TSTP Solution File: SET677+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET677+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 05:28:02 EDT 2022
% Result : Theorem 0.21s 0.49s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 28 ( 12 unt; 0 nHn; 28 RR)
% Number of literals : 64 ( 0 equ; 39 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
ilf_type(u,set_type),
file('SET677+3.p',unknown),
[] ).
cnf(4,axiom,
ilf_type(skc4,identity_relation_of_type(skc3)),
file('SET677+3.p',unknown),
[] ).
cnf(5,axiom,
subset(identity_relation_of(skc3),skc4),
file('SET677+3.p',unknown),
[] ).
cnf(31,axiom,
( ~ equal(range__dfg(skc3,skc3,skc4),skc3)
| ~ equal(domain__dfg(skc3,skc3,skc4),skc3) ),
file('SET677+3.p',unknown),
[] ).
cnf(40,axiom,
( ~ ilf_type(u,identity_relation_of_type(v))
| ~ ilf_type(v,set_type)
| ~ ilf_type(u,set_type)
| ilf_type(u,relation_type(v,v)) ),
file('SET677+3.p',unknown),
[] ).
cnf(52,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,relation_type(u,v))
| equal(range__dfg(u,v,w),range_of(w)) ),
file('SET677+3.p',unknown),
[] ).
cnf(54,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,relation_type(u,v))
| equal(domain__dfg(u,v,w),domain_of(w)) ),
file('SET677+3.p',unknown),
[] ).
cnf(62,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,relation_type(u,v))
| ~ subset(identity_relation_of(v),w)
| equal(range__dfg(u,v,w),v) ),
file('SET677+3.p',unknown),
[] ).
cnf(65,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,relation_type(v,u))
| ~ subset(identity_relation_of(v),w)
| equal(domain__dfg(v,u,w),v) ),
file('SET677+3.p',unknown),
[] ).
cnf(92,plain,
( ~ ilf_type(u,identity_relation_of_type(v))
| ilf_type(u,relation_type(v,v)) ),
inference(mrr,[status(thm)],[40,3]),
[iquote('0:MRR:40.1,40.2,3.0,3.0')] ).
cnf(97,plain,
( ~ ilf_type(u,relation_type(v,w))
| equal(range__dfg(v,w,u),range_of(u)) ),
inference(mrr,[status(thm)],[52,3]),
[iquote('0:MRR:52.0,52.1,3.0,3.0')] ).
cnf(100,plain,
( ~ ilf_type(u,relation_type(v,w))
| equal(domain__dfg(v,w,u),domain_of(u)) ),
inference(mrr,[status(thm)],[54,3]),
[iquote('0:MRR:54.0,54.1,3.0,3.0')] ).
cnf(108,plain,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,relation_type(u,v))
| ~ subset(identity_relation_of(v),w)
| equal(range_of(w),v) ),
inference(rew,[status(thm),theory(equality)],[97,62]),
[iquote('0:Rew:97.1,62.4')] ).
cnf(109,plain,
( ~ ilf_type(u,relation_type(v,w))
| ~ subset(identity_relation_of(w),u)
| equal(range_of(u),w) ),
inference(mrr,[status(thm)],[108,3]),
[iquote('0:MRR:108.0,108.1,3.0,3.0')] ).
cnf(114,plain,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,relation_type(v,u))
| ~ subset(identity_relation_of(v),w)
| equal(domain_of(w),v) ),
inference(rew,[status(thm),theory(equality)],[100,65]),
[iquote('0:Rew:100.1,65.4')] ).
cnf(115,plain,
( ~ ilf_type(u,relation_type(v,w))
| ~ subset(identity_relation_of(v),u)
| equal(domain_of(u),v) ),
inference(mrr,[status(thm)],[114,3]),
[iquote('0:MRR:114.0,114.1,3.0,3.0')] ).
cnf(119,plain,
( ~ ilf_type(skc4,relation_type(u,skc3))
| equal(range_of(skc4),skc3) ),
inference(res,[status(thm),theory(equality)],[5,109]),
[iquote('0:Res:5.0,109.1')] ).
cnf(120,plain,
( ~ ilf_type(skc4,relation_type(skc3,u))
| equal(domain_of(skc4),skc3) ),
inference(res,[status(thm),theory(equality)],[5,115]),
[iquote('0:Res:5.0,115.1')] ).
cnf(124,plain,
ilf_type(skc4,relation_type(skc3,skc3)),
inference(res,[status(thm),theory(equality)],[4,92]),
[iquote('0:Res:4.0,92.0')] ).
cnf(146,plain,
equal(domain_of(skc4),skc3),
inference(res,[status(thm),theory(equality)],[124,120]),
[iquote('0:Res:124.0,120.0')] ).
cnf(149,plain,
equal(range_of(skc4),skc3),
inference(res,[status(thm),theory(equality)],[124,119]),
[iquote('0:Res:124.0,119.0')] ).
cnf(289,plain,
equal(range__dfg(skc3,skc3,skc4),range_of(skc4)),
inference(res,[status(thm),theory(equality)],[124,97]),
[iquote('0:Res:124.0,97.0')] ).
cnf(294,plain,
equal(range__dfg(skc3,skc3,skc4),skc3),
inference(rew,[status(thm),theory(equality)],[149,289]),
[iquote('0:Rew:149.0,289.0')] ).
cnf(295,plain,
( ~ equal(skc3,skc3)
| ~ equal(domain__dfg(skc3,skc3,skc4),skc3) ),
inference(rew,[status(thm),theory(equality)],[294,31]),
[iquote('0:Rew:294.0,31.0')] ).
cnf(296,plain,
~ equal(domain__dfg(skc3,skc3,skc4),skc3),
inference(obv,[status(thm),theory(equality)],[295]),
[iquote('0:Obv:295.0')] ).
cnf(305,plain,
equal(domain__dfg(skc3,skc3,skc4),domain_of(skc4)),
inference(res,[status(thm),theory(equality)],[124,100]),
[iquote('0:Res:124.0,100.0')] ).
cnf(311,plain,
equal(domain__dfg(skc3,skc3,skc4),skc3),
inference(rew,[status(thm),theory(equality)],[146,305]),
[iquote('0:Rew:146.0,305.0')] ).
cnf(312,plain,
$false,
inference(mrr,[status(thm)],[311,296]),
[iquote('0:MRR:311.0,296.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET677+3 : TPTP v8.1.0. Released v2.2.0.
% 0.13/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 10 01:26:07 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.21/0.49
% 0.21/0.49 SPASS V 3.9
% 0.21/0.49 SPASS beiseite: Proof found.
% 0.21/0.49 % SZS status Theorem
% 0.21/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.49 SPASS derived 179 clauses, backtracked 0 clauses, performed 0 splits and kept 186 clauses.
% 0.21/0.49 SPASS allocated 97920 KBytes.
% 0.21/0.49 SPASS spent 0:00:00.12 on the problem.
% 0.21/0.49 0:00:00.04 for the input.
% 0.21/0.49 0:00:00.04 for the FLOTTER CNF translation.
% 0.21/0.49 0:00:00.00 for inferences.
% 0.21/0.49 0:00:00.00 for the backtracking.
% 0.21/0.49 0:00:00.02 for the reduction.
% 0.21/0.49
% 0.21/0.49
% 0.21/0.49 Here is a proof with depth 2, length 28 :
% 0.21/0.49 % SZS output start Refutation
% See solution above
% 0.21/0.49 Formulae used in the proof : p34 prove_relset_1_44 p5 p32 p30 p2 p1
% 0.21/0.49
%------------------------------------------------------------------------------