TSTP Solution File: SET144-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET144-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 05:24:29 EDT 2022
% Result : Unsatisfiable 44.62s 44.83s
% Output : Refutation 44.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 16 ( 3 unt; 5 nHn; 16 RR)
% Number of literals : 33 ( 0 equ; 14 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(intersection(y__dfg,x__dfg),intersection(x__dfg,y__dfg)),
file('SET144-6.p',unknown),
[] ).
cnf(3,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET144-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET144-6.p',unknown),
[] ).
cnf(8,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET144-6.p',unknown),
[] ).
cnf(22,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET144-6.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET144-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET144-6.p',unknown),
[] ).
cnf(117,plain,
( ~ subclass(intersection(x__dfg,y__dfg),intersection(y__dfg,x__dfg))
| ~ subclass(intersection(y__dfg,x__dfg),intersection(x__dfg,y__dfg)) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.2,1.0')] ).
cnf(163,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),v) ),
inference(res,[status(thm),theory(equality)],[3,23]),
[iquote('0:Res:3.1,23.0')] ).
cnf(169,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),u) ),
inference(res,[status(thm),theory(equality)],[3,22]),
[iquote('0:Res:3.1,22.0')] ).
cnf(789,plain,
( ~ member(not_subclass_element(u,intersection(v,w)),w)
| ~ member(not_subclass_element(u,intersection(v,w)),v)
| subclass(u,intersection(v,w)) ),
inference(res,[status(thm),theory(equality)],[24,4]),
[iquote('0:Res:24.2,4.0')] ).
cnf(11001,plain,
( ~ member(not_subclass_element(intersection(u,v),intersection(w,u)),w)
| subclass(intersection(u,v),intersection(w,u))
| subclass(intersection(u,v),intersection(w,u)) ),
inference(res,[status(thm),theory(equality)],[169,789]),
[iquote('0:Res:169.1,789.0')] ).
cnf(11022,plain,
( ~ member(not_subclass_element(intersection(u,v),intersection(w,u)),w)
| subclass(intersection(u,v),intersection(w,u)) ),
inference(obv,[status(thm),theory(equality)],[11001]),
[iquote('0:Obv:11001.1')] ).
cnf(67649,plain,
( subclass(intersection(u,v),intersection(v,u))
| subclass(intersection(u,v),intersection(v,u)) ),
inference(res,[status(thm),theory(equality)],[163,11022]),
[iquote('0:Res:163.1,11022.0')] ).
cnf(67664,plain,
subclass(intersection(u,v),intersection(v,u)),
inference(obv,[status(thm),theory(equality)],[67649]),
[iquote('0:Obv:67649.0')] ).
cnf(67665,plain,
$false,
inference(mrr,[status(thm)],[117,67664]),
[iquote('0:MRR:117.1,117.0,67664.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET144-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n020.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 : Sun Jul 10 14:45:13 EDT 2022
% 0.13/0.34 % CPUTime :
% 44.62/44.83
% 44.62/44.83 SPASS V 3.9
% 44.62/44.83 SPASS beiseite: Proof found.
% 44.62/44.83 % SZS status Theorem
% 44.62/44.83 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 44.62/44.83 SPASS derived 49812 clauses, backtracked 239 clauses, performed 8 splits and kept 17890 clauses.
% 44.62/44.83 SPASS allocated 132652 KBytes.
% 44.62/44.83 SPASS spent 0:0:43.66 on the problem.
% 44.62/44.83 0:00:00.04 for the input.
% 44.62/44.83 0:00:00.00 for the FLOTTER CNF translation.
% 44.62/44.83 0:00:00.52 for inferences.
% 44.62/44.83 0:00:05.16 for the backtracking.
% 44.62/44.83 0:0:37.45 for the reduction.
% 44.62/44.83
% 44.62/44.83
% 44.62/44.83 Here is a proof with depth 3, length 16 :
% 44.62/44.83 % SZS output start Refutation
% See solution above
% 44.62/44.83 Formulae used in the proof : prove_commutativity_of_intersection_1 not_subclass_members1 not_subclass_members2 subclass_implies_equal intersection1 intersection2 intersection3
% 44.62/44.83
%------------------------------------------------------------------------------