TSTP Solution File: SET839-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET839-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 05:29:07 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of clauses : 15 ( 4 unt; 5 nHn; 15 RR)
% Number of literals : 34 ( 0 equ; 14 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
c_in(u,c_insert(u,v,w),w),
file('SET839-2.p',unknown),
[] ).
cnf(2,axiom,
( c_lessequals(u,v,tc_set(w))
| c_in(c_Main_OsubsetI__1(u,v,w),u,w) ),
file('SET839-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(c_Main_OsubsetI__1(u,v,w),v,w)
| c_lessequals(u,v,tc_set(w)) ),
file('SET839-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_lessequals(u,v,tc_set(w))
| ~ c_lessequals(v,u,tc_set(w))
| equal(u,v) ),
file('SET839-2.p',unknown),
[] ).
cnf(5,axiom,
~ c_lessequals(v_S,c_insert(u,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a))),
file('SET839-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ c_in(u,v_S,tc_set(t_a))
| ~ c_in(v,v_S,tc_set(t_a))
| c_lessequals(u,v,tc_set(t_a)) ),
file('SET839-2.p',unknown),
[] ).
cnf(12,plain,
( ~ c_in(u,v_S,tc_set(t_a))
| ~ c_in(v,v_S,tc_set(t_a))
| ~ c_lessequals(v,u,tc_set(t_a))
| equal(u,v) ),
inference(res,[status(thm),theory(equality)],[6,4]),
[iquote('0:Res:6.2,4.0')] ).
cnf(13,plain,
( ~ c_in(u,v_S,tc_set(t_a))
| ~ c_in(v,v_S,tc_set(t_a))
| equal(u,v) ),
inference(mrr,[status(thm)],[12,6]),
[iquote('0:MRR:12.2,6.2')] ).
cnf(14,plain,
( ~ c_in(u,v_S,tc_set(t_a))
| c_lessequals(v_S,v,tc_set(tc_set(t_a)))
| equal(c_Main_OsubsetI__1(v_S,v,tc_set(t_a)),u) ),
inference(res,[status(thm),theory(equality)],[2,13]),
[iquote('0:Res:2.1,13.0')] ).
cnf(15,plain,
( c_lessequals(v_S,u,tc_set(tc_set(t_a)))
| c_lessequals(v_S,v,tc_set(tc_set(t_a)))
| equal(c_Main_OsubsetI__1(v_S,v,tc_set(t_a)),c_Main_OsubsetI__1(v_S,u,tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[2,14]),
[iquote('0:Res:2.1,14.0')] ).
cnf(27,plain,
( c_lessequals(v_S,u,tc_set(tc_set(t_a)))
| equal(c_Main_OsubsetI__1(v_S,c_insert(v,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_Main_OsubsetI__1(v_S,u,tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[15,5]),
[iquote('0:Res:15.1,5.0')] ).
cnf(54,plain,
( ~ c_in(c_Main_OsubsetI__1(v_S,c_insert(u,c_emptyset,tc_set(t_a)),tc_set(t_a)),v,tc_set(t_a))
| c_lessequals(v_S,v,tc_set(tc_set(t_a)))
| c_lessequals(v_S,v,tc_set(tc_set(t_a))) ),
inference(spl,[status(thm),theory(equality)],[27,3]),
[iquote('0:SpL:27.1,3.0')] ).
cnf(58,plain,
( ~ c_in(c_Main_OsubsetI__1(v_S,c_insert(u,c_emptyset,tc_set(t_a)),tc_set(t_a)),v,tc_set(t_a))
| c_lessequals(v_S,v,tc_set(tc_set(t_a))) ),
inference(obv,[status(thm),theory(equality)],[54]),
[iquote('0:Obv:54.1')] ).
cnf(116,plain,
c_lessequals(v_S,c_insert(c_Main_OsubsetI__1(v_S,c_insert(u,c_emptyset,tc_set(t_a)),tc_set(t_a)),v,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(res,[status(thm),theory(equality)],[1,58]),
[iquote('0:Res:1.0,58.0')] ).
cnf(119,plain,
$false,
inference(unc,[status(thm)],[116,5]),
[iquote('0:UnC:116.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET839-2 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n019.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jul 10 14:13:53 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.19/0.41
% 0.19/0.41 SPASS V 3.9
% 0.19/0.41 SPASS beiseite: Proof found.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.41 SPASS derived 77 clauses, backtracked 1 clauses, performed 1 splits and kept 22 clauses.
% 0.19/0.41 SPASS allocated 63173 KBytes.
% 0.19/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.41 0:00:00.03 for the input.
% 0.19/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.41 0:00:00.00 for inferences.
% 0.19/0.41 0:00:00.00 for the backtracking.
% 0.19/0.41 0:00:00.00 for the reduction.
% 0.19/0.41
% 0.19/0.41
% 0.19/0.41 Here is a proof with depth 6, length 15 :
% 0.19/0.41 % SZS output start Refutation
% See solution above
% 0.19/0.41 Formulae used in the proof : cls_Set_OinsertCI_1 cls_Set_OsubsetI_0 cls_Set_OsubsetI_1 cls_Set_Osubset__antisym_0 cls_conjecture_0 cls_conjecture_1
% 0.19/0.41
%------------------------------------------------------------------------------