TSTP Solution File: SET047-5 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET047-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 : Unsatisfiable 0.19s 0.40s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of clauses : 27 ( 12 unt; 7 nHn; 27 RR)
% Number of literals : 50 ( 0 equ; 19 neg)
% Maximal clause size : 4 ( 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,
( ~ element(u,v)
| ~ set_equal(v,w)
| element(u,w) ),
file('SET047-5.p',unknown),
[] ).
cnf(2,axiom,
( ~ element(u,v)
| ~ set_equal(w,v)
| element(u,w) ),
file('SET047-5.p',unknown),
[] ).
cnf(3,axiom,
( set_equal(u,v)
| element(f(u,v),v)
| element(f(u,v),u) ),
file('SET047-5.p',unknown),
[] ).
cnf(4,axiom,
( ~ element(f(u,v),u)
| ~ element(f(u,v),v)
| set_equal(u,v) ),
file('SET047-5.p',unknown),
[] ).
cnf(5,axiom,
( set_equal(b,a)
| set_equal(a,b) ),
file('SET047-5.p',unknown),
[] ).
cnf(6,axiom,
( ~ set_equal(a,b)
| ~ set_equal(b,a) ),
file('SET047-5.p',unknown),
[] ).
cnf(7,plain,
set_equal(b,a),
inference(spt,[spt(split,[position(s1)])],[5]),
[iquote('1:Spt:5.0')] ).
cnf(8,plain,
~ set_equal(a,b),
inference(mrr,[status(thm)],[6,7]),
[iquote('1:MRR:6.1,7.0')] ).
cnf(10,plain,
( ~ set_equal(u,v)
| set_equal(w,u)
| element(f(w,u),w)
| element(f(w,u),v) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.1,1.0')] ).
cnf(26,plain,
( set_equal(u,b)
| element(f(u,b),u)
| element(f(u,b),a) ),
inference(res,[status(thm),theory(equality)],[7,10]),
[iquote('1:Res:7.0,10.0')] ).
cnf(28,plain,
( set_equal(a,b)
| element(f(a,b),a) ),
inference(fac,[status(thm)],[26]),
[iquote('1:Fac:26.1,26.2')] ).
cnf(34,plain,
element(f(a,b),a),
inference(mrr,[status(thm)],[28,8]),
[iquote('1:MRR:28.0,8.0')] ).
cnf(37,plain,
( ~ set_equal(u,a)
| element(f(a,b),u) ),
inference(res,[status(thm),theory(equality)],[34,2]),
[iquote('1:Res:34.0,2.0')] ).
cnf(38,plain,
( ~ element(f(a,b),b)
| set_equal(a,b) ),
inference(res,[status(thm),theory(equality)],[34,4]),
[iquote('1:Res:34.0,4.0')] ).
cnf(39,plain,
~ element(f(a,b),b),
inference(mrr,[status(thm)],[38,8]),
[iquote('1:MRR:38.1,8.0')] ).
cnf(49,plain,
~ set_equal(b,a),
inference(res,[status(thm),theory(equality)],[37,39]),
[iquote('1:Res:37.1,39.0')] ).
cnf(50,plain,
$false,
inference(mrr,[status(thm)],[49,7]),
[iquote('1:MRR:49.0,7.0')] ).
cnf(51,plain,
~ set_equal(b,a),
inference(spt,[spt(split,[position(sa)])],[50,7]),
[iquote('1:Spt:50.0,5.0,7.0')] ).
cnf(52,plain,
set_equal(a,b),
inference(spt,[spt(split,[position(s2)])],[5]),
[iquote('1:Spt:50.0,5.1')] ).
cnf(54,plain,
( set_equal(u,a)
| element(f(u,a),u)
| element(f(u,a),b) ),
inference(res,[status(thm),theory(equality)],[52,10]),
[iquote('1:Res:52.0,10.0')] ).
cnf(64,plain,
( set_equal(b,a)
| element(f(b,a),b) ),
inference(fac,[status(thm)],[54]),
[iquote('1:Fac:54.1,54.2')] ).
cnf(70,plain,
element(f(b,a),b),
inference(mrr,[status(thm)],[64,51]),
[iquote('1:MRR:64.0,51.0')] ).
cnf(73,plain,
( ~ set_equal(u,b)
| element(f(b,a),u) ),
inference(res,[status(thm),theory(equality)],[70,2]),
[iquote('1:Res:70.0,2.0')] ).
cnf(74,plain,
( ~ element(f(b,a),a)
| set_equal(b,a) ),
inference(res,[status(thm),theory(equality)],[70,4]),
[iquote('1:Res:70.0,4.0')] ).
cnf(75,plain,
~ element(f(b,a),a),
inference(mrr,[status(thm)],[74,51]),
[iquote('1:MRR:74.1,51.0')] ).
cnf(86,plain,
~ set_equal(a,b),
inference(res,[status(thm),theory(equality)],[73,75]),
[iquote('1:Res:73.1,75.0')] ).
cnf(87,plain,
$false,
inference(mrr,[status(thm)],[86,52]),
[iquote('1:MRR:86.0,52.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET047-5 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n027.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 00:54:32 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.40
% 0.19/0.40 SPASS V 3.9
% 0.19/0.40 SPASS beiseite: Proof found.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.40 SPASS derived 68 clauses, backtracked 3 clauses, performed 1 splits and kept 61 clauses.
% 0.19/0.40 SPASS allocated 63147 KBytes.
% 0.19/0.40 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.40 0:00:00.03 for the input.
% 0.19/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.40 0:00:00.00 for inferences.
% 0.19/0.40 0:00:00.00 for the backtracking.
% 0.19/0.40 0:00:00.00 for the reduction.
% 0.19/0.40
% 0.19/0.40
% 0.19/0.40 Here is a proof with depth 5, length 27 :
% 0.19/0.40 % SZS output start Refutation
% See solution above
% 0.19/0.40 Formulae used in the proof : element_substitution1 element_substitution2 clause_3 clause_4 prove_symmetry1 prove_symmetry2
% 0.19/0.40
%------------------------------------------------------------------------------