TSTP Solution File: SEU331+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU331+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 10.93s 11.13s
% Output : Refutation 10.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU331+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n023.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 15:27:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 10.93/11.13
% 10.93/11.13 SPASS V 3.9
% 10.93/11.13 SPASS beiseite: Proof found.
% 10.93/11.13 % SZS status Theorem
% 10.93/11.13 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.93/11.13 SPASS derived 11804 clauses, backtracked 423 clauses, performed 11 splits and kept 7495 clauses.
% 10.93/11.13 SPASS allocated 109005 KBytes.
% 10.93/11.13 SPASS spent 0:0:10.79 on the problem.
% 10.93/11.13 0:00:00.04 for the input.
% 10.93/11.13 0:00:00.07 for the FLOTTER CNF translation.
% 10.93/11.13 0:00:00.21 for inferences.
% 10.93/11.13 0:00:00.18 for the backtracking.
% 10.93/11.13 0:0:10.16 for the reduction.
% 10.93/11.13
% 10.93/11.13
% 10.93/11.13 Here is a proof with depth 6, length 147 :
% 10.93/11.13 % SZS output start Refutation
% 10.93/11.13 1[0:Inp] || -> one_sorted_str(skc9)*.
% 10.93/11.13 11[0:Inp] || -> empty(empty_set)*.
% 10.93/11.13 25[0:Inp] || empty(powerset(u))* -> .
% 10.93/11.13 26[0:Inp] || -> relation(skf17(u,v))*.
% 10.93/11.13 27[0:Inp] || -> element(skf25(u),u)*.
% 10.93/11.13 41[0:Inp] empty(u) || -> relation(u)*.
% 10.93/11.13 43[0:Inp] || empty(unordered_pair(u,v))* -> .
% 10.93/11.13 44[0:Inp] || -> element(skc10,powerset(powerset(the_carrier(skc9))))*.
% 10.93/11.13 46[0:Inp] empty(u) || -> empty(relation_dom(u))*.
% 10.93/11.13 48[0:Inp] empty(u) || -> equal(u,empty_set)*.
% 10.93/11.13 51[0:Inp] empty(u) || in(v,u)* -> .
% 10.93/11.13 53[0:Inp] || -> element(u,powerset(the_carrier(v)))* SkP1(w,v,u)*.
% 10.93/11.13 70[0:Inp] || element(u,v) -> empty(v) in(u,v)*.
% 10.93/11.13 88[0:Inp] || equal(u,subset_complement(the_carrier(v),w))*+ -> SkP1(u,v,w)*.
% 10.93/11.13 90[0:Inp] || -> SkP0(u,v) in(skf20(u,v),complements_of_subsets(the_carrier(v),u))*.
% 10.93/11.13 91[0:Inp] || equal(skf19(u,v),skf18(u,v))**+ -> SkP0(w,x)*.
% 10.93/11.13 92[0:Inp] || in(u,complements_of_subsets(the_carrier(skc9),skc10))*+ -> SkP1(skf13(u),skc9,u)*.
% 10.93/11.13 98[0:Inp] || in(skf23(u,v),v)* in(ordered_pair(skf23(u,v),w),u)*+ -> .
% 10.93/11.13 100[0:Inp] relation(u) || equal(v,relation_dom(u))* in(ordered_pair(w,x),u)*+ -> in(w,v)*.
% 10.93/11.13 101[0:Inp] one_sorted_str(u) || SkP0(v,u) element(v,powerset(powerset(the_carrier(u))))* -> function(skf17(v,u)).
% 10.93/11.13 104[0:Inp] relation(u) || in(v,w)* equal(w,relation_dom(u))*+ -> in(ordered_pair(v,skf21(u,v)),u)*.
% 10.93/11.13 105[0:Inp] || in(u,complements_of_subsets(the_carrier(skc9),skc10))*+ SkP1(v,skc9,u)* SkP1(w,skc9,u)* -> equal(w,v)*.
% 10.93/11.13 106[0:Inp] relation(u) || -> equal(v,relation_dom(u)) in(skf23(u,v),v) in(ordered_pair(skf23(u,v),skf24(v,u)),u)*.
% 10.93/11.13 107[0:Inp] || element(skf20(u,v),powerset(the_carrier(v)))* -> equal(subset_complement(the_carrier(v),skf20(u,v)),skf18(u,v)) SkP0(u,v).
% 10.93/11.13 108[0:Inp] || element(skf20(u,v),powerset(the_carrier(v)))* -> equal(subset_complement(the_carrier(v),skf20(u,v)),skf19(u,v)) SkP0(u,v).
% 10.93/11.13 109[0:Inp] function(u) relation(u) || equal(relation_dom(u),complements_of_subsets(the_carrier(skc9),skc10))*+ -> in(skf14(v),complements_of_subsets(the_carrier(skc9),skc10))*.
% 10.93/11.13 110[0:Inp] function(u) relation(u) || in(v,relation_dom(u)) in(ordered_pair(v,w),u)* -> equal(w,apply(u,v)).
% 10.93/11.13 111[0:Inp] function(u) relation(u) || in(v,relation_dom(u)) equal(w,apply(u,v)) -> in(ordered_pair(v,w),u)*.
% 10.93/11.13 112[0:Inp] function(u) relation(u) || equal(relation_dom(u),complements_of_subsets(the_carrier(skc9),skc10)) SkP1(apply(u,skf14(u)),skc9,skf14(u))* -> .
% 10.93/11.13 113[0:Inp] one_sorted_str(u) || SkP0(v,u) element(v,powerset(powerset(the_carrier(u)))) in(ordered_pair(w,x),skf17(v,u))* -> in(w,complements_of_subsets(the_carrier(u),v)).
% 10.93/11.13 114[0:Inp] one_sorted_str(u) || SkP0(v,u) element(v,powerset(powerset(the_carrier(u)))) in(w,complements_of_subsets(the_carrier(u),v)) -> element(w,powerset(the_carrier(u))) in(ordered_pair(w,x),skf17(v,u))*.
% 10.93/11.13 115[0:Inp] one_sorted_str(u) || SkP0(v,u) element(w,powerset(the_carrier(u))) element(v,powerset(powerset(the_carrier(u)))) in(ordered_pair(w,x),skf17(v,u))* -> equal(x,subset_complement(the_carrier(u),w)).
% 10.93/11.13 116[0:Inp] one_sorted_str(u) || SkP0(v,u) element(v,powerset(powerset(the_carrier(u)))) equal(w,subset_complement(the_carrier(u),x)) in(x,complements_of_subsets(the_carrier(u),v)) -> in(ordered_pair(x,w),skf17(v,u))*.
% 10.93/11.13 118[0:Rew:107.1,108.1] || element(skf20(u,v),powerset(the_carrier(v)))* -> equal(skf19(u,v),skf18(u,v)) SkP0(u,v).
% 10.93/11.13 119[0:MRR:118.1,91.0] || element(skf20(u,v),powerset(the_carrier(v)))* -> SkP0(u,v).
% 10.93/11.13 156[0:Res:44.0,113.1] one_sorted_str(skc9) || SkP0(skc10,skc9) in(ordered_pair(u,v),skf17(skc10,skc9))* -> in(u,complements_of_subsets(the_carrier(skc9),skc10)).
% 10.93/11.13 157[0:Res:44.0,101.2] one_sorted_str(skc9) || SkP0(skc10,skc9) -> function(skf17(skc10,skc9))*.
% 10.93/11.13 158[0:Res:44.0,115.2] one_sorted_str(skc9) || in(ordered_pair(u,v),skf17(skc10,skc9))* SkP0(skc10,skc9) element(u,powerset(the_carrier(skc9))) -> equal(v,subset_complement(the_carrier(skc9),u)).
% 10.93/11.13 159[0:Res:44.0,116.2] one_sorted_str(skc9) || in(u,complements_of_subsets(the_carrier(skc9),skc10)) SkP0(skc10,skc9) equal(v,subset_complement(the_carrier(skc9),u)) -> in(ordered_pair(u,v),skf17(skc10,skc9))*.
% 10.93/11.13 182[0:MRR:157.0,1.0] || SkP0(skc10,skc9) -> function(skf17(skc10,skc9))*.
% 10.93/11.13 186[0:MRR:156.0,1.0] || SkP0(skc10,skc9) in(ordered_pair(u,v),skf17(skc10,skc9))* -> in(u,complements_of_subsets(the_carrier(skc9),skc10)).
% 10.93/11.13 188[0:MRR:158.0,1.0] || element(u,powerset(the_carrier(skc9))) SkP0(skc10,skc9) in(ordered_pair(u,v),skf17(skc10,skc9))* -> equal(v,subset_complement(the_carrier(skc9),u)).
% 10.93/11.13 189[0:MRR:159.0,1.0] || equal(u,subset_complement(the_carrier(skc9),v)) in(v,complements_of_subsets(the_carrier(skc9),skc10)) SkP0(skc10,skc9) -> in(ordered_pair(v,u),skf17(skc10,skc9))*.
% 10.93/11.13 195[1:Spt:109.0,109.1,109.2] function(u) relation(u) || equal(relation_dom(u),complements_of_subsets(the_carrier(skc9),skc10))* -> .
% 10.93/11.13 211[0:EmS:48.0,46.1] empty(u) || -> equal(relation_dom(u),empty_set)**.
% 10.93/11.13 626[0:Res:53.0,119.0] || -> SkP1(u,v,skf20(w,v))* SkP0(w,v).
% 10.93/11.13 642[0:EqR:88.0] || -> SkP1(subset_complement(the_carrier(u),v),u,v)*.
% 10.93/11.13 796[0:EqR:104.2] relation(u) || in(v,relation_dom(u)) -> in(ordered_pair(v,skf21(u,v)),u)*.
% 10.93/11.13 797[0:SpL:211.1,104.2] empty(u) relation(u) || in(v,w)* equal(w,empty_set) -> in(ordered_pair(v,skf21(u,v)),u)*.
% 10.93/11.13 798[0:SSi:797.1,41.1] empty(u) || in(v,w)* equal(w,empty_set) -> in(ordered_pair(v,skf21(u,v)),u)*.
% 10.93/11.13 799[0:MRR:798.3,51.1] empty(u) || in(v,w)* equal(w,empty_set) -> .
% 10.93/11.13 800[0:EmS:799.0,11.0] || in(u,v)* equal(v,empty_set) -> .
% 10.93/11.13 803[0:Res:70.2,800.0] || element(u,v)* equal(v,empty_set) -> empty(v).
% 10.93/11.13 806[0:Res:27.0,803.0] || equal(u,empty_set) -> empty(u)*.
% 10.93/11.13 818[0:Res:90.1,105.0] || SkP1(u,skc9,skf20(skc10,skc9))* SkP1(v,skc9,skf20(skc10,skc9))* -> SkP0(skc10,skc9) equal(v,u)*.
% 10.93/11.13 819[0:MRR:818.0,818.1,626.0,626.0] || -> SkP0(skc10,skc9)* equal(u,v)*.
% 10.93/11.13 820[0:MRR:188.1,819.0] || element(u,powerset(the_carrier(skc9))) in(ordered_pair(u,v),skf17(skc10,skc9))* -> equal(v,subset_complement(the_carrier(skc9),u)).
% 10.93/11.13 860[0:Res:806.1,25.0] || equal(powerset(u),empty_set)** -> .
% 10.93/11.13 861[0:Res:806.1,43.0] || equal(unordered_pair(u,v),empty_set)** -> .
% 10.93/11.13 868[0:Res:106.3,100.2] relation(u) relation(u) || equal(v,relation_dom(u)) -> equal(w,relation_dom(u)) in(skf23(u,w),w)* in(skf23(u,w),v)*.
% 10.93/11.13 876[0:Obv:868.0] relation(u) || equal(v,relation_dom(u))+ -> equal(w,relation_dom(u)) in(skf23(u,w),w)* in(skf23(u,w),v)*.
% 10.93/11.13 878[2:Spt:819.1] || -> equal(u,v)*.
% 10.93/11.13 879[2:UnC:878.0,860.0] || -> .
% 10.93/11.13 880[2:Spt:879.0,819.0] || -> SkP0(skc10,skc9)*.
% 10.93/11.13 881[2:MRR:182.0,880.0] || -> function(skf17(skc10,skc9))*.
% 10.93/11.13 882[2:MRR:186.0,880.0] || in(ordered_pair(u,v),skf17(skc10,skc9))* -> in(u,complements_of_subsets(the_carrier(skc9),skc10)).
% 10.93/11.13 884[2:MRR:189.2,880.0] || equal(u,subset_complement(the_carrier(skc9),v)) in(v,complements_of_subsets(the_carrier(skc9),skc10)) -> in(ordered_pair(v,u),skf17(skc10,skc9))*.
% 10.93/11.13 953[0:Res:106.3,113.3] relation(skf17(u,v)) one_sorted_str(v) || SkP0(u,v) element(u,powerset(powerset(the_carrier(v)))) -> equal(w,relation_dom(skf17(u,v))) in(skf23(skf17(u,v),w),w)* in(skf23(skf17(u,v),w),complements_of_subsets(the_carrier(v),u))*.
% 10.93/11.13 954[0:Res:111.4,113.3] function(skf17(u,v)) relation(skf17(u,v)) one_sorted_str(v) || in(w,relation_dom(skf17(u,v))) equal(x,apply(skf17(u,v),w))* SkP0(u,v) element(u,powerset(powerset(the_carrier(v)))) -> in(w,complements_of_subsets(the_carrier(v),u))*.
% 10.93/11.13 956[0:SSi:953.0,26.0] one_sorted_str(u) || SkP0(v,u) element(v,powerset(powerset(the_carrier(u))))+ -> equal(w,relation_dom(skf17(v,u))) in(skf23(skf17(v,u),w),w)* in(skf23(skf17(v,u),w),complements_of_subsets(the_carrier(u),v))*.
% 10.93/11.13 957[0:AED:954.4] function(skf17(u,v)) relation(skf17(u,v)) one_sorted_str(v) || in(w,relation_dom(skf17(u,v))) SkP0(u,v) element(u,powerset(powerset(the_carrier(v)))) -> in(w,complements_of_subsets(the_carrier(v),u))*.
% 10.93/11.13 958[0:SSi:957.1,26.0] function(skf17(u,v)) one_sorted_str(v) || in(w,relation_dom(skf17(u,v))) SkP0(u,v) element(u,powerset(powerset(the_carrier(v)))) -> in(w,complements_of_subsets(the_carrier(v),u))*.
% 10.93/11.13 959[0:MRR:958.0,101.3] one_sorted_str(u) || in(v,relation_dom(skf17(w,u))) SkP0(w,u) element(w,powerset(powerset(the_carrier(u)))) -> in(v,complements_of_subsets(the_carrier(u),w))*.
% 10.93/11.13 991[0:Res:114.5,110.3] one_sorted_str(u) function(skf17(v,u)) relation(skf17(v,u)) || SkP0(v,u) element(v,powerset(powerset(the_carrier(u)))) in(w,complements_of_subsets(the_carrier(u),v))* in(w,relation_dom(skf17(v,u))) -> element(w,powerset(the_carrier(u))) equal(x,apply(skf17(v,u),w))*.
% 10.93/11.13 998[0:SSi:991.2,26.0] one_sorted_str(u) function(skf17(v,u)) || SkP0(v,u) element(v,powerset(powerset(the_carrier(u)))) in(w,complements_of_subsets(the_carrier(u),v))* in(w,relation_dom(skf17(v,u))) -> element(w,powerset(the_carrier(u))) equal(x,apply(skf17(v,u),w))*.
% 10.93/11.13 999[0:MRR:998.1,101.3] one_sorted_str(u) || SkP0(v,u) element(v,powerset(powerset(the_carrier(u)))) in(w,complements_of_subsets(the_carrier(u),v))* in(w,relation_dom(skf17(v,u))) -> element(w,powerset(the_carrier(u))) equal(x,apply(skf17(v,u),w))*.
% 10.93/11.13 1000[0:MRR:999.3,959.4] one_sorted_str(u) || SkP0(v,u) element(v,powerset(powerset(the_carrier(u))))+ in(w,relation_dom(skf17(v,u)))* -> element(w,powerset(the_carrier(u))) equal(x,apply(skf17(v,u),w))*.
% 10.93/11.13 1061[0:Res:111.4,115.4] function(skf17(u,v)) relation(skf17(u,v)) one_sorted_str(v) || in(w,relation_dom(skf17(u,v)))* equal(x,apply(skf17(u,v),w))* SkP0(u,v) element(w,powerset(the_carrier(v))) element(u,powerset(powerset(the_carrier(v)))) -> equal(x,subset_complement(the_carrier(v),w)).
% 10.93/11.13 1064[0:SSi:1061.1,26.0] function(skf17(u,v)) one_sorted_str(v) || in(w,relation_dom(skf17(u,v)))* equal(x,apply(skf17(u,v),w))* SkP0(u,v) element(w,powerset(the_carrier(v))) element(u,powerset(powerset(the_carrier(v)))) -> equal(x,subset_complement(the_carrier(v),w)).
% 10.93/11.13 1065[0:MRR:1064.0,101.3] one_sorted_str(u) || in(v,relation_dom(skf17(w,u)))* equal(x,apply(skf17(w,u),v))*+ SkP0(w,u) element(v,powerset(the_carrier(u))) element(w,powerset(powerset(the_carrier(u)))) -> equal(x,subset_complement(the_carrier(u),v)).
% 10.93/11.13 1069[0:Res:116.5,98.1] one_sorted_str(u) || SkP0(v,u) element(v,powerset(powerset(the_carrier(u)))) equal(w,subset_complement(the_carrier(u),skf23(skf17(v,u),x)))* in(skf23(skf17(v,u),x),complements_of_subsets(the_carrier(u),v))* in(skf23(skf17(v,u),x),x)* -> .
% 10.93/11.13 1082[0:AED:1069.3] one_sorted_str(u) || SkP0(v,u) element(v,powerset(powerset(the_carrier(u)))) in(skf23(skf17(v,u),w),complements_of_subsets(the_carrier(u),v))*+ in(skf23(skf17(v,u),w),w)* -> .
% 10.93/11.13 1660[2:Res:106.3,882.0] relation(skf17(skc10,skc9)) || -> equal(u,relation_dom(skf17(skc10,skc9))) in(skf23(skf17(skc10,skc9),u),u)* in(skf23(skf17(skc10,skc9),u),complements_of_subsets(the_carrier(skc9),skc10))*.
% 10.93/11.13 1661[2:Res:111.4,882.0] function(skf17(skc10,skc9)) relation(skf17(skc10,skc9)) || in(u,relation_dom(skf17(skc10,skc9))) equal(v,apply(skf17(skc10,skc9),u))* -> in(u,complements_of_subsets(the_carrier(skc9),skc10))*.
% 10.93/11.13 1665[2:SSi:1660.0,881.0,26.0,1.0] || -> equal(u,relation_dom(skf17(skc10,skc9))) in(skf23(skf17(skc10,skc9),u),u)* in(skf23(skf17(skc10,skc9),u),complements_of_subsets(the_carrier(skc9),skc10))*.
% 10.93/11.13 1666[2:AED:1661.3] function(skf17(skc10,skc9)) relation(skf17(skc10,skc9)) || in(u,relation_dom(skf17(skc10,skc9))) -> in(u,complements_of_subsets(the_carrier(skc9),skc10))*.
% 10.93/11.13 1667[2:SSi:1666.1,1666.0,881.0,26.0,1.0,881.0,26.0,1.0] || in(u,relation_dom(skf17(skc10,skc9))) -> in(u,complements_of_subsets(the_carrier(skc9),skc10))*.
% 10.93/11.13 2101[0:Res:796.2,110.3] relation(u) function(u) relation(u) || in(v,relation_dom(u))* in(v,relation_dom(u))* -> equal(skf21(u,v),apply(u,v)).
% 10.93/11.13 2118[0:Obv:2101.3] function(u) relation(u) || in(v,relation_dom(u))* -> equal(skf21(u,v),apply(u,v)).
% 10.93/11.13 2498[0:Res:796.2,820.1] relation(skf17(skc10,skc9)) || in(u,relation_dom(skf17(skc10,skc9)))* element(u,powerset(the_carrier(skc9))) -> equal(skf21(skf17(skc10,skc9),u),subset_complement(the_carrier(skc9),u)).
% 10.93/11.13 2527[2:Res:884.2,98.1] || equal(u,subset_complement(the_carrier(skc9),skf23(skf17(skc10,skc9),v)))* in(skf23(skf17(skc10,skc9),v),complements_of_subsets(the_carrier(skc9),skc10))* in(skf23(skf17(skc10,skc9),v),v)* -> .
% 10.93/11.13 2542[2:AED:2527.0] || in(skf23(skf17(skc10,skc9),u),complements_of_subsets(the_carrier(skc9),skc10))*+ in(skf23(skf17(skc10,skc9),u),u)* -> .
% 10.93/11.13 2784[0:EqR:876.1] relation(u) || -> equal(v,relation_dom(u)) in(skf23(u,v),v)* in(skf23(u,v),relation_dom(u))*.
% 10.93/11.13 3775[2:Res:1667.1,1082.3] one_sorted_str(skc9) || in(skf23(skf17(skc10,skc9),u),relation_dom(skf17(skc10,skc9)))* SkP0(skc10,skc9) element(skc10,powerset(powerset(the_carrier(skc9)))) in(skf23(skf17(skc10,skc9),u),u)* -> .
% 10.93/11.13 3777[2:SSi:3775.0,1.0] || in(skf23(skf17(skc10,skc9),u),relation_dom(skf17(skc10,skc9)))* SkP0(skc10,skc9) element(skc10,powerset(powerset(the_carrier(skc9)))) in(skf23(skf17(skc10,skc9),u),u)* -> .
% 10.93/11.13 3778[2:MRR:3777.1,3777.2,880.0,44.0] || in(skf23(skf17(skc10,skc9),u),relation_dom(skf17(skc10,skc9)))* in(skf23(skf17(skc10,skc9),u),u)* -> .
% 10.93/11.13 4119[0:Res:44.0,956.2] one_sorted_str(skc9) || SkP0(skc10,skc9) -> equal(u,relation_dom(skf17(skc10,skc9))) in(skf23(skf17(skc10,skc9),u),u)* in(skf23(skf17(skc10,skc9),u),complements_of_subsets(the_carrier(skc9),skc10))*.
% 10.93/11.13 4293[0:EqR:1065.2] one_sorted_str(u) || in(v,relation_dom(skf17(w,u)))* SkP0(w,u) element(v,powerset(the_carrier(u))) element(w,powerset(powerset(the_carrier(u)))) -> equal(apply(skf17(w,u),v),subset_complement(the_carrier(u),v)).
% 10.93/11.13 4299[0:MRR:4293.3,1000.4] one_sorted_str(u) || in(v,relation_dom(skf17(w,u)))* SkP0(w,u) element(w,powerset(powerset(the_carrier(u)))) -> equal(apply(skf17(w,u),v),subset_complement(the_carrier(u),v)).
% 10.93/11.13 4302[0:Rew:4299.4,1000.5] one_sorted_str(u) || SkP0(v,u) element(v,powerset(powerset(the_carrier(u))))+ in(w,relation_dom(skf17(v,u)))* -> element(w,powerset(the_carrier(u))) equal(x,subset_complement(the_carrier(u),w))*.
% 10.93/11.13 4400[0:Res:44.0,4302.2] one_sorted_str(skc9) || SkP0(skc10,skc9) in(u,relation_dom(skf17(skc10,skc9)))* -> element(u,powerset(the_carrier(skc9))) equal(v,subset_complement(the_carrier(skc9),u))*.
% 10.93/11.13 4428[0:SSi:4400.0,1.0] || SkP0(skc10,skc9) in(u,relation_dom(skf17(skc10,skc9)))* -> element(u,powerset(the_carrier(skc9))) equal(v,subset_complement(the_carrier(skc9),u))*.
% 10.93/11.13 7123[2:Res:2784.2,2542.0] relation(skf17(skc10,skc9)) || in(skf23(skf17(skc10,skc9),complements_of_subsets(the_carrier(skc9),skc10)),complements_of_subsets(the_carrier(skc9),skc10))* -> equal(complements_of_subsets(the_carrier(skc9),skc10),relation_dom(skf17(skc10,skc9))) in(skf23(skf17(skc10,skc9),complements_of_subsets(the_carrier(skc9),skc10)),relation_dom(skf17(skc10,skc9))).
% 10.93/11.13 7129[2:SSi:7123.0,881.0,26.0,1.0] || in(skf23(skf17(skc10,skc9),complements_of_subsets(the_carrier(skc9),skc10)),complements_of_subsets(the_carrier(skc9),skc10))* -> equal(complements_of_subsets(the_carrier(skc9),skc10),relation_dom(skf17(skc10,skc9))) in(skf23(skf17(skc10,skc9),complements_of_subsets(the_carrier(skc9),skc10)),relation_dom(skf17(skc10,skc9))).
% 10.93/11.13 7130[2:MRR:7129.2,3778.0] || in(skf23(skf17(skc10,skc9),complements_of_subsets(the_carrier(skc9),skc10)),complements_of_subsets(the_carrier(skc9),skc10))* -> equal(complements_of_subsets(the_carrier(skc9),skc10),relation_dom(skf17(skc10,skc9))).
% 10.93/11.13 7988[2:Fac:1665.1,1665.2] || -> equal(complements_of_subsets(the_carrier(skc9),skc10),relation_dom(skf17(skc10,skc9))) in(skf23(skf17(skc10,skc9),complements_of_subsets(the_carrier(skc9),skc10)),complements_of_subsets(the_carrier(skc9),skc10))*.
% 10.93/11.13 8012[2:MRR:7988.1,7130.0] || -> equal(complements_of_subsets(the_carrier(skc9),skc10),relation_dom(skf17(skc10,skc9)))**.
% 10.93/11.13 8013[2:Rew:8012.0,195.2] function(u) relation(u) || equal(relation_dom(u),relation_dom(skf17(skc10,skc9)))* -> .
% 10.93/11.13 10105[2:EqR:8013.2] function(skf17(skc10,skc9)) relation(skf17(skc10,skc9)) || -> .
% 10.93/11.13 10110[2:SSi:10105.1,10105.0,881.0,26.0,1.0,881.0,26.0,1.0] || -> .
% 10.93/11.13 10112[1:Spt:10110.0,109.3] || -> in(skf14(u),complements_of_subsets(the_carrier(skc9),skc10))*.
% 10.93/11.13 10116[0:MRR:4428.0,819.0] || in(u,relation_dom(skf17(skc10,skc9)))*+ -> element(u,powerset(the_carrier(skc9))) equal(v,subset_complement(the_carrier(skc9),u))*.
% 10.98/11.21 10131[0:SSi:2498.0,26.0,1.0] || in(u,relation_dom(skf17(skc10,skc9)))* element(u,powerset(the_carrier(skc9))) -> equal(skf21(skf17(skc10,skc9),u),subset_complement(the_carrier(skc9),u)).
% 10.98/11.21 10132[0:MRR:10131.1,10116.1] || in(u,relation_dom(skf17(skc10,skc9)))* -> equal(skf21(skf17(skc10,skc9),u),subset_complement(the_carrier(skc9),u)).
% 10.98/11.21 10143[0:SSi:4119.0,1.0] || SkP0(skc10,skc9) -> equal(u,relation_dom(skf17(skc10,skc9))) in(skf23(skf17(skc10,skc9),u),u)* in(skf23(skf17(skc10,skc9),u),complements_of_subsets(the_carrier(skc9),skc10))*.
% 10.98/11.21 10144[0:MRR:10143.0,819.0] || -> equal(u,relation_dom(skf17(skc10,skc9))) in(skf23(skf17(skc10,skc9),u),u)* in(skf23(skf17(skc10,skc9),u),complements_of_subsets(the_carrier(skc9),skc10))*.
% 10.98/11.21 10174[2:Spt:819.1] || -> equal(u,v)*.
% 10.98/11.21 10175[2:UnC:10174.0,861.0] || -> .
% 10.98/11.21 10176[2:Spt:10175.0,819.0] || -> SkP0(skc10,skc9)*.
% 10.98/11.21 10177[2:MRR:182.0,10176.0] || -> function(skf17(skc10,skc9))*.
% 10.98/11.21 10178[2:MRR:186.0,10176.0] || in(ordered_pair(u,v),skf17(skc10,skc9))* -> in(u,complements_of_subsets(the_carrier(skc9),skc10)).
% 10.98/11.21 10181[2:MRR:189.2,10176.0] || equal(u,subset_complement(the_carrier(skc9),v)) in(v,complements_of_subsets(the_carrier(skc9),skc10)) -> in(ordered_pair(v,u),skf17(skc10,skc9))*.
% 10.98/11.21 10264[1:Res:10112.0,92.0] || -> SkP1(skf13(skf14(u)),skc9,skf14(u))*.
% 10.98/11.21 10402[1:Res:10112.0,105.0] || SkP1(u,skc9,skf14(v))*+ SkP1(w,skc9,skf14(v))* -> equal(w,u)*.
% 10.98/11.21 10511[2:Res:796.2,10178.0] relation(skf17(skc10,skc9)) || in(u,relation_dom(skf17(skc10,skc9))) -> in(u,complements_of_subsets(the_carrier(skc9),skc10))*.
% 10.98/11.21 10518[2:SSi:10511.0,10177.0,26.0,1.0] || in(u,relation_dom(skf17(skc10,skc9))) -> in(u,complements_of_subsets(the_carrier(skc9),skc10))*.
% 10.98/11.21 10677[2:Res:10181.2,98.1] || equal(u,subset_complement(the_carrier(skc9),skf23(skf17(skc10,skc9),v)))* in(skf23(skf17(skc10,skc9),v),complements_of_subsets(the_carrier(skc9),skc10))* in(skf23(skf17(skc10,skc9),v),v)* -> .
% 10.98/11.21 10693[2:AED:10677.0] || in(skf23(skf17(skc10,skc9),u),complements_of_subsets(the_carrier(skc9),skc10))*+ in(skf23(skf17(skc10,skc9),u),u)* -> .
% 10.98/11.21 11387[1:Res:10264.0,10402.0] || SkP1(u,skc9,skf14(v))* -> equal(u,skf13(skf14(v))).
% 10.98/11.21 11759[2:Res:2784.2,10693.0] relation(skf17(skc10,skc9)) || in(skf23(skf17(skc10,skc9),complements_of_subsets(the_carrier(skc9),skc10)),complements_of_subsets(the_carrier(skc9),skc10))* -> equal(complements_of_subsets(the_carrier(skc9),skc10),relation_dom(skf17(skc10,skc9))) in(skf23(skf17(skc10,skc9),complements_of_subsets(the_carrier(skc9),skc10)),relation_dom(skf17(skc10,skc9))).
% 10.98/11.21 11763[2:Res:10518.1,10693.0] || in(skf23(skf17(skc10,skc9),u),relation_dom(skf17(skc10,skc9)))* in(skf23(skf17(skc10,skc9),u),u)* -> .
% 10.98/11.21 11765[2:SSi:11759.0,10177.0,26.0,1.0] || in(skf23(skf17(skc10,skc9),complements_of_subsets(the_carrier(skc9),skc10)),complements_of_subsets(the_carrier(skc9),skc10))* -> equal(complements_of_subsets(the_carrier(skc9),skc10),relation_dom(skf17(skc10,skc9))) in(skf23(skf17(skc10,skc9),complements_of_subsets(the_carrier(skc9),skc10)),relation_dom(skf17(skc10,skc9))).
% 10.98/11.21 11766[2:MRR:11765.2,11763.0] || in(skf23(skf17(skc10,skc9),complements_of_subsets(the_carrier(skc9),skc10)),complements_of_subsets(the_carrier(skc9),skc10))* -> equal(complements_of_subsets(the_carrier(skc9),skc10),relation_dom(skf17(skc10,skc9))).
% 10.98/11.21 12221[0:Fac:10144.1,10144.2] || -> equal(complements_of_subsets(the_carrier(skc9),skc10),relation_dom(skf17(skc10,skc9))) in(skf23(skf17(skc10,skc9),complements_of_subsets(the_carrier(skc9),skc10)),complements_of_subsets(the_carrier(skc9),skc10))*.
% 10.98/11.21 12242[2:MRR:12221.1,11766.0] || -> equal(complements_of_subsets(the_carrier(skc9),skc10),relation_dom(skf17(skc10,skc9)))**.
% 10.98/11.21 12243[2:Rew:12242.0,10112.0] || -> in(skf14(u),relation_dom(skf17(skc10,skc9)))*.
% 10.98/11.21 12269[2:Rew:12242.0,112.2] function(u) relation(u) || equal(relation_dom(u),relation_dom(skf17(skc10,skc9))) SkP1(apply(u,skf14(u)),skc9,skf14(u))* -> .
% 10.98/11.21 13477[2:Res:12243.0,2118.2] function(skf17(skc10,skc9)) relation(skf17(skc10,skc9)) || -> equal(skf21(skf17(skc10,skc9),skf14(u)),apply(skf17(skc10,skc9),skf14(u)))**.
% 10.98/11.21 13481[2:Res:12243.0,10132.0] || -> equal(skf21(skf17(skc10,skc9),skf14(u)),subset_complement(the_carrier(skc9),skf14(u)))**.
% 10.98/11.21 13486[2:Rew:13481.0,13477.2] function(skf17(skc10,skc9)) relation(skf17(skc10,skc9)) || -> equal(apply(skf17(skc10,skc9),skf14(u)),subset_complement(the_carrier(skc9),skf14(u)))**.
% 10.98/11.21 13487[2:SSi:13486.1,13486.0,10177.0,26.0,1.0,10177.0,26.0,1.0] || -> equal(apply(skf17(skc10,skc9),skf14(u)),subset_complement(the_carrier(skc9),skf14(u)))**.
% 10.98/11.21 13911[1:Res:642.0,11387.0] || -> equal(subset_complement(the_carrier(skc9),skf14(u)),skf13(skf14(u)))**.
% 10.98/11.21 13918[2:Rew:13911.0,13487.0] || -> equal(apply(skf17(skc10,skc9),skf14(u)),skf13(skf14(u)))**.
% 10.98/11.21 13991[2:SpL:13918.0,12269.3] function(skf17(skc10,skc9)) relation(skf17(skc10,skc9)) || equal(relation_dom(skf17(skc10,skc9)),relation_dom(skf17(skc10,skc9))) SkP1(skf13(skf14(skf17(skc10,skc9))),skc9,skf14(skf17(skc10,skc9)))* -> .
% 10.98/11.21 13992[2:Obv:13991.2] function(skf17(skc10,skc9)) relation(skf17(skc10,skc9)) || SkP1(skf13(skf14(skf17(skc10,skc9))),skc9,skf14(skf17(skc10,skc9)))* -> .
% 10.98/11.21 13993[2:SSi:13992.1,13992.0,10177.0,26.0,1.0,10177.0,26.0,1.0] || SkP1(skf13(skf14(skf17(skc10,skc9))),skc9,skf14(skf17(skc10,skc9)))* -> .
% 10.98/11.21 13994[2:MRR:13993.0,10264.0] || -> .
% 10.98/11.21 % SZS output end Refutation
% 10.98/11.21 Formulae used in the proof : s2_funct_1__e4_7_1__tops_2 fc4_relat_1 fc1_subset_1 s1_funct_1__e4_7_1__tops_2__1 rc3_relat_1 existence_m1_subset_1 cc1_relat_1 fc3_subset_1 fc7_relat_1 t6_boole t7_boole t2_subset d4_relat_1 antisymmetry_r2_hidden d4_funct_1
% 10.98/11.21
%------------------------------------------------------------------------------