%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM925+3 : TPTP v9.2.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:58:53 PM UTC 2026
% Result : Theorem 2.67s 2.23s
% Output : CNFRefutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 62 ( 55 unt; 0 def)
% Number of atoms : 75 ( 50 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 16 ~; 9 |; 1 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 7 con; 0-2 aty)
% Number of variables : 36 ( 3 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_809_succ__Bit0,axiom,
! [X22] : succ(bit0(X22)) = bit1(X22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_809_succ__Bit0) ).
fof(fact_103_Bit0__def,axiom,
! [X22] : bit0(X22) = plus_plus_int(X22,X22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_Bit0__def) ).
fof(fact_814_succ__def,axiom,
! [X22] : succ(X22) = plus_plus_int(X22,one_one_int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_814_succ__def) ).
fof(fact_97_Bit0__Pls,axiom,
bit0(pls) = pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_Bit0__Pls) ).
fof(fact_12_add__special_I2_J,axiom,
! [X7] : plus_plus_int(one_one_int,number_number_of_int(X7)) = number_number_of_int(plus_plus_int(bit1(pls),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_add__special_I2_J) ).
fof(conj_0,conjecture,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_767_nat__number__of__def,axiom,
! [X14] : number_number_of_nat(X14) = nat(number_number_of_int(X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_767_nat__number__of__def) ).
fof(fact_16_one__add__one__is__two,axiom,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_one__add__one__is__two) ).
fof(fact_98_Pls__def,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_Pls__def) ).
fof(fact_25_semiring__norm_I110_J,axiom,
one_one_int = number_number_of_int(bit1(pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_semiring__norm_I110_J) ).
fof(fact_19_semiring__one__add__one__is__two,axiom,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_semiring__one__add__one__is__two) ).
fof(fact_231_field__power__not__zero,axiom,
! [X65,X66] :
( is_int(X66)
=> ( X66 != zero_zero_int
=> hAPP_nat_int(power_power_int(X66),X65) != zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_field__power__not__zero) ).
fof(gsy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint,hypothesis,
! [X1,X2] :
( ( is_int(X1)
& is_int(X2) )
=> is_int(plus_plus_int(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint,hypothesis,
! [X1,X2] : is_int(hAPP_nat_int(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint) ).
fof(fact_79_bin__less__0__simps_I1_J,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_bin__less__0__simps_I1_J) ).
fof(gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint,hypothesis,
is_int(one_one_int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint) ).
fof(fact_0_n1pos,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).
fof(c_0_17,plain,
! [X4611] : succ(bit0(X4611)) = bit1(X4611),
inference(variable_rename,[status(thm)],[fact_809_succ__Bit0]) ).
fof(c_0_18,plain,
! [X3062] : bit0(X3062) = plus_plus_int(X3062,X3062),
inference(variable_rename,[status(thm)],[fact_103_Bit0__def]) ).
fof(c_0_19,plain,
! [X4619] : succ(X4619) = plus_plus_int(X4619,one_one_int),
inference(variable_rename,[status(thm)],[fact_814_succ__def]) ).
cnf(c_0_20,plain,
succ(bit0(X1)) = bit1(X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
bit0(X1) = plus_plus_int(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
succ(X1) = plus_plus_int(X1,one_one_int),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
bit0(pls) = pls,
inference(split_conjunct,[status(thm)],[fact_97_Bit0__Pls]) ).
fof(c_0_24,plain,
! [X2960] : plus_plus_int(one_one_int,number_number_of_int(X2960)) = number_number_of_int(plus_plus_int(bit1(pls),X2960)),
inference(variable_rename,[status(thm)],[fact_12_add__special_I2_J]) ).
fof(c_0_25,negated_conjecture,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(c_0_26,plain,
! [X4518] : number_number_of_nat(X4518) = nat(number_number_of_int(X4518)),
inference(variable_rename,[status(thm)],[fact_767_nat__number__of__def]) ).
cnf(c_0_27,plain,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))),
inference(split_conjunct,[status(thm)],[fact_16_one__add__one__is__two]) ).
cnf(c_0_28,plain,
plus_plus_int(plus_plus_int(X1,X1),one_one_int) = bit1(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_29,plain,
plus_plus_int(pls,pls) = pls,
inference(rw,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_30,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_98_Pls__def]) ).
cnf(c_0_31,plain,
plus_plus_int(one_one_int,number_number_of_int(X1)) = number_number_of_int(plus_plus_int(bit1(pls),X1)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(split_conjunct,[status(thm)],[fact_25_semiring__norm_I110_J]) ).
cnf(c_0_33,negated_conjecture,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,plain,
number_number_of_nat(X1) = nat(number_number_of_int(X1)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,plain,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(plus_plus_int(plus_plus_int(plus_plus_int(pls,pls),one_one_int),plus_plus_int(plus_plus_int(pls,pls),one_one_int))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_21]),c_0_28]),c_0_28]) ).
cnf(c_0_36,plain,
plus_plus_int(zero_zero_int,zero_zero_int) = zero_zero_int,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_30]),c_0_30]) ).
cnf(c_0_37,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
inference(split_conjunct,[status(thm)],[fact_19_semiring__one__add__one__is__two]) ).
cnf(c_0_38,plain,
plus_plus_int(one_one_int,number_number_of_int(X1)) = number_number_of_int(plus_plus_int(plus_plus_int(plus_plus_int(pls,pls),one_one_int),X1)),
inference(rw,[status(thm)],[c_0_31,c_0_28]) ).
cnf(c_0_39,plain,
one_one_int = number_number_of_int(plus_plus_int(plus_plus_int(pls,pls),one_one_int)),
inference(rw,[status(thm)],[c_0_32,c_0_28]) ).
cnf(c_0_40,negated_conjecture,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat(number_number_of_int(plus_plus_int(plus_plus_int(plus_plus_int(pls,pls),one_one_int),plus_plus_int(plus_plus_int(pls,pls),one_one_int))))) = zero_zero_int,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_21]),c_0_34]),c_0_28]),c_0_28]) ).
cnf(c_0_41,plain,
number_number_of_int(plus_plus_int(plus_plus_int(zero_zero_int,one_one_int),plus_plus_int(zero_zero_int,one_one_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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_30]),c_0_30]),c_0_36]),c_0_30]),c_0_30]),c_0_36]) ).
cnf(c_0_42,plain,
plus_plus_nat(one_one_nat,one_one_nat) = nat(number_number_of_int(plus_plus_int(plus_plus_int(plus_plus_int(pls,pls),one_one_int),plus_plus_int(plus_plus_int(pls,pls),one_one_int)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_21]),c_0_34]),c_0_28]),c_0_28]) ).
cnf(c_0_43,plain,
number_number_of_int(plus_plus_int(plus_plus_int(zero_zero_int,one_one_int),X1)) = plus_plus_int(one_one_int,number_number_of_int(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_30]),c_0_30]),c_0_36]) ).
cnf(c_0_44,plain,
number_number_of_int(plus_plus_int(zero_zero_int,one_one_int)) = one_one_int,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_30]),c_0_30]),c_0_36]) ).
fof(c_0_45,plain,
! [X3248,X3249] :
( ~ is_int(X3249)
| X3249 = zero_zero_int
| hAPP_nat_int(power_power_int(X3249),X3248) != zero_zero_int ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_231_field__power__not__zero])]) ).
cnf(c_0_46,negated_conjecture,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat(plus_plus_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)],[c_0_40,c_0_30]),c_0_30]),c_0_36]),c_0_30]),c_0_30]),c_0_36]),c_0_41]) ).
cnf(c_0_47,plain,
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_42,c_0_30]),c_0_30]),c_0_36]),c_0_30]),c_0_30]),c_0_36]),c_0_43]),c_0_44]) ).
cnf(c_0_48,plain,
( X1 = zero_zero_int
| ~ is_int(X1)
| hAPP_nat_int(power_power_int(X1),X2) != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_49,negated_conjecture,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),plus_plus_nat(one_one_nat,one_one_nat)) = zero_zero_int,
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
fof(c_0_50,hypothesis,
! [X2933,X2934] :
( ~ is_int(X2933)
| ~ is_int(X2934)
| is_int(plus_plus_int(X2933,X2934)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint])]) ).
fof(c_0_51,hypothesis,
! [X2950,X2951] : is_int(hAPP_nat_int(X2950,X2951)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint]) ).
fof(c_0_52,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)),
inference(fof_simplification,[status(thm)],[fact_79_bin__less__0__simps_I1_J]) ).
cnf(c_0_53,negated_conjecture,
( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,hypothesis,
( is_int(plus_plus_int(X1,X2))
| ~ is_int(X1)
| ~ is_int(X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_55,hypothesis,
is_int(hAPP_nat_int(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_56,hypothesis,
is_int(one_one_int),
inference(split_conjunct,[status(thm)],[gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint]) ).
cnf(c_0_57,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_58,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
inference(split_conjunct,[status(thm)],[fact_0_n1pos]) ).
cnf(c_0_59,negated_conjecture,
plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]),c_0_56])]) ).
cnf(c_0_60,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),zero_zero_int)),
inference(rw,[status(thm)],[c_0_57,c_0_30]) ).
cnf(c_0_61,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59]),c_0_60]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM925+3 : TPTP v9.2.1. Released v5.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.32 % Computer : n022.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 01:18:51 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.67/2.23 % Version : CSE_E---1.7
% 2.67/2.23 % Problem : theBenchmark.p
% 2.67/2.23 % SZS status Theorem for theBenchmark.p
% 2.67/2.23 % SZS output start CNFRefutation
% See solution above
% 2.67/2.23 % Total time : 1.588s
%------------------------------------------------------------------------------