TSTP Solution File: SET075-6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET075-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 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 05:23:37 EDT 2022
% Result : Unsatisfiable 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 24 ( 8 unt; 3 nHn; 24 RR)
% Number of literals : 42 ( 0 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
member(ordered_pair(x__dfg,y__dfg),cross_product(u__dfg,v__dfg)),
file('SET075-6.p',unknown),
[] ).
cnf(2,axiom,
equal(unordered_pair(x__dfg,y__dfg),null_class),
file('SET075-6.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET075-6.p',unknown),
[] ).
cnf(6,axiom,
subclass(u,universal_class),
file('SET075-6.p',unknown),
[] ).
cnf(8,axiom,
( ~ equal(u,v)
| subclass(v,u) ),
file('SET075-6.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(v,u)) ),
file('SET075-6.p',unknown),
[] ).
cnf(17,axiom,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| member(v,x) ),
file('SET075-6.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET075-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET075-6.p',unknown),
[] ).
cnf(69,axiom,
( equal(u,null_class)
| equal(intersection(u,regular(u)),null_class) ),
file('SET075-6.p',unknown),
[] ).
cnf(100,plain,
member(y__dfg,v__dfg),
inference(res,[status(thm),theory(equality)],[1,17]),
[iquote('0:Res:1.0,17.0')] ).
cnf(138,plain,
( ~ member(y__dfg,universal_class)
| member(y__dfg,null_class) ),
inference(spr,[status(thm),theory(equality)],[2,12]),
[iquote('0:SpR:2.0,12.1')] ).
cnf(156,plain,
( ~ member(u,null_class)
| equal(v,null_class)
| member(u,v) ),
inference(spl,[status(thm),theory(equality)],[69,23]),
[iquote('0:SpL:69.1,23.0')] ).
cnf(301,plain,
( ~ subclass(v__dfg,u)
| member(y__dfg,u) ),
inference(res,[status(thm),theory(equality)],[100,3]),
[iquote('0:Res:100.0,3.0')] ).
cnf(329,plain,
member(y__dfg,universal_class),
inference(res,[status(thm),theory(equality)],[6,301]),
[iquote('0:Res:6.0,301.0')] ).
cnf(333,plain,
member(y__dfg,null_class),
inference(mrr,[status(thm)],[138,329]),
[iquote('0:MRR:138.0,329.0')] ).
cnf(338,plain,
( ~ subclass(null_class,u)
| member(y__dfg,u) ),
inference(res,[status(thm),theory(equality)],[333,3]),
[iquote('0:Res:333.0,3.0')] ).
cnf(339,plain,
( equal(u,null_class)
| member(y__dfg,u) ),
inference(res,[status(thm),theory(equality)],[333,156]),
[iquote('0:Res:333.0,156.0')] ).
cnf(341,plain,
( ~ member(y__dfg,u)
| equal(complement(u),null_class) ),
inference(res,[status(thm),theory(equality)],[339,26]),
[iquote('0:Res:339.1,26.1')] ).
cnf(406,plain,
( ~ equal(u,null_class)
| member(y__dfg,u) ),
inference(res,[status(thm),theory(equality)],[8,338]),
[iquote('0:Res:8.1,338.0')] ).
cnf(450,plain,
( ~ equal(complement(u),null_class)
| ~ member(y__dfg,u) ),
inference(res,[status(thm),theory(equality)],[406,26]),
[iquote('0:Res:406.1,26.1')] ).
cnf(456,plain,
( ~ equal(null_class,null_class)
| ~ member(y__dfg,u) ),
inference(rew,[status(thm),theory(equality)],[341,450]),
[iquote('0:Rew:341.1,450.0')] ).
cnf(457,plain,
~ member(y__dfg,u),
inference(obv,[status(thm),theory(equality)],[456]),
[iquote('0:Obv:456.0')] ).
cnf(458,plain,
$false,
inference(unc,[status(thm)],[457,333]),
[iquote('0:UnC:457.0,333.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET075-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n005.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 15:22:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.48
% 0.19/0.48 SPASS V 3.9
% 0.19/0.48 SPASS beiseite: Proof found.
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.48 SPASS derived 361 clauses, backtracked 0 clauses, performed 0 splits and kept 339 clauses.
% 0.19/0.48 SPASS allocated 76150 KBytes.
% 0.19/0.48 SPASS spent 0:00:00.13 on the problem.
% 0.19/0.48 0:00:00.04 for the input.
% 0.19/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.48 0:00:00.01 for inferences.
% 0.19/0.48 0:00:00.00 for the backtracking.
% 0.19/0.48 0:00:00.06 for the reduction.
% 0.19/0.48
% 0.19/0.48
% 0.19/0.48 Here is a proof with depth 4, length 24 :
% 0.19/0.48 % SZS output start Refutation
% See solution above
% 0.19/0.48 Formulae used in the proof : prove_corollary_to_unordered_pair_axiom3_1 prove_corollary_to_unordered_pair_axiom3_2 subclass_members class_elements_are_sets equal_implies_subclass2 unordered_pair3 cartesian_product2 intersection1 complement1 regularity2
% 0.19/0.48
%------------------------------------------------------------------------------