TSTP Solution File: SET013-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET013-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 05:22:28 EDT 2022
% Result : Unsatisfiable 1.82s 2.01s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 28 ( 13 unt; 2 nHn; 28 RR)
% Number of literals : 48 ( 0 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(intersection(as,bs),cs),
file('SET013-3.p',unknown),
[] ).
cnf(2,axiom,
equal(intersection(bs,as),ds),
file('SET013-3.p',unknown),
[] ).
cnf(3,axiom,
~ equal(ds,cs),
file('SET013-3.p',unknown),
[] ).
cnf(6,axiom,
( equal(u,v)
| member(f1(u,v),v)
| member(f1(u,v),u) ),
file('SET013-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ member(f1(u,v),v)
| ~ member(f1(u,v),u)
| equal(u,v) ),
file('SET013-3.p',unknown),
[] ).
cnf(31,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET013-3.p',unknown),
[] ).
cnf(32,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET013-3.p',unknown),
[] ).
cnf(33,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET013-3.p',unknown),
[] ).
cnf(152,plain,
( ~ member(f1(cs,ds),ds)
| ~ member(f1(cs,ds),cs) ),
inference(res,[status(thm),theory(equality)],[7,3]),
[iquote('0:Res:7.2,3.0')] ).
cnf(153,plain,
( member(f1(cs,ds),ds)
| member(f1(cs,ds),cs) ),
inference(res,[status(thm),theory(equality)],[6,3]),
[iquote('0:Res:6.2,3.0')] ).
cnf(291,plain,
( ~ member(u,ds)
| member(u,as) ),
inference(spl,[status(thm),theory(equality)],[2,32]),
[iquote('0:SpL:2.0,32.0')] ).
cnf(292,plain,
( ~ member(u,cs)
| member(u,bs) ),
inference(spl,[status(thm),theory(equality)],[1,32]),
[iquote('0:SpL:1.0,32.0')] ).
cnf(311,plain,
( ~ member(u,ds)
| member(u,bs) ),
inference(spl,[status(thm),theory(equality)],[2,31]),
[iquote('0:SpL:2.0,31.0')] ).
cnf(312,plain,
( ~ member(u,cs)
| member(u,as) ),
inference(spl,[status(thm),theory(equality)],[1,31]),
[iquote('0:SpL:1.0,31.0')] ).
cnf(2934,plain,
( ~ member(u,as)
| ~ member(u,bs)
| member(u,ds) ),
inference(spr,[status(thm),theory(equality)],[2,33]),
[iquote('0:SpR:2.0,33.2')] ).
cnf(2935,plain,
( ~ member(u,bs)
| ~ member(u,as)
| member(u,cs) ),
inference(spr,[status(thm),theory(equality)],[1,33]),
[iquote('0:SpR:1.0,33.2')] ).
cnf(5104,plain,
member(f1(cs,ds),ds),
inference(spt,[spt(split,[position(s1)])],[153]),
[iquote('1:Spt:153.0')] ).
cnf(5105,plain,
~ member(f1(cs,ds),cs),
inference(mrr,[status(thm)],[152,5104]),
[iquote('1:MRR:152.0,5104.0')] ).
cnf(5111,plain,
member(f1(cs,ds),bs),
inference(res,[status(thm),theory(equality)],[5104,311]),
[iquote('1:Res:5104.0,311.0')] ).
cnf(5112,plain,
member(f1(cs,ds),as),
inference(res,[status(thm),theory(equality)],[5104,291]),
[iquote('1:Res:5104.0,291.0')] ).
cnf(8079,plain,
( ~ member(f1(cs,ds),bs)
| ~ member(f1(cs,ds),as) ),
inference(res,[status(thm),theory(equality)],[2935,5105]),
[iquote('1:Res:2935.2,5105.0')] ).
cnf(8081,plain,
$false,
inference(mrr,[status(thm)],[8079,5111,5112]),
[iquote('1:MRR:8079.0,8079.1,5111.0,5112.0')] ).
cnf(8084,plain,
~ member(f1(cs,ds),ds),
inference(spt,[spt(split,[position(sa)])],[8081,5104]),
[iquote('1:Spt:8081.0,153.0,5104.0')] ).
cnf(8085,plain,
member(f1(cs,ds),cs),
inference(spt,[spt(split,[position(s2)])],[153]),
[iquote('1:Spt:8081.0,153.1')] ).
cnf(8099,plain,
member(f1(cs,ds),as),
inference(res,[status(thm),theory(equality)],[8085,312]),
[iquote('1:Res:8085.0,312.0')] ).
cnf(8100,plain,
member(f1(cs,ds),bs),
inference(res,[status(thm),theory(equality)],[8085,292]),
[iquote('1:Res:8085.0,292.0')] ).
cnf(8197,plain,
( ~ member(f1(cs,ds),as)
| ~ member(f1(cs,ds),bs) ),
inference(res,[status(thm),theory(equality)],[2934,8084]),
[iquote('1:Res:2934.2,8084.0')] ).
cnf(8200,plain,
$false,
inference(mrr,[status(thm)],[8197,8099,8100]),
[iquote('1:MRR:8197.0,8197.1,8099.0,8100.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET013-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 09:33:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.82/2.01
% 1.82/2.01 SPASS V 3.9
% 1.82/2.01 SPASS beiseite: Proof found.
% 1.82/2.01 % SZS status Theorem
% 1.82/2.01 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.82/2.01 SPASS derived 6784 clauses, backtracked 1532 clauses, performed 20 splits and kept 4772 clauses.
% 1.82/2.01 SPASS allocated 81729 KBytes.
% 1.82/2.01 SPASS spent 0:00:01.62 on the problem.
% 1.82/2.01 0:00:00.04 for the input.
% 1.82/2.01 0:00:00.00 for the FLOTTER CNF translation.
% 1.82/2.01 0:00:00.08 for inferences.
% 1.82/2.01 0:00:00.07 for the backtracking.
% 1.82/2.01 0:00:01.35 for the reduction.
% 1.82/2.01
% 1.82/2.01
% 1.82/2.01 Here is a proof with depth 3, length 28 :
% 1.82/2.01 % SZS output start Refutation
% See solution above
% 1.82/2.01 Formulae used in the proof : intersection_of_a_and_b_is_c intersection_of_b_and_a_is_d prove_c_equals_d extensionality2 extensionality3 intersection1 intersection2 intersection3
% 1.82/2.01
%------------------------------------------------------------------------------