TSTP Solution File: SET108-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET108-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 05:24:08 EDT 2022
% Result : Unsatisfiable 0.34s 0.52s
% Output : Refutation 0.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of clauses : 6 ( 5 unt; 0 nHn; 6 RR)
% Number of literals : 7 ( 0 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
member(ordered_pair(y__dfg,z__dfg),cross_product(universal_class,universal_class)),
file('SET108-6.p',unknown),
[] ).
cnf(2,axiom,
~ member(ordered_pair(first(ordered_pair(y__dfg,z__dfg)),second(ordered_pair(y__dfg,z__dfg))),cross_product(universal_class,universal_class)),
file('SET108-6.p',unknown),
[] ).
cnf(19,axiom,
( ~ member(u,cross_product(v,w))
| equal(ordered_pair(first(u),second(u)),u) ),
file('SET108-6.p',unknown),
[] ).
cnf(605,plain,
equal(ordered_pair(first(ordered_pair(y__dfg,z__dfg)),second(ordered_pair(y__dfg,z__dfg))),ordered_pair(y__dfg,z__dfg)),
inference(res,[status(thm),theory(equality)],[1,19]),
[iquote('0:Res:1.0,19.0')] ).
cnf(607,plain,
~ member(ordered_pair(y__dfg,z__dfg),cross_product(universal_class,universal_class)),
inference(rew,[status(thm),theory(equality)],[605,2]),
[iquote('0:Rew:605.0,2.0')] ).
cnf(611,plain,
$false,
inference(mrr,[status(thm)],[607,1]),
[iquote('0:MRR:607.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET108-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n005.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 18:19:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.34/0.52
% 0.34/0.52 SPASS V 3.9
% 0.34/0.52 SPASS beiseite: Proof found.
% 0.34/0.52 % SZS status Theorem
% 0.34/0.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.34/0.52 SPASS derived 449 clauses, backtracked 0 clauses, performed 0 splits and kept 425 clauses.
% 0.34/0.52 SPASS allocated 76326 KBytes.
% 0.34/0.52 SPASS spent 0:00:00.16 on the problem.
% 0.34/0.52 0:00:00.04 for the input.
% 0.34/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.34/0.52 0:00:00.01 for inferences.
% 0.34/0.52 0:00:00.00 for the backtracking.
% 0.34/0.52 0:00:00.08 for the reduction.
% 0.34/0.52
% 0.34/0.52
% 0.34/0.52 Here is a proof with depth 1, length 6 :
% 0.34/0.52 % SZS output start Refutation
% See solution above
% 0.34/0.52 Formulae used in the proof : prove_existence_of_1st_and_2nd_1_1 prove_existence_of_1st_and_2nd_1_2 cartesian_product4
% 0.34/0.52
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