TSTP Solution File: SET881+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET881+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 05:29:33 EDT 2022
% Result : Theorem 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 9 RR)
% Number of literals : 13 ( 0 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
equal(unordered_pair(u,v),unordered_pair(v,u)),
file('SET881+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(set_difference(singleton(skc5),unordered_pair(skc5,skc4)),empty_set),
file('SET881+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ in(u,v)
| equal(set_difference(singleton(u),v),empty_set) ),
file('SET881+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ equal(u,v)
| ~ equal(w,unordered_pair(x,v))
| in(u,w) ),
file('SET881+1.p',unknown),
[] ).
cnf(15,plain,
~ equal(set_difference(singleton(skc5),unordered_pair(skc4,skc5)),empty_set),
inference(rew,[status(thm),theory(equality)],[4,6]),
[iquote('0:Rew:4.0,6.0')] ).
cnf(16,plain,
~ in(skc5,unordered_pair(skc4,skc5)),
inference(res,[status(thm),theory(equality)],[8,15]),
[iquote('0:Res:8.1,15.0')] ).
cnf(29,plain,
( ~ equal(u,v)
| in(u,unordered_pair(w,v)) ),
inference(eqr,[status(thm),theory(equality)],[10]),
[iquote('0:EqR:10.1')] ).
cnf(34,plain,
~ equal(skc5,skc5),
inference(res,[status(thm),theory(equality)],[29,16]),
[iquote('0:Res:29.1,16.0')] ).
cnf(36,plain,
$false,
inference(obv,[status(thm),theory(equality)],[34]),
[iquote('0:Obv:34.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : SET881+1 : TPTP v8.1.0. Released v3.2.0.
% 0.01/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 11:55:25 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.43
% 0.19/0.43 SPASS V 3.9
% 0.19/0.43 SPASS beiseite: Proof found.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43 SPASS derived 17 clauses, backtracked 0 clauses, performed 0 splits and kept 21 clauses.
% 0.19/0.43 SPASS allocated 85285 KBytes.
% 0.19/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.43 0:00:00.04 for the input.
% 0.19/0.43 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.43 0:00:00.00 for inferences.
% 0.19/0.43 0:00:00.00 for the backtracking.
% 0.19/0.43 0:00:00.00 for the reduction.
% 0.19/0.43
% 0.19/0.43
% 0.19/0.43 Here is a proof with depth 2, length 9 :
% 0.19/0.43 % SZS output start Refutation
% See solution above
% 0.19/0.43 Formulae used in the proof : commutativity_k2_tarski t22_zfmisc_1 l36_zfmisc_1 d2_tarski antisymmetry_r2_hidden
% 0.19/0.43
%------------------------------------------------------------------------------