TSTP Solution File: SEU017+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU017+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 14:33:34 EDT 2022
% Result : Theorem 272.09s 272.27s
% Output : Refutation 297.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU017+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n029.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 07:11:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 272.09/272.27
% 272.09/272.27 SPASS V 3.9
% 272.09/272.27 SPASS beiseite: Proof found.
% 272.09/272.27 % SZS status Theorem
% 272.09/272.27 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 272.09/272.27 SPASS derived 53081 clauses, backtracked 3306 clauses, performed 19 splits and kept 26013 clauses.
% 272.09/272.27 SPASS allocated 190770 KBytes.
% 272.09/272.27 SPASS spent 0:4:31.83 on the problem.
% 272.09/272.27 0:00:00.04 for the input.
% 272.09/272.27 0:00:00.08 for the FLOTTER CNF translation.
% 272.09/272.27 0:00:01.46 for inferences.
% 272.09/272.27 0:0:14.62 for the backtracking.
% 272.09/272.27 0:4:14.62 for the reduction.
% 272.09/272.27
% 272.09/272.27
% 272.09/272.27 Here is a proof with depth 9, length 254 :
% 272.09/272.27 % SZS output start Refutation
% 272.09/272.27 1[0:Inp] || -> function(skc10)*.
% 272.09/272.27 2[0:Inp] || -> relation(skc10)*.
% 272.09/272.27 3[0:Inp] || -> one_to_one(skc9)*.
% 272.09/272.27 4[0:Inp] || -> function(skc9)*.
% 272.09/272.27 5[0:Inp] || -> relation(skc9)*.
% 272.09/272.27 8[0:Inp] || -> relation_empty_yielding(empty_set)*.
% 272.09/272.27 10[0:Inp] || -> empty(empty_set)*.
% 272.09/272.27 11[0:Inp] || -> relation(empty_set)*.
% 272.09/272.27 21[0:Inp] || -> relation(identity_relation(u))*.
% 272.09/272.27 22[0:Inp] || -> function(identity_relation(u))*.
% 272.09/272.27 24[0:Inp] || -> empty(skf17(u))*.
% 272.09/272.27 27[0:Inp] || -> equal(relation_dom(skc9),skc11)**.
% 272.09/272.27 28[0:Inp] || -> equal(relation_dom(skc10),skc11)**.
% 272.09/272.27 29[0:Inp] || -> subset(relation_rng(skc10),skc11)*.
% 272.09/272.27 30[0:Inp] || -> element(skf15(u),u)*.
% 272.09/272.27 32[0:Inp] || equal(identity_relation(skc11),skc10)** -> .
% 272.09/272.27 33[0:Inp] || -> equal(relation_composition(skc10,skc9),skc9)**.
% 272.09/272.27 34[0:Inp] empty(u) || -> function(u)*.
% 272.09/272.27 35[0:Inp] empty(u) || -> relation(u)*.
% 272.09/272.27 37[0:Inp] || -> element(skf17(u),powerset(u))*.
% 272.09/272.27 38[0:Inp] empty(u) || -> empty(relation_dom(u))*.
% 272.09/272.27 43[0:Inp] empty(u) || -> equal(u,empty_set)*.
% 272.09/272.27 45[0:Inp] empty(u) || in(v,u)* -> .
% 272.09/272.27 48[0:Inp] || subset(u,v) -> element(u,powerset(v))*.
% 272.09/272.27 49[0:Inp] relation(u) || empty(relation_dom(u))* -> empty(u).
% 272.09/272.27 50[0:Inp] relation(u) || empty(relation_rng(u))* -> empty(u).
% 272.09/272.27 51[0:Inp] || element(u,v)* -> empty(v) in(u,v).
% 272.09/272.27 54[0:Inp] relation(u) empty(v) || -> empty(relation_composition(u,v))*.
% 272.09/272.27 58[0:Inp] || in(u,v)* element(v,powerset(w))*+ -> element(u,w)*.
% 272.09/272.27 59[0:Inp] empty(u) || in(v,w)* element(w,powerset(u))*+ -> .
% 272.09/272.27 60[0:Inp] function(u) relation(u) || -> one_to_one(u) in(skf14(u),relation_dom(u))*.
% 272.09/272.27 61[0:Inp] function(u) relation(u) || -> one_to_one(u) in(skf13(u),relation_dom(u))*.
% 272.09/272.27 62[0:Inp] function(u) relation(u) || equal(skf14(u),skf13(u))** -> one_to_one(u).
% 272.09/272.27 63[0:Inp] relation(u) function(u) || equal(u,identity_relation(v))*+ -> equal(relation_dom(u),v)*.
% 272.09/272.27 65[0:Inp] relation(u) function(u) function(v) relation(v) || -> function(relation_composition(v,u))*.
% 272.09/272.27 66[0:Inp] function(u) relation(u) || -> one_to_one(u) equal(apply(u,skf14(u)),apply(u,skf13(u)))**.
% 272.09/272.27 68[0:Inp] relation(u) function(u) || equal(relation_dom(u),v)*+ -> equal(u,identity_relation(v))* in(skf18(v,w),v)*.
% 272.09/272.27 70[0:Inp] function(u) relation(u) || -> equal(v,relation_rng(u)) in(skf11(u,v),v)* in(skf12(u,w),relation_dom(u))*.
% 272.09/272.27 71[0:Inp] function(u) relation(u) || in(v,w)* equal(w,relation_rng(u))*+ -> in(skf9(u,x),relation_dom(u))*.
% 272.09/272.27 72[0:Inp] function(u) relation(u) || in(v,w)* equal(w,relation_rng(u))*+ -> equal(apply(u,skf9(u,v)),v)**.
% 272.09/272.27 74[0:Inp] relation(u) function(u) || equal(relation_dom(u),v) equal(apply(u,skf18(v,u)),skf18(v,u))** -> equal(u,identity_relation(v)).
% 272.09/272.27 75[0:Inp] function(u) relation(u) || in(v,relation_dom(u))* equal(w,relation_rng(u))* equal(x,apply(u,v))*+ -> in(x,w)*.
% 272.09/272.27 76[0:Inp] relation(u) function(u) relation(v) function(v) || in(w,relation_dom(u)) -> equal(apply(relation_composition(u,v),w),apply(v,apply(u,w)))**.
% 272.09/272.27 77[0:Inp] function(u) relation(u) one_to_one(u) || in(v,relation_dom(u))* in(w,relation_dom(u))* equal(apply(u,v),apply(u,w))*+ -> equal(v,w).
% 272.09/272.27 84[0:Res:5.0,71.0] function(skc9) || in(u,v)* equal(v,relation_rng(skc9)) -> in(skf9(skc9,w),relation_dom(skc9))*.
% 272.09/272.27 85[0:Res:5.0,70.0] function(skc9) || -> in(skf12(skc9,u),relation_dom(skc9))* in(skf11(skc9,v),v)* equal(v,relation_rng(skc9)).
% 272.09/272.27 87[0:Res:5.0,68.1] function(skc9) || equal(relation_dom(skc9),u) -> in(skf18(u,v),u)* equal(identity_relation(u),skc9).
% 272.09/272.27 95[0:Res:5.0,49.0] || empty(relation_dom(skc9))* -> empty(skc9).
% 272.09/272.27 96[0:Res:5.0,50.0] || empty(relation_rng(skc9))* -> empty(skc9).
% 272.09/272.27 100[0:Res:5.0,54.1] empty(u) || -> empty(relation_composition(skc9,u))*.
% 272.09/272.27 105[0:Res:4.0,76.0] relation(skc9) function(u) relation(u) || in(v,relation_dom(u)) -> equal(apply(relation_composition(u,skc9),v),apply(skc9,apply(u,v)))**.
% 272.09/272.27 106[0:Res:4.0,75.1] relation(skc9) || equal(u,relation_rng(skc9)) in(v,relation_dom(skc9))* equal(w,apply(skc9,v))* -> in(w,u)*.
% 272.09/272.27 122[0:Res:3.0,77.0] relation(skc9) function(skc9) || in(u,relation_dom(skc9))* in(v,relation_dom(skc9))* equal(apply(skc9,v),apply(skc9,u))* -> equal(v,u).
% 272.09/272.27 128[0:Res:2.0,72.0] function(skc10) || in(u,v)* equal(v,relation_rng(skc10)) -> equal(apply(skc10,skf9(skc10,u)),u)**.
% 272.09/272.27 129[0:Res:2.0,71.0] function(skc10) || in(u,v)* equal(v,relation_rng(skc10)) -> in(skf9(skc10,w),relation_dom(skc10))*.
% 272.09/272.27 132[0:Res:2.0,68.1] function(skc10) || equal(relation_dom(skc10),u) -> in(skf18(u,v),u)* equal(identity_relation(u),skc10).
% 272.09/272.27 133[0:Res:2.0,66.0] function(skc10) || -> equal(apply(skc10,skf14(skc10)),apply(skc10,skf13(skc10)))** one_to_one(skc10).
% 272.09/272.27 136[0:Res:2.0,62.0] function(skc10) || equal(skf14(skc10),skf13(skc10))** -> one_to_one(skc10).
% 272.09/272.27 137[0:Res:2.0,60.0] function(skc10) || -> in(skf14(skc10),relation_dom(skc10))* one_to_one(skc10).
% 272.09/272.27 138[0:Res:2.0,61.0] function(skc10) || -> in(skf13(skc10),relation_dom(skc10))* one_to_one(skc10).
% 272.09/272.27 141[0:Res:2.0,50.0] || empty(relation_rng(skc10))* -> empty(skc10).
% 272.09/272.27 151[0:Res:1.0,75.1] relation(skc10) || equal(u,relation_rng(skc10)) in(v,relation_dom(skc10))* equal(w,apply(skc10,v))* -> in(w,u)*.
% 272.09/272.27 167[0:Rew:27.0,95.0] || empty(skc11)* -> empty(skc9).
% 272.09/272.27 169[0:Rew:28.0,137.1] function(skc10) || -> in(skf14(skc10),skc11)* one_to_one(skc10).
% 272.09/272.27 170[0:MRR:169.0,1.0] || -> one_to_one(skc10) in(skf14(skc10),skc11)*.
% 272.09/272.27 171[0:Rew:28.0,138.1] function(skc10) || -> in(skf13(skc10),skc11)* one_to_one(skc10).
% 272.09/272.27 172[0:MRR:171.0,1.0] || -> one_to_one(skc10) in(skf13(skc10),skc11)*.
% 272.09/272.27 175[0:MRR:136.0,1.0] || equal(skf14(skc10),skf13(skc10))** -> one_to_one(skc10).
% 272.09/272.27 186[0:MRR:133.0,1.0] || -> one_to_one(skc10) equal(apply(skc10,skf14(skc10)),apply(skc10,skf13(skc10)))**.
% 272.09/272.27 188[0:Rew:27.0,87.1] function(skc9) || equal(skc11,u) -> in(skf18(u,v),u)* equal(identity_relation(u),skc9).
% 272.09/272.27 189[0:MRR:188.0,4.0] || equal(skc11,u) -> equal(identity_relation(u),skc9) in(skf18(u,v),u)*.
% 272.09/272.27 192[0:Rew:189.2,132.3,28.0,132.1] function(skc10) || equal(skc11,u) -> in(skf18(u,v),u)* equal(skc10,skc9).
% 272.09/272.27 193[0:MRR:192.0,1.0] || equal(skc11,u) -> equal(skc10,skc9) in(skf18(u,v),u)*.
% 272.09/272.27 195[0:Rew:27.0,84.3] function(skc9) || in(u,v)* equal(v,relation_rng(skc9)) -> in(skf9(skc9,w),skc11)*.
% 272.09/272.27 196[0:MRR:195.0,4.0] || in(u,v)* equal(v,relation_rng(skc9)) -> in(skf9(skc9,w),skc11)*.
% 272.09/272.27 197[0:Rew:27.0,85.1] function(skc9) || -> in(skf12(skc9,u),skc11)* in(skf11(skc9,v),v)* equal(v,relation_rng(skc9)).
% 272.09/272.27 198[0:MRR:197.0,4.0] || -> equal(u,relation_rng(skc9)) in(skf11(skc9,u),u)* in(skf12(skc9,v),skc11)*.
% 272.09/272.27 201[0:Rew:28.0,129.3] function(skc10) || in(u,v)* equal(v,relation_rng(skc10)) -> in(skf9(skc10,w),skc11)*.
% 272.09/272.27 202[0:MRR:201.0,1.0] || in(u,v)* equal(v,relation_rng(skc10))+ -> in(skf9(skc10,w),skc11)*.
% 272.09/272.27 208[0:MRR:128.0,1.0] || in(u,v)* equal(v,relation_rng(skc10))+ -> equal(apply(skc10,skf9(skc10,u)),u)**.
% 272.09/272.27 213[0:Rew:28.0,151.2] relation(skc10) || equal(u,relation_rng(skc10)) in(v,skc11) equal(w,apply(skc10,v))* -> in(w,u)*.
% 272.09/272.27 214[0:MRR:213.0,2.0] || in(u,skc11) equal(v,relation_rng(skc10)) equal(w,apply(skc10,u))*+ -> in(w,v)*.
% 272.09/272.27 219[0:Rew:27.0,106.2] relation(skc9) || equal(u,relation_rng(skc9)) in(v,skc11) equal(w,apply(skc9,v))* -> in(w,u)*.
% 272.09/272.27 220[0:MRR:219.0,5.0] || in(u,skc11) equal(v,relation_rng(skc9)) equal(w,apply(skc9,u))*+ -> in(w,v)*.
% 272.09/272.27 229[0:MRR:105.0,5.0] relation(u) function(u) || in(v,relation_dom(u)) -> equal(apply(relation_composition(u,skc9),v),apply(skc9,apply(u,v)))**.
% 272.09/272.27 234[0:Rew:27.0,122.3,27.0,122.2] relation(skc9) function(skc9) || in(u,skc11) in(v,skc11) equal(apply(skc9,v),apply(skc9,u))* -> equal(v,u).
% 272.09/272.27 235[0:MRR:234.0,234.1,5.0,4.0] || in(u,skc11) in(v,skc11) equal(apply(skc9,u),apply(skc9,v))* -> equal(u,v).
% 272.09/272.27 238[1:Spt:193.1] || -> equal(skc10,skc9)**.
% 272.09/272.27 244[1:Rew:238.0,29.0] || -> subset(relation_rng(skc9),skc11)*.
% 272.09/272.27 267[1:Rew:238.0,33.0] || -> equal(relation_composition(skc9,skc9),skc9)**.
% 272.09/272.27 268[1:Rew:238.0,32.0] || equal(identity_relation(skc11),skc9)** -> .
% 272.09/272.27 280[2:Spt:198.0,198.1] || -> equal(u,relation_rng(skc9)) in(skf11(skc9,u),u)*.
% 272.09/272.27 283[0:EmS:43.0,24.0] || -> equal(skf17(u),empty_set)**.
% 272.09/272.27 291[0:Rew:283.0,37.0] || -> element(empty_set,powerset(u))*.
% 272.09/272.27 299[0:EmS:43.0,38.1] empty(u) || -> equal(relation_dom(u),empty_set)**.
% 272.09/272.27 303[0:EmS:43.0,100.1] empty(u) || -> equal(relation_composition(skc9,u),empty_set)**.
% 272.09/272.27 312[2:Res:280.1,45.1] empty(u) || -> equal(u,relation_rng(skc9))*.
% 272.09/272.27 317[0:SpR:299.1,27.0] empty(skc9) || -> equal(skc11,empty_set)**.
% 272.09/272.27 344[2:SpL:312.1,96.0] empty(u) || empty(u)* -> empty(skc9)*.
% 272.09/272.27 345[2:Obv:344.0] || empty(u)*+ -> empty(skc9)*.
% 272.09/272.27 349[2:Res:10.0,345.0] || -> empty(skc9)*.
% 272.09/272.27 350[2:MRR:317.0,349.0] || -> equal(skc11,empty_set)**.
% 272.09/272.27 353[2:Rew:350.0,268.0] || equal(identity_relation(empty_set),skc9)** -> .
% 272.09/272.27 355[2:Rew:350.0,189.0] || equal(empty_set,u) -> equal(identity_relation(u),skc9) in(skf18(u,v),u)*.
% 272.09/272.27 360[2:Rew:350.0,196.2] || in(u,v)* equal(v,relation_rng(skc9)) -> in(skf9(skc9,w),empty_set)*.
% 272.09/272.27 364[2:EmS:43.0,349.0] || -> equal(skc9,empty_set)**.
% 272.09/272.27 367[2:Rew:364.0,280.0] || -> equal(u,relation_rng(empty_set)) in(skf11(skc9,u),u)*.
% 272.09/272.27 376[2:Rew:364.0,360.1] || in(u,v)* equal(v,relation_rng(empty_set)) -> in(skf9(skc9,w),empty_set)*.
% 272.09/272.27 403[2:Rew:364.0,353.0] || equal(identity_relation(empty_set),empty_set)** -> .
% 272.09/272.27 405[2:Rew:364.0,355.1] || equal(empty_set,u) -> equal(identity_relation(u),empty_set) in(skf18(u,v),u)*.
% 272.09/272.27 409[2:Rew:364.0,367.1] || -> equal(u,relation_rng(empty_set)) in(skf11(empty_set,u),u)*.
% 272.09/272.27 411[2:Rew:364.0,376.2] || in(u,v)* equal(v,relation_rng(empty_set)) -> in(skf9(empty_set,w),empty_set)*.
% 272.09/272.27 475[0:Res:30.0,51.0] || -> empty(u) in(skf15(u),u)*.
% 272.09/272.27 550[0:Res:291.0,59.2] empty(u) || in(v,empty_set)* -> .
% 272.09/272.27 553[0:EmS:550.0,10.0] || in(u,empty_set)* -> .
% 272.09/272.27 554[2:MRR:411.2,553.0] || in(u,v)* equal(v,relation_rng(empty_set)) -> .
% 272.09/272.27 556[2:Res:409.1,553.0] || -> equal(relation_rng(empty_set),empty_set)**.
% 272.09/272.27 587[2:Rew:556.0,554.1] || in(u,v)* equal(v,empty_set) -> .
% 272.09/272.27 590[2:MRR:405.2,587.0] || equal(empty_set,u) -> equal(identity_relation(u),empty_set)**.
% 272.09/272.27 604[0:Res:48.1,58.1] || subset(u,v)*+ in(w,u)* -> element(w,v)*.
% 272.09/272.27 615[2:SpL:590.1,403.0] || equal(empty_set,empty_set)* equal(empty_set,empty_set)* -> .
% 272.09/272.27 618[2:Obv:615.1] || -> .
% 272.09/272.27 619[2:Spt:618.0,198.2] || -> in(skf12(skc9,u),skc11)*.
% 272.09/272.27 659[0:EqR:63.2] relation(identity_relation(u)) function(identity_relation(u)) || -> equal(relation_dom(identity_relation(u)),u)**.
% 272.09/272.27 660[0:SSi:659.1,659.0,22.0,21.0,22.0,21.0] || -> equal(relation_dom(identity_relation(u)),u)**.
% 272.09/272.27 665[0:SpL:660.0,49.1] relation(identity_relation(u)) || empty(u) -> empty(identity_relation(u))*.
% 272.09/272.27 666[0:SSi:665.0,22.0,21.0] || empty(u) -> empty(identity_relation(u))*.
% 272.09/272.27 670[0:EmS:43.0,666.1] || empty(u) -> equal(identity_relation(u),empty_set)**.
% 272.09/272.27 683[0:SpR:303.1,65.4] empty(u) relation(u) function(u) function(skc9) relation(skc9) || -> function(empty_set)*.
% 272.09/272.27 686[0:SSi:683.4,683.3,683.2,683.1,5.1,4.1,3.0,5.0,4.0,3.0,34.0,35.0] empty(u) || -> function(empty_set)*.
% 272.09/272.27 687[0:EmS:686.0,10.0] || -> function(empty_set)*.
% 272.09/272.27 690[0:SpR:670.1,660.0] || empty(u)*+ -> equal(relation_dom(empty_set),u)*.
% 272.09/272.27 696[0:Res:10.0,690.0] || -> equal(relation_dom(empty_set),empty_set)**.
% 272.09/272.27 699[0:SpR:696.0,61.3] function(empty_set) relation(empty_set) || -> one_to_one(empty_set) in(skf13(empty_set),empty_set)*.
% 272.09/272.27 703[0:SSi:699.1,699.0,8.0,10.0,11.0,687.0,8.0,10.0,11.0,687.0] || -> one_to_one(empty_set) in(skf13(empty_set),empty_set)*.
% 272.09/272.27 704[0:MRR:703.1,553.0] || -> one_to_one(empty_set)*.
% 272.09/272.27 723[0:EqR:68.2] relation(u) function(u) || -> equal(identity_relation(relation_dom(u)),u) in(skf18(relation_dom(u),v),relation_dom(u))*.
% 272.09/272.27 802[0:SpR:696.0,70.4] function(empty_set) relation(empty_set) || -> equal(u,relation_rng(empty_set)) in(skf11(empty_set,u),u)* in(skf12(empty_set,v),empty_set)*.
% 272.09/272.27 809[0:SSi:802.1,802.0,8.0,10.0,11.0,687.0,704.0,8.0,10.0,11.0,687.0,704.0] || -> equal(u,relation_rng(empty_set)) in(skf11(empty_set,u),u)* in(skf12(empty_set,v),empty_set)*.
% 272.09/272.27 810[0:MRR:809.2,553.0] || -> equal(u,relation_rng(empty_set)) in(skf11(empty_set,u),u)*.
% 272.09/272.27 822[0:Res:810.1,553.0] || -> equal(relation_rng(empty_set),empty_set)**.
% 272.09/272.27 829[0:EqR:72.3] function(u) relation(u) || in(v,relation_rng(u)) -> equal(apply(u,skf9(u,v)),v)**.
% 272.09/272.27 835[0:SpL:822.0,71.3] function(empty_set) relation(empty_set) || in(u,v)* equal(v,empty_set) -> in(skf9(empty_set,w),relation_dom(empty_set))*.
% 272.09/272.27 836[0:Rew:696.0,835.4] function(empty_set) relation(empty_set) || in(u,v)* equal(v,empty_set) -> in(skf9(empty_set,w),empty_set)*.
% 272.09/272.27 837[0:SSi:836.1,836.0,8.0,10.0,11.0,687.0,704.0,8.0,10.0,11.0,687.0,704.0] || in(u,v)* equal(v,empty_set) -> in(skf9(empty_set,w),empty_set)*.
% 272.09/272.27 838[0:MRR:837.2,553.0] || in(u,v)* equal(v,empty_set) -> .
% 272.09/272.27 887[2:Res:619.0,838.0] || equal(skc11,empty_set)** -> .
% 272.09/272.27 890[2:MRR:317.1,887.0] empty(skc9) || -> .
% 272.09/272.27 891[2:MRR:167.1,890.0] || empty(skc11)* -> .
% 272.09/272.27 892[2:MRR:96.1,890.0] || empty(relation_rng(skc9))* -> .
% 272.09/272.27 927[1:SpR:267.0,76.5] relation(skc9) function(skc9) relation(skc9) function(skc9) || in(u,relation_dom(skc9)) -> equal(apply(skc9,apply(skc9,u)),apply(skc9,u))**.
% 272.09/272.27 932[1:Obv:927.1] relation(skc9) function(skc9) || in(u,relation_dom(skc9)) -> equal(apply(skc9,apply(skc9,u)),apply(skc9,u))**.
% 272.09/272.27 933[1:Rew:27.0,932.2] relation(skc9) function(skc9) || in(u,skc11) -> equal(apply(skc9,apply(skc9,u)),apply(skc9,u))**.
% 272.09/272.27 934[1:SSi:933.1,933.0,5.0,4.0,3.0,5.0,4.0,3.0] || in(u,skc11) -> equal(apply(skc9,apply(skc9,u)),apply(skc9,u))**.
% 272.09/272.27 1140[1:Res:244.0,604.0] || in(u,relation_rng(skc9))* -> element(u,skc11).
% 272.09/272.27 1247[1:SpL:934.1,77.5] function(skc9) relation(skc9) one_to_one(skc9) || in(u,skc11) in(v,relation_dom(skc9))* in(apply(skc9,u),relation_dom(skc9))* equal(apply(skc9,v),apply(skc9,u))* -> equal(v,apply(skc9,u)).
% 272.09/272.27 1252[1:Rew:27.0,1247.5,27.0,1247.4] function(skc9) relation(skc9) one_to_one(skc9) || in(u,skc11) in(v,skc11) in(apply(skc9,u),skc11)* equal(apply(skc9,v),apply(skc9,u))* -> equal(v,apply(skc9,u)).
% 272.09/272.27 1253[1:SSi:1252.2,1252.1,1252.0,5.0,4.0,3.0,5.0,4.0,3.0,5.0,4.0,3.0] || in(u,skc11) in(v,skc11) in(apply(skc9,u),skc11)* equal(apply(skc9,v),apply(skc9,u))* -> equal(v,apply(skc9,u)).
% 272.09/272.27 1284[0:EqR:196.1] || in(u,relation_rng(skc9))* -> in(skf9(skc9,v),skc11)*.
% 272.09/272.27 1329[0:Res:475.1,1284.0] || -> empty(relation_rng(skc9)) in(skf9(skc9,u),skc11)*.
% 272.09/272.27 1340[2:MRR:1329.0,892.0] || -> in(skf9(skc9,u),skc11)*.
% 272.09/272.27 1436[0:EqR:220.2] || in(u,skc11) equal(v,relation_rng(skc9)) -> in(apply(skc9,u),v)*.
% 272.09/272.27 1479[0:SpR:27.0,723.3] relation(skc9) function(skc9) || -> equal(identity_relation(relation_dom(skc9)),skc9) in(skf18(skc11,u),skc11)*.
% 272.09/272.27 1489[0:Rew:27.0,1479.2] relation(skc9) function(skc9) || -> equal(identity_relation(skc11),skc9) in(skf18(skc11,u),skc11)*.
% 272.09/272.27 1490[0:SSi:1489.1,1489.0,5.0,4.0,3.0,5.0,4.0,3.0] || -> equal(identity_relation(skc11),skc9) in(skf18(skc11,u),skc11)*.
% 272.09/272.27 1491[1:MRR:1490.0,268.0] || -> in(skf18(skc11,u),skc11)*.
% 272.09/272.27 1535[1:SpR:829.3,934.1] function(skc9) relation(skc9) || in(u,relation_rng(skc9)) in(skf9(skc9,u),skc11)* -> equal(apply(skc9,u),u).
% 272.09/272.27 1541[1:SSi:1535.1,1535.0,5.0,4.0,3.0,5.0,4.0,3.0] || in(u,relation_rng(skc9)) in(skf9(skc9,u),skc11)* -> equal(apply(skc9,u),u).
% 272.09/272.27 1542[2:MRR:1541.1,1340.0] || in(u,relation_rng(skc9))* -> equal(apply(skc9,u),u).
% 272.09/272.27 2904[1:Res:1436.2,1140.0] || in(u,skc11) equal(relation_rng(skc9),relation_rng(skc9)) -> element(apply(skc9,u),skc11)*.
% 272.09/272.27 2908[1:Obv:2904.1] || in(u,skc11) -> element(apply(skc9,u),skc11)*.
% 272.09/272.27 2924[1:Res:2908.1,51.0] || in(u,skc11) -> empty(skc11) in(apply(skc9,u),skc11)*.
% 272.09/272.27 2925[2:MRR:2924.1,891.0] || in(u,skc11) -> in(apply(skc9,u),skc11)*.
% 272.09/272.27 2926[2:MRR:1253.2,2925.1] || in(u,skc11) in(v,skc11) equal(apply(skc9,v),apply(skc9,u))* -> equal(v,apply(skc9,u)).
% 272.09/272.27 4573[2:EqR:2926.2] || in(u,skc11) in(u,skc11) -> equal(apply(skc9,u),u)**.
% 272.09/272.27 4606[2:Obv:4573.0] || in(u,skc11) -> equal(apply(skc9,u),u)**.
% 272.09/272.27 4612[2:Rew:4606.1,220.2] || in(u,skc11)* equal(v,relation_rng(skc9))+ equal(w,u)* -> in(w,v)*.
% 272.09/272.27 4876[2:EqR:4612.1] || in(u,skc11)*+ equal(v,u)* -> in(v,relation_rng(skc9))*.
% 272.09/272.27 5019[2:Res:1491.0,4876.0] || equal(u,skf18(skc11,v))*+ -> in(u,relation_rng(skc9))*.
% 272.09/272.27 5990[2:EqR:5019.0] || -> in(skf18(skc11,u),relation_rng(skc9))*.
% 272.09/272.27 6001[2:Res:5990.0,1542.0] || -> equal(apply(skc9,skf18(skc11,u)),skf18(skc11,u))**.
% 297.16/297.35 6084[2:SpL:6001.0,74.3] relation(skc9) function(skc9) || equal(relation_dom(skc9),skc11) equal(skf18(skc11,skc9),skf18(skc11,skc9))* -> equal(identity_relation(skc11),skc9).
% 297.16/297.35 6094[2:Obv:6084.3] relation(skc9) function(skc9) || equal(relation_dom(skc9),skc11) -> equal(identity_relation(skc11),skc9)**.
% 297.16/297.35 6095[2:Rew:27.0,6094.2] relation(skc9) function(skc9) || equal(skc11,skc11) -> equal(identity_relation(skc11),skc9)**.
% 297.16/297.35 6096[2:Obv:6095.2] relation(skc9) function(skc9) || -> equal(identity_relation(skc11),skc9)**.
% 297.16/297.35 6097[2:SSi:6096.1,6096.0,5.0,4.0,3.0,5.0,4.0,3.0] || -> equal(identity_relation(skc11),skc9)**.
% 297.16/297.35 6098[2:MRR:6097.0,268.0] || -> .
% 297.16/297.35 6110[1:Spt:6098.0,193.1,238.0] || equal(skc10,skc9)** -> .
% 297.16/297.35 6111[1:Spt:6098.0,193.0,193.2] || equal(skc11,u) -> in(skf18(u,v),u)*.
% 297.16/297.35 6197[1:Res:6111.1,553.0] || equal(skc11,empty_set)** -> .
% 297.16/297.35 6205[1:MRR:317.1,6197.0] empty(skc9) || -> .
% 297.16/297.35 6207[1:MRR:167.1,6205.0] || empty(skc11)* -> .
% 297.16/297.35 6208[1:MRR:96.1,6205.0] || empty(relation_rng(skc9))* -> .
% 297.16/297.35 6211[2:Spt:172.0] || -> one_to_one(skc10)*.
% 297.16/297.35 6213[3:Spt:198.0,198.1] || -> equal(u,relation_rng(skc9)) in(skf11(skc9,u),u)*.
% 297.16/297.35 6224[3:Res:6213.1,553.0] || -> equal(relation_rng(skc9),empty_set)**.
% 297.16/297.35 6307[3:Rew:6224.0,6208.0] || empty(empty_set)* -> .
% 297.16/297.35 6308[3:MRR:6307.0,10.0] || -> .
% 297.16/297.35 6362[3:Spt:6308.0,198.2] || -> in(skf12(skc9,u),skc11)*.
% 297.16/297.35 6368[3:Res:6362.0,45.1] empty(skc11) || -> .
% 297.16/297.35 6475[0:Res:29.0,604.0] || in(u,relation_rng(skc10))* -> element(u,skc11).
% 297.16/297.35 6488[0:SpR:28.0,299.1] empty(skc10) || -> equal(skc11,empty_set)**.
% 297.16/297.35 6491[0:SpR:28.0,723.3] relation(skc10) function(skc10) || -> equal(identity_relation(relation_dom(skc10)),skc10) in(skf18(skc11,u),skc11)*.
% 297.16/297.35 6501[1:MRR:6488.1,6197.0] empty(skc10) || -> .
% 297.16/297.35 6502[1:MRR:141.1,6501.0] || empty(relation_rng(skc10))* -> .
% 297.16/297.35 6503[0:Rew:28.0,6491.2] relation(skc10) function(skc10) || -> equal(identity_relation(skc11),skc10) in(skf18(skc11,u),skc11)*.
% 297.16/297.35 6504[0:Rew:1490.0,6503.2] relation(skc10) function(skc10) || -> equal(skc10,skc9) in(skf18(skc11,u),skc11)*.
% 297.16/297.35 6505[2:SSi:6504.1,6504.0,2.0,1.0,6211.0,2.0,1.0,6211.0] || -> equal(skc10,skc9) in(skf18(skc11,u),skc11)*.
% 297.16/297.35 6506[2:MRR:6505.0,6110.0] || -> in(skf18(skc11,u),skc11)*.
% 297.16/297.35 6527[0:SpR:33.0,229.3] relation(skc10) function(skc10) || in(u,relation_dom(skc10)) -> equal(apply(skc9,apply(skc10,u)),apply(skc9,u))**.
% 297.16/297.35 6535[0:Rew:28.0,6527.2] relation(skc10) function(skc10) || in(u,skc11) -> equal(apply(skc9,apply(skc10,u)),apply(skc9,u))**.
% 297.16/297.35 6536[2:SSi:6535.1,6535.0,2.0,1.0,6211.0,2.0,1.0,6211.0] || in(u,skc11) -> equal(apply(skc9,apply(skc10,u)),apply(skc9,u))**.
% 297.16/297.35 6747[0:EqR:202.1] || in(u,relation_rng(skc10))*+ -> in(skf9(skc10,v),skc11)*.
% 297.16/297.35 6803[0:EqR:208.1] || in(u,relation_rng(skc10)) -> equal(apply(skc10,skf9(skc10,u)),u)**.
% 297.16/297.35 7004[0:EqR:214.2] || in(u,skc11) equal(v,relation_rng(skc10)) -> in(apply(skc10,u),v)*.
% 297.16/297.35 7273[0:Res:475.1,6747.0] || -> empty(relation_rng(skc10)) in(skf9(skc10,u),skc11)*.
% 297.16/297.35 7296[1:MRR:7273.0,6502.0] || -> in(skf9(skc10,u),skc11)*.
% 297.16/297.35 7391[2:SpL:6536.1,235.2] || in(u,skc11) in(v,skc11) in(apply(skc10,u),skc11)* equal(apply(skc9,v),apply(skc9,u))* -> equal(v,apply(skc10,u))*.
% 297.16/297.35 7488[0:Res:7004.2,6475.0] || in(u,skc11) equal(relation_rng(skc10),relation_rng(skc10)) -> element(apply(skc10,u),skc11)*.
% 297.16/297.35 7495[0:Obv:7488.1] || in(u,skc11) -> element(apply(skc10,u),skc11)*.
% 297.16/297.35 7507[0:Res:7495.1,51.0] || in(u,skc11) -> empty(skc11) in(apply(skc10,u),skc11)*.
% 297.16/297.35 7508[3:MRR:7507.1,6368.0] || in(u,skc11) -> in(apply(skc10,u),skc11)*.
% 297.16/297.35 7509[3:MRR:7391.2,7508.1] || in(u,skc11) in(v,skc11) equal(apply(skc9,v),apply(skc9,u))*+ -> equal(v,apply(skc10,u))*.
% 297.16/297.35 41333[3:EqR:7509.2] || in(u,skc11) in(u,skc11) -> equal(apply(skc10,u),u)**.
% 297.16/297.35 41422[3:Obv:41333.0] || in(u,skc11) -> equal(apply(skc10,u),u)**.
% 297.16/297.35 41448[3:Rew:41422.1,214.2] || in(u,skc11)* equal(v,relation_rng(skc10))+ equal(w,u)* -> in(w,v)*.
% 297.16/297.35 42844[3:EqR:41448.1] || in(u,skc11)*+ equal(v,u)* -> in(v,relation_rng(skc10))*.
% 297.16/297.35 43213[3:Res:6506.0,42844.0] || equal(u,skf18(skc11,v))*+ -> in(u,relation_rng(skc10))*.
% 297.16/297.35 43836[3:SpR:41422.1,6803.1] || in(skf9(skc10,u),skc11)* in(u,relation_rng(skc10)) -> equal(skf9(skc10,u),u).
% 297.16/297.35 44018[3:MRR:43836.0,7296.0] || in(u,relation_rng(skc10))* -> equal(skf9(skc10,u),u).
% 297.16/297.35 44019[3:Rew:44018.1,6803.1] || in(u,relation_rng(skc10))* -> equal(apply(skc10,u),u).
% 297.16/297.35 47803[3:EqR:43213.0] || -> in(skf18(skc11,u),relation_rng(skc10))*.
% 297.16/297.35 47813[3:Res:47803.0,44019.0] || -> equal(apply(skc10,skf18(skc11,u)),skf18(skc11,u))**.
% 297.16/297.35 48034[3:SpL:47813.0,74.3] relation(skc10) function(skc10) || equal(relation_dom(skc10),skc11) equal(skf18(skc11,skc10),skf18(skc11,skc10))* -> equal(identity_relation(skc11),skc10).
% 297.16/297.35 48071[3:Obv:48034.3] relation(skc10) function(skc10) || equal(relation_dom(skc10),skc11) -> equal(identity_relation(skc11),skc10)**.
% 297.16/297.35 48072[3:Rew:28.0,48071.2] relation(skc10) function(skc10) || equal(skc11,skc11) -> equal(identity_relation(skc11),skc10)**.
% 297.16/297.35 48073[3:Obv:48072.2] relation(skc10) function(skc10) || -> equal(identity_relation(skc11),skc10)**.
% 297.16/297.35 48074[3:SSi:48073.1,48073.0,2.0,1.0,6211.0,2.0,1.0,6211.0] || -> equal(identity_relation(skc11),skc10)**.
% 297.16/297.35 48075[3:MRR:48074.0,32.0] || -> .
% 297.16/297.35 48147[2:Spt:48075.0,172.0,6211.0] || one_to_one(skc10)* -> .
% 297.16/297.35 48148[2:Spt:48075.0,172.1] || -> in(skf13(skc10),skc11)*.
% 297.16/297.35 48149[2:MRR:170.0,48147.0] || -> in(skf14(skc10),skc11)*.
% 297.16/297.35 48153[2:MRR:175.1,48147.0] || equal(skf14(skc10),skf13(skc10))** -> .
% 297.16/297.35 48164[1:MRR:7507.1,6207.0] || in(u,skc11) -> in(apply(skc10,u),skc11)*.
% 297.16/297.35 48168[2:MRR:186.0,48147.0] || -> equal(apply(skc10,skf14(skc10)),apply(skc10,skf13(skc10)))**.
% 297.16/297.35 48302[0:SSi:6535.1,6535.0,2.0,1.0,2.0,1.0] || in(u,skc11) -> equal(apply(skc9,apply(skc10,u)),apply(skc9,u))**.
% 297.16/297.35 51041[0:SpL:48302.1,235.2] || in(u,skc11) in(v,skc11) in(apply(skc10,u),skc11)* equal(apply(skc9,v),apply(skc9,u))* -> equal(v,apply(skc10,u))*.
% 297.16/297.35 51068[1:MRR:51041.2,48164.1] || in(u,skc11) in(v,skc11) equal(apply(skc9,v),apply(skc9,u))*+ -> equal(v,apply(skc10,u))*.
% 297.16/297.35 71879[1:EqR:51068.2] || in(u,skc11) in(u,skc11) -> equal(apply(skc10,u),u)**.
% 297.16/297.35 71970[1:Obv:71879.0] || in(u,skc11) -> equal(apply(skc10,u),u)**.
% 297.16/297.35 74997[2:SpR:71970.1,48168.0] || in(skf14(skc10),skc11) -> equal(apply(skc10,skf13(skc10)),skf14(skc10))**.
% 297.16/297.35 75144[2:MRR:74997.0,48149.0] || -> equal(apply(skc10,skf13(skc10)),skf14(skc10))**.
% 297.16/297.35 76143[2:SpR:75144.0,71970.1] || in(skf13(skc10),skc11)* -> equal(skf14(skc10),skf13(skc10)).
% 297.16/297.35 76177[2:MRR:76143.0,76143.1,48148.0,48153.0] || -> .
% 297.16/297.35 % SZS output end Refutation
% 297.16/297.35 Formulae used in the proof : t50_funct_1 fc12_relat_1 fc4_relat_1 fc2_funct_1 rc2_subset_1 existence_m1_subset_1 cc1_funct_1 cc1_relat_1 fc7_relat_1 t6_boole t7_boole t3_subset fc5_relat_1 fc6_relat_1 t2_subset fc10_relat_1 t4_subset t5_subset d8_funct_1 t34_funct_1 fc1_funct_1 d5_funct_1 antisymmetry_r2_hidden t23_funct_1
% 297.16/297.35
%------------------------------------------------------------------------------