TSTP Solution File: SET858-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET858-2 : TPTP v8.1.0. Released v3.2.0.
% 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 05:29:21 EDT 2022
% Result : Unsatisfiable 0.18s 0.49s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 19 ( 6 unt; 11 nHn; 19 RR)
% Number of literals : 64 ( 0 equ; 32 neg)
% Maximal clause size : 8 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_lessequals(u,v,tc_set(w))
| ~ c_lessequals(v,x,tc_set(w))
| c_lessequals(u,x,tc_set(w)) ),
file('SET858-2.p',unknown),
[] ).
cnf(2,axiom,
c_lessequals(u,c_Zorn_Osucc(v,u,w),tc_set(tc_set(w))),
file('SET858-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(u,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
| ~ c_in(x,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
| c_lessequals(u,x,tc_set(tc_set(w)))
| c_lessequals(c_Zorn_Osucc(v,x,w),u,tc_set(tc_set(w)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v,x,w),c_Zorn_OTFin(v,w),tc_set(tc_set(w))) ),
file('SET858-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_in(u,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
| ~ c_in(x,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
| c_lessequals(u,x,tc_set(tc_set(w)))
| c_lessequals(c_Zorn_Osucc(v,x,w),u,tc_set(tc_set(w)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v,x,w),x,tc_set(tc_set(w))) ),
file('SET858-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal(c_Zorn_OTFin__linear__lemma1__1(u,v,w),v)
| ~ c_in(x,c_Zorn_OTFin(u,w),tc_set(tc_set(w)))
| ~ c_in(v,c_Zorn_OTFin(u,w),tc_set(tc_set(w)))
| c_lessequals(x,v,tc_set(tc_set(w)))
| c_lessequals(c_Zorn_Osucc(u,v,w),x,tc_set(tc_set(w))) ),
file('SET858-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ c_in(u,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
| ~ c_in(x,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
| ~ c_lessequals(c_Zorn_Osucc(v,c_Zorn_OTFin__linear__lemma1__1(v,x,w),w),x,tc_set(tc_set(w)))
| c_lessequals(u,x,tc_set(tc_set(w)))
| c_lessequals(c_Zorn_Osucc(v,x,w),u,tc_set(tc_set(w))) ),
file('SET858-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ c_lessequals(u,v,tc_set(tc_set(w)))
| ~ c_in(v,c_Zorn_OTFin(x,w),tc_set(tc_set(w)))
| ~ c_in(u,c_Zorn_OTFin(x,w),tc_set(tc_set(w)))
| equal(u,v)
| c_lessequals(c_Zorn_Osucc(x,u,w),v,tc_set(tc_set(w))) ),
file('SET858-2.p',unknown),
[] ).
cnf(8,axiom,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('SET858-2.p',unknown),
[] ).
cnf(9,axiom,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('SET858-2.p',unknown),
[] ).
cnf(10,axiom,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
file('SET858-2.p',unknown),
[] ).
cnf(11,axiom,
~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
file('SET858-2.p',unknown),
[] ).
cnf(42,plain,
( ~ c_lessequals(c_Zorn_Osucc(u,v,w),x,tc_set(tc_set(w)))
| c_lessequals(v,x,tc_set(tc_set(w))) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.0')] ).
cnf(113,plain,
( ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(u,v,w),v,tc_set(tc_set(w)))
| ~ c_in(v,c_Zorn_OTFin(u,w),tc_set(tc_set(w)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(u,v,w),c_Zorn_OTFin(u,w),tc_set(tc_set(w)))
| ~ c_in(x,c_Zorn_OTFin(u,w),tc_set(tc_set(w)))
| ~ c_in(v,c_Zorn_OTFin(u,w),tc_set(tc_set(w)))
| equal(c_Zorn_OTFin__linear__lemma1__1(u,v,w),v)
| c_lessequals(x,v,tc_set(tc_set(w)))
| c_lessequals(c_Zorn_Osucc(u,v,w),x,tc_set(tc_set(w))) ),
inference(res,[status(thm),theory(equality)],[7,6]),
[iquote('0:Res:7.4,6.2')] ).
cnf(115,plain,
( ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(u,v,w),v,tc_set(tc_set(w)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(u,v,w),c_Zorn_OTFin(u,w),tc_set(tc_set(w)))
| ~ c_in(x,c_Zorn_OTFin(u,w),tc_set(tc_set(w)))
| ~ c_in(v,c_Zorn_OTFin(u,w),tc_set(tc_set(w)))
| equal(c_Zorn_OTFin__linear__lemma1__1(u,v,w),v)
| c_lessequals(x,v,tc_set(tc_set(w)))
| c_lessequals(c_Zorn_Osucc(u,v,w),x,tc_set(tc_set(w))) ),
inference(obv,[status(thm),theory(equality)],[113]),
[iquote('0:Obv:113.1')] ).
cnf(116,plain,
( ~ c_in(u,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
| ~ c_in(x,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
| c_lessequals(u,x,tc_set(tc_set(w)))
| c_lessequals(c_Zorn_Osucc(v,x,w),u,tc_set(tc_set(w))) ),
inference(mrr,[status(thm)],[115,4,3,5]),
[iquote('0:MRR:115.0,115.1,115.4,4.4,3.4,5.0')] ).
cnf(264,plain,
( ~ c_in(u,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
| ~ c_in(x,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
| c_lessequals(u,x,tc_set(tc_set(w)))
| c_lessequals(x,u,tc_set(tc_set(w))) ),
inference(res,[status(thm),theory(equality)],[116,42]),
[iquote('0:Res:116.3,42.0')] ).
cnf(272,plain,
( ~ c_in(u,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(v_m,u,tc_set(tc_set(t_a)))
| c_lessequals(u,v_m,tc_set(tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[8,264]),
[iquote('0:Res:8.0,264.0')] ).
cnf(274,plain,
( c_lessequals(v_m,v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[9,272]),
[iquote('0:Res:9.0,272.0')] ).
cnf(277,plain,
$false,
inference(mrr,[status(thm)],[274,11,10]),
[iquote('0:MRR:274.0,274.1,11.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET858-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n011.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 : Mon Jul 11 00:59:27 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.49
% 0.18/0.49 SPASS V 3.9
% 0.18/0.49 SPASS beiseite: Proof found.
% 0.18/0.49 % SZS status Theorem
% 0.18/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.49 SPASS derived 253 clauses, backtracked 7 clauses, performed 2 splits and kept 155 clauses.
% 0.18/0.49 SPASS allocated 63807 KBytes.
% 0.18/0.49 SPASS spent 0:00:00.15 on the problem.
% 0.18/0.49 0:00:00.04 for the input.
% 0.18/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.49 0:00:00.01 for inferences.
% 0.18/0.49 0:00:00.00 for the backtracking.
% 0.18/0.49 0:00:00.07 for the reduction.
% 0.18/0.49
% 0.18/0.49
% 0.18/0.49 Here is a proof with depth 4, length 19 :
% 0.18/0.49 % SZS output start Refutation
% See solution above
% 0.18/0.49 Formulae used in the proof : cls_Set_Osubset__trans_0 cls_Zorn_OAbrial__axiom1_0 cls_Zorn_OTFin__linear__lemma1_0 cls_Zorn_OTFin__linear__lemma1_1 cls_Zorn_OTFin__linear__lemma1_2 cls_Zorn_OTFin__linear__lemma1_3 cls_Zorn_OTFin__linear__lemma2_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3
% 0.18/0.49
%------------------------------------------------------------------------------