TSTP Solution File: SEU225+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU225+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 14:35:14 EDT 2022
% Result : Theorem 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 31 ( 10 unt; 4 nHn; 31 RR)
% Number of literals : 79 ( 0 equ; 48 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 : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc11),
file('SEU225+3.p',unknown),
[] ).
cnf(2,axiom,
function(skc11),
file('SEU225+3.p',unknown),
[] ).
cnf(23,axiom,
in(skc12,skc13),
file('SEU225+3.p',unknown),
[] ).
cnf(45,axiom,
( ~ relation(u)
| relation(relation_dom_restriction(u,v)) ),
file('SEU225+3.p',unknown),
[] ).
cnf(54,axiom,
~ equal(apply(relation_dom_restriction(skc11,skc13),skc12),apply(skc11,skc12)),
file('SEU225+3.p',unknown),
[] ).
cnf(60,axiom,
( ~ relation(u)
| ~ function(u)
| function(relation_dom_restriction(u,v)) ),
file('SEU225+3.p',unknown),
[] ).
cnf(65,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,relation_dom(relation_dom_restriction(u,w)))
| in(v,relation_dom(u)) ),
file('SEU225+3.p',unknown),
[] ).
cnf(67,axiom,
( ~ function(u)
| ~ relation(u)
| ~ equal(v,empty_set)
| in(w,relation_dom(u))
| equal(v,apply(u,w)) ),
file('SEU225+3.p',unknown),
[] ).
cnf(68,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,w)
| ~ in(v,relation_dom(u))
| in(v,relation_dom(relation_dom_restriction(u,w))) ),
file('SEU225+3.p',unknown),
[] ).
cnf(72,axiom,
( ~ relation(u)
| ~ function(u)
| ~ relation(v)
| ~ function(v)
| ~ in(w,relation_dom(u))
| ~ equal(u,relation_dom_restriction(v,x))
| equal(apply(u,w),apply(v,w)) ),
file('SEU225+3.p',unknown),
[] ).
cnf(85,plain,
( ~ relation(skc11)
| ~ equal(u,empty_set)
| equal(u,apply(skc11,v))
| in(v,relation_dom(skc11)) ),
inference(res,[status(thm),theory(equality)],[2,67]),
[iquote('0:Res:2.0,67.1')] ).
cnf(86,plain,
( ~ relation(skc11)
| ~ in(u,relation_dom(relation_dom_restriction(skc11,v)))
| in(u,relation_dom(skc11)) ),
inference(res,[status(thm),theory(equality)],[2,65]),
[iquote('0:Res:2.0,65.1')] ).
cnf(88,plain,
( ~ relation(skc11)
| function(relation_dom_restriction(skc11,u)) ),
inference(res,[status(thm),theory(equality)],[2,60]),
[iquote('0:Res:2.0,60.0')] ).
cnf(108,plain,
relation(relation_dom_restriction(skc11,u)),
inference(res,[status(thm),theory(equality)],[1,45]),
[iquote('0:Res:1.0,45.0')] ).
cnf(116,plain,
( ~ function(u)
| ~ relation(u)
| ~ in(skc12,relation_dom(u))
| in(skc12,relation_dom(relation_dom_restriction(u,skc13))) ),
inference(res,[status(thm),theory(equality)],[23,68]),
[iquote('0:Res:23.0,68.2')] ).
cnf(123,plain,
( ~ function(skc11)
| ~ relation(skc11)
| ~ function(relation_dom_restriction(skc11,skc13))
| ~ relation(relation_dom_restriction(skc11,skc13))
| ~ in(skc12,relation_dom(relation_dom_restriction(skc11,skc13)))
| ~ equal(relation_dom_restriction(skc11,skc13),relation_dom_restriction(skc11,u)) ),
inference(res,[status(thm),theory(equality)],[72,54]),
[iquote('0:Res:72.6,54.0')] ).
cnf(128,plain,
( ~ relation(relation_dom_restriction(skc11,skc13))
| ~ function(relation_dom_restriction(skc11,skc13))
| ~ equal(apply(skc11,skc12),empty_set)
| in(skc12,relation_dom(relation_dom_restriction(skc11,skc13))) ),
inference(res,[status(thm),theory(equality)],[67,54]),
[iquote('0:Res:67.3,54.0')] ).
cnf(129,plain,
function(relation_dom_restriction(skc11,u)),
inference(mrr,[status(thm)],[88,1]),
[iquote('0:MRR:88.0,1.0')] ).
cnf(131,plain,
( ~ in(u,relation_dom(relation_dom_restriction(skc11,v)))
| in(u,relation_dom(skc11)) ),
inference(mrr,[status(thm)],[86,1]),
[iquote('0:MRR:86.0,1.0')] ).
cnf(133,plain,
( ~ equal(u,empty_set)
| in(v,relation_dom(skc11))
| equal(u,apply(skc11,v)) ),
inference(mrr,[status(thm)],[85,1]),
[iquote('0:MRR:85.0,1.0')] ).
cnf(138,plain,
( ~ equal(apply(skc11,skc12),empty_set)
| in(skc12,relation_dom(relation_dom_restriction(skc11,skc13))) ),
inference(mrr,[status(thm)],[128,108,129]),
[iquote('0:MRR:128.0,128.1,108.0,129.0')] ).
cnf(147,plain,
( ~ in(skc12,relation_dom(relation_dom_restriction(skc11,skc13)))
| ~ equal(relation_dom_restriction(skc11,skc13),relation_dom_restriction(skc11,u)) ),
inference(mrr,[status(thm)],[123,2,1,129,108]),
[iquote('0:MRR:123.0,123.1,123.2,123.3,2.0,1.0,129.0,108.0')] ).
cnf(158,plain,
( ~ function(skc11)
| ~ in(skc12,relation_dom(skc11))
| in(skc12,relation_dom(relation_dom_restriction(skc11,skc13))) ),
inference(res,[status(thm),theory(equality)],[1,116]),
[iquote('0:Res:1.0,116.0')] ).
cnf(172,plain,
( ~ in(skc12,relation_dom(skc11))
| in(skc12,relation_dom(relation_dom_restriction(skc11,skc13))) ),
inference(mrr,[status(thm)],[158,2]),
[iquote('0:MRR:158.0,2.0')] ).
cnf(735,plain,
( ~ equal(apply(skc11,skc12),empty_set)
| in(skc12,relation_dom(skc11)) ),
inference(res,[status(thm),theory(equality)],[138,131]),
[iquote('0:Res:138.1,131.0')] ).
cnf(887,plain,
( in(u,relation_dom(skc11))
| equal(apply(skc11,u),empty_set) ),
inference(eqr,[status(thm),theory(equality)],[133]),
[iquote('0:EqR:133.0')] ).
cnf(889,plain,
( ~ equal(empty_set,empty_set)
| in(skc12,relation_dom(skc11)) ),
inference(rew,[status(thm),theory(equality)],[887,735]),
[iquote('0:Rew:887.1,735.0')] ).
cnf(891,plain,
in(skc12,relation_dom(skc11)),
inference(obv,[status(thm),theory(equality)],[889]),
[iquote('0:Obv:889.0')] ).
cnf(892,plain,
in(skc12,relation_dom(relation_dom_restriction(skc11,skc13))),
inference(mrr,[status(thm)],[172,891]),
[iquote('0:MRR:172.0,891.0')] ).
cnf(897,plain,
~ equal(relation_dom_restriction(skc11,skc13),relation_dom_restriction(skc11,u)),
inference(mrr,[status(thm)],[147,892]),
[iquote('0:MRR:147.0,892.0')] ).
cnf(899,plain,
$false,
inference(obv,[status(thm),theory(equality)],[897]),
[iquote('0:Obv:897.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU225+3 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n029.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 : Mon Jun 20 06:52:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.51
% 0.19/0.51 SPASS V 3.9
% 0.19/0.51 SPASS beiseite: Proof found.
% 0.19/0.51 % SZS status Theorem
% 0.19/0.51 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.51 SPASS derived 659 clauses, backtracked 0 clauses, performed 1 splits and kept 385 clauses.
% 0.19/0.51 SPASS allocated 98444 KBytes.
% 0.19/0.51 SPASS spent 0:00:00.17 on the problem.
% 0.19/0.51 0:00:00.04 for the input.
% 0.19/0.51 0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.51 0:00:00.01 for inferences.
% 0.19/0.51 0:00:00.00 for the backtracking.
% 0.19/0.51 0:00:00.05 for the reduction.
% 0.19/0.51
% 0.19/0.51
% 0.19/0.51 Here is a proof with depth 2, length 31 :
% 0.19/0.51 % SZS output start Refutation
% See solution above
% 0.19/0.51 Formulae used in the proof : t72_funct_1 dt_k7_relat_1 fc4_funct_1 l82_funct_1 d4_funct_1 t68_funct_1
% 0.19/0.51
%------------------------------------------------------------------------------