TSTP Solution File: SEU394+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU394+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 14:36:54 EDT 2022
% Result : Theorem 224.39s 224.69s
% Output : Refutation 225.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU394+2 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.11 % Command : run_spass %d %s
% 0.11/0.32 % Computer : n011.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sun Jun 19 16:01:08 EDT 2022
% 0.11/0.32 % CPUTime :
% 224.39/224.69
% 224.39/224.69 SPASS V 3.9
% 224.39/224.69 SPASS beiseite: Proof found.
% 224.39/224.69 % SZS status Theorem
% 224.39/224.69 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 224.39/224.69 SPASS derived 14797 clauses, backtracked 696 clauses, performed 32 splits and kept 15665 clauses.
% 224.39/224.69 SPASS allocated 207904 KBytes.
% 224.39/224.69 SPASS spent 0:3:44.34 on the problem.
% 224.39/224.69 0:00:00.06 for the input.
% 224.39/224.69 0:3:23.97 for the FLOTTER CNF translation.
% 224.39/224.69 0:00:00.24 for inferences.
% 224.39/224.69 0:00:00.24 for the backtracking.
% 224.39/224.69 0:0:15.74 for the reduction.
% 224.39/224.69
% 224.39/224.69
% 224.39/224.69 Here is a proof with depth 6, length 206 :
% 224.39/224.69 % SZS output start Refutation
% 224.39/224.69 1[0:Inp] || -> one_sorted_str(skc56)*.
% 224.39/224.69 16[0:Inp] || -> relation_empty_yielding(empty_set)*.
% 224.39/224.69 20[0:Inp] || -> epsilon_transitive(empty_set)*.
% 224.39/224.69 21[0:Inp] || -> epsilon_connected(empty_set)*.
% 224.39/224.69 22[0:Inp] || -> ordinal(empty_set)*.
% 224.39/224.69 26[0:Inp] || -> v1_membered(empty_set)*.
% 224.39/224.69 27[0:Inp] || -> v2_membered(empty_set)*.
% 224.39/224.69 28[0:Inp] || -> v3_membered(empty_set)*.
% 224.39/224.69 29[0:Inp] || -> v4_membered(empty_set)*.
% 224.39/224.69 30[0:Inp] || -> v5_membered(empty_set)*.
% 224.39/224.69 129[0:Inp] || -> relation(skc444)*.
% 224.39/224.69 130[0:Inp] || -> function(skc444)*.
% 224.39/224.69 131[0:Inp] || -> one_to_one(skc444)*.
% 224.39/224.69 132[0:Inp] || -> empty(skc444)*.
% 224.39/224.69 303[0:Inp] || empty(skc57)* -> .
% 224.39/224.69 304[0:Inp] || empty_carrier(skc56)* -> .
% 224.39/224.69 379[0:Inp] || -> relation(identity_relation(u))*.
% 224.39/224.69 380[0:Inp] || -> function(identity_relation(u))*.
% 224.39/224.69 381[0:Inp] || -> reflexive(identity_relation(u))*.
% 224.39/224.69 382[0:Inp] || -> symmetric(identity_relation(u))*.
% 224.39/224.69 383[0:Inp] || -> antisymmetric(identity_relation(u))*.
% 224.39/224.69 384[0:Inp] || -> transitive(identity_relation(u))*.
% 224.39/224.69 464[0:Inp] || -> empty(skf599(u))*.
% 224.39/224.69 471[0:Inp] || -> natural(skf599(u))*.
% 224.39/224.69 472[0:Inp] || -> finite(skf599(u))*.
% 224.39/224.69 496[0:Inp] || -> subset(u,u)*.
% 224.39/224.69 515[0:Inp] || -> equal(cast_to_subset(u),u)**.
% 224.39/224.69 517[0:Inp] || -> element(skf570(u),u)*.
% 224.39/224.69 536[0:Inp] || proper_subset(u,u)* -> .
% 224.39/224.69 558[0:Inp] || -> filtered_subset(skc57,boole_POSet(cast_as_carrier_subset(skc56)))*.
% 224.39/224.69 559[0:Inp] || -> upper_relstr_subset(skc57,boole_POSet(cast_as_carrier_subset(skc56)))*.
% 224.39/224.69 572[0:Inp] empty(u) || -> relation(u)*.
% 224.39/224.69 589[0:Inp] || -> in(u,skf513(v,u))*.
% 224.39/224.69 650[0:Inp] || -> equal(powerset(u),k1_pcomps_1(u))**.
% 224.39/224.69 667[0:Inp] || -> equal(set_union2(u,empty_set),u)**.
% 224.39/224.69 669[0:Inp] || -> equal(singleton(empty_set),powerset(empty_set))**.
% 224.39/224.69 671[0:Inp] || -> subset(set_difference(u,v),u)*l.
% 224.39/224.69 674[0:Inp] || -> equal(set_difference(empty_set,u),empty_set)**.
% 224.39/224.69 676[0:Inp] || -> equal(relation_rng(identity_relation(u)),u)**.
% 224.39/224.69 713[0:Inp] empty(u) || -> empty(relation_inverse(u))*.
% 224.39/224.69 793[0:Inp] || -> equal(the_carrier(boole_POSet(u)),powerset(u))**.
% 224.39/224.69 797[0:Inp] empty(u) || -> equal(u,empty_set)*.
% 224.39/224.69 802[0:Inp] || -> proper_element(skc57,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(skc56)))))*.
% 224.39/224.69 803[0:Inp] || -> element(skc57,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(skc56)))))*.
% 224.39/224.69 805[0:Inp] || -> equal(set_union2(u,v),set_union2(v,u))*.
% 224.39/224.69 817[0:Inp] || -> equal(set_union2(u,singleton(u)),succ(u))**.
% 224.39/224.69 902[0:Inp] || -> in(u,v) disjoint(singleton(u),v)*.
% 224.39/224.69 927[0:Inp] || disjoint(u,v)*+ -> disjoint(v,u)*.
% 224.39/224.69 940[0:Inp] empty(u) || in(v,u)* -> .
% 224.39/224.69 942[0:Inp] || in(u,v)*+ in(v,u)* -> .
% 224.39/224.69 983[0:Inp] relation(u) || -> equal(relation_inverse(relation_inverse(u)),u)**.
% 224.39/224.69 989[0:Inp] || -> SkP10(u,v) in(skf631(u,v),v)*.
% 224.39/224.69 995[0:Inp] || -> SkP15(u,v) in(skf659(u,v),v)*.
% 224.39/224.69 1013[0:Inp] || -> SkP32(u,v) in(skf878(u,v),v)*.
% 224.39/224.69 1021[0:Inp] one_sorted_str(u) || -> equal(the_carrier(u),cast_as_carrier_subset(u))**.
% 224.39/224.69 1028[0:Inp] || -> disjoint(u,v) in(skf929(v,u),u)*.
% 224.39/224.69 1063[0:Inp] empty_carrier(u) one_sorted_str(u) || -> empty(the_carrier(u))*.
% 224.39/224.69 1073[0:Inp] || disjoint(u,v) -> equal(set_intersection2(u,v),empty_set)**.
% 224.39/224.69 1096[0:Inp] one_sorted_str(u) || empty(cast_as_carrier_subset(u))* -> empty_carrier(u).
% 224.39/224.69 1100[0:Inp] relation(u) || empty(relation_rng(u))* -> empty(u).
% 224.39/224.69 1131[0:Inp] || element(u,v)* -> empty(v) in(u,v).
% 224.39/224.69 1142[0:Inp] ordinal(u) || -> being_limit_ordinal(u) in(skf930(u),u)*.
% 224.39/224.69 1149[0:Inp] || disjoint(u,v) -> equal(set_difference(u,v),u)**.
% 224.39/224.69 1152[0:Inp] || equal(filter_of_net_str(skc56,net_of_bool_filter(skc56,cast_as_carrier_subset(skc56),skc57)),skc57)** -> .
% 224.39/224.69 1235[0:Inp] || subset(u,v) -> proper_subset(u,v)* equal(u,v).
% 224.39/224.69 1311[0:Inp] || in(u,set_intersection2(v,w))* disjoint(v,w) -> .
% 224.39/224.69 1324[0:Inp] || subset(u,v)* subset(v,u)* -> equal(v,u).
% 224.39/224.69 1447[0:Inp] || element(u,powerset(v))* -> equal(subset_complement(v,u),set_difference(v,u)).
% 224.39/224.69 1469[0:Inp] || element(u,powerset(v))* in(w,u)* -> in(w,v)*.
% 224.39/224.69 1484[0:Inp] || element(u,powerset(powerset(v)))* -> equal(union_of_subsets(v,u),union(u)).
% 224.39/224.69 1754[0:Inp] || element(u,powerset(v)) in(w,subset_complement(v,u))* in(w,u) -> .
% 224.39/224.69 1985[0:Inp] || element(u,powerset(v)) element(w,v) -> equal(v,empty_set) in(w,u) in(w,subset_complement(v,u))*.
% 224.39/224.69 1994[0:Inp] || element(u,powerset(powerset(v))) -> equal(subset_complement(v,union_of_subsets(v,u)),meet_of_subsets(v,complements_of_subsets(v,u)))** equal(u,empty_set).
% 224.39/224.69 2130[0:Inp] || element(u,powerset(powerset(v))) -> equal(subset_difference(v,cast_to_subset(v),union_of_subsets(v,u)),meet_of_subsets(v,complements_of_subsets(v,u)))** equal(u,empty_set).
% 224.39/224.69 2575[0:Inp] empty(u) || upper_relstr_subset(v,boole_POSet(w)) proper_element(v,powerset(the_carrier(boole_POSet(w))))* element(v,powerset(the_carrier(boole_POSet(w)))) in(u,v)* filtered_subset(v,boole_POSet(w)) -> empty(w) empty(v).
% 224.39/224.69 2641[0:Inp] one_sorted_str(u) || filtered_subset(v,boole_POSet(cast_as_carrier_subset(u))) upper_relstr_subset(v,boole_POSet(cast_as_carrier_subset(u))) element(v,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(u))))) -> empty_carrier(u) empty(v) equal(filter_of_net_str(u,net_of_bool_filter(u,cast_as_carrier_subset(u),v)),set_difference(v,singleton(empty_set)))**.
% 224.39/224.69 2734[0:Rew:650.0,669.0] || -> equal(singleton(empty_set),k1_pcomps_1(empty_set))**.
% 224.39/224.69 2753[0:Rew:650.0,793.0] || -> equal(the_carrier(boole_POSet(u)),k1_pcomps_1(u))**.
% 224.39/224.69 2797[0:Rew:650.0,803.0,2753.0,803.0] || -> element(skc57,k1_pcomps_1(k1_pcomps_1(cast_as_carrier_subset(skc56))))*.
% 224.39/224.69 2798[0:Rew:650.0,802.0,2753.0,802.0] || -> proper_element(skc57,k1_pcomps_1(k1_pcomps_1(cast_as_carrier_subset(skc56))))*.
% 224.39/224.69 2815[0:Rew:1021.1,1063.2] one_sorted_str(u) empty_carrier(u) || -> empty(cast_as_carrier_subset(u))*.
% 224.39/224.69 2818[0:Rew:1073.1,1311.0] || disjoint(u,v)* in(w,empty_set)* -> .
% 224.39/224.69 2879[0:Rew:650.0,1484.0,650.0,1484.0] || element(u,k1_pcomps_1(k1_pcomps_1(v)))* -> equal(union_of_subsets(v,u),union(u)).
% 224.39/224.69 2880[0:Rew:650.0,1469.0] || in(u,v)* element(v,k1_pcomps_1(w))* -> in(u,w)*.
% 224.39/224.69 2887[0:Rew:650.0,1447.0] || element(u,k1_pcomps_1(v))* -> equal(subset_complement(v,u),set_difference(v,u)).
% 224.39/224.69 2926[0:Rew:2887.1,1754.1,650.0,1754.0] || in(u,v) element(v,k1_pcomps_1(w)) in(u,set_difference(w,v))* -> .
% 224.39/224.69 3026[0:Rew:2887.1,1985.4,650.0,1985.0] || element(u,v) element(w,k1_pcomps_1(v)) -> in(u,w) equal(v,empty_set) in(u,set_difference(v,w))*.
% 224.39/224.69 3033[0:Rew:2879.1,1994.1,650.0,1994.0,650.0,1994.0] || element(u,k1_pcomps_1(k1_pcomps_1(v))) -> equal(u,empty_set) equal(meet_of_subsets(v,complements_of_subsets(v,u)),subset_complement(v,union(u)))**.
% 224.39/224.69 3085[0:Rew:515.0,2130.1,2879.1,2130.1,3033.1,2130.1,650.0,2130.0,650.0,2130.0] || element(u,k1_pcomps_1(k1_pcomps_1(v))) -> equal(u,empty_set) equal(subset_difference(v,v,union(u)),subset_complement(v,union(u)))**.
% 224.39/224.69 3315[0:Rew:2753.0,2575.3,650.0,2575.3,2753.0,2575.2,650.0,2575.2] empty(u) || upper_relstr_subset(v,boole_POSet(w)) proper_element(v,k1_pcomps_1(k1_pcomps_1(w)))* element(v,k1_pcomps_1(k1_pcomps_1(w))) in(u,v)* filtered_subset(v,boole_POSet(w)) -> empty(w) empty(v).
% 224.39/224.69 3316[0:MRR:3315.7,940.0] empty(u) || in(u,v)* filtered_subset(v,boole_POSet(w)) upper_relstr_subset(v,boole_POSet(w)) element(v,k1_pcomps_1(k1_pcomps_1(w))) proper_element(v,k1_pcomps_1(k1_pcomps_1(w)))* -> empty(w).
% 224.39/224.69 3372[0:Rew:2734.0,2641.6,2753.0,2641.3,650.0,2641.3] one_sorted_str(u) || upper_relstr_subset(v,boole_POSet(cast_as_carrier_subset(u))) filtered_subset(v,boole_POSet(cast_as_carrier_subset(u))) element(v,k1_pcomps_1(k1_pcomps_1(cast_as_carrier_subset(u)))) -> empty(v) empty_carrier(u) equal(filter_of_net_str(u,net_of_bool_filter(u,cast_as_carrier_subset(u),v)),set_difference(v,k1_pcomps_1(empty_set)))**.
% 224.39/224.69 3646[0:Res:1.0,2815.1] empty_carrier(skc56) || -> empty(cast_as_carrier_subset(skc56))*.
% 224.39/224.69 3649[0:Res:1.0,1096.0] || empty(cast_as_carrier_subset(skc56))* -> empty_carrier(skc56).
% 224.39/224.69 4182[0:Res:1131.2,303.0] || element(u,skc57)* -> in(u,skc57).
% 224.39/224.69 4336[0:Res:2797.0,3372.3] one_sorted_str(skc56) || filtered_subset(skc57,boole_POSet(cast_as_carrier_subset(skc56))) upper_relstr_subset(skc57,boole_POSet(cast_as_carrier_subset(skc56))) -> empty_carrier(skc56) empty(skc57) equal(filter_of_net_str(skc56,net_of_bool_filter(skc56,cast_as_carrier_subset(skc56),skc57)),set_difference(skc57,k1_pcomps_1(empty_set)))**.
% 224.39/224.69 4411[0:Res:2797.0,3026.0] || element(u,k1_pcomps_1(cast_as_carrier_subset(skc56))) -> in(u,skc57) in(u,set_difference(k1_pcomps_1(cast_as_carrier_subset(skc56)),skc57))* equal(k1_pcomps_1(cast_as_carrier_subset(skc56)),empty_set).
% 224.39/224.69 4418[0:Res:2797.0,2926.0] || in(u,skc57) in(u,set_difference(k1_pcomps_1(cast_as_carrier_subset(skc56)),skc57))* -> .
% 224.39/224.69 4424[0:Res:2797.0,2880.0] || in(u,skc57) -> in(u,k1_pcomps_1(cast_as_carrier_subset(skc56)))*.
% 224.39/224.69 4430[0:Res:2797.0,3085.0] || -> equal(empty_set,skc57) equal(subset_difference(cast_as_carrier_subset(skc56),cast_as_carrier_subset(skc56),union(skc57)),subset_complement(cast_as_carrier_subset(skc56),union(skc57)))**.
% 224.39/224.69 4496[0:Res:2798.0,3316.2] empty(u) || upper_relstr_subset(skc57,boole_POSet(cast_as_carrier_subset(skc56))) element(skc57,k1_pcomps_1(k1_pcomps_1(cast_as_carrier_subset(skc56))))* in(u,skc57)* filtered_subset(skc57,boole_POSet(cast_as_carrier_subset(skc56))) -> empty(cast_as_carrier_subset(skc56)).
% 224.39/224.69 4503[0:Res:1235.1,1152.0] || subset(filter_of_net_str(skc56,net_of_bool_filter(skc56,cast_as_carrier_subset(skc56),skc57)),skc57) -> proper_subset(filter_of_net_str(skc56,net_of_bool_filter(skc56,cast_as_carrier_subset(skc56),skc57)),skc57)*.
% 224.39/224.69 4546[0:Res:1324.2,1152.0] || subset(skc57,filter_of_net_str(skc56,net_of_bool_filter(skc56,cast_as_carrier_subset(skc56),skc57))) subset(filter_of_net_str(skc56,net_of_bool_filter(skc56,cast_as_carrier_subset(skc56),skc57)),skc57)*l -> .
% 224.39/224.69 4588[0:MRR:3649.1,304.0] || empty(cast_as_carrier_subset(skc56))* -> .
% 224.39/224.69 4589[0:MRR:3646.1,4588.0] empty_carrier(skc56) || -> .
% 224.39/224.69 4790[0:MRR:4496.1,4496.2,4496.4,4496.5,559.0,2797.0,558.0,4588.0] empty(u) || in(u,skc57)* -> .
% 224.39/224.69 4815[0:MRR:4336.0,4336.1,4336.2,4336.3,4336.4,1.0,558.0,559.0,4589.0,303.0] || -> equal(filter_of_net_str(skc56,net_of_bool_filter(skc56,cast_as_carrier_subset(skc56),skc57)),set_difference(skc57,k1_pcomps_1(empty_set)))**.
% 224.39/224.69 4826[0:Rew:4815.0,4546.0] || subset(skc57,set_difference(skc57,k1_pcomps_1(empty_set))) subset(filter_of_net_str(skc56,net_of_bool_filter(skc56,cast_as_carrier_subset(skc56),skc57)),skc57)*l -> .
% 224.39/224.69 4828[0:Rew:4815.0,4503.0] || subset(set_difference(skc57,k1_pcomps_1(empty_set)),skc57) -> proper_subset(filter_of_net_str(skc56,net_of_bool_filter(skc56,cast_as_carrier_subset(skc56),skc57)),skc57)*.
% 224.39/224.69 4834[0:Rew:4815.0,4828.1] || subset(set_difference(skc57,k1_pcomps_1(empty_set)),skc57) -> proper_subset(set_difference(skc57,k1_pcomps_1(empty_set)),skc57)*.
% 224.39/224.69 4835[0:MRR:4834.0,671.0] || -> proper_subset(set_difference(skc57,k1_pcomps_1(empty_set)),skc57)*.
% 224.39/224.69 4843[0:Rew:4815.0,4826.1] || subset(skc57,set_difference(skc57,k1_pcomps_1(empty_set))) subset(set_difference(skc57,k1_pcomps_1(empty_set)),skc57)*l -> .
% 224.39/224.69 4844[0:MRR:4843.1,671.0] || subset(skc57,set_difference(skc57,k1_pcomps_1(empty_set)))*r -> .
% 224.39/224.69 5715[1:Spt:4411.3] || -> equal(k1_pcomps_1(cast_as_carrier_subset(skc56)),empty_set)**.
% 224.39/224.69 5855[1:Rew:5715.0,4418.1] || in(u,skc57) in(u,set_difference(empty_set,skc57))* -> .
% 224.39/224.69 5961[1:Rew:5715.0,4424.1] || in(u,skc57) -> in(u,empty_set)*.
% 224.39/224.69 5991[1:Rew:674.0,5855.1] || in(u,skc57) in(u,empty_set)* -> .
% 224.39/224.69 5992[1:MRR:5991.1,5961.1] || in(u,skc57)* -> .
% 224.39/224.69 5993[1:MRR:4182.1,5992.0] || element(u,skc57)* -> .
% 224.39/224.69 6011[1:UnC:5993.0,517.0] || -> .
% 224.39/224.69 6106[1:Spt:6011.0,4411.3,5715.0] || equal(k1_pcomps_1(cast_as_carrier_subset(skc56)),empty_set)** -> .
% 224.39/224.69 6107[1:Spt:6011.0,4411.0,4411.1,4411.2] || element(u,k1_pcomps_1(cast_as_carrier_subset(skc56))) -> in(u,skc57) in(u,set_difference(k1_pcomps_1(cast_as_carrier_subset(skc56)),skc57))*.
% 224.39/224.69 6110[2:Spt:4430.0] || -> equal(empty_set,skc57)**.
% 224.39/224.69 6123[2:Rew:6110.0,4844.0] || subset(skc57,set_difference(skc57,k1_pcomps_1(skc57)))*r -> .
% 224.39/224.69 6219[2:Rew:6110.0,674.0] || -> equal(set_difference(skc57,u),skc57)**.
% 224.39/224.69 6397[2:Rew:6219.0,6123.0] || subset(skc57,skc57)* -> .
% 224.39/224.69 6398[2:MRR:6397.0,496.0] || -> .
% 224.39/224.69 6449[2:Spt:6398.0,4430.0,6110.0] || equal(empty_set,skc57)** -> .
% 224.39/224.69 6450[2:Spt:6398.0,4430.1] || -> equal(subset_difference(cast_as_carrier_subset(skc56),cast_as_carrier_subset(skc56),union(skc57)),subset_complement(cast_as_carrier_subset(skc56),union(skc57)))**.
% 224.39/224.69 6704[0:EmS:797.0,713.1] empty(u) || -> equal(relation_inverse(u),empty_set)**.
% 224.39/224.69 6708[0:EmS:797.0,464.0] || -> equal(skf599(u),empty_set)**.
% 224.39/224.69 6711[0:EmS:797.0,132.0] || -> equal(empty_set,skc444)**.
% 224.39/224.69 6716[0:Rew:6711.0,16.0] || -> relation_empty_yielding(skc444)*.
% 224.39/224.69 6719[0:Rew:6711.0,20.0] || -> epsilon_transitive(skc444)*.
% 224.39/224.69 6720[0:Rew:6711.0,21.0] || -> epsilon_connected(skc444)*.
% 224.39/224.69 6721[0:Rew:6711.0,22.0] || -> ordinal(skc444)*.
% 224.39/224.69 6724[0:Rew:6711.0,26.0] || -> v1_membered(skc444)*.
% 224.39/224.69 6725[0:Rew:6711.0,27.0] || -> v2_membered(skc444)*.
% 224.39/224.69 6726[0:Rew:6711.0,28.0] || -> v3_membered(skc444)*.
% 224.39/224.69 6727[0:Rew:6711.0,29.0] || -> v4_membered(skc444)*.
% 224.39/224.69 6728[0:Rew:6711.0,30.0] || -> v5_membered(skc444)*.
% 224.39/224.69 6734[0:Rew:6711.0,4835.0] || -> proper_subset(set_difference(skc57,k1_pcomps_1(skc444)),skc57)*.
% 224.39/224.69 6735[0:Rew:6711.0,2734.0] || -> equal(singleton(skc444),k1_pcomps_1(skc444))**.
% 224.39/224.69 6744[0:Rew:6711.0,667.0] || -> equal(set_union2(u,skc444),u)**.
% 224.39/224.69 6824[0:Rew:6711.0,2818.1] || disjoint(u,v)*+ in(w,skc444)* -> .
% 224.39/224.69 6882[0:Rew:6711.0,6708.0] || -> equal(skf599(u),skc444)**.
% 224.39/224.69 6883[0:Rew:6882.0,471.0] || -> natural(skc444)*.
% 224.39/224.69 6887[0:Rew:6882.0,472.0] || -> finite(skc444)*.
% 224.39/224.69 6896[0:Rew:6711.0,6704.1] empty(u) || -> equal(relation_inverse(u),skc444)**.
% 224.39/224.69 7142[0:SpR:6735.0,817.0] || -> equal(set_union2(skc444,k1_pcomps_1(skc444)),succ(skc444))**.
% 224.39/224.69 7576[0:SpR:805.0,6744.0] || -> equal(set_union2(skc444,u),u)**.
% 224.39/224.69 7590[0:Rew:7576.0,7142.0] || -> equal(k1_pcomps_1(skc444),succ(skc444))**.
% 224.39/224.69 7592[0:Rew:7590.0,6735.0] || -> equal(singleton(skc444),succ(skc444))**.
% 224.39/224.69 7594[0:Rew:7590.0,6734.0] || -> proper_subset(set_difference(skc57,succ(skc444)),skc57)*.
% 224.39/224.69 7750[0:SpR:7592.0,902.1] || -> in(skc444,u) disjoint(succ(skc444),u)*.
% 224.39/224.69 7913[0:Res:7750.1,927.0] || -> in(skc444,u) disjoint(u,succ(skc444))*.
% 224.39/224.69 8001[0:SpR:6896.1,983.1] empty(u) relation(u) || -> equal(relation_inverse(skc444),u)*.
% 224.39/224.69 8002[0:SSi:8001.1,572.1] empty(u) || -> equal(relation_inverse(skc444),u)*.
% 224.39/224.69 8335[0:SpR:8002.1,382.0] empty(identity_relation(u)) || -> symmetric(relation_inverse(skc444))*.
% 224.39/224.69 8336[0:SpR:8002.1,383.0] empty(identity_relation(u)) || -> antisymmetric(relation_inverse(skc444))*.
% 224.39/224.69 8337[0:SpR:8002.1,384.0] empty(identity_relation(u)) || -> transitive(relation_inverse(skc444))*.
% 224.39/224.69 8338[0:SpR:8002.1,381.0] empty(identity_relation(u)) || -> reflexive(relation_inverse(skc444))*.
% 224.39/224.69 9532[0:Res:902.1,6824.0] || in(u,skc444)*+ -> in(v,w)*.
% 224.39/224.69 9792[0:Res:589.0,942.0] || in(skf513(u,v),v)* -> .
% 224.39/224.69 9899[0:Res:1013.1,9532.0] || -> SkP32(u,skc444)* in(v,w)*.
% 224.39/224.69 9904[3:Spt:9899.1] || -> in(u,v)*.
% 224.39/224.69 9905[3:UnC:9904.0,9792.0] || -> .
% 224.39/224.69 9906[3:Spt:9905.0,9899.0] || -> SkP32(u,skc444)*.
% 224.39/224.69 9921[0:Res:995.1,9532.0] || -> SkP15(u,skc444)* in(v,w)*.
% 224.39/224.69 9923[4:Spt:9921.1] || -> in(u,v)*.
% 224.39/224.69 9924[4:UnC:9923.0,9792.0] || -> .
% 224.39/224.69 9925[4:Spt:9924.0,9921.0] || -> SkP15(u,skc444)*.
% 224.39/224.69 9942[0:Res:989.1,9532.0] || -> SkP10(u,skc444)* in(v,w)*.
% 224.39/224.69 9944[5:Spt:9942.1] || -> in(u,v)*.
% 224.39/224.69 9945[5:UnC:9944.0,9792.0] || -> .
% 224.39/224.69 9946[5:Spt:9945.0,9942.0] || -> SkP10(u,skc444)*.
% 224.39/224.69 9963[0:Res:1028.1,9532.0] || -> disjoint(skc444,u)* in(v,w)*.
% 224.39/224.69 9965[6:Spt:9963.1] || -> in(u,v)*.
% 224.39/224.69 9966[6:UnC:9965.0,9792.0] || -> .
% 224.39/224.69 9967[6:Spt:9966.0,9963.0] || -> disjoint(skc444,u)*.
% 224.39/224.69 9968[6:Res:9967.0,6824.0] || in(u,skc444)* -> .
% 224.39/224.69 10374[0:SpL:676.0,1100.1] relation(identity_relation(u)) || empty(u) -> empty(identity_relation(u))*.
% 224.39/224.69 10380[0:SSi:10374.0,382.0,383.0,384.0,381.0,380.0,379.0] || empty(u) -> empty(identity_relation(u))*.
% 224.39/224.69 10389[0:SoR:8338.0,10380.1] || empty(u)*+ -> reflexive(relation_inverse(skc444))*.
% 224.39/224.69 10390[0:SoR:8337.0,10380.1] || empty(u)*+ -> transitive(relation_inverse(skc444))*.
% 225.05/225.29 10391[0:SoR:8336.0,10380.1] || empty(u)*+ -> antisymmetric(relation_inverse(skc444))*.
% 225.05/225.29 10392[0:SoR:8335.0,10380.1] || empty(u)*+ -> symmetric(relation_inverse(skc444))*.
% 225.05/225.29 10426[0:Res:132.0,10389.0] || -> reflexive(relation_inverse(skc444))*.
% 225.05/225.29 10428[0:SpR:6896.1,10426.0] empty(skc444) || -> reflexive(skc444)*.
% 225.05/225.29 10430[0:SSi:10428.0,131.0,130.0,132.0,129.0,6716.0,6719.0,6720.0,6721.0,6724.0,6725.0,6726.0,6727.0,6728.0,6883.0,6887.0] || -> reflexive(skc444)*.
% 225.05/225.29 10435[0:Res:132.0,10390.0] || -> transitive(relation_inverse(skc444))*.
% 225.05/225.29 10437[0:SpR:6896.1,10435.0] empty(skc444) || -> transitive(skc444)*.
% 225.05/225.29 10439[0:SSi:10437.0,131.0,130.0,132.0,129.0,6716.0,6719.0,6720.0,6721.0,6724.0,6725.0,6726.0,6727.0,6728.0,6883.0,6887.0,10430.0] || -> transitive(skc444)*.
% 225.05/225.29 10441[0:Res:132.0,10391.0] || -> antisymmetric(relation_inverse(skc444))*.
% 225.05/225.29 10443[0:SpR:6896.1,10441.0] empty(skc444) || -> antisymmetric(skc444)*.
% 225.05/225.29 10445[0:SSi:10443.0,131.0,130.0,132.0,129.0,6716.0,6719.0,6720.0,6721.0,6724.0,6725.0,6726.0,6727.0,6728.0,6883.0,6887.0,10430.0,10439.0] || -> antisymmetric(skc444)*.
% 225.05/225.29 10449[0:Res:132.0,10392.0] || -> symmetric(relation_inverse(skc444))*.
% 225.05/225.29 10451[0:SpR:6896.1,10449.0] empty(skc444) || -> symmetric(skc444)*.
% 225.05/225.29 10453[0:SSi:10451.0,131.0,130.0,132.0,129.0,6716.0,6719.0,6720.0,6721.0,6724.0,6725.0,6726.0,6727.0,6728.0,6883.0,6887.0,10430.0,10439.0,10445.0] || -> symmetric(skc444)*.
% 225.05/225.29 10714[6:Res:1142.2,9968.0] ordinal(skc444) || -> being_limit_ordinal(skc444)*.
% 225.05/225.29 10716[6:SSi:10714.0,131.0,130.0,132.0,129.0,6716.0,6719.0,6720.0,6721.0,6724.0,6725.0,6726.0,6727.0,6728.0,6883.0,6887.0,10430.0,10439.0,10445.0,10453.0] || -> being_limit_ordinal(skc444)*.
% 225.05/225.29 19050[0:SpR:1149.1,7594.0] || disjoint(skc57,succ(skc444))* -> proper_subset(skc57,skc57).
% 225.05/225.29 19055[0:MRR:19050.1,536.0] || disjoint(skc57,succ(skc444))* -> .
% 225.05/225.29 19778[0:Res:7913.1,19055.0] || -> in(skc444,skc57)*.
% 225.05/225.29 19779[0:Res:19778.0,4790.1] empty(skc444) || -> .
% 225.05/225.29 19785[6:SSi:19779.0,131.0,130.0,132.0,129.0,6716.0,6719.0,6720.0,6721.0,6724.0,6725.0,6726.0,6727.0,6728.0,6883.0,6887.0,10430.0,10439.0,10445.0,10453.0,10716.0] || -> .
% 225.05/225.29 % SZS output end Refutation
% 225.05/225.29 Formulae used in the proof : t15_yellow19 fc2_ordinal1 fc6_membered rc1_partfun1 fc2_partfun1 rc2_finset_1 reflexivity_r1_tarski d4_subset_1 existence_m1_subset_1 irreflexivity_r2_xboole_0 cc1_relat_1 d4_tarski t9_tarski redefinition_k1_pcomps_1 t1_boole t1_zfmisc_1 t36_xboole_1 t4_boole t71_relat_1 fc11_relat_1 t4_waybel_7 t6_boole commutativity_k2_xboole_0 d1_ordinal1 l28_zfmisc_1 symmetry_r1_xboole_0 t7_boole antisymmetry_r2_hidden involutiveness_k4_relat_1 s1_funct_1__e10_24__wellord2__1 rc4_funct_1 l1_zfmisc_1 s1_tarski__e10_24__wellord2__1 s2_funct_1__e10_24__wellord2 t12_pre_topc t3_xboole_0 d1_struct_0 d7_xboole_0 fc2_pre_topc fc6_relat_1 t2_subset t41_ordinal1 rc3_ordinal1 t83_xboole_1 d8_xboole_0 t4_xboole_0 d10_xboole_0 d5_subset_1 l3_subset_1 redefinition_k5_setfam_1 t54_subset_1 t50_subset_1 t11_tops_2 t47_setfam_1 t2_yellow19 t14_yellow19
% 225.05/225.29
%------------------------------------------------------------------------------