%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET849-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 05:29:15 EDT 2022
% Result : Unsatisfiable 0.21s 0.42s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 5 unt; 0 nHn; 7 RR)
% Number of literals : 9 ( 0 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
c_lessequals(u,u,tc_set(v)),
file('SET849-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_lessequals(u,c_Zorn_OTFin(v,w),tc_set(tc_set(tc_set(w))))
| c_in(c_Union(u,tc_set(w)),c_Zorn_OTFin(v,w),tc_set(tc_set(w))) ),
file('SET849-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(c_Union(c_Zorn_OTFin(u,v),tc_set(v)),c_Zorn_OTFin(u,v),tc_set(tc_set(v)))
| equal(c_Zorn_Osucc(u,c_Union(c_Zorn_OTFin(u,v),tc_set(v)),v),c_Union(c_Zorn_OTFin(u,v),tc_set(v))) ),
file('SET849-2.p',unknown),
[] ).
cnf(4,axiom,
~ equal(c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))),
file('SET849-2.p',unknown),
[] ).
cnf(5,plain,
~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(res,[status(thm),theory(equality)],[3,4]),
[iquote('0:Res:3.1,4.0')] ).
cnf(6,plain,
~ c_lessequals(c_Zorn_OTFin(v_S,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
inference(res,[status(thm),theory(equality)],[2,5]),
[iquote('0:Res:2.1,5.0')] ).
cnf(7,plain,
$false,
inference(mrr,[status(thm)],[6,1]),
[iquote('0:MRR:6.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SET849-2 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 10 14:51:46 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.42
% 0.21/0.42 SPASS V 3.9
% 0.21/0.42 SPASS beiseite: Proof found.
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.42 SPASS derived 2 clauses, backtracked 0 clauses, performed 0 splits and kept 6 clauses.
% 0.21/0.42 SPASS allocated 63089 KBytes.
% 0.21/0.42 SPASS spent 0:00:00.06 on the problem.
% 0.21/0.42 0:00:00.04 for the input.
% 0.21/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.42 0:00:00.00 for inferences.
% 0.21/0.42 0:00:00.00 for the backtracking.
% 0.21/0.42 0:00:00.00 for the reduction.
% 0.21/0.42
% 0.21/0.42
% 0.21/0.42 Here is a proof with depth 2, length 7 :
% 0.21/0.42 % SZS output start Refutation
% See solution above
% 0.21/0.42 Formulae used in the proof : cls_Set_Osubset__refl_0 cls_Zorn_OTFin__UnionI_0 cls_Zorn_Oequal__succ__Union_1 cls_conjecture_1
% 0.21/0.42
%------------------------------------------------------------------------------