TSTP Solution File: SET017-6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET017-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 0.41s
% 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(1,axiom,
equal(unordered_pair(x__dfg,z__dfg),unordered_pair(x__dfg,y__dfg)),
file('SET017-6.p',unknown),
[] ).
cnf(2,axiom,
member(ordered_pair(y__dfg,z__dfg),cross_product(universal_class,universal_class)),
file('SET017-6.p',unknown),
[] ).
cnf(3,axiom,
~ equal(z__dfg,y__dfg),
file('SET017-6.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET017-6.p',unknown),
[] ).
cnf(13,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(v,u)) ),
file('SET017-6.p',unknown),
[] ).
cnf(15,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET017-6.p',unknown),
[] ).
cnf(17,axiom,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| member(u,w) ),
file('SET017-6.p',unknown),
[] ).
cnf(18,axiom,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| member(v,x) ),
file('SET017-6.p',unknown),
[] ).
cnf(99,plain,
( ~ member(z__dfg,unordered_pair(u,y__dfg))
| equal(z__dfg,u) ),
inference(res,[status(thm),theory(equality)],[11,3]),
[iquote('0:Res:11.2,3.0')] ).
cnf(102,plain,
( ~ member(y__dfg,unordered_pair(u,z__dfg))
| equal(y__dfg,u) ),
inference(res,[status(thm),theory(equality)],[11,3]),
[iquote('0:Res:11.2,3.0')] ).
cnf(105,plain,
member(y__dfg,universal_class),
inference(res,[status(thm),theory(equality)],[2,17]),
[iquote('0:Res:2.0,17.0')] ).
cnf(106,plain,
member(z__dfg,universal_class),
inference(res,[status(thm),theory(equality)],[2,18]),
[iquote('0:Res:2.0,18.0')] ).
cnf(120,plain,
~ member(z__dfg,unordered_pair(y__dfg,y__dfg)),
inference(res,[status(thm),theory(equality)],[99,3]),
[iquote('0:Res:99.1,3.0')] ).
cnf(124,plain,
~ member(z__dfg,singleton(y__dfg)),
inference(rew,[status(thm),theory(equality)],[15,120]),
[iquote('0:Rew:15.0,120.0')] ).
cnf(145,plain,
( ~ member(y__dfg,unordered_pair(x__dfg,y__dfg))
| equal(y__dfg,x__dfg) ),
inference(spl,[status(thm),theory(equality)],[1,102]),
[iquote('0:SpL:1.0,102.0')] ).
cnf(163,plain,
( ~ member(z__dfg,universal_class)
| member(z__dfg,unordered_pair(x__dfg,y__dfg)) ),
inference(spr,[status(thm),theory(equality)],[1,13]),
[iquote('0:SpR:1.0,13.1')] ).
cnf(165,plain,
( ~ member(y__dfg,universal_class)
| equal(y__dfg,x__dfg) ),
inference(res,[status(thm),theory(equality)],[13,145]),
[iquote('0:Res:13.1,145.0')] ).
cnf(167,plain,
equal(y__dfg,x__dfg),
inference(mrr,[status(thm)],[165,105]),
[iquote('0:MRR:165.0,105.0')] ).
cnf(170,plain,
~ member(z__dfg,singleton(x__dfg)),
inference(rew,[status(thm),theory(equality)],[167,124]),
[iquote('0:Rew:167.0,124.0')] ).
cnf(187,plain,
( ~ member(z__dfg,universal_class)
| member(z__dfg,unordered_pair(x__dfg,x__dfg)) ),
inference(rew,[status(thm),theory(equality)],[167,163]),
[iquote('0:Rew:167.0,163.1')] ).
cnf(188,plain,
( ~ member(z__dfg,universal_class)
| member(z__dfg,singleton(x__dfg)) ),
inference(rew,[status(thm),theory(equality)],[15,187]),
[iquote('0:Rew:15.0,187.1')] ).
cnf(189,plain,
member(z__dfg,singleton(x__dfg)),
inference(mrr,[status(thm)],[188,106]),
[iquote('0:MRR:188.0,106.0')] ).
cnf(190,plain,
$false,
inference(mrr,[status(thm)],[189,170]),
[iquote('0:MRR:189.0,170.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET017-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 08:15:27 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.41
% 0.20/0.41 SPASS V 3.9
% 0.20/0.41 SPASS beiseite: Proof found.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.41 SPASS derived 72 clauses, backtracked 0 clauses, performed 0 splits and kept 139 clauses.
% 0.20/0.41 SPASS allocated 75835 KBytes.
% 0.20/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.20/0.41 0:00:00.03 for the input.
% 0.20/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.41 0:00:00.00 for inferences.
% 0.20/0.41 0:00:00.00 for the backtracking.
% 0.20/0.41 0:00:00.01 for the reduction.
% 0.20/0.41
% 0.20/0.41
% 0.20/0.41 Here is a proof with depth 3, length 23 :
% 0.20/0.41 % SZS output start Refutation
% See solution above
% 0.20/0.41 Formulae used in the proof : prove_left_cancellation_1 prove_left_cancellation_2 prove_left_cancellation_3 unordered_pair_member unordered_pair3 singleton_set cartesian_product1 cartesian_product2
% 0.20/0.41
%------------------------------------------------------------------------------