TSTP Solution File: SET162+3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET162+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 05:24:39 EDT 2022
% Result : Theorem 0.21s 0.53s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 19 ( 8 unt; 6 nHn; 19 RR)
% Number of literals : 33 ( 0 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ member(u,empty_set),
file('SET162+3.p',unknown),
[] ).
cnf(3,axiom,
~ equal(union(skc1,empty_set),skc1),
file('SET162+3.p',unknown),
[] ).
cnf(7,axiom,
equal(union(u,v),union(v,u)),
file('SET162+3.p',unknown),
[] ).
cnf(9,axiom,
( subset(u,v)
| member(skf3(v,u),u) ),
file('SET162+3.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,v)
| member(u,union(w,v)) ),
file('SET162+3.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(skf3(u,v),u)
| subset(w,u) ),
file('SET162+3.p',unknown),
[] ).
cnf(13,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal(v,u) ),
file('SET162+3.p',unknown),
[] ).
cnf(17,axiom,
( ~ member(u,union(v,w))
| member(u,v)
| member(u,w) ),
file('SET162+3.p',unknown),
[] ).
cnf(20,plain,
~ equal(union(empty_set,skc1),skc1),
inference(rew,[status(thm),theory(equality)],[7,3]),
[iquote('0:Rew:7.0,3.0')] ).
cnf(21,plain,
( ~ subset(skc1,union(empty_set,skc1))
| ~ subset(union(empty_set,skc1),skc1) ),
inference(res,[status(thm),theory(equality)],[13,20]),
[iquote('0:Res:13.2,20.0')] ).
cnf(41,plain,
( ~ member(skf3(union(u,v),w),v)
| subset(x,union(u,v)) ),
inference(res,[status(thm),theory(equality)],[11,12]),
[iquote('0:Res:11.1,12.0')] ).
cnf(92,plain,
( subset(union(u,v),w)
| member(skf3(w,union(u,v)),u)
| member(skf3(w,union(u,v)),v) ),
inference(res,[status(thm),theory(equality)],[9,17]),
[iquote('0:Res:9.1,17.0')] ).
cnf(180,plain,
( subset(u,union(v,u))
| subset(w,union(v,u)) ),
inference(res,[status(thm),theory(equality)],[9,41]),
[iquote('0:Res:9.1,41.0')] ).
cnf(182,plain,
subset(u,union(v,u)),
inference(con,[status(thm)],[180]),
[iquote('0:Con:180.1')] ).
cnf(183,plain,
~ subset(union(empty_set,skc1),skc1),
inference(mrr,[status(thm)],[21,182]),
[iquote('0:MRR:21.0,182.0')] ).
cnf(497,plain,
( subset(union(empty_set,u),v)
| member(skf3(v,union(empty_set,u)),u) ),
inference(res,[status(thm),theory(equality)],[92,2]),
[iquote('0:Res:92.1,2.0')] ).
cnf(947,plain,
( subset(union(empty_set,u),u)
| subset(v,u) ),
inference(res,[status(thm),theory(equality)],[497,12]),
[iquote('0:Res:497.1,12.0')] ).
cnf(952,plain,
subset(union(empty_set,u),u),
inference(con,[status(thm)],[947]),
[iquote('0:Con:947.1')] ).
cnf(953,plain,
$false,
inference(unc,[status(thm)],[952,183]),
[iquote('0:UnC:952.0,183.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET162+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n016.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 : Mon Jul 11 03:07:27 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.53
% 0.21/0.53 SPASS V 3.9
% 0.21/0.53 SPASS beiseite: Proof found.
% 0.21/0.53 % SZS status Theorem
% 0.21/0.53 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.53 SPASS derived 771 clauses, backtracked 0 clauses, performed 0 splits and kept 295 clauses.
% 0.21/0.53 SPASS allocated 98274 KBytes.
% 0.21/0.53 SPASS spent 0:00:00.16 on the problem.
% 0.21/0.53 0:00:00.03 for the input.
% 0.21/0.53 0:00:00.03 for the FLOTTER CNF translation.
% 0.21/0.53 0:00:00.01 for inferences.
% 0.21/0.53 0:00:00.00 for the backtracking.
% 0.21/0.53 0:00:00.06 for the reduction.
% 0.21/0.53
% 0.21/0.53
% 0.21/0.53 Here is a proof with depth 3, length 19 :
% 0.21/0.53 % SZS output start Refutation
% See solution above
% 0.21/0.53 Formulae used in the proof : empty_set_defn prove_union_empty_set commutativity_of_union subset_defn union_defn equal_defn
% 0.21/0.53
%------------------------------------------------------------------------------