TSTP Solution File: NUM926+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM926+1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% 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 : 600s
% DateTime : Mon Jul 18 14:31:47 EDT 2022
% Result : Theorem 106.92s 107.12s
% Output : Refutation 107.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM926+1 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jul 5 14:56:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 106.92/107.12
% 106.92/107.12 SPASS V 3.9
% 106.92/107.12 SPASS beiseite: Proof found.
% 106.92/107.12 % SZS status Theorem
% 106.92/107.12 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 106.92/107.12 SPASS derived 56214 clauses, backtracked 1441 clauses, performed 5 splits and kept 19861 clauses.
% 106.92/107.12 SPASS allocated 161328 KBytes.
% 106.92/107.12 SPASS spent 0:1:46.68 on the problem.
% 106.92/107.12 0:00:00.04 for the input.
% 106.92/107.12 0:00:00.04 for the FLOTTER CNF translation.
% 106.92/107.12 0:00:00.68 for inferences.
% 106.92/107.12 0:00:09.92 for the backtracking.
% 106.92/107.12 0:1:35.52 for the reduction.
% 106.92/107.12
% 106.92/107.12
% 106.92/107.12 Here is a proof with depth 9, length 100 :
% 106.92/107.12 % SZS output start Refutation
% 106.92/107.12 1[0:Inp] || -> ord_less_eq_int(one_one_int,t)*r.
% 106.92/107.12 5[0:Inp] || -> equal(number_number_of_int(u),u)**.
% 106.92/107.12 6[0:Inp] || -> equal(power_power_int(u,one_one_nat),u)**.
% 106.92/107.12 9[0:Inp] || -> equal(number_number_of_nat(bit1(pls)),one_one_nat)**.
% 106.92/107.12 16[0:Inp] || -> equal(plus_plus_nat(u,v),plus_plus_nat(v,u))*.
% 106.92/107.12 17[0:Inp] || -> equal(times_times_int(u,v),times_times_int(v,u))*.
% 106.92/107.12 18[0:Inp] || -> equal(plus_plus_int(u,v),plus_plus_int(v,u))*.
% 106.92/107.12 21[0:Inp] || -> equal(number_number_of_int(bit0(bit1(pls))),plus_plus_int(one_one_int,one_one_int))**.
% 106.92/107.12 22[0:Inp] || ord_less_int(u,v)* equal(u,v) -> .
% 106.92/107.12 23[0:Inp] || -> equal(number_number_of_nat(bit0(bit1(pls))),plus_plus_nat(one_one_nat,one_one_nat))**.
% 106.92/107.12 27[0:Inp] || ord_less_eq_int(pls,u) -> ord_less_int(pls,bit1(u))*.
% 106.92/107.12 29[0:Inp] || ord_less_int(u,pls) -> ord_less_int(bit1(u),pls)*.
% 106.92/107.12 36[0:Inp] || -> ord_less_int(u,v)* equal(v,u) ord_less_int(v,u)*.
% 106.92/107.12 44[0:Inp] || ord_less_int(u,v) -> ord_less_int(bit1(u),bit1(v))*.
% 106.92/107.12 52[0:Inp] || ord_less_int(u,v) -> ord_less_int(bit0(u),bit0(v))*.
% 106.92/107.12 64[0:Inp] || ord_less_int(u,v)* -> ord_less_eq_int(bit1(u),bit0(v)).
% 106.92/107.12 68[0:Inp] || ord_less_eq_int(u,v) -> ord_less_int(bit0(u),bit1(v))*.
% 106.92/107.12 70[0:Inp] || ord_less_eq_int(plus_plus_int(u,one_one_int),v)*+ -> ord_less_int(u,v)*.
% 106.92/107.12 71[0:Inp] || ord_less_int(u,v)*+ -> ord_less_eq_int(plus_plus_int(u,one_one_int),v)*.
% 106.92/107.12 87[0:Inp] || ord_less_int(u,v) -> ord_less_int(bit1(u),bit0(v))*.
% 106.92/107.12 95[0:Inp] || -> equal(power_power_int(u,number_number_of_nat(bit0(bit1(pls)))),times_times_int(u,u))*.
% 106.92/107.12 97[0:Inp] || -> equal(number_number_of_int(plus_plus_int(bit1(pls),u)),plus_plus_int(one_one_int,number_number_of_int(u)))**.
% 106.92/107.12 101[0:Inp] || -> ord_less_int(number_number_of_int(u),number_number_of_int(v))* ord_less_eq_int(number_number_of_int(v),number_number_of_int(u)).
% 106.92/107.12 106[0:Inp] || ord_less_eq_int(u,v)* ord_less_eq_int(v,w)* -> ord_less_eq_int(u,w)*.
% 106.92/107.12 107[0:Inp] || ord_less_eq_int(u,v)*+ ord_less_eq_int(v,u)* -> equal(v,u).
% 106.92/107.12 111[0:Inp] || ord_less_int(u,v) -> ord_less_int(plus_plus_int(u,w),plus_plus_int(v,w))*.
% 106.92/107.12 135[0:Inp] || ord_less_int(u,pls) -> equal(plus_plus_nat(number_number_of_nat(u),number_number_of_nat(v)),number_number_of_nat(v))**.
% 106.92/107.12 157[0:Inp] || equal(plus_plus_int(power_power_int(u,number_number_of_nat(bit0(bit1(pls)))),power_power_int(v,number_number_of_nat(bit0(bit1(pls))))),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))** -> .
% 106.92/107.12 158[0:Inp] || ord_less_int(one_one_int,t) -> equal(plus_plus_int(power_power_int(skc8,number_number_of_nat(bit0(bit1(pls)))),power_power_int(skc7,number_number_of_nat(bit0(bit1(pls))))),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))**.
% 106.92/107.12 159[0:Inp] || equal(t,one_one_int) -> equal(plus_plus_int(power_power_int(skc6,number_number_of_nat(bit0(bit1(pls)))),power_power_int(skc5,number_number_of_nat(bit0(bit1(pls))))),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))**.
% 106.92/107.12 165[0:Rew:5.0,21.0] || -> equal(plus_plus_int(one_one_int,one_one_int),bit0(bit1(pls)))**.
% 106.92/107.12 178[0:Rew:5.0,97.0,5.0,97.0] || -> equal(plus_plus_int(bit1(pls),u),plus_plus_int(one_one_int,u))**.
% 106.92/107.12 181[0:Rew:23.0,95.0] || -> equal(power_power_int(u,plus_plus_nat(one_one_nat,one_one_nat)),times_times_int(u,u))*.
% 106.92/107.12 199[0:Rew:5.0,101.1,5.0,101.1,5.0,101.0,5.0,101.0] || -> ord_less_eq_int(u,v) ord_less_int(v,u)*.
% 106.92/107.12 210[0:Rew:23.0,157.0,18.0,157.0,17.0,157.0,5.0,157.0] || equal(plus_plus_int(power_power_int(u,plus_plus_nat(one_one_nat,one_one_nat)),power_power_int(v,plus_plus_nat(one_one_nat,one_one_nat))),plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))** -> .
% 106.92/107.12 211[0:Rew:18.0,158.1,181.0,158.1,18.0,158.1,181.0,158.1,23.0,158.1,18.0,158.1,5.0,158.1,17.0,158.1,18.0,158.1] || ord_less_int(one_one_int,t) -> equal(plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))),plus_plus_int(times_times_int(skc7,skc7),times_times_int(skc8,skc8)))**.
% 106.92/107.12 212[0:Rew:18.0,159.1,181.0,159.1,18.0,159.1,181.0,159.1,23.0,159.1,18.0,159.1,5.0,159.1,17.0,159.1,18.0,159.1] || equal(t,one_one_int) -> equal(plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))),plus_plus_int(times_times_int(skc5,skc5),times_times_int(skc6,skc6)))**.
% 106.92/107.12 277[0:Res:29.1,22.0] || ord_less_int(u,pls)* equal(bit1(u),pls) -> .
% 106.92/107.12 318[0:Res:87.1,22.0] || ord_less_int(u,v)* equal(bit1(u),bit0(v)) -> .
% 106.92/107.12 369[0:Res:52.1,22.0] || ord_less_int(u,v)* equal(bit0(u),bit0(v)) -> .
% 106.92/107.12 496[0:Res:199.1,277.0] || equal(bit1(u),pls)** -> ord_less_eq_int(pls,u).
% 106.92/107.12 515[0:Res:199.1,318.0] || equal(bit1(u),bit0(v))* -> ord_less_eq_int(v,u).
% 106.92/107.12 523[0:Res:52.1,369.0] || ord_less_int(u,v)* equal(bit0(bit0(u)),bit0(bit0(v)))*+ -> .
% 106.92/107.12 1558[0:SpR:165.0,111.1] || ord_less_int(u,one_one_int) -> ord_less_int(plus_plus_int(u,one_one_int),bit0(bit1(pls)))*.
% 106.92/107.12 1573[0:SpR:165.0,111.1] || ord_less_int(one_one_int,u) -> ord_less_int(bit0(bit1(pls)),plus_plus_int(u,one_one_int))*.
% 106.92/107.12 1602[0:SpR:178.0,1558.1] || ord_less_int(bit1(pls),one_one_int) -> ord_less_int(plus_plus_int(one_one_int,one_one_int),bit0(bit1(pls)))*.
% 106.92/107.12 1610[0:Rew:165.0,1602.1] || ord_less_int(bit1(pls),one_one_int) -> ord_less_int(bit0(bit1(pls)),bit0(bit1(pls)))*.
% 106.92/107.12 1622[0:SpR:9.0,135.1] || ord_less_int(u,pls) -> equal(plus_plus_nat(number_number_of_nat(u),one_one_nat),one_one_nat)**.
% 106.92/107.12 1628[0:Rew:16.0,1622.1] || ord_less_int(u,pls) -> equal(plus_plus_nat(one_one_nat,number_number_of_nat(u)),one_one_nat)**.
% 106.92/107.12 1640[0:SpR:9.0,1628.1] || ord_less_int(bit1(pls),pls)* -> equal(plus_plus_nat(one_one_nat,one_one_nat),one_one_nat).
% 106.92/107.12 1647[0:Res:36.0,1640.0] || -> equal(bit1(pls),pls) ord_less_int(pls,bit1(pls))* equal(plus_plus_nat(one_one_nat,one_one_nat),one_one_nat).
% 106.92/107.12 1692[0:SpR:178.0,1573.1] || ord_less_int(one_one_int,bit1(pls)) -> ord_less_int(bit0(bit1(pls)),plus_plus_int(one_one_int,one_one_int))*.
% 106.92/107.12 1707[0:Rew:165.0,1692.1] || ord_less_int(one_one_int,bit1(pls)) -> ord_less_int(bit0(bit1(pls)),bit0(bit1(pls)))*.
% 106.92/107.12 2460[0:Res:27.1,22.0] || ord_less_eq_int(pls,u) equal(bit1(u),pls)** -> .
% 106.92/107.12 2461[0:MRR:2460.0,496.1] || equal(bit1(u),pls)** -> .
% 106.92/107.12 2465[0:MRR:1647.0,2461.0] || -> ord_less_int(pls,bit1(pls))* equal(plus_plus_nat(one_one_nat,one_one_nat),one_one_nat).
% 106.92/107.12 2503[1:Spt:2465.1] || -> equal(plus_plus_nat(one_one_nat,one_one_nat),one_one_nat)**.
% 106.92/107.12 2530[1:Rew:2503.0,210.0] || equal(plus_plus_int(power_power_int(u,one_one_nat),power_power_int(v,one_one_nat)),plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))* -> .
% 106.92/107.12 2668[1:Rew:6.0,2530.0,6.0,2530.0] || equal(plus_plus_int(u,v),plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))* -> .
% 106.92/107.12 2669[1:Obv:2668.0] || -> .
% 106.92/107.12 2688[1:Spt:2669.0,2465.1,2503.0] || equal(plus_plus_nat(one_one_nat,one_one_nat),one_one_nat)** -> .
% 106.92/107.12 2689[1:Spt:2669.0,2465.0] || -> ord_less_int(pls,bit1(pls))*.
% 106.92/107.12 4277[0:Res:1610.1,22.0] || ord_less_int(bit1(pls),one_one_int)* equal(bit0(bit1(pls)),bit0(bit1(pls))) -> .
% 106.92/107.12 4279[0:Obv:4277.1] || ord_less_int(bit1(pls),one_one_int)* -> .
% 106.92/107.12 4318[0:Res:36.0,4279.0] || -> equal(bit1(pls),one_one_int) ord_less_int(one_one_int,bit1(pls))*.
% 106.92/107.12 4321[2:Spt:4318.0] || -> equal(bit1(pls),one_one_int)**.
% 106.92/107.12 4323[2:Rew:4321.0,165.0] || -> equal(plus_plus_int(one_one_int,one_one_int),bit0(one_one_int))**.
% 106.92/107.12 4334[2:Rew:4321.0,23.0] || -> equal(plus_plus_nat(one_one_nat,one_one_nat),number_number_of_nat(bit0(one_one_int)))**.
% 106.92/107.12 4346[2:Rew:4321.0,2689.0] || -> ord_less_int(pls,one_one_int)*.
% 106.92/107.12 4363[2:Rew:4321.0,211.1] || ord_less_int(one_one_int,t) -> equal(plus_plus_int(times_times_int(skc7,skc7),times_times_int(skc8,skc8)),plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(one_one_int)))))**.
% 106.92/107.12 4364[2:Rew:4321.0,212.1] || equal(t,one_one_int) -> equal(plus_plus_int(times_times_int(skc5,skc5),times_times_int(skc6,skc6)),plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(one_one_int)))))**.
% 107.62/107.81 4365[2:Rew:4321.0,210.0] || equal(plus_plus_int(power_power_int(u,plus_plus_nat(one_one_nat,one_one_nat)),power_power_int(v,plus_plus_nat(one_one_nat,one_one_nat))),plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(one_one_int)))))** -> .
% 107.62/107.81 4511[2:Rew:4334.0,181.0] || -> equal(power_power_int(u,number_number_of_nat(bit0(one_one_int))),times_times_int(u,u))*.
% 107.62/107.81 4661[2:Rew:4334.0,4365.0] || equal(plus_plus_int(power_power_int(u,number_number_of_nat(bit0(one_one_int))),power_power_int(v,number_number_of_nat(bit0(one_one_int)))),plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(one_one_int)))))** -> .
% 107.62/107.81 5765[2:Res:4346.0,71.0] || -> ord_less_eq_int(plus_plus_int(pls,one_one_int),one_one_int)*l.
% 107.62/107.81 5771[0:Res:44.1,71.0] || ord_less_int(u,v)* -> ord_less_eq_int(plus_plus_int(bit1(u),one_one_int),bit1(v))*.
% 107.62/107.81 5784[2:Rew:18.0,5765.0] || -> ord_less_eq_int(plus_plus_int(one_one_int,pls),one_one_int)*l.
% 107.62/107.81 5794[0:Rew:18.0,5771.1] || ord_less_int(u,v)*+ -> ord_less_eq_int(plus_plus_int(one_one_int,bit1(u)),bit1(v))*.
% 107.62/107.81 5835[0:Res:36.0,64.0] || -> equal(u,v) ord_less_int(u,v)* ord_less_eq_int(bit1(v),bit0(u)).
% 107.62/107.81 5916[0:Res:68.1,22.0] || ord_less_eq_int(u,v) equal(bit0(u),bit1(v))* -> .
% 107.62/107.81 5917[0:MRR:5916.0,515.1] || equal(bit0(u),bit1(v))* -> .
% 107.62/107.81 6071[0:SpL:18.0,70.0] || ord_less_eq_int(plus_plus_int(one_one_int,u),v)*+ -> ord_less_int(u,v)*.
% 107.62/107.81 8113[0:CRe:106.1,1.0] || ord_less_eq_int(u,one_one_int)*+ -> ord_less_eq_int(u,t)*.
% 107.62/107.81 9715[2:SpL:4511.0,4661.0] || equal(plus_plus_int(power_power_int(u,number_number_of_nat(bit0(one_one_int))),times_times_int(v,v)),plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(one_one_int)))))** -> .
% 107.62/107.81 11881[0:EqR:523.1] || ord_less_int(u,u)* -> .
% 107.62/107.81 64894[2:Res:5784.0,8113.0] || -> ord_less_eq_int(plus_plus_int(one_one_int,pls),t)*l.
% 107.62/107.81 65041[2:Res:64894.0,6071.0] || -> ord_less_int(pls,t)*.
% 107.62/107.81 65067[2:Res:65041.0,5794.0] || -> ord_less_eq_int(plus_plus_int(one_one_int,bit1(pls)),bit1(t))*l.
% 107.62/107.81 65096[2:Rew:4323.0,65067.0,4321.0,65067.0] || -> ord_less_eq_int(bit0(one_one_int),bit1(t))*l.
% 107.62/107.81 70887[2:Res:65096.0,107.0] || ord_less_eq_int(bit1(t),bit0(one_one_int))*r -> equal(bit0(one_one_int),bit1(t)).
% 107.62/107.81 70909[2:MRR:70887.1,5917.0] || ord_less_eq_int(bit1(t),bit0(one_one_int))*r -> .
% 107.62/107.81 79710[2:SpL:4511.0,9715.0] || equal(plus_plus_int(times_times_int(u,u),times_times_int(v,v)),plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(one_one_int)))))** -> .
% 107.62/107.81 79723[2:MRR:4363.1,79710.0] || ord_less_int(one_one_int,t)* -> .
% 107.62/107.81 79724[2:MRR:4364.1,79710.0] || equal(t,one_one_int)** -> .
% 107.62/107.81 79823[2:Res:5835.1,79723.0] || -> equal(t,one_one_int) ord_less_eq_int(bit1(t),bit0(one_one_int))*r.
% 107.62/107.81 80052[2:MRR:79823.0,79823.1,79724.0,70909.0] || -> .
% 107.62/107.81 80060[2:Spt:80052.0,4318.0,4321.0] || equal(bit1(pls),one_one_int)** -> .
% 107.62/107.81 80061[2:Spt:80052.0,4318.1] || -> ord_less_int(one_one_int,bit1(pls))*.
% 107.62/107.81 80149[0:MRR:1707.1,11881.0] || ord_less_int(one_one_int,bit1(pls))* -> .
% 107.62/107.81 80150[2:MRR:80149.0,80061.0] || -> .
% 107.62/107.81 % SZS output end Refutation
% 107.62/107.81 Formulae used in the proof : fact_0_tpos fact_111_number__of__is__id fact_34_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J fact_64_Numeral1__eq1__nat fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J fact_110_zmult__commute fact_114_zadd__commute fact_24_one__add__one__is__two fact_28_zless__le fact_47_nat__1__add__1 fact_66_rel__simps_I5_J fact_115_rel__simps_I12_J fact_29_zless__linear fact_49_rel__simps_I17_J fact_54_rel__simps_I14_J fact_68_rel__simps_I33_J fact_70_rel__simps_I15_J fact_72_add1__zle__eq fact_117_rel__simps_I16_J fact_18_power2__eq__square fact_22_add__special_I2_J fact_38_le__number__of__eq__not__less fact_30_zle__trans fact_31_zle__antisym fact_60_zadd__strict__right__mono fact_62_add__nat__number__of conj_0 fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06 fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06
% 107.62/107.81
%------------------------------------------------------------------------------