TSTP Solution File: SEU301+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU301+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% 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 : Tue Jul 19 14:36:01 EDT 2022
% Result : Theorem 1.39s 1.61s
% Output : Refutation 1.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU301+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : run_spass %d %s
% 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 : Sun Jun 19 16:03:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.39/1.61
% 1.39/1.61 SPASS V 3.9
% 1.39/1.61 SPASS beiseite: Proof found.
% 1.39/1.61 % SZS status Theorem
% 1.39/1.61 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.39/1.61 SPASS derived 4498 clauses, backtracked 1555 clauses, performed 100 splits and kept 3753 clauses.
% 1.39/1.61 SPASS allocated 101212 KBytes.
% 1.39/1.61 SPASS spent 0:00:01.27 on the problem.
% 1.39/1.61 0:00:00.04 for the input.
% 1.39/1.61 0:00:00.06 for the FLOTTER CNF translation.
% 1.39/1.61 0:00:00.07 for inferences.
% 1.39/1.61 0:00:00.04 for the backtracking.
% 1.39/1.61 0:00:00.98 for the reduction.
% 1.39/1.61
% 1.39/1.61
% 1.39/1.61 Here is a proof with depth 7, length 180 :
% 1.39/1.61 % SZS output start Refutation
% 1.39/1.61 1[0:Inp] || -> ordinal(skc18)*.
% 1.39/1.61 2[0:Inp] || -> SkP1(empty_set)*.
% 1.39/1.61 58[0:Inp] || -> empty(empty_set)*.
% 1.39/1.61 59[0:Inp] || -> ordinal(skc43)*.
% 1.39/1.61 61[0:Inp] || SkP1(skc18)* -> .
% 1.39/1.61 63[0:Inp] || -> empty(skf18(u))*.
% 1.39/1.61 78[0:Inp] || empty(omega)* -> .
% 1.39/1.61 79[0:Inp] || -> ordinal(skf28(u))*.
% 1.39/1.61 81[0:Inp] || empty(powerset(u))* -> .
% 1.39/1.61 82[0:Inp] || -> subset(u,skf26(u))*.
% 1.39/1.61 83[0:Inp] || -> SkC0 in(skc43,omega)*.
% 1.39/1.61 86[0:Inp] || -> in(u,succ(u))*.
% 1.39/1.61 87[0:Inp] || -> subset(u,skf17(u,v))*.
% 1.39/1.61 88[0:Inp] || -> SkP1(u) in(u,omega)*.
% 1.39/1.61 89[0:Inp] || -> element(skf18(u),powerset(u))*.
% 1.39/1.61 90[0:Inp] || -> element(skf19(u),powerset(u))*.
% 1.39/1.61 98[0:Inp] || -> element(skf20(u),powerset(u))*.
% 1.39/1.61 102[0:Inp] || -> element(skc46,powerset(powerset(skc43)))*.
% 1.39/1.61 103[0:Inp] || equal(skc46,empty_set) -> SkC0*.
% 1.39/1.61 106[0:Inp] || -> element(skf16(u),powerset(powerset(u)))*.
% 1.39/1.61 107[0:Inp] || empty(skf19(u))* -> empty(u).
% 1.39/1.61 108[0:Inp] || empty(skf20(u))* -> empty(u).
% 1.39/1.61 109[0:Inp] || element(u,omega)* -> epsilon_transitive(u).
% 1.39/1.61 110[0:Inp] || element(u,omega)* -> epsilon_connected(u).
% 1.39/1.61 111[0:Inp] || element(u,omega)* -> ordinal(u).
% 1.39/1.61 112[0:Inp] || element(u,omega)* -> natural(u).
% 1.39/1.61 116[0:Inp] empty(u) || -> equal(u,empty_set)*.
% 1.39/1.61 117[0:Inp] || equal(skf16(u),empty_set)** -> SkP1(u).
% 1.39/1.61 123[0:Inp] || in(u,v) -> element(u,v)*.
% 1.39/1.61 124[0:Inp] empty(u) || in(v,u)* -> .
% 1.39/1.61 130[0:Inp] SkP1(u) ordinal(u) || -> SkP1(succ(u))*.
% 1.39/1.61 131[0:Inp] being_limit_ordinal(u) || -> SkP0(u) in(skf13(u),u)*.
% 1.39/1.61 132[0:Inp] being_limit_ordinal(u) || SkP1(skf13(u))* -> SkP0(u).
% 1.39/1.61 140[0:Inp] || in(u,skc46) -> SkC0 in(skf26(u),skc46)*.
% 1.39/1.61 141[0:Inp] || element(u,v)* -> empty(v) in(u,v).
% 1.39/1.61 145[0:Inp] || in(u,skc46)* equal(skf26(u),u) -> SkC0.
% 1.39/1.61 146[0:Inp] ordinal(u) || -> being_limit_ordinal(u) equal(succ(skf28(u)),u)**.
% 1.39/1.61 147[0:Inp] SkP0(u) ordinal(u) || -> SkP1(u)* equal(u,empty_set).
% 1.39/1.61 149[0:Inp] || in(u,skf16(v)) -> SkP1(v) in(skf17(u,v),skf16(v))*.
% 1.39/1.61 150[0:Inp] || in(u,skf16(v))* equal(skf17(u,v),u) -> SkP1(v).
% 1.39/1.61 152[0:Inp] SkP1(u) || in(u,omega) element(v,powerset(powerset(u)))*+ -> equal(v,empty_set) in(skf15(v),v)*.
% 1.39/1.61 153[0:Inp] ordinal(u) || SkC0 in(u,omega) element(v,powerset(powerset(u)))* -> equal(v,empty_set) in(skf23(v),v)*.
% 1.39/1.61 154[0:Inp] ordinal(u) || in(u,omega) in(u,skc43) element(v,powerset(powerset(u)))*+ -> SkC0 equal(v,empty_set) in(skf25(v),v)*.
% 1.39/1.61 155[0:Inp] SkP1(u) || in(v,w) in(u,omega) element(w,powerset(powerset(u)))*+ subset(skf15(w),v)* -> equal(w,empty_set) equal(v,skf15(w)).
% 1.39/1.61 156[0:Inp] ordinal(u) || SkC0 in(v,w) in(u,omega) element(w,powerset(powerset(u)))* subset(skf23(w),v)* -> equal(w,empty_set) equal(v,skf23(w)).
% 1.39/1.61 157[0:Inp] ordinal(u) || in(v,w) in(u,omega) in(u,skc43) element(w,powerset(powerset(u)))*+ subset(skf25(w),v)* -> SkC0 equal(w,empty_set) equal(v,skf25(w)).
% 1.39/1.61 161[0:Res:2.0,152.0] || element(u,powerset(powerset(empty_set)))*+ in(empty_set,omega) -> equal(u,empty_set) in(skf15(u),u)*.
% 1.39/1.61 164[0:Res:1.0,156.0] || subset(skf23(u),v)* SkC0 in(v,u) in(skc18,omega) element(u,powerset(powerset(skc18)))* -> equal(v,skf23(u)) equal(u,empty_set).
% 1.39/1.61 166[0:Res:1.0,153.0] || SkC0 in(skc18,omega) element(u,powerset(powerset(skc18)))* -> in(skf23(u),u)* equal(u,empty_set).
% 1.39/1.61 182[0:Res:117.1,61.0] || equal(skf16(skc18),empty_set)** -> .
% 1.39/1.61 183[0:Res:88.1,61.0] || -> in(skc18,omega)*.
% 1.39/1.61 184[0:Res:149.2,61.0] || in(u,skf16(skc18)) -> in(skf17(u,skc18),skf16(skc18))*.
% 1.39/1.61 185[0:Res:150.2,61.0] || in(u,skf16(skc18))* equal(skf17(u,skc18),u) -> .
% 1.39/1.61 207[0:Res:87.0,157.1] ordinal(u) || in(u,omega) in(u,skc43) element(v,powerset(powerset(u)))* in(skf17(skf25(v),w),v)*+ -> SkC0 equal(v,empty_set) equal(skf17(skf25(v),w),skf25(v)).
% 1.39/1.61 214[0:Res:106.0,154.3] ordinal(u) || in(u,omega) in(u,skc43) -> SkC0 equal(skf16(u),empty_set) in(skf25(skf16(u)),skf16(u))*.
% 1.39/1.61 216[0:Res:106.0,152.2] SkP1(u) || in(u,omega) -> equal(skf16(u),empty_set) in(skf15(skf16(u)),skf16(u))*.
% 1.39/1.61 252[0:Res:102.0,152.2] SkP1(skc43) || in(skc43,omega) -> equal(skc46,empty_set) in(skf15(skc46),skc46)*.
% 1.39/1.61 260[0:Res:82.0,155.1] SkP1(u) || in(u,omega) element(v,powerset(powerset(u)))*+ in(skf26(skf15(v)),v)* -> equal(v,empty_set) equal(skf26(skf15(v)),skf15(v)).
% 1.39/1.61 261[0:Res:87.0,155.1] SkP1(u) || in(u,omega) element(v,powerset(powerset(u)))* in(skf17(skf15(v),w),v)*+ -> equal(v,empty_set) equal(skf17(skf15(v),w),skf15(v)).
% 1.39/1.61 273[0:MRR:166.1,183.0] || SkC0 element(u,powerset(powerset(skc18)))* -> equal(u,empty_set) in(skf23(u),u)*.
% 1.39/1.61 275[0:MRR:164.3,183.0] || SkC0 in(u,v) element(v,powerset(powerset(skc18)))* subset(skf23(v),u)* -> equal(v,empty_set) equal(u,skf23(v)).
% 1.39/1.61 330[0:Res:106.0,275.3] || subset(skf23(skf16(skc18)),u)* SkC0 in(u,skf16(skc18)) -> equal(u,skf23(skf16(skc18))) equal(skf16(skc18),empty_set).
% 1.39/1.61 332[0:Res:106.0,273.1] || SkC0 -> in(skf23(skf16(skc18)),skf16(skc18))* equal(skf16(skc18),empty_set).
% 1.39/1.61 354[0:Res:183.0,155.2] SkP1(u) || in(u,omega) element(omega,powerset(powerset(u)))* subset(skf15(omega),skc18) -> equal(omega,empty_set) equal(skf15(omega),skc18).
% 1.39/1.61 359[0:MRR:332.2,182.0] || SkC0 -> in(skf23(skf16(skc18)),skf16(skc18))*.
% 1.39/1.61 361[0:MRR:330.4,182.0] || SkC0 in(u,skf16(skc18)) subset(skf23(skf16(skc18)),u)* -> equal(u,skf23(skf16(skc18))).
% 1.39/1.61 364[1:Spt:154.0,154.1,154.2,154.3,154.5,154.6] ordinal(u) || in(u,omega) in(u,skc43) element(v,powerset(powerset(u)))*+ -> equal(v,empty_set) in(skf25(v),v)*.
% 1.39/1.61 366[2:Spt:207.0,207.1,207.2,207.3,207.4,207.6,207.7] ordinal(u) || in(u,omega) in(u,skc43) element(v,powerset(powerset(u)))* in(skf17(skf25(v),w),v)*+ -> equal(v,empty_set) equal(skf17(skf25(v),w),skf25(v)).
% 1.39/1.61 367[3:Spt:214.0,214.1,214.2,214.4,214.5] ordinal(u) || in(u,omega) in(u,skc43) -> equal(skf16(u),empty_set) in(skf25(skf16(u)),skf16(u))*.
% 1.39/1.61 447[0:EmS:116.0,63.0] || -> equal(skf18(u),empty_set)**.
% 1.39/1.61 477[0:Rew:447.0,89.0] || -> element(empty_set,powerset(u))*.
% 1.39/1.61 550[0:Res:123.1,109.0] || in(u,omega)* -> epsilon_transitive(u).
% 1.39/1.61 551[0:Res:123.1,110.0] || in(u,omega)* -> epsilon_connected(u).
% 1.39/1.61 552[0:Res:123.1,111.0] || in(u,omega)* -> ordinal(u).
% 1.39/1.61 553[0:Res:123.1,112.0] || in(u,omega)* -> natural(u).
% 1.39/1.61 560[3:MRR:367.0,552.1] || in(u,omega) in(u,skc43) -> equal(skf16(u),empty_set) in(skf25(skf16(u)),skf16(u))*.
% 1.39/1.61 561[1:MRR:364.0,552.1] || in(u,omega) in(u,skc43) element(v,powerset(powerset(u)))*+ -> equal(v,empty_set) in(skf25(v),v)*.
% 1.39/1.61 563[2:MRR:366.0,552.1] || in(u,omega) in(u,skc43) element(v,powerset(powerset(u)))* in(skf17(skf25(v),w),v)*+ -> equal(v,empty_set) equal(skf17(skf25(v),w),skf25(v)).
% 1.39/1.61 590[0:Res:88.1,552.0] || -> SkP1(u)* ordinal(u).
% 1.39/1.61 592[0:MRR:147.1,590.1] SkP0(u) || -> SkP1(u)* equal(u,empty_set).
% 1.39/1.61 692[0:Res:98.0,141.0] || -> empty(powerset(u)) in(skf20(u),powerset(u))*.
% 1.39/1.61 693[0:Res:90.0,141.0] || -> empty(powerset(u)) in(skf19(u),powerset(u))*.
% 1.39/1.61 694[0:Res:477.0,141.0] || -> empty(powerset(u)) in(empty_set,powerset(u))*.
% 1.39/1.61 697[0:MRR:694.0,81.0] || -> in(empty_set,powerset(u))*.
% 1.39/1.61 698[0:MRR:692.0,81.0] || -> in(skf20(u),powerset(u))*.
% 1.39/1.61 699[0:MRR:693.0,81.0] || -> in(skf19(u),powerset(u))*.
% 1.39/1.61 702[0:Res:697.0,124.1] empty(powerset(u)) || -> .
% 1.39/1.61 705[0:SpR:146.2,86.0] ordinal(u) || -> being_limit_ordinal(u) in(skf28(u),u)*.
% 1.39/1.61 710[0:SpR:146.2,130.2] ordinal(u) SkP1(skf28(u)) ordinal(skf28(u)) || -> being_limit_ordinal(u) SkP1(u)*.
% 1.39/1.61 718[0:SSi:710.2,79.0] ordinal(u) SkP1(skf28(u)) || -> being_limit_ordinal(u) SkP1(u)*.
% 1.39/1.61 719[0:MRR:718.0,590.1] SkP1(skf28(u)) || -> being_limit_ordinal(u) SkP1(u)*.
% 1.39/1.61 1164[0:Res:123.1,161.0] || in(u,powerset(powerset(empty_set)))*+ in(empty_set,omega) -> equal(u,empty_set) in(skf15(u),u)*.
% 1.39/1.61 1229[0:Res:216.3,185.0] SkP1(skc18) || in(skc18,omega) equal(skf17(skf15(skf16(skc18)),skc18),skf15(skf16(skc18)))** -> equal(skf16(skc18),empty_set).
% 1.39/1.61 1231[0:MRR:1229.1,1229.3,183.0,182.0] SkP1(skc18) || equal(skf17(skf15(skf16(skc18)),skc18),skf15(skf16(skc18)))** -> .
% 1.39/1.61 1661[0:Res:102.0,260.2] SkP1(skc43) || in(skc43,omega) in(skf26(skf15(skc46)),skc46)* -> equal(skc46,empty_set) equal(skf26(skf15(skc46)),skf15(skc46)).
% 1.39/1.63 1716[0:Res:184.1,261.3] SkP1(u) || in(skf15(skf16(skc18)),skf16(skc18)) in(u,omega) element(skf16(skc18),powerset(powerset(u)))* -> equal(skf16(skc18),empty_set) equal(skf17(skf15(skf16(skc18)),skc18),skf15(skf16(skc18))).
% 1.39/1.63 1719[0:MRR:1716.1,1716.4,152.4,182.0] SkP1(u) || in(u,omega) element(skf16(skc18),powerset(powerset(u)))* -> equal(skf17(skf15(skf16(skc18)),skc18),skf15(skf16(skc18))).
% 1.39/1.63 1776[4:Spt:354.4] || -> equal(omega,empty_set)**.
% 1.39/1.63 1800[4:Rew:1776.0,78.0] || empty(empty_set)* -> .
% 1.39/1.63 1907[4:MRR:1800.0,58.0] || -> .
% 1.39/1.63 1908[4:Spt:1907.0,354.4,1776.0] || equal(omega,empty_set)** -> .
% 1.39/1.63 1909[4:Spt:1907.0,354.0,354.1,354.2,354.3,354.5] SkP1(u) || in(u,omega) element(omega,powerset(powerset(u)))* subset(skf15(omega),skc18) -> equal(skf15(omega),skc18).
% 1.39/1.63 1912[5:Spt:83.0] || -> SkC0*.
% 1.39/1.63 1913[5:MRR:359.0,1912.0] || -> in(skf23(skf16(skc18)),skf16(skc18))*.
% 1.39/1.63 1915[5:MRR:361.0,1912.0] || in(u,skf16(skc18)) subset(skf23(skf16(skc18)),u)* -> equal(u,skf23(skf16(skc18))).
% 1.39/1.63 1953[5:Res:1913.0,185.0] || equal(skf17(skf23(skf16(skc18)),skc18),skf23(skf16(skc18)))** -> .
% 1.39/1.63 2156[5:Res:87.0,1915.1] || in(skf17(skf23(skf16(skc18)),u),skf16(skc18))* -> equal(skf17(skf23(skf16(skc18)),u),skf23(skf16(skc18))).
% 1.39/1.63 2249[0:Res:698.0,1164.0] || in(empty_set,omega) -> equal(skf20(powerset(empty_set)),empty_set) in(skf15(skf20(powerset(empty_set))),skf20(powerset(empty_set)))*.
% 1.39/1.63 2250[0:Res:699.0,1164.0] || in(empty_set,omega) -> equal(skf19(powerset(empty_set)),empty_set) in(skf15(skf19(powerset(empty_set))),skf19(powerset(empty_set)))*.
% 1.39/1.63 2280[5:Res:149.2,2156.0] || in(skf23(skf16(skc18)),skf16(skc18))* -> SkP1(skc18) equal(skf17(skf23(skf16(skc18)),skc18),skf23(skf16(skc18))).
% 1.39/1.63 2282[5:MRR:2280.0,2280.1,2280.2,1913.0,61.0,1953.0] || -> .
% 1.39/1.63 2283[5:Spt:2282.0,83.0,1912.0] || SkC0* -> .
% 1.39/1.63 2284[5:Spt:2282.0,83.1] || -> in(skc43,omega)*.
% 1.39/1.63 2286[5:MRR:103.1,2283.0] || equal(skc46,empty_set)** -> .
% 1.39/1.63 2287[5:MRR:140.1,2283.0] || in(u,skc46) -> in(skf26(u),skc46)*.
% 1.39/1.63 2288[5:MRR:145.2,2283.0] || in(u,skc46)* equal(skf26(u),u) -> .
% 1.39/1.63 2289[5:MRR:252.1,252.2,2284.0,2286.0] SkP1(skc43) || -> in(skf15(skc46),skc46)*.
% 1.39/1.63 2291[5:MRR:1661.1,1661.3,2284.0,2286.0] SkP1(skc43) || in(skf26(skf15(skc46)),skc46)* -> equal(skf26(skf15(skc46)),skf15(skc46)).
% 1.39/1.63 2295[5:Res:2284.0,553.0] || -> natural(skc43)*.
% 1.39/1.63 2297[5:Res:2284.0,551.0] || -> epsilon_connected(skc43)*.
% 1.39/1.63 2298[5:Res:2284.0,550.0] || -> epsilon_transitive(skc43)*.
% 1.39/1.63 2519[6:Spt:2250.1] || -> equal(skf19(powerset(empty_set)),empty_set)**.
% 1.39/1.63 2526[6:SpL:2519.0,107.0] || empty(empty_set) -> empty(powerset(empty_set))*.
% 1.39/1.63 2528[6:MRR:2526.0,2526.1,58.0,702.0] || -> .
% 1.39/1.63 2529[6:Spt:2528.0,2250.1,2519.0] || equal(skf19(powerset(empty_set)),empty_set)** -> .
% 1.39/1.63 2530[6:Spt:2528.0,2250.0,2250.2] || in(empty_set,omega) -> in(skf15(skf19(powerset(empty_set))),skf19(powerset(empty_set)))*.
% 1.39/1.63 2550[7:Spt:2249.1] || -> equal(skf20(powerset(empty_set)),empty_set)**.
% 1.39/1.63 2556[7:SpL:2550.0,108.0] || empty(empty_set) -> empty(powerset(empty_set))*.
% 1.39/1.63 2558[7:MRR:2556.0,2556.1,58.0,702.0] || -> .
% 1.39/1.63 2559[7:Spt:2558.0,2249.1,2550.0] || equal(skf20(powerset(empty_set)),empty_set)** -> .
% 1.39/1.63 2560[7:Spt:2558.0,2249.0,2249.2] || in(empty_set,omega) -> in(skf15(skf20(powerset(empty_set))),skf20(powerset(empty_set)))*.
% 1.39/1.63 2618[3:Res:560.3,150.0] || in(u,omega) in(u,skc43) equal(skf17(skf25(skf16(u)),u),skf25(skf16(u)))** -> equal(skf16(u),empty_set) SkP1(u).
% 1.39/1.63 2619[3:MRR:2618.0,2618.3,88.1,117.0] || in(u,skc43) equal(skf17(skf25(skf16(u)),u),skf25(skf16(u)))** -> SkP1(u).
% 1.39/1.63 2808[0:Res:106.0,1719.2] SkP1(skc18) || in(skc18,omega) -> equal(skf17(skf15(skf16(skc18)),skc18),skf15(skf16(skc18)))**.
% 1.39/1.63 2810[0:MRR:2808.1,2808.2,183.0,1231.1] SkP1(skc18) || -> .
% 1.39/1.63 3197[2:Res:149.2,563.3] || in(skf25(skf16(u)),skf16(u))* in(v,omega) in(v,skc43) element(skf16(u),powerset(powerset(v)))* -> SkP1(u) equal(skf16(u),empty_set) equal(skf17(skf25(skf16(u)),u),skf25(skf16(u))).
% 1.39/1.63 3199[2:MRR:3197.0,3197.5,561.4,117.0] || in(u,omega) in(u,skc43) element(skf16(v),powerset(powerset(u)))*+ -> SkP1(v) equal(skf17(skf25(skf16(v)),v),skf25(skf16(v)))**.
% 1.39/1.63 3202[2:Res:106.0,3199.2] || in(u,omega) in(u,skc43) -> SkP1(u) equal(skf17(skf25(skf16(u)),u),skf25(skf16(u)))**.
% 1.39/1.63 3204[3:MRR:3202.0,3202.3,88.1,2619.1] || in(u,skc43)* -> SkP1(u).
% 1.39/1.63 3205[3:Res:131.2,3204.0] being_limit_ordinal(skc43) || -> SkP0(skc43) SkP1(skf13(skc43))*.
% 1.39/1.63 3207[3:Res:705.2,3204.0] ordinal(skc43) || -> being_limit_ordinal(skc43) SkP1(skf28(skc43))*.
% 1.39/1.63 3208[3:MRR:3205.2,132.1] being_limit_ordinal(skc43) || -> SkP0(skc43)*.
% 1.39/1.63 3209[5:SSi:3207.0,59.0,2295.0,2297.0,2298.0] || -> being_limit_ordinal(skc43) SkP1(skf28(skc43))*.
% 1.39/1.63 3239[5:SoR:719.0,3209.1] || -> being_limit_ordinal(skc43) SkP1(skc43)* being_limit_ordinal(skc43).
% 1.39/1.63 3240[5:Obv:3239.0] || -> SkP1(skc43)* being_limit_ordinal(skc43).
% 1.39/1.63 3241[8:Spt:3240.0] || -> SkP1(skc43)*.
% 1.39/1.63 3243[8:MRR:2289.0,3241.0] || -> in(skf15(skc46),skc46)*.
% 1.39/1.63 3244[8:MRR:2291.0,3241.0] || in(skf26(skf15(skc46)),skc46)* -> equal(skf26(skf15(skc46)),skf15(skc46)).
% 1.39/1.63 3247[8:Res:3243.0,2288.0] || equal(skf26(skf15(skc46)),skf15(skc46))** -> .
% 1.39/1.63 3254[8:MRR:3244.1,3247.0] || in(skf26(skf15(skc46)),skc46)* -> .
% 1.39/1.63 3261[8:Res:2287.1,3254.0] || in(skf15(skc46),skc46)* -> .
% 1.39/1.63 3262[8:MRR:3261.0,3243.0] || -> .
% 1.39/1.63 3263[8:Spt:3262.0,3240.0,3241.0] || SkP1(skc43)* -> .
% 1.39/1.63 3264[8:Spt:3262.0,3240.1] || -> being_limit_ordinal(skc43)*.
% 1.39/1.63 3265[8:MRR:3208.0,3264.0] || -> SkP0(skc43)*.
% 1.39/1.63 3271[8:Res:592.1,3263.0] SkP0(skc43) || -> equal(skc43,empty_set)**.
% 1.39/1.63 3275[8:SSi:3271.0,59.0,2295.0,2297.0,2298.0,3264.0,3265.0] || -> equal(skc43,empty_set)**.
% 1.39/1.63 3326[8:Rew:3275.0,3263.0] || SkP1(empty_set)* -> .
% 1.39/1.63 3396[8:MRR:3326.0,2.0] || -> .
% 1.39/1.63 3398[3:Spt:3396.0,214.3] || -> SkC0*.
% 1.39/1.63 3399[3:MRR:359.0,3398.0] || -> in(skf23(skf16(skc18)),skf16(skc18))*.
% 1.39/1.63 3402[3:MRR:361.0,3398.0] || in(u,skf16(skc18)) subset(skf23(skf16(skc18)),u)* -> equal(u,skf23(skf16(skc18))).
% 1.39/1.63 3677[3:Res:3399.0,185.0] || equal(skf17(skf23(skf16(skc18)),skc18),skf23(skf16(skc18)))** -> .
% 1.39/1.63 3975[3:Res:87.0,3402.1] || in(skf17(skf23(skf16(skc18)),u),skf16(skc18))* -> equal(skf17(skf23(skf16(skc18)),u),skf23(skf16(skc18))).
% 1.39/1.63 4079[3:Res:149.2,3975.0] || in(skf23(skf16(skc18)),skf16(skc18))* -> SkP1(skc18) equal(skf17(skf23(skf16(skc18)),skc18),skf23(skf16(skc18))).
% 1.39/1.63 4081[3:MRR:4079.0,4079.1,4079.2,3399.0,2810.0,3677.0] || -> .
% 1.39/1.63 4082[2:Spt:4081.0,207.5] || -> SkC0*.
% 1.39/1.63 4083[2:MRR:359.0,4082.0] || -> in(skf23(skf16(skc18)),skf16(skc18))*.
% 1.39/1.63 4086[2:MRR:361.0,4082.0] || in(u,skf16(skc18)) subset(skf23(skf16(skc18)),u)* -> equal(u,skf23(skf16(skc18))).
% 1.39/1.63 4359[2:Res:4083.0,185.0] || equal(skf17(skf23(skf16(skc18)),skc18),skf23(skf16(skc18)))** -> .
% 1.39/1.63 4642[2:Res:87.0,4086.1] || in(skf17(skf23(skf16(skc18)),u),skf16(skc18))* -> equal(skf17(skf23(skf16(skc18)),u),skf23(skf16(skc18))).
% 1.39/1.63 4747[2:Res:149.2,4642.0] || in(skf23(skf16(skc18)),skf16(skc18))* -> SkP1(skc18) equal(skf17(skf23(skf16(skc18)),skc18),skf23(skf16(skc18))).
% 1.39/1.63 4749[2:MRR:4747.0,4747.1,4747.2,4083.0,2810.0,4359.0] || -> .
% 1.39/1.63 4750[1:Spt:4749.0,154.4] || -> SkC0*.
% 1.39/1.63 4751[1:MRR:359.0,4750.0] || -> in(skf23(skf16(skc18)),skf16(skc18))*.
% 1.39/1.63 4754[1:MRR:361.0,4750.0] || in(u,skf16(skc18)) subset(skf23(skf16(skc18)),u)* -> equal(u,skf23(skf16(skc18))).
% 1.39/1.63 4991[1:Res:4751.0,185.0] || equal(skf17(skf23(skf16(skc18)),skc18),skf23(skf16(skc18)))** -> .
% 1.39/1.63 5198[1:Res:87.0,4754.1] || in(skf17(skf23(skf16(skc18)),u),skf16(skc18))* -> equal(skf17(skf23(skf16(skc18)),u),skf23(skf16(skc18))).
% 1.39/1.63 5324[1:Res:149.2,5198.0] || in(skf23(skf16(skc18)),skf16(skc18))* -> SkP1(skc18) equal(skf17(skf23(skf16(skc18)),skc18),skf23(skf16(skc18))).
% 1.39/1.63 5326[1:MRR:5324.0,5324.1,5324.2,4751.0,2810.0,4991.0] || -> .
% 1.39/1.63 % SZS output end Refutation
% 1.39/1.63 Formulae used in the proof : s1_ordinal2__e18_27__finset_1 fc4_relat_1 cc3_ordinal1 existence_m1_subset_1 reflexivity_r1_tarski fc1_xboole_0 s2_ordinal1__e18_27__finset_1__1 rc2_finset_1 fc1_ordinal2 t42_ordinal1 fc1_subset_1 t10_ordinal1 rc3_finset_1 rc1_subset_1 cc3_arytm_3 t6_boole t1_subset t7_boole t2_subset
% 1.39/1.63
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