%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM925+4 : 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 : n017.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 04:58:54 PM UTC 2026
% Result : Theorem 3.14s 3.10s
% Output : CNFRefutation 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 26 unt; 0 def)
% Number of atoms : 41 ( 24 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 8 |; 1 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 13 con; 0-2 aty)
% Number of variables : 24 ( 3 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_1907_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X563] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X563),X563) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X563),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1907_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
fof(fact_151_Pls__def,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_Pls__def) ).
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_3105_int__Suc,axiom,
! [X16] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X16)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3105_int__Suc) ).
fof(fact_1130_no__zero__divisors,axiom,
! [X292,X293] :
( ( is_int(X292)
& is_int(X293) )
=> ( X293 != zero_zero_int
=> ( X292 != zero_zero_int
=> hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X293),X292) != zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1130_no__zero__divisors) ).
fof(fact_1856_order__less__irrefl,axiom,
! [X543] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X543),X543)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1856_order__less__irrefl) ).
fof(fact_0_n1pos,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_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_8,negated_conjecture,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_zero_int,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(c_0_9,plain,
! [X2171] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X2171),X2171) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X2171),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
inference(variable_rename,[status(thm)],[fact_1907_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J]) ).
cnf(c_0_10,negated_conjecture,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_zero_int,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_151_Pls__def]) ).
cnf(c_0_12,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X1) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,hypothesis,
! [X1843,X1844] : is_int(hAPP_nat_int(X1843,X1844)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint]) ).
fof(c_0_14,plain,
! [X2294] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X2294)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,X2294)),
inference(variable_rename,[status(thm)],[fact_3105_int__Suc]) ).
fof(c_0_15,plain,
! [X1912,X1913] :
( ~ is_int(X1912)
| ~ is_int(X1913)
| X1913 = zero_zero_int
| X1912 = zero_zero_int
| hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1913),X1912) != zero_zero_int ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1130_no__zero__divisors])]) ).
cnf(c_0_16,negated_conjecture,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int)))) = zero_zero_int,
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_17,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X1) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int)))),
inference(rw,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_18,hypothesis,
is_int(hAPP_nat_int(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X1)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_20,plain,
! [X543] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X543),X543)),
inference(fof_simplification,[status(thm)],[fact_1856_order__less__irrefl]) ).
cnf(c_0_21,plain,
( X2 = zero_zero_int
| X1 = zero_zero_int
| ~ is_int(X1)
| ~ is_int(X2)
| hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X2),X1) != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,negated_conjecture,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) = zero_zero_int,
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,hypothesis,
is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,X1))),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_24,plain,
! [X2634] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2634),X2634)),
inference(variable_rename,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_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_26,negated_conjecture,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_27,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM925+4 : 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
% 0.14/0.31 % Computer : n017.cluster.edu
% 0.14/0.31 % Model : x86_64 x86_64
% 0.14/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31 % Memory : 8042.1875MB
% 0.14/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.31 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 01:17:13 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 3.14/3.10 % Version : CSE_E---1.7
% 3.14/3.10 % Problem : theBenchmark.p
% 3.14/3.10 % SZS status Theorem for theBenchmark.p
% 3.14/3.10 % SZS output start CNFRefutation
% See solution above
% 3.14/3.11 % Total time : 2.606s
%------------------------------------------------------------------------------