TSTP Solution File: SET840-2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET840-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 05:29:08 EDT 2022
% Result : Unsatisfiable 0.22s 0.45s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of clauses : 31 ( 7 unt; 10 nHn; 31 RR)
% Number of literals : 62 ( 0 equ; 21 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 3 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,v,w)
| ~ c_in(v,x,tc_set(w))
| c_in(u,c_Union(x,w),w) ),
file('SET840-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(u,v,w)
| c_in(u,c_insert(x,v,w),w) ),
file('SET840-2.p',unknown),
[] ).
cnf(3,axiom,
c_in(u,c_insert(u,v,w),w),
file('SET840-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_in(u,c_insert(v,w,x),x)
| equal(u,v)
| c_in(u,w,x) ),
file('SET840-2.p',unknown),
[] ).
cnf(5,axiom,
( c_lessequals(u,v,tc_set(w))
| c_in(c_Main_OsubsetI__1(u,v,w),u,w) ),
file('SET840-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ c_in(c_Main_OsubsetI__1(u,v,w),v,w)
| c_lessequals(u,v,tc_set(w)) ),
file('SET840-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ c_lessequals(u,v,tc_set(w))
| ~ c_lessequals(v,u,tc_set(w))
| equal(u,v) ),
file('SET840-2.p',unknown),
[] ).
cnf(8,axiom,
~ c_lessequals(v_S,c_insert(u,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
file('SET840-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ c_in(u,v_S,tc_set(t_b))
| c_lessequals(c_Union(v_S,t_b),u,tc_set(t_b)) ),
file('SET840-2.p',unknown),
[] ).
cnf(12,plain,
( ~ c_in(c_Main_OsubsetI__1(u,c_insert(v,w,x),x),w,x)
| c_lessequals(u,c_insert(v,w,x),tc_set(x)) ),
inference(res,[status(thm),theory(equality)],[2,6]),
[iquote('0:Res:2.1,6.0')] ).
cnf(15,plain,
( ~ c_in(u,v_S,tc_set(t_b))
| ~ c_lessequals(u,c_Union(v_S,t_b),tc_set(t_b))
| equal(c_Union(v_S,t_b),u) ),
inference(res,[status(thm),theory(equality)],[9,7]),
[iquote('0:Res:9.1,7.0')] ).
cnf(19,plain,
( c_lessequals(c_insert(u,v,w),x,tc_set(w))
| equal(c_Main_OsubsetI__1(c_insert(u,v,w),x,w),u)
| c_in(c_Main_OsubsetI__1(c_insert(u,v,w),x,w),v,w) ),
inference(res,[status(thm),theory(equality)],[5,4]),
[iquote('0:Res:5.1,4.0')] ).
cnf(20,plain,
( ~ c_in(u,v,w)
| c_in(u,c_Union(c_insert(v,x,tc_set(w)),w),w) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.0,1.1')] ).
cnf(23,plain,
( ~ c_in(c_Main_OsubsetI__1(u,c_Union(c_insert(v,w,tc_set(x)),x),x),v,x)
| c_lessequals(u,c_Union(c_insert(v,w,tc_set(x)),x),tc_set(x)) ),
inference(res,[status(thm),theory(equality)],[20,6]),
[iquote('0:Res:20.1,6.0')] ).
cnf(28,plain,
( c_lessequals(u,c_insert(v,u,w),tc_set(w))
| c_lessequals(u,c_insert(v,u,w),tc_set(w)) ),
inference(res,[status(thm),theory(equality)],[5,12]),
[iquote('0:Res:5.1,12.0')] ).
cnf(30,plain,
c_lessequals(u,c_insert(v,u,w),tc_set(w)),
inference(obv,[status(thm),theory(equality)],[28]),
[iquote('0:Obv:28.0')] ).
cnf(31,plain,
( ~ c_lessequals(c_insert(u,v,w),v,tc_set(w))
| equal(c_insert(u,v,w),v) ),
inference(res,[status(thm),theory(equality)],[30,7]),
[iquote('0:Res:30.0,7.0')] ).
cnf(46,plain,
( c_lessequals(c_insert(u,v,w),v,tc_set(w))
| equal(c_Main_OsubsetI__1(c_insert(u,v,w),v,w),u)
| c_lessequals(c_insert(u,v,w),v,tc_set(w)) ),
inference(res,[status(thm),theory(equality)],[19,6]),
[iquote('0:Res:19.2,6.0')] ).
cnf(53,plain,
( equal(c_Main_OsubsetI__1(c_insert(u,v,w),v,w),u)
| c_lessequals(c_insert(u,v,w),v,tc_set(w)) ),
inference(obv,[status(thm),theory(equality)],[46]),
[iquote('0:Obv:46.0')] ).
cnf(57,plain,
( equal(c_Main_OsubsetI__1(c_insert(u,v,w),v,w),u)
| equal(c_insert(u,v,w),v) ),
inference(res,[status(thm),theory(equality)],[53,31]),
[iquote('0:Res:53.1,31.0')] ).
cnf(62,plain,
( ~ c_in(u,v,w)
| equal(c_insert(u,v,w),v)
| c_lessequals(c_insert(u,v,w),v,tc_set(w)) ),
inference(spl,[status(thm),theory(equality)],[57,6]),
[iquote('0:SpL:57.0,6.0')] ).
cnf(65,plain,
( ~ c_in(u,v,w)
| equal(c_insert(u,v,w),v) ),
inference(mrr,[status(thm)],[62,31]),
[iquote('0:MRR:62.2,31.0')] ).
cnf(128,plain,
( c_lessequals(u,c_Union(c_insert(u,v,tc_set(w)),w),tc_set(w))
| c_lessequals(u,c_Union(c_insert(u,v,tc_set(w)),w),tc_set(w)) ),
inference(res,[status(thm),theory(equality)],[5,23]),
[iquote('0:Res:5.1,23.0')] ).
cnf(133,plain,
c_lessequals(u,c_Union(c_insert(u,v,tc_set(w)),w),tc_set(w)),
inference(obv,[status(thm),theory(equality)],[128]),
[iquote('0:Obv:128.0')] ).
cnf(141,plain,
( ~ c_in(u,v,tc_set(w))
| c_lessequals(u,c_Union(v,w),tc_set(w)) ),
inference(spr,[status(thm),theory(equality)],[65,133]),
[iquote('0:SpR:65.1,133.0')] ).
cnf(144,plain,
( ~ c_in(u,v_S,tc_set(t_b))
| equal(c_Union(v_S,t_b),u) ),
inference(mrr,[status(thm)],[15,141]),
[iquote('0:MRR:15.1,141.1')] ).
cnf(145,plain,
( c_lessequals(v_S,u,tc_set(tc_set(t_b)))
| equal(c_Main_OsubsetI__1(v_S,u,tc_set(t_b)),c_Union(v_S,t_b)) ),
inference(res,[status(thm),theory(equality)],[5,144]),
[iquote('0:Res:5.1,144.0')] ).
cnf(149,plain,
equal(c_Main_OsubsetI__1(v_S,c_insert(u,c_emptyset,tc_set(t_b)),tc_set(t_b)),c_Union(v_S,t_b)),
inference(res,[status(thm),theory(equality)],[145,8]),
[iquote('0:Res:145.0,8.0')] ).
cnf(162,plain,
( ~ c_in(c_Union(v_S,t_b),c_insert(u,c_emptyset,tc_set(t_b)),tc_set(t_b))
| c_lessequals(v_S,c_insert(u,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))) ),
inference(spl,[status(thm),theory(equality)],[149,6]),
[iquote('0:SpL:149.0,6.0')] ).
cnf(168,plain,
~ c_in(c_Union(v_S,t_b),c_insert(u,c_emptyset,tc_set(t_b)),tc_set(t_b)),
inference(mrr,[status(thm)],[162,8]),
[iquote('0:MRR:162.1,8.0')] ).
cnf(169,plain,
$false,
inference(unc,[status(thm)],[168,3]),
[iquote('0:UnC:168.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET840-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jul 10 04:42:52 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.22/0.45
% 0.22/0.45 SPASS V 3.9
% 0.22/0.45 SPASS beiseite: Proof found.
% 0.22/0.45 % SZS status Theorem
% 0.22/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.45 SPASS derived 135 clauses, backtracked 0 clauses, performed 0 splits and kept 93 clauses.
% 0.22/0.45 SPASS allocated 63466 KBytes.
% 0.22/0.45 SPASS spent 0:00:00.09 on the problem.
% 0.22/0.45 0:00:00.03 for the input.
% 0.22/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.45 0:00:00.01 for inferences.
% 0.22/0.45 0:00:00.00 for the backtracking.
% 0.22/0.45 0:00:00.02 for the reduction.
% 0.22/0.45
% 0.22/0.45
% 0.22/0.45 Here is a proof with depth 6, length 31 :
% 0.22/0.45 % SZS output start Refutation
% See solution above
% 0.22/0.45 Formulae used in the proof : cls_Set_OUnionI_0 cls_Set_OinsertCI_0 cls_Set_OinsertCI_1 cls_Set_OinsertE_0 cls_Set_OsubsetI_0 cls_Set_OsubsetI_1 cls_Set_Osubset__antisym_0 cls_conjecture_0 cls_conjecture_1
% 0.22/0.45
%------------------------------------------------------------------------------