TSTP Solution File: SET025-8 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET025-8 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 05:22:48 EDT 2022
% Result : Unsatisfiable 0.21s 0.50s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 5 unt; 0 nHn; 7 RR)
% Number of literals : 9 ( 0 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(10,axiom,
little_set(ordered_pair(u,v)),
file('SET025-8.p',unknown),
[] ).
cnf(11,axiom,
ordered_pair_predicate(a),
file('SET025-8.p',unknown),
[] ).
cnf(12,axiom,
~ little_set(a),
file('SET025-8.p',unknown),
[] ).
cnf(25,axiom,
( ~ ordered_pair_predicate(u)
| equal(ordered_pair(f2(u),f3(u)),u) ),
file('SET025-8.p',unknown),
[] ).
cnf(410,plain,
( ~ ordered_pair_predicate(u)
| little_set(u) ),
inference(spr,[status(thm),theory(equality)],[25,10]),
[iquote('0:SpR:25.1,10.0')] ).
cnf(417,plain,
~ ordered_pair_predicate(a),
inference(res,[status(thm),theory(equality)],[410,12]),
[iquote('0:Res:410.1,12.0')] ).
cnf(419,plain,
$false,
inference(ssi,[status(thm)],[417,11]),
[iquote('0:SSi:417.0,11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET025-8 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 11 05:11:03 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.21/0.50
% 0.21/0.50 SPASS V 3.9
% 0.21/0.50 SPASS beiseite: Proof found.
% 0.21/0.50 % SZS status Theorem
% 0.21/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.50 SPASS derived 252 clauses, backtracked 8 clauses, performed 3 splits and kept 370 clauses.
% 0.21/0.50 SPASS allocated 76137 KBytes.
% 0.21/0.50 SPASS spent 0:00:00.14 on the problem.
% 0.21/0.50 0:00:00.04 for the input.
% 0.21/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.50 0:00:00.01 for inferences.
% 0.21/0.50 0:00:00.00 for the backtracking.
% 0.21/0.50 0:00:00.05 for the reduction.
% 0.21/0.50
% 0.21/0.50
% 0.21/0.50 Here is a proof with depth 2, length 7 :
% 0.21/0.50 % SZS output start Refutation
% See solution above
% 0.21/0.50 Formulae used in the proof : ordered_pairs_are_small1 an_ordered_pair_predicate prove_predicate_is_small ordered_pair_predicate3
% 0.21/0.50
%------------------------------------------------------------------------------