TSTP Solution File: SET241-6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET241-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 05:25:13 EDT 2022
% Result : Unsatisfiable 1.06s 1.24s
% Output : Refutation 1.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 16 ( 8 unt; 3 nHn; 16 RR)
% Number of literals : 25 ( 0 equ; 8 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 : 14 ( 14 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
member(ordered_pair(u__dfg,v__dfg),restrict(xr,x__dfg,y__dfg)),
file('SET241-6.p',unknown),
[] ).
cnf(2,axiom,
~ member(v__dfg,y__dfg),
file('SET241-6.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET241-6.p',unknown),
[] ).
cnf(4,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET241-6.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET241-6.p',unknown),
[] ).
cnf(17,axiom,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| member(v,x) ),
file('SET241-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET241-6.p',unknown),
[] ).
cnf(30,axiom,
equal(intersection(u,cross_product(v,w)),restrict(u,v,w)),
file('SET241-6.p',unknown),
[] ).
cnf(123,plain,
~ member(ordered_pair(u,v__dfg),cross_product(v,y__dfg)),
inference(res,[status(thm),theory(equality)],[17,2]),
[iquote('0:Res:17.1,2.0')] ).
cnf(124,plain,
( ~ subclass(restrict(xr,x__dfg,y__dfg),u)
| member(ordered_pair(u__dfg,v__dfg),u) ),
inference(res,[status(thm),theory(equality)],[1,3]),
[iquote('0:Res:1.0,3.1')] ).
cnf(182,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),v) ),
inference(res,[status(thm),theory(equality)],[4,24]),
[iquote('0:Res:4.1,24.0')] ).
cnf(4132,plain,
( subclass(intersection(u,v),v)
| subclass(intersection(u,v),v) ),
inference(res,[status(thm),theory(equality)],[182,5]),
[iquote('0:Res:182.1,5.0')] ).
cnf(4134,plain,
subclass(intersection(u,v),v),
inference(obv,[status(thm),theory(equality)],[4132]),
[iquote('0:Obv:4132.0')] ).
cnf(4153,plain,
subclass(restrict(u,v,w),cross_product(v,w)),
inference(spr,[status(thm),theory(equality)],[30,4134]),
[iquote('0:SpR:30.0,4134.0')] ).
cnf(5107,plain,
member(ordered_pair(u__dfg,v__dfg),cross_product(x__dfg,y__dfg)),
inference(res,[status(thm),theory(equality)],[4153,124]),
[iquote('0:Res:4153.0,124.0')] ).
cnf(5108,plain,
$false,
inference(mrr,[status(thm)],[5107,123]),
[iquote('0:MRR:5107.0,123.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET241-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n006.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 10:35:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.06/1.24
% 1.06/1.24 SPASS V 3.9
% 1.06/1.24 SPASS beiseite: Proof found.
% 1.06/1.24 % SZS status Theorem
% 1.06/1.24 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.06/1.24 SPASS derived 4479 clauses, backtracked 138 clauses, performed 4 splits and kept 2127 clauses.
% 1.06/1.24 SPASS allocated 80307 KBytes.
% 1.06/1.24 SPASS spent 0:00:00.86 on the problem.
% 1.06/1.24 0:00:00.04 for the input.
% 1.06/1.24 0:00:00.00 for the FLOTTER CNF translation.
% 1.06/1.24 0:00:00.07 for inferences.
% 1.06/1.24 0:00:00.02 for the backtracking.
% 1.06/1.24 0:00:00.68 for the reduction.
% 1.06/1.24
% 1.06/1.24
% 1.06/1.24 Here is a proof with depth 4, length 16 :
% 1.06/1.24 % SZS output start Refutation
% See solution above
% 1.06/1.24 Formulae used in the proof : prove_restriction_alternate_defn4_1 prove_restriction_alternate_defn4_2 subclass_members not_subclass_members1 not_subclass_members2 cartesian_product2 intersection2 restriction1
% 1.06/1.24
%------------------------------------------------------------------------------