TSTP Solution File: SET663+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET663+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 05:27:56 EDT 2022
% Result : Theorem 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 24 ( 11 unt; 0 nHn; 24 RR)
% Number of literals : 46 ( 0 equ; 27 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
ilf_type(u,set_type),
file('SET663+3.p',unknown),
[] ).
cnf(7,axiom,
~ equal(skc6,empty_set),
file('SET663+3.p',unknown),
[] ).
cnf(12,axiom,
ilf_type(skc6,relation_type(skc4,skc5)),
file('SET663+3.p',unknown),
[] ).
cnf(13,axiom,
ilf_type(skc6,relation_type(empty_set,skc5)),
file('SET663+3.p',unknown),
[] ).
cnf(29,axiom,
( ~ relation_like(u)
| ~ ilf_type(u,set_type)
| ilf_type(u,binary_relation_type) ),
file('SET663+3.p',unknown),
[] ).
cnf(32,axiom,
( ~ ilf_type(u,set_type)
| ~ subset(u,empty_set)
| equal(u,empty_set) ),
file('SET663+3.p',unknown),
[] ).
cnf(34,axiom,
( ~ ilf_type(u,binary_relation_type)
| ~ equal(domain_of(u),empty_set)
| equal(u,empty_set) ),
file('SET663+3.p',unknown),
[] ).
cnf(43,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,subset_type(cross_product(u,v)))
| relation_like(w) ),
file('SET663+3.p',unknown),
[] ).
cnf(44,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,relation_type(u,v))
| subset(domain_of(w),u) ),
file('SET663+3.p',unknown),
[] ).
cnf(51,axiom,
( ~ ilf_type(u,relation_type(v,w))
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,set_type)
| ilf_type(u,subset_type(cross_product(v,w))) ),
file('SET663+3.p',unknown),
[] ).
cnf(72,plain,
( ~ relation_like(u)
| ilf_type(u,binary_relation_type) ),
inference(mrr,[status(thm)],[29,6]),
[iquote('0:MRR:29.1,6.0')] ).
cnf(75,plain,
( ~ subset(u,empty_set)
| equal(u,empty_set) ),
inference(mrr,[status(thm)],[32,6]),
[iquote('0:MRR:32.0,6.0')] ).
cnf(79,plain,
( ~ ilf_type(u,subset_type(cross_product(v,w)))
| relation_like(u) ),
inference(mrr,[status(thm)],[43,6]),
[iquote('0:MRR:43.0,43.1,6.0,6.0')] ).
cnf(88,plain,
( ~ ilf_type(u,relation_type(v,w))
| subset(domain_of(u),v) ),
inference(mrr,[status(thm)],[44,6]),
[iquote('0:MRR:44.0,44.1,6.0,6.0')] ).
cnf(89,plain,
( ~ ilf_type(u,relation_type(v,w))
| ilf_type(u,subset_type(cross_product(v,w))) ),
inference(mrr,[status(thm)],[51,6]),
[iquote('0:MRR:51.1,51.2,6.0,6.0')] ).
cnf(102,plain,
( ~ ilf_type(skc6,binary_relation_type)
| ~ equal(domain_of(skc6),empty_set) ),
inference(res,[status(thm),theory(equality)],[34,7]),
[iquote('0:Res:34.2,7.0')] ).
cnf(114,plain,
subset(domain_of(skc6),empty_set),
inference(res,[status(thm),theory(equality)],[13,88]),
[iquote('0:Res:13.0,88.0')] ).
cnf(120,plain,
ilf_type(skc6,subset_type(cross_product(skc4,skc5))),
inference(res,[status(thm),theory(equality)],[12,89]),
[iquote('0:Res:12.0,89.0')] ).
cnf(132,plain,
equal(domain_of(skc6),empty_set),
inference(res,[status(thm),theory(equality)],[114,75]),
[iquote('0:Res:114.0,75.0')] ).
cnf(139,plain,
( ~ ilf_type(skc6,binary_relation_type)
| ~ equal(empty_set,empty_set) ),
inference(rew,[status(thm),theory(equality)],[132,102]),
[iquote('0:Rew:132.0,102.1')] ).
cnf(140,plain,
~ ilf_type(skc6,binary_relation_type),
inference(obv,[status(thm),theory(equality)],[139]),
[iquote('0:Obv:139.1')] ).
cnf(142,plain,
~ relation_like(skc6),
inference(res,[status(thm),theory(equality)],[72,140]),
[iquote('0:Res:72.1,140.0')] ).
cnf(156,plain,
relation_like(skc6),
inference(res,[status(thm),theory(equality)],[120,79]),
[iquote('0:Res:120.0,79.0')] ).
cnf(158,plain,
$false,
inference(mrr,[status(thm)],[156,142]),
[iquote('0:MRR:156.0,142.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET663+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n027.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 10:00:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.47
% 0.19/0.47 SPASS V 3.9
% 0.19/0.47 SPASS beiseite: Proof found.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 55 clauses, backtracked 0 clauses, performed 0 splits and kept 82 clauses.
% 0.19/0.47 SPASS allocated 97854 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.11 on the problem.
% 0.19/0.47 0:00:00.04 for the input.
% 0.19/0.47 0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.00 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.01 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 2, length 24 :
% 0.19/0.47 % SZS output start Refutation
% See solution above
% 0.19/0.47 Formulae used in the proof : p33 prove_relset_1_26 p13 p1 p2 p28 p3 p6
% 0.19/0.47
%------------------------------------------------------------------------------