%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM924_2 : 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 : n018.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 0.14s 5.58s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of formulae : 65 ( 65 unt; 0 typ; 0 def)
% Number of atoms : 65 ( 52 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 11 ( 11 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 67 !; 0 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
int: $tType ).
tff(decl_sort2,type,
nat: $tType ).
tff(decl_26,type,
one_one_int: int ).
tff(decl_29,type,
plus_plus_int: ( int * int ) > int ).
tff(decl_32,type,
times_times_int: ( int * int ) > int ).
tff(decl_35,type,
zero_zero_int: int ).
tff(decl_40,type,
bit0: int > int ).
tff(decl_41,type,
bit1: int > int ).
tff(decl_43,type,
pls: int ).
tff(decl_44,type,
number_number_of_int: int > int ).
tff(decl_45,type,
number_number_of_nat: int > nat ).
tff(decl_47,type,
ord_less_int: ( int * int ) > $o ).
tff(decl_53,type,
power_power_int: ( nat * int ) > int ).
tff(decl_62,type,
m: int ).
tff(decl_64,type,
s: int ).
tff(decl_65,type,
t: int ).
tff(decl_66,type,
esk1_0: int ).
tff(conj_0,conjecture,
ord_less_int(plus_plus_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) ).
tff(fact_438_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X500: int] : ( times_times_int(X500,X500) = power_power_int(X500,number_number_of_nat(bit0(bit1(pls)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_438_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
tff(fact_180_Bit0__def,axiom,
! [X20: int] : ( bit0(X20) = plus_plus_int(X20,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_Bit0__def) ).
tff(fact_234_Bit1__def,axiom,
! [X20: int] : ( bit1(X20) = plus_plus_int(plus_plus_int(one_one_int,X20),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_Bit1__def) ).
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_30__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_,axiom,
~ ! [X18: int] : ( plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) != times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_) ).
tff(fact_133_zero__is__num__zero,axiom,
zero_zero_int = number_number_of_int(pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_zero__is__num__zero) ).
tff(fact_181_zadd__0__right,axiom,
! [X21: int] : ( plus_plus_int(X21,zero_zero_int) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_zadd__0__right) ).
tff(fact_218_add__number__of__left,axiom,
! [X164: int,X165: int,X167: int] : ( plus_plus_int(number_number_of_int(X164),plus_plus_int(number_number_of_int(X165),X167)) = plus_plus_int(number_number_of_int(plus_plus_int(X164,X165)),X167) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_add__number__of__left) ).
tff(fact_3_t,axiom,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_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_132_zadd__commute,axiom,
! [X21: int,X19: int] : ( plus_plus_int(X21,X19) = plus_plus_int(X19,X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_zadd__commute) ).
tff(fact_94_zadd__zmult__distrib,axiom,
! [X29: int,X30: int,X19: int] : ( times_times_int(plus_plus_int(X29,X30),X19) = plus_plus_int(times_times_int(X29,X19),times_times_int(X30,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_zadd__zmult__distrib) ).
tff(fact_92_zmult__1,axiom,
! [X21: int] : ( times_times_int(one_one_int,X21) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_zmult__1) ).
tff(fact_35_zmult__commute,axiom,
! [X21: int,X19: int] : ( times_times_int(X21,X19) = times_times_int(X19,X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_zmult__commute) ).
tff(fact_131_zadd__left__commute,axiom,
! [X97: int,X98: int,X21: int] : ( plus_plus_int(X97,plus_plus_int(X98,X21)) = plus_plus_int(X98,plus_plus_int(X97,X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_zadd__left__commute) ).
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,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_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(fact_362_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [X377: int] : ( times_times_int(X377,zero_zero_int) = zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
tff(c_0_17,negated_conjecture,
~ ord_less_int(plus_plus_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]) ).
tff(c_0_18,plain,
! [X1576: int] : ( times_times_int(X1576,X1576) = power_power_int(X1576,number_number_of_nat(bit0(bit1(pls)))) ),
inference(variable_rename,[status(thm)],[fact_438_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J]) ).
tff(c_0_19,plain,
! [X1089: int] : ( bit0(X1089) = plus_plus_int(X1089,X1089) ),
inference(variable_rename,[status(thm)],[fact_180_Bit0__def]) ).
tff(c_0_20,plain,
! [X1150: int] : ( bit1(X1150) = plus_plus_int(plus_plus_int(one_one_int,X1150),X1150) ),
inference(variable_rename,[status(thm)],[fact_234_Bit1__def]) ).
tff(c_0_21,plain,
! [X838: int] : ( number_number_of_int(X838) = X838 ),
inference(variable_rename,[status(thm)],[fact_34_number__of__is__id]) ).
tff(c_0_22,negated_conjecture,
~ ord_less_int(plus_plus_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_17]) ).
tff(c_0_23,plain,
~ ! [X18: int] : ( plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) != times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),X18) ),
inference(fof_simplification,[status(thm)],[fact_30__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_]) ).
tcf(c_0_24,plain,
! [X3: int] : times_times_int(X3,X3) = power_power_int(X3,number_number_of_nat(bit0(bit1(pls)))),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
tcf(c_0_25,plain,
! [X3: int] : bit0(X3) = plus_plus_int(X3,X3),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
tcf(c_0_26,plain,
! [X3: int] : bit1(X3) = plus_plus_int(plus_plus_int(one_one_int,X3),X3),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
tcf(c_0_27,plain,
zero_zero_int = number_number_of_int(pls),
inference(split_conjunct,[status(thm)],[fact_133_zero__is__num__zero]) ).
tcf(c_0_28,plain,
! [X3: int] : number_number_of_int(X3) = X3,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
tff(c_0_29,plain,
! [X1090: int] : ( plus_plus_int(X1090,zero_zero_int) = X1090 ),
inference(variable_rename,[status(thm)],[fact_181_zadd__0__right]) ).
tff(c_0_30,plain,
! [X1126: int,X1127: int,X1128: int] : ( plus_plus_int(number_number_of_int(X1126),plus_plus_int(number_number_of_int(X1127),X1128)) = plus_plus_int(number_number_of_int(plus_plus_int(X1126,X1127)),X1128) ),
inference(variable_rename,[status(thm)],[fact_218_add__number__of__left]) ).
tff(c_0_31,negated_conjecture,
~ ord_less_int(plus_plus_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_22]) ).
tff(c_0_32,plain,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
tcf(c_0_33,plain,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_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_34,plain,
! [X3: int] : times_times_int(X3,X3) = power_power_int(X3,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_26]) ).
tcf(c_0_35,plain,
pls = zero_zero_int,
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
tcf(c_0_36,plain,
! [X3: int] : plus_plus_int(X3,zero_zero_int) = X3,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
tff(c_0_37,plain,
! [X1018: int,X1019: int] : ( plus_plus_int(X1018,X1019) = plus_plus_int(X1019,X1018) ),
inference(variable_rename,[status(thm)],[fact_132_zadd__commute]) ).
tcf(c_0_38,plain,
! [X3: int,X4: int,X7: int] : plus_plus_int(number_number_of_int(X3),plus_plus_int(number_number_of_int(X4),X7)) = plus_plus_int(number_number_of_int(plus_plus_int(X3,X4)),X7),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
tff(c_0_39,plain,
! [X940: int,X941: int,X942: int] : ( times_times_int(plus_plus_int(X940,X941),X942) = plus_plus_int(times_times_int(X940,X942),times_times_int(X941,X942)) ),
inference(variable_rename,[status(thm)],[fact_94_zadd__zmult__distrib]) ).
tff(c_0_40,plain,
! [X937: int] : ( times_times_int(one_one_int,X937) = X937 ),
inference(variable_rename,[status(thm)],[fact_92_zmult__1]) ).
tff(c_0_41,plain,
! [X839: int,X840: int] : ( times_times_int(X839,X840) = times_times_int(X840,X839) ),
inference(variable_rename,[status(thm)],[fact_35_zmult__commute]) ).
tff(c_0_42,plain,
! [X1015: int,X1016: int,X1017: int] : ( plus_plus_int(X1015,plus_plus_int(X1016,X1017)) = plus_plus_int(X1016,plus_plus_int(X1015,X1017)) ),
inference(variable_rename,[status(thm)],[fact_131_zadd__left__commute]) ).
tcf(c_0_43,negated_conjecture,
~ ord_less_int(plus_plus_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_31]) ).
tcf(c_0_44,plain,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
tcf(c_0_45,plain,
plus_plus_int(power_power_int(s,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(plus_plus_int(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)),plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_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_33,c_0_28]),c_0_25]),c_0_25]),c_0_25]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]) ).
tcf(c_0_46,plain,
! [X3: int] : power_power_int(X3,number_number_of_nat(plus_plus_int(one_one_int,one_one_int))) = times_times_int(X3,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_34,c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]) ).
tcf(c_0_47,plain,
! [X4: int,X3: int] : plus_plus_int(X3,X4) = plus_plus_int(X4,X3),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
tcf(c_0_48,plain,
! [X3: int,X4: int,X7: int] : plus_plus_int(X3,plus_plus_int(X4,X7)) = plus_plus_int(plus_plus_int(X3,X4),X7),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_28]),c_0_28]),c_0_28]) ).
tcf(c_0_49,plain,
! [X3: int,X4: int,X7: int] : times_times_int(plus_plus_int(X3,X4),X7) = plus_plus_int(times_times_int(X3,X7),times_times_int(X4,X7)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
tcf(c_0_50,plain,
! [X3: int] : times_times_int(one_one_int,X3) = X3,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
tcf(c_0_51,plain,
! [X4: int,X3: int] : times_times_int(X3,X4) = times_times_int(X4,X3),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
tcf(c_0_52,plain,
! [X3: int,X4: int,X7: int] : plus_plus_int(X3,plus_plus_int(X4,X7)) = plus_plus_int(X4,plus_plus_int(X3,X7)),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
tcf(c_0_53,plain,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_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]) ).
tff(c_0_54,plain,
! [X1403: int] : ( times_times_int(X1403,zero_zero_int) = zero_zero_int ),
inference(variable_rename,[status(thm)],[fact_362_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J]) ).
tcf(c_0_55,negated_conjecture,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_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_43,c_0_25]),c_0_26]),c_0_26]) ).
tcf(c_0_56,plain,
plus_plus_int(power_power_int(s,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(plus_plus_int(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)),plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls))),m),one_one_int),esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_28]),c_0_25]),c_0_25]),c_0_25]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]) ).
tcf(c_0_57,plain,
plus_plus_int(one_one_int,times_times_int(s,s)) = plus_plus_int(t,plus_plus_int(times_times_int(t,m),plus_plus_int(times_times_int(t,m),plus_plus_int(times_times_int(t,m),times_times_int(t,m))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_45,c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_46]),c_0_47]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_48]),c_0_49]),c_0_50]),c_0_49]),c_0_50]),c_0_49]),c_0_50]),c_0_50]),c_0_48]),c_0_48]),c_0_48]),c_0_49]),c_0_51]),c_0_49]),c_0_51]),c_0_49]),c_0_51]),c_0_49]),c_0_51]),c_0_50]),c_0_47]),c_0_52]),c_0_52]),c_0_52]) ).
tcf(c_0_58,plain,
ord_less_int(times_times_int(plus_plus_int(times_times_int(plus_plus_int(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)),plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(plus_plus_int(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)),plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_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_53,c_0_28]),c_0_28]),c_0_25]),c_0_25]),c_0_25]),c_0_25]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]) ).
tcf(c_0_59,plain,
! [X3: int] : times_times_int(X3,zero_zero_int) = zero_zero_int,
inference(split_conjunct,[status(thm)],[c_0_54]) ).
tcf(c_0_60,negated_conjecture,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(plus_plus_int(one_one_int,one_one_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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]) ).
tcf(c_0_61,plain,
plus_plus_int(t,plus_plus_int(times_times_int(t,m),plus_plus_int(times_times_int(t,m),plus_plus_int(times_times_int(t,m),times_times_int(t,m))))) = plus_plus_int(esk1_0,plus_plus_int(times_times_int(esk1_0,m),plus_plus_int(times_times_int(esk1_0,m),plus_plus_int(times_times_int(esk1_0,m),times_times_int(esk1_0,m))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_56,c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_46]),c_0_47]),c_0_57]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_48]),c_0_49]),c_0_50]),c_0_49]),c_0_50]),c_0_49]),c_0_50]),c_0_50]),c_0_48]),c_0_48]),c_0_48]),c_0_49]),c_0_51]),c_0_49]),c_0_51]),c_0_49]),c_0_51]),c_0_49]),c_0_51]),c_0_50]),c_0_47]),c_0_52]),c_0_52]),c_0_52]) ).
tcf(c_0_62,plain,
ord_less_int(plus_plus_int(t,plus_plus_int(times_times_int(t,m),plus_plus_int(times_times_int(t,m),plus_plus_int(times_times_int(t,m),times_times_int(t,m))))),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_58,c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_48]),c_0_49]),c_0_50]),c_0_49]),c_0_50]),c_0_49]),c_0_50]),c_0_50]),c_0_48]),c_0_48]),c_0_48]),c_0_49]),c_0_51]),c_0_49]),c_0_51]),c_0_49]),c_0_51]),c_0_49]),c_0_51]),c_0_50]),c_0_47]),c_0_52]),c_0_52]),c_0_52]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_35]),c_0_36]),c_0_48]),c_0_49]),c_0_50]),c_0_49]),c_0_50]),c_0_49]),c_0_50]),c_0_50]),c_0_48]),c_0_48]),c_0_48]),c_0_59]) ).
tcf(c_0_63,negated_conjecture,
~ ord_less_int(plus_plus_int(esk1_0,plus_plus_int(times_times_int(esk1_0,m),plus_plus_int(times_times_int(esk1_0,m),plus_plus_int(times_times_int(esk1_0,m),times_times_int(esk1_0,m))))),zero_zero_int),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_47]),c_0_46]),c_0_57]),c_0_61]) ).
cnf(c_0_64,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_61]),c_0_63]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM924_2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.38 % Computer : n018.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Mon Sep 21 03:19:03 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.58 % Version: 3.5.1
% 0.14/5.58 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/5.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.58 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/5.58 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.58 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.58 % Starting sh5l with 300s (1) cores
% 0.14/5.58 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 847705 completed with status 0
% 0.14/5.58 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.14/5.58 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/5.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.58 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/5.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/5.58 % No SInE strategy applied
% 0.14/5.58 % Search class: FGHSM-FSLM31-DFFFFFNN
% 0.14/5.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/5.58 % Starting SubtermCWHack with 136s (1) cores
% 0.14/5.58 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.14/5.58 % Starting C07_19_nc_SAT001_MinMin_p005000_rr with 354s (1) cores
% 0.14/5.58 % Starting U----_206c_10_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/5.58 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.14/5.58 % U----_206c_10_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 847715 completed with status 0
% 0.14/5.58 % Result found by U----_206c_10_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 0.14/5.58 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/5.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.58 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/5.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/5.58 % No SInE strategy applied
% 0.14/5.58 % Search class: FGHSM-FSLM31-DFFFFFNN
% 0.14/5.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/5.58 % Starting SubtermCWHack with 136s (1) cores
% 0.14/5.58 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.14/5.58 % Starting C07_19_nc_SAT001_MinMin_p005000_rr with 354s (1) cores
% 0.14/5.58 % Starting U----_206c_10_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/5.58 % Preprocessing time : 0.012 s
% 0.14/5.58 % Presaturation interreduction done
% 0.14/5.58
% 0.14/5.58 % Proof found!
% 0.14/5.58 % SZS status Theorem
% 0.14/5.58 % SZS output start CNFRefutation
% See solution above
% 0.14/5.58 % Parsed axioms : 745
% 0.14/5.58 % Removed by relevancy pruning/SinE : 0
% 0.14/5.58 % Initial clauses : 977
% 0.14/5.58 % Removed in clause preprocessing : 90
% 0.14/5.58 % Initial clauses in saturation : 887
% 0.14/5.58 % Processed clauses : 952
% 0.14/5.58 % ...of these trivial : 168
% 0.14/5.58 % ...subsumed : 136
% 0.14/5.58 % ...remaining for further processing : 647
% 0.14/5.58 % Other redundant clauses eliminated : 93
% 0.14/5.58 % Clauses deleted for lack of memory : 0
% 0.14/5.58 % Backward-subsumed : 2
% 0.14/5.58 % Backward-rewritten : 37
% 0.14/5.58 % Generated clauses : 75
% 0.14/5.58 % ...of the previous two non-redundant : 69
% 0.14/5.58 % ...aggressively subsumed : 0
% 0.14/5.58 % Contextual simplify-reflections : 2
% 0.14/5.58 % Paramodulations : 0
% 0.14/5.58 % Factorizations : 0
% 0.14/5.58 % NegExts : 0
% 0.14/5.58 % Equation resolutions : 93
% 0.14/5.58 % Disequality decompositions : 0
% 0.14/5.58 % Total rewrite steps : 3565
% 0.14/5.58 % ...of those cached : 3249
% 0.14/5.58 % Propositional unsat checks : 0
% 0.14/5.58 % Propositional check models : 0
% 0.14/5.58 % Propositional check unsatisfiable : 0
% 0.14/5.58 % Propositional clauses : 0
% 0.14/5.58 % Propositional clauses after purity: 0
% 0.14/5.58 % Propositional unsat core size : 0
% 0.14/5.58 % Propositional preprocessing time : 0.000
% 0.14/5.58 % Propositional encoding time : 0.000
% 0.14/5.58 % Propositional solver time : 0.000
% 0.14/5.58 % Success case prop preproc time : 0.000
% 0.14/5.58 % Success case prop encoding time : 0.000
% 0.14/5.58 % Success case prop solver time : 0.000
% 0.14/5.58 % Current number of processed clauses : 533
% 0.14/5.58 % Positive orientable unit clauses : 141
% 0.14/5.58 % Positive unorientable unit clauses: 21
% 0.14/5.58 % Negative unit clauses : 19
% 0.14/5.58 % Non-unit-clauses : 352
% 0.14/5.58 % Current number of unprocessed clauses: 4
% 0.14/5.58 % ...number of literals in the above : 4
% 0.14/5.58 % Current number of archived formulas : 0
% 0.14/5.58 % Current number of archived clauses : 42
% 0.14/5.58 % Clause-clause subsumption calls (NU) : 26249
% 0.14/5.58 % Rec. Clause-clause subsumption calls : 14375
% 0.14/5.58 % Non-unit clause-clause subsumptions : 100
% 0.14/5.58 % Unit Clause-clause subsumption calls : 1178
% 0.14/5.58 % Rewrite failures with RHS unbound : 0
% 0.14/5.58 % BW rewrite match attempts : 234
% 0.14/5.58 % BW rewrite match successes : 92
% 0.14/5.58 % Condensation attempts : 0
% 0.14/5.58 % Condensation successes : 0
% 0.14/5.58 % Termbank termtop insertions : 72545
% 0.14/5.58 % Search garbage collected termcells : 7742
% 0.14/5.58
% 0.14/5.58 % -------------------------------------------------
% 0.14/5.58 % User time : 0.095 s
% 0.14/5.58 % System time : 0.024 s
% 0.14/5.58 % Total time : 0.119 s
% 0.14/5.58 % Maximum resident set size: 7068 pages
% 0.14/5.58
% 0.14/5.58 % -------------------------------------------------
% 0.14/5.58 % User time : 0.370 s
% 0.14/5.58 % System time : 0.073 s
% 0.14/5.58 % Total time : 0.443 s
% 0.14/5.58 % Maximum resident set size: 5632 pages
% 0.14/5.58 % E exiting
%------------------------------------------------------------------------------