TSTP Solution File: SET842-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET842-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 05:29:09 EDT 2022
% Result : Unsatisfiable 0.12s 0.41s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 15 ( 3 unt; 3 nHn; 15 RR)
% Number of literals : 30 ( 0 equ; 13 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_in(u,c_Union(v,w),w)
| c_in(c_Main_OUnionE__1(u,v,w),v,tc_set(w)) ),
file('SET842-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(u,c_Union(v,w),w)
| c_in(u,c_Main_OUnionE__1(u,v,w),w) ),
file('SET842-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(u,v,w)
| ~ c_lessequals(v,x,tc_set(w))
| c_in(u,x,w) ),
file('SET842-2.p',unknown),
[] ).
cnf(4,axiom,
( c_lessequals(u,v,tc_set(w))
| c_in(c_Main_OsubsetI__1(u,v,w),u,w) ),
file('SET842-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ c_in(c_Main_OsubsetI__1(u,v,w),v,w)
| c_lessequals(u,v,tc_set(w)) ),
file('SET842-2.p',unknown),
[] ).
cnf(6,axiom,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('SET842-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ c_in(u,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(u,v_m,tc_set(tc_set(t_a))) ),
file('SET842-2.p',unknown),
[] ).
cnf(17,plain,
( ~ c_in(u,c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| c_lessequals(c_Main_OUnionE__1(u,v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[1,7]),
[iquote('0:Res:1.1,7.0')] ).
cnf(20,plain,
( ~ c_in(u,c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| ~ c_in(v,c_Main_OUnionE__1(u,v_Y,tc_set(t_a)),tc_set(t_a))
| c_in(v,v_m,tc_set(t_a)) ),
inference(res,[status(thm),theory(equality)],[17,3]),
[iquote('0:Res:17.1,3.1')] ).
cnf(25,plain,
( ~ c_in(u,c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| ~ c_in(u,c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| c_in(u,v_m,tc_set(t_a)) ),
inference(res,[status(thm),theory(equality)],[2,20]),
[iquote('0:Res:2.1,20.1')] ).
cnf(26,plain,
( ~ c_in(u,c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| c_in(u,v_m,tc_set(t_a)) ),
inference(obv,[status(thm),theory(equality)],[25]),
[iquote('0:Obv:25.0')] ).
cnf(28,plain,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),u,tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),u,tc_set(t_a)),v_m,tc_set(t_a)) ),
inference(res,[status(thm),theory(equality)],[4,26]),
[iquote('0:Res:4.1,26.0')] ).
cnf(31,plain,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[28,5]),
[iquote('0:Res:28.1,5.0')] ).
cnf(32,plain,
c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(obv,[status(thm),theory(equality)],[31]),
[iquote('0:Obv:31.0')] ).
cnf(33,plain,
$false,
inference(mrr,[status(thm)],[32,6]),
[iquote('0:MRR:32.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET842-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n003.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 : Sun Jul 10 05:19:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.41
% 0.12/0.41 SPASS V 3.9
% 0.12/0.41 SPASS beiseite: Proof found.
% 0.12/0.41 % SZS status Theorem
% 0.12/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.41 SPASS derived 19 clauses, backtracked 0 clauses, performed 0 splits and kept 21 clauses.
% 0.12/0.41 SPASS allocated 63126 KBytes.
% 0.12/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.12/0.41 0:00:00.03 for the input.
% 0.12/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.12/0.41 0:00:00.00 for inferences.
% 0.12/0.41 0:00:00.00 for the backtracking.
% 0.12/0.41 0:00:00.00 for the reduction.
% 0.12/0.41
% 0.12/0.41
% 0.12/0.41 Here is a proof with depth 5, length 15 :
% 0.12/0.41 % SZS output start Refutation
% See solution above
% 0.12/0.41 Formulae used in the proof : cls_Set_OUnionE_0 cls_Set_OUnionE_1 cls_Set_OsubsetD_0 cls_Set_OsubsetI_0 cls_Set_OsubsetI_1 cls_conjecture_3 cls_conjecture_4
% 0.12/0.41
%------------------------------------------------------------------------------