%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM924+6 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 : Theorem 1.29s 0.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of formulae : 65 ( 65 unt; 0 def)
% Number of atoms : 65 ( 52 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 : 10 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 63 ( 1 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_127_add__Pls__right,axiom,
! [X14] : plus_plus(int,X14,pls) = ti(int,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_add__Pls__right) ).
fof(fact_22_number__of__is__id,axiom,
! [X14] : number_number_of(int,X14) = ti(int,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_number__of__is__id) ).
fof(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/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(tsy_c_Int_OBit0_arg1,hypothesis,
! [X1] : bit0(ti(int,X1)) = bit0(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit0_arg1) ).
fof(fact_130_Bit0__def,axiom,
! [X14] : bit0(X14) = plus_plus(int,X14,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_Bit0__def) ).
fof(fact_67_plus__numeral__code_I9_J,axiom,
! [X12,X11] : plus_plus(int,number_number_of(int,X12),number_number_of(int,X11)) = number_number_of(int,plus_plus(int,X12,X11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_plus__numeral__code_I9_J) ).
fof(fact_96_zadd__commute,axiom,
! [X15,X11] : plus_plus(int,X15,X11) = plus_plus(int,X11,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_zadd__commute) ).
fof(fact_162_Bit1__def,axiom,
! [X14] : bit1(X14) = plus_plus(int,plus_plus(int,one_one(int),X14),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_Bit1__def) ).
fof(fact_128_add__Pls,axiom,
! [X14] : plus_plus(int,pls,X14) = ti(int,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_add__Pls) ).
fof(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/sandbox2/benchmark/theBenchmark.p',fact_3_t) ).
fof(fact_94_zadd__assoc,axiom,
! [X18,X19,X20] : plus_plus(int,plus_plus(int,X18,X19),X20) = plus_plus(int,X18,plus_plus(int,X19,X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_zadd__assoc) ).
fof(fact_95_zadd__left__commute,axiom,
! [X5,X6,X15] : plus_plus(int,X5,plus_plus(int,X6,X15)) = plus_plus(int,X6,plus_plus(int,X5,X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_zadd__left__commute) ).
fof(fact_23_zmult__commute,axiom,
! [X15,X11] : times_times(int,X15,X11) = times_times(int,X11,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_zmult__commute) ).
fof(fact_61_nat__1__add__1,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_nat__1__add__1) ).
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,
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/sandbox2/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
fof(fact_62_mult__Pls,axiom,
! [X11] : times_times(int,pls,X11) = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_mult__Pls) ).
fof(fact_120_Pls__def,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_Pls__def) ).
fof(c_0_17,plain,
! [X434] : plus_plus(int,X434,pls) = ti(int,X434),
inference(variable_rename,[status(thm)],[fact_127_add__Pls__right]) ).
fof(c_0_18,plain,
! [X231] : number_number_of(int,X231) = ti(int,X231),
inference(variable_rename,[status(thm)],[fact_22_number__of__is__id]) ).
fof(c_0_19,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]) ).
fof(c_0_20,hypothesis,
! [X162] : bit0(ti(int,X162)) = bit0(X162),
inference(variable_rename,[status(thm)],[tsy_c_Int_OBit0_arg1]) ).
fof(c_0_21,plain,
! [X438] : bit0(X438) = plus_plus(int,X438,X438),
inference(variable_rename,[status(thm)],[fact_130_Bit0__def]) ).
fof(c_0_22,plain,
! [X318,X319] : plus_plus(int,number_number_of(int,X318),number_number_of(int,X319)) = number_number_of(int,plus_plus(int,X318,X319)),
inference(variable_rename,[status(thm)],[fact_67_plus__numeral__code_I9_J]) ).
cnf(c_0_23,plain,
plus_plus(int,X1,pls) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
number_number_of(int,X1) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_25,plain,
! [X380,X381] : plus_plus(int,X380,X381) = plus_plus(int,X381,X380),
inference(variable_rename,[status(thm)],[fact_96_zadd__commute]) ).
fof(c_0_26,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_19]) ).
fof(c_0_27,plain,
! [X493] : bit1(X493) = plus_plus(int,plus_plus(int,one_one(int),X493),X493),
inference(variable_rename,[status(thm)],[fact_162_Bit1__def]) ).
fof(c_0_28,plain,
! [X435] : plus_plus(int,pls,X435) = ti(int,X435),
inference(variable_rename,[status(thm)],[fact_128_add__Pls]) ).
cnf(c_0_29,hypothesis,
bit0(ti(int,X1)) = bit0(X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,plain,
bit0(X1) = plus_plus(int,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,plain,
plus_plus(int,number_number_of(int,X1),number_number_of(int,X2)) = number_number_of(int,plus_plus(int,X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,plain,
number_number_of(int,X1) = plus_plus(int,X1,pls),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_33,plain,
plus_plus(int,X1,X2) = plus_plus(int,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_34,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_26]) ).
cnf(c_0_35,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]) ).
cnf(c_0_36,plain,
bit1(X1) = plus_plus(int,plus_plus(int,one_one(int),X1),X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,plain,
plus_plus(int,pls,X1) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_38,plain,
! [X374,X375,X376] : plus_plus(int,plus_plus(int,X374,X375),X376) = plus_plus(int,X374,plus_plus(int,X375,X376)),
inference(variable_rename,[status(thm)],[fact_94_zadd__assoc]) ).
fof(c_0_39,plain,
! [X377,X378,X379] : plus_plus(int,X377,plus_plus(int,X378,X379)) = plus_plus(int,X378,plus_plus(int,X377,X379)),
inference(variable_rename,[status(thm)],[fact_95_zadd__left__commute]) ).
cnf(c_0_40,hypothesis,
plus_plus(int,ti(int,X1),ti(int,X1)) = plus_plus(int,X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_30]) ).
cnf(c_0_41,plain,
plus_plus(int,plus_plus(int,X1,pls),plus_plus(int,X2,pls)) = plus_plus(int,pls,plus_plus(int,X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_32]),c_0_32]),c_0_33]) ).
fof(c_0_42,plain,
! [X232,X233] : times_times(int,X232,X233) = times_times(int,X233,X232),
inference(variable_rename,[status(thm)],[fact_23_zmult__commute]) ).
cnf(c_0_43,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
inference(split_conjunct,[status(thm)],[fact_61_nat__1__add__1]) ).
cnf(c_0_44,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_34]) ).
cnf(c_0_45,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]) ).
cnf(c_0_46,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,number_number_of(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)],[c_0_35,c_0_30]),c_0_30]),c_0_30]),c_0_36]),c_0_36]),c_0_36]),c_0_36]),c_0_36]),c_0_36]) ).
cnf(c_0_47,plain,
plus_plus(int,X1,pls) = plus_plus(int,pls,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_24]),c_0_32]) ).
cnf(c_0_48,plain,
plus_plus(int,plus_plus(int,X1,X2),X3) = plus_plus(int,X1,plus_plus(int,X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_49,plain,
plus_plus(int,X1,plus_plus(int,X2,X3)) = plus_plus(int,X2,plus_plus(int,X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_50,hypothesis,
plus_plus(int,pls,plus_plus(int,X1,X1)) = plus_plus(int,X1,X1),
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_24]),c_0_32]),c_0_24]),c_0_32]),c_0_41]) ).
cnf(c_0_51,plain,
times_times(int,X1,X2) = times_times(int,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_52,plain,
! [X311] : times_times(int,pls,X311) = pls,
inference(variable_rename,[status(thm)],[fact_62_mult__Pls]) ).
cnf(c_0_53,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = 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_43,c_0_30]),c_0_36]),c_0_36]) ).
cnf(c_0_54,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_44,c_0_30]),c_0_36]),c_0_36]) ).
cnf(c_0_55,plain,
pls = zero_zero(int),
inference(split_conjunct,[status(thm)],[fact_120_Pls__def]) ).
cnf(c_0_56,plain,
ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(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,number_number_of(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)],[c_0_45,c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_36]),c_0_36]),c_0_36]),c_0_36]),c_0_36]),c_0_36]),c_0_36]),c_0_36]) ).
cnf(c_0_57,plain,
times_times(int,t,plus_plus(int,one_one(int),times_times(int,m,plus_plus(int,one_one(int),plus_plus(int,one_one(int),plus_plus(int,one_one(int),one_one(int))))))) = plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_46,c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_48]),c_0_48]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_48]),c_0_48]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_48]),c_0_32]),c_0_48]),c_0_48]),c_0_48]),c_0_47]),c_0_49]),c_0_50]),c_0_51]),c_0_33]),c_0_51]),c_0_33]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_48]),c_0_48]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_50]),c_0_50]) ).
cnf(c_0_58,plain,
times_times(int,pls,X1) = pls,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_59,plain,
number_number_of(nat,plus_plus(int,plus_plus(int,pls,plus_plus(int,pls,one_one(int))),plus_plus(int,pls,plus_plus(int,pls,one_one(int))))) = plus_plus(nat,one_one(nat),one_one(nat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_47]),c_0_47]),c_0_47]),c_0_47]) ).
cnf(c_0_60,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)),pls),
inference(rw,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_61,plain,
ord_less(int,plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,plus_plus(int,one_one(int),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)],[inference(rw,[status(thm)],[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_47]),c_0_47]),c_0_47]),c_0_47]),c_0_48]),c_0_48]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_48]),c_0_48]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_48]),c_0_32]),c_0_48]),c_0_48]),c_0_48]),c_0_47]),c_0_49]),c_0_50]),c_0_51]),c_0_33]),c_0_51]),c_0_57]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_48]),c_0_48]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_48]),c_0_48]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_48]),c_0_32]),c_0_48]),c_0_48]),c_0_48]),c_0_47]),c_0_49]),c_0_50]),c_0_51]),c_0_33]),c_0_55]),c_0_51]),c_0_58]) ).
cnf(c_0_62,plain,
number_number_of(nat,plus_plus(int,one_one(int),one_one(int))) = plus_plus(nat,one_one(nat),one_one(nat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_48]),c_0_48]),c_0_49]),c_0_49]),c_0_50]),c_0_50]),c_0_50]),c_0_50]) ).
cnf(c_0_63,negated_conjecture,
~ ord_less(int,plus_plus(int,one_one(int),power_power(int,s,plus_plus(nat,one_one(nat),one_one(nat)))),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)],[c_0_60,c_0_33]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_59]) ).
cnf(c_0_64,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62]),c_0_63]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM924+6 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n005.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 21 03:17:03 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.40 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.44 Running first-order theorem proving
% 0.11/0.44 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
% 1.29/0.73 % Version: 3.5.1
% 1.29/0.73 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.29/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.29/0.73 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.29/0.73 % Starting new_bool_3 with 300s (1) cores
% 1.29/0.73 % Starting new_bool_1 with 300s (1) cores
% 1.29/0.73 % Starting sh5l with 300s (1) cores
% 1.29/0.73 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2426947 completed with status 0
% 1.29/0.73 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 1.29/0.73 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.29/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.29/0.73 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.29/0.73 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.29/0.73 % No SInE strategy applied
% 1.29/0.73 % Search class: FGHSM-FSLM32-DFFFFFNN
% 1.29/0.73 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 1.29/0.73 % Starting SubtermCWHack with 136s (1) cores
% 1.29/0.73 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.29/0.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 113s (1) cores
% 1.29/0.73 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 113s (1) cores
% 1.29/0.73 % Starting U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 1.29/0.73 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2426954 completed with status 0
% 1.29/0.73 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.29/0.73 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.29/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.29/0.73 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.29/0.73 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.29/0.73 % No SInE strategy applied
% 1.29/0.73 % Search class: FGHSM-FSLM32-DFFFFFNN
% 1.29/0.73 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 1.29/0.73 % Starting SubtermCWHack with 136s (1) cores
% 1.29/0.73 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.29/0.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 113s (1) cores
% 1.29/0.73 % Preprocessing time : 0.022 s
% 1.29/0.73 % Presaturation interreduction done
% 1.29/0.73
% 1.29/0.73 % Proof found!
% 1.29/0.73 % SZS status Theorem
% 1.29/0.73 % SZS output start CNFRefutation
% See solution above
% 1.29/0.74 % Parsed axioms : 650
% 1.29/0.74 % Removed by relevancy pruning/SinE : 0
% 1.29/0.74 % Initial clauses : 850
% 1.29/0.74 % Removed in clause preprocessing : 8
% 1.29/0.74 % Initial clauses in saturation : 842
% 1.29/0.74 % Processed clauses : 1083
% 1.29/0.74 % ...of these trivial : 9
% 1.29/0.74 % ...subsumed : 83
% 1.29/0.74 % ...remaining for further processing : 990
% 1.29/0.74 % Other redundant clauses eliminated : 24
% 1.29/0.74 % Clauses deleted for lack of memory : 0
% 1.29/0.74 % Backward-subsumed : 2
% 1.29/0.74 % Backward-rewritten : 97
% 1.29/0.74 % Generated clauses : 23
% 1.29/0.74 % ...of the previous two non-redundant : 114
% 1.29/0.74 % ...aggressively subsumed : 0
% 1.29/0.74 % Contextual simplify-reflections : 1
% 1.29/0.74 % Paramodulations : 2
% 1.29/0.74 % Factorizations : 0
% 1.29/0.74 % NegExts : 0
% 1.29/0.74 % Equation resolutions : 24
% 1.29/0.74 % Disequality decompositions : 0
% 1.29/0.74 % Total rewrite steps : 3359
% 1.29/0.74 % ...of those cached : 3215
% 1.29/0.74 % Propositional unsat checks : 0
% 1.29/0.74 % Propositional check models : 0
% 1.29/0.74 % Propositional check unsatisfiable : 0
% 1.29/0.74 % Propositional clauses : 0
% 1.29/0.74 % Propositional clauses after purity: 0
% 1.29/0.74 % Propositional unsat core size : 0
% 1.29/0.74 % Propositional preprocessing time : 0.000
% 1.29/0.74 % Propositional encoding time : 0.000
% 1.29/0.74 % Propositional solver time : 0.000
% 1.29/0.74 % Success case prop preproc time : 0.000
% 1.29/0.74 % Success case prop encoding time : 0.000
% 1.29/0.74 % Success case prop solver time : 0.000
% 1.29/0.74 % Current number of processed clauses : 128
% 1.29/0.74 % Positive orientable unit clauses : 113
% 1.29/0.74 % Positive unorientable unit clauses: 0
% 1.29/0.74 % Negative unit clauses : 13
% 1.29/0.74 % Non-unit-clauses : 2
% 1.29/0.74 % Current number of unprocessed clauses: 615
% 1.29/0.74 % ...number of literals in the above : 1526
% 1.29/0.74 % Current number of archived formulas : 0
% 1.29/0.74 % Current number of archived clauses : 843
% 1.29/0.74 % Clause-clause subsumption calls (NU) : 40651
% 1.29/0.74 % Rec. Clause-clause subsumption calls : 21018
% 1.29/0.74 % Non-unit clause-clause subsumptions : 75
% 1.29/0.74 % Unit Clause-clause subsumption calls : 1158
% 1.29/0.74 % Rewrite failures with RHS unbound : 0
% 1.29/0.74 % BW rewrite match attempts : 905
% 1.29/0.74 % BW rewrite match successes : 92
% 1.29/0.74 % Condensation attempts : 0
% 1.29/0.74 % Condensation successes : 0
% 1.29/0.74 % Termbank termtop insertions : 87693
% 1.29/0.74 % Search garbage collected termcells : 9643
% 1.29/0.74
% 1.29/0.74 % -------------------------------------------------
% 1.29/0.74 % User time : 0.207 s
% 1.29/0.74 % System time : 0.024 s
% 1.29/0.74 % Total time : 0.231 s
% 1.29/0.74 % Maximum resident set size: 6944 pages
% 1.29/0.74
% 1.29/0.74 % -------------------------------------------------
% 1.29/0.74 % User time : 0.781 s
% 1.29/0.74 % System time : 0.079 s
% 1.29/0.74 % Total time : 0.860 s
% 1.29/0.74 % Maximum resident set size: 5632 pages
% 1.29/0.74 % E exiting
%------------------------------------------------------------------------------