TSTP Solution File: SET862-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET862-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 05:29:24 EDT 2022
% Result : Unsatisfiable 0.56s 0.76s
% Output : Refutation 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET862-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jul 9 22:47:41 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.56/0.76
% 0.56/0.76 SPASS V 3.9
% 0.56/0.76 SPASS beiseite: Proof found.
% 0.56/0.76 % SZS status Theorem
% 0.56/0.76 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.56/0.76 SPASS derived 803 clauses, backtracked 15 clauses, performed 6 splits and kept 573 clauses.
% 0.56/0.76 SPASS allocated 64535 KBytes.
% 0.56/0.76 SPASS spent 0:00:00.39 on the problem.
% 0.56/0.76 0:00:00.04 for the input.
% 0.56/0.76 0:00:00.00 for the FLOTTER CNF translation.
% 0.56/0.76 0:00:00.04 for inferences.
% 0.56/0.76 0:00:00.01 for the backtracking.
% 0.56/0.76 0:00:00.27 for the reduction.
% 0.56/0.76
% 0.56/0.76
% 0.56/0.76 Here is a proof with depth 19, length 79 :
% 0.56/0.76 % SZS output start Refutation
% 0.56/0.76 1[0:Inp] || c_lessequals(u,v,tc_set(w))*+ c_lessequals(v,u,tc_set(w))* -> equal(u,v).
% 0.56/0.76 2[0:Inp] || c_in(u,v,w)* c_lessequals(v,x,tc_set(w))*+ -> c_in(u,x,w)*.
% 0.56/0.76 3[0:Inp] || -> c_lessequals(u,v,tc_set(w)) c_in(c_Main_OsubsetI__1(u,v,w),u,w)*.
% 0.56/0.76 4[0:Inp] || c_in(c_Main_OsubsetI__1(u,v,w),v,w)* -> c_lessequals(u,v,tc_set(w)).
% 0.56/0.76 5[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)))*.
% 0.56/0.76 6[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)))*.
% 0.56/0.76 7[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))*.
% 0.56/0.76 8[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)*.
% 0.56/0.76 9[0:Inp] || -> c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))*.
% 0.56/0.76 10[0:Inp] || -> c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))*.
% 0.56/0.76 11[0:Inp] || -> c_in(v_y,v_S,tc_set(t_a))*.
% 0.56/0.76 12[0:Inp] || c_in(u,v_c,tc_set(t_a))* -> c_lessequals(u,v_y,tc_set(t_a)).
% 0.56/0.76 13[0:Inp] || c_in(u,v_S,tc_set(t_a)) -> c_in(v_x(u),v_S,tc_set(t_a))*.
% 0.56/0.76 14[0:Inp] || c_in(u,v_S,tc_set(t_a)) -> c_lessequals(u,v_x(u),tc_set(t_a))*.
% 0.56/0.76 15[0:Inp] || equal(v_x(u),u) c_in(u,v_S,tc_set(t_a))* -> .
% 0.56/0.76 16[0:Res:11.0,13.0] || -> c_in(v_x(v_y),v_S,tc_set(t_a))*.
% 0.56/0.76 17[0:Res:11.0,14.0] || -> c_lessequals(v_y,v_x(v_y),tc_set(t_a))*.
% 0.56/0.76 18[0:Res:11.0,15.1] || equal(v_x(v_y),v_y)** -> .
% 0.56/0.76 24[0:Res:10.0,6.1] || 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)))*.
% 0.56/0.76 25[0:Res:10.0,5.1] || 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)))*.
% 0.56/0.76 31[0:Res:9.0,8.1] || c_in(u,v,t_a)* c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,w,t_a),w,tc_set(t_a))* c_in(c_union(c_insert(v,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)))*+ -> c_in(u,w,t_a)*.
% 0.56/0.76 32[0:Res:9.0,7.1] || c_in(u,v,t_a)* c_in(c_union(c_insert(v,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)))*+ -> c_in(u,w,t_a)* c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,w,t_a),v_c,tc_set(t_a))*.
% 0.56/0.76 61[0:Res:17.0,1.0] || c_lessequals(v_x(v_y),v_y,tc_set(t_a))* -> equal(v_x(v_y),v_y).
% 0.56/0.76 65[0:MRR:61.1,18.0] || c_lessequals(v_x(v_y),v_y,tc_set(t_a))* -> .
% 0.56/0.76 67[0:Res:17.0,2.1] || c_in(u,v_y,t_a) -> c_in(u,v_x(v_y),t_a)*.
% 0.56/0.76 71[0:Res:67.1,4.0] || c_in(c_Main_OsubsetI__1(u,v_x(v_y),t_a),v_y,t_a)* -> c_lessequals(u,v_x(v_y),tc_set(t_a)).
% 0.56/0.76 98[0:Res:25.2,8.3] || 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)*.
% 0.56/0.76 99[0:Res:25.2,7.2] || 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))*.
% 0.56/0.76 100[0:MRR:99.2,9.0] || 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))*.
% 0.56/0.76 101[0:MRR:98.2,9.0] || 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)*.
% 0.56/0.76 244[0:Res:16.0,100.0] || c_in(u,v_x(v_y),t_a)*+ -> c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),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))*.
% 0.56/0.76 435[1:Spt:244.0,244.2,244.3] || c_in(u,v_x(v_y),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))*.
% 0.56/0.76 436[1:Res:3.1,435.0] || -> c_lessequals(v_x(v_y),u,tc_set(t_a)) c_in(c_Main_OsubsetI__1(v_x(v_y),u,t_a),v,t_a)* c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v,t_a),v_c,tc_set(t_a))*.
% 0.56/0.76 449[1:Res:436.1,4.0] || -> c_lessequals(v_x(v_y),u,tc_set(t_a)) c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,u,t_a),v_c,tc_set(t_a))* c_lessequals(v_x(v_y),u,tc_set(t_a)).
% 0.56/0.76 475[1:Obv:449.0] || -> c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,u,t_a),v_c,tc_set(t_a))* c_lessequals(v_x(v_y),u,tc_set(t_a)).
% 0.56/0.76 485[1:Res:475.0,12.0] || -> c_lessequals(v_x(v_y),u,tc_set(t_a)) c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,u,t_a),v_y,tc_set(t_a))*.
% 0.56/0.76 487[1:Res:485.1,101.2] || c_in(u,v_S,tc_set(t_a)) c_in(v,u,t_a)* -> c_lessequals(v_x(v_y),v_y,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,v_y,t_a)*.
% 0.56/0.76 491[1:MRR:487.2,65.0] || 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)*.
% 0.56/0.76 550[1:Res:16.0,491.0] || c_in(u,v_x(v_y),t_a)*+ -> c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a))* c_in(u,v_y,t_a).
% 0.56/0.76 553[2:Spt:550.0,550.2] || c_in(u,v_x(v_y),t_a)* -> c_in(u,v_y,t_a).
% 0.56/0.76 554[2:Res:3.1,553.0] || -> c_lessequals(v_x(v_y),u,tc_set(t_a)) c_in(c_Main_OsubsetI__1(v_x(v_y),u,t_a),v_y,t_a)*.
% 0.56/0.76 561[2:Res:554.1,4.0] || -> c_lessequals(v_x(v_y),v_y,tc_set(t_a))* c_lessequals(v_x(v_y),v_y,tc_set(t_a))*.
% 0.56/0.76 567[2:Obv:561.0] || -> c_lessequals(v_x(v_y),v_y,tc_set(t_a))*.
% 0.56/0.76 568[2:MRR:567.0,65.0] || -> .
% 0.56/0.76 573[2:Spt:568.0,550.1] || -> c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a))*.
% 0.56/0.76 574[2:Res:573.0,12.0] || -> c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_y,tc_set(t_a))*.
% 0.56/0.76 577[2:Res:574.0,2.1] || c_in(u,c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),t_a)* -> c_in(u,v_y,t_a).
% 0.56/0.76 587[2:Res:3.1,577.0] || -> c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),u,tc_set(t_a)) c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),u,t_a),v_y,t_a)*.
% 0.56/0.76 594[2:Res:587.1,71.0] || -> c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_y),tc_set(t_a))* c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_y),tc_set(t_a))*.
% 0.56/0.76 599[2:Obv:594.0] || -> c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_y),tc_set(t_a))*.
% 0.56/0.76 604[2:Res:599.0,24.1] || c_in(v_x(v_y),v_S,tc_set(t_a)) -> c_in(c_union(c_insert(v_x(v_y),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)))*.
% 0.56/0.76 606[2:MRR:604.0,16.0] || -> c_in(c_union(c_insert(v_x(v_y),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)))*.
% 0.56/0.76 640[2:Res:606.0,31.2] || c_in(u,v_x(v_y),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)*.
% 0.56/0.76 661[2:Res:485.1,640.1] || c_in(u,v_x(v_y),t_a)* -> c_lessequals(v_x(v_y),v_y,tc_set(t_a))* c_in(u,v_y,t_a).
% 0.56/0.76 669[2:MRR:661.1,2.1] || c_in(u,v_x(v_y),t_a)* -> c_in(u,v_y,t_a).
% 0.56/0.76 670[2:Res:3.1,669.0] || -> c_lessequals(v_x(v_y),u,tc_set(t_a)) c_in(c_Main_OsubsetI__1(v_x(v_y),u,t_a),v_y,t_a)*.
% 0.56/0.76 677[2:Res:670.1,4.0] || -> c_lessequals(v_x(v_y),v_y,tc_set(t_a))* c_lessequals(v_x(v_y),v_y,tc_set(t_a))*.
% 0.56/0.76 683[2:Obv:677.0] || -> c_lessequals(v_x(v_y),v_y,tc_set(t_a))*.
% 0.56/0.76 684[2:MRR:683.0,65.0] || -> .
% 0.56/0.76 689[1:Spt:684.0,244.1] || -> c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a))*.
% 0.56/0.76 690[1:Res:689.0,12.0] || -> c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_y,tc_set(t_a))*.
% 0.56/0.76 702[1:Res:690.0,2.1] || c_in(u,c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),t_a)* -> c_in(u,v_y,t_a).
% 0.56/0.76 703[1:Res:3.1,702.0] || -> c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),u,tc_set(t_a)) c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),u,t_a),v_y,t_a)*.
% 0.56/0.76 708[1:Res:703.1,71.0] || -> c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_y),tc_set(t_a))* c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_y),tc_set(t_a))*.
% 0.56/0.76 713[1:Obv:708.0] || -> c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_y),tc_set(t_a))*.
% 0.56/0.76 724[1:Res:713.0,24.1] || c_in(v_x(v_y),v_S,tc_set(t_a)) -> c_in(c_union(c_insert(v_x(v_y),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)))*.
% 0.56/0.76 726[1:MRR:724.0,16.0] || -> c_in(c_union(c_insert(v_x(v_y),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)))*.
% 0.56/0.76 746[1:Res:726.0,31.2] || c_in(u,v_x(v_y),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)*.
% 0.56/0.76 747[1:Res:726.0,32.1] || c_in(u,v_x(v_y),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))*.
% 0.56/0.76 765[1:Res:3.1,747.0] || -> c_lessequals(v_x(v_y),u,tc_set(t_a)) c_in(c_Main_OsubsetI__1(v_x(v_y),u,t_a),v,t_a)* c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v,t_a),v_c,tc_set(t_a))*.
% 0.56/0.76 927[1:Res:765.1,4.0] || -> c_lessequals(v_x(v_y),u,tc_set(t_a)) c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,u,t_a),v_c,tc_set(t_a))* c_lessequals(v_x(v_y),u,tc_set(t_a)).
% 0.56/0.76 964[1:Obv:927.0] || -> c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,u,t_a),v_c,tc_set(t_a))* c_lessequals(v_x(v_y),u,tc_set(t_a)).
% 0.56/0.76 975[1:Res:964.0,12.0] || -> c_lessequals(v_x(v_y),u,tc_set(t_a)) c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,u,t_a),v_y,tc_set(t_a))*.
% 0.56/0.76 978[1:Res:975.1,746.1] || c_in(u,v_x(v_y),t_a)* -> c_lessequals(v_x(v_y),v_y,tc_set(t_a))* c_in(u,v_y,t_a).
% 0.56/0.76 982[1:MRR:978.1,2.1] || c_in(u,v_x(v_y),t_a)* -> c_in(u,v_y,t_a).
% 0.56/0.76 985[1:Res:3.1,982.0] || -> c_lessequals(v_x(v_y),u,tc_set(t_a)) c_in(c_Main_OsubsetI__1(v_x(v_y),u,t_a),v_y,t_a)*.
% 0.56/0.76 993[1:Res:985.1,4.0] || -> c_lessequals(v_x(v_y),v_y,tc_set(t_a))* c_lessequals(v_x(v_y),v_y,tc_set(t_a))*.
% 0.56/0.76 999[1:Obv:993.0] || -> c_lessequals(v_x(v_y),v_y,tc_set(t_a))*.
% 0.56/0.76 1000[1:MRR:999.0,65.0] || -> .
% 0.56/0.76 % SZS output end Refutation
% 0.56/0.76 Formulae used in the proof : cls_Set_Osubset__antisym_0 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_2 cls_conjecture_3 cls_conjecture_4 cls_conjecture_5 cls_conjecture_6
% 0.56/0.76
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