TSTP Solution File: SEU027+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU027+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 14:33:37 EDT 2022
% Result : Theorem 35.14s 35.32s
% Output : Refutation 37.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU027+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 20 13:30:14 EDT 2022
% 0.14/0.34 % CPUTime :
% 35.14/35.32
% 35.14/35.32 SPASS V 3.9
% 35.14/35.32 SPASS beiseite: Proof found.
% 35.14/35.32 % SZS status Theorem
% 35.14/35.32 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 35.14/35.32 SPASS derived 20990 clauses, backtracked 645 clauses, performed 19 splits and kept 11703 clauses.
% 35.14/35.32 SPASS allocated 126713 KBytes.
% 35.14/35.32 SPASS spent 0:0:34.95 on the problem.
% 35.14/35.32 0:00:00.04 for the input.
% 35.14/35.32 0:00:00.09 for the FLOTTER CNF translation.
% 35.14/35.32 0:00:00.36 for inferences.
% 35.14/35.32 0:00:01.73 for the backtracking.
% 35.14/35.32 0:0:32.43 for the reduction.
% 35.14/35.32
% 35.14/35.32
% 35.14/35.32 Here is a proof with depth 8, length 302 :
% 35.14/35.32 % SZS output start Refutation
% 35.14/35.32 1[0:Inp] || -> relation(skc11)*.
% 35.14/35.32 2[0:Inp] || -> relation(skc10)*.
% 35.14/35.32 3[0:Inp] || -> function(skc10)*.
% 35.14/35.32 4[0:Inp] || -> function(skc11)*.
% 35.14/35.32 5[0:Inp] || -> one_to_one(skc10)*.
% 35.14/35.32 10[0:Inp] || -> empty(empty_set)*.
% 35.14/35.32 27[0:Inp] || -> empty(skf17(u))*.
% 35.14/35.32 30[0:Inp] || -> element(skf15(u),u)*.
% 35.14/35.32 32[0:Inp] || -> equal(relation_dom(skc10),relation_rng(skc11))**.
% 35.14/35.32 33[0:Inp] || -> equal(relation_dom(skc11),relation_rng(skc10))**.
% 35.14/35.32 34[0:Inp] || equal(function_inverse(skc10),skc11)** -> .
% 35.14/35.32 35[0:Inp] empty(u) || -> function(u)*.
% 35.14/35.32 36[0:Inp] empty(u) || -> relation(u)*.
% 35.14/35.32 38[0:Inp] || -> element(skf17(u),powerset(u))*.
% 35.14/35.32 39[0:Inp] empty(u) || -> empty(relation_dom(u))*.
% 35.14/35.32 41[0:Inp] empty(u) || -> empty(relation_rng(u))*.
% 35.14/35.32 44[0:Inp] empty(u) || -> equal(u,empty_set)*.
% 35.14/35.32 46[0:Inp] empty(u) || in(v,u)* -> .
% 35.14/35.32 50[0:Inp] function(u) relation(u) || -> relation(function_inverse(u))*.
% 35.14/35.32 51[0:Inp] function(u) relation(u) || -> function(function_inverse(u))*.
% 35.14/35.32 52[0:Inp] relation(u) || empty(relation_dom(u))* -> empty(u).
% 35.14/35.32 54[0:Inp] || element(u,v)* -> empty(v) in(u,v).
% 35.14/35.32 55[0:Inp] || -> in(u,relation_rng(v)) SkP0(w,x,v,u)*.
% 35.14/35.32 57[0:Inp] || -> equal(u,apply(v,w)) SkP0(v,u,x,w)*.
% 35.14/35.32 60[0:Inp] empty(u) || in(v,w)* element(w,powerset(u))*+ -> .
% 35.14/35.32 61[0:Inp] || in(u,relation_dom(v)) equal(w,apply(v,u)) -> SkP0(x,u,v,w)*.
% 35.14/35.32 64[0:Inp] function(u) relation(u) || -> equal(v,relation_rng(u)) in(skf13(u,v),v)* in(skf14(u,w),relation_dom(u))*.
% 35.14/35.32 65[0:Inp] function(u) relation(u) || in(v,w)* equal(w,relation_rng(u))*+ -> in(skf11(u,x),relation_dom(u))*.
% 35.14/35.32 66[0:Inp] || equal(apply(skc11,u),v)* in(v,relation_dom(skc10))* in(u,relation_dom(skc11))* -> equal(apply(skc10,v),u)*.
% 35.14/35.32 67[0:Inp] || equal(apply(skc10,u),v)* in(u,relation_dom(skc10))* in(v,relation_dom(skc11))* -> equal(apply(skc11,v),u)*.
% 35.14/35.32 69[0:Inp] function(u) relation(u) || in(v,w)* equal(w,relation_rng(u))*+ -> equal(apply(u,skf11(u,v)),v)**.
% 35.14/35.32 72[0:Inp] function(u) relation(u) one_to_one(v) function(v) relation(v) || equal(u,function_inverse(v))*+ -> equal(relation_dom(u),relation_rng(v))*.
% 35.14/35.32 74[0:Inp] function(u) relation(u) function(v) relation(v) || equal(relation_dom(v),relation_dom(u))*+ -> equal(v,u) in(skf22(v,w),relation_dom(v))*.
% 35.14/35.32 78[0:Inp] function(u) relation(u) one_to_one(v) function(v) relation(v) || equal(relation_dom(u),relation_rng(v)) SkP0(u,skf18(v,u),v,skf19(v,u))*+ -> equal(u,function_inverse(v)) in(skf20(v,w),relation_dom(v))*.
% 35.14/35.32 79[0:Inp] function(u) relation(u) one_to_one(v) function(v) relation(v) || equal(relation_dom(u),relation_rng(v)) SkP0(u,skf18(v,u),v,skf19(v,u))* -> equal(u,function_inverse(v)) equal(apply(v,skf20(v,u)),skf21(u,v)).
% 35.14/35.32 80[0:Inp] function(u) relation(u) one_to_one(v) function(v) relation(v) || equal(relation_dom(u),relation_rng(v)) in(skf21(u,v),relation_rng(v)) equal(apply(u,skf21(u,v)),skf20(v,u)) SkP0(u,skf18(v,u),v,skf19(v,u))* -> equal(u,function_inverse(v)).
% 35.14/35.32 82[0:Rew:33.0,66.2,32.0,66.1] || in(u,relation_rng(skc10))* in(v,relation_rng(skc11))* equal(apply(skc11,u),v)* -> equal(apply(skc10,v),u)*.
% 35.14/35.32 83[0:Rew:33.0,67.2,32.0,67.1] || in(u,relation_rng(skc10))* in(v,relation_rng(skc11))* equal(apply(skc10,v),u)* -> equal(apply(skc11,u),v)*.
% 35.14/35.32 97[0:Res:4.0,74.1] relation(skc11) relation(u) function(u) || equal(relation_dom(skc11),relation_dom(u))* -> in(skf22(skc11,v),relation_dom(skc11))* equal(skc11,u).
% 35.14/35.32 102[0:Res:4.0,69.1] relation(skc11) || in(u,v)* equal(v,relation_rng(skc11)) -> equal(apply(skc11,skf11(skc11,u)),u)**.
% 35.14/35.32 103[0:Res:4.0,65.1] relation(skc11) || in(u,v)* equal(v,relation_rng(skc11)) -> in(skf11(skc11,w),relation_dom(skc11))*.
% 35.14/35.32 104[0:Res:4.0,64.1] relation(skc11) || -> in(skf14(skc11,u),relation_dom(skc11))* in(skf13(skc11,v),v)* equal(v,relation_rng(skc11)).
% 35.14/35.32 107[0:Res:4.0,80.4] relation(u) function(u) one_to_one(u) relation(skc11) || equal(apply(skc11,skf21(skc11,u)),skf20(u,skc11)) equal(relation_dom(skc11),relation_rng(u)) SkP0(skc11,skf18(u,skc11),u,skf19(u,skc11))* in(skf21(skc11,u),relation_rng(u)) -> equal(function_inverse(u),skc11).
% 35.14/35.32 108[0:Res:4.0,79.4] relation(u) function(u) one_to_one(u) relation(skc11) || SkP0(skc11,skf18(u,skc11),u,skf19(u,skc11))* equal(relation_dom(skc11),relation_rng(u)) -> equal(apply(u,skf20(u,skc11)),skf21(skc11,u)) equal(function_inverse(u),skc11).
% 35.14/35.32 109[0:Res:4.0,78.4] relation(u) function(u) one_to_one(u) relation(skc11) || SkP0(skc11,skf18(u,skc11),u,skf19(u,skc11))* equal(relation_dom(skc11),relation_rng(u)) -> in(skf20(u,v),relation_dom(u))* equal(function_inverse(u),skc11).
% 35.14/35.32 127[0:Res:3.0,69.1] relation(skc10) || in(u,v)* equal(v,relation_rng(skc10)) -> equal(apply(skc10,skf11(skc10,u)),u)**.
% 35.14/35.32 128[0:Res:3.0,65.1] relation(skc10) || in(u,v)* equal(v,relation_rng(skc10)) -> in(skf11(skc10,w),relation_dom(skc10))*.
% 35.14/35.32 129[0:Res:3.0,64.1] relation(skc10) || -> in(skf14(skc10,u),relation_dom(skc10))* in(skf13(skc10,v),v)* equal(v,relation_rng(skc10)).
% 35.14/35.32 149[0:Res:2.0,72.0] function(skc10) one_to_one(skc10) relation(u) function(u) || equal(u,function_inverse(skc10))* -> equal(relation_dom(u),relation_rng(skc10))**.
% 35.14/35.32 157[0:Res:2.0,52.0] || empty(relation_dom(skc10))* -> empty(skc10).
% 35.14/35.32 172[0:Rew:32.0,157.0] || empty(relation_rng(skc11))* -> empty(skc10).
% 35.14/35.32 173[0:Rew:33.0,103.3] relation(skc11) || in(u,v)* equal(v,relation_rng(skc11)) -> in(skf11(skc11,w),relation_rng(skc10))*.
% 35.14/35.32 174[0:MRR:173.0,1.0] || in(u,v)* equal(v,relation_rng(skc11))+ -> in(skf11(skc11,w),relation_rng(skc10))*.
% 35.14/35.32 175[0:Rew:33.0,104.1] relation(skc11) || -> in(skf14(skc11,u),relation_rng(skc10))* in(skf13(skc11,v),v)* equal(v,relation_rng(skc11)).
% 35.14/35.32 176[0:MRR:175.0,1.0] || -> equal(u,relation_rng(skc11)) in(skf13(skc11,u),u)* in(skf14(skc11,v),relation_rng(skc10))*.
% 35.14/35.32 177[0:Rew:32.0,128.3] relation(skc10) || in(u,v)* equal(v,relation_rng(skc10)) -> in(skf11(skc10,w),relation_rng(skc11))*.
% 35.14/35.32 178[0:MRR:177.0,2.0] || in(u,v)* equal(v,relation_rng(skc10))+ -> in(skf11(skc10,w),relation_rng(skc11))*.
% 35.14/35.32 179[0:Rew:32.0,129.1] relation(skc10) || -> in(skf14(skc10,u),relation_rng(skc11))* in(skf13(skc10,v),v)* equal(v,relation_rng(skc10)).
% 35.14/35.32 180[0:MRR:179.0,2.0] || -> equal(u,relation_rng(skc10)) in(skf13(skc10,u),u)* in(skf14(skc10,v),relation_rng(skc11))*.
% 35.14/35.32 183[0:MRR:102.0,1.0] || in(u,v)* equal(v,relation_rng(skc11))+ -> equal(apply(skc11,skf11(skc11,u)),u)**.
% 35.14/35.32 184[0:MRR:127.0,2.0] || in(u,v)* equal(v,relation_rng(skc10))+ -> equal(apply(skc10,skf11(skc10,u)),u)**.
% 35.14/35.32 191[0:MRR:149.0,149.1,3.0,5.0] function(u) relation(u) || equal(u,function_inverse(skc10))*+ -> equal(relation_dom(u),relation_rng(skc10))**.
% 35.14/35.32 211[0:Rew:33.0,97.4,33.0,97.3] relation(skc11) relation(u) function(u) || equal(relation_dom(u),relation_rng(skc10))** -> in(skf22(skc11,v),relation_rng(skc10))* equal(skc11,u).
% 35.14/35.32 212[0:MRR:211.0,1.0] function(u) relation(u) || equal(relation_dom(u),relation_rng(skc10))**+ -> equal(skc11,u) in(skf22(skc11,v),relation_rng(skc10))*.
% 35.14/35.32 245[0:Rew:33.0,109.5] relation(u) function(u) one_to_one(u) relation(skc11) || SkP0(skc11,skf18(u,skc11),u,skf19(u,skc11))* equal(relation_rng(skc10),relation_rng(u)) -> in(skf20(u,v),relation_dom(u))* equal(function_inverse(u),skc11).
% 35.14/35.32 246[0:MRR:245.3,1.0] one_to_one(u) function(u) relation(u) || equal(relation_rng(skc10),relation_rng(u)) SkP0(skc11,skf18(u,skc11),u,skf19(u,skc11))*+ -> equal(function_inverse(u),skc11) in(skf20(u,v),relation_dom(u))*.
% 35.14/35.32 254[0:Rew:33.0,108.5] relation(u) function(u) one_to_one(u) relation(skc11) || SkP0(skc11,skf18(u,skc11),u,skf19(u,skc11))* equal(relation_rng(skc10),relation_rng(u)) -> equal(apply(u,skf20(u,skc11)),skf21(skc11,u)) equal(function_inverse(u),skc11).
% 35.14/35.32 255[0:MRR:254.3,1.0] one_to_one(u) function(u) relation(u) || equal(relation_rng(skc10),relation_rng(u)) SkP0(skc11,skf18(u,skc11),u,skf19(u,skc11))* -> equal(function_inverse(u),skc11) equal(apply(u,skf20(u,skc11)),skf21(skc11,u)).
% 35.14/35.32 261[0:Rew:33.0,107.5] relation(u) function(u) one_to_one(u) relation(skc11) || equal(apply(skc11,skf21(skc11,u)),skf20(u,skc11)) equal(relation_rng(skc10),relation_rng(u)) SkP0(skc11,skf18(u,skc11),u,skf19(u,skc11))* in(skf21(skc11,u),relation_rng(u)) -> equal(function_inverse(u),skc11).
% 35.14/35.32 262[0:MRR:261.3,1.0] one_to_one(u) function(u) relation(u) || equal(relation_rng(skc10),relation_rng(u)) in(skf21(skc11,u),relation_rng(u)) equal(apply(skc11,skf21(skc11,u)),skf20(u,skc11)) SkP0(skc11,skf18(u,skc11),u,skf19(u,skc11))* -> equal(function_inverse(u),skc11).
% 35.14/35.32 264[1:Spt:212.0,212.1,212.2,212.3] function(u) relation(u) || equal(relation_dom(u),relation_rng(skc10))** -> equal(skc11,u).
% 35.14/35.32 276[0:EmS:44.0,27.0] || -> equal(skf17(u),empty_set)**.
% 35.14/35.32 288[0:Rew:276.0,38.0] || -> element(empty_set,powerset(u))*.
% 35.14/35.32 293[0:EmS:44.0,41.1] empty(u) || -> equal(relation_rng(u),empty_set)**.
% 35.14/35.32 298[0:EmS:44.0,39.1] empty(u) || -> equal(relation_dom(u),empty_set)**.
% 35.14/35.32 602[0:Res:30.0,54.0] || -> empty(u) in(skf15(u),u)*.
% 35.14/35.32 625[0:Res:288.0,60.2] empty(u) || in(v,empty_set)* -> .
% 35.14/35.32 628[0:EmS:625.0,10.0] || in(u,empty_set)* -> .
% 35.14/35.32 695[0:SpL:293.1,65.3] empty(u) function(u) relation(u) || in(v,w)* equal(w,empty_set) -> in(skf11(u,x),relation_dom(u))*.
% 35.14/35.32 759[0:EqR:69.3] function(u) relation(u) || in(v,relation_rng(u)) -> equal(apply(u,skf11(u,v)),v)**.
% 35.14/35.32 1010[0:Res:55.1,79.6] function(u) relation(u) one_to_one(v) function(v) relation(v) || equal(relation_dom(u),relation_rng(v)) -> in(skf19(v,u),relation_rng(v))* equal(u,function_inverse(v)) equal(apply(v,skf20(v,u)),skf21(u,v)).
% 35.14/35.32 1053[0:Res:61.2,80.8] function(u) relation(u) one_to_one(v) function(v) relation(v) || in(skf18(v,u),relation_dom(v)) equal(apply(v,skf18(v,u)),skf19(v,u))+ equal(relation_dom(u),relation_rng(v)) in(skf21(u,v),relation_rng(v))* equal(apply(u,skf21(u,v)),skf20(v,u))** -> equal(u,function_inverse(v)).
% 35.14/35.32 1292[0:Rew:298.1,695.5] empty(u) function(u) relation(u) || in(v,w)* equal(w,empty_set) -> in(skf11(u,x),empty_set)*.
% 35.14/35.32 1293[0:SSi:1292.2,1292.1,36.1,35.1] empty(u) || in(v,w)* equal(w,empty_set) -> in(skf11(u,x),empty_set)*.
% 35.14/35.32 1294[0:MRR:1293.3,628.0] empty(u) || in(v,w)* equal(w,empty_set) -> .
% 35.14/35.32 1395[0:EqR:83.2] || in(apply(skc10,u),relation_rng(skc10))* in(u,relation_rng(skc11)) -> equal(apply(skc11,apply(skc10,u)),u).
% 35.14/35.32 1474[0:EqR:174.1] || in(u,relation_rng(skc11))*+ -> in(skf11(skc11,v),relation_rng(skc10))*.
% 35.14/35.32 1483[0:EqR:178.1] || in(u,relation_rng(skc10))*+ -> in(skf11(skc10,v),relation_rng(skc11))*.
% 35.14/35.32 1561[0:EqR:191.2] function(function_inverse(skc10)) relation(function_inverse(skc10)) || -> equal(relation_dom(function_inverse(skc10)),relation_rng(skc10))**.
% 35.14/35.32 1562[0:SSi:1561.1,1561.0,51.0,2.0,3.0,5.2,50.0,2.0,3.0,5.2,51.0,2.0,3.0,5.2,50.0,2.0,3.0,5.2] || -> equal(relation_dom(function_inverse(skc10)),relation_rng(skc10))**.
% 35.14/35.32 1593[0:EqR:183.1] || in(u,relation_rng(skc11)) -> equal(apply(skc11,skf11(skc11,u)),u)**.
% 35.14/35.32 1608[0:EqR:184.1] || in(u,relation_rng(skc10)) -> equal(apply(skc10,skf11(skc10,u)),u)**.
% 35.14/35.32 1622[0:Res:602.1,1474.0] || -> empty(relation_rng(skc11)) in(skf11(skc11,u),relation_rng(skc10))*.
% 35.14/35.32 1636[0:Res:602.1,1483.0] || -> empty(relation_rng(skc10)) in(skf11(skc10,u),relation_rng(skc11))*.
% 35.14/35.32 1806[0:EmS:1294.0,10.0] || in(u,v)* equal(v,empty_set) -> .
% 35.14/35.32 1807[0:Res:602.1,1806.0] || equal(u,empty_set) -> empty(u)*.
% 35.14/35.32 1832[0:SpL:759.3,1395.0] function(skc10) relation(skc10) || in(u,relation_rng(skc10)) in(u,relation_rng(skc10)) in(skf11(skc10,u),relation_rng(skc11)) -> equal(apply(skc11,apply(skc10,skf11(skc10,u))),skf11(skc10,u))**.
% 35.14/35.32 1837[0:Obv:1832.2] function(skc10) relation(skc10) || in(u,relation_rng(skc10)) in(skf11(skc10,u),relation_rng(skc11)) -> equal(apply(skc11,apply(skc10,skf11(skc10,u))),skf11(skc10,u))**.
% 35.14/35.32 1838[0:Rew:759.3,1837.4] function(skc10) relation(skc10) || in(u,relation_rng(skc10)) in(skf11(skc10,u),relation_rng(skc11))* -> equal(apply(skc11,u),skf11(skc10,u)).
% 35.14/35.32 1839[0:SSi:1838.1,1838.0,2.0,3.0,5.0,2.0,3.0,5.0] || in(u,relation_rng(skc10)) in(skf11(skc10,u),relation_rng(skc11))* -> equal(apply(skc11,u),skf11(skc10,u)).
% 35.14/35.32 1886[0:Res:1807.1,52.1] relation(u) || equal(relation_dom(u),empty_set)** -> empty(u).
% 35.14/35.32 1933[0:SpL:32.0,1886.1] relation(skc10) || equal(relation_rng(skc11),empty_set)** -> empty(skc10).
% 35.14/35.32 3700[0:Res:55.1,246.4] one_to_one(u) function(u) relation(u) || equal(relation_rng(skc10),relation_rng(u)) -> in(skf19(u,skc11),relation_rng(u)) equal(function_inverse(u),skc11) in(skf20(u,v),relation_dom(u))*.
% 35.14/35.32 3702[0:Res:57.1,246.4] one_to_one(u) function(u) relation(u) || equal(relation_rng(skc10),relation_rng(u)) -> equal(apply(skc11,skf19(u,skc11)),skf18(u,skc11)) equal(function_inverse(u),skc11) in(skf20(u,v),relation_dom(u))*.
% 35.14/35.32 3703[0:Res:61.2,246.4] one_to_one(u) function(u) relation(u) || in(skf18(u,skc11),relation_dom(u)) equal(apply(u,skf18(u,skc11)),skf19(u,skc11)) equal(relation_rng(skc10),relation_rng(u)) -> equal(function_inverse(u),skc11) in(skf20(u,v),relation_dom(u))*.
% 35.14/35.32 4048[0:Res:55.1,255.4] one_to_one(u) function(u) relation(u) || equal(relation_rng(skc10),relation_rng(u)) -> in(skf19(u,skc11),relation_rng(u))* equal(function_inverse(u),skc11) equal(apply(u,skf20(u,skc11)),skf21(skc11,u)).
% 35.14/35.32 4050[0:Res:57.1,255.4] one_to_one(u) function(u) relation(u) || equal(relation_rng(skc10),relation_rng(u))+ -> equal(apply(skc11,skf19(u,skc11)),skf18(u,skc11))** equal(function_inverse(u),skc11) equal(apply(u,skf20(u,skc11)),skf21(skc11,u))**.
% 35.14/35.32 4051[0:Res:61.2,255.4] one_to_one(u) function(u) relation(u) || in(skf18(u,skc11),relation_dom(u))* equal(apply(u,skf18(u,skc11)),skf19(u,skc11)) equal(relation_rng(skc10),relation_rng(u)) -> equal(function_inverse(u),skc11) equal(apply(u,skf20(u,skc11)),skf21(skc11,u)).
% 35.14/35.32 4617[0:Res:55.1,262.6] one_to_one(u) function(u) relation(u) || equal(relation_rng(skc10),relation_rng(u)) in(skf21(skc11,u),relation_rng(u))* equal(apply(skc11,skf21(skc11,u)),skf20(u,skc11)) -> in(skf19(u,skc11),relation_rng(u)) equal(function_inverse(u),skc11).
% 35.14/35.32 4619[0:Res:57.1,262.6] one_to_one(u) function(u) relation(u) || equal(relation_rng(skc10),relation_rng(u)) in(skf21(skc11,u),relation_rng(u))* equal(apply(skc11,skf21(skc11,u)),skf20(u,skc11)) -> equal(apply(skc11,skf19(u,skc11)),skf18(u,skc11)) equal(function_inverse(u),skc11).
% 35.14/35.32 4620[0:Res:61.2,262.6] one_to_one(u) function(u) relation(u) || in(skf18(u,skc11),relation_dom(u)) equal(apply(u,skf18(u,skc11)),skf19(u,skc11)) equal(relation_rng(skc10),relation_rng(u)) in(skf21(skc11,u),relation_rng(u))* equal(apply(skc11,skf21(skc11,u)),skf20(u,skc11)) -> equal(function_inverse(u),skc11).
% 35.14/35.32 4881[1:SpL:1562.0,264.2] function(function_inverse(skc10)) relation(function_inverse(skc10)) || equal(relation_rng(skc10),relation_rng(skc10)) -> equal(function_inverse(skc10),skc11)**.
% 35.14/35.32 4882[1:Obv:4881.2] function(function_inverse(skc10)) relation(function_inverse(skc10)) || -> equal(function_inverse(skc10),skc11)**.
% 35.14/35.32 4883[1:SSi:4882.1,4882.0,51.0,2.0,3.0,5.2,50.0,2.0,3.0,5.2,51.0,2.0,3.0,5.2,50.0,2.0,3.0,5.2] || -> equal(function_inverse(skc10),skc11)**.
% 35.14/35.32 4884[1:MRR:4883.0,34.0] || -> .
% 35.14/35.32 4892[1:Spt:4884.0,212.4] || -> in(skf22(skc11,u),relation_rng(skc10))*.
% 35.14/35.32 4895[0:SSi:1933.0,2.0,3.0,5.0] || equal(relation_rng(skc11),empty_set)** -> empty(skc10).
% 35.14/35.32 4898[0:MRR:1839.1,1483.1] || in(u,relation_rng(skc10))* -> equal(apply(skc11,u),skf11(skc10,u)).
% 35.14/35.32 4905[0:Rew:4898.1,82.2] || in(u,relation_rng(skc10))* in(v,relation_rng(skc11))* equal(skf11(skc10,u),v)*+ -> equal(apply(skc10,v),u)*.
% 35.14/35.32 4956[1:SpR:293.1,4892.0] empty(skc10) || -> in(skf22(skc11,u),empty_set)*.
% 35.14/35.32 4957[1:Res:4892.0,46.1] empty(relation_rng(skc10)) || -> .
% 35.14/35.32 4958[1:Res:4892.0,1806.0] || equal(relation_rng(skc10),empty_set)** -> .
% 35.14/35.32 4961[1:MRR:1636.0,4957.0] || -> in(skf11(skc10,u),relation_rng(skc11))*.
% 35.14/35.32 4968[1:MRR:4956.1,628.0] empty(skc10) || -> .
% 35.14/35.32 4969[1:MRR:172.1,4968.0] || empty(relation_rng(skc11))* -> .
% 35.14/35.32 4970[1:MRR:4895.1,4968.0] || equal(relation_rng(skc11),empty_set)** -> .
% 35.14/35.32 4971[1:MRR:1622.0,4969.0] || -> in(skf11(skc11,u),relation_rng(skc10))*.
% 35.14/35.32 4993[2:Spt:176.0,176.1] || -> equal(u,relation_rng(skc11)) in(skf13(skc11,u),u)*.
% 35.14/35.32 5005[2:Res:4993.1,628.0] || -> equal(relation_rng(skc11),empty_set)**.
% 35.14/35.32 5010[2:MRR:5005.0,4970.0] || -> .
% 35.14/35.32 5011[2:Spt:5010.0,176.2] || -> in(skf14(skc11,u),relation_rng(skc10))*.
% 35.14/35.32 5018[3:Spt:180.0,180.1] || -> equal(u,relation_rng(skc10)) in(skf13(skc10,u),u)*.
% 35.14/35.32 5030[3:Res:5018.1,628.0] || -> equal(relation_rng(skc10),empty_set)**.
% 35.14/35.32 5035[3:MRR:5030.0,4958.0] || -> .
% 35.14/35.32 5036[3:Spt:5035.0,180.2] || -> in(skf14(skc10,u),relation_rng(skc11))*.
% 35.14/35.32 5505[1:Res:4971.0,4898.0] || -> equal(apply(skc11,skf11(skc11,u)),skf11(skc10,skf11(skc11,u)))**.
% 35.14/35.32 5526[1:Rew:5505.0,1593.1] || in(u,relation_rng(skc11)) -> equal(skf11(skc10,skf11(skc11,u)),u)**.
% 35.14/35.32 5939[1:SpR:5526.1,1608.1] || in(u,relation_rng(skc11)) in(skf11(skc11,u),relation_rng(skc10))* -> equal(apply(skc10,u),skf11(skc11,u)).
% 35.14/35.32 5944[1:MRR:5939.1,4971.0] || in(u,relation_rng(skc11))* -> equal(apply(skc10,u),skf11(skc11,u)).
% 35.14/35.32 5948[1:Rew:5944.1,4905.3] || in(u,relation_rng(skc10))* in(v,relation_rng(skc11))* equal(skf11(skc10,u),v)*+ -> equal(skf11(skc11,v),u)*.
% 35.14/35.32 5990[1:EqR:5948.2] || in(u,relation_rng(skc10)) in(skf11(skc10,u),relation_rng(skc11))* -> equal(skf11(skc11,skf11(skc10,u)),u).
% 35.14/35.32 5997[1:MRR:5990.1,4961.0] || in(u,relation_rng(skc10)) -> equal(skf11(skc11,skf11(skc10,u)),u)**.
% 35.14/35.32 6022[1:Res:4961.0,5944.0] || -> equal(apply(skc10,skf11(skc10,u)),skf11(skc11,skf11(skc10,u)))**.
% 35.14/35.32 15408[0:SpR:32.0,3700.6] one_to_one(skc10) function(skc10) relation(skc10) || equal(relation_rng(skc10),relation_rng(skc10)) -> in(skf19(skc10,skc11),relation_rng(skc10)) equal(function_inverse(skc10),skc11) in(skf20(skc10,u),relation_rng(skc11))*.
% 35.14/35.32 15419[0:Obv:15408.3] one_to_one(skc10) function(skc10) relation(skc10) || -> in(skf19(skc10,skc11),relation_rng(skc10)) equal(function_inverse(skc10),skc11) in(skf20(skc10,u),relation_rng(skc11))*.
% 35.14/35.32 15420[0:SSi:15419.2,15419.1,15419.0,2.0,3.0,5.0,2.0,3.0,5.0,2.0,3.0,5.0] || -> in(skf19(skc10,skc11),relation_rng(skc10)) equal(function_inverse(skc10),skc11) in(skf20(skc10,u),relation_rng(skc11))*.
% 35.14/35.32 15421[0:MRR:15420.1,34.0] || -> in(skf19(skc10,skc11),relation_rng(skc10)) in(skf20(skc10,u),relation_rng(skc11))*.
% 35.14/35.32 17152[0:Res:4048.4,4898.0] one_to_one(skc10) function(skc10) relation(skc10) || equal(relation_rng(skc10),relation_rng(skc10)) -> equal(function_inverse(skc10),skc11) equal(apply(skc10,skf20(skc10,skc11)),skf21(skc11,skc10)) equal(apply(skc11,skf19(skc10,skc11)),skf11(skc10,skf19(skc10,skc11)))**.
% 35.14/35.32 17173[0:Obv:17152.3] one_to_one(skc10) function(skc10) relation(skc10) || -> equal(function_inverse(skc10),skc11) equal(apply(skc10,skf20(skc10,skc11)),skf21(skc11,skc10)) equal(apply(skc11,skf19(skc10,skc11)),skf11(skc10,skf19(skc10,skc11)))**.
% 35.14/35.32 17174[0:SSi:17173.2,17173.1,17173.0,2.0,3.0,5.0,2.0,3.0,5.0,2.0,3.0,5.0] || -> equal(function_inverse(skc10),skc11) equal(apply(skc10,skf20(skc10,skc11)),skf21(skc11,skc10)) equal(apply(skc11,skf19(skc10,skc11)),skf11(skc10,skf19(skc10,skc11)))**.
% 35.14/35.32 17175[0:MRR:17174.0,34.0] || -> equal(apply(skc10,skf20(skc10,skc11)),skf21(skc11,skc10)) equal(apply(skc11,skf19(skc10,skc11)),skf11(skc10,skf19(skc10,skc11)))**.
% 35.14/35.32 17231[0:SpR:32.0,3702.6] one_to_one(skc10) function(skc10) relation(skc10) || equal(relation_rng(skc10),relation_rng(skc10)) -> equal(apply(skc11,skf19(skc10,skc11)),skf18(skc10,skc11)) equal(function_inverse(skc10),skc11) in(skf20(skc10,u),relation_rng(skc11))*.
% 35.14/35.32 17242[0:Obv:17231.3] one_to_one(skc10) function(skc10) relation(skc10) || -> equal(apply(skc11,skf19(skc10,skc11)),skf18(skc10,skc11)) equal(function_inverse(skc10),skc11) in(skf20(skc10,u),relation_rng(skc11))*.
% 35.14/35.32 17243[0:SSi:17242.2,17242.1,17242.0,2.0,3.0,5.0,2.0,3.0,5.0,2.0,3.0,5.0] || -> equal(apply(skc11,skf19(skc10,skc11)),skf18(skc10,skc11)) equal(function_inverse(skc10),skc11) in(skf20(skc10,u),relation_rng(skc11))*.
% 35.14/35.32 17244[0:MRR:17243.1,34.0] || -> equal(apply(skc11,skf19(skc10,skc11)),skf18(skc10,skc11)) in(skf20(skc10,u),relation_rng(skc11))*.
% 35.14/35.32 18448[0:EqR:4050.3] one_to_one(skc10) function(skc10) relation(skc10) || -> equal(apply(skc11,skf19(skc10,skc11)),skf18(skc10,skc11))** equal(function_inverse(skc10),skc11) equal(apply(skc10,skf20(skc10,skc11)),skf21(skc11,skc10)).
% 35.14/35.32 18451[0:Rew:17175.1,18448.3] one_to_one(skc10) function(skc10) relation(skc10) || -> equal(skf11(skc10,skf19(skc10,skc11)),skf18(skc10,skc11)) equal(function_inverse(skc10),skc11) equal(apply(skc10,skf20(skc10,skc11)),skf21(skc11,skc10))**.
% 35.14/35.32 18452[0:SSi:18451.2,18451.1,18451.0,2.0,3.0,5.0,2.0,3.0,5.0,2.0,3.0,5.0] || -> equal(skf11(skc10,skf19(skc10,skc11)),skf18(skc10,skc11)) equal(function_inverse(skc10),skc11) equal(apply(skc10,skf20(skc10,skc11)),skf21(skc11,skc10))**.
% 35.14/35.32 18453[0:MRR:18452.1,34.0] || -> equal(skf11(skc10,skf19(skc10,skc11)),skf18(skc10,skc11)) equal(apply(skc10,skf20(skc10,skc11)),skf21(skc11,skc10))**.
% 35.14/35.32 18454[0:Rew:18453.0,17175.1] || -> equal(apply(skc10,skf20(skc10,skc11)),skf21(skc11,skc10)) equal(apply(skc11,skf19(skc10,skc11)),skf18(skc10,skc11))**.
% 35.14/35.32 20628[0:SpR:32.0,3703.7] one_to_one(skc10) function(skc10) relation(skc10) || in(skf18(skc10,skc11),relation_dom(skc10)) equal(apply(skc10,skf18(skc10,skc11)),skf19(skc10,skc11)) equal(relation_rng(skc10),relation_rng(skc10)) -> equal(function_inverse(skc10),skc11) in(skf20(skc10,u),relation_rng(skc11))*.
% 35.14/35.32 20637[0:Obv:20628.5] one_to_one(skc10) function(skc10) relation(skc10) || in(skf18(skc10,skc11),relation_dom(skc10)) equal(apply(skc10,skf18(skc10,skc11)),skf19(skc10,skc11)) -> equal(function_inverse(skc10),skc11) in(skf20(skc10,u),relation_rng(skc11))*.
% 35.14/35.32 20638[1:Rew:5944.1,20637.4,32.0,20637.3] one_to_one(skc10) function(skc10) relation(skc10) || in(skf18(skc10,skc11),relation_rng(skc11)) equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) -> equal(function_inverse(skc10),skc11) in(skf20(skc10,u),relation_rng(skc11))*.
% 35.14/35.32 20639[1:SSi:20638.2,20638.1,20638.0,2.0,3.0,5.0,2.0,3.0,5.0,2.0,3.0,5.0] || in(skf18(skc10,skc11),relation_rng(skc11)) equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) -> equal(function_inverse(skc10),skc11) in(skf20(skc10,u),relation_rng(skc11))*.
% 35.14/35.32 20640[1:MRR:20639.2,34.0] || in(skf18(skc10,skc11),relation_rng(skc11)) equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) -> in(skf20(skc10,u),relation_rng(skc11))*.
% 35.14/35.32 21214[0:SpL:32.0,4051.3] one_to_one(skc10) function(skc10) relation(skc10) || in(skf18(skc10,skc11),relation_rng(skc11))* equal(apply(skc10,skf18(skc10,skc11)),skf19(skc10,skc11)) equal(relation_rng(skc10),relation_rng(skc10)) -> equal(function_inverse(skc10),skc11) equal(apply(skc10,skf20(skc10,skc11)),skf21(skc11,skc10)).
% 35.14/35.32 21218[0:Obv:21214.5] one_to_one(skc10) function(skc10) relation(skc10) || in(skf18(skc10,skc11),relation_rng(skc11))* equal(apply(skc10,skf18(skc10,skc11)),skf19(skc10,skc11)) -> equal(function_inverse(skc10),skc11) equal(apply(skc10,skf20(skc10,skc11)),skf21(skc11,skc10)).
% 35.14/35.32 21219[1:Rew:5944.1,21218.4] one_to_one(skc10) function(skc10) relation(skc10) || in(skf18(skc10,skc11),relation_rng(skc11))* equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) -> equal(function_inverse(skc10),skc11) equal(apply(skc10,skf20(skc10,skc11)),skf21(skc11,skc10)).
% 35.14/35.32 21220[1:SSi:21219.2,21219.1,21219.0,2.0,3.0,5.0,2.0,3.0,5.0,2.0,3.0,5.0] || in(skf18(skc10,skc11),relation_rng(skc11))* equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) -> equal(function_inverse(skc10),skc11) equal(apply(skc10,skf20(skc10,skc11)),skf21(skc11,skc10)).
% 35.14/35.32 21221[1:MRR:21220.2,34.0] || in(skf18(skc10,skc11),relation_rng(skc11))* equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) -> equal(apply(skc10,skf20(skc10,skc11)),skf21(skc11,skc10)).
% 35.14/35.32 23888[4:Spt:17244.1] || -> in(skf20(skc10,u),relation_rng(skc11))*.
% 35.14/35.32 23907[4:Res:23888.0,5944.0] || -> equal(apply(skc10,skf20(skc10,u)),skf11(skc11,skf20(skc10,u)))**.
% 35.14/35.32 23908[4:Rew:23907.0,21221.2] || in(skf18(skc10,skc11),relation_rng(skc11))* equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) -> equal(skf11(skc11,skf20(skc10,skc11)),skf21(skc11,skc10)).
% 35.14/35.32 23910[4:Rew:23907.0,18454.0] || -> equal(skf11(skc11,skf20(skc10,skc11)),skf21(skc11,skc10)) equal(apply(skc11,skf19(skc10,skc11)),skf18(skc10,skc11))**.
% 35.14/35.32 23911[4:Rew:23907.0,18453.1] || -> equal(skf11(skc10,skf19(skc10,skc11)),skf18(skc10,skc11)) equal(skf11(skc11,skf20(skc10,skc11)),skf21(skc11,skc10))**.
% 35.14/35.32 26206[5:Spt:23910.0] || -> equal(skf11(skc11,skf20(skc10,skc11)),skf21(skc11,skc10))**.
% 35.14/35.32 26208[5:SpR:26206.0,4971.0] || -> in(skf21(skc11,skc10),relation_rng(skc10))*.
% 35.14/35.32 26209[5:SpR:26206.0,5526.1] || in(skf20(skc10,skc11),relation_rng(skc11))* -> equal(skf11(skc10,skf21(skc11,skc10)),skf20(skc10,skc11)).
% 35.14/35.32 26210[5:SpR:26206.0,5505.0] || -> equal(apply(skc11,skf21(skc11,skc10)),skf11(skc10,skf21(skc11,skc10)))**.
% 35.14/35.32 26241[5:MRR:26209.0,23888.0] || -> equal(skf11(skc10,skf21(skc11,skc10)),skf20(skc10,skc11))**.
% 35.14/35.32 26242[5:Rew:26241.0,26210.0] || -> equal(apply(skc11,skf21(skc11,skc10)),skf20(skc10,skc11))**.
% 35.14/35.32 26274[5:Res:26208.0,4620.6] one_to_one(skc10) function(skc10) relation(skc10) || in(skf18(skc10,skc11),relation_dom(skc10))* equal(apply(skc10,skf18(skc10,skc11)),skf19(skc10,skc11)) equal(relation_rng(skc10),relation_rng(skc10)) equal(apply(skc11,skf21(skc11,skc10)),skf20(skc10,skc11)) -> equal(function_inverse(skc10),skc11).
% 35.14/35.32 26275[5:Res:26208.0,4619.4] one_to_one(skc10) function(skc10) relation(skc10) || equal(relation_rng(skc10),relation_rng(skc10)) equal(apply(skc11,skf21(skc11,skc10)),skf20(skc10,skc11))** -> equal(apply(skc11,skf19(skc10,skc11)),skf18(skc10,skc11)) equal(function_inverse(skc10),skc11).
% 35.14/35.32 26276[5:Res:26208.0,4617.4] one_to_one(skc10) function(skc10) relation(skc10) || equal(relation_rng(skc10),relation_rng(skc10)) equal(apply(skc11,skf21(skc11,skc10)),skf20(skc10,skc11)) -> in(skf19(skc10,skc11),relation_rng(skc10))* equal(function_inverse(skc10),skc11).
% 35.14/35.32 26284[5:Obv:26276.3] one_to_one(skc10) function(skc10) relation(skc10) || equal(apply(skc11,skf21(skc11,skc10)),skf20(skc10,skc11)) -> in(skf19(skc10,skc11),relation_rng(skc10))* equal(function_inverse(skc10),skc11).
% 35.14/35.32 26285[5:Rew:26242.0,26284.3] one_to_one(skc10) function(skc10) relation(skc10) || equal(skf20(skc10,skc11),skf20(skc10,skc11)) -> in(skf19(skc10,skc11),relation_rng(skc10))* equal(function_inverse(skc10),skc11).
% 35.14/35.32 26286[5:Obv:26285.3] one_to_one(skc10) function(skc10) relation(skc10) || -> in(skf19(skc10,skc11),relation_rng(skc10))* equal(function_inverse(skc10),skc11).
% 35.14/35.32 26287[5:SSi:26286.2,26286.1,26286.0,2.0,3.0,5.0,2.0,3.0,5.0,2.0,3.0,5.0] || -> in(skf19(skc10,skc11),relation_rng(skc10))* equal(function_inverse(skc10),skc11).
% 35.14/35.32 26288[5:MRR:26287.1,34.0] || -> in(skf19(skc10,skc11),relation_rng(skc10))*.
% 35.14/35.32 26290[5:Obv:26275.3] one_to_one(skc10) function(skc10) relation(skc10) || equal(apply(skc11,skf21(skc11,skc10)),skf20(skc10,skc11))** -> equal(apply(skc11,skf19(skc10,skc11)),skf18(skc10,skc11)) equal(function_inverse(skc10),skc11).
% 35.14/35.32 26291[5:Rew:26242.0,26290.3] one_to_one(skc10) function(skc10) relation(skc10) || equal(skf20(skc10,skc11),skf20(skc10,skc11)) -> equal(apply(skc11,skf19(skc10,skc11)),skf18(skc10,skc11))** equal(function_inverse(skc10),skc11).
% 35.14/35.32 26292[5:Obv:26291.3] one_to_one(skc10) function(skc10) relation(skc10) || -> equal(apply(skc11,skf19(skc10,skc11)),skf18(skc10,skc11))** equal(function_inverse(skc10),skc11).
% 35.14/35.32 26293[5:SSi:26292.2,26292.1,26292.0,2.0,3.0,5.0,2.0,3.0,5.0,2.0,3.0,5.0] || -> equal(apply(skc11,skf19(skc10,skc11)),skf18(skc10,skc11))** equal(function_inverse(skc10),skc11).
% 35.14/35.32 26294[5:MRR:26293.1,34.0] || -> equal(apply(skc11,skf19(skc10,skc11)),skf18(skc10,skc11))**.
% 35.14/35.32 26295[5:Obv:26274.5] one_to_one(skc10) function(skc10) relation(skc10) || in(skf18(skc10,skc11),relation_dom(skc10))* equal(apply(skc10,skf18(skc10,skc11)),skf19(skc10,skc11)) equal(apply(skc11,skf21(skc11,skc10)),skf20(skc10,skc11)) -> equal(function_inverse(skc10),skc11).
% 35.14/35.32 26296[5:Rew:5944.1,26295.4,32.0,26295.3] one_to_one(skc10) function(skc10) relation(skc10) || in(skf18(skc10,skc11),relation_rng(skc11))* equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) equal(apply(skc11,skf21(skc11,skc10)),skf20(skc10,skc11)) -> equal(function_inverse(skc10),skc11).
% 35.14/35.32 26297[5:Rew:26242.0,26296.5] one_to_one(skc10) function(skc10) relation(skc10) || in(skf18(skc10,skc11),relation_rng(skc11))* equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) equal(skf20(skc10,skc11),skf20(skc10,skc11)) -> equal(function_inverse(skc10),skc11).
% 35.14/35.32 26298[5:Obv:26297.5] one_to_one(skc10) function(skc10) relation(skc10) || in(skf18(skc10,skc11),relation_rng(skc11))* equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) -> equal(function_inverse(skc10),skc11).
% 35.14/35.32 26299[5:SSi:26298.2,26298.1,26298.0,2.0,3.0,5.0,2.0,3.0,5.0,2.0,3.0,5.0] || in(skf18(skc10,skc11),relation_rng(skc11))* equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) -> equal(function_inverse(skc10),skc11).
% 35.14/35.32 26300[5:MRR:26299.2,34.0] || in(skf18(skc10,skc11),relation_rng(skc11))* equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) -> .
% 35.14/35.32 26314[5:Res:26288.0,4898.0] || -> equal(apply(skc11,skf19(skc10,skc11)),skf11(skc10,skf19(skc10,skc11)))**.
% 35.14/35.32 26321[5:Rew:26294.0,26314.0] || -> equal(skf11(skc10,skf19(skc10,skc11)),skf18(skc10,skc11))**.
% 35.14/35.32 26632[5:SpR:26321.0,759.3] function(skc10) relation(skc10) || in(skf19(skc10,skc11),relation_rng(skc10))* -> equal(apply(skc10,skf18(skc10,skc11)),skf19(skc10,skc11)).
% 35.14/35.32 26633[5:SpR:26321.0,4961.0] || -> in(skf18(skc10,skc11),relation_rng(skc11))*.
% 35.14/35.32 26635[5:SpR:26321.0,6022.0] || -> equal(apply(skc10,skf18(skc10,skc11)),skf11(skc11,skf18(skc10,skc11)))**.
% 35.14/35.32 26667[5:MRR:26300.0,26633.0] || equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11))** -> .
% 35.14/35.32 26688[5:Rew:26635.0,26632.3] function(skc10) relation(skc10) || in(skf19(skc10,skc11),relation_rng(skc10))* -> equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)).
% 35.14/35.32 26689[5:SSi:26688.1,26688.0,2.0,3.0,5.0,2.0,3.0,5.0] || in(skf19(skc10,skc11),relation_rng(skc10))* -> equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)).
% 35.14/35.32 26690[5:MRR:26689.0,26288.0] || -> equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11))**.
% 35.14/35.32 26691[5:MRR:26690.0,26667.0] || -> .
% 35.14/35.32 26700[5:Spt:26691.0,23910.0,26206.0] || equal(skf11(skc11,skf20(skc10,skc11)),skf21(skc11,skc10))** -> .
% 35.14/35.32 26701[5:Spt:26691.0,23910.1] || -> equal(apply(skc11,skf19(skc10,skc11)),skf18(skc10,skc11))**.
% 35.14/35.32 26703[5:MRR:23911.1,26700.0] || -> equal(skf11(skc10,skf19(skc10,skc11)),skf18(skc10,skc11))**.
% 35.14/35.32 26708[5:MRR:23908.2,26700.0] || in(skf18(skc10,skc11),relation_rng(skc11))* equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) -> .
% 35.14/35.32 26822[5:SpR:26703.0,4961.0] || -> in(skf18(skc10,skc11),relation_rng(skc11))*.
% 35.14/35.32 26823[5:SpR:26703.0,5997.1] || in(skf19(skc10,skc11),relation_rng(skc10))* -> equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)).
% 35.14/35.32 26856[5:MRR:26708.0,26822.0] || equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11))** -> .
% 35.14/35.32 26870[5:MRR:26823.1,26856.0] || in(skf19(skc10,skc11),relation_rng(skc10))* -> .
% 35.14/35.32 26905[5:Res:1010.6,26870.0] function(skc11) relation(skc11) one_to_one(skc10) function(skc10) relation(skc10) || equal(relation_dom(skc11),relation_rng(skc10)) -> equal(function_inverse(skc10),skc11) equal(apply(skc10,skf20(skc10,skc11)),skf21(skc11,skc10))**.
% 35.14/35.32 26911[5:Rew:23907.0,26905.7,33.0,26905.5] function(skc11) relation(skc11) one_to_one(skc10) function(skc10) relation(skc10) || equal(relation_rng(skc10),relation_rng(skc10)) -> equal(function_inverse(skc10),skc11) equal(skf11(skc11,skf20(skc10,skc11)),skf21(skc11,skc10))**.
% 35.14/35.32 26912[5:Obv:26911.5] function(skc11) relation(skc11) one_to_one(skc10) function(skc10) relation(skc10) || -> equal(function_inverse(skc10),skc11) equal(skf11(skc11,skf20(skc10,skc11)),skf21(skc11,skc10))**.
% 35.14/35.32 26913[5:SSi:26912.4,26912.3,26912.2,26912.1,26912.0,2.0,3.0,5.0,2.0,3.0,5.0,2.0,3.0,5.0,1.0,4.0,1.0,4.0] || -> equal(function_inverse(skc10),skc11) equal(skf11(skc11,skf20(skc10,skc11)),skf21(skc11,skc10))**.
% 35.14/35.32 26914[5:MRR:26913.0,26913.1,34.0,26700.0] || -> .
% 35.14/35.32 26915[4:Spt:26914.0,17244.0] || -> equal(apply(skc11,skf19(skc10,skc11)),skf18(skc10,skc11))**.
% 35.14/35.32 27031[5:Spt:15421.1] || -> in(skf20(skc10,u),relation_rng(skc11))*.
% 35.14/35.32 27051[5:Res:27031.0,5944.0] || -> equal(apply(skc10,skf20(skc10,u)),skf11(skc11,skf20(skc10,u)))**.
% 35.14/35.32 27059[5:Rew:27051.0,21221.2] || in(skf18(skc10,skc11),relation_rng(skc11))* equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) -> equal(skf11(skc11,skf20(skc10,skc11)),skf21(skc11,skc10)).
% 35.14/35.32 27063[5:Rew:27051.0,18453.1] || -> equal(skf11(skc10,skf19(skc10,skc11)),skf18(skc10,skc11)) equal(skf11(skc11,skf20(skc10,skc11)),skf21(skc11,skc10))**.
% 35.14/35.32 27183[6:Spt:27063.0] || -> equal(skf11(skc10,skf19(skc10,skc11)),skf18(skc10,skc11))**.
% 35.14/35.32 27185[6:SpR:27183.0,4961.0] || -> in(skf18(skc10,skc11),relation_rng(skc11))*.
% 35.14/35.32 27186[6:SpR:27183.0,5997.1] || in(skf19(skc10,skc11),relation_rng(skc10))* -> equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)).
% 35.14/35.32 27187[6:SpR:27183.0,6022.0] || -> equal(apply(skc10,skf18(skc10,skc11)),skf11(skc11,skf18(skc10,skc11)))**.
% 35.14/35.32 27229[6:MRR:27059.0,27185.0] || equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) -> equal(skf11(skc11,skf20(skc10,skc11)),skf21(skc11,skc10))**.
% 35.14/35.32 27436[6:SpL:27187.0,1053.6] function(skc11) relation(skc11) one_to_one(skc10) function(skc10) relation(skc10) || in(skf18(skc10,skc11),relation_dom(skc10)) equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) equal(relation_dom(skc11),relation_rng(skc10)) in(skf21(skc11,skc10),relation_rng(skc10))* equal(apply(skc11,skf21(skc11,skc10)),skf20(skc10,skc11)) -> equal(function_inverse(skc10),skc11).
% 35.14/35.32 27493[6:Rew:4898.1,27436.9,33.0,27436.7,32.0,27436.5] function(skc11) relation(skc11) one_to_one(skc10) function(skc10) relation(skc10) || in(skf18(skc10,skc11),relation_rng(skc11)) equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) equal(relation_rng(skc10),relation_rng(skc10)) in(skf21(skc11,skc10),relation_rng(skc10))* equal(skf11(skc10,skf21(skc11,skc10)),skf20(skc10,skc11)) -> equal(function_inverse(skc10),skc11).
% 35.14/35.32 27494[6:Obv:27493.7] function(skc11) relation(skc11) one_to_one(skc10) function(skc10) relation(skc10) || in(skf18(skc10,skc11),relation_rng(skc11)) equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) in(skf21(skc11,skc10),relation_rng(skc10))* equal(skf11(skc10,skf21(skc11,skc10)),skf20(skc10,skc11)) -> equal(function_inverse(skc10),skc11).
% 35.14/35.32 27495[6:SSi:27494.4,27494.3,27494.2,27494.1,27494.0,2.0,3.0,5.0,2.0,3.0,5.0,2.0,3.0,5.0,1.0,4.0,1.0,4.0] || in(skf18(skc10,skc11),relation_rng(skc11)) equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) in(skf21(skc11,skc10),relation_rng(skc10))* equal(skf11(skc10,skf21(skc11,skc10)),skf20(skc10,skc11)) -> equal(function_inverse(skc10),skc11).
% 35.14/35.32 27496[6:MRR:27495.0,27495.4,27185.0,34.0] || equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) in(skf21(skc11,skc10),relation_rng(skc10))* equal(skf11(skc10,skf21(skc11,skc10)),skf20(skc10,skc11)) -> .
% 35.14/35.32 28076[6:SpR:27229.1,4971.0] || equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) -> in(skf21(skc11,skc10),relation_rng(skc10))*.
% 35.14/35.32 28077[6:SpR:27229.1,5526.1] || equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) in(skf20(skc10,skc11),relation_rng(skc11))* -> equal(skf11(skc10,skf21(skc11,skc10)),skf20(skc10,skc11)).
% 35.14/35.32 28106[6:MRR:27496.1,28076.1] || equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11))** equal(skf11(skc10,skf21(skc11,skc10)),skf20(skc10,skc11)) -> .
% 35.14/35.32 28113[6:MRR:28077.1,27031.0] || equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11))** -> equal(skf11(skc10,skf21(skc11,skc10)),skf20(skc10,skc11)).
% 35.14/35.32 28114[6:MRR:28113.1,28106.1] || equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11))** -> .
% 35.14/35.32 28115[6:MRR:27186.1,28114.0] || in(skf19(skc10,skc11),relation_rng(skc10))* -> .
% 35.14/35.32 28118[6:Res:4048.4,28115.0] one_to_one(skc10) function(skc10) relation(skc10) || equal(relation_rng(skc10),relation_rng(skc10)) -> equal(function_inverse(skc10),skc11) equal(apply(skc10,skf20(skc10,skc11)),skf21(skc11,skc10))**.
% 35.14/35.32 28119[6:Obv:28118.3] one_to_one(skc10) function(skc10) relation(skc10) || -> equal(function_inverse(skc10),skc11) equal(apply(skc10,skf20(skc10,skc11)),skf21(skc11,skc10))**.
% 35.14/35.32 28120[6:Rew:27051.0,28119.4] one_to_one(skc10) function(skc10) relation(skc10) || -> equal(function_inverse(skc10),skc11) equal(skf11(skc11,skf20(skc10,skc11)),skf21(skc11,skc10))**.
% 35.14/35.32 28121[6:SSi:28120.2,28120.1,28120.0,2.0,3.0,5.0,2.0,3.0,5.0,2.0,3.0,5.0] || -> equal(function_inverse(skc10),skc11) equal(skf11(skc11,skf20(skc10,skc11)),skf21(skc11,skc10))**.
% 35.14/35.32 28122[6:MRR:28121.0,34.0] || -> equal(skf11(skc11,skf20(skc10,skc11)),skf21(skc11,skc10))**.
% 35.14/35.32 28126[6:SpR:28122.0,4971.0] || -> in(skf21(skc11,skc10),relation_rng(skc10))*.
% 35.14/35.32 28127[6:SpR:28122.0,5526.1] || in(skf20(skc10,skc11),relation_rng(skc11))* -> equal(skf11(skc10,skf21(skc11,skc10)),skf20(skc10,skc11)).
% 35.14/35.32 28128[6:SpR:28122.0,5505.0] || -> equal(apply(skc11,skf21(skc11,skc10)),skf11(skc10,skf21(skc11,skc10)))**.
% 35.14/35.32 28158[6:MRR:28127.0,27031.0] || -> equal(skf11(skc10,skf21(skc11,skc10)),skf20(skc10,skc11))**.
% 35.14/35.32 28159[6:Rew:28158.0,28128.0] || -> equal(apply(skc11,skf21(skc11,skc10)),skf20(skc10,skc11))**.
% 35.14/35.32 28193[6:Res:28126.0,4617.4] one_to_one(skc10) function(skc10) relation(skc10) || equal(relation_rng(skc10),relation_rng(skc10)) equal(apply(skc11,skf21(skc11,skc10)),skf20(skc10,skc11)) -> in(skf19(skc10,skc11),relation_rng(skc10))* equal(function_inverse(skc10),skc11).
% 35.14/35.32 28201[6:Obv:28193.3] one_to_one(skc10) function(skc10) relation(skc10) || equal(apply(skc11,skf21(skc11,skc10)),skf20(skc10,skc11)) -> in(skf19(skc10,skc11),relation_rng(skc10))* equal(function_inverse(skc10),skc11).
% 35.14/35.32 28202[6:Rew:28159.0,28201.3] one_to_one(skc10) function(skc10) relation(skc10) || equal(skf20(skc10,skc11),skf20(skc10,skc11)) -> in(skf19(skc10,skc11),relation_rng(skc10))* equal(function_inverse(skc10),skc11).
% 35.14/35.32 28203[6:Obv:28202.3] one_to_one(skc10) function(skc10) relation(skc10) || -> in(skf19(skc10,skc11),relation_rng(skc10))* equal(function_inverse(skc10),skc11).
% 35.14/35.32 28204[6:SSi:28203.2,28203.1,28203.0,2.0,3.0,5.0,2.0,3.0,5.0,2.0,3.0,5.0] || -> in(skf19(skc10,skc11),relation_rng(skc10))* equal(function_inverse(skc10),skc11).
% 35.14/35.32 28205[6:MRR:28204.0,28204.1,28115.0,34.0] || -> .
% 35.14/35.32 28210[6:Spt:28205.0,27063.0,27183.0] || equal(skf11(skc10,skf19(skc10,skc11)),skf18(skc10,skc11))** -> .
% 35.14/35.32 28211[6:Spt:28205.0,27063.1] || -> equal(skf11(skc11,skf20(skc10,skc11)),skf21(skc11,skc10))**.
% 35.14/35.32 28213[6:SpR:28211.0,4971.0] || -> in(skf21(skc11,skc10),relation_rng(skc10))*.
% 35.14/35.32 28214[6:SpR:28211.0,5526.1] || in(skf20(skc10,skc11),relation_rng(skc11))* -> equal(skf11(skc10,skf21(skc11,skc10)),skf20(skc10,skc11)).
% 35.14/35.32 28215[6:SpR:28211.0,5505.0] || -> equal(apply(skc11,skf21(skc11,skc10)),skf11(skc10,skf21(skc11,skc10)))**.
% 35.14/35.32 28245[6:MRR:28214.0,27031.0] || -> equal(skf11(skc10,skf21(skc11,skc10)),skf20(skc10,skc11))**.
% 35.14/35.32 28246[6:Rew:28245.0,28215.0] || -> equal(apply(skc11,skf21(skc11,skc10)),skf20(skc10,skc11))**.
% 35.14/35.32 28280[6:Res:28213.0,4617.4] one_to_one(skc10) function(skc10) relation(skc10) || equal(relation_rng(skc10),relation_rng(skc10)) equal(apply(skc11,skf21(skc11,skc10)),skf20(skc10,skc11)) -> in(skf19(skc10,skc11),relation_rng(skc10))* equal(function_inverse(skc10),skc11).
% 35.14/35.32 28288[6:Obv:28280.3] one_to_one(skc10) function(skc10) relation(skc10) || equal(apply(skc11,skf21(skc11,skc10)),skf20(skc10,skc11)) -> in(skf19(skc10,skc11),relation_rng(skc10))* equal(function_inverse(skc10),skc11).
% 35.14/35.32 28289[6:Rew:28246.0,28288.3] one_to_one(skc10) function(skc10) relation(skc10) || equal(skf20(skc10,skc11),skf20(skc10,skc11)) -> in(skf19(skc10,skc11),relation_rng(skc10))* equal(function_inverse(skc10),skc11).
% 35.14/35.32 28290[6:Obv:28289.3] one_to_one(skc10) function(skc10) relation(skc10) || -> in(skf19(skc10,skc11),relation_rng(skc10))* equal(function_inverse(skc10),skc11).
% 35.14/35.32 28291[6:SSi:28290.2,28290.1,28290.0,2.0,3.0,5.0,2.0,3.0,5.0,2.0,3.0,5.0] || -> in(skf19(skc10,skc11),relation_rng(skc10))* equal(function_inverse(skc10),skc11).
% 35.14/35.32 28292[6:MRR:28291.1,34.0] || -> in(skf19(skc10,skc11),relation_rng(skc10))*.
% 35.14/35.32 28346[6:Res:28292.0,4898.0] || -> equal(apply(skc11,skf19(skc10,skc11)),skf11(skc10,skf19(skc10,skc11)))**.
% 35.14/35.32 28353[6:Rew:26915.0,28346.0] || -> equal(skf11(skc10,skf19(skc10,skc11)),skf18(skc10,skc11))**.
% 35.14/35.32 28354[6:MRR:28353.0,28210.0] || -> .
% 35.14/35.32 28360[5:Spt:28354.0,15421.0] || -> in(skf19(skc10,skc11),relation_rng(skc10))*.
% 35.14/35.32 28406[5:Res:28360.0,4898.0] || -> equal(apply(skc11,skf19(skc10,skc11)),skf11(skc10,skf19(skc10,skc11)))**.
% 35.14/35.32 28413[5:Rew:26915.0,28406.0] || -> equal(skf11(skc10,skf19(skc10,skc11)),skf18(skc10,skc11))**.
% 35.14/35.32 28425[5:SpR:28413.0,4961.0] || -> in(skf18(skc10,skc11),relation_rng(skc11))*.
% 35.14/35.32 28426[5:SpR:28413.0,5997.1] || in(skf19(skc10,skc11),relation_rng(skc10))* -> equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)).
% 35.14/35.32 28459[5:MRR:20640.0,28425.0] || equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) -> in(skf20(skc10,u),relation_rng(skc11))*.
% 37.03/37.27 28460[5:MRR:21221.0,28425.0] || equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) -> equal(apply(skc10,skf20(skc10,skc11)),skf21(skc11,skc10))**.
% 37.03/37.27 28474[5:MRR:28426.0,28360.0] || -> equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11))**.
% 37.03/37.27 28480[5:Rew:28474.0,28459.0] || equal(skf19(skc10,skc11),skf19(skc10,skc11)) -> in(skf20(skc10,u),relation_rng(skc11))*.
% 37.03/37.27 28481[5:Obv:28480.0] || -> in(skf20(skc10,u),relation_rng(skc11))*.
% 37.03/37.27 28482[5:Rew:28474.0,28460.0] || equal(skf19(skc10,skc11),skf19(skc10,skc11)) -> equal(apply(skc10,skf20(skc10,skc11)),skf21(skc11,skc10))**.
% 37.03/37.27 28483[5:Obv:28482.0] || -> equal(apply(skc10,skf20(skc10,skc11)),skf21(skc11,skc10))**.
% 37.03/37.27 28511[5:Res:28481.0,5944.0] || -> equal(apply(skc10,skf20(skc10,u)),skf11(skc11,skf20(skc10,u)))**.
% 37.03/37.27 28512[5:Rew:28511.0,28483.0] || -> equal(skf11(skc11,skf20(skc10,skc11)),skf21(skc11,skc10))**.
% 37.03/37.27 28555[5:SpR:28512.0,4971.0] || -> in(skf21(skc11,skc10),relation_rng(skc10))*.
% 37.03/37.27 28556[5:SpR:28512.0,5526.1] || in(skf20(skc10,skc11),relation_rng(skc11))* -> equal(skf11(skc10,skf21(skc11,skc10)),skf20(skc10,skc11)).
% 37.03/37.27 28557[5:SpR:28512.0,5505.0] || -> equal(apply(skc11,skf21(skc11,skc10)),skf11(skc10,skf21(skc11,skc10)))**.
% 37.03/37.27 28587[5:MRR:28556.0,28481.0] || -> equal(skf11(skc10,skf21(skc11,skc10)),skf20(skc10,skc11))**.
% 37.03/37.27 28588[5:Rew:28587.0,28557.0] || -> equal(apply(skc11,skf21(skc11,skc10)),skf20(skc10,skc11))**.
% 37.03/37.27 28620[5:Res:28555.0,4620.6] one_to_one(skc10) function(skc10) relation(skc10) || in(skf18(skc10,skc11),relation_dom(skc10))* equal(apply(skc10,skf18(skc10,skc11)),skf19(skc10,skc11)) equal(relation_rng(skc10),relation_rng(skc10)) equal(apply(skc11,skf21(skc11,skc10)),skf20(skc10,skc11)) -> equal(function_inverse(skc10),skc11).
% 37.03/37.27 28633[5:Obv:28620.5] one_to_one(skc10) function(skc10) relation(skc10) || in(skf18(skc10,skc11),relation_dom(skc10))* equal(apply(skc10,skf18(skc10,skc11)),skf19(skc10,skc11)) equal(apply(skc11,skf21(skc11,skc10)),skf20(skc10,skc11)) -> equal(function_inverse(skc10),skc11).
% 37.03/37.27 28634[5:Rew:5944.1,28633.4,32.0,28633.3] one_to_one(skc10) function(skc10) relation(skc10) || in(skf18(skc10,skc11),relation_rng(skc11))* equal(skf11(skc11,skf18(skc10,skc11)),skf19(skc10,skc11)) equal(apply(skc11,skf21(skc11,skc10)),skf20(skc10,skc11)) -> equal(function_inverse(skc10),skc11).
% 37.03/37.27 28635[5:Rew:28588.0,28634.5,28474.0,28634.4] one_to_one(skc10) function(skc10) relation(skc10) || in(skf18(skc10,skc11),relation_rng(skc11))* equal(skf19(skc10,skc11),skf19(skc10,skc11)) equal(skf20(skc10,skc11),skf20(skc10,skc11)) -> equal(function_inverse(skc10),skc11).
% 37.03/37.27 28636[5:Obv:28635.5] one_to_one(skc10) function(skc10) relation(skc10) || in(skf18(skc10,skc11),relation_rng(skc11))* -> equal(function_inverse(skc10),skc11).
% 37.03/37.27 28637[5:SSi:28636.2,28636.1,28636.0,2.0,3.0,5.0,2.0,3.0,5.0,2.0,3.0,5.0] || in(skf18(skc10,skc11),relation_rng(skc11))* -> equal(function_inverse(skc10),skc11).
% 37.03/37.27 28638[5:MRR:28637.0,28637.1,28425.0,34.0] || -> .
% 37.03/37.27 % SZS output end Refutation
% 37.03/37.27 Formulae used in the proof : t60_funct_1 fc4_relat_1 rc2_subset_1 existence_m1_subset_1 cc1_funct_1 cc1_relat_1 fc7_relat_1 fc8_relat_1 t6_boole t7_boole dt_k2_funct_1 fc5_relat_1 t2_subset t54_funct_1 t5_subset d5_funct_1 antisymmetry_r2_hidden t9_funct_1
% 37.03/37.27
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