%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET844-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 05:29:11 EDT 2022
% Result : Unsatisfiable 0.61s 0.84s
% Output : Refutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 13 ( 7 unt; 1 nHn; 13 RR)
% Number of literals : 23 ( 0 equ; 11 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( c_lessequals(c_Union(u,v),w,tc_set(v))
| c_in(c_Main_OUnion__least__1(u,w,v),u,tc_set(v)) ),
file('SET844-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_lessequals(c_Main_OUnion__least__1(u,v,w),v,tc_set(w))
| c_lessequals(c_Union(u,w),v,tc_set(w)) ),
file('SET844-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ equal(c_Zorn_Osucc(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))) ),
file('SET844-1.p',unknown),
[] ).
cnf(8,axiom,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('SET844-1.p',unknown),
[] ).
cnf(9,axiom,
equal(c_Zorn_Osucc(v_S,v_m,t_a),v_m),
file('SET844-1.p',unknown),
[] ).
cnf(10,axiom,
~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('SET844-1.p',unknown),
[] ).
cnf(1385,plain,
( ~ c_in(u,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ equal(c_Zorn_Osucc(v_S,v_m,t_a),v_m)
| c_lessequals(u,v_m,tc_set(tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[8,7]),
[iquote('0:Res:8.0,7.0')] ).
cnf(1404,plain,
~ c_lessequals(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),v_m,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(res,[status(thm),theory(equality)],[2,10]),
[iquote('0:Res:2.1,10.0')] ).
cnf(1405,plain,
c_in(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),v_m,tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(res,[status(thm),theory(equality)],[1,10]),
[iquote('0:Res:1.1,10.0')] ).
cnf(1408,plain,
( ~ c_in(u,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ equal(v_m,v_m)
| c_lessequals(u,v_m,tc_set(tc_set(t_a))) ),
inference(rew,[status(thm),theory(equality)],[9,1385]),
[iquote('0:Rew:9.0,1385.1')] ).
cnf(1409,plain,
( ~ c_in(u,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(u,v_m,tc_set(tc_set(t_a))) ),
inference(obv,[status(thm),theory(equality)],[1408]),
[iquote('0:Obv:1408.1')] ).
cnf(1783,plain,
c_lessequals(c_Main_OUnion__least__1(c_Zorn_OTFin(v_S,t_a),v_m,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(res,[status(thm),theory(equality)],[1405,1409]),
[iquote('0:Res:1405.0,1409.0')] ).
cnf(1786,plain,
$false,
inference(mrr,[status(thm)],[1783,1404]),
[iquote('0:MRR:1783.0,1404.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET844-1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 08:12:05 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.61/0.84
% 0.61/0.84 SPASS V 3.9
% 0.61/0.84 SPASS beiseite: Proof found.
% 0.61/0.84 % SZS status Theorem
% 0.61/0.84 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.61/0.84 SPASS derived 342 clauses, backtracked 0 clauses, performed 0 splits and kept 1441 clauses.
% 0.61/0.84 SPASS allocated 78132 KBytes.
% 0.61/0.84 SPASS spent 0:00:00.47 on the problem.
% 0.61/0.84 0:00:00.09 for the input.
% 0.61/0.84 0:00:00.00 for the FLOTTER CNF translation.
% 0.61/0.84 0:00:00.03 for inferences.
% 0.61/0.84 0:00:00.00 for the backtracking.
% 0.61/0.84 0:00:00.12 for the reduction.
% 0.61/0.84
% 0.61/0.84
% 0.61/0.84 Here is a proof with depth 2, length 13 :
% 0.61/0.84 % SZS output start Refutation
% See solution above
% 0.61/0.84 Formulae used in the proof : cls_Set_OUnion__least_0 cls_Set_OUnion__least_1 cls_Zorn_Oeq__succ__upper_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2
% 0.61/0.84
%------------------------------------------------------------------------------