%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM925+2 : 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 : n013.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 1.75s 1.94s
% Output : CNFRefutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 31 unt; 0 def)
% Number of atoms : 51 ( 38 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 27 ( 14 ~; 8 |; 3 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 8 con; 0-2 aty)
% Number of variables : 28 ( 2 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
hAPP_nat_int(power_power_int(hAPP_int_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_568_succ__Bit0,axiom,
! [X21] : succ(bit0(X21)) = bit1(X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_568_succ__Bit0) ).
fof(fact_103_Bit0__def,axiom,
! [X21] : bit0(X21) = hAPP_int_int(plus_plus_int(X21),X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_Bit0__def) ).
fof(fact_573_succ__def,axiom,
! [X21] : succ(X21) = hAPP_int_int(plus_plus_int(X21),one_one_int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_succ__def) ).
fof(fact_105_zadd__0,axiom,
! [X17] : hAPP_int_int(plus_plus_int(zero_zero_int),X17) = X17,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_zadd__0) ).
fof(fact_98_Pls__def,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_Pls__def) ).
fof(fact_19_semiring__one__add__one__is__two,axiom,
hAPP_nat_nat(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,
! [X64,X65] :
( X65 != zero_zero_int
=> hAPP_nat_int(power_power_int(X65),X64) != zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_field__power__not__zero) ).
fof(fact_447_zless__le,axiom,
! [X30,X25] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X30),X25))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X30),X25))
& X30 != X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_zless__le) ).
fof(fact_0_n1pos,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_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_10,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_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_11,plain,
! [X2558] : succ(bit0(X2558)) = bit1(X2558),
inference(variable_rename,[status(thm)],[fact_568_succ__Bit0]) ).
fof(c_0_12,plain,
! [X1673] : bit0(X1673) = hAPP_int_int(plus_plus_int(X1673),X1673),
inference(variable_rename,[status(thm)],[fact_103_Bit0__def]) ).
fof(c_0_13,plain,
! [X2566] : succ(X2566) = hAPP_int_int(plus_plus_int(X2566),one_one_int),
inference(variable_rename,[status(thm)],[fact_573_succ__def]) ).
fof(c_0_14,plain,
! [X1675] : hAPP_int_int(plus_plus_int(zero_zero_int),X1675) = X1675,
inference(variable_rename,[status(thm)],[fact_105_zadd__0]) ).
cnf(c_0_15,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_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_10]) ).
cnf(c_0_16,plain,
succ(bit0(X1)) = bit1(X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
bit0(X1) = hAPP_int_int(plus_plus_int(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
succ(X1) = hAPP_int_int(plus_plus_int(X1),one_one_int),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
hAPP_int_int(plus_plus_int(zero_zero_int),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_98_Pls__def]) ).
cnf(c_0_21,plain,
hAPP_nat_nat(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]) ).
fof(c_0_22,plain,
! [X1861,X1862] :
( X1862 = zero_zero_int
| hAPP_nat_int(power_power_int(X1862),X1861) != zero_zero_int ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_231_field__power__not__zero])]) ).
cnf(c_0_23,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)),hAPP_int_int(plus_plus_int(hAPP_int_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)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_17]),c_0_18]),c_0_18]) ).
cnf(c_0_24,plain,
hAPP_int_int(plus_plus_int(pls),X1) = X1,
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)),hAPP_int_int(plus_plus_int(hAPP_int_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)],[inference(rw,[status(thm)],[c_0_21,c_0_16]),c_0_17]),c_0_17]),c_0_18]),c_0_18]) ).
cnf(c_0_26,plain,
( X1 = zero_zero_int
| hAPP_nat_int(power_power_int(X1),X2) != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(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)],[c_0_23,c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_20]) ).
cnf(c_0_28,plain,
number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)) = hAPP_nat_nat(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_25,c_0_24]),c_0_24]),c_0_24]),c_0_24]) ).
fof(c_0_29,plain,
! [X2313,X2314] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2313),X2314))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2313),X2314)) )
& ( X2313 != X2314
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2313),X2314)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2313),X2314))
| X2313 = X2314
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2313),X2314)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_447_zless__le])])]) ).
cnf(c_0_30,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(split_conjunct,[status(thm)],[fact_0_n1pos]) ).
cnf(c_0_31,plain,
( X1 = pls
| hAPP_nat_int(power_power_int(X1),X2) != pls ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_20]),c_0_20]) ).
cnf(c_0_32,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)) = pls,
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
( X1 != X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(rw,[status(thm)],[c_0_30,c_0_20]) ).
cnf(c_0_35,negated_conjecture,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = pls,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1)),
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_37,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM925+2 : 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
% 0.14/0.33 % Computer : n013.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 01:17:41 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.75/1.94 % Version : CSE_E---1.7
% 1.75/1.94 % Problem : theBenchmark.p
% 1.75/1.94 % SZS status Theorem for theBenchmark.p
% 1.75/1.94 % SZS output start CNFRefutation
% See solution above
% 1.75/1.95 % Total time : 1.479s
%------------------------------------------------------------------------------