TSTP Solution File: SET600+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET600+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 : Tue Jul 19 05:27:18 EDT 2022
% Result : Theorem 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET600+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n020.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 : Sat Jul 9 23:20:43 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.48
% 0.20/0.48 SPASS V 3.9
% 0.20/0.48 SPASS beiseite: Proof found.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.48 SPASS derived 329 clauses, backtracked 9 clauses, performed 2 splits and kept 194 clauses.
% 0.20/0.48 SPASS allocated 97843 KBytes.
% 0.20/0.48 SPASS spent 0:00:00.12 on the problem.
% 0.20/0.48 0:00:00.03 for the input.
% 0.20/0.48 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.48 0:00:00.01 for inferences.
% 0.20/0.48 0:00:00.00 for the backtracking.
% 0.20/0.48 0:00:00.03 for the reduction.
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 Here is a proof with depth 6, length 76 :
% 0.20/0.48 % SZS output start Refutation
% 0.20/0.48 2[0:Inp] || member(u,empty_set)* -> .
% 0.20/0.48 3[0:Inp] || -> empty(u) member(skf4(u),u)*.
% 0.20/0.48 5[0:Inp] || equal(u,v) -> subset(v,u)*.
% 0.20/0.48 6[0:Inp] || -> equal(union(u,v),union(v,u))*.
% 0.20/0.48 7[0:Inp] empty(u) || member(v,u)* -> .
% 0.20/0.48 8[0:Inp] || -> equal(empty_set,skc2) equal(union(skc2,skc3),empty_set)**.
% 0.20/0.48 9[0:Inp] || -> equal(empty_set,skc3) equal(union(skc2,skc3),empty_set)**.
% 0.20/0.48 10[0:Inp] || -> subset(u,v) member(skf3(v,u),u)*.
% 0.20/0.48 11[0:Inp] || member(u,v) -> member(u,union(v,w))*.
% 0.20/0.48 12[0:Inp] || member(u,v) -> member(u,union(w,v))*.
% 0.20/0.48 13[0:Inp] || member(skf3(u,v),u)*+ -> subset(w,u)*.
% 0.20/0.48 14[0:Inp] || subset(u,v)*+ subset(v,u)* -> equal(v,u).
% 0.20/0.48 15[0:Inp] || member(u,v)*+ subset(v,w)* -> member(u,w)*.
% 0.20/0.48 18[0:Inp] || member(u,union(v,w))* -> member(u,v) member(u,w).
% 0.20/0.48 19[0:Inp] || -> equal(u,v) member(skf5(v,u),v)* member(skf5(v,u),u)*.
% 0.20/0.48 20[0:Inp] || equal(empty_set,skc3) equal(empty_set,skc2) equal(union(skc2,skc3),empty_set)** -> .
% 0.20/0.48 22[0:Rew:9.0,8.0] || -> equal(skc3,skc2) equal(union(skc2,skc3),empty_set)**.
% 0.20/0.48 23[0:Rew:22.0,9.0] || -> equal(empty_set,skc2) equal(union(skc2,skc3),empty_set)**.
% 0.20/0.48 24[1:Spt:23.0] || -> equal(empty_set,skc2)**.
% 0.20/0.48 25[1:Rew:24.0,20.2] || equal(empty_set,skc3) equal(empty_set,skc2) equal(union(skc2,skc3),skc2)** -> .
% 0.20/0.48 26[1:Rew:24.0,22.1] || -> equal(skc3,skc2) equal(union(skc2,skc3),skc2)**.
% 0.20/0.48 27[1:Rew:24.0,2.0] || member(u,skc2)* -> .
% 0.20/0.48 28[1:Rew:24.0,25.1,24.0,25.0] || equal(skc3,skc2) equal(skc2,skc2) equal(union(skc2,skc3),skc2)** -> .
% 0.20/0.48 29[1:Obv:28.1] || equal(skc3,skc2) equal(union(skc2,skc3),skc2)** -> .
% 0.20/0.48 37[2:Spt:26.0] || -> equal(skc3,skc2)**.
% 0.20/0.49 38[2:Rew:37.0,29.0] || equal(skc2,skc2) equal(union(skc2,skc3),skc2)** -> .
% 0.20/0.49 39[2:Obv:38.0] || equal(union(skc2,skc3),skc2)** -> .
% 0.20/0.49 40[2:Rew:37.0,39.0] || equal(union(skc2,skc2),skc2)** -> .
% 0.20/0.49 44[1:Res:10.1,27.0] || -> subset(skc2,u)*.
% 0.20/0.49 45[0:Res:10.1,7.1] empty(u) || -> subset(u,v)*.
% 0.20/0.49 52[0:Res:12.1,13.0] || member(skf3(union(u,v),w),v)*+ -> subset(x,union(u,v))*.
% 0.20/0.49 58[1:Res:44.0,14.0] || subset(u,skc2)* -> equal(u,skc2).
% 0.20/0.49 59[0:Res:45.1,14.0] empty(u) || subset(v,u)* -> equal(v,u).
% 0.20/0.49 63[1:Res:45.1,58.0] empty(u) || -> equal(u,skc2)*.
% 0.20/0.49 66[0:Res:3.1,15.0] || subset(u,v) -> empty(u) member(skf4(u),v)*.
% 0.20/0.49 76[1:Res:66.2,27.0] || subset(u,skc2)* -> empty(u).
% 0.20/0.49 78[0:Res:66.2,7.1] empty(u) || subset(v,u)* -> empty(v).
% 0.20/0.49 80[1:Res:5.1,76.0] || equal(skc2,u) -> empty(u)*.
% 0.20/0.49 96[0:Res:3.1,18.0] || -> empty(union(u,v)) member(skf4(union(u,v)),u)* member(skf4(union(u,v)),v)*.
% 0.20/0.49 113[1:Res:19.1,27.0] || -> equal(u,skc2) member(skf5(skc2,u),u)*.
% 0.20/0.49 122[1:Res:113.1,15.0] || subset(u,v) -> equal(u,skc2) member(skf5(skc2,u),v)*.
% 0.20/0.49 158[1:Res:122.2,7.1] empty(u) || subset(v,u)* -> equal(v,skc2).
% 0.20/0.49 181[0:Res:10.1,52.0] || -> subset(u,union(v,u))* subset(w,union(v,u))*.
% 0.20/0.49 183[0:Con:181.1] || -> subset(u,union(v,u))*.
% 0.20/0.49 185[0:SpR:6.0,183.0] || -> subset(u,union(u,v))*.
% 0.20/0.49 187[1:Res:183.0,158.1] empty(union(u,v)) || -> equal(v,skc2)*.
% 0.20/0.49 222[1:SoR:187.0,80.1] || equal(union(u,v),skc2)** -> equal(v,skc2).
% 0.20/0.49 276[1:Res:96.1,27.0] || -> empty(union(skc2,u)) member(skf4(union(skc2,u)),u)*.
% 0.20/0.49 286[1:Res:276.1,27.0] || -> empty(union(skc2,skc2))*.
% 0.20/0.49 294[1:EmS:63.0,286.0] || -> equal(union(skc2,skc2),skc2)**.
% 0.20/0.49 305[2:MRR:294.0,40.0] || -> .
% 0.20/0.49 306[2:Spt:305.0,26.0,37.0] || equal(skc3,skc2)** -> .
% 0.20/0.49 307[2:Spt:305.0,26.1] || -> equal(union(skc2,skc3),skc2)**.
% 0.20/0.49 330[2:SpL:307.0,222.0] || equal(skc2,skc2) -> equal(skc3,skc2)**.
% 0.20/0.49 340[2:Obv:330.0] || -> equal(skc3,skc2)**.
% 0.20/0.49 341[2:MRR:340.0,306.0] || -> .
% 0.20/0.49 346[1:Spt:341.0,23.0,24.0] || equal(empty_set,skc2)** -> .
% 0.20/0.49 347[1:Spt:341.0,23.1] || -> equal(union(skc2,skc3),empty_set)**.
% 0.20/0.49 348[1:SpR:347.0,183.0] || -> subset(skc3,empty_set)*.
% 0.20/0.49 349[1:SpR:347.0,11.1] || member(u,skc2) -> member(u,empty_set)*.
% 0.20/0.49 351[1:SpR:347.0,185.0] || -> subset(skc2,empty_set)*.
% 0.20/0.49 352[1:SpR:347.0,96.2] || -> empty(union(skc2,skc3)) member(skf4(union(skc2,skc3)),skc2)* member(skf4(empty_set),skc3).
% 0.20/0.49 353[1:SpR:347.0,12.1] || member(u,skc3) -> member(u,empty_set)*.
% 0.20/0.49 361[1:MRR:349.1,2.0] || member(u,skc2)* -> .
% 0.20/0.49 362[1:MRR:353.1,2.0] || member(u,skc3)* -> .
% 0.20/0.49 363[1:Rew:347.0,352.1,347.0,352.0] || -> empty(empty_set) member(skf4(empty_set),skc2) member(skf4(empty_set),skc3)*.
% 0.20/0.49 364[1:MRR:363.1,363.2,361.0,362.0] || -> empty(empty_set)*.
% 0.20/0.49 369[1:Res:348.0,78.1] empty(empty_set) || -> empty(skc3)*.
% 0.20/0.49 370[1:Res:348.0,59.1] empty(empty_set) || -> equal(empty_set,skc3)**.
% 0.20/0.49 372[1:SSi:369.0,364.0] || -> empty(skc3)*.
% 0.20/0.49 373[1:SSi:370.0,364.0] || -> equal(empty_set,skc3)**.
% 0.20/0.49 378[1:Rew:373.0,346.0] || equal(skc3,skc2)** -> .
% 0.20/0.49 379[1:Rew:373.0,351.0] || -> subset(skc2,skc3)*.
% 0.20/0.49 391[1:Res:379.0,59.1] empty(skc3) || -> equal(skc3,skc2)**.
% 0.20/0.49 394[1:SSi:391.0,372.0] || -> equal(skc3,skc2)**.
% 0.20/0.49 395[1:MRR:394.0,378.0] || -> .
% 0.20/0.49 % SZS output end Refutation
% 0.20/0.49 Formulae used in the proof : empty_set_defn empty_defn equal_defn commutativity_of_union prove_th59 subset_defn union_defn equal_member_defn
% 0.20/0.49
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