%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM924_30 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 : Unsatisfiable 3.10s 1.54s
% Output : CNFRefutation 3.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 55 ( 51 unt; 0 typ; 0 def)
% Number of atoms : 80 ( 69 equ)
% Maximal formula atoms : 18 ( 1 avg)
% Number of connectives : 43 ( 18 ~; 17 |; 7 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 17 ( 3 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 65 !; 0 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
fun_int_bool: $tType ).
tff(decl_sort2,type,
fun_int_int: $tType ).
tff(decl_sort3,type,
fun_int_fun_int_bool: $tType ).
tff(decl_sort4,type,
int: $tType ).
tff(decl_sort5,type,
nat: $tType ).
tff(decl_sort6,type,
fun_nat_int: $tType ).
tff(decl_sort7,type,
bool: $tType ).
tff(decl_31,type,
one_one_int: int ).
tff(decl_34,type,
plus_plus_int: int > fun_int_int ).
tff(decl_37,type,
times_times_int: int > fun_int_int ).
tff(decl_40,type,
zero_zero_int: int ).
tff(decl_48,type,
bit0: int > int ).
tff(decl_49,type,
bit1: int > int ).
tff(decl_50,type,
min: int ).
tff(decl_51,type,
pls: int ).
tff(decl_52,type,
number_number_of_int: int > int ).
tff(decl_53,type,
number_number_of_nat: int > nat ).
tff(decl_55,type,
ord_less_int: fun_int_fun_int_bool ).
tff(decl_61,type,
power_power_int: int > fun_nat_int ).
tff(decl_80,type,
hAPP_int_bool: ( int * fun_int_bool ) > bool ).
tff(decl_81,type,
hAPP_int_int: ( int * fun_int_int ) > int ).
tff(decl_83,type,
hAPP_i1948725293t_bool: ( int * fun_int_fun_int_bool ) > fun_int_bool ).
tff(decl_85,type,
hAPP_nat_int: ( nat * fun_nat_int ) > int ).
tff(decl_92,type,
hBOOL: bool > $o ).
tff(decl_94,type,
m: int ).
tff(decl_96,type,
s: int ).
tff(decl_97,type,
t: int ).
tff(fact_34_number__of__is__id,axiom,
! [X20: int] : ( number_number_of_int(X20) = X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_number__of__is__id) ).
tff(fact_285_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X204: int] : ( hAPP_int_int(times_times_int(X204),X204) = hAPP_nat_int(power_power_int(X204),number_number_of_nat(bit0(bit1(pls)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
tff(fact_182_Bit0__def,axiom,
! [X20: int] : ( bit0(X20) = hAPP_int_int(plus_plus_int(X20),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_Bit0__def) ).
tff(fact_236_Bit1__def,axiom,
! [X20: int] : ( bit1(X20) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X20)),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_Bit1__def) ).
tff(fact_183_zadd__0__right,axiom,
! [X21: int] : ( hAPP_int_int(plus_plus_int(X21),zero_zero_int) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_zadd__0__right) ).
tff(fact_135_zero__is__num__zero,axiom,
zero_zero_int = number_number_of_int(pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_zero__is__num__zero) ).
tff(fact_220_add__number__of__left,axiom,
! [X167: int,X168: int,X170: int] : ( hAPP_int_int(plus_plus_int(number_number_of_int(X167)),hAPP_int_int(plus_plus_int(number_number_of_int(X168)),X170)) = hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X167),X168))),X170) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_add__number__of__left) ).
tff(fact_155_not__sum__squares__lt__zero,axiom,
! [X132: int,X133: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X132),X132)),hAPP_int_int(times_times_int(X133),X133))),zero_zero_int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_not__sum__squares__lt__zero) ).
tff(fact_480_zmult__eq__1__iff,axiom,
! [X139: int,X138: int] :
( ( hAPP_int_int(times_times_int(X139),X138) = one_one_int )
<=> ( ( ( X138 = number_number_of_int(min) )
& ( X139 = number_number_of_int(min) ) )
| ( ( X138 = one_one_int )
& ( X139 = one_one_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_480_zmult__eq__1__iff) ).
tff(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) ).
tff(fact_134_zadd__commute,axiom,
! [X21: int,X19: int] : ( hAPP_int_int(plus_plus_int(X21),X19) = hAPP_int_int(plus_plus_int(X19),X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_zadd__commute) ).
tff(fact_35_zmult__commute,axiom,
! [X21: int,X19: int] : ( hAPP_int_int(times_times_int(X21),X19) = hAPP_int_int(times_times_int(X19),X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_zmult__commute) ).
tff(fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [X383: int] : ( hAPP_int_int(times_times_int(X383),zero_zero_int) = zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
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(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) ).
tff(c_0_14,plain,
! [X1767: int] : ( number_number_of_int(X1767) = X1767 ),
inference(variable_rename,[status(thm)],[fact_34_number__of__is__id]) ).
tff(c_0_15,plain,
! [X2129: int] : ( hAPP_int_int(times_times_int(X2129),X2129) = hAPP_nat_int(power_power_int(X2129),number_number_of_nat(bit0(bit1(pls)))) ),
inference(variable_rename,[status(thm)],[fact_285_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J]) ).
tff(c_0_16,plain,
! [X2021: int] : ( bit0(X2021) = hAPP_int_int(plus_plus_int(X2021),X2021) ),
inference(variable_rename,[status(thm)],[fact_182_Bit0__def]) ).
tff(c_0_17,plain,
! [X2082: int] : ( bit1(X2082) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X2082)),X2082) ),
inference(variable_rename,[status(thm)],[fact_236_Bit1__def]) ).
tff(c_0_18,plain,
! [X2022: int] : ( hAPP_int_int(plus_plus_int(X2022),zero_zero_int) = X2022 ),
inference(variable_rename,[status(thm)],[fact_183_zadd__0__right]) ).
tcf(c_0_19,plain,
zero_zero_int = number_number_of_int(pls),
inference(split_conjunct,[status(thm)],[fact_135_zero__is__num__zero]) ).
tcf(c_0_20,plain,
! [X3: int] : number_number_of_int(X3) = X3,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
tcf(c_0_21,plain,
! [X3: int] : hAPP_int_int(times_times_int(X3),X3) = hAPP_nat_int(power_power_int(X3),number_number_of_nat(bit0(bit1(pls)))),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
tcf(c_0_22,plain,
! [X3: int] : bit0(X3) = hAPP_int_int(plus_plus_int(X3),X3),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
tcf(c_0_23,plain,
! [X3: int] : bit1(X3) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X3)),X3),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
tcf(c_0_24,plain,
! [X3: int] : hAPP_int_int(plus_plus_int(X3),zero_zero_int) = X3,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
tcf(c_0_25,plain,
pls = zero_zero_int,
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
tff(c_0_26,plain,
! [X2058: int,X2059: int,X2060: int] : ( hAPP_int_int(plus_plus_int(number_number_of_int(X2058)),hAPP_int_int(plus_plus_int(number_number_of_int(X2059)),X2060)) = hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X2058),X2059))),X2060) ),
inference(variable_rename,[status(thm)],[fact_220_add__number__of__left]) ).
tff(c_0_27,plain,
! [X132: int,X133: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X132),X132)),hAPP_int_int(times_times_int(X133),X133))),zero_zero_int)),
inference(fof_simplification,[status(thm)],[fact_155_not__sum__squares__lt__zero]) ).
tff(c_0_28,plain,
! [X2555: int,X2556: int] :
( ( ( hAPP_int_int(times_times_int(X2555),X2556) = one_one_int )
| ( X2556 != number_number_of_int(min) )
| ( X2555 != number_number_of_int(min) ) )
& ( ( hAPP_int_int(times_times_int(X2555),X2556) = one_one_int )
| ( X2556 != one_one_int )
| ( X2555 != one_one_int ) )
& ( ( hAPP_int_int(times_times_int(X2555),X2556) != one_one_int )
| ( X2556 = one_one_int )
| ( X2556 = number_number_of_int(min) ) )
& ( ( hAPP_int_int(times_times_int(X2555),X2556) != one_one_int )
| ( X2556 = one_one_int )
| ( X2555 = number_number_of_int(min) ) )
& ( ( hAPP_int_int(times_times_int(X2555),X2556) != one_one_int )
| ( X2555 = one_one_int )
| ( X2556 = number_number_of_int(min) ) )
& ( ( hAPP_int_int(times_times_int(X2555),X2556) != one_one_int )
| ( X2555 = one_one_int )
| ( X2555 = number_number_of_int(min) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_480_zmult__eq__1__iff])])])]) ).
tcf(c_0_29,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]) ).
tcf(c_0_30,plain,
! [X3: int] : hAPP_int_int(times_times_int(X3),X3) = hAPP_nat_int(power_power_int(X3),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_21,c_0_22]),c_0_23]),c_0_23]) ).
tcf(c_0_31,plain,
! [X3: int] : hAPP_int_int(plus_plus_int(X3),pls) = X3,
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
tff(c_0_32,plain,
! [X1950: int,X1951: int] : ( hAPP_int_int(plus_plus_int(X1950),X1951) = hAPP_int_int(plus_plus_int(X1951),X1950) ),
inference(variable_rename,[status(thm)],[fact_134_zadd__commute]) ).
tcf(c_0_33,plain,
! [X3: int,X4: int,X7: int] : hAPP_int_int(plus_plus_int(number_number_of_int(X3)),hAPP_int_int(plus_plus_int(number_number_of_int(X4)),X7)) = hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X3),X4))),X7),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
tff(c_0_34,plain,
! [X1768: int,X1769: int] : ( hAPP_int_int(times_times_int(X1768),X1769) = hAPP_int_int(times_times_int(X1769),X1768) ),
inference(variable_rename,[status(thm)],[fact_35_zmult__commute]) ).
tff(c_0_35,plain,
! [X2338: int] : ( hAPP_int_int(times_times_int(X2338),zero_zero_int) = zero_zero_int ),
inference(variable_rename,[status(thm)],[fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J]) ).
tff(c_0_36,plain,
! [X1989: int,X1990: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X1989),X1989)),hAPP_int_int(times_times_int(X1990),X1990))),zero_zero_int)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_27])]) ).
tcf(c_0_37,plain,
! [X3: int,X4: int] :
( ( X4 != number_number_of_int(min) )
| ( X3 != number_number_of_int(min) )
| ( hAPP_int_int(times_times_int(X3),X4) = one_one_int ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
tcf(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(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]) ).
tcf(c_0_39,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(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)],[inference(rw,[status(thm)],[c_0_29,c_0_20]),c_0_22]),c_0_22]),c_0_22]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]) ).
tcf(c_0_40,plain,
! [X3: int] : hAPP_int_int(times_times_int(X3),X3) = hAPP_nat_int(power_power_int(X3),number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),one_one_int))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_31]),c_0_31]),c_0_31]) ).
tcf(c_0_41,plain,
! [X4: int,X3: int] : hAPP_int_int(plus_plus_int(X3),X4) = hAPP_int_int(plus_plus_int(X4),X3),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
tcf(c_0_42,plain,
! [X3: int,X4: int,X7: int] : hAPP_int_int(plus_plus_int(X3),hAPP_int_int(plus_plus_int(X4),X7)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X3),X4)),X7),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_20]),c_0_20]),c_0_20]) ).
tcf(c_0_43,plain,
! [X4: int,X3: int] : hAPP_int_int(times_times_int(X3),X4) = hAPP_int_int(times_times_int(X4),X3),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
tcf(c_0_44,plain,
! [X3: int] : hAPP_int_int(times_times_int(X3),zero_zero_int) = zero_zero_int,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
tcf(c_0_45,plain,
! [X3: int,X4: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X3)),hAPP_int_int(times_times_int(X4),X4))),zero_zero_int)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
tcf(c_0_46,plain,
! [X4: int,X3: int] :
( ( X3 != min )
| ( X4 != min )
| ( hAPP_int_int(times_times_int(X3),X4) = one_one_int ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_20]),c_0_20]) ).
tcf(c_0_47,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(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(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_20]),c_0_20]),c_0_22]),c_0_22]),c_0_22]),c_0_22]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]) ).
tcf(c_0_48,plain,
hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),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)))))) = 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)],[c_0_39,c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_40]),c_0_41]),c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_42]),c_0_43]),c_0_41]),c_0_43]) ).
tcf(c_0_49,plain,
! [X3: int] : hAPP_int_int(times_times_int(X3),pls) = pls,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_25]),c_0_25]) ).
tcf(c_0_50,plain,
! [X3: int,X4: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X3),X3)),hAPP_int_int(times_times_int(X4),X4))),pls)),
inference(rw,[status(thm)],[c_0_45,c_0_25]) ).
tcf(c_0_51,plain,
hAPP_int_int(times_times_int(min),min) = one_one_int,
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_46])]) ).
tcf(c_0_52,plain,
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))),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)],[c_0_47,c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_42]),c_0_43]),c_0_41]),c_0_43]),c_0_48]),c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_42]),c_0_43]),c_0_41]),c_0_25]),c_0_49]) ).
tcf(c_0_53,plain,
! [X3: int] : ~ 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(X3),X3))),pls)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_41]) ).
cnf(c_0_54,plain,
$false,
inference(sr,[status(thm)],[c_0_52,c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM924_30 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n020.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 03:17:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 3.10/1.54 % Version: 3.5.1
% 3.10/1.54 % Preprocessing class: FMLSSMSMSSSNFFN.
% 3.10/1.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.10/1.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 3.10/1.54 % Starting new_bool_3 with 600s (2) cores
% 3.10/1.54 % Starting new_bool_1 with 600s (2) cores
% 3.10/1.54 % Starting sh5l with 300s (1) cores
% 3.10/1.54 % new_bool_3 with pid 1886866 completed with status 9
% 3.10/1.54 % new_bool_1 with pid 1886867 completed with status 9
% 3.10/1.54 % sh5l with pid 1886868 completed with status 9
% 3.10/1.54 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 1886865 completed with status 0
% 3.10/1.54 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 3.10/1.54 % Preprocessing class: FMLSSMSMSSSNFFN.
% 3.10/1.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.10/1.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 3.10/1.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.10/1.54 % No SInE strategy applied
% 3.10/1.54 % Search class: FGHSM-SSLM31-DFFFFFNN
% 3.10/1.54 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 3.10/1.54 % Starting SubtermCWHack with 82s (1) cores
% 3.10/1.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 91s (1) cores
% 3.10/1.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S2S with 82s (1) cores
% 3.10/1.54 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S2S with pid 1886962 completed with status 0
% 3.10/1.54 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S2S
% 3.10/1.54 % Preprocessing class: FMLSSMSMSSSNFFN.
% 3.10/1.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.10/1.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 3.10/1.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.10/1.54 % No SInE strategy applied
% 3.10/1.54 % Search class: FGHSM-SSLM31-DFFFFFNN
% 3.10/1.54 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 3.10/1.54 % Starting SubtermCWHack with 82s (1) cores
% 3.10/1.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 91s (1) cores
% 3.10/1.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S2S with 82s (1) cores
% 3.10/1.54 % Preprocessing time : 0.032 s
% 3.10/1.54 % Presaturation interreduction done
% 3.10/1.54
% 3.10/1.54 % Proof found!
% 3.10/1.54 % SZS status Unsatisfiable
% 3.10/1.54 % SZS output start CNFRefutation
% See solution above
% 3.10/1.54 % Parsed axioms : 1298
% 3.10/1.54 % Removed by relevancy pruning/SinE : 0
% 3.10/1.54 % Initial clauses : 1824
% 3.10/1.54 % Removed in clause preprocessing : 208
% 3.10/1.54 % Initial clauses in saturation : 1616
% 3.10/1.54 % Processed clauses : 3911
% 3.10/1.54 % ...of these trivial : 216
% 3.10/1.54 % ...subsumed : 1188
% 3.10/1.54 % ...remaining for further processing : 2507
% 3.10/1.54 % Other redundant clauses eliminated : 235
% 3.10/1.54 % Clauses deleted for lack of memory : 0
% 3.10/1.54 % Backward-subsumed : 13
% 3.10/1.54 % Backward-rewritten : 17
% 3.10/1.54 % Generated clauses : 22387
% 3.10/1.54 % ...of the previous two non-redundant : 19540
% 3.10/1.54 % ...aggressively subsumed : 0
% 3.10/1.54 % Contextual simplify-reflections : 3
% 3.10/1.54 % Paramodulations : 22139
% 3.10/1.54 % Factorizations : 14
% 3.10/1.54 % NegExts : 0
% 3.10/1.54 % Equation resolutions : 254
% 3.10/1.54 % Disequality decompositions : 0
% 3.10/1.54 % Total rewrite steps : 12253
% 3.10/1.54 % ...of those cached : 10079
% 3.10/1.54 % Propositional unsat checks : 0
% 3.10/1.54 % Propositional check models : 0
% 3.10/1.54 % Propositional check unsatisfiable : 0
% 3.10/1.54 % Propositional clauses : 0
% 3.10/1.54 % Propositional clauses after purity: 0
% 3.10/1.54 % Propositional unsat core size : 0
% 3.10/1.54 % Propositional preprocessing time : 0.000
% 3.10/1.54 % Propositional encoding time : 0.000
% 3.10/1.54 % Propositional solver time : 0.000
% 3.10/1.54 % Success case prop preproc time : 0.000
% 3.10/1.54 % Success case prop encoding time : 0.000
% 3.10/1.54 % Success case prop solver time : 0.000
% 3.10/1.54 % Current number of processed clauses : 1297
% 3.10/1.54 % Positive orientable unit clauses : 294
% 3.10/1.54 % Positive unorientable unit clauses: 46
% 3.10/1.54 % Negative unit clauses : 115
% 3.10/1.54 % Non-unit-clauses : 842
% 3.10/1.54 % Current number of unprocessed clauses: 18269
% 3.10/1.54 % ...number of literals in the above : 42321
% 3.10/1.54 % Current number of archived formulas : 0
% 3.10/1.54 % Current number of archived clauses : 1085
% 3.10/1.54 % Clause-clause subsumption calls (NU) : 226559
% 3.10/1.54 % Rec. Clause-clause subsumption calls : 105231
% 3.10/1.54 % Non-unit clause-clause subsumptions : 442
% 3.10/1.54 % Unit Clause-clause subsumption calls : 27895
% 3.10/1.54 % Rewrite failures with RHS unbound : 0
% 3.10/1.54 % BW rewrite match attempts : 4224
% 3.10/1.54 % BW rewrite match successes : 262
% 3.10/1.54 % Condensation attempts : 0
% 3.10/1.54 % Condensation successes : 0
% 3.10/1.54 % Termbank termtop insertions : 738124
% 3.10/1.54 % Search garbage collected termcells : 18914
% 3.10/1.54
% 3.10/1.54 % -------------------------------------------------
% 3.10/1.54 % User time : 0.996 s
% 3.10/1.54 % System time : 0.051 s
% 3.10/1.54 % Total time : 1.047 s
% 3.10/1.54 % Maximum resident set size: 11968 pages
% 3.10/1.54
% 3.10/1.54 % -------------------------------------------------
% 3.10/1.54 % User time : 2.858 s
% 3.10/1.54 % System time : 0.232 s
% 3.10/1.54 % Total time : 3.090 s
% 3.10/1.54 % Maximum resident set size: 7424 pages
% 3.10/1.54 % E exiting
%------------------------------------------------------------------------------