TSTP Solution File: SEU332+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU332+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 14:36:20 EDT 2022
% Result : Theorem 25.59s 25.85s
% Output : Refutation 25.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU332+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n010.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 03:55:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 25.59/25.85
% 25.59/25.85 SPASS V 3.9
% 25.59/25.85 SPASS beiseite: Proof found.
% 25.59/25.85 % SZS status Theorem
% 25.59/25.85 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.59/25.85 SPASS derived 13759 clauses, backtracked 1120 clauses, performed 45 splits and kept 7778 clauses.
% 25.59/25.85 SPASS allocated 121148 KBytes.
% 25.59/25.85 SPASS spent 0:0:25.50 on the problem.
% 25.59/25.85 0:00:00.03 for the input.
% 25.59/25.85 0:00:00.13 for the FLOTTER CNF translation.
% 25.59/25.85 0:00:01.08 for inferences.
% 25.59/25.85 0:00:01.08 for the backtracking.
% 25.59/25.85 0:0:22.73 for the reduction.
% 25.59/25.85
% 25.59/25.85
% 25.59/25.85 Here is a proof with depth 22, length 220 :
% 25.59/25.85 % SZS output start Refutation
% 25.59/25.85 1[0:Inp] || -> one_sorted_str(skc4)*.
% 25.59/25.85 21[0:Inp] || -> element(skc5,powerset(powerset(the_carrier(skc4))))*.
% 25.59/25.85 23[0:Inp] || -> in(skf15(u),u)* in(skf16(v),skc5)*.
% 25.59/25.85 44[0:Inp] || -> in(skf15(u),u)* in(skf15(u),cartesian_product2(skc5,skc6))*.
% 25.59/25.85 60[0:Inp] || element(u,powerset(v)) -> element(subset_complement(v,u),powerset(v))*.
% 25.59/25.85 61[0:Inp] || equal(skf27(u,v),skf27(u,v))* -> SkP0(w,x)*.
% 25.59/25.85 62[0:Inp] || -> in(skf15(u),u) equal(ordered_pair(skf16(u),skf17(u)),skf15(u))**.
% 25.59/25.85 63[0:Inp] || element(u,powerset(v)) -> equal(subset_complement(v,subset_complement(v,u)),u)**.
% 25.59/25.85 66[0:Inp] || element(skf16(u),powerset(the_carrier(skc4)))* -> equal(subset_complement(the_carrier(skc4),skf16(u)),skf17(u)).
% 25.59/25.85 69[0:Inp] || element(skf25(u,v,w),powerset(the_carrier(v)))* -> equal(subset_complement(the_carrier(v),skf25(u,v,w)),skf26(w,v,u)).
% 25.59/25.85 70[0:Inp] one_sorted_str(u) || in(v,skf24(u,w,x))* SkP0(u,x) element(x,powerset(powerset(the_carrier(u)))) -> in(v,cartesian_product2(x,w)).
% 25.59/25.85 71[0:Inp] one_sorted_str(u) || in(v,skf24(u,w,x))* SkP0(u,x) element(x,powerset(powerset(the_carrier(u)))) -> in(skf25(x,y,z),x)*.
% 25.59/25.85 72[0:Inp] || in(u,v)* in(w,cartesian_product2(v,x))+ equal(ordered_pair(u,y),w)* -> element(u,powerset(the_carrier(z)))* in(w,skf24(z,x,v))*.
% 25.59/25.85 73[0:Inp] || in(u,skc5) in(skf15(v),v)* in(skf15(v),cartesian_product2(skc5,skc6))*+ equal(ordered_pair(u,w),skf15(v))* -> element(u,powerset(the_carrier(skc4)))*.
% 25.59/25.85 74[0:Inp] || in(u,v)* in(w,cartesian_product2(v,x)) equal(y,subset_complement(the_carrier(z),u))*+ equal(ordered_pair(u,y),w)* -> in(w,skf24(z,x,v))*.
% 25.59/25.85 75[0:Inp] || in(u,skc5) equal(v,subset_complement(the_carrier(skc4),u))*+ in(skf15(w),w)* in(skf15(w),cartesian_product2(skc5,skc6))* equal(ordered_pair(u,v),skf15(w))* -> .
% 25.59/25.85 76[0:Inp] one_sorted_str(u) || in(v,skf24(u,w,x))* SkP0(u,x) element(x,powerset(powerset(the_carrier(u)))) -> equal(ordered_pair(skf25(x,u,v),skf26(v,u,x)),v)**.
% 25.59/25.85 77[0:Obv:61.0] || -> SkP0(u,v)*.
% 25.59/25.85 78[0:MRR:70.2,77.0] one_sorted_str(u) || element(v,powerset(powerset(the_carrier(u)))) in(w,skf24(u,x,v))* -> in(w,cartesian_product2(v,x)).
% 25.59/25.85 79[0:MRR:71.2,77.0] one_sorted_str(u) || element(v,powerset(powerset(the_carrier(u))))+ in(w,skf24(u,x,v))* -> in(skf25(v,y,z),v)*.
% 25.59/25.85 80[0:MRR:76.2,77.0] one_sorted_str(u) || element(v,powerset(powerset(the_carrier(u))))+ in(w,skf24(u,x,v))* -> equal(ordered_pair(skf25(v,u,w),skf26(w,u,v)),w)**.
% 25.59/25.85 83[0:Res:1.0,78.0] || element(u,powerset(powerset(the_carrier(skc4)))) in(v,skf24(skc4,w,u))* -> in(v,cartesian_product2(u,w)).
% 25.59/25.85 99[0:Res:21.0,80.2] one_sorted_str(skc4) || in(u,skf24(skc4,v,skc5))* -> equal(ordered_pair(skf25(skc5,skc4,u),skf26(u,skc4,skc5)),u)**.
% 25.59/25.85 100[0:Res:21.0,79.2] one_sorted_str(skc4) || in(u,skf24(skc4,v,skc5))* -> in(skf25(skc5,w,x),skc5)*.
% 25.59/25.85 101[0:Res:21.0,78.2] one_sorted_str(skc4) || in(u,skf24(skc4,v,skc5))* -> in(u,cartesian_product2(skc5,v)).
% 25.59/25.85 119[0:MRR:101.0,1.0] || in(u,skf24(skc4,v,skc5))* -> in(u,cartesian_product2(skc5,v)).
% 25.59/25.85 120[0:MRR:100.0,1.0] || in(u,skf24(skc4,v,skc5))*+ -> in(skf25(skc5,w,x),skc5)*.
% 25.59/25.85 121[0:MRR:99.0,1.0] || in(u,skf24(skc4,v,skc5))*+ -> equal(ordered_pair(skf25(skc5,skc4,u),skf26(u,skc4,skc5)),u)**.
% 25.59/25.85 125[1:Spt:23.0] || -> in(skf15(u),u)*.
% 25.59/25.85 126[1:MRR:73.1,125.0] || in(u,skc5) in(skf15(v),cartesian_product2(skc5,skc6))*+ equal(ordered_pair(u,w),skf15(v))* -> element(u,powerset(the_carrier(skc4)))*.
% 25.59/25.85 127[1:MRR:75.2,125.0] || in(u,skc5) equal(v,subset_complement(the_carrier(skc4),u))*+ in(skf15(w),cartesian_product2(skc5,skc6))* equal(ordered_pair(u,v),skf15(w))* -> .
% 25.59/25.85 443[1:EqR:127.1] || in(u,skc5) in(skf15(v),cartesian_product2(skc5,skc6))* equal(ordered_pair(u,subset_complement(the_carrier(skc4),u)),skf15(v))*+ -> .
% 25.59/25.85 446[1:Res:125.0,119.0] || -> in(skf15(skf24(skc4,u,skc5)),cartesian_product2(skc5,u))*.
% 25.59/25.85 449[1:Res:446.0,126.1] || in(u,skc5) equal(ordered_pair(u,v),skf15(skf24(skc4,skc6,skc5)))*+ -> element(u,powerset(the_carrier(skc4)))*.
% 25.59/25.85 460[0:EqR:74.2] || in(u,v)* in(w,cartesian_product2(v,x)) equal(ordered_pair(u,subset_complement(the_carrier(y),u)),w)*+ -> in(w,skf24(y,x,v))*.
% 25.59/25.85 461[0:SpL:63.1,74.2] || element(u,powerset(the_carrier(v))) in(subset_complement(the_carrier(v),u),w)* in(x,cartesian_product2(w,y)) equal(z,u) equal(ordered_pair(subset_complement(the_carrier(v),u),z),x)*+ -> in(x,skf24(v,y,w))*.
% 25.59/25.85 473[1:Res:125.0,120.0] || -> in(skf25(skc5,u,v),skc5)*.
% 25.59/25.85 501[1:Res:125.0,121.0] || -> equal(ordered_pair(skf25(skc5,skc4,skf15(skf24(skc4,u,skc5))),skf26(skf15(skf24(skc4,u,skc5)),skc4,skc5)),skf15(skf24(skc4,u,skc5)))**.
% 25.59/25.85 502[1:Res:125.0,83.1] || element(u,powerset(powerset(the_carrier(skc4)))) -> in(skf15(skf24(skc4,v,u)),cartesian_product2(u,v))*.
% 25.59/25.85 526[1:SpL:501.0,449.1] || in(skf25(skc5,skc4,skf15(skf24(skc4,u,skc5))),skc5) equal(skf15(skf24(skc4,u,skc5)),skf15(skf24(skc4,skc6,skc5))) -> element(skf25(skc5,skc4,skf15(skf24(skc4,u,skc5))),powerset(the_carrier(skc4)))*.
% 25.59/25.85 528[1:MRR:526.0,473.0] || equal(skf15(skf24(skc4,u,skc5)),skf15(skf24(skc4,skc6,skc5))) -> element(skf25(skc5,skc4,skf15(skf24(skc4,u,skc5))),powerset(the_carrier(skc4)))*.
% 25.59/25.85 577[1:Res:528.1,69.0] || equal(skf15(skf24(skc4,u,skc5)),skf15(skf24(skc4,skc6,skc5))) -> equal(subset_complement(the_carrier(skc4),skf25(skc5,skc4,skf15(skf24(skc4,u,skc5)))),skf26(skf15(skf24(skc4,u,skc5)),skc4,skc5))**.
% 25.59/25.85 601[0:EqR:460.2] || in(u,v) in(ordered_pair(u,subset_complement(the_carrier(w),u)),cartesian_product2(v,x)) -> in(ordered_pair(u,subset_complement(the_carrier(w),u)),skf24(w,x,v))*.
% 25.59/25.85 639[0:EqR:461.4] || element(u,powerset(the_carrier(v))) in(subset_complement(the_carrier(v),u),w) in(ordered_pair(subset_complement(the_carrier(v),u),x),cartesian_product2(w,y)) equal(x,u) -> in(ordered_pair(subset_complement(the_carrier(v),u),x),skf24(v,y,w))*.
% 25.59/25.85 745[0:SpR:63.1,639.4] || element(u,powerset(the_carrier(v))) element(subset_complement(the_carrier(v),u),powerset(the_carrier(v))) in(subset_complement(the_carrier(v),subset_complement(the_carrier(v),u)),w) in(ordered_pair(subset_complement(the_carrier(v),subset_complement(the_carrier(v),u)),x),cartesian_product2(w,y))* equal(x,subset_complement(the_carrier(v),u)) -> in(ordered_pair(u,x),skf24(v,y,w)).
% 25.59/25.85 758[0:Rew:63.1,745.3,63.1,745.2] || element(u,powerset(the_carrier(v))) element(subset_complement(the_carrier(v),u),powerset(the_carrier(v)))* in(u,w) in(ordered_pair(u,x),cartesian_product2(w,y)) equal(x,subset_complement(the_carrier(v),u)) -> in(ordered_pair(u,x),skf24(v,y,w))*.
% 25.59/25.85 759[0:MRR:758.1,60.1] || element(u,powerset(the_carrier(v))) in(u,w) in(ordered_pair(u,x),cartesian_product2(w,y)) equal(x,subset_complement(the_carrier(v),u)) -> in(ordered_pair(u,x),skf24(v,y,w))*.
% 25.59/25.85 891[0:Res:759.4,121.0] || element(u,powerset(the_carrier(skc4))) in(u,skc5) in(ordered_pair(u,v),cartesian_product2(skc5,w))*+ equal(v,subset_complement(the_carrier(skc4),u)) -> equal(ordered_pair(skf25(skc5,skc4,ordered_pair(u,v)),skf26(ordered_pair(u,v),skc4,skc5)),ordered_pair(u,v))**.
% 25.59/25.85 1177[1:SpL:577.1,443.2] || equal(skf15(skf24(skc4,u,skc5)),skf15(skf24(skc4,skc6,skc5))) in(skf25(skc5,skc4,skf15(skf24(skc4,u,skc5))),skc5) in(skf15(v),cartesian_product2(skc5,skc6))* equal(ordered_pair(skf25(skc5,skc4,skf15(skf24(skc4,u,skc5))),skf26(skf15(skf24(skc4,u,skc5)),skc4,skc5)),skf15(v))* -> .
% 25.59/25.85 1204[1:Rew:501.0,1177.3] || equal(skf15(skf24(skc4,u,skc5)),skf15(skf24(skc4,skc6,skc5))) in(skf25(skc5,skc4,skf15(skf24(skc4,u,skc5))),skc5)* in(skf15(v),cartesian_product2(skc5,skc6))* equal(skf15(skf24(skc4,u,skc5)),skf15(v))* -> .
% 25.59/25.85 1205[1:MRR:1204.1,473.0] || equal(skf15(skf24(skc4,u,skc5)),skf15(skf24(skc4,skc6,skc5)))*+ in(skf15(v),cartesian_product2(skc5,skc6))* equal(skf15(skf24(skc4,u,skc5)),skf15(v))* -> .
% 25.59/25.85 1430[1:EqR:1205.0] || in(skf15(u),cartesian_product2(skc5,skc6))* equal(skf15(skf24(skc4,skc6,skc5)),skf15(u)) -> .
% 25.59/25.85 1444[1:Res:502.1,1430.0] || element(skc5,powerset(powerset(the_carrier(skc4))))* equal(skf15(skf24(skc4,skc6,skc5)),skf15(skf24(skc4,skc6,skc5))) -> .
% 25.59/25.85 1447[1:Obv:1444.1] || element(skc5,powerset(powerset(the_carrier(skc4))))* -> .
% 25.59/25.85 1448[1:MRR:1447.0,21.0] || -> .
% 25.59/25.85 1449[1:Spt:1448.0,23.1] || -> in(skf16(u),skc5)*.
% 25.59/25.85 1456[0:Res:44.0,119.0] || -> in(skf15(skf24(skc4,u,skc5)),cartesian_product2(skc5,skc6))* in(skf15(skf24(skc4,u,skc5)),cartesian_product2(skc5,u))*.
% 25.59/25.85 1468[0:Res:44.1,72.1] || in(u,skc5) equal(ordered_pair(u,v),skf15(w))*+ -> in(skf15(w),w)* element(u,powerset(the_carrier(x)))* in(skf15(w),skf24(x,skc6,skc5))*.
% 25.59/25.85 1471[0:SpR:62.1,759.4] || element(skf16(u),powerset(the_carrier(v))) in(skf16(u),w) in(ordered_pair(skf16(u),skf17(u)),cartesian_product2(w,x))* equal(subset_complement(the_carrier(v),skf16(u)),skf17(u)) -> in(skf15(u),u) in(skf15(u),skf24(v,x,w))*.
% 25.59/25.85 1473[0:Rew:62.1,1471.2] || element(skf16(u),powerset(the_carrier(v))) in(skf16(u),w) in(skf15(u),cartesian_product2(w,x)) equal(subset_complement(the_carrier(v),skf16(u)),skf17(u))+ -> in(skf15(u),u)* in(skf15(u),skf24(v,x,w))*.
% 25.59/25.85 1474[0:Res:44.0,120.0] || -> in(skf15(skf24(skc4,u,skc5)),cartesian_product2(skc5,skc6))* in(skf25(skc5,v,w),skc5)*.
% 25.59/25.85 1484[2:Spt:1474.1] || -> in(skf25(skc5,u,v),skc5)*.
% 25.59/25.85 1486[0:Fac:1456.0,1456.1] || -> in(skf15(skf24(skc4,skc6,skc5)),cartesian_product2(skc5,skc6))*.
% 25.59/25.85 1492[0:Res:1486.0,72.1] || in(u,skc5) equal(ordered_pair(u,v),skf15(skf24(skc4,skc6,skc5)))*+ -> element(u,powerset(the_carrier(w)))* in(skf15(skf24(skc4,skc6,skc5)),skf24(w,skc6,skc5))*.
% 25.59/25.85 1496[0:Res:1486.0,73.2] || in(u,skc5) in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))* equal(ordered_pair(u,v),skf15(skf24(skc4,skc6,skc5)))* -> element(u,powerset(the_carrier(skc4)))*.
% 25.59/25.85 1498[0:MRR:1496.1,1492.3] || in(u,skc5) equal(ordered_pair(u,v),skf15(skf24(skc4,skc6,skc5)))*+ -> element(u,powerset(the_carrier(skc4)))*.
% 25.59/25.85 1505[0:EqR:75.1] || in(u,skc5) in(skf15(v),v)* in(skf15(v),cartesian_product2(skc5,skc6))* equal(ordered_pair(u,subset_complement(the_carrier(skc4),u)),skf15(v))*+ -> .
% 25.59/25.85 1507[0:SpL:62.1,1498.1] || in(skf16(u),skc5) equal(skf15(u),skf15(skf24(skc4,skc6,skc5))) -> in(skf15(u),u)* element(skf16(u),powerset(the_carrier(skc4)))*.
% 25.59/25.85 1508[1:MRR:1507.0,1449.0] || equal(skf15(u),skf15(skf24(skc4,skc6,skc5)))+ -> in(skf15(u),u)* element(skf16(u),powerset(the_carrier(skc4)))*.
% 25.59/25.85 1509[1:EqR:1508.0] || -> in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))* element(skf16(skf24(skc4,skc6,skc5)),powerset(the_carrier(skc4))).
% 25.59/25.85 1511[1:Res:1509.0,121.0] || -> element(skf16(skf24(skc4,skc6,skc5)),powerset(the_carrier(skc4))) equal(ordered_pair(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skf26(skf15(skf24(skc4,skc6,skc5)),skc4,skc5)),skf15(skf24(skc4,skc6,skc5)))**.
% 25.59/25.85 1557[0:SpL:62.1,1468.1] || in(skf16(u),skc5) equal(skf15(u),skf15(v))* -> in(skf15(u),u)* in(skf15(v),v)* element(skf16(u),powerset(the_carrier(w)))* in(skf15(v),skf24(w,skc6,skc5))*.
% 25.59/25.85 1558[1:MRR:1557.0,1449.0] || equal(skf15(u),skf15(v))*+ -> in(skf15(u),u)* in(skf15(v),v)* element(skf16(u),powerset(the_carrier(w)))* in(skf15(v),skf24(w,skc6,skc5))*.
% 25.59/25.85 1579[1:EqR:1558.0] || -> in(skf15(u),u)* in(skf15(u),u)* element(skf16(u),powerset(the_carrier(v))) in(skf15(u),skf24(v,skc6,skc5))*.
% 25.59/25.85 1580[1:Obv:1579.0] || -> in(skf15(u),u)* element(skf16(u),powerset(the_carrier(v))) in(skf15(u),skf24(v,skc6,skc5))*.
% 25.59/25.85 1588[1:Fac:1580.0,1580.2] || -> element(skf16(skf24(u,skc6,skc5)),powerset(the_carrier(u))) in(skf15(skf24(u,skc6,skc5)),skf24(u,skc6,skc5))*.
% 25.59/25.85 1606[1:Res:1580.2,121.0] || -> in(skf15(u),u) element(skf16(u),powerset(the_carrier(skc4))) equal(ordered_pair(skf25(skc5,skc4,skf15(u)),skf26(skf15(u),skc4,skc5)),skf15(u))**.
% 25.59/25.85 1669[1:SpL:1511.1,1498.1] || in(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skc5) equal(skf15(skf24(skc4,skc6,skc5)),skf15(skf24(skc4,skc6,skc5))) -> element(skf16(skf24(skc4,skc6,skc5)),powerset(the_carrier(skc4))) element(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),powerset(the_carrier(skc4)))*.
% 25.59/25.85 1671[1:Obv:1669.1] || in(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skc5) -> element(skf16(skf24(skc4,skc6,skc5)),powerset(the_carrier(skc4))) element(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),powerset(the_carrier(skc4)))*.
% 25.59/25.85 1672[2:MRR:1671.0,1484.0] || -> element(skf16(skf24(skc4,skc6,skc5)),powerset(the_carrier(skc4))) element(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),powerset(the_carrier(skc4)))*.
% 25.59/25.85 1678[3:Spt:1672.0] || -> element(skf16(skf24(skc4,skc6,skc5)),powerset(the_carrier(skc4)))*.
% 25.59/25.85 1694[3:Res:1678.0,66.0] || -> equal(subset_complement(the_carrier(skc4),skf16(skf24(skc4,skc6,skc5))),skf17(skf24(skc4,skc6,skc5)))**.
% 25.59/25.85 1894[3:SpL:1694.0,460.2] || in(skf16(skf24(skc4,skc6,skc5)),u)* in(v,cartesian_product2(u,w)) equal(ordered_pair(skf16(skf24(skc4,skc6,skc5)),skf17(skf24(skc4,skc6,skc5))),v)*+ -> in(v,skf24(skc4,w,u))*.
% 25.59/25.85 2457[3:SpL:62.1,1894.2] || in(skf16(skf24(skc4,skc6,skc5)),u)*+ in(v,cartesian_product2(u,w)) equal(skf15(skf24(skc4,skc6,skc5)),v) -> in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))* in(v,skf24(skc4,w,u))*.
% 25.59/25.85 2927[4:Spt:2457.0,2457.1,2457.2,2457.4] || in(skf16(skf24(skc4,skc6,skc5)),u)*+ in(v,cartesian_product2(u,w)) equal(skf15(skf24(skc4,skc6,skc5)),v) -> in(v,skf24(skc4,w,u))*.
% 25.59/25.85 2928[4:Res:1449.0,2927.0] || in(u,cartesian_product2(skc5,v)) equal(skf15(skf24(skc4,skc6,skc5)),u) -> in(u,skf24(skc4,v,skc5))*.
% 25.59/25.85 2958[4:Res:2928.2,121.0] || in(u,cartesian_product2(skc5,v))* equal(skf15(skf24(skc4,skc6,skc5)),u)+ -> equal(ordered_pair(skf25(skc5,skc4,u),skf26(u,skc4,skc5)),u)**.
% 25.59/25.85 2967[4:EqR:2958.1] || in(skf15(skf24(skc4,skc6,skc5)),cartesian_product2(skc5,u))*+ -> equal(ordered_pair(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skf26(skf15(skf24(skc4,skc6,skc5)),skc4,skc5)),skf15(skf24(skc4,skc6,skc5)))**.
% 25.59/25.85 2968[4:Res:1486.0,2967.0] || -> equal(ordered_pair(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skf26(skf15(skf24(skc4,skc6,skc5)),skc4,skc5)),skf15(skf24(skc4,skc6,skc5)))**.
% 25.59/25.85 2982[4:SpL:2968.0,1498.1] || in(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skc5) equal(skf15(skf24(skc4,skc6,skc5)),skf15(skf24(skc4,skc6,skc5))) -> element(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),powerset(the_carrier(skc4)))*.
% 25.59/25.85 2991[4:Obv:2982.1] || in(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skc5) -> element(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),powerset(the_carrier(skc4)))*.
% 25.59/25.85 2992[4:MRR:2991.0,1484.0] || -> element(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),powerset(the_carrier(skc4)))*.
% 25.59/25.85 3018[4:Res:2992.0,69.0] || -> equal(subset_complement(the_carrier(skc4),skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5)))),skf26(skf15(skf24(skc4,skc6,skc5)),skc4,skc5))**.
% 25.59/25.85 3282[4:SpL:3018.0,1505.3] || in(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skc5) in(skf15(u),u)* in(skf15(u),cartesian_product2(skc5,skc6))* equal(ordered_pair(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skf26(skf15(skf24(skc4,skc6,skc5)),skc4,skc5)),skf15(u))* -> .
% 25.59/25.85 3332[4:Rew:2968.0,3282.3] || in(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skc5)* in(skf15(u),u)* in(skf15(u),cartesian_product2(skc5,skc6))* equal(skf15(skf24(skc4,skc6,skc5)),skf15(u)) -> .
% 25.59/25.85 3333[4:MRR:3332.0,1484.0] || in(skf15(u),u)* in(skf15(u),cartesian_product2(skc5,skc6))* equal(skf15(skf24(skc4,skc6,skc5)),skf15(u))+ -> .
% 25.59/25.85 3603[4:EqR:3333.2] || in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))* in(skf15(skf24(skc4,skc6,skc5)),cartesian_product2(skc5,skc6)) -> .
% 25.59/25.85 3604[4:MRR:3603.1,1486.0] || in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))* -> .
% 25.59/25.85 3609[4:Res:2928.2,3604.0] || in(skf15(skf24(skc4,skc6,skc5)),cartesian_product2(skc5,skc6))* equal(skf15(skf24(skc4,skc6,skc5)),skf15(skf24(skc4,skc6,skc5))) -> .
% 25.59/25.85 3612[4:Obv:3609.1] || in(skf15(skf24(skc4,skc6,skc5)),cartesian_product2(skc5,skc6))* -> .
% 25.59/25.85 3613[4:MRR:3612.0,1486.0] || -> .
% 25.59/25.85 3614[4:Spt:3613.0,2457.3] || -> in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))*.
% 25.59/25.85 3616[4:Res:3614.0,121.0] || -> equal(ordered_pair(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skf26(skf15(skf24(skc4,skc6,skc5)),skc4,skc5)),skf15(skf24(skc4,skc6,skc5)))**.
% 25.59/25.85 3634[4:SpL:3616.0,1498.1] || in(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skc5) equal(skf15(skf24(skc4,skc6,skc5)),skf15(skf24(skc4,skc6,skc5))) -> element(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),powerset(the_carrier(skc4)))*.
% 25.59/25.85 3643[4:Obv:3634.1] || in(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skc5) -> element(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),powerset(the_carrier(skc4)))*.
% 25.59/25.85 3644[4:MRR:3643.0,1484.0] || -> element(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),powerset(the_carrier(skc4)))*.
% 25.59/25.85 3670[4:Res:3644.0,69.0] || -> equal(subset_complement(the_carrier(skc4),skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5)))),skf26(skf15(skf24(skc4,skc6,skc5)),skc4,skc5))**.
% 25.59/25.85 3795[0:SpL:62.1,891.2] || element(skf16(u),powerset(the_carrier(skc4))) in(skf16(u),skc5) in(skf15(u),cartesian_product2(skc5,v))* equal(subset_complement(the_carrier(skc4),skf16(u)),skf17(u)) -> in(skf15(u),u) equal(ordered_pair(skf25(skc5,skc4,ordered_pair(skf16(u),skf17(u))),skf26(ordered_pair(skf16(u),skf17(u)),skc4,skc5)),ordered_pair(skf16(u),skf17(u)))**.
% 25.59/25.85 3796[0:Rew:62.1,3795.5,66.1,3795.3] || element(skf16(u),powerset(the_carrier(skc4))) in(skf16(u),skc5) in(skf15(u),cartesian_product2(skc5,v))* equal(skf17(u),skf17(u)) -> in(skf15(u),u) equal(ordered_pair(skf25(skc5,skc4,skf15(u)),skf26(skf15(u),skc4,skc5)),skf15(u))**.
% 25.59/25.85 3797[0:Obv:3796.3] || element(skf16(u),powerset(the_carrier(skc4))) in(skf16(u),skc5) in(skf15(u),cartesian_product2(skc5,v))* -> in(skf15(u),u) equal(ordered_pair(skf25(skc5,skc4,skf15(u)),skf26(skf15(u),skc4,skc5)),skf15(u))**.
% 25.59/25.85 3798[1:MRR:3797.0,3797.1,1606.1,1449.0] || in(skf15(u),cartesian_product2(skc5,v))*+ -> in(skf15(u),u) equal(ordered_pair(skf25(skc5,skc4,skf15(u)),skf26(skf15(u),skc4,skc5)),skf15(u))**.
% 25.59/25.85 3845[4:SpL:3670.0,1505.3] || in(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skc5) in(skf15(u),u)* in(skf15(u),cartesian_product2(skc5,skc6))* equal(ordered_pair(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skf26(skf15(skf24(skc4,skc6,skc5)),skc4,skc5)),skf15(u))* -> .
% 25.59/25.85 3896[4:Rew:3616.0,3845.3] || in(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skc5)* in(skf15(u),u)* in(skf15(u),cartesian_product2(skc5,skc6))* equal(skf15(skf24(skc4,skc6,skc5)),skf15(u)) -> .
% 25.59/25.85 3897[4:MRR:3896.0,1484.0] || in(skf15(u),u)* in(skf15(u),cartesian_product2(skc5,skc6))* equal(skf15(skf24(skc4,skc6,skc5)),skf15(u))+ -> .
% 25.59/25.85 4145[4:EqR:3897.2] || in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))* in(skf15(skf24(skc4,skc6,skc5)),cartesian_product2(skc5,skc6)) -> .
% 25.59/25.85 4146[4:MRR:4145.0,4145.1,3614.0,1486.0] || -> .
% 25.59/25.85 4147[3:Spt:4146.0,1672.0,1678.0] || element(skf16(skf24(skc4,skc6,skc5)),powerset(the_carrier(skc4)))* -> .
% 25.59/25.85 4148[3:Spt:4146.0,1672.1] || -> element(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),powerset(the_carrier(skc4)))*.
% 25.59/25.85 4150[3:MRR:1511.0,4147.0] || -> equal(ordered_pair(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skf26(skf15(skf24(skc4,skc6,skc5)),skc4,skc5)),skf15(skf24(skc4,skc6,skc5)))**.
% 25.59/25.85 4170[3:Res:4148.0,69.0] || -> equal(subset_complement(the_carrier(skc4),skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5)))),skf26(skf15(skf24(skc4,skc6,skc5)),skc4,skc5))**.
% 25.59/25.85 4321[3:SpL:4170.0,1505.3] || in(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skc5) in(skf15(u),u)* in(skf15(u),cartesian_product2(skc5,skc6))* equal(ordered_pair(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skf26(skf15(skf24(skc4,skc6,skc5)),skc4,skc5)),skf15(u))* -> .
% 25.59/25.85 4375[3:Rew:4150.0,4321.3] || in(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skc5)* in(skf15(u),u)* in(skf15(u),cartesian_product2(skc5,skc6))* equal(skf15(skf24(skc4,skc6,skc5)),skf15(u)) -> .
% 25.59/25.85 4376[3:MRR:4375.0,1484.0] || in(skf15(u),u)* in(skf15(u),cartesian_product2(skc5,skc6))* equal(skf15(skf24(skc4,skc6,skc5)),skf15(u))+ -> .
% 25.59/25.85 4685[3:EqR:4376.2] || in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))* in(skf15(skf24(skc4,skc6,skc5)),cartesian_product2(skc5,skc6)) -> .
% 25.59/25.85 4686[3:MRR:4685.1,1486.0] || in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))* -> .
% 25.59/25.85 4689[3:Res:1588.1,4686.0] || -> element(skf16(skf24(skc4,skc6,skc5)),powerset(the_carrier(skc4)))*.
% 25.59/25.85 4691[3:MRR:4689.0,4147.0] || -> .
% 25.59/25.85 4692[2:Spt:4691.0,1474.0] || -> in(skf15(skf24(skc4,u,skc5)),cartesian_product2(skc5,skc6))*.
% 25.59/25.85 4709[1:Res:1580.2,120.0] || -> in(skf15(u),u)* element(skf16(u),powerset(the_carrier(skc4)))* in(skf25(skc5,v,w),skc5)*.
% 25.59/25.85 4710[1:Res:1588.1,120.0] || -> element(skf16(skf24(skc4,skc6,skc5)),powerset(the_carrier(skc4)))* in(skf25(skc5,u,v),skc5)*.
% 25.59/25.85 4714[1:MRR:1671.0,4710.1] || -> element(skf16(skf24(skc4,skc6,skc5)),powerset(the_carrier(skc4))) element(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),powerset(the_carrier(skc4)))*.
% 25.59/25.85 4730[3:Spt:4710.1] || -> in(skf25(skc5,u,v),skc5)*.
% 25.59/25.85 4732[4:Spt:4714.0] || -> element(skf16(skf24(skc4,skc6,skc5)),powerset(the_carrier(skc4)))*.
% 25.59/25.85 4748[4:Res:4732.0,66.0] || -> equal(subset_complement(the_carrier(skc4),skf16(skf24(skc4,skc6,skc5))),skf17(skf24(skc4,skc6,skc5)))**.
% 25.59/25.85 4895[4:SpL:4748.0,1473.3] || element(skf16(skf24(skc4,skc6,skc5)),powerset(the_carrier(skc4))) in(skf16(skf24(skc4,skc6,skc5)),u) in(skf15(skf24(skc4,skc6,skc5)),cartesian_product2(u,v)) equal(skf17(skf24(skc4,skc6,skc5)),skf17(skf24(skc4,skc6,skc5))) -> in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))* in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,v,u))*.
% 25.59/25.85 4975[4:Obv:4895.3] || element(skf16(skf24(skc4,skc6,skc5)),powerset(the_carrier(skc4))) in(skf16(skf24(skc4,skc6,skc5)),u) in(skf15(skf24(skc4,skc6,skc5)),cartesian_product2(u,v)) -> in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))* in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,v,u))*.
% 25.59/25.85 4976[4:MRR:4975.0,4732.0] || in(skf16(skf24(skc4,skc6,skc5)),u) in(skf15(skf24(skc4,skc6,skc5)),cartesian_product2(u,v)) -> in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))* in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,v,u))*.
% 25.59/25.85 5362[1:Res:44.1,3798.0] || -> in(skf15(u),u) in(skf15(u),u) equal(ordered_pair(skf25(skc5,skc4,skf15(u)),skf26(skf15(u),skc4,skc5)),skf15(u))**.
% 25.59/25.85 5376[1:Obv:5362.0] || -> in(skf15(u),u) equal(ordered_pair(skf25(skc5,skc4,skf15(u)),skf26(skf15(u),skc4,skc5)),skf15(u))**.
% 25.59/25.85 5389[1:SpL:5376.1,1498.1] || in(skf25(skc5,skc4,skf15(u)),skc5) equal(skf15(u),skf15(skf24(skc4,skc6,skc5))) -> in(skf15(u),u)* element(skf25(skc5,skc4,skf15(u)),powerset(the_carrier(skc4)))*.
% 25.59/25.85 5404[3:MRR:5389.0,4730.0] || equal(skf15(u),skf15(skf24(skc4,skc6,skc5)))+ -> in(skf15(u),u)* element(skf25(skc5,skc4,skf15(u)),powerset(the_carrier(skc4)))*.
% 25.59/25.85 5422[3:EqR:5404.0] || -> in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5)) element(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),powerset(the_carrier(skc4)))*.
% 25.59/25.85 5446[3:Res:5422.1,69.0] || -> in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5)) equal(subset_complement(the_carrier(skc4),skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5)))),skf26(skf15(skf24(skc4,skc6,skc5)),skc4,skc5))**.
% 25.59/25.85 5638[5:Spt:5446.0] || -> in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))*.
% 25.59/25.85 5640[5:Res:5638.0,121.0] || -> equal(ordered_pair(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skf26(skf15(skf24(skc4,skc6,skc5)),skc4,skc5)),skf15(skf24(skc4,skc6,skc5)))**.
% 25.59/25.85 5659[5:SpL:5640.0,1498.1] || in(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skc5) equal(skf15(skf24(skc4,skc6,skc5)),skf15(skf24(skc4,skc6,skc5))) -> element(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),powerset(the_carrier(skc4)))*.
% 25.59/25.85 5678[5:Obv:5659.1] || in(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skc5) -> element(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),powerset(the_carrier(skc4)))*.
% 25.59/25.85 5679[5:MRR:5678.0,4730.0] || -> element(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),powerset(the_carrier(skc4)))*.
% 25.59/25.85 5720[5:Res:5679.0,69.0] || -> equal(subset_complement(the_carrier(skc4),skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5)))),skf26(skf15(skf24(skc4,skc6,skc5)),skc4,skc5))**.
% 25.59/25.85 5941[5:SpL:5720.0,1505.3] || in(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skc5) in(skf15(u),u)* in(skf15(u),cartesian_product2(skc5,skc6))* equal(ordered_pair(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skf26(skf15(skf24(skc4,skc6,skc5)),skc4,skc5)),skf15(u))* -> .
% 25.59/25.85 6006[5:Rew:5640.0,5941.3] || in(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skc5)* in(skf15(u),u)* in(skf15(u),cartesian_product2(skc5,skc6))* equal(skf15(skf24(skc4,skc6,skc5)),skf15(u)) -> .
% 25.59/25.85 6007[5:MRR:6006.0,4730.0] || in(skf15(u),u)* in(skf15(u),cartesian_product2(skc5,skc6))* equal(skf15(skf24(skc4,skc6,skc5)),skf15(u))+ -> .
% 25.59/25.85 6304[5:EqR:6007.2] || in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))* in(skf15(skf24(skc4,skc6,skc5)),cartesian_product2(skc5,skc6)) -> .
% 25.59/25.85 6305[5:MRR:6304.0,6304.1,5638.0,4692.0] || -> .
% 25.59/25.85 6306[5:Spt:6305.0,5446.0,5638.0] || in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))* -> .
% 25.59/25.85 6307[5:Spt:6305.0,5446.1] || -> equal(subset_complement(the_carrier(skc4),skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5)))),skf26(skf15(skf24(skc4,skc6,skc5)),skc4,skc5))**.
% 25.59/25.85 6350[5:MRR:4976.2,6306.0] || in(skf16(skf24(skc4,skc6,skc5)),u) in(skf15(skf24(skc4,skc6,skc5)),cartesian_product2(u,v)) -> in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,v,u))*.
% 25.59/25.85 6917[5:Res:6350.2,6306.0] || in(skf16(skf24(skc4,skc6,skc5)),skc5) in(skf15(skf24(skc4,skc6,skc5)),cartesian_product2(skc5,skc6))* -> .
% 25.59/25.85 6918[5:MRR:6917.0,6917.1,1449.0,4692.0] || -> .
% 25.59/25.85 6920[4:Spt:6918.0,4714.0,4732.0] || element(skf16(skf24(skc4,skc6,skc5)),powerset(the_carrier(skc4)))* -> .
% 25.59/25.85 6921[4:Spt:6918.0,4714.1] || -> element(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),powerset(the_carrier(skc4)))*.
% 25.59/25.85 6923[4:MRR:1511.0,6920.0] || -> equal(ordered_pair(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skf26(skf15(skf24(skc4,skc6,skc5)),skc4,skc5)),skf15(skf24(skc4,skc6,skc5)))**.
% 25.59/25.85 6943[4:Res:6921.0,69.0] || -> equal(subset_complement(the_carrier(skc4),skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5)))),skf26(skf15(skf24(skc4,skc6,skc5)),skc4,skc5))**.
% 25.59/25.85 7206[4:SpL:6943.0,1505.3] || in(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skc5) in(skf15(u),u)* in(skf15(u),cartesian_product2(skc5,skc6))* equal(ordered_pair(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skf26(skf15(skf24(skc4,skc6,skc5)),skc4,skc5)),skf15(u))* -> .
% 25.59/25.85 7272[4:Rew:6923.0,7206.3] || in(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skc5)* in(skf15(u),u)* in(skf15(u),cartesian_product2(skc5,skc6))* equal(skf15(skf24(skc4,skc6,skc5)),skf15(u)) -> .
% 25.59/25.85 7273[4:MRR:7272.0,4730.0] || in(skf15(u),u)* in(skf15(u),cartesian_product2(skc5,skc6))* equal(skf15(skf24(skc4,skc6,skc5)),skf15(u))+ -> .
% 25.59/25.85 7690[4:EqR:7273.2] || in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))* in(skf15(skf24(skc4,skc6,skc5)),cartesian_product2(skc5,skc6)) -> .
% 25.59/25.85 7691[4:MRR:7690.1,4692.0] || in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))* -> .
% 25.59/25.85 7694[4:Res:1588.1,7691.0] || -> element(skf16(skf24(skc4,skc6,skc5)),powerset(the_carrier(skc4)))*.
% 25.59/25.85 7696[4:MRR:7694.0,6920.0] || -> .
% 25.59/25.85 7697[3:Spt:7696.0,4710.0] || -> element(skf16(skf24(skc4,skc6,skc5)),powerset(the_carrier(skc4)))*.
% 25.59/25.85 7719[3:Res:7697.0,66.0] || -> equal(subset_complement(the_carrier(skc4),skf16(skf24(skc4,skc6,skc5))),skf17(skf24(skc4,skc6,skc5)))**.
% 25.59/25.85 7878[3:SpL:7719.0,1473.3] || element(skf16(skf24(skc4,skc6,skc5)),powerset(the_carrier(skc4))) in(skf16(skf24(skc4,skc6,skc5)),u) in(skf15(skf24(skc4,skc6,skc5)),cartesian_product2(u,v)) equal(skf17(skf24(skc4,skc6,skc5)),skf17(skf24(skc4,skc6,skc5))) -> in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))* in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,v,u))*.
% 25.59/25.85 7962[3:Obv:7878.3] || element(skf16(skf24(skc4,skc6,skc5)),powerset(the_carrier(skc4))) in(skf16(skf24(skc4,skc6,skc5)),u) in(skf15(skf24(skc4,skc6,skc5)),cartesian_product2(u,v)) -> in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))* in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,v,u))*.
% 25.59/25.85 7963[3:MRR:7962.0,7697.0] || in(skf16(skf24(skc4,skc6,skc5)),u) in(skf15(skf24(skc4,skc6,skc5)),cartesian_product2(u,v)) -> in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))* in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,v,u))*.
% 25.59/25.85 8083[4:Spt:4709.0,4709.1] || -> in(skf15(u),u)* element(skf16(u),powerset(the_carrier(skc4)))*.
% 25.59/25.85 8128[4:Res:8083.1,66.0] || -> in(skf15(u),u)* equal(subset_complement(the_carrier(skc4),skf16(u)),skf17(u))**.
% 25.59/25.85 8294[4:SpR:8128.1,601.2] || in(skf16(u),v) in(ordered_pair(skf16(u),subset_complement(the_carrier(skc4),skf16(u))),cartesian_product2(v,w))* -> in(skf15(u),u) in(ordered_pair(skf16(u),skf17(u)),skf24(skc4,w,v)).
% 25.59/25.85 8318[4:SpL:8128.1,1505.3] || in(skf16(u),skc5) in(skf15(v),v)* in(skf15(v),cartesian_product2(skc5,skc6))* equal(ordered_pair(skf16(u),skf17(u)),skf15(v))* -> in(skf15(u),u).
% 25.59/25.85 8411[4:Rew:62.1,8318.3] || in(skf16(u),skc5)* in(skf15(v),v)* in(skf15(v),cartesian_product2(skc5,skc6))* equal(skf15(u),skf15(v))* -> in(skf15(u),u)*.
% 25.59/25.85 8412[4:MRR:8411.0,1449.0] || in(skf15(u),u)* in(skf15(u),cartesian_product2(skc5,skc6))*+ equal(skf15(v),skf15(u))* -> in(skf15(v),v)*.
% 25.59/25.85 8414[4:Rew:62.1,8294.3,62.1,8294.1,8128.1,8294.1] || in(skf16(u),v) in(skf15(u),cartesian_product2(v,w))+ -> in(skf15(u),u)* in(skf15(u),skf24(skc4,w,v))*.
% 25.59/25.85 8985[4:Res:4692.0,8412.1] || in(skf15(skf24(skc4,u,skc5)),skf24(skc4,u,skc5))*+ equal(skf15(v),skf15(skf24(skc4,u,skc5)))* -> in(skf15(v),v)*.
% 25.59/25.85 9238[4:Res:44.1,8414.1] || in(skf16(u),skc5) -> in(skf15(u),u)* in(skf15(u),u)* in(skf15(u),skf24(skc4,skc6,skc5))*.
% 25.59/25.85 9259[4:Obv:9238.1] || in(skf16(u),skc5) -> in(skf15(u),u)* in(skf15(u),skf24(skc4,skc6,skc5))*.
% 25.59/25.85 9260[4:MRR:9259.0,1449.0] || -> in(skf15(u),u)* in(skf15(u),skf24(skc4,skc6,skc5))*.
% 25.59/25.85 9266[4:Fac:9260.0,9260.1] || -> in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))*.
% 25.59/25.85 9268[4:Res:9260.0,121.0] || -> in(skf15(skf24(skc4,u,skc5)),skf24(skc4,skc6,skc5)) equal(ordered_pair(skf25(skc5,skc4,skf15(skf24(skc4,u,skc5))),skf26(skf15(skf24(skc4,u,skc5)),skc4,skc5)),skf15(skf24(skc4,u,skc5)))**.
% 25.59/25.85 9292[4:MRR:9268.0,121.0] || -> equal(ordered_pair(skf25(skc5,skc4,skf15(skf24(skc4,u,skc5))),skf26(skf15(skf24(skc4,u,skc5)),skc4,skc5)),skf15(skf24(skc4,u,skc5)))**.
% 25.59/25.85 9346[4:SpL:9292.0,1498.1] || in(skf25(skc5,skc4,skf15(skf24(skc4,u,skc5))),skc5) equal(skf15(skf24(skc4,u,skc5)),skf15(skf24(skc4,skc6,skc5))) -> element(skf25(skc5,skc4,skf15(skf24(skc4,u,skc5))),powerset(the_carrier(skc4)))*.
% 25.59/25.85 9539[4:Res:9266.0,8985.0] || equal(skf15(u),skf15(skf24(skc4,skc6,skc5)))*+ -> in(skf15(u),u)*.
% 25.59/25.85 13297[4:Res:9266.0,120.0] || -> in(skf25(skc5,u,v),skc5)*.
% 25.59/25.85 13311[4:MRR:9346.0,13297.0] || equal(skf15(skf24(skc4,u,skc5)),skf15(skf24(skc4,skc6,skc5))) -> element(skf25(skc5,skc4,skf15(skf24(skc4,u,skc5))),powerset(the_carrier(skc4)))*.
% 25.59/25.85 14389[4:Res:13311.1,69.0] || equal(skf15(skf24(skc4,u,skc5)),skf15(skf24(skc4,skc6,skc5))) -> equal(subset_complement(the_carrier(skc4),skf25(skc5,skc4,skf15(skf24(skc4,u,skc5)))),skf26(skf15(skf24(skc4,u,skc5)),skc4,skc5))**.
% 25.59/25.85 15430[4:SpL:14389.1,1505.3] || equal(skf15(skf24(skc4,u,skc5)),skf15(skf24(skc4,skc6,skc5))) in(skf25(skc5,skc4,skf15(skf24(skc4,u,skc5))),skc5) in(skf15(v),v)* in(skf15(v),cartesian_product2(skc5,skc6))* equal(ordered_pair(skf25(skc5,skc4,skf15(skf24(skc4,u,skc5))),skf26(skf15(skf24(skc4,u,skc5)),skc4,skc5)),skf15(v))* -> .
% 25.59/25.85 15500[4:Rew:9292.0,15430.4] || equal(skf15(skf24(skc4,u,skc5)),skf15(skf24(skc4,skc6,skc5))) in(skf25(skc5,skc4,skf15(skf24(skc4,u,skc5))),skc5)* in(skf15(v),v)* in(skf15(v),cartesian_product2(skc5,skc6))* equal(skf15(skf24(skc4,u,skc5)),skf15(v))* -> .
% 25.59/25.85 15501[4:MRR:15500.1,13297.0] || equal(skf15(skf24(skc4,u,skc5)),skf15(skf24(skc4,skc6,skc5)))*+ in(skf15(v),v)* in(skf15(v),cartesian_product2(skc5,skc6))* equal(skf15(skf24(skc4,u,skc5)),skf15(v))* -> .
% 25.59/25.85 16301[4:EqR:15501.0] || in(skf15(u),u)* in(skf15(u),cartesian_product2(skc5,skc6))* equal(skf15(skf24(skc4,skc6,skc5)),skf15(u)) -> .
% 25.59/25.85 16302[4:MRR:16301.0,9539.1] || in(skf15(u),cartesian_product2(skc5,skc6))* equal(skf15(skf24(skc4,skc6,skc5)),skf15(u)) -> .
% 25.59/25.85 16411[4:Res:4692.0,16302.0] || equal(skf15(skf24(skc4,skc6,skc5)),skf15(skf24(skc4,u,skc5)))* -> .
% 25.59/25.85 16421[4:Obv:16411.0] || -> .
% 25.59/25.85 16426[4:Spt:16421.0,4709.2] || -> in(skf25(skc5,u,v),skc5)*.
% 25.59/25.85 16428[4:MRR:5389.0,16426.0] || equal(skf15(u),skf15(skf24(skc4,skc6,skc5)))+ -> in(skf15(u),u)* element(skf25(skc5,skc4,skf15(u)),powerset(the_carrier(skc4)))*.
% 25.59/25.85 17072[4:EqR:16428.0] || -> in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5)) element(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),powerset(the_carrier(skc4)))*.
% 25.59/25.85 17073[5:Spt:17072.0] || -> in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))*.
% 25.59/25.85 17075[5:Res:17073.0,121.0] || -> equal(ordered_pair(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skf26(skf15(skf24(skc4,skc6,skc5)),skc4,skc5)),skf15(skf24(skc4,skc6,skc5)))**.
% 25.59/25.85 17095[5:SpL:17075.0,1498.1] || in(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skc5) equal(skf15(skf24(skc4,skc6,skc5)),skf15(skf24(skc4,skc6,skc5))) -> element(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),powerset(the_carrier(skc4)))*.
% 25.83/26.11 17124[5:Obv:17095.1] || in(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skc5) -> element(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),powerset(the_carrier(skc4)))*.
% 25.83/26.11 17125[5:MRR:17124.0,16426.0] || -> element(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),powerset(the_carrier(skc4)))*.
% 25.83/26.11 17182[5:Res:17125.0,69.0] || -> equal(subset_complement(the_carrier(skc4),skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5)))),skf26(skf15(skf24(skc4,skc6,skc5)),skc4,skc5))**.
% 25.83/26.11 17431[5:SpL:17182.0,1505.3] || in(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skc5) in(skf15(u),u)* in(skf15(u),cartesian_product2(skc5,skc6))* equal(ordered_pair(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skf26(skf15(skf24(skc4,skc6,skc5)),skc4,skc5)),skf15(u))* -> .
% 25.83/26.11 17505[5:Rew:17075.0,17431.3] || in(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),skc5)* in(skf15(u),u)* in(skf15(u),cartesian_product2(skc5,skc6))* equal(skf15(skf24(skc4,skc6,skc5)),skf15(u)) -> .
% 25.83/26.11 17506[5:MRR:17505.0,16426.0] || in(skf15(u),u)* in(skf15(u),cartesian_product2(skc5,skc6))* equal(skf15(skf24(skc4,skc6,skc5)),skf15(u))+ -> .
% 25.83/26.11 18085[5:EqR:17506.2] || in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))* in(skf15(skf24(skc4,skc6,skc5)),cartesian_product2(skc5,skc6)) -> .
% 25.83/26.11 18086[5:MRR:18085.0,18085.1,17073.0,4692.0] || -> .
% 25.83/26.11 18087[5:Spt:18086.0,17072.0,17073.0] || in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,skc6,skc5))* -> .
% 25.83/26.11 18088[5:Spt:18086.0,17072.1] || -> element(skf25(skc5,skc4,skf15(skf24(skc4,skc6,skc5))),powerset(the_carrier(skc4)))*.
% 25.83/26.11 18090[5:MRR:7963.2,18087.0] || in(skf16(skf24(skc4,skc6,skc5)),u) in(skf15(skf24(skc4,skc6,skc5)),cartesian_product2(u,v)) -> in(skf15(skf24(skc4,skc6,skc5)),skf24(skc4,v,u))*.
% 25.83/26.11 18743[5:Res:18090.2,18087.0] || in(skf16(skf24(skc4,skc6,skc5)),skc5) in(skf15(skf24(skc4,skc6,skc5)),cartesian_product2(skc5,skc6))* -> .
% 25.83/26.11 18744[5:MRR:18743.0,18743.1,1449.0,4692.0] || -> .
% 25.83/26.11 % SZS output end Refutation
% 25.83/26.11 Formulae used in the proof : s1_xboole_0__e4_7_2__tops_2__1 antisymmetry_r2_hidden dt_k3_subset_1 involutiveness_k3_subset_1 s1_tarski__e4_7_2__tops_2__2
% 25.83/26.11
%------------------------------------------------------------------------------