%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET650+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 05:27:51 EDT 2022
% Result : Theorem 77.39s 77.58s
% Output : Refutation 77.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 37 ( 7 unt; 6 nHn; 37 RR)
% Number of literals : 100 ( 0 equ; 61 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
ilf_type(u,set_type),
file('SET650+3.p',unknown),
[] ).
cnf(9,axiom,
ilf_type(skc6,relation_type(skc4,skc5)),
file('SET650+3.p',unknown),
[] ).
cnf(23,axiom,
( ~ subset(range_of(skc6),skc5)
| ~ subset(domain_of(skc6),skc4) ),
file('SET650+3.p',unknown),
[] ).
cnf(25,axiom,
( ~ relation_like(u)
| ~ ilf_type(u,set_type)
| ilf_type(u,binary_relation_type) ),
file('SET650+3.p',unknown),
[] ).
cnf(33,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(skf18(v,u),u)
| subset(u,v) ),
file('SET650+3.p',unknown),
[] ).
cnf(34,axiom,
( ~ member(skf18(u,v),u)
| ~ ilf_type(v,set_type)
| ~ ilf_type(u,set_type)
| subset(v,u) ),
file('SET650+3.p',unknown),
[] ).
cnf(36,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,subset_type(cross_product(u,v)))
| relation_like(w) ),
file('SET650+3.p',unknown),
[] ).
cnf(42,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('SET650+3.p',unknown),
[] ).
cnf(44,axiom,
( ~ member(u,range_of(v))
| ~ ilf_type(v,binary_relation_type)
| ~ ilf_type(u,set_type)
| member(ordered_pair(skf16(v,u),u),v) ),
file('SET650+3.p',unknown),
[] ).
cnf(45,axiom,
( ~ member(u,domain_of(v))
| ~ ilf_type(v,binary_relation_type)
| ~ ilf_type(u,set_type)
| member(ordered_pair(u,skf15(v,u)),v) ),
file('SET650+3.p',unknown),
[] ).
cnf(56,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,set_type)
| ~ ilf_type(x,set_type)
| ~ ilf_type(y,relation_type(u,v))
| ~ member(ordered_pair(w,x),y)
| member(x,v) ),
file('SET650+3.p',unknown),
[] ).
cnf(57,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,set_type)
| ~ ilf_type(x,set_type)
| ~ ilf_type(y,relation_type(u,v))
| ~ member(ordered_pair(w,x),y)
| member(w,u) ),
file('SET650+3.p',unknown),
[] ).
cnf(64,plain,
( ~ relation_like(u)
| ilf_type(u,binary_relation_type) ),
inference(mrr,[status(thm)],[25,4]),
[iquote('0:MRR:25.1,4.0')] ).
cnf(69,plain,
( subset(u,v)
| member(skf18(v,u),u) ),
inference(mrr,[status(thm)],[33,4]),
[iquote('0:MRR:33.0,33.1,4.0,4.0')] ).
cnf(70,plain,
( ~ ilf_type(u,subset_type(cross_product(v,w)))
| relation_like(u) ),
inference(mrr,[status(thm)],[36,4]),
[iquote('0:MRR:36.0,36.1,4.0,4.0')] ).
cnf(72,plain,
( ~ member(skf18(u,v),u)
| subset(v,u) ),
inference(mrr,[status(thm)],[34,4]),
[iquote('0:MRR:34.1,34.2,4.0,4.0')] ).
cnf(78,plain,
( ~ ilf_type(u,relation_type(v,w))
| ilf_type(u,subset_type(cross_product(v,w))) ),
inference(mrr,[status(thm)],[42,4]),
[iquote('0:MRR:42.1,42.2,4.0,4.0')] ).
cnf(80,plain,
( ~ ilf_type(u,binary_relation_type)
| ~ member(v,range_of(u))
| member(ordered_pair(skf16(u,v),v),u) ),
inference(mrr,[status(thm)],[44,4]),
[iquote('0:MRR:44.2,4.0')] ).
cnf(81,plain,
( ~ ilf_type(u,binary_relation_type)
| ~ member(v,domain_of(u))
| member(ordered_pair(v,skf15(u,v)),u) ),
inference(mrr,[status(thm)],[45,4]),
[iquote('0:MRR:45.2,4.0')] ).
cnf(90,plain,
( ~ ilf_type(u,relation_type(v,w))
| ~ member(ordered_pair(x,y),u)
| member(y,w) ),
inference(mrr,[status(thm)],[56,4]),
[iquote('0:MRR:56.0,56.1,56.2,56.3,4.0,4.0,4.0,4.0')] ).
cnf(91,plain,
( ~ ilf_type(u,relation_type(v,w))
| ~ member(ordered_pair(x,y),u)
| member(x,v) ),
inference(mrr,[status(thm)],[57,4]),
[iquote('0:MRR:57.0,57.1,57.2,57.3,4.0,4.0,4.0,4.0')] ).
cnf(92,plain,
( ~ member(ordered_pair(u,v),skc6)
| member(u,skc4) ),
inference(res,[status(thm),theory(equality)],[9,91]),
[iquote('0:Res:9.0,91.0')] ).
cnf(93,plain,
( ~ member(ordered_pair(u,v),skc6)
| member(v,skc5) ),
inference(res,[status(thm),theory(equality)],[9,90]),
[iquote('0:Res:9.0,90.0')] ).
cnf(94,plain,
ilf_type(skc6,subset_type(cross_product(skc4,skc5))),
inference(res,[status(thm),theory(equality)],[9,78]),
[iquote('0:Res:9.0,78.0')] ).
cnf(101,plain,
relation_like(skc6),
inference(res,[status(thm),theory(equality)],[94,70]),
[iquote('0:Res:94.0,70.0')] ).
cnf(296,plain,
( ~ ilf_type(skc6,binary_relation_type)
| ~ member(u,range_of(skc6))
| member(u,skc5) ),
inference(res,[status(thm),theory(equality)],[80,93]),
[iquote('0:Res:80.2,93.0')] ).
cnf(310,plain,
( ~ ilf_type(skc6,binary_relation_type)
| subset(range_of(skc6),u)
| member(skf18(u,range_of(skc6)),skc5) ),
inference(res,[status(thm),theory(equality)],[69,296]),
[iquote('0:Res:69.1,296.1')] ).
cnf(352,plain,
( ~ ilf_type(skc6,binary_relation_type)
| ~ member(u,domain_of(skc6))
| member(u,skc4) ),
inference(res,[status(thm),theory(equality)],[81,92]),
[iquote('0:Res:81.2,92.0')] ).
cnf(367,plain,
( ~ ilf_type(skc6,binary_relation_type)
| subset(domain_of(skc6),u)
| member(skf18(u,domain_of(skc6)),skc4) ),
inference(res,[status(thm),theory(equality)],[69,352]),
[iquote('0:Res:69.1,352.1')] ).
cnf(32419,plain,
( ~ ilf_type(skc6,binary_relation_type)
| subset(range_of(skc6),skc5)
| subset(range_of(skc6),skc5) ),
inference(res,[status(thm),theory(equality)],[310,72]),
[iquote('0:Res:310.2,72.0')] ).
cnf(32421,plain,
( ~ ilf_type(skc6,binary_relation_type)
| subset(range_of(skc6),skc5) ),
inference(obv,[status(thm),theory(equality)],[32419]),
[iquote('0:Obv:32419.1')] ).
cnf(32437,plain,
( ~ ilf_type(skc6,binary_relation_type)
| ~ subset(domain_of(skc6),skc4) ),
inference(res,[status(thm),theory(equality)],[32421,23]),
[iquote('0:Res:32421.1,23.0')] ).
cnf(32454,plain,
( ~ ilf_type(skc6,binary_relation_type)
| subset(domain_of(skc6),skc4)
| subset(domain_of(skc6),skc4) ),
inference(res,[status(thm),theory(equality)],[367,72]),
[iquote('0:Res:367.2,72.0')] ).
cnf(32456,plain,
( ~ ilf_type(skc6,binary_relation_type)
| subset(domain_of(skc6),skc4) ),
inference(obv,[status(thm),theory(equality)],[32454]),
[iquote('0:Obv:32454.1')] ).
cnf(32457,plain,
~ ilf_type(skc6,binary_relation_type),
inference(mrr,[status(thm)],[32456,32437]),
[iquote('0:MRR:32456.1,32437.1')] ).
cnf(32458,plain,
~ relation_like(skc6),
inference(res,[status(thm),theory(equality)],[64,32457]),
[iquote('0:Res:64.1,32457.0')] ).
cnf(32459,plain,
$false,
inference(ssi,[status(thm)],[32458,101]),
[iquote('0:SSi:32458.0,101.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET650+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 08:43:32 EDT 2022
% 0.12/0.34 % CPUTime :
% 77.39/77.58
% 77.39/77.58 SPASS V 3.9
% 77.39/77.58 SPASS beiseite: Proof found.
% 77.39/77.58 % SZS status Theorem
% 77.39/77.58 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 77.39/77.58 SPASS derived 31061 clauses, backtracked 402 clauses, performed 20 splits and kept 21351 clauses.
% 77.39/77.58 SPASS allocated 139339 KBytes.
% 77.39/77.58 SPASS spent 0:1:15.55 on the problem.
% 77.39/77.58 0:00:00.03 for the input.
% 77.39/77.58 0:00:00.04 for the FLOTTER CNF translation.
% 77.39/77.58 0:00:00.58 for inferences.
% 77.39/77.58 0:00:01.30 for the backtracking.
% 77.39/77.58 0:1:13.08 for the reduction.
% 77.39/77.58
% 77.39/77.58
% 77.39/77.58 Here is a proof with depth 5, length 37 :
% 77.39/77.58 % SZS output start Refutation
% See solution above
% 77.39/77.58 Formulae used in the proof : p26 prove_relset_1_12 p13 p10 p23 p8 p6 p4 p3
% 77.39/77.58
%------------------------------------------------------------------------------