TSTP Solution File: SET863-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET863-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 05:29:25 EDT 2022
% Result : Unsatisfiable 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET863-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 07:18:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.45
% 0.19/0.45 SPASS V 3.9
% 0.19/0.45 SPASS beiseite: Proof found.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 SPASS derived 217 clauses, backtracked 9 clauses, performed 2 splits and kept 179 clauses.
% 0.19/0.45 SPASS allocated 63615 KBytes.
% 0.19/0.45 SPASS spent 0:00:00.11 on the problem.
% 0.19/0.45 0:00:00.04 for the input.
% 0.19/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.45 0:00:00.01 for inferences.
% 0.19/0.45 0:00:00.00 for the backtracking.
% 0.19/0.45 0:00:00.03 for the reduction.
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 Here is a proof with depth 18, length 64 :
% 0.19/0.45 % SZS output start Refutation
% 0.19/0.45 1[0:Inp] || c_in(u,v,w)* c_lessequals(v,x,tc_set(w))*+ -> c_in(u,x,w)*.
% 0.19/0.45 2[0:Inp] || -> c_lessequals(u,v,tc_set(w)) c_in(c_Main_OsubsetI__1(u,v,w),u,w)*.
% 0.19/0.45 3[0:Inp] || c_in(c_Main_OsubsetI__1(u,v,w),v,w)* -> c_lessequals(u,v,tc_set(w)).
% 0.19/0.45 4[0:Inp] || c_in(u,v,tc_set(w)) c_in(x,c_Zorn_Ochain(v,w),tc_set(tc_set(w)))+ -> c_in(c_Zorn_Ochain__extend__1(x,u,w),x,tc_set(w))* c_in(c_union(c_insert(u,c_emptyset,tc_set(w)),x,tc_set(w)),c_Zorn_Ochain(v,w),tc_set(tc_set(w)))*.
% 0.19/0.45 5[0:Inp] || c_in(u,v,tc_set(w)) c_in(x,c_Zorn_Ochain(v,w),tc_set(tc_set(w)))+ c_lessequals(c_Zorn_Ochain__extend__1(x,u,w),u,tc_set(w))* -> c_in(c_union(c_insert(u,c_emptyset,tc_set(w)),x,tc_set(w)),c_Zorn_Ochain(v,w),tc_set(tc_set(w)))*.
% 0.19/0.45 6[0:Inp] || c_in(u,v,w)* c_in(x,c_Zorn_Omaxchain(y,w),tc_set(tc_set(w))) c_in(c_union(c_insert(v,c_emptyset,tc_set(w)),x,tc_set(w)),c_Zorn_Ochain(y,w),tc_set(tc_set(w)))*+ -> c_in(u,z,w)* c_in(c_Zorn_Omaxchain__super__lemma__1(x,z,w),x,tc_set(w))*.
% 0.19/0.45 7[0:Inp] || c_in(u,v,w)* c_in(x,c_Zorn_Omaxchain(y,w),tc_set(tc_set(w))) c_lessequals(c_Zorn_Omaxchain__super__lemma__1(x,z,w),z,tc_set(w))* c_in(c_union(c_insert(v,c_emptyset,tc_set(w)),x,tc_set(w)),c_Zorn_Ochain(y,w),tc_set(tc_set(w)))*+ -> c_in(u,z,w)*.
% 0.19/0.45 8[0:Inp] || -> c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))*.
% 0.19/0.45 9[0:Inp] || -> c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))*.
% 0.19/0.45 10[0:Inp] || -> c_in(v_x,v_S,tc_set(t_a))*.
% 0.19/0.45 11[0:Inp] || -> c_lessequals(v_y,v_x,tc_set(t_a))*.
% 0.19/0.45 12[0:Inp] || -> c_in(v_xa,v_x,t_a)*.
% 0.19/0.45 13[0:Inp] || c_in(v_xa,v_y,t_a)* -> .
% 0.19/0.45 14[0:Inp] || c_in(u,v_c,tc_set(t_a)) -> c_lessequals(u,v_y,tc_set(t_a))*.
% 0.19/0.45 17[0:Res:11.0,1.1] || c_in(u,v_y,t_a) -> c_in(u,v_x,t_a)*.
% 0.19/0.45 18[0:Res:14.1,1.1] || c_in(u,v_c,tc_set(t_a))*+ c_in(v,u,t_a)* -> c_in(v,v_y,t_a)*.
% 0.19/0.45 20[0:Res:17.1,3.0] || c_in(c_Main_OsubsetI__1(u,v_x,t_a),v_y,t_a)* -> c_lessequals(u,v_x,tc_set(t_a)).
% 0.19/0.45 24[0:Res:9.0,4.1] || c_in(u,v_S,tc_set(t_a)) -> c_in(c_Zorn_Ochain__extend__1(v_c,u,t_a),v_c,tc_set(t_a)) c_in(c_union(c_insert(u,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))*.
% 0.19/0.45 33[0:Res:9.0,5.1] || c_in(u,v_S,tc_set(t_a)) c_lessequals(c_Zorn_Ochain__extend__1(v_c,u,t_a),u,tc_set(t_a))*+ -> c_in(c_union(c_insert(u,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))*.
% 0.19/0.45 42[0:Res:24.2,6.2] || c_in(u,v_S,tc_set(t_a)) c_in(v,u,t_a)* c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) -> c_in(c_Zorn_Ochain__extend__1(v_c,u,t_a),v_c,tc_set(t_a))* c_in(v,w,t_a)* c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,w,t_a),v_c,tc_set(t_a))*.
% 0.19/0.45 43[0:MRR:42.2,8.0] || c_in(u,v_S,tc_set(t_a))+ c_in(v,u,t_a)* -> c_in(c_Zorn_Ochain__extend__1(v_c,u,t_a),v_c,tc_set(t_a))* c_in(v,w,t_a)* c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,w,t_a),v_c,tc_set(t_a))*.
% 0.19/0.45 48[0:Res:10.0,43.0] || c_in(u,v_x,t_a)*+ -> c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))* c_in(u,v,t_a)* c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v,t_a),v_c,tc_set(t_a))*.
% 0.19/0.45 50[1:Spt:48.0,48.2,48.3] || c_in(u,v_x,t_a)*+ -> c_in(u,v,t_a)* c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v,t_a),v_c,tc_set(t_a))*.
% 0.19/0.45 51[1:Res:12.0,50.0] || -> c_in(v_xa,u,t_a) c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,u,t_a),v_c,tc_set(t_a))*.
% 0.19/0.45 55[0:Res:24.2,7.3] || c_in(u,v_S,tc_set(t_a)) c_in(v,u,t_a)* c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,w,t_a),w,tc_set(t_a))* -> c_in(c_Zorn_Ochain__extend__1(v_c,u,t_a),v_c,tc_set(t_a))* c_in(v,w,t_a)*.
% 0.19/0.45 58[0:MRR:55.2,8.0] || c_in(u,v_S,tc_set(t_a)) c_in(v,u,t_a)* c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,w,t_a),w,tc_set(t_a))*+ -> c_in(c_Zorn_Ochain__extend__1(v_c,u,t_a),v_c,tc_set(t_a))* c_in(v,w,t_a)*.
% 0.19/0.45 59[1:Res:51.1,18.0] || c_in(u,c_Zorn_Omaxchain__super__lemma__1(v_c,v,t_a),t_a)* -> c_in(v_xa,v,t_a) c_in(u,v_y,t_a).
% 0.19/0.45 60[1:Res:2.1,59.0] || -> c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,u,t_a),v,tc_set(t_a)) c_in(v_xa,u,t_a) c_in(c_Main_OsubsetI__1(c_Zorn_Omaxchain__super__lemma__1(v_c,u,t_a),v,t_a),v_y,t_a)*.
% 0.19/0.45 101[1:Res:60.2,3.0] || -> c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,u,t_a),v_y,tc_set(t_a))* c_in(v_xa,u,t_a) c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,u,t_a),v_y,tc_set(t_a))*.
% 0.19/0.45 102[1:Obv:101.0] || -> c_in(v_xa,u,t_a) c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,u,t_a),v_y,tc_set(t_a))*.
% 0.19/0.45 107[1:Res:102.1,58.2] || c_in(u,v_S,tc_set(t_a)) c_in(v,u,t_a)* -> c_in(v_xa,v_y,t_a) c_in(c_Zorn_Ochain__extend__1(v_c,u,t_a),v_c,tc_set(t_a))* c_in(v,v_y,t_a)*.
% 0.19/0.45 109[1:MRR:107.2,13.0] || c_in(u,v_S,tc_set(t_a))+ c_in(v,u,t_a)* -> c_in(c_Zorn_Ochain__extend__1(v_c,u,t_a),v_c,tc_set(t_a))* c_in(v,v_y,t_a)*.
% 0.19/0.45 151[1:Res:10.0,109.0] || c_in(u,v_x,t_a)*+ -> c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))* c_in(u,v_y,t_a).
% 0.19/0.45 153[2:Spt:151.0,151.2] || c_in(u,v_x,t_a)* -> c_in(u,v_y,t_a).
% 0.19/0.45 154[2:Res:12.0,153.0] || -> c_in(v_xa,v_y,t_a)*.
% 0.19/0.45 161[2:MRR:154.0,13.0] || -> .
% 0.19/0.45 162[2:Spt:161.0,151.1] || -> c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))*.
% 0.19/0.45 163[2:Res:162.0,18.0] || c_in(u,c_Zorn_Ochain__extend__1(v_c,v_x,t_a),t_a)* -> c_in(u,v_y,t_a).
% 0.19/0.45 168[2:Res:2.1,163.0] || -> c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),u,tc_set(t_a)) c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),u,t_a),v_y,t_a)*.
% 0.19/0.45 170[2:Res:168.1,20.0] || -> c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,tc_set(t_a))* c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,tc_set(t_a))*.
% 0.19/0.45 172[2:Obv:170.0] || -> c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,tc_set(t_a))*.
% 0.19/0.45 174[2:Res:172.0,33.1] || c_in(v_x,v_S,tc_set(t_a)) -> c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))*.
% 0.19/0.45 176[2:MRR:174.0,10.0] || -> c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))*.
% 0.19/0.45 185[2:Res:176.0,7.3] || c_in(u,v_x,t_a)* c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,v,t_a),v,tc_set(t_a))* -> c_in(u,v,t_a)*.
% 0.19/0.45 188[2:MRR:185.1,8.0] || c_in(u,v_x,t_a)* c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,v,t_a),v,tc_set(t_a))*+ -> c_in(u,v,t_a)*.
% 0.19/0.45 195[2:Res:102.1,188.1] || c_in(u,v_x,t_a)* -> c_in(v_xa,v_y,t_a)* c_in(u,v_y,t_a).
% 0.19/0.45 199[2:MRR:195.1,13.0] || c_in(u,v_x,t_a)* -> c_in(u,v_y,t_a).
% 0.19/0.45 206[2:Res:12.0,199.0] || -> c_in(v_xa,v_y,t_a)*.
% 0.19/0.45 214[2:MRR:206.0,13.0] || -> .
% 0.19/0.45 215[1:Spt:214.0,48.1] || -> c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))*.
% 0.19/0.45 217[1:Res:215.0,18.0] || c_in(u,c_Zorn_Ochain__extend__1(v_c,v_x,t_a),t_a)* -> c_in(u,v_y,t_a).
% 0.19/0.45 219[1:Res:2.1,217.0] || -> c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),u,tc_set(t_a)) c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),u,t_a),v_y,t_a)*.
% 0.19/0.45 220[1:Res:219.1,20.0] || -> c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,tc_set(t_a))* c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,tc_set(t_a))*.
% 0.19/0.45 222[1:Obv:220.0] || -> c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,tc_set(t_a))*.
% 0.19/0.45 224[1:Res:222.0,33.1] || c_in(v_x,v_S,tc_set(t_a)) -> c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))*.
% 0.19/0.45 226[1:MRR:224.0,10.0] || -> c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))*.
% 0.19/0.45 237[1:Res:226.0,7.3] || c_in(u,v_x,t_a)* c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,v,t_a),v,tc_set(t_a))* -> c_in(u,v,t_a)*.
% 0.19/0.45 238[1:Res:226.0,6.2] || c_in(u,v_x,t_a)* c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) -> c_in(u,v,t_a)* c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v,t_a),v_c,tc_set(t_a))*.
% 0.19/0.46 240[1:MRR:238.1,8.0] || c_in(u,v_x,t_a)*+ -> c_in(u,v,t_a)* c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v,t_a),v_c,tc_set(t_a))*.
% 0.19/0.46 241[1:MRR:237.1,8.0] || c_in(u,v_x,t_a)* c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,v,t_a),v,tc_set(t_a))*+ -> c_in(u,v,t_a)*.
% 0.19/0.46 263[1:Res:14.1,241.1] || c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,tc_set(t_a))* c_in(u,v_x,t_a)* -> c_in(u,v_y,t_a).
% 0.19/0.46 264[1:MRR:263.0,240.2] || c_in(u,v_x,t_a)* -> c_in(u,v_y,t_a).
% 0.19/0.46 265[1:Res:12.0,264.0] || -> c_in(v_xa,v_y,t_a)*.
% 0.19/0.46 270[1:MRR:265.0,13.0] || -> .
% 0.19/0.46 % SZS output end Refutation
% 0.19/0.46 Formulae used in the proof : cls_Set_OsubsetD_0 cls_Set_OsubsetI_0 cls_Set_OsubsetI_1 cls_Zorn_Ochain__extend_0 cls_Zorn_Ochain__extend_1 cls_Zorn_Omaxchain__super__lemma_0 cls_Zorn_Omaxchain__super__lemma_1 cls_conjecture_0 cls_conjecture_1 cls_conjecture_3 cls_conjecture_4 cls_conjecture_5 cls_conjecture_6 cls_conjecture_7
% 0.19/0.46
%------------------------------------------------------------------------------