TSTP Solution File: NUM924_1 by SPASS+T---2.2.22
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS+T---2.2.22
% Problem : NUM924_1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : spasst-tptp-script %s %d
% Computer : n021.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 14:39:28 EDT 2022
% Result : Theorem 3.44s 2.71s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 24
% Syntax : Number of clauses : 74 ( 27 unt; 8 nHn; 74 RR)
% Number of literals : 162 ( 0 equ; 102 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
int(m),
file('NUM924_1.p',unknown),
[] ).
cnf(5,axiom,
int(pls),
file('NUM924_1.p',unknown),
[] ).
cnf(9,axiom,
int(one_one_int),
file('NUM924_1.p',unknown),
[] ).
cnf(15,axiom,
equal(number_number_of_int(pls),zero_zero_int),
file('NUM924_1.p',unknown),
[] ).
cnf(21,axiom,
( ~ int(U)
| ord_less_eq_int(U,U) ),
file('NUM924_1.p',unknown),
[] ).
cnf(24,axiom,
( ~ int(U)
| int(bit1(U)) ),
file('NUM924_1.p',unknown),
[] ).
cnf(25,axiom,
( ~ int(U)
| int(bit0(U)) ),
file('NUM924_1.p',unknown),
[] ).
cnf(26,axiom,
( ~ int(U)
| equal(number_number_of_int(U),U) ),
file('NUM924_1.p',unknown),
[] ).
cnf(29,axiom,
( ~ int(U)
| equal(times_times_int(pls,U),pls) ),
file('NUM924_1.p',unknown),
[] ).
cnf(30,axiom,
equal(number_number_of_nat(bit0(bit1(pls))),plus_plus_nat(one_one_nat,one_one_nat)),
file('NUM924_1.p',unknown),
[] ).
cnf(35,axiom,
( ~ int(U)
| ~ ord_less_int(zero_zero_int,U)
| ord_less_eq_int(one_one_int,U) ),
file('NUM924_1.p',unknown),
[] ).
cnf(36,axiom,
( ~ int(U)
| ~ ord_less_eq_int(one_one_int,U)
| ord_less_int(zero_zero_int,U) ),
file('NUM924_1.p',unknown),
[] ).
cnf(41,axiom,
( ~ int(U)
| ~ int(V)
| int(times_times_int(U,V)) ),
file('NUM924_1.p',unknown),
[] ).
cnf(43,axiom,
( ~ int(U)
| ~ int(V)
| int(plus_plus_int(U,V)) ),
file('NUM924_1.p',unknown),
[] ).
cnf(66,axiom,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
file('NUM924_1.p',unknown),
[] ).
cnf(68,axiom,
( ~ ord_less_eq_int(bit1(pls),U)
| ~ int(U)
| ord_less_eq_int(one_one_int,number_number_of_int(U)) ),
file('NUM924_1.p',unknown),
[] ).
cnf(70,axiom,
( ~ ord_less_eq_int(U,bit1(pls))
| ~ int(U)
| ord_less_eq_int(number_number_of_int(U),one_one_int) ),
file('NUM924_1.p',unknown),
[] ).
cnf(77,axiom,
( ~ int(U)
| ~ int(V)
| equal(times_times_int(U,V),times_times_int(V,U)) ),
file('NUM924_1.p',unknown),
[] ).
cnf(128,axiom,
( ~ equal(U,zero_zero_int)
| ~ int(U)
| equal(power_power_int(U,number_number_of_nat(bit0(bit1(pls)))),zero_zero_int) ),
file('NUM924_1.p',unknown),
[] ).
cnf(132,axiom,
( ~ int(U)
| ~ int(V)
| ord_less_eq_int(number_number_of_int(V),number_number_of_int(U))
| ord_less_int(number_number_of_int(U),number_number_of_int(V)) ),
file('NUM924_1.p',unknown),
[] ).
cnf(137,axiom,
( ~ equal(U,zero_zero_int)
| ~ ord_less_int(zero_zero_int,power_power_int(U,number_number_of_nat(bit0(bit1(pls)))))
| ~ int(U) ),
file('NUM924_1.p',unknown),
[] ).
cnf(138,axiom,
( ~ int(U)
| ~ int(V)
| ~ ord_less_eq_int(U,V)
| ~ ord_less_eq_int(V,U)
| equal(U,V) ),
file('NUM924_1.p',unknown),
[] ).
cnf(148,axiom,
equal(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('NUM924_1.p',unknown),
[] ).
cnf(161,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('NUM924_1.p',unknown),
[] ).
cnf(185,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int),zero_zero_int),
inference(rew,[status(thm),theory(equality)],[30,66]),
[iquote('0:Rew:30.0,66.0')] ).
cnf(192,plain,
( ~ int(U)
| ~ ord_less_eq_int(U,bit1(pls))
| ord_less_eq_int(U,one_one_int) ),
inference(rew,[status(thm),theory(equality)],[26,70]),
[iquote('0:Rew:26.1,70.2')] ).
cnf(194,plain,
( ~ int(U)
| ~ ord_less_eq_int(bit1(pls),U)
| ord_less_eq_int(one_one_int,U) ),
inference(rew,[status(thm),theory(equality)],[26,68]),
[iquote('0:Rew:26.1,68.2')] ).
cnf(200,plain,
( ~ int(U)
| ~ equal(U,zero_zero_int)
| equal(power_power_int(U,plus_plus_nat(one_one_nat,one_one_nat)),zero_zero_int) ),
inference(rew,[status(thm),theory(equality)],[30,128]),
[iquote('0:Rew:30.0,128.2')] ).
cnf(211,plain,
( ~ int(U)
| ~ equal(U,zero_zero_int)
| ~ ord_less_int(zero_zero_int,zero_zero_int) ),
inference(rew,[status(thm),theory(equality)],[200,137,30]),
[iquote('0:Rew:200.2,137.1,30.0,137.1')] ).
cnf(215,plain,
( ~ int(U)
| ~ int(V)
| ord_less_int(V,U)
| ord_less_eq_int(U,V) ),
inference(rew,[status(thm),theory(equality)],[26,132]),
[iquote('0:Rew:26.1,132.3,26.1,132.3,26.1,132.2,26.1,132.2')] ).
cnf(219,plain,
equal(plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),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(rew,[status(thm),theory(equality)],[30,148]),
[iquote('0:Rew:30.0,148.0')] ).
cnf(220,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),zero_zero_int),
inference(rew,[status(thm),theory(equality)],[219,185]),
[iquote('0:Rew:219.0,185.0')] ).
cnf(258,plain,
( ~ int(pls)
| equal(zero_zero_int,pls) ),
inference(spr,[status(thm),theory(equality)],[26,15]),
[iquote('0:SpR:26.1,15.0')] ).
cnf(260,plain,
equal(zero_zero_int,pls),
inference(mrr,[status(thm)],[258,5]),
[iquote('0:MRR:258.0,5.0')] ).
cnf(265,plain,
( ~ int(U)
| ~ ord_less_int(pls,U)
| ord_less_eq_int(one_one_int,U) ),
inference(rew,[status(thm),theory(equality)],[260,35]),
[iquote('0:Rew:260.0,35.1')] ).
cnf(266,plain,
( ~ int(U)
| ~ ord_less_eq_int(one_one_int,U)
| ord_less_int(pls,U) ),
inference(rew,[status(thm),theory(equality)],[260,36]),
[iquote('0:Rew:260.0,36.2')] ).
cnf(281,plain,
( ~ int(U)
| ~ equal(U,pls)
| ~ ord_less_int(zero_zero_int,zero_zero_int) ),
inference(rew,[status(thm),theory(equality)],[260,211]),
[iquote('0:Rew:260.0,211.1')] ).
cnf(292,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),pls),
inference(rew,[status(thm),theory(equality)],[260,220]),
[iquote('0:Rew:260.0,220.0')] ).
cnf(295,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),pls)),
inference(rew,[status(thm),theory(equality)],[260,161]),
[iquote('0:Rew:260.0,161.0')] ).
cnf(298,plain,
( ~ int(U)
| ~ equal(U,pls)
| ~ ord_less_int(pls,pls) ),
inference(rew,[status(thm),theory(equality)],[260,281]),
[iquote('0:Rew:260.0,281.2')] ).
cnf(339,plain,
( ~ int(pls)
| ~ ord_less_int(pls,pls) ),
inference(eqr,[status(thm),theory(equality)],[298]),
[iquote('0:EqR:298.1')] ).
cnf(340,plain,
~ ord_less_int(pls,pls),
inference(mrr,[status(thm)],[339,5]),
[iquote('0:MRR:339.0,5.0')] ).
cnf(341,plain,
( ~ int(pls)
| ~ ord_less_eq_int(one_one_int,pls) ),
inference(res,[status(thm),theory(equality)],[266,340]),
[iquote('0:Res:266.2,340.0')] ).
cnf(342,plain,
~ ord_less_eq_int(one_one_int,pls),
inference(mrr,[status(thm)],[341,5]),
[iquote('0:MRR:341.0,5.0')] ).
cnf(391,plain,
( ~ int(bit1(pls))
| ~ int(bit1(pls))
| ord_less_eq_int(bit1(pls),one_one_int) ),
inference(res,[status(thm),theory(equality)],[21,192]),
[iquote('0:Res:21.1,192.1')] ).
cnf(395,plain,
( ~ int(bit1(pls))
| ord_less_eq_int(bit1(pls),one_one_int) ),
inference(obv,[status(thm),theory(equality)],[391]),
[iquote('0:Obv:391.0')] ).
cnf(464,plain,
( ~ int(U)
| ~ int(pls)
| ~ int(U)
| ord_less_eq_int(U,pls)
| ord_less_eq_int(one_one_int,U) ),
inference(res,[status(thm),theory(equality)],[215,265]),
[iquote('0:Res:215.2,265.1')] ).
cnf(470,plain,
( ~ int(pls)
| ~ int(U)
| ord_less_eq_int(U,pls)
| ord_less_eq_int(one_one_int,U) ),
inference(obv,[status(thm),theory(equality)],[464]),
[iquote('0:Obv:464.0')] ).
cnf(471,plain,
( ~ int(U)
| ord_less_eq_int(U,pls)
| ord_less_eq_int(one_one_int,U) ),
inference(mrr,[status(thm)],[470,5]),
[iquote('0:MRR:470.0,5.0')] ).
cnf(482,plain,
( ~ int(U)
| ord_less_eq_int(bit1(U),pls)
| ord_less_eq_int(one_one_int,bit1(U)) ),
inference(res,[status(thm),theory(equality)],[24,471]),
[iquote('0:Res:24.1,471.0')] ).
cnf(959,plain,
( ~ int(pls)
| ~ int(pls)
| ord_less_eq_int(one_one_int,bit1(pls))
| ord_less_eq_int(one_one_int,pls) ),
inference(res,[status(thm),theory(equality)],[482,194]),
[iquote('0:Res:482.1,194.1')] ).
cnf(961,plain,
( ~ int(pls)
| ord_less_eq_int(one_one_int,bit1(pls))
| ord_less_eq_int(one_one_int,pls) ),
inference(obv,[status(thm),theory(equality)],[959]),
[iquote('0:Obv:959.0')] ).
cnf(962,plain,
ord_less_eq_int(one_one_int,bit1(pls)),
inference(mrr,[status(thm)],[961,5,342]),
[iquote('0:MRR:961.0,961.2,5.0,342.0')] ).
cnf(1056,plain,
( ~ int(pls)
| ~ int(U)
| ~ int(U)
| equal(times_times_int(U,pls),pls) ),
inference(spr,[status(thm),theory(equality)],[77,29]),
[iquote('0:SpR:77.2,29.1')] ).
cnf(1086,plain,
( ~ int(pls)
| ~ int(U)
| equal(times_times_int(U,pls),pls) ),
inference(obv,[status(thm),theory(equality)],[1056]),
[iquote('0:Obv:1056.1')] ).
cnf(1087,plain,
( ~ int(U)
| equal(times_times_int(U,pls),pls) ),
inference(mrr,[status(thm)],[1086,5]),
[iquote('0:MRR:1086.0,5.0')] ).
cnf(3169,plain,
( ~ int(one_one_int)
| ~ int(bit1(pls))
| ~ ord_less_eq_int(bit1(pls),one_one_int)
| equal(bit1(pls),one_one_int) ),
inference(res,[status(thm),theory(equality)],[962,138]),
[iquote('0:Res:962.0,138.2')] ).
cnf(7587,plain,
( ~ int(bit1(pls))
| ~ ord_less_eq_int(bit1(pls),one_one_int)
| equal(bit1(pls),one_one_int) ),
inference(mrr,[status(thm)],[3169,9]),
[iquote('0:MRR:3169.0,9.0')] ).
cnf(7588,plain,
( ~ int(bit1(pls))
| equal(bit1(pls),one_one_int) ),
inference(mrr,[status(thm)],[7587,395]),
[iquote('0:MRR:7587.1,395.1')] ).
cnf(8405,plain,
( ~ int(pls)
| equal(bit1(pls),one_one_int) ),
inference(res,[status(thm),theory(equality)],[24,7588]),
[iquote('0:Res:24.1,7588.0')] ).
cnf(8406,plain,
equal(bit1(pls),one_one_int),
inference(mrr,[status(thm)],[8405,5]),
[iquote('0:MRR:8405.0,5.0')] ).
cnf(9707,plain,
~ ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(one_one_int))),m),one_one_int),t),pls),
inference(rew,[status(thm),theory(equality)],[8406,292]),
[iquote('0:Rew:8406.0,292.0')] ).
cnf(9710,plain,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(one_one_int))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(one_one_int))),m),one_one_int),pls)),
inference(rew,[status(thm),theory(equality)],[8406,295]),
[iquote('0:Rew:8406.0,295.0')] ).
cnf(10822,plain,
( ~ int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(one_one_int))),m),one_one_int))
| ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(one_one_int))),m),one_one_int),t),pls) ),
inference(spr,[status(thm),theory(equality)],[1087,9710]),
[iquote('0:SpR:1087.1,9710.0')] ).
cnf(10839,plain,
~ int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(one_one_int))),m),one_one_int)),
inference(mrr,[status(thm)],[10822,9707]),
[iquote('0:MRR:10822.1,9707.0')] ).
cnf(10852,plain,
( ~ int(times_times_int(number_number_of_int(bit0(bit0(one_one_int))),m))
| ~ int(one_one_int) ),
inference(res,[status(thm),theory(equality)],[43,10839]),
[iquote('0:Res:43.2,10839.0')] ).
cnf(10853,plain,
~ int(times_times_int(number_number_of_int(bit0(bit0(one_one_int))),m)),
inference(mrr,[status(thm)],[10852,9]),
[iquote('0:MRR:10852.1,9.0')] ).
cnf(10863,plain,
( ~ int(number_number_of_int(bit0(bit0(one_one_int))))
| ~ int(m) ),
inference(res,[status(thm),theory(equality)],[41,10853]),
[iquote('0:Res:41.2,10853.0')] ).
cnf(10864,plain,
~ int(number_number_of_int(bit0(bit0(one_one_int)))),
inference(mrr,[status(thm)],[10863,4]),
[iquote('0:MRR:10863.1,4.0')] ).
cnf(10870,plain,
( ~ int(bit0(bit0(one_one_int)))
| ~ int(bit0(bit0(one_one_int))) ),
inference(spl,[status(thm),theory(equality)],[26,10864]),
[iquote('0:SpL:26.1,10864.0')] ).
cnf(10871,plain,
~ int(bit0(bit0(one_one_int))),
inference(obv,[status(thm),theory(equality)],[10870]),
[iquote('0:Obv:10870.0')] ).
cnf(10877,plain,
~ int(bit0(one_one_int)),
inference(res,[status(thm),theory(equality)],[25,10871]),
[iquote('0:Res:25.1,10871.0')] ).
cnf(10898,plain,
~ int(one_one_int),
inference(res,[status(thm),theory(equality)],[25,10877]),
[iquote('0:Res:25.1,10877.0')] ).
cnf(10899,plain,
$false,
inference(mrr,[status(thm)],[10898,9]),
[iquote('0:MRR:10898.0,9.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM924_1 : TPTP v8.1.0. Released v5.3.0.
% 0.11/0.12 % Command : spasst-tptp-script %s %d
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jul 6 20:18:19 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.47 % Using EUF theory
% 3.44/2.71
% 3.44/2.71
% 3.44/2.71 % SZS status Theorem for /tmp/SPASST_12411_n021.cluster.edu
% 3.44/2.71
% 3.44/2.71 SPASS V 2.2.22 in combination with yices.
% 3.44/2.71 SPASS beiseite: Proof found by SPASS.
% 3.44/2.71 Problem: /tmp/SPASST_12411_n021.cluster.edu
% 3.44/2.71 SPASS derived 6858 clauses, backtracked 1293 clauses and kept 3768 clauses.
% 3.44/2.71 SPASS backtracked 11 times (0 times due to theory inconsistency).
% 3.44/2.71 SPASS allocated 13820 KBytes.
% 3.44/2.71 SPASS spent 0:00:01.38 on the problem.
% 3.44/2.71 0:00:00.00 for the input.
% 3.44/2.71 0:00:00.02 for the FLOTTER CNF translation.
% 3.44/2.71 0:00:00.04 for inferences.
% 3.44/2.71 0:00:00.05 for the backtracking.
% 3.44/2.71 0:00:01.09 for the reduction.
% 3.44/2.71 0:00:00.10 for interacting with the SMT procedure.
% 3.44/2.71
% 3.44/2.71
% 3.44/2.71 % SZS output start CNFRefutation for /tmp/SPASST_12411_n021.cluster.edu
% See solution above
% 3.44/2.71
% 3.44/2.71 Formulae used in the proof : fof_sy_v_m fof_sy_c_Int_OPls fof_sy_c_Groups_Oone__class_Oone_000tc__Int__Oint fof_fact_105_zero__is__num__zero fof_fact_23_zle__refl fof_sy_c_Int_OBit1 fof_sy_c_Int_OBit0 fof_fact_24_number__of__is__id fof_fact_66_mult__Pls fof_fact_65_nat__1__add__1 fof_fact_81_int__one__le__iff__zero__less fof_sy_c_Groups_Otimes__class_Otimes_000tc__Int__Oint fof_sy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint fof_conj_0 fof_fact_64_le__special_I2_J fof_fact_63_le__special_I4_J fof_fact_25_zmult__commute fof_fact_16_zero__eq__power2 fof_fact_53_le__number__of__eq__not__less fof_fact_11_zero__less__power2 fof_fact_32_zle__antisym fof_fact_3_t 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
% 4.69/3.22
% 4.69/3.22 SPASS+T ended
%------------------------------------------------------------------------------