TSTP Solution File: SET114-7 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET114-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% 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 05:24:12 EDT 2022
% Result : Unsatisfiable 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 9 ( 6 unt; 3 nHn; 9 RR)
% Number of literals : 12 ( 0 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(64,axiom,
( member(ordered_pair(first(u),second(u)),cross_product(universal_class,universal_class))
| equal(second(u),u) ),
file('SET114-7.p',unknown),
[] ).
cnf(66,axiom,
( equal(second(u),u)
| equal(ordered_pair(first(u),second(u)),u) ),
file('SET114-7.p',unknown),
[] ).
cnf(69,axiom,
~ member(ordered_pair(first(x__dfg),second(x__dfg)),cross_product(universal_class,universal_class)),
file('SET114-7.p',unknown),
[] ).
cnf(70,axiom,
~ equal(second(x__dfg),x__dfg),
file('SET114-7.p',unknown),
[] ).
cnf(165,plain,
( member(u,cross_product(universal_class,universal_class))
| equal(second(u),u) ),
inference(rew,[status(thm),theory(equality)],[66,64]),
[iquote('0:Rew:66.0,64.0')] ).
cnf(170,plain,
member(x__dfg,cross_product(universal_class,universal_class)),
inference(res,[status(thm),theory(equality)],[165,70]),
[iquote('0:Res:165.1,70.0')] ).
cnf(171,plain,
equal(ordered_pair(first(x__dfg),second(x__dfg)),x__dfg),
inference(res,[status(thm),theory(equality)],[66,70]),
[iquote('0:Res:66.1,70.0')] ).
cnf(210,plain,
~ member(x__dfg,cross_product(universal_class,universal_class)),
inference(rew,[status(thm),theory(equality)],[171,69]),
[iquote('0:Rew:171.0,69.0')] ).
cnf(211,plain,
$false,
inference(mrr,[status(thm)],[210,170]),
[iquote('0:MRR:210.0,170.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET114-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n005.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 02:58:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.43
% 0.18/0.43 SPASS V 3.9
% 0.18/0.43 SPASS beiseite: Proof found.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 SPASS derived 13 clauses, backtracked 0 clauses, performed 0 splits and kept 157 clauses.
% 0.18/0.43 SPASS allocated 75823 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.18/0.43 0:00:00.04 for the input.
% 0.18/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.43 0:00:00.00 for inferences.
% 0.18/0.43 0:00:00.00 for the backtracking.
% 0.18/0.43 0:00:00.01 for the reduction.
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 Here is a proof with depth 1, length 9 :
% 0.18/0.43 % SZS output start Refutation
% See solution above
% 0.18/0.43 Formulae used in the proof : existence_of_1st_and_2nd_3 existence_of_1st_and_2nd_5 prove_unique_1st_and_2nd_in_pair_of_non_sets2_1 prove_unique_2nd_in_pair_of_non_sets
% 0.18/0.43
%------------------------------------------------------------------------------