%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET013+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 05:22:29 EDT 2022
% Result : Theorem 48.54s 48.71s
% Output : Refutation 48.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 16 ( 3 unt; 5 nHn; 16 RR)
% Number of literals : 33 ( 0 equ; 14 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(intersection(skc3,skc2),intersection(skc2,skc3)),
file('SET013+4.p',unknown),
[] ).
cnf(7,axiom,
( subset(u,v)
| member(skf3(v,u),u) ),
file('SET013+4.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(skf3(u,v),u)
| subset(w,u) ),
file('SET013+4.p',unknown),
[] ).
cnf(13,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET013+4.p',unknown),
[] ).
cnf(14,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET013+4.p',unknown),
[] ).
cnf(24,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal_set(v,u) ),
file('SET013+4.p',unknown),
[] ).
cnf(30,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(v,w)) ),
file('SET013+4.p',unknown),
[] ).
cnf(31,plain,
( ~ subset(intersection(skc2,skc3),intersection(skc3,skc2))
| ~ subset(intersection(skc3,skc2),intersection(skc2,skc3)) ),
inference(res,[status(thm),theory(equality)],[24,6]),
[iquote('0:Res:24.2,6.0')] ).
cnf(51,plain,
( subset(intersection(u,v),w)
| member(skf3(w,intersection(u,v)),v) ),
inference(res,[status(thm),theory(equality)],[7,14]),
[iquote('0:Res:7.1,14.0')] ).
cnf(53,plain,
( subset(intersection(u,v),w)
| member(skf3(w,intersection(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[7,13]),
[iquote('0:Res:7.1,13.0')] ).
cnf(192,plain,
( ~ member(skf3(intersection(u,v),w),u)
| ~ member(skf3(intersection(u,v),w),v)
| subset(x,intersection(u,v)) ),
inference(res,[status(thm),theory(equality)],[30,12]),
[iquote('0:Res:30.2,12.0')] ).
cnf(3967,plain,
( ~ member(skf3(intersection(u,v),intersection(w,u)),v)
| subset(intersection(w,u),intersection(u,v))
| subset(x,intersection(u,v)) ),
inference(res,[status(thm),theory(equality)],[51,192]),
[iquote('0:Res:51.1,192.0')] ).
cnf(3973,plain,
( ~ member(skf3(intersection(u,v),intersection(w,u)),v)
| subset(intersection(w,u),intersection(u,v)) ),
inference(con,[status(thm)],[3967]),
[iquote('0:Con:3967.2')] ).
cnf(36466,plain,
( subset(intersection(u,v),intersection(v,u))
| subset(intersection(u,v),intersection(v,u)) ),
inference(res,[status(thm),theory(equality)],[53,3973]),
[iquote('0:Res:53.1,3973.0')] ).
cnf(36535,plain,
subset(intersection(u,v),intersection(v,u)),
inference(obv,[status(thm),theory(equality)],[36466]),
[iquote('0:Obv:36466.0')] ).
cnf(36536,plain,
$false,
inference(mrr,[status(thm)],[31,36535]),
[iquote('0:MRR:31.1,31.0,36535.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET013+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 9 20:55:57 EDT 2022
% 0.13/0.33 % CPUTime :
% 48.54/48.71
% 48.54/48.71 SPASS V 3.9
% 48.54/48.71 SPASS beiseite: Proof found.
% 48.54/48.71 % SZS status Theorem
% 48.54/48.71 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 48.54/48.71 SPASS derived 32380 clauses, backtracked 0 clauses, performed 0 splits and kept 17321 clauses.
% 48.54/48.71 SPASS allocated 117077 KBytes.
% 48.54/48.71 SPASS spent 0:0:47.18 on the problem.
% 48.54/48.71 0:00:00.03 for the input.
% 48.54/48.71 0:00:00.04 for the FLOTTER CNF translation.
% 48.54/48.71 0:00:00.44 for inferences.
% 48.54/48.71 0:00:00.00 for the backtracking.
% 48.54/48.71 0:0:46.10 for the reduction.
% 48.54/48.71
% 48.54/48.71
% 48.54/48.71 Here is a proof with depth 3, length 16 :
% 48.54/48.71 % SZS output start Refutation
% See solution above
% 48.54/48.71 Formulae used in the proof : thI06 subset intersection equal_set
% 48.54/48.71
%------------------------------------------------------------------------------