TSTP Solution File: SET047+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET047+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 05:23:09 EDT 2022
% Result : Theorem 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of clauses : 27 ( 10 unt; 6 nHn; 27 RR)
% Number of literals : 51 ( 0 equ; 20 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( set_equal(skc3,skc2)
| set_equal(skc2,skc3) ),
file('SET047+1.p',unknown),
[] ).
cnf(2,axiom,
( ~ set_equal(skc3,skc2)
| ~ set_equal(skc2,skc3) ),
file('SET047+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ set_equal(u,v)
| ~ element(w,u)
| element(w,v) ),
file('SET047+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ set_equal(u,v)
| ~ element(w,v)
| element(w,u) ),
file('SET047+1.p',unknown),
[] ).
cnf(5,axiom,
( set_equal(u,v)
| element(skf1(v,u),v)
| element(skf1(v,u),u) ),
file('SET047+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ element(skf1(u,v),u)
| ~ element(skf1(u,v),v)
| set_equal(v,u) ),
file('SET047+1.p',unknown),
[] ).
cnf(7,plain,
set_equal(skc3,skc2),
inference(spt,[spt(split,[position(s1)])],[1]),
[iquote('1:Spt:1.0')] ).
cnf(8,plain,
~ set_equal(skc2,skc3),
inference(mrr,[status(thm)],[2,7]),
[iquote('1:MRR:2.0,7.0')] ).
cnf(9,plain,
( ~ element(u,skc2)
| element(u,skc3) ),
inference(res,[status(thm),theory(equality)],[7,4]),
[iquote('1:Res:7.0,4.0')] ).
cnf(10,plain,
( ~ element(u,skc3)
| element(u,skc2) ),
inference(res,[status(thm),theory(equality)],[7,3]),
[iquote('1:Res:7.0,3.0')] ).
cnf(14,plain,
( set_equal(skc2,u)
| element(skf1(u,skc2),u)
| element(skf1(u,skc2),skc3) ),
inference(res,[status(thm),theory(equality)],[5,9]),
[iquote('1:Res:5.2,9.0')] ).
cnf(28,plain,
( set_equal(skc2,skc3)
| element(skf1(skc3,skc2),skc3) ),
inference(fac,[status(thm)],[14]),
[iquote('1:Fac:14.1,14.2')] ).
cnf(31,plain,
element(skf1(skc3,skc2),skc3),
inference(mrr,[status(thm)],[28,8]),
[iquote('1:MRR:28.0,8.0')] ).
cnf(34,plain,
( ~ element(skf1(skc3,skc2),skc2)
| set_equal(skc2,skc3) ),
inference(res,[status(thm),theory(equality)],[31,6]),
[iquote('1:Res:31.0,6.0')] ).
cnf(35,plain,
~ element(skf1(skc3,skc2),skc2),
inference(mrr,[status(thm)],[34,8]),
[iquote('1:MRR:34.1,8.0')] ).
cnf(37,plain,
~ element(skf1(skc3,skc2),skc3),
inference(res,[status(thm),theory(equality)],[10,35]),
[iquote('1:Res:10.1,35.0')] ).
cnf(39,plain,
$false,
inference(mrr,[status(thm)],[37,31]),
[iquote('1:MRR:37.0,31.0')] ).
cnf(40,plain,
~ set_equal(skc3,skc2),
inference(spt,[spt(split,[position(sa)])],[39,7]),
[iquote('1:Spt:39.0,1.0,7.0')] ).
cnf(41,plain,
set_equal(skc2,skc3),
inference(spt,[spt(split,[position(s2)])],[1]),
[iquote('1:Spt:39.0,1.1')] ).
cnf(42,plain,
( ~ element(u,skc2)
| element(u,skc3) ),
inference(res,[status(thm),theory(equality)],[41,3]),
[iquote('1:Res:41.0,3.0')] ).
cnf(43,plain,
( ~ element(u,skc3)
| element(u,skc2) ),
inference(res,[status(thm),theory(equality)],[41,4]),
[iquote('1:Res:41.0,4.0')] ).
cnf(44,plain,
( set_equal(u,skc2)
| element(skf1(skc2,u),u)
| element(skf1(skc2,u),skc3) ),
inference(res,[status(thm),theory(equality)],[5,42]),
[iquote('1:Res:5.1,42.0')] ).
cnf(46,plain,
( ~ element(skf1(skc2,u),skc3)
| ~ element(skf1(skc2,u),u)
| set_equal(u,skc2) ),
inference(res,[status(thm),theory(equality)],[43,6]),
[iquote('1:Res:43.1,6.0')] ).
cnf(48,plain,
( set_equal(skc3,skc2)
| element(skf1(skc2,skc3),skc3) ),
inference(fac,[status(thm)],[44]),
[iquote('1:Fac:44.1,44.2')] ).
cnf(51,plain,
element(skf1(skc2,skc3),skc3),
inference(mrr,[status(thm)],[48,40]),
[iquote('1:MRR:48.0,40.0')] ).
cnf(60,plain,
( ~ element(skf1(skc2,skc3),skc3)
| set_equal(skc3,skc2) ),
inference(res,[status(thm),theory(equality)],[51,46]),
[iquote('1:Res:51.0,46.0')] ).
cnf(61,plain,
$false,
inference(mrr,[status(thm)],[60,51,40]),
[iquote('1:MRR:60.0,60.1,51.0,40.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET047+1 : TPTP v8.1.0. Released v2.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n012.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 : Sun Jul 10 18:05:43 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.43
% 0.20/0.43 SPASS V 3.9
% 0.20/0.43 SPASS beiseite: Proof found.
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.43 SPASS derived 38 clauses, backtracked 3 clauses, performed 1 splits and kept 28 clauses.
% 0.20/0.43 SPASS allocated 85164 KBytes.
% 0.20/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.20/0.43 0:00:00.03 for the input.
% 0.20/0.43 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.43 0:00:00.00 for inferences.
% 0.20/0.43 0:00:00.00 for the backtracking.
% 0.20/0.43 0:00:00.00 for the reduction.
% 0.20/0.43
% 0.20/0.43
% 0.20/0.43 Here is a proof with depth 6, length 27 :
% 0.20/0.43 % SZS output start Refutation
% See solution above
% 0.20/0.43 Formulae used in the proof : pel43 pel43_1
% 0.20/0.43
%------------------------------------------------------------------------------