TSTP Solution File: SET231-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET231-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 05:25:10 EDT 2022
% Result : Unsatisfiable 0.19s 0.44s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 5 unt; 1 nHn; 7 RR)
% Number of literals : 9 ( 0 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ subclass(cross_product(x__dfg,y__dfg),z__dfg),
file('SET231-6.p',unknown),
[] ).
cnf(2,axiom,
~ equal(ordered_pair(first(not_subclass_element(cross_product(x__dfg,y__dfg),z__dfg)),second(not_subclass_element(cross_product(x__dfg,y__dfg),z__dfg))),not_subclass_element(cross_product(x__dfg,y__dfg),z__dfg)),
file('SET231-6.p',unknown),
[] ).
cnf(4,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET231-6.p',unknown),
[] ).
cnf(19,axiom,
( ~ member(u,cross_product(v,w))
| equal(ordered_pair(first(u),second(u)),u) ),
file('SET231-6.p',unknown),
[] ).
cnf(123,plain,
~ member(not_subclass_element(cross_product(x__dfg,y__dfg),z__dfg),cross_product(u,v)),
inference(res,[status(thm),theory(equality)],[19,2]),
[iquote('0:Res:19.1,2.0')] ).
cnf(200,plain,
subclass(cross_product(x__dfg,y__dfg),z__dfg),
inference(res,[status(thm),theory(equality)],[4,123]),
[iquote('0:Res:4.1,123.0')] ).
cnf(201,plain,
$false,
inference(mrr,[status(thm)],[200,1]),
[iquote('0:MRR:200.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET231-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n006.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 04:52:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.44
% 0.19/0.44 SPASS V 3.9
% 0.19/0.44 SPASS beiseite: Proof found.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 SPASS derived 73 clauses, backtracked 0 clauses, performed 1 splits and kept 163 clauses.
% 0.19/0.44 SPASS allocated 75880 KBytes.
% 0.19/0.44 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.44 0:00:00.04 for the input.
% 0.19/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.44 0:00:00.00 for inferences.
% 0.19/0.44 0:00:00.00 for the backtracking.
% 0.19/0.44 0:00:00.02 for the reduction.
% 0.19/0.44
% 0.19/0.44
% 0.19/0.44 Here is a proof with depth 2, length 7 :
% 0.19/0.44 % SZS output start Refutation
% See solution above
% 0.19/0.44 Formulae used in the proof : prove_cross_product_property6_1 prove_cross_product_property6_2 not_subclass_members1 cartesian_product4
% 0.19/0.44
%------------------------------------------------------------------------------