TSTP Solution File: SYO605+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SYO605+1 : TPTP v8.1.0. Released v7.0.0.
% 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 : Thu Jul 21 19:55:02 EDT 2022
% Result : Theorem 0.60s 0.82s
% Output : Refutation 0.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO605+1 : TPTP v8.1.0. Released v7.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n026.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 : Fri Jul 8 21:44:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.60/0.82
% 0.60/0.82 SPASS V 3.9
% 0.60/0.82 SPASS beiseite: Proof found.
% 0.60/0.82 % SZS status Theorem
% 0.60/0.82 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.60/0.82 SPASS derived 3842 clauses, backtracked 521 clauses, performed 30 splits and kept 1622 clauses.
% 0.60/0.82 SPASS allocated 100190 KBytes.
% 0.60/0.82 SPASS spent 0:00:00.46 on the problem.
% 0.60/0.82 0:00:00.03 for the input.
% 0.60/0.82 0:00:00.04 for the FLOTTER CNF translation.
% 0.60/0.82 0:00:00.05 for inferences.
% 0.60/0.82 0:00:00.02 for the backtracking.
% 0.60/0.82 0:00:00.28 for the reduction.
% 0.60/0.82
% 0.60/0.82
% 0.60/0.82 Here is a proof with depth 15, length 233 :
% 0.60/0.82 % SZS output start Refutation
% 0.60/0.82 1[0:Inp] || SkP0(skc3,u)* -> .
% 0.60/0.82 2[0:Inp] || SkP1(skc3,u)* -> .
% 0.60/0.82 3[0:Inp] || SkP3(u,skf11(u),v)* -> .
% 0.60/0.82 4[0:Inp] || SkP4(u,skf11(u),v)* -> .
% 0.60/0.82 8[0:Inp] || SkP5(u,v)*+ -> g_true_only(v,v)*.
% 0.60/0.82 10[0:Inp] || g_both(u,v) -> g_true(u,v)*.
% 0.60/0.82 11[0:Inp] || g_both(u,v) -> g_false(u,v)*.
% 0.60/0.82 12[0:Inp] || g_false_only(u,v) -> g_false(u,v)*.
% 0.60/0.82 13[0:Inp] || g_true_only(u,u)*+ g_false_only(u,skc3)* -> .
% 0.60/0.82 14[0:Inp] || g_both(u,u)*+ g_false_only(u,skc3)* -> .
% 0.60/0.82 16[0:Inp] || SkC2+ -> g_false_only(u,u)* SkP5(skc7,u)*.
% 0.60/0.82 20[0:Inp] || SkP6(u,v,w)* -> g_false_only(w,u).
% 0.60/0.82 21[0:Inp] || g_true_only(u,v) g_false(u,v)* -> .
% 0.60/0.82 22[0:Inp] || g_false_only(u,v) g_true(u,v)* -> .
% 0.60/0.82 23[0:Inp] || g_false_only(u,v) g_false_only(u,skf11(v))* -> .
% 0.60/0.82 24[0:Inp] || g_both(u,v) g_false_only(u,skf11(v))* -> .
% 0.60/0.82 25[0:Inp] || -> g_false_only(u,v)* g_both(u,v) g_true_only(u,v).
% 0.60/0.82 26[0:Inp] || SkP0(u,v)*+ -> g_false_only(v,v)* g_both(v,v).
% 0.60/0.82 30[0:Inp] || g_true_only(u,v)+ g_both(u,u)* -> SkP0(v,u)*.
% 0.60/0.82 31[0:Inp] || g_true_only(u,v)+ g_false_only(u,u)* -> SkP0(v,u)*.
% 0.60/0.82 32[0:Inp] || g_both(u,v)+ g_true_only(u,u)* -> SkP1(v,u)*.
% 0.60/0.82 33[0:Inp] || g_both(u,v)+ g_false_only(u,u)* -> SkP1(v,u)*.
% 0.60/0.82 37[0:Inp] SkP2(u) || -> SkC1 g_true_only(v,u) SkP6(u,skf18(u),v)*.
% 0.60/0.82 38[0:Inp] || g_true_only(u,v) g_both(u,w) -> SkP3(w,v,u)*.
% 0.60/0.82 39[0:Inp] || g_true_only(u,v) g_true_only(u,w) -> SkP3(w,v,u)*.
% 0.60/0.82 40[0:Inp] || g_both(u,v) g_false_only(u,w) -> SkP4(w,v,u)*.
% 0.60/0.82 43[0:Inp] || SkC1 SkC0 -> SkC2 g_false_only(skf14(u),u) SkP4(skc4,u,skf13(u))* SkP3(skc4,u,skf12(u)).
% 0.60/0.82 44[0:Inp] || g_both(u,u)*+ g_both(u,v)* -> SkC0 SkP1(v,skf16(v))* SkP0(v,skf15(v)) g_false_only(skf17(v),v).
% 0.60/0.82 45[0:Inp] || SkC1 SkC0 -> SkC2 g_both(skf14(u),skc4) g_false_only(skf14(u),skc4)* SkP4(skc4,v,skf13(v))* SkP3(skc4,v,skf12(v)).
% 0.60/0.82 46[0:Inp] || g_both(u,v)*+ g_both(u,w)* -> SkP2(v) g_false_only(skf21(w,x),w)* SkP4(v,w,skf20(w,v))* SkP3(v,w,skf19(w,v)).
% 0.60/0.82 47[0:Inp] || g_both(u,u)*+ g_both(u,v)* -> SkC0 SkP1(v,skf16(v))* SkP0(v,skf15(v)) g_both(skf17(w),skf17(w))* g_true_only(skf17(w),skf17(w)).
% 0.60/0.82 48[0:Inp] || g_both(u,v)*+ g_both(u,w)* -> SkP2(v) g_both(skf21(w,v),v) g_false_only(skf21(w,v),v) SkP4(v,w,skf20(w,v))* SkP3(v,w,skf19(w,v)).
% 0.60/0.82 51[1:Spt:37.0,37.2,37.3] SkP2(u) || -> g_true_only(v,u) SkP6(u,skf18(u),v)*.
% 0.60/0.82 53[2:Spt:47.0,47.1,47.3,47.4] || g_both(u,u)*+ g_both(u,v)* -> SkP1(v,skf16(v))* SkP0(v,skf15(v)).
% 0.60/0.82 59[0:Res:11.1,21.1] || g_both(u,v)* g_true_only(u,v) -> .
% 0.60/0.82 60[0:Res:12.1,21.1] || g_false_only(u,v)* g_true_only(u,v) -> .
% 0.60/0.82 61[0:Res:10.1,22.1] || g_both(u,v) g_false_only(u,v)* -> .
% 0.60/0.82 67[1:Res:51.2,20.0] SkP2(u) || -> g_true_only(v,u) g_false_only(v,u)*.
% 0.60/0.82 68[1:Res:67.2,61.1] SkP2(u) || g_both(v,u)* -> g_true_only(v,u).
% 0.60/0.82 72[1:MRR:68.2,59.1] SkP2(u) || g_both(v,u)* -> .
% 0.60/0.82 73[1:MRR:46.2,72.0] || g_both(u,v)*+ g_both(u,w)* -> g_false_only(skf21(w,x),w)* SkP4(v,w,skf20(w,v))* SkP3(v,w,skf19(w,v)).
% 0.60/0.82 74[1:MRR:48.2,72.0] || g_both(u,v)*+ g_both(u,w)* -> g_both(skf21(w,v),v) g_false_only(skf21(w,v),v) SkP4(v,w,skf20(w,v))* SkP3(v,w,skf19(w,v)).
% 0.60/0.82 77[0:Res:25.0,24.1] || g_both(u,v) -> g_both(u,skf11(v))* g_true_only(u,skf11(v)).
% 0.60/0.82 78[0:Res:25.0,23.1] || g_false_only(u,v) -> g_both(u,skf11(v))* g_true_only(u,skf11(v)).
% 0.60/0.82 94[0:Res:39.2,3.0] || g_true_only(u,skf11(v))* g_true_only(u,v) -> .
% 0.60/0.82 97[0:Res:77.1,14.0] || g_both(skf11(u),u) g_false_only(skf11(u),skc3) -> g_true_only(skf11(u),skf11(u))*.
% 0.60/0.82 98[2:Res:77.1,53.0] || g_both(skf11(u),u) g_both(skf11(u),v)* -> g_true_only(skf11(u),skf11(u))* SkP1(v,skf16(v))* SkP0(v,skf15(v)).
% 0.60/0.82 103[0:MRR:97.2,13.0] || g_both(skf11(u),u)*+ g_false_only(skf11(u),skc3)* -> .
% 0.60/0.82 105[0:Res:78.1,14.0] || g_false_only(skf11(u),u) g_false_only(skf11(u),skc3) -> g_true_only(skf11(u),skf11(u))*.
% 0.60/0.82 112[0:MRR:105.2,13.0] || g_false_only(skf11(u),u)*+ g_false_only(skf11(u),skc3)* -> .
% 0.60/0.82 118[0:Res:25.0,112.0] || g_false_only(skf11(u),skc3)* -> g_both(skf11(u),u)* g_true_only(skf11(u),u).
% 0.60/0.82 121[0:MRR:118.1,103.0] || g_false_only(skf11(u),skc3)*+ -> g_true_only(skf11(u),u)*.
% 0.60/0.82 122[0:Res:25.0,121.0] || -> g_both(skf11(u),skc3)* g_true_only(skf11(u),skc3) g_true_only(skf11(u),u)*.
% 0.60/0.82 124[0:Res:40.2,4.0] || g_both(u,skf11(v))* g_false_only(u,v) -> .
% 0.60/0.82 127[0:MRR:78.1,124.0] || g_false_only(u,v) -> g_true_only(u,skf11(v))*.
% 0.60/0.82 128[0:Res:127.1,30.0] || g_false_only(u,v)+ g_both(u,u)* -> SkP0(skf11(v),u)*.
% 0.60/0.82 129[0:Res:127.1,31.0] || g_false_only(u,v)+ g_false_only(u,u)* -> SkP0(skf11(v),u)*.
% 0.60/0.82 134[0:Res:122.0,32.0] || g_true_only(skf11(u),skf11(u))* -> g_true_only(skf11(u),skc3) g_true_only(skf11(u),u) SkP1(skc3,skf11(u)).
% 0.60/0.82 139[0:Res:122.2,31.0] || g_false_only(skf11(u),skf11(u))* -> g_both(skf11(u),skc3) g_true_only(skf11(u),skc3) SkP0(u,skf11(u)).
% 0.60/0.82 143[0:MRR:134.2,134.3,94.1,2.0] || g_true_only(skf11(u),skf11(u))* -> g_true_only(skf11(u),skc3).
% 0.60/0.82 145[0:Res:38.2,3.0] || g_true_only(u,skf11(v))* g_both(u,v) -> .
% 0.60/0.82 152[2:MRR:98.2,145.0] || g_both(skf11(u),u)*+ g_both(skf11(u),v)* -> SkP1(v,skf16(v))* SkP0(v,skf15(v)).
% 0.60/0.82 187[1:Res:122.0,73.0] || g_both(skf11(u),v)*+ -> g_true_only(skf11(u),skc3) g_true_only(skf11(u),u)* g_false_only(skf21(v,w),v)* SkP4(skc3,v,skf20(v,skc3))* SkP3(skc3,v,skf19(v,skc3)).
% 0.60/0.82 290[1:Res:122.0,74.0] || g_both(skf11(u),v)*+ -> g_true_only(skf11(u),skc3) g_true_only(skf11(u),u)* g_both(skf21(v,skc3),skc3) g_false_only(skf21(v,skc3),skc3) SkP4(skc3,v,skf20(v,skc3))* SkP3(skc3,v,skf19(v,skc3)).
% 0.60/0.82 315[0:Res:25.0,129.0] || g_false_only(u,u)*+ -> g_both(u,v) g_true_only(u,v) SkP0(skf11(v),u)*.
% 0.60/0.82 323[0:Res:25.0,128.0] || g_both(u,u)*+ -> g_both(u,v) g_true_only(u,v) SkP0(skf11(v),u)*.
% 0.60/0.82 341[2:Res:122.0,152.0] || g_both(skf11(skc3),u) -> g_true_only(skf11(skc3),skc3) g_true_only(skf11(skc3),skc3) SkP1(u,skf16(u))* SkP0(u,skf15(u)).
% 0.60/0.82 342[2:Obv:341.1] || g_both(skf11(skc3),u) -> g_true_only(skf11(skc3),skc3) SkP1(u,skf16(u))* SkP0(u,skf15(u)).
% 0.60/0.82 435[0:Res:25.0,315.0] || -> g_both(u,u)* g_true_only(u,u) g_both(u,v) g_true_only(u,v) SkP0(skf11(v),u)*.
% 0.60/0.82 437[0:MRR:435.0,323.0] || -> g_true_only(u,u)* g_both(u,v) g_true_only(u,v) SkP0(skf11(v),u)*.
% 0.60/0.82 440[0:Res:437.0,13.0] || g_false_only(u,skc3) -> g_both(u,v) g_true_only(u,v) SkP0(skf11(v),u)*.
% 0.60/0.82 466[0:Res:440.3,26.0] || g_false_only(u,skc3)* -> g_both(u,v)* g_true_only(u,v) g_false_only(u,u)* g_both(u,u).
% 0.60/0.82 468[0:MRR:466.4,14.0] || g_false_only(u,skc3)*+ -> g_both(u,v)* g_true_only(u,v) g_false_only(u,u)*.
% 0.60/0.82 469[0:Res:25.0,468.0] || -> g_both(u,skc3) g_true_only(u,skc3) g_both(u,v)* g_true_only(u,v) g_false_only(u,u)*.
% 0.60/0.82 471[0:Con:469.2] || -> g_both(u,skc3) g_true_only(u,skc3) g_false_only(u,u)*.
% 0.60/0.82 472[0:MRR:139.0,471.2] || -> g_both(skf11(u),skc3) g_true_only(skf11(u),skc3) SkP0(u,skf11(u))*.
% 0.60/0.82 480[0:Res:471.2,24.1] || g_both(skf11(u),u)*+ -> g_both(skf11(u),skc3)* g_true_only(skf11(u),skc3).
% 0.60/0.82 513[0:Res:472.2,1.0] || -> g_both(skf11(skc3),skc3)* g_true_only(skf11(skc3),skc3).
% 0.60/0.82 516[3:Spt:513.1] || -> g_true_only(skf11(skc3),skc3)*.
% 0.60/0.82 517[3:Res:516.0,30.0] || g_both(skf11(skc3),skf11(skc3))* -> SkP0(skc3,skf11(skc3)).
% 0.60/0.82 518[3:Res:516.0,31.0] || g_false_only(skf11(skc3),skf11(skc3))* -> SkP0(skc3,skf11(skc3)).
% 0.60/0.82 519[3:MRR:517.1,1.0] || g_both(skf11(skc3),skf11(skc3))* -> .
% 0.60/0.82 520[3:MRR:518.1,1.0] || g_false_only(skf11(skc3),skf11(skc3))* -> .
% 0.60/0.82 532[3:Res:25.0,520.0] || -> g_both(skf11(skc3),skf11(skc3))* g_true_only(skf11(skc3),skf11(skc3)).
% 0.60/0.82 535[3:MRR:532.0,519.0] || -> g_true_only(skf11(skc3),skf11(skc3))*.
% 0.60/0.82 541[3:Res:535.0,94.0] || g_true_only(skf11(skc3),skc3)* -> .
% 0.60/0.82 543[3:MRR:541.0,516.0] || -> .
% 0.60/0.82 544[3:Spt:543.0,513.1,516.0] || g_true_only(skf11(skc3),skc3)* -> .
% 0.60/0.82 545[3:Spt:543.0,513.0] || -> g_both(skf11(skc3),skc3)*.
% 0.60/0.82 547[3:MRR:342.1,544.0] || g_both(skf11(skc3),u) -> SkP1(u,skf16(u))* SkP0(u,skf15(u)).
% 0.60/0.82 666[0:Res:122.0,480.0] || -> g_true_only(skf11(skc3),skc3) g_true_only(skf11(skc3),skc3) g_both(skf11(skc3),skc3)* g_true_only(skf11(skc3),skc3).
% 0.60/0.82 669[0:Obv:666.1] || -> g_both(skf11(skc3),skc3)* g_true_only(skf11(skc3),skc3).
% 0.60/0.82 676[3:Res:547.1,2.0] || g_both(skf11(skc3),skc3) -> SkP0(skc3,skf15(skc3))*.
% 0.60/0.82 679[3:MRR:676.0,676.1,545.0,1.0] || -> .
% 0.60/0.82 680[2:Spt:679.0,47.2,47.5,47.6] || -> SkC0 g_both(skf17(u),skf17(u))* g_true_only(skf17(u),skf17(u)).
% 0.60/0.82 713[3:Spt:43.2] || -> SkC2*.
% 0.60/0.82 716[3:MRR:16.0,713.0] || -> g_false_only(u,u)* SkP5(skc7,u)*.
% 0.60/0.82 762[3:Res:716.1,8.0] || -> g_false_only(u,u)* g_true_only(u,u).
% 0.60/0.82 785[3:Res:762.0,24.1] || g_both(skf11(u),u) -> g_true_only(skf11(u),skf11(u))*.
% 0.60/0.82 796[3:MRR:785.1,145.0] || g_both(skf11(u),u)* -> .
% 0.60/0.82 798[3:MRR:669.0,796.0] || -> g_true_only(skf11(skc3),skc3)*.
% 0.60/0.82 800[3:Res:798.0,31.0] || g_false_only(skf11(skc3),skf11(skc3))* -> SkP0(skc3,skf11(skc3)).
% 0.60/0.82 801[3:MRR:800.1,1.0] || g_false_only(skf11(skc3),skf11(skc3))* -> .
% 0.60/0.82 805[3:Res:762.0,801.0] || -> g_true_only(skf11(skc3),skf11(skc3))*.
% 0.60/0.82 825[3:Res:805.0,94.0] || g_true_only(skf11(skc3),skc3)* -> .
% 0.60/0.82 827[3:MRR:825.0,798.0] || -> .
% 0.60/0.82 828[3:Spt:827.0,43.2,713.0] || SkC2* -> .
% 0.60/0.82 829[3:Spt:827.0,43.0,43.1,43.3,43.4,43.5] || SkC1 SkC0 -> g_false_only(skf14(u),u) SkP4(skc4,u,skf13(u))* SkP3(skc4,u,skf12(u)).
% 0.60/0.82 849[0:Res:669.0,33.0] || g_false_only(skf11(skc3),skf11(skc3))* -> g_true_only(skf11(skc3),skc3) SkP1(skc3,skf11(skc3)).
% 0.60/0.82 853[0:MRR:849.2,2.0] || g_false_only(skf11(skc3),skf11(skc3))* -> g_true_only(skf11(skc3),skc3).
% 0.60/0.82 896[0:Res:25.0,853.0] || -> g_both(skf11(skc3),skf11(skc3))* g_true_only(skf11(skc3),skf11(skc3)) g_true_only(skf11(skc3),skc3).
% 0.60/0.82 901[0:MRR:896.1,143.0] || -> g_both(skf11(skc3),skf11(skc3))* g_true_only(skf11(skc3),skc3).
% 0.60/0.82 902[4:Spt:901.1] || -> g_true_only(skf11(skc3),skc3)*.
% 0.60/0.82 903[4:Res:902.0,30.0] || g_both(skf11(skc3),skf11(skc3))* -> SkP0(skc3,skf11(skc3)).
% 0.60/0.82 904[4:Res:902.0,31.0] || g_false_only(skf11(skc3),skf11(skc3))* -> SkP0(skc3,skf11(skc3)).
% 0.60/0.82 905[4:MRR:903.1,1.0] || g_both(skf11(skc3),skf11(skc3))* -> .
% 0.60/0.82 906[4:MRR:904.1,1.0] || g_false_only(skf11(skc3),skf11(skc3))* -> .
% 0.60/0.82 916[4:Res:25.0,906.0] || -> g_both(skf11(skc3),skf11(skc3))* g_true_only(skf11(skc3),skf11(skc3)).
% 0.60/0.82 919[4:MRR:916.0,905.0] || -> g_true_only(skf11(skc3),skf11(skc3))*.
% 0.60/0.82 925[4:Res:919.0,94.0] || g_true_only(skf11(skc3),skc3)* -> .
% 0.60/0.82 927[4:MRR:925.0,902.0] || -> .
% 0.60/0.82 928[4:Spt:927.0,901.1,902.0] || g_true_only(skf11(skc3),skc3)* -> .
% 0.60/0.82 929[4:Spt:927.0,901.0] || -> g_both(skf11(skc3),skf11(skc3))*.
% 0.60/0.82 3302[4:Res:929.0,187.0] || -> g_true_only(skf11(skc3),skc3) g_true_only(skf11(skc3),skc3) g_false_only(skf21(skf11(skc3),u),skf11(skc3))* SkP4(skc3,skf11(skc3),skf20(skf11(skc3),skc3))* SkP3(skc3,skf11(skc3),skf19(skf11(skc3),skc3)).
% 0.60/0.82 3308[4:Obv:3302.0] || -> g_true_only(skf11(skc3),skc3) g_false_only(skf21(skf11(skc3),u),skf11(skc3))* SkP4(skc3,skf11(skc3),skf20(skf11(skc3),skc3))* SkP3(skc3,skf11(skc3),skf19(skf11(skc3),skc3)).
% 0.60/0.82 3309[4:MRR:3308.0,3308.2,3308.3,928.0,4.0,3.0] || -> g_false_only(skf21(skf11(skc3),u),skf11(skc3))*.
% 0.60/0.82 3377[4:Res:3309.0,24.1] || g_both(skf21(skf11(skc3),u),skc3)* -> .
% 0.60/0.82 3378[4:Res:3309.0,23.1] || g_false_only(skf21(skf11(skc3),u),skc3)* -> .
% 0.60/0.82 3394[4:Res:929.0,290.0] || -> g_true_only(skf11(skc3),skc3) g_true_only(skf11(skc3),skc3) g_both(skf21(skf11(skc3),skc3),skc3) g_false_only(skf21(skf11(skc3),skc3),skc3) SkP4(skc3,skf11(skc3),skf20(skf11(skc3),skc3))* SkP3(skc3,skf11(skc3),skf19(skf11(skc3),skc3)).
% 0.60/0.82 3399[4:Obv:3394.0] || -> g_true_only(skf11(skc3),skc3) g_both(skf21(skf11(skc3),skc3),skc3) g_false_only(skf21(skf11(skc3),skc3),skc3) SkP4(skc3,skf11(skc3),skf20(skf11(skc3),skc3))* SkP3(skc3,skf11(skc3),skf19(skf11(skc3),skc3)).
% 0.60/0.82 3400[4:MRR:3399.0,3399.1,3399.2,3399.3,3399.4,928.0,3377.0,3378.0,4.0,3.0] || -> .
% 0.60/0.82 3407[1:Spt:3400.0,37.1] || -> SkC1*.
% 0.60/0.82 3408[1:MRR:43.0,3407.0] || SkC0 -> SkC2 g_false_only(skf14(u),u) SkP4(skc4,u,skf13(u))* SkP3(skc4,u,skf12(u)).
% 0.60/0.82 3409[1:MRR:45.0,3407.0] || SkC0 -> SkC2 g_both(skf14(u),skc4) g_false_only(skf14(u),skc4)* SkP4(skc4,v,skf13(v))* SkP3(skc4,v,skf12(v)).
% 0.60/0.82 3410[2:Spt:44.0,44.1,44.3,44.4,44.5] || g_both(u,u)*+ g_both(u,v)* -> SkP1(v,skf16(v))* SkP0(v,skf15(v)) g_false_only(skf17(v),v).
% 0.60/0.82 3413[3:Spt:47.0,47.1,47.3,47.4] || g_both(u,u)*+ g_both(u,v)* -> SkP1(v,skf16(v))* SkP0(v,skf15(v)).
% 0.60/0.82 3418[4:Spt:669.0] || -> g_both(skf11(skc3),skc3)*.
% 0.60/0.82 3435[4:Res:3418.0,59.0] || g_true_only(skf11(skc3),skc3)* -> .
% 0.60/0.82 3440[4:MRR:901.1,3435.0] || -> g_both(skf11(skc3),skf11(skc3))*.
% 0.60/0.82 3465[4:Res:3440.0,3413.0] || g_both(skf11(skc3),u) -> SkP1(u,skf16(u))* SkP0(u,skf15(u)).
% 0.60/0.82 3730[4:Res:3465.1,2.0] || g_both(skf11(skc3),skc3) -> SkP0(skc3,skf15(skc3))*.
% 0.60/0.82 3733[4:MRR:3730.0,3730.1,3418.0,1.0] || -> .
% 0.60/0.82 3734[4:Spt:3733.0,669.0,3418.0] || g_both(skf11(skc3),skc3)* -> .
% 0.60/0.82 3735[4:Spt:3733.0,669.1] || -> g_true_only(skf11(skc3),skc3)*.
% 0.60/0.82 3736[4:Res:3735.0,30.0] || g_both(skf11(skc3),skf11(skc3))* -> SkP0(skc3,skf11(skc3)).
% 0.60/0.82 3737[4:Res:3735.0,31.0] || g_false_only(skf11(skc3),skf11(skc3))* -> SkP0(skc3,skf11(skc3)).
% 0.60/0.82 3740[4:MRR:3736.1,1.0] || g_both(skf11(skc3),skf11(skc3))* -> .
% 0.60/0.82 3741[4:MRR:3737.1,1.0] || g_false_only(skf11(skc3),skf11(skc3))* -> .
% 0.60/0.82 3749[4:Res:25.0,3741.0] || -> g_both(skf11(skc3),skf11(skc3))* g_true_only(skf11(skc3),skf11(skc3)).
% 0.60/0.82 3751[4:MRR:3749.0,3740.0] || -> g_true_only(skf11(skc3),skf11(skc3))*.
% 0.60/0.82 3759[4:Res:3751.0,94.0] || g_true_only(skf11(skc3),skc3)* -> .
% 0.60/0.82 3761[4:MRR:3759.0,3735.0] || -> .
% 0.60/0.82 3762[3:Spt:3761.0,47.2,47.5,47.6] || -> SkC0 g_both(skf17(u),skf17(u))* g_true_only(skf17(u),skf17(u)).
% 0.60/0.82 3785[3:Res:3762.1,14.0] || g_false_only(skf17(u),skc3) -> SkC0 g_true_only(skf17(u),skf17(u))*.
% 0.60/0.82 3786[3:MRR:3785.2,13.0] || g_false_only(skf17(u),skc3)* -> SkC0.
% 0.60/0.82 3801[4:Spt:669.0] || -> g_both(skf11(skc3),skc3)*.
% 0.60/0.82 3819[4:Res:3801.0,32.0] || g_true_only(skf11(skc3),skf11(skc3))* -> SkP1(skc3,skf11(skc3)).
% 0.60/0.82 3820[4:Res:3801.0,59.0] || g_true_only(skf11(skc3),skc3)* -> .
% 0.60/0.82 3825[4:MRR:901.1,3820.0] || -> g_both(skf11(skc3),skf11(skc3))*.
% 0.60/0.82 3826[4:MRR:853.1,3820.0] || g_false_only(skf11(skc3),skf11(skc3))* -> .
% 0.60/0.82 3827[4:MRR:3819.1,2.0] || g_true_only(skf11(skc3),skf11(skc3))* -> .
% 0.60/0.82 3854[5:Spt:3408.1] || -> SkC2*.
% 0.60/0.82 3858[5:MRR:16.0,3854.0] || -> g_false_only(u,u)* SkP5(skc7,u)*.
% 0.60/0.82 3902[5:Res:3858.0,3826.0] || -> SkP5(skc7,skf11(skc3))*.
% 0.60/0.82 3908[5:Res:3902.0,8.0] || -> g_true_only(skf11(skc3),skf11(skc3))*.
% 0.60/0.82 3910[5:MRR:3908.0,3827.0] || -> .
% 0.60/0.82 3911[5:Spt:3910.0,3408.1,3854.0] || SkC2* -> .
% 0.60/0.82 3912[5:Spt:3910.0,3408.0,3408.2,3408.3,3408.4] || SkC0 -> g_false_only(skf14(u),u) SkP4(skc4,u,skf13(u))* SkP3(skc4,u,skf12(u)).
% 0.60/0.82 3913[5:MRR:3409.1,3911.0] || SkC0+ -> g_both(skf14(u),skc4) g_false_only(skf14(u),skc4)* SkP4(skc4,v,skf13(v))* SkP3(skc4,v,skf12(v)).
% 0.60/0.82 3914[5:Res:3912.2,4.0] || SkC0 -> g_false_only(skf14(skf11(skc4)),skf11(skc4)) SkP3(skc4,skf11(skc4),skf12(skf11(skc4)))*.
% 0.60/0.82 3917[5:MRR:3914.2,3.0] || SkC0 -> g_false_only(skf14(skf11(skc4)),skf11(skc4))*.
% 0.60/0.82 3922[5:Res:3917.1,24.1] || SkC0 g_both(skf14(skf11(skc4)),skc4)* -> .
% 0.60/0.82 3923[5:Res:3917.1,23.1] || SkC0 g_false_only(skf14(skf11(skc4)),skc4)* -> .
% 0.60/0.82 3928[6:Spt:3913.3,3913.4] || -> SkP4(skc4,u,skf13(u))* SkP3(skc4,u,skf12(u)).
% 0.60/0.82 3929[6:Res:3928.0,4.0] || -> SkP3(skc4,skf11(skc4),skf12(skf11(skc4)))*.
% 0.60/0.82 3932[6:MRR:3929.0,3.0] || -> .
% 0.60/0.82 3933[6:Spt:3932.0,3913.0,3913.1,3913.2] || SkC0 -> g_both(skf14(u),skc4) g_false_only(skf14(u),skc4)*.
% 0.60/0.82 3938[6:Res:3933.2,3923.1] || SkC0 SkC0 -> g_both(skf14(skf11(skc4)),skc4)*.
% 0.60/0.82 3939[6:Obv:3938.0] || SkC0 -> g_both(skf14(skf11(skc4)),skc4)*.
% 0.60/0.82 3940[6:MRR:3939.1,3922.1] || SkC0* -> .
% 0.60/0.82 3942[6:MRR:3786.1,3940.0] || g_false_only(skf17(u),skc3)* -> .
% 0.60/0.82 4035[4:Res:3825.0,3410.0] || g_both(skf11(skc3),u) -> SkP1(u,skf16(u))* SkP0(u,skf15(u)) g_false_only(skf17(u),u).
% 0.60/0.82 4191[4:Res:4035.1,2.0] || g_both(skf11(skc3),skc3) -> SkP0(skc3,skf15(skc3))* g_false_only(skf17(skc3),skc3).
% 0.60/0.82 4194[6:MRR:4191.0,4191.1,4191.2,3801.0,1.0,3942.0] || -> .
% 0.60/0.82 4195[4:Spt:4194.0,669.0,3801.0] || g_both(skf11(skc3),skc3)* -> .
% 0.60/0.82 4196[4:Spt:4194.0,669.1] || -> g_true_only(skf11(skc3),skc3)*.
% 0.60/0.82 4197[4:Res:4196.0,30.0] || g_both(skf11(skc3),skf11(skc3))* -> SkP0(skc3,skf11(skc3)).
% 0.60/0.82 4198[4:Res:4196.0,31.0] || g_false_only(skf11(skc3),skf11(skc3))* -> SkP0(skc3,skf11(skc3)).
% 0.60/0.82 4201[4:MRR:4197.1,1.0] || g_both(skf11(skc3),skf11(skc3))* -> .
% 0.60/0.82 4202[4:MRR:4198.1,1.0] || g_false_only(skf11(skc3),skf11(skc3))* -> .
% 0.60/0.82 4210[4:Res:25.0,4202.0] || -> g_both(skf11(skc3),skf11(skc3))* g_true_only(skf11(skc3),skf11(skc3)).
% 0.60/0.82 4212[4:MRR:4210.0,4201.0] || -> g_true_only(skf11(skc3),skf11(skc3))*.
% 0.68/0.85 4220[4:Res:4212.0,94.0] || g_true_only(skf11(skc3),skc3)* -> .
% 0.68/0.85 4222[4:MRR:4220.0,4196.0] || -> .
% 0.68/0.85 4223[2:Spt:4222.0,44.2] || -> SkC0*.
% 0.68/0.85 4224[2:MRR:3408.0,4223.0] || -> SkC2 g_false_only(skf14(u),u) SkP4(skc4,u,skf13(u))* SkP3(skc4,u,skf12(u)).
% 0.68/0.85 4225[2:MRR:3409.0,4223.0] || -> SkC2 g_both(skf14(u),skc4) g_false_only(skf14(u),skc4)* SkP4(skc4,v,skf13(v))* SkP3(skc4,v,skf12(v)).
% 0.68/0.85 4230[3:Spt:669.0] || -> g_both(skf11(skc3),skc3)*.
% 0.68/0.85 4250[3:Res:4230.0,32.0] || g_true_only(skf11(skc3),skf11(skc3))* -> SkP1(skc3,skf11(skc3)).
% 0.68/0.85 4251[3:Res:4230.0,59.0] || g_true_only(skf11(skc3),skc3)* -> .
% 0.68/0.85 4257[3:MRR:853.1,4251.0] || g_false_only(skf11(skc3),skf11(skc3))* -> .
% 0.68/0.85 4258[3:MRR:4250.1,2.0] || g_true_only(skf11(skc3),skf11(skc3))* -> .
% 0.68/0.85 4289[4:Spt:4224.0] || -> SkC2*.
% 0.68/0.85 4293[4:MRR:16.0,4289.0] || -> g_false_only(u,u)* SkP5(skc7,u)*.
% 0.68/0.85 4325[4:Res:4293.0,4257.0] || -> SkP5(skc7,skf11(skc3))*.
% 0.68/0.85 4331[4:Res:4325.0,8.0] || -> g_true_only(skf11(skc3),skf11(skc3))*.
% 0.68/0.85 4333[4:MRR:4331.0,4258.0] || -> .
% 0.68/0.85 4334[4:Spt:4333.0,4224.0,4289.0] || SkC2* -> .
% 0.68/0.85 4335[4:Spt:4333.0,4224.1,4224.2,4224.3] || -> g_false_only(skf14(u),u) SkP4(skc4,u,skf13(u))* SkP3(skc4,u,skf12(u)).
% 0.68/0.85 4336[4:MRR:4225.0,4334.0] || -> g_both(skf14(u),skc4) g_false_only(skf14(u),skc4)* SkP4(skc4,v,skf13(v))* SkP3(skc4,v,skf12(v)).
% 0.68/0.85 4337[4:Res:4335.1,4.0] || -> g_false_only(skf14(skf11(skc4)),skf11(skc4)) SkP3(skc4,skf11(skc4),skf12(skf11(skc4)))*.
% 0.68/0.85 4340[4:MRR:4337.1,3.0] || -> g_false_only(skf14(skf11(skc4)),skf11(skc4))*.
% 0.68/0.85 4345[4:Res:4340.0,24.1] || g_both(skf14(skf11(skc4)),skc4)* -> .
% 0.68/0.85 4346[4:Res:4340.0,23.1] || g_false_only(skf14(skf11(skc4)),skc4)* -> .
% 0.68/0.85 4347[4:Res:25.0,4346.0] || -> g_both(skf14(skf11(skc4)),skc4)* g_true_only(skf14(skf11(skc4)),skc4).
% 0.68/0.85 4348[4:MRR:4347.0,4345.0] || -> g_true_only(skf14(skf11(skc4)),skc4)*.
% 0.68/0.85 4355[5:Spt:4336.2,4336.3] || -> SkP4(skc4,u,skf13(u))* SkP3(skc4,u,skf12(u)).
% 0.68/0.85 4356[5:Res:4355.0,4.0] || -> SkP3(skc4,skf11(skc4),skf12(skf11(skc4)))*.
% 0.68/0.85 4359[5:MRR:4356.0,3.0] || -> .
% 0.68/0.85 4360[5:Spt:4359.0,4336.0,4336.1] || -> g_both(skf14(u),skc4) g_false_only(skf14(u),skc4)*.
% 0.68/0.85 4364[5:Res:4360.1,60.0] || g_true_only(skf14(u),skc4) -> g_both(skf14(u),skc4)*.
% 0.68/0.85 4367[5:MRR:4364.1,59.0] || g_true_only(skf14(u),skc4)* -> .
% 0.68/0.85 4368[5:UnC:4367.0,4348.0] || -> .
% 0.68/0.85 4369[3:Spt:4368.0,669.0,4230.0] || g_both(skf11(skc3),skc3)* -> .
% 0.68/0.85 4370[3:Spt:4368.0,669.1] || -> g_true_only(skf11(skc3),skc3)*.
% 0.68/0.85 4371[3:Res:4370.0,30.0] || g_both(skf11(skc3),skf11(skc3))* -> SkP0(skc3,skf11(skc3)).
% 0.68/0.85 4372[3:Res:4370.0,31.0] || g_false_only(skf11(skc3),skf11(skc3))* -> SkP0(skc3,skf11(skc3)).
% 0.68/0.85 4375[3:MRR:4371.1,1.0] || g_both(skf11(skc3),skf11(skc3))* -> .
% 0.68/0.85 4376[3:MRR:4372.1,1.0] || g_false_only(skf11(skc3),skf11(skc3))* -> .
% 0.68/0.85 4384[3:Res:25.0,4376.0] || -> g_both(skf11(skc3),skf11(skc3))* g_true_only(skf11(skc3),skf11(skc3)).
% 0.68/0.85 4386[3:MRR:4384.0,4375.0] || -> g_true_only(skf11(skc3),skf11(skc3))*.
% 0.68/0.85 4392[3:Res:4386.0,94.0] || g_true_only(skf11(skc3),skc3)* -> .
% 0.68/0.85 4394[3:MRR:4392.0,4370.0] || -> .
% 0.68/0.85 % SZS output end Refutation
% 0.68/0.85 Formulae used in the proof : nc4 both_g false_only_g true_only_g exhaustion_g
% 0.68/0.85
%------------------------------------------------------------------------------