TSTP Solution File: SEU220+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU220+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 14:35:10 EDT 2022
% Result : Theorem 1.65s 1.88s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 28 ( 10 unt; 0 nHn; 28 RR)
% Number of literals : 98 ( 0 equ; 79 neg)
% Maximal clause size : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
one_to_one(skc10),
file('SEU220+3.p',unknown),
[] ).
cnf(2,axiom,
function(skc10),
file('SEU220+3.p',unknown),
[] ).
cnf(3,axiom,
relation(skc10),
file('SEU220+3.p',unknown),
[] ).
cnf(28,axiom,
in(skc11,relation_rng(skc10)),
file('SEU220+3.p',unknown),
[] ).
cnf(46,axiom,
( ~ function(u)
| ~ relation(u)
| relation(function_inverse(u)) ),
file('SEU220+3.p',unknown),
[] ).
cnf(47,axiom,
( ~ function(u)
| ~ relation(u)
| function(function_inverse(u)) ),
file('SEU220+3.p',unknown),
[] ).
cnf(62,axiom,
( ~ one_to_one(u)
| ~ function(u)
| ~ relation(u)
| equal(relation_dom(function_inverse(u)),relation_rng(u)) ),
file('SEU220+3.p',unknown),
[] ).
cnf(67,axiom,
( ~ equal(apply(skc10,apply(function_inverse(skc10),skc11)),skc11)
| ~ equal(apply(relation_composition(function_inverse(skc10),skc10),skc11),skc11) ),
file('SEU220+3.p',unknown),
[] ).
cnf(69,axiom,
( ~ in(u,relation_rng(v))
| ~ equal(w,apply(x,u))
| ~ skP0(x,w,v,u)
| equal(u,apply(v,w)) ),
file('SEU220+3.p',unknown),
[] ).
cnf(70,axiom,
( ~ function(u)
| ~ relation(u)
| ~ one_to_one(v)
| ~ function(v)
| ~ relation(v)
| ~ equal(u,function_inverse(v))
| skP0(u,w,v,x) ),
file('SEU220+3.p',unknown),
[] ).
cnf(72,axiom,
( ~ relation(u)
| ~ function(u)
| ~ relation(v)
| ~ function(v)
| ~ in(w,relation_dom(u))
| equal(apply(relation_composition(u,v),w),apply(v,apply(u,w))) ),
file('SEU220+3.p',unknown),
[] ).
cnf(88,plain,
( ~ function(skc10)
| ~ one_to_one(skc10)
| equal(relation_dom(function_inverse(skc10)),relation_rng(skc10)) ),
inference(res,[status(thm),theory(equality)],[3,62]),
[iquote('0:Res:3.0,62.0')] ).
cnf(91,plain,
( ~ function(skc10)
| relation(function_inverse(skc10)) ),
inference(res,[status(thm),theory(equality)],[3,46]),
[iquote('0:Res:3.0,46.0')] ).
cnf(92,plain,
( ~ function(skc10)
| function(function_inverse(skc10)) ),
inference(res,[status(thm),theory(equality)],[3,47]),
[iquote('0:Res:3.0,47.0')] ).
cnf(148,plain,
relation(function_inverse(skc10)),
inference(mrr,[status(thm)],[91,2]),
[iquote('0:MRR:91.0,2.0')] ).
cnf(149,plain,
function(function_inverse(skc10)),
inference(mrr,[status(thm)],[92,2]),
[iquote('0:MRR:92.0,2.0')] ).
cnf(150,plain,
equal(relation_dom(function_inverse(skc10)),relation_rng(skc10)),
inference(mrr,[status(thm)],[88,2,1]),
[iquote('0:MRR:88.0,88.1,2.0,1.0')] ).
cnf(580,plain,
( ~ function(u)
| ~ relation(u)
| ~ one_to_one(v)
| ~ function(v)
| ~ relation(v)
| ~ equal(u,function_inverse(v))
| ~ in(w,relation_rng(v))
| ~ equal(x,apply(u,w))
| equal(w,apply(v,x)) ),
inference(res,[status(thm),theory(equality)],[70,69]),
[iquote('0:Res:70.6,69.2')] ).
cnf(615,plain,
( ~ relation(function_inverse(skc10))
| ~ function(function_inverse(skc10))
| ~ relation(skc10)
| ~ function(skc10)
| ~ in(skc11,relation_dom(function_inverse(skc10)))
| ~ equal(apply(skc10,apply(function_inverse(skc10),skc11)),skc11)
| ~ equal(apply(skc10,apply(function_inverse(skc10),skc11)),skc11) ),
inference(spl,[status(thm),theory(equality)],[72,67]),
[iquote('0:SpL:72.5,67.1')] ).
cnf(622,plain,
( ~ relation(function_inverse(skc10))
| ~ function(function_inverse(skc10))
| ~ relation(skc10)
| ~ function(skc10)
| ~ in(skc11,relation_dom(function_inverse(skc10)))
| ~ equal(apply(skc10,apply(function_inverse(skc10),skc11)),skc11) ),
inference(obv,[status(thm),theory(equality)],[615]),
[iquote('0:Obv:615.5')] ).
cnf(623,plain,
( ~ relation(function_inverse(skc10))
| ~ function(function_inverse(skc10))
| ~ relation(skc10)
| ~ function(skc10)
| ~ in(skc11,relation_rng(skc10))
| ~ equal(apply(skc10,apply(function_inverse(skc10),skc11)),skc11) ),
inference(rew,[status(thm),theory(equality)],[150,622]),
[iquote('0:Rew:150.0,622.4')] ).
cnf(624,plain,
( ~ in(skc11,relation_rng(skc10))
| ~ equal(apply(skc10,apply(function_inverse(skc10),skc11)),skc11) ),
inference(ssi,[status(thm)],[623,1,2,3,149,148]),
[iquote('0:SSi:623.3,623.2,623.1,623.0,1.0,2.0,3.0,1.0,2.0,3.0,149.0,148.0,149.0,148.0')] ).
cnf(625,plain,
~ equal(apply(skc10,apply(function_inverse(skc10),skc11)),skc11),
inference(mrr,[status(thm)],[624,28]),
[iquote('0:MRR:624.0,28.0')] ).
cnf(1714,plain,
( ~ function(u)
| ~ relation(u)
| ~ one_to_one(v)
| ~ function(v)
| ~ relation(v)
| ~ equal(u,function_inverse(v))
| ~ in(w,relation_rng(v))
| equal(apply(v,apply(u,w)),w) ),
inference(eqr,[status(thm),theory(equality)],[580]),
[iquote('0:EqR:580.7')] ).
cnf(4432,plain,
( ~ function(function_inverse(skc10))
| ~ relation(function_inverse(skc10))
| ~ one_to_one(skc10)
| ~ function(skc10)
| ~ relation(skc10)
| ~ equal(function_inverse(skc10),function_inverse(skc10))
| ~ in(skc11,relation_rng(skc10))
| ~ equal(skc11,skc11) ),
inference(spl,[status(thm),theory(equality)],[1714,625]),
[iquote('0:SpL:1714.7,625.0')] ).
cnf(4443,plain,
( ~ function(function_inverse(skc10))
| ~ relation(function_inverse(skc10))
| ~ one_to_one(skc10)
| ~ function(skc10)
| ~ relation(skc10)
| ~ in(skc11,relation_rng(skc10)) ),
inference(obv,[status(thm),theory(equality)],[4432]),
[iquote('0:Obv:4432.7')] ).
cnf(4444,plain,
~ in(skc11,relation_rng(skc10)),
inference(ssi,[status(thm)],[4443,1,2,3,149,148]),
[iquote('0:SSi:4443.4,4443.3,4443.2,4443.1,4443.0,1.0,2.0,3.0,1.0,2.0,3.0,1.0,2.0,3.0,149.0,148.0,149.0,148.0')] ).
cnf(4445,plain,
$false,
inference(mrr,[status(thm)],[4444,28]),
[iquote('0:MRR:4444.0,28.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU220+3 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n019.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 Jun 19 03:15:09 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.65/1.88
% 1.65/1.88 SPASS V 3.9
% 1.65/1.88 SPASS beiseite: Proof found.
% 1.65/1.88 % SZS status Theorem
% 1.65/1.88 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.65/1.88 SPASS derived 3453 clauses, backtracked 0 clauses, performed 1 splits and kept 1804 clauses.
% 1.65/1.88 SPASS allocated 102681 KBytes.
% 1.65/1.88 SPASS spent 0:00:01.45 on the problem.
% 1.65/1.88 0:00:00.03 for the input.
% 1.65/1.88 0:00:00.05 for the FLOTTER CNF translation.
% 1.65/1.88 0:00:00.06 for inferences.
% 1.65/1.88 0:00:00.00 for the backtracking.
% 1.65/1.88 0:00:01.25 for the reduction.
% 1.65/1.88
% 1.65/1.88
% 1.65/1.88 Here is a proof with depth 3, length 28 :
% 1.65/1.88 % SZS output start Refutation
% See solution above
% 1.65/1.88 Formulae used in the proof : t57_funct_1 dt_k2_funct_1 t55_funct_1 t54_funct_1 t23_funct_1
% 1.65/1.88
%------------------------------------------------------------------------------