TSTP Solution File: SET863-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET863-1 : 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 05:29:25 EDT 2022
% Result : Unsatisfiable 1.21s 1.43s
% Output : Refutation 1.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of clauses : 52 ( 20 unt; 12 nHn; 52 RR)
% Number of literals : 106 ( 0 equ; 48 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 14 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ 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))) ),
file('SET863-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ 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))) ),
file('SET863-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ 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)) ),
file('SET863-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ 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) ),
file('SET863-1.p',unknown),
[] ).
cnf(7,axiom,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('SET863-1.p',unknown),
[] ).
cnf(8,axiom,
c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
file('SET863-1.p',unknown),
[] ).
cnf(10,axiom,
c_in(v_x,v_S,tc_set(t_a)),
file('SET863-1.p',unknown),
[] ).
cnf(11,axiom,
c_lessequals(v_y,v_x,tc_set(t_a)),
file('SET863-1.p',unknown),
[] ).
cnf(12,axiom,
c_in(v_xa,v_x,t_a),
file('SET863-1.p',unknown),
[] ).
cnf(13,axiom,
~ c_in(v_xa,v_y,t_a),
file('SET863-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ c_in(u,v_c,tc_set(t_a))
| c_lessequals(u,v_y,tc_set(t_a)) ),
file('SET863-1.p',unknown),
[] ).
cnf(271,axiom,
( ~ c_in(c_List_Olist_OCons(u,v,w),c_List_Olists(x,w),tc_List_Olist(w))
| c_in(u,x,w) ),
file('SET863-1.p',unknown),
[] ).
cnf(272,axiom,
( ~ c_in(u,v,w)
| ~ c_in(x,c_List_Olists(v,w),tc_List_Olist(w))
| c_in(c_List_Olist_OCons(u,x,w),c_List_Olists(v,w),tc_List_Olist(w)) ),
file('SET863-1.p',unknown),
[] ).
cnf(273,axiom,
c_in(c_List_Olist_ONil,c_List_Olists(u,v),tc_List_Olist(v)),
file('SET863-1.p',unknown),
[] ).
cnf(316,axiom,
( ~ c_lessequals(u,v,tc_set(w))
| equal(u,v)
| c_less(u,v,tc_set(w)) ),
file('SET863-1.p',unknown),
[] ).
cnf(320,axiom,
( ~ c_in(u,v,w)
| ~ c_lessequals(v,x,tc_set(w))
| c_in(u,x,w) ),
file('SET863-1.p',unknown),
[] ).
cnf(321,axiom,
( c_lessequals(u,v,tc_set(w))
| c_in(c_Main_OsubsetI__1(u,v,w),u,w) ),
file('SET863-1.p',unknown),
[] ).
cnf(322,axiom,
( ~ c_in(c_Main_OsubsetI__1(u,v,w),v,w)
| c_lessequals(u,v,tc_set(w)) ),
file('SET863-1.p',unknown),
[] ).
cnf(1373,plain,
( ~ c_in(u,c_Zorn_Omaxchain(v,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(u,w,t_a),w,tc_set(t_a))
| ~ c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),u,tc_set(t_a)),c_Zorn_Ochain(v,t_a),tc_set(tc_set(t_a)))
| c_in(v_xa,w,t_a) ),
inference(res,[status(thm),theory(equality)],[12,6]),
[iquote('0:Res:12.0,6.0')] ).
cnf(1374,plain,
( ~ c_in(u,c_Zorn_Omaxchain(v,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),u,tc_set(t_a)),c_Zorn_Ochain(v,t_a),tc_set(tc_set(t_a)))
| c_in(v_xa,w,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(u,w,t_a),u,tc_set(t_a)) ),
inference(res,[status(thm),theory(equality)],[12,5]),
[iquote('0:Res:12.0,5.0')] ).
cnf(1376,plain,
( ~ c_in(u,c_List_Olists(v_x,t_a),tc_List_Olist(t_a))
| c_in(c_List_Olist_OCons(v_xa,u,t_a),c_List_Olists(v_x,t_a),tc_List_Olist(t_a)) ),
inference(res,[status(thm),theory(equality)],[12,272]),
[iquote('0:Res:12.0,272.0')] ).
cnf(1394,plain,
~ c_in(c_List_Olist_OCons(v_xa,u,t_a),c_List_Olists(v_y,t_a),tc_List_Olist(t_a)),
inference(res,[status(thm),theory(equality)],[271,13]),
[iquote('0:Res:271.1,13.0')] ).
cnf(1408,plain,
( ~ c_in(u,v_y,t_a)
| c_in(u,v_x,t_a) ),
inference(res,[status(thm),theory(equality)],[11,320]),
[iquote('0:Res:11.0,320.1')] ).
cnf(1417,plain,
( equal(v_x,v_y)
| c_less(v_y,v_x,tc_set(t_a)) ),
inference(res,[status(thm),theory(equality)],[11,316]),
[iquote('0:Res:11.0,316.0')] ).
cnf(1436,plain,
( ~ c_in(u,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(u,v_x,t_a),v_x,tc_set(t_a))
| c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),u,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[10,3]),
[iquote('0:Res:10.0,3.0')] ).
cnf(1437,plain,
( ~ c_in(u,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(u,v_x,t_a),u,tc_set(t_a))
| c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),u,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[10,2]),
[iquote('0:Res:10.0,2.0')] ).
cnf(1545,plain,
( ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,u,t_a),u,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)))
| c_in(v_xa,u,t_a) ),
inference(res,[status(thm),theory(equality)],[7,1373]),
[iquote('0:Res:7.0,1373.0')] ).
cnf(1546,plain,
( ~ 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)))
| 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)) ),
inference(res,[status(thm),theory(equality)],[7,1374]),
[iquote('0:Res:7.0,1374.0')] ).
cnf(1549,plain,
( ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,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))) ),
inference(res,[status(thm),theory(equality)],[8,1436]),
[iquote('0:Res:8.0,1436.0')] ).
cnf(1551,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,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))) ),
inference(res,[status(thm),theory(equality)],[8,1437]),
[iquote('0:Res:8.0,1437.0')] ).
cnf(1555,plain,
equal(v_x,v_y),
inference(spt,[spt(split,[position(s1)])],[1417]),
[iquote('1:Spt:1417.0')] ).
cnf(1592,plain,
( ~ c_in(u,c_List_Olists(v_y,t_a),tc_List_Olist(t_a))
| c_in(c_List_Olist_OCons(v_xa,u,t_a),c_List_Olists(v_x,t_a),tc_List_Olist(t_a)) ),
inference(rew,[status(thm),theory(equality)],[1555,1376]),
[iquote('1:Rew:1555.0,1376.0')] ).
cnf(1612,plain,
( ~ c_in(u,c_List_Olists(v_y,t_a),tc_List_Olist(t_a))
| c_in(c_List_Olist_OCons(v_xa,u,t_a),c_List_Olists(v_y,t_a),tc_List_Olist(t_a)) ),
inference(rew,[status(thm),theory(equality)],[1555,1592]),
[iquote('1:Rew:1555.0,1592.1')] ).
cnf(1613,plain,
~ c_in(u,c_List_Olists(v_y,t_a),tc_List_Olist(t_a)),
inference(mrr,[status(thm)],[1612,1394]),
[iquote('1:MRR:1612.1,1394.0')] ).
cnf(1614,plain,
$false,
inference(unc,[status(thm)],[1613,273]),
[iquote('1:UnC:1613.0,273.0')] ).
cnf(1619,plain,
~ equal(v_x,v_y),
inference(spt,[spt(split,[position(sa)])],[1614,1555]),
[iquote('1:Spt:1614.0,1417.0,1555.0')] ).
cnf(1620,plain,
c_less(v_y,v_x,tc_set(t_a)),
inference(spt,[spt(split,[position(s2)])],[1417]),
[iquote('1:Spt:1614.0,1417.1')] ).
cnf(1622,plain,
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))),
inference(spt,[spt(split,[position(s2s1)])],[1551]),
[iquote('2:Spt:1551.1')] ).
cnf(1623,plain,
( 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)) ),
inference(mrr,[status(thm)],[1546,1622]),
[iquote('2:MRR:1546.0,1622.0')] ).
cnf(1624,plain,
( ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,u,t_a),u,tc_set(t_a))
| c_in(v_xa,u,t_a) ),
inference(mrr,[status(thm)],[1545,1622]),
[iquote('2:MRR:1545.1,1622.0')] ).
cnf(1832,plain,
( ~ c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,tc_set(t_a))
| c_in(v_xa,v_y,t_a) ),
inference(res,[status(thm),theory(equality)],[14,1624]),
[iquote('2:Res:14.1,1624.0')] ).
cnf(1833,plain,
$false,
inference(mrr,[status(thm)],[1832,1623,13]),
[iquote('2:MRR:1832.0,1832.1,1623.1,13.0')] ).
cnf(1834,plain,
~ 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))),
inference(spt,[spt(split,[position(s2sa)])],[1833,1622]),
[iquote('2:Spt:1833.0,1551.1,1622.0')] ).
cnf(1835,plain,
c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a)),
inference(spt,[spt(split,[position(s2s2)])],[1551]),
[iquote('2:Spt:1833.0,1551.0')] ).
cnf(1836,plain,
~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,tc_set(t_a)),
inference(mrr,[status(thm)],[1549,1834]),
[iquote('2:MRR:1549.1,1834.0')] ).
cnf(1923,plain,
( ~ c_in(c_Main_OsubsetI__1(u,v_x,t_a),v_y,t_a)
| c_lessequals(u,v_x,tc_set(t_a)) ),
inference(res,[status(thm),theory(equality)],[1408,322]),
[iquote('0:Res:1408.1,322.0')] ).
cnf(2256,plain,
( ~ c_in(u,v_c,tc_set(t_a))
| ~ c_in(v,u,t_a)
| c_in(v,v_y,t_a) ),
inference(res,[status(thm),theory(equality)],[14,320]),
[iquote('0:Res:14.1,320.1')] ).
cnf(2469,plain,
( ~ c_in(u,c_Zorn_Ochain__extend__1(v_c,v_x,t_a),t_a)
| c_in(u,v_y,t_a) ),
inference(res,[status(thm),theory(equality)],[1835,2256]),
[iquote('2:Res:1835.0,2256.0')] ).
cnf(2473,plain,
( 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) ),
inference(res,[status(thm),theory(equality)],[321,2469]),
[iquote('2:Res:321.1,2469.0')] ).
cnf(3898,plain,
( 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)) ),
inference(res,[status(thm),theory(equality)],[2473,1923]),
[iquote('2:Res:2473.1,1923.0')] ).
cnf(3902,plain,
c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,tc_set(t_a)),
inference(obv,[status(thm),theory(equality)],[3898]),
[iquote('2:Obv:3898.0')] ).
cnf(3903,plain,
$false,
inference(mrr,[status(thm)],[3902,1836]),
[iquote('2:MRR:3902.0,1836.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET863-1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 18:22:42 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.21/1.43
% 1.21/1.43 SPASS V 3.9
% 1.21/1.43 SPASS beiseite: Proof found.
% 1.21/1.43 % SZS status Theorem
% 1.21/1.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.21/1.43 SPASS derived 2124 clauses, backtracked 101 clauses, performed 4 splits and kept 2464 clauses.
% 1.21/1.43 SPASS allocated 80612 KBytes.
% 1.21/1.43 SPASS spent 0:00:01.06 on the problem.
% 1.21/1.43 0:00:00.09 for the input.
% 1.21/1.43 0:00:00.00 for the FLOTTER CNF translation.
% 1.21/1.43 0:00:00.09 for inferences.
% 1.21/1.43 0:00:00.00 for the backtracking.
% 1.21/1.43 0:00:00.61 for the reduction.
% 1.21/1.43
% 1.21/1.43
% 1.21/1.43 Here is a proof with depth 6, length 52 :
% 1.21/1.43 % SZS output start Refutation
% See solution above
% 1.21/1.43 Formulae used in the proof : 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 cls_List_OlistsE_1 cls_List_Olists_OCons_0 cls_List_Olists_ONil_0 cls_Set_OpsubsetI_0 cls_Set_OsubsetD_0 cls_Set_OsubsetI_0 cls_Set_OsubsetI_1
% 1.21/1.43
%------------------------------------------------------------------------------