%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM924_40 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 01:51:00 PM UTC 2026
% Result : Unsatisfiable 0.18s 58.14s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 52 ( 52 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 43 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of types : 12 ( 11 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 20 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 40 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
int: $tType ).
tff(decl_sort2,type,
fun_int_int: $tType ).
tff(decl_sort3,type,
fun_int_bool: $tType ).
tff(decl_sort4,type,
fun_nat_nat: $tType ).
tff(decl_sort5,type,
nat: $tType ).
tff(decl_sort6,type,
fun_int_fun_int_bool: $tType ).
tff(decl_sort7,type,
bool: $tType ).
tff(decl_sort8,type,
fun_int_fun_int_int: $tType ).
tff(decl_sort9,type,
fun_int_nat: $tType ).
tff(decl_sort10,type,
fun_nat_int: $tType ).
tff(decl_sort11,type,
fun_int_fun_nat_int: $tType ).
tff(decl_292,type,
minus_minus_int: fun_int_fun_int_int ).
tff(decl_299,type,
one_one_int: int ).
tff(decl_300,type,
one_one_nat: nat ).
tff(decl_306,type,
plus_plus_int: fun_int_fun_int_int ).
tff(decl_317,type,
times_times_int: fun_int_fun_int_int ).
tff(decl_328,type,
zero_zero_int: int ).
tff(decl_329,type,
zero_zero_nat: nat ).
tff(decl_351,type,
bit0: fun_int_int ).
tff(decl_352,type,
bit1: fun_int_int ).
tff(decl_353,type,
min: int ).
tff(decl_354,type,
pls: int ).
tff(decl_363,type,
number_number_of_int: fun_int_int ).
tff(decl_364,type,
number_number_of_nat: fun_int_nat ).
tff(decl_374,type,
succ: fun_int_int ).
tff(decl_392,type,
suc: fun_nat_nat ).
tff(decl_424,type,
ord_less_int: fun_int_fun_int_bool ).
tff(decl_445,type,
power_power_int: fun_int_fun_nat_int ).
tff(decl_605,type,
hAPP_int_bool: ( int * fun_int_bool ) > bool ).
tff(decl_606,type,
hAPP_int_int: ( int * fun_int_int ) > int ).
tff(decl_607,type,
hAPP_int_nat: ( int * fun_int_nat ) > nat ).
tff(decl_612,type,
hAPP_i1948725293t_bool: ( int * fun_int_fun_int_bool ) > fun_int_bool ).
tff(decl_613,type,
hAPP_int_fun_int_int: ( int * fun_int_fun_int_int ) > fun_int_int ).
tff(decl_622,type,
hAPP_int_fun_nat_int: ( int * fun_int_fun_nat_int ) > fun_nat_int ).
tff(decl_647,type,
hAPP_nat_int: ( nat * fun_nat_int ) > int ).
tff(decl_648,type,
hAPP_nat_nat: ( nat * fun_nat_nat ) > nat ).
tff(decl_1083,type,
hBOOL: bool > $o ).
tff(decl_1091,type,
m: int ).
tff(decl_1093,type,
s: int ).
tff(decl_1094,type,
t: int ).
tff(fact_53_number__of__is__id,axiom,
! [X30: int] : ( hAPP_int_int(number_number_of_int,X30) = X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_number__of__is__id) ).
tff(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/sandbox2/benchmark/theBenchmark.p',fact_243_one__is__num__one) ).
tff(fact_256_Pls__def,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_Pls__def) ).
tff(fact_3196_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/sandbox2/benchmark/theBenchmark.p',fact_3196_semiring__norm_I115_J) ).
tff(fact_3057_One__nat__def,axiom,
one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3057_One__nat__def) ).
tff(fact_434_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X287: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X287),X287) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X287),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_434_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
tff(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/sandbox2/benchmark/theBenchmark.p',fact_3_t) ).
tff(fact_199_zadd__commute,axiom,
! [X31: int,X29: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X31),X29) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X29),X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_zadd__commute) ).
tff(fact_54_zmult__commute,axiom,
! [X31: int,X29: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X31),X29) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X29),X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_zmult__commute) ).
tff(fact_232_not__sum__squares__lt__zero,axiom,
! [X188: int,X189: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X188),X188)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X189),X189))),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_not__sum__squares__lt__zero) ).
tff(fact_590_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [X655: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X655),zero_zero_int) = zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_590_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
tff(fact_1502__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)) = 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/sandbox2/benchmark/theBenchmark.p',fact_1502__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
tff(fact_3296_diff__bin__simps_I2_J,axiom,
! [X30: int] : ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X30),min) = hAPP_int_int(succ,X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3296_diff__bin__simps_I2_J) ).
tff(fact_129_zmult__1,axiom,
! [X31: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),X31) = X31 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_zmult__1) ).
tff(fact_3294_succ__def,axiom,
! [X30: int] : ( hAPP_int_int(succ,X30) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X30),one_one_int) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3294_succ__def) ).
tff(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/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) ).
tff(c_0_16,plain,
! [X8022: int] : ( hAPP_int_int(number_number_of_int,X8022) = X8022 ),
inference(variable_rename,[status(thm)],[fact_53_number__of__is__id]) ).
tcf(c_0_17,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]) ).
tcf(c_0_18,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_256_Pls__def]) ).
tcf(c_0_19,plain,
! [X1: int] : hAPP_int_int(number_number_of_int,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
tcf(c_0_20,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_3196_semiring__norm_I115_J]) ).
tcf(c_0_21,plain,
hAPP_int_int(bit1,zero_zero_int) = one_one_int,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
tcf(c_0_22,plain,
one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
inference(split_conjunct,[status(thm)],[fact_3057_One__nat__def]) ).
tff(c_0_23,plain,
! [X8573: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X8573),X8573) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X8573),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]) ).
tcf(c_0_24,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]) ).
tcf(c_0_25,plain,
hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int)) = hAPP_nat_nat(suc,one_one_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_18]),c_0_21]),c_0_22]) ).
tff(c_0_26,plain,
! [X8298: int,X8299: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X8298),X8299) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X8299),X8298) ),
inference(variable_rename,[status(thm)],[fact_199_zadd__commute]) ).
tcf(c_0_27,plain,
! [X1: int] : 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_23]) ).
tff(c_0_28,plain,
! [X8023: int,X8024: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X8023),X8024) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X8024),X8023) ),
inference(variable_rename,[status(thm)],[fact_54_zmult__commute]) ).
tff(c_0_29,plain,
! [X188: int,X189: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X188),X188)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X189),X189))),zero_zero_int)),
inference(fof_simplification,[status(thm)],[fact_232_not__sum__squares__lt__zero]) ).
tff(c_0_30,plain,
! [X8989: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X8989),zero_zero_int) = zero_zero_int ),
inference(variable_rename,[status(thm)],[fact_590_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J]) ).
tcf(c_0_31,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)) = 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_1502__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096]) ).
tcf(c_0_32,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_nat_nat(suc,one_one_nat))),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(bit0,hAPP_int_int(bit0,one_one_int))),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_24,c_0_18]),c_0_21]),c_0_25]),c_0_18]),c_0_21]),c_0_19]) ).
tff(c_0_33,plain,
! [X15215: int] : ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X15215),min) = hAPP_int_int(succ,X15215) ),
inference(variable_rename,[status(thm)],[fact_3296_diff__bin__simps_I2_J]) ).
tcf(c_0_34,plain,
! [X2: int,X1: int] : 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_26]) ).
tcf(c_0_35,plain,
! [X1: int] : 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_nat_nat(suc,one_one_nat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_18]),c_0_21]),c_0_25]) ).
tcf(c_0_36,plain,
! [X2: int,X1: int] : 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_28]) ).
tff(c_0_37,plain,
! [X8360: int,X8361: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X8360),X8360)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X8361),X8361))),zero_zero_int)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_29])]) ).
tff(c_0_38,plain,
! [X8155: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),X8155) = X8155 ),
inference(variable_rename,[status(thm)],[fact_129_zmult__1]) ).
tff(c_0_39,plain,
! [X15214: int] : ( hAPP_int_int(succ,X15214) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X15214),one_one_int) ),
inference(variable_rename,[status(thm)],[fact_3294_succ__def]) ).
tcf(c_0_40,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]) ).
tcf(c_0_41,plain,
! [X1: int] : 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]) ).
tcf(c_0_42,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_nat_nat(suc,one_one_nat))),min) = 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(bit0,hAPP_int_int(bit0,one_one_int))),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)],[c_0_31,c_0_18]),c_0_21]),c_0_25]),c_0_19]),c_0_18]),c_0_21]),c_0_25]),c_0_32]) ).
tcf(c_0_43,plain,
! [X1: int] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),min) = hAPP_int_int(succ,X1),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
tcf(c_0_44,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_34]),c_0_34]),c_0_35]),c_0_36]),c_0_36]) ).
tcf(c_0_45,plain,
! [X1: int,X2: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X2),X2))),zero_zero_int)),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
tcf(c_0_46,plain,
! [X1: int] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
tcf(c_0_47,plain,
! [X1: int] : hAPP_int_int(succ,X1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
tcf(c_0_48,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(bit0,hAPP_int_int(bit0,one_one_int))),m)),one_one_int)),t)),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)],[c_0_40,c_0_18]),c_0_21]),c_0_19]),c_0_18]),c_0_21]),c_0_19]),c_0_41]) ).
tcf(c_0_49,plain,
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)) = hAPP_int_int(succ,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_36]),c_0_34]),c_0_36]),c_0_35]),c_0_43]),c_0_44]) ).
tcf(c_0_50,plain,
! [X1: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(succ,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X1))),zero_zero_int)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_51,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_34]),c_0_36]),c_0_36]),c_0_44]),c_0_49]),c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM924_40 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.58 % Computer : n016.cluster.edu
% 0.12/0.58 % Model : x86_64 x86_64
% 0.12/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.58 % Memory : 8046.5625MB
% 0.12/0.58 % OS : Linux 6.8.0-71-generic
% 0.12/0.58 % CPULimit : 300
% 0.12/0.58 % WCLimit : 300
% 0.12/0.58 % DateTime : Mon Sep 21 03:21:54 UTC 2026
% 0.12/0.59 % CPUTime :
% 0.12/0.59 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.63 Running first-order theorem proving
% 0.15/0.63 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.18/58.14 % Version: 3.5.1
% 0.18/58.14 % Preprocessing class: FMLLSMLLSSSNFFN.
% 0.18/58.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/58.14 % Starting new_bool_3 with 900s (3) cores
% 0.18/58.14 % Starting new_bool_1 with 900s (3) cores
% 0.18/58.14 % Starting sh5l with 300s (1) cores
% 0.18/58.14 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 0.18/58.14 % new_bool_1 with pid 1438787 completed with status 9
% 0.18/58.14 % new_bool_3 with pid 1438786 completed with status 9
% 0.18/58.14 % sh5l with pid 1438788 completed with status 9
% 0.18/58.14 % G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with pid 1438789 completed with status 0
% 0.18/58.14 % Result found by G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y
% 0.18/58.14 % Preprocessing class: FMLLSMLLSSSNFFN.
% 0.18/58.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/58.14 % Starting new_bool_3 with 900s (3) cores
% 0.18/58.14 % Starting new_bool_1 with 900s (3) cores
% 0.18/58.14 % Starting sh5l with 300s (1) cores
% 0.18/58.14 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 0.18/58.14 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/58.14 % No SInE strategy applied
% 0.18/58.14 % Search class: FGHSM-SMLM32-DFFFFFNN
% 0.18/58.14 % Scheduled 13 strats onto 1 cores with 299 seconds (299 total)
% 0.18/58.14 % Starting SubtermCWHack with 27s (1) cores
% 0.18/58.14 % SubtermCWHack with pid 1438829 completed with status 8
% 0.18/58.14 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 30s (1) cores
% 0.18/58.14 % G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with pid 1439104 completed with status 0
% 0.18/58.14 % Result found by G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y
% 0.18/58.14 % Preprocessing class: FMLLSMLLSSSNFFN.
% 0.18/58.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/58.14 % Starting new_bool_3 with 900s (3) cores
% 0.18/58.14 % Starting new_bool_1 with 900s (3) cores
% 0.18/58.14 % Starting sh5l with 300s (1) cores
% 0.18/58.14 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 0.18/58.14 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/58.14 % No SInE strategy applied
% 0.18/58.14 % Search class: FGHSM-SMLM32-DFFFFFNN
% 0.18/58.14 % Scheduled 13 strats onto 1 cores with 299 seconds (299 total)
% 0.18/58.14 % Starting SubtermCWHack with 27s (1) cores
% 0.18/58.14 % SubtermCWHack with pid 1438829 completed with status 8
% 0.18/58.14 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 30s (1) cores
% 0.18/58.14 % Preprocessing time : 0.248 s
% 0.18/58.14
% 0.18/58.14 % Proof found!
% 0.18/58.14 % SZS status Unsatisfiable
% 0.18/58.14 % SZS output start CNFRefutation
% See solution above
% 0.18/58.14 % Parsed axioms : 7016
% 0.18/58.14 % Removed by relevancy pruning/SinE : 0
% 0.18/58.14 % Initial clauses : 9485
% 0.18/58.14 % Removed in clause preprocessing : 1881
% 0.18/58.14 % Initial clauses in saturation : 7604
% 0.18/58.14 % Processed clauses : 11004
% 0.18/58.14 % ...of these trivial : 1041
% 0.18/58.14 % ...subsumed : 3208
% 0.18/58.14 % ...remaining for further processing : 6754
% 0.18/58.14 % Other redundant clauses eliminated : 1056
% 0.18/58.14 % Clauses deleted for lack of memory : 0
% 0.18/58.14 % Backward-subsumed : 109
% 0.18/58.14 % Backward-rewritten : 236
% 0.18/58.14 % Generated clauses : 476190
% 0.18/58.14 % ...of the previous two non-redundant : 454655
% 0.18/58.14 % ...aggressively subsumed : 0
% 0.18/58.14 % Contextual simplify-reflections : 51
% 0.18/58.14 % Paramodulations : 474744
% 0.18/58.14 % Factorizations : 141
% 0.18/58.14 % NegExts : 0
% 0.18/58.14 % Equation resolutions : 1305
% 0.18/58.14 % Disequality decompositions : 0
% 0.18/58.14 % Total rewrite steps : 109460
% 0.18/58.14 % ...of those cached : 93434
% 0.18/58.14 % Propositional unsat checks : 1
% 0.18/58.14 % Propositional check models : 0
% 0.18/58.14 % Propositional check unsatisfiable : 0
% 0.18/58.14 % Propositional clauses : 0
% 0.18/58.14 % Propositional clauses after purity: 0
% 0.18/58.14 % Propositional unsat core size : 0
% 0.18/58.14 % Propositional preprocessing time : 0.000
% 0.18/58.14 % Propositional encoding time : 0.611
% 0.18/58.14 % Propositional solver time : 0.265
% 0.18/58.14 % Success case prop preproc time : 0.000
% 0.18/58.14 % Success case prop encoding time : 0.000
% 0.18/58.14 % Success case prop solver time : 0.000
% 0.18/58.14 % Current number of processed clauses : 6341
% 0.18/58.14 % Positive orientable unit clauses : 1665
% 0.18/58.14 % Positive unorientable unit clauses: 129
% 0.18/58.14 % Negative unit clauses : 119
% 0.18/58.14 % Non-unit-clauses : 4428
% 0.18/58.14 % Current number of unprocessed clauses: 440332
% 0.18/58.14 % ...number of literals in the above : 1759374
% 0.18/58.14 % Current number of archived formulas : 0
% 0.18/58.14 % Current number of archived clauses : 364
% 0.18/58.14 % Clause-clause subsumption calls (NU) : 5091588
% 0.18/58.14 % Rec. Clause-clause subsumption calls : 1441720
% 0.18/58.14 % Non-unit clause-clause subsumptions : 1886
% 0.18/58.14 % Unit Clause-clause subsumption calls : 407360
% 0.18/58.14 % Rewrite failures with RHS unbound : 0
% 0.18/58.14 % BW rewrite match attempts : 16755
% 0.18/58.14 % BW rewrite match successes : 638
% 0.18/58.14 % Condensation attempts : 0
% 0.18/58.14 % Condensation successes : 0
% 0.18/58.14 % Termbank termtop insertions : 16647980
% 0.18/58.14 % Search garbage collected termcells : 82778
% 0.18/58.14
% 0.18/58.14 % -------------------------------------------------
% 0.18/58.14 % User time : 55.608 s
% 0.18/58.14 % System time : 1.352 s
% 0.18/58.14 % Total time : 56.960 s
% 0.18/58.14 % Maximum resident set size: 44300 pages
% 0.18/58.14
% 0.18/58.14 % -------------------------------------------------
% 0.18/58.14 % User time : 56.250 s
% 0.18/58.14 % System time : 1.555 s
% 0.18/58.14 % Total time : 57.805 s
% 0.18/58.14 % Maximum resident set size: 17664 pages
% 0.18/58.14 % E exiting
%------------------------------------------------------------------------------