%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM141-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 : Mon Jul 18 14:24:19 EDT 2022
% Result : Unsatisfiable 78.54s 78.70s
% Output : Refutation 78.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 17 ( 6 unt; 5 nHn; 17 RR)
% Number of literals : 29 ( 0 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
member(x__dfg,universal_class),
file('NUM141-1.p',unknown),
[] ).
cnf(2,axiom,
~ member(x__dfg,successor(x__dfg)),
file('NUM141-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(v,u)) ),
file('NUM141-1.p',unknown),
[] ).
cnf(14,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('NUM141-1.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('NUM141-1.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('NUM141-1.p',unknown),
[] ).
cnf(27,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('NUM141-1.p',unknown),
[] ).
cnf(28,axiom,
equal(complement(intersection(complement(u),complement(v))),union(u,v)),
file('NUM141-1.p',unknown),
[] ).
cnf(45,axiom,
equal(union(u,singleton(u)),successor(u)),
file('NUM141-1.p',unknown),
[] ).
cnf(167,plain,
( member(x__dfg,u)
| member(x__dfg,complement(u)) ),
inference(res,[status(thm),theory(equality)],[1,27]),
[iquote('0:Res:1.0,27.0')] ).
cnf(340,plain,
( ~ member(u,universal_class)
| member(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[14,12]),
[iquote('0:SpR:14.0,12.1')] ).
cnf(591,plain,
( member(x__dfg,intersection(complement(u),complement(v)))
| member(x__dfg,union(u,v)) ),
inference(spr,[status(thm),theory(equality)],[28,167]),
[iquote('0:SpR:28.0,167.1')] ).
cnf(114882,plain,
( member(x__dfg,union(u,v))
| member(x__dfg,complement(v)) ),
inference(res,[status(thm),theory(equality)],[591,24]),
[iquote('0:Res:591.0,24.0')] ).
cnf(115351,plain,
( member(x__dfg,successor(u))
| member(x__dfg,complement(singleton(u))) ),
inference(spr,[status(thm),theory(equality)],[45,114882]),
[iquote('0:SpR:45.0,114882.0')] ).
cnf(115551,plain,
( ~ member(x__dfg,singleton(u))
| member(x__dfg,successor(u)) ),
inference(res,[status(thm),theory(equality)],[115351,26]),
[iquote('0:Res:115351.1,26.1')] ).
cnf(115595,plain,
( ~ member(x__dfg,universal_class)
| member(x__dfg,successor(x__dfg)) ),
inference(res,[status(thm),theory(equality)],[340,115551]),
[iquote('0:Res:340.1,115551.0')] ).
cnf(115600,plain,
$false,
inference(mrr,[status(thm)],[115595,1,2]),
[iquote('0:MRR:115595.0,115595.1,1.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : NUM141-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jul 5 14:19:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 78.54/78.70
% 78.54/78.70 SPASS V 3.9
% 78.54/78.70 SPASS beiseite: Proof found.
% 78.54/78.70 % SZS status Theorem
% 78.54/78.70 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 78.54/78.70 SPASS derived 93931 clauses, backtracked 12281 clauses, performed 67 splits and kept 41168 clauses.
% 78.54/78.70 SPASS allocated 153089 KBytes.
% 78.54/78.70 SPASS spent 0:1:16.26 on the problem.
% 78.54/78.70 0:00:00.03 for the input.
% 78.54/78.70 0:00:00.00 for the FLOTTER CNF translation.
% 78.54/78.70 0:00:01.15 for inferences.
% 78.54/78.70 0:00:08.37 for the backtracking.
% 78.54/78.70 0:01:05.26 for the reduction.
% 78.54/78.70
% 78.54/78.70
% 78.54/78.70 Here is a proof with depth 6, length 17 :
% 78.54/78.70 % SZS output start Refutation
% See solution above
% 78.54/78.70 Formulae used in the proof : prove_successor_of_set_is_set2_1 prove_successor_of_set_is_set2_2 unordered_pair3 singleton_set intersection2 complement1 complement2 union successor
% 78.54/78.70
%------------------------------------------------------------------------------