%------------------------------------------------------------------------------
% File : SPASS+T---2.2.22
% Problem : NUM925_1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : spasst-tptp-script %s %d
% Computer : n026.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 : 600s
% DateTime : Mon Jul 18 14:39:32 EDT 2022
% Result : Theorem 1.00s 1.33s
% Output : Refutation 1.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 26 ( 13 unt; 0 nHn; 26 RR)
% Number of literals : 50 ( 0 equ; 32 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
nat(n),
file('NUM925_1.p',unknown),
[] ).
cnf(7,axiom,
int(one_one_int),
file('NUM925_1.p',unknown),
[] ).
cnf(10,axiom,
equal(zero_zero_int,pls),
file('NUM925_1.p',unknown),
[] ).
cnf(21,axiom,
~ ord_less_int(pls,pls),
file('NUM925_1.p',unknown),
[] ).
cnf(32,axiom,
ord_less_int(zero_zero_int,plus_plus_int(one_one_int,semiri1621563631at_int(n))),
file('NUM925_1.p',unknown),
[] ).
cnf(34,axiom,
( ~ nat(U)
| int(semiri1621563631at_int(U)) ),
file('NUM925_1.p',unknown),
[] ).
cnf(47,axiom,
equal(number_number_of_nat(bit0(bit1(pls))),plus_plus_nat(one_one_nat,one_one_nat)),
file('NUM925_1.p',unknown),
[] ).
cnf(62,axiom,
( ~ int(U)
| ~ int(V)
| int(plus_plus_int(U,V)) ),
file('NUM925_1.p',unknown),
[] ).
cnf(67,axiom,
( ~ int(U)
| ~ equal(U,pls)
| equal(bit0(U),pls) ),
file('NUM925_1.p',unknown),
[] ).
cnf(73,axiom,
( ~ int(U)
| ~ ord_less_int(pls,U)
| ord_less_int(pls,bit0(U)) ),
file('NUM925_1.p',unknown),
[] ).
cnf(85,axiom,
equal(power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))),zero_zero_int),
file('NUM925_1.p',unknown),
[] ).
cnf(141,axiom,
( ~ equal(power_power_int(U,number_number_of_nat(bit0(bit1(pls)))),zero_zero_int)
| ~ int(U)
| equal(U,zero_zero_int) ),
file('NUM925_1.p',unknown),
[] ).
cnf(181,plain,
ord_less_int(pls,plus_plus_int(one_one_int,semiri1621563631at_int(n))),
inference(rew,[status(thm),theory(equality)],[10,32]),
[iquote('0:Rew:10.0,32.0')] ).
cnf(192,plain,
equal(power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),plus_plus_nat(one_one_nat,one_one_nat)),pls),
inference(rew,[status(thm),theory(equality)],[47,85,10]),
[iquote('0:Rew:47.0,85.0,10.0,85.0')] ).
cnf(214,plain,
( ~ int(U)
| ~ equal(power_power_int(U,plus_plus_nat(one_one_nat,one_one_nat)),pls)
| equal(U,pls) ),
inference(rew,[status(thm),theory(equality)],[10,141,47]),
[iquote('0:Rew:10.0,141.2,47.0,141.0,10.0,141.0')] ).
cnf(229,plain,
( ~ int(plus_plus_int(one_one_int,semiri1621563631at_int(n)))
| equal(plus_plus_int(one_one_int,semiri1621563631at_int(n)),pls) ),
inference(res,[status(thm),theory(equality)],[192,214]),
[iquote('0:Res:192.0,214.0')] ).
cnf(377,plain,
( ~ int(U)
| ~ equal(U,pls)
| ~ int(U)
| ~ ord_less_int(pls,U)
| ord_less_int(pls,pls) ),
inference(spr,[status(thm),theory(equality)],[67,73]),
[iquote('0:SpR:67.2,73.2')] ).
cnf(378,plain,
( ~ equal(U,pls)
| ~ int(U)
| ~ ord_less_int(pls,U)
| ord_less_int(pls,pls) ),
inference(obv,[status(thm),theory(equality)],[377]),
[iquote('0:Obv:377.0')] ).
cnf(379,plain,
( ~ equal(U,pls)
| ~ int(U)
| ~ ord_less_int(pls,U) ),
inference(mrr,[status(thm)],[378,21]),
[iquote('0:MRR:378.3,21.0')] ).
cnf(509,plain,
( ~ equal(plus_plus_int(one_one_int,semiri1621563631at_int(n)),pls)
| ~ int(plus_plus_int(one_one_int,semiri1621563631at_int(n))) ),
inference(res,[status(thm),theory(equality)],[181,379]),
[iquote('0:Res:181.0,379.2')] ).
cnf(513,plain,
( ~ equal(pls,pls)
| ~ int(plus_plus_int(one_one_int,semiri1621563631at_int(n))) ),
inference(rew,[status(thm),theory(equality)],[229,509]),
[iquote('0:Rew:229.1,509.0')] ).
cnf(514,plain,
~ int(plus_plus_int(one_one_int,semiri1621563631at_int(n))),
inference(obv,[status(thm),theory(equality)],[513]),
[iquote('0:Obv:513.0')] ).
cnf(519,plain,
( ~ int(one_one_int)
| ~ int(semiri1621563631at_int(n)) ),
inference(res,[status(thm),theory(equality)],[62,514]),
[iquote('0:Res:62.2,514.0')] ).
cnf(520,plain,
~ int(semiri1621563631at_int(n)),
inference(mrr,[status(thm)],[519,7]),
[iquote('0:MRR:519.0,7.0')] ).
cnf(528,plain,
~ nat(n),
inference(res,[status(thm),theory(equality)],[34,520]),
[iquote('0:Res:34.1,520.0')] ).
cnf(529,plain,
$false,
inference(mrr,[status(thm)],[528,2]),
[iquote('0:MRR:528.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM925_1 : TPTP v8.1.0. Released v5.3.0.
% 0.12/0.12 % Command : spasst-tptp-script %s %d
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jul 5 12:22:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.47 % Using EUF theory
% 1.00/1.33
% 1.00/1.33
% 1.00/1.33 % SZS status Theorem for /tmp/SPASST_7433_n026.cluster.edu
% 1.00/1.33
% 1.00/1.33 SPASS V 2.2.22 in combination with yices.
% 1.00/1.33 SPASS beiseite: Proof found by SPASS.
% 1.00/1.33 Problem: /tmp/SPASST_7433_n026.cluster.edu
% 1.00/1.33 SPASS derived 210 clauses, backtracked 0 clauses and kept 181 clauses.
% 1.00/1.33 SPASS backtracked 0 times (0 times due to theory inconsistency).
% 1.00/1.33 SPASS allocated 6790 KBytes.
% 1.00/1.33 SPASS spent 0:00:00.05 on the problem.
% 1.00/1.33 0:00:00.00 for the input.
% 1.00/1.33 0:00:00.01 for the FLOTTER CNF translation.
% 1.00/1.33 0:00:00.00 for inferences.
% 1.00/1.33 0:00:00.00 for the backtracking.
% 1.00/1.33 0:00:00.01 for the reduction.
% 1.00/1.33 0:00:00.00 for interacting with the SMT procedure.
% 1.00/1.33
% 1.00/1.33
% 1.00/1.33 % SZS output start CNFRefutation for /tmp/SPASST_7433_n026.cluster.edu
% See solution above
% 1.00/1.33
% 1.00/1.33 Formulae used in the proof : fof_sy_v_n____ fof_sy_c_Groups_Oone__class_Oone_000tc__Int__Oint fof_fact_78_Pls__def fof_fact_36_rel__simps_I2_J fof_fact_0_n1pos fof_sy_c_Nat_Osemiring__1__class_Oof__nat_000tc__Int__Oint fof_fact_12_semiring__one__add__one__is__two fof_sy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint fof_fact_75_rel__simps_I44_J fof_fact_60_rel__simps_I4_J fof_conj_0 fof_fact_7_zero__eq__power2
% 1.05/1.35
% 1.05/1.35 SPASS+T ended
%------------------------------------------------------------------------------