------------------------------------------------------------------------