TSTP Solution File: SET017-7 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET017-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 05:22:37 EDT 2022
% Result : Unsatisfiable 0.20s 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 23 ( 12 unt; 1 nHn; 23 RR)
% Number of literals : 35 ( 0 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| member(u,universal_class) ),
file('SET017-7.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| member(v,universal_class) ),
file('SET017-7.p',unknown),
[] ).
cnf(23,axiom,
equal(unordered_pair(x__dfg,z__dfg),unordered_pair(x__dfg,y__dfg)),
file('SET017-7.p',unknown),
[] ).
cnf(24,axiom,
member(ordered_pair(y__dfg,z__dfg),cross_product(universal_class,universal_class)),
file('SET017-7.p',unknown),
[] ).
cnf(25,axiom,
~ equal(z__dfg,y__dfg),
file('SET017-7.p',unknown),
[] ).
cnf(33,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET017-7.p',unknown),
[] ).
cnf(35,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(v,u)) ),
file('SET017-7.p',unknown),
[] ).
cnf(37,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET017-7.p',unknown),
[] ).
cnf(125,plain,
( ~ member(z__dfg,unordered_pair(u,y__dfg))
| equal(z__dfg,u) ),
inference(res,[status(thm),theory(equality)],[33,25]),
[iquote('0:Res:33.2,25.0')] ).
cnf(131,plain,
( ~ member(y__dfg,unordered_pair(u,z__dfg))
| equal(y__dfg,u) ),
inference(res,[status(thm),theory(equality)],[33,25]),
[iquote('0:Res:33.2,25.0')] ).
cnf(143,plain,
member(y__dfg,universal_class),
inference(res,[status(thm),theory(equality)],[24,3]),
[iquote('0:Res:24.0,3.0')] ).
cnf(144,plain,
member(z__dfg,universal_class),
inference(res,[status(thm),theory(equality)],[24,4]),
[iquote('0:Res:24.0,4.0')] ).
cnf(154,plain,
~ member(z__dfg,unordered_pair(y__dfg,y__dfg)),
inference(res,[status(thm),theory(equality)],[125,25]),
[iquote('0:Res:125.1,25.0')] ).
cnf(158,plain,
~ member(z__dfg,singleton(y__dfg)),
inference(rew,[status(thm),theory(equality)],[37,154]),
[iquote('0:Rew:37.0,154.0')] ).
cnf(210,plain,
( ~ member(y__dfg,unordered_pair(x__dfg,y__dfg))
| equal(y__dfg,x__dfg) ),
inference(spl,[status(thm),theory(equality)],[23,131]),
[iquote('0:SpL:23.0,131.0')] ).
cnf(272,plain,
( ~ member(z__dfg,universal_class)
| member(z__dfg,unordered_pair(x__dfg,y__dfg)) ),
inference(spr,[status(thm),theory(equality)],[23,35]),
[iquote('0:SpR:23.0,35.1')] ).
cnf(277,plain,
( ~ member(y__dfg,universal_class)
| equal(y__dfg,x__dfg) ),
inference(res,[status(thm),theory(equality)],[35,210]),
[iquote('0:Res:35.1,210.0')] ).
cnf(278,plain,
equal(y__dfg,x__dfg),
inference(mrr,[status(thm)],[277,143]),
[iquote('0:MRR:277.0,143.0')] ).
cnf(283,plain,
~ member(z__dfg,singleton(x__dfg)),
inference(rew,[status(thm),theory(equality)],[278,158]),
[iquote('0:Rew:278.0,158.0')] ).
cnf(308,plain,
( ~ member(z__dfg,universal_class)
| member(z__dfg,unordered_pair(x__dfg,x__dfg)) ),
inference(rew,[status(thm),theory(equality)],[278,272]),
[iquote('0:Rew:278.0,272.1')] ).
cnf(309,plain,
( ~ member(z__dfg,universal_class)
| member(z__dfg,singleton(x__dfg)) ),
inference(rew,[status(thm),theory(equality)],[37,308]),
[iquote('0:Rew:37.0,308.1')] ).
cnf(310,plain,
member(z__dfg,singleton(x__dfg)),
inference(mrr,[status(thm)],[309,144]),
[iquote('0:MRR:309.0,144.0')] ).
cnf(311,plain,
$false,
inference(mrr,[status(thm)],[310,283]),
[iquote('0:MRR:310.0,283.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET017-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n023.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 : Mon Jul 11 10:25:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.44
% 0.20/0.44 SPASS V 3.9
% 0.20/0.44 SPASS beiseite: Proof found.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.44 SPASS derived 162 clauses, backtracked 0 clauses, performed 1 splits and kept 184 clauses.
% 0.20/0.44 SPASS allocated 75913 KBytes.
% 0.20/0.44 SPASS spent 0:00:00.09 on the problem.
% 0.20/0.44 0:00:00.04 for the input.
% 0.20/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.44 0:00:00.00 for inferences.
% 0.20/0.44 0:00:00.00 for the backtracking.
% 0.20/0.44 0:00:00.02 for the reduction.
% 0.20/0.44
% 0.20/0.44
% 0.20/0.44 Here is a proof with depth 3, length 23 :
% 0.20/0.44 % SZS output start Refutation
% See solution above
% 0.20/0.44 Formulae used in the proof : corollary_1_to_cartesian_product corollary_2_to_cartesian_product prove_left_cancellation_1 prove_left_cancellation_2 prove_left_cancellation_3 unordered_pair_member unordered_pair3 singleton_set
% 0.20/0.44
%------------------------------------------------------------------------------