TSTP Solution File: SET015+4 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET015+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 05:22:33 EDT 2022
% Result : Theorem 18.10s 18.29s
% Output : Refutation 18.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 16 ( 3 unt; 6 nHn; 16 RR)
% Number of literals : 33 ( 0 equ; 11 neg)
% Maximal clause size : 3 ( 2 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(6,axiom,
~ equal_set(union(skc3,skc2),union(skc2,skc3)),
file('SET015+4.p',unknown),
[] ).
cnf(7,axiom,
( subset(u,v)
| member(skf3(v,u),u) ),
file('SET015+4.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(skf3(u,v),u)
| subset(w,u) ),
file('SET015+4.p',unknown),
[] ).
cnf(15,axiom,
( ~ member(u,v)
| member(u,union(v,w)) ),
file('SET015+4.p',unknown),
[] ).
cnf(16,axiom,
( ~ member(u,v)
| member(u,union(w,v)) ),
file('SET015+4.p',unknown),
[] ).
cnf(24,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal_set(v,u) ),
file('SET015+4.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,union(v,w))
| member(u,v)
| member(u,w) ),
file('SET015+4.p',unknown),
[] ).
cnf(31,plain,
( ~ subset(union(skc2,skc3),union(skc3,skc2))
| ~ subset(union(skc3,skc2),union(skc2,skc3)) ),
inference(res,[status(thm),theory(equality)],[24,6]),
[iquote('0:Res:24.2,6.0')] ).
cnf(45,plain,
( ~ member(skf3(union(u,v),w),v)
| subset(x,union(u,v)) ),
inference(res,[status(thm),theory(equality)],[16,12]),
[iquote('0:Res:16.1,12.0')] ).
cnf(46,plain,
( ~ member(skf3(union(u,v),w),u)
| subset(x,union(u,v)) ),
inference(res,[status(thm),theory(equality)],[15,12]),
[iquote('0:Res:15.1,12.0')] ).
cnf(177,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)],[7,25]),
[iquote('0:Res:7.1,25.0')] ).
cnf(3284,plain,
( subset(union(u,v),union(v,w))
| member(skf3(union(v,w),union(u,v)),u)
| subset(x,union(v,w)) ),
inference(res,[status(thm),theory(equality)],[177,46]),
[iquote('0:Res:177.2,46.0')] ).
cnf(3293,plain,
( subset(union(u,v),union(v,w))
| member(skf3(union(v,w),union(u,v)),u) ),
inference(con,[status(thm)],[3284]),
[iquote('0:Con:3284.2')] ).
cnf(24611,plain,
( subset(union(u,v),union(v,u))
| subset(w,union(v,u)) ),
inference(res,[status(thm),theory(equality)],[3293,45]),
[iquote('0:Res:3293.1,45.0')] ).
cnf(24639,plain,
subset(union(u,v),union(v,u)),
inference(con,[status(thm)],[24611]),
[iquote('0:Con:24611.1')] ).
cnf(24640,plain,
$false,
inference(mrr,[status(thm)],[31,24639]),
[iquote('0:MRR:31.1,31.0,24639.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET015+4 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 07:16:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 18.10/18.29
% 18.10/18.29 SPASS V 3.9
% 18.10/18.29 SPASS beiseite: Proof found.
% 18.10/18.29 % SZS status Theorem
% 18.10/18.29 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.10/18.29 SPASS derived 21589 clauses, backtracked 0 clauses, performed 0 splits and kept 10802 clauses.
% 18.10/18.29 SPASS allocated 106115 KBytes.
% 18.10/18.29 SPASS spent 0:0:17.44 on the problem.
% 18.10/18.29 0:00:00.03 for the input.
% 18.10/18.29 0:00:00.04 for the FLOTTER CNF translation.
% 18.10/18.29 0:00:00.27 for inferences.
% 18.10/18.29 0:00:00.00 for the backtracking.
% 18.10/18.29 0:0:16.79 for the reduction.
% 18.10/18.29
% 18.10/18.29
% 18.10/18.29 Here is a proof with depth 3, length 16 :
% 18.10/18.29 % SZS output start Refutation
% See solution above
% 18.10/18.29 Formulae used in the proof : thI07 subset union equal_set
% 18.10/18.29
%------------------------------------------------------------------------------