TSTP Solution File: SET853-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET853-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 05:29:18 EDT 2022
% Result : Unsatisfiable 0.21s 0.48s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of clauses : 26 ( 12 unt; 9 nHn; 26 RR)
% Number of literals : 64 ( 0 equ; 31 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 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,u,tc_set(w))
| equal(u,v) ),
file('SET853-2.p',unknown),
[] ).
cnf(2,axiom,
c_lessequals(u,u,tc_set(v)),
file('SET853-2.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('SET853-2.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('SET853-2.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('SET853-2.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('SET853-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ c_lessequals(u,v,tc_set(tc_set(w)))
| c_lessequals(u,c_Zorn_Osucc(x,v,w),tc_set(tc_set(w))) ),
file('SET853-2.p',unknown),
[] ).
cnf(8,axiom,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('SET853-2.p',unknown),
[] ).
cnf(9,axiom,
c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('SET853-2.p',unknown),
[] ).
cnf(10,axiom,
c_lessequals(v_xa,c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
file('SET853-2.p',unknown),
[] ).
cnf(11,axiom,
~ equal(c_Zorn_Osucc(v_S,v_x,t_a),v_xa),
file('SET853-2.p',unknown),
[] ).
cnf(12,axiom,
~ c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
file('SET853-2.p',unknown),
[] ).
cnf(13,axiom,
( ~ c_lessequals(u,v_x,tc_set(tc_set(t_a)))
| ~ c_in(u,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| equal(u,v_x)
| c_lessequals(c_Zorn_Osucc(v_S,u,t_a),v_x,tc_set(tc_set(t_a))) ),
file('SET853-2.p',unknown),
[] ).
cnf(16,plain,
( ~ c_lessequals(v_xa,v_x,tc_set(tc_set(t_a)))
| equal(v_xa,v_x)
| c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[9,13]),
[iquote('0:Res:9.0,13.1')] ).
cnf(29,plain,
( ~ equal(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x)
| ~ c_in(u,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(u,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),u,tc_set(tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[8,5]),
[iquote('0:Res:8.0,5.0')] ).
cnf(58,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| equal(c_Zorn_Osucc(v_S,v_x,t_a),v_xa) ),
inference(res,[status(thm),theory(equality)],[10,1]),
[iquote('0:Res:10.0,1.0')] ).
cnf(60,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a))),
inference(mrr,[status(thm)],[58,11]),
[iquote('0:MRR:58.1,11.0')] ).
cnf(65,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),v_x,tc_set(tc_set(t_a))),
inference(res,[status(thm),theory(equality)],[7,12]),
[iquote('0:Res:7.1,12.0')] ).
cnf(69,plain,
( ~ c_lessequals(v_xa,v_x,tc_set(tc_set(t_a)))
| equal(v_xa,v_x) ),
inference(mrr,[status(thm)],[16,65]),
[iquote('0:MRR:16.2,65.0')] ).
cnf(177,plain,
( ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(u,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| equal(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x)
| c_lessequals(u,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),u,tc_set(tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[13,6]),
[iquote('0:Res:13.3,6.2')] ).
cnf(181,plain,
( ~ c_in(u,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(u,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),u,tc_set(tc_set(t_a))) ),
inference(mrr,[status(thm)],[177,4,3,8,29]),
[iquote('0:MRR:177.0,177.1,177.3,177.4,4.4,3.4,8.0,29.0')] ).
cnf(184,plain,
( ~ c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[181,60]),
[iquote('0:Res:181.2,60.0')] ).
cnf(192,plain,
c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))),
inference(mrr,[status(thm)],[184,9]),
[iquote('0:MRR:184.0,9.0')] ).
cnf(193,plain,
equal(v_xa,v_x),
inference(mrr,[status(thm)],[69,192]),
[iquote('0:MRR:69.0,192.0')] ).
cnf(197,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
inference(rew,[status(thm),theory(equality)],[193,12]),
[iquote('0:Rew:193.0,12.0')] ).
cnf(218,plain,
$false,
inference(mrr,[status(thm)],[197,2]),
[iquote('0:MRR:197.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SET853-2 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sat Jul 9 17:51:15 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.48
% 0.21/0.48 SPASS V 3.9
% 0.21/0.48 SPASS beiseite: Proof found.
% 0.21/0.48 % SZS status Theorem
% 0.21/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.48 SPASS derived 164 clauses, backtracked 34 clauses, performed 4 splits and kept 136 clauses.
% 0.21/0.48 SPASS allocated 63392 KBytes.
% 0.21/0.48 SPASS spent 0:00:00.10 on the problem.
% 0.21/0.48 0:00:00.04 for the input.
% 0.21/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.48 0:00:00.00 for inferences.
% 0.21/0.48 0:00:00.00 for the backtracking.
% 0.21/0.48 0:00:00.04 for the reduction.
% 0.21/0.48
% 0.21/0.48
% 0.21/0.48 Here is a proof with depth 2, length 26 :
% 0.21/0.48 % SZS output start Refutation
% See solution above
% 0.21/0.48 Formulae used in the proof : cls_Set_Osubset__antisym_0 cls_Set_Osubset__refl_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_Osucc__trans_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4 cls_conjecture_5
% 0.21/0.48
%------------------------------------------------------------------------------