TSTP Solution File: SEU023+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU023+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 14:33:36 EDT 2022
% Result : Theorem 0.47s 0.64s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 22 ( 9 unt; 0 nHn; 22 RR)
% Number of literals : 73 ( 0 equ; 59 neg)
% Maximal clause size : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
one_to_one(skc10),
file('SEU023+1.p',unknown),
[] ).
cnf(2,axiom,
function(skc10),
file('SEU023+1.p',unknown),
[] ).
cnf(3,axiom,
relation(skc10),
file('SEU023+1.p',unknown),
[] ).
cnf(28,axiom,
in(skc11,relation_dom(skc10)),
file('SEU023+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ function(u)
| ~ relation(u)
| relation(function_inverse(u)) ),
file('SEU023+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ function(u)
| ~ relation(u)
| function(function_inverse(u)) ),
file('SEU023+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ equal(apply(function_inverse(skc10),apply(skc10,skc11)),skc11)
| ~ equal(apply(relation_composition(skc10,function_inverse(skc10)),skc11),skc11) ),
file('SEU023+1.p',unknown),
[] ).
cnf(70,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('SEU023+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ function(u)
| ~ relation(u)
| ~ one_to_one(v)
| ~ function(v)
| ~ relation(v)
| ~ in(w,relation_dom(v))
| ~ equal(u,function_inverse(v))
| ~ equal(x,apply(v,w))
| equal(w,apply(u,x)) ),
file('SEU023+1.p',unknown),
[] ).
cnf(87,plain,
( ~ function(skc10)
| relation(function_inverse(skc10)) ),
inference(res,[status(thm),theory(equality)],[3,46]),
[iquote('0:Res:3.0,46.0')] ).
cnf(88,plain,
( ~ function(skc10)
| function(function_inverse(skc10)) ),
inference(res,[status(thm),theory(equality)],[3,47]),
[iquote('0:Res:3.0,47.0')] ).
cnf(142,plain,
relation(function_inverse(skc10)),
inference(mrr,[status(thm)],[87,2]),
[iquote('0:MRR:87.0,2.0')] ).
cnf(143,plain,
function(function_inverse(skc10)),
inference(mrr,[status(thm)],[88,2]),
[iquote('0:MRR:88.0,2.0')] ).
cnf(485,plain,
( ~ relation(skc10)
| ~ function(skc10)
| ~ relation(function_inverse(skc10))
| ~ function(function_inverse(skc10))
| ~ in(skc11,relation_dom(skc10))
| ~ equal(apply(function_inverse(skc10),apply(skc10,skc11)),skc11)
| ~ equal(apply(function_inverse(skc10),apply(skc10,skc11)),skc11) ),
inference(spl,[status(thm),theory(equality)],[70,65]),
[iquote('0:SpL:70.5,65.1')] ).
cnf(488,plain,
( ~ relation(skc10)
| ~ function(skc10)
| ~ relation(function_inverse(skc10))
| ~ function(function_inverse(skc10))
| ~ in(skc11,relation_dom(skc10))
| ~ equal(apply(function_inverse(skc10),apply(skc10,skc11)),skc11) ),
inference(obv,[status(thm),theory(equality)],[485]),
[iquote('0:Obv:485.5')] ).
cnf(489,plain,
( ~ in(skc11,relation_dom(skc10))
| ~ equal(apply(function_inverse(skc10),apply(skc10,skc11)),skc11) ),
inference(ssi,[status(thm)],[488,143,142,1,2,3]),
[iquote('0:SSi:488.3,488.2,488.1,488.0,143.0,142.0,143.0,142.0,1.0,2.0,3.0,1.0,2.0,3.0')] ).
cnf(490,plain,
~ equal(apply(function_inverse(skc10),apply(skc10,skc11)),skc11),
inference(mrr,[status(thm)],[489,28]),
[iquote('0:MRR:489.0,28.0')] ).
cnf(551,plain,
( ~ function(u)
| ~ relation(u)
| ~ one_to_one(v)
| ~ function(v)
| ~ relation(v)
| ~ in(w,relation_dom(v))
| ~ equal(u,function_inverse(v))
| equal(apply(u,apply(v,w)),w) ),
inference(eqr,[status(thm),theory(equality)],[72]),
[iquote('0:EqR:72.7')] ).
cnf(1192,plain,
( ~ function(function_inverse(skc10))
| ~ relation(function_inverse(skc10))
| ~ one_to_one(skc10)
| ~ function(skc10)
| ~ relation(skc10)
| ~ in(skc11,relation_dom(skc10))
| ~ equal(function_inverse(skc10),function_inverse(skc10))
| ~ equal(skc11,skc11) ),
inference(spl,[status(thm),theory(equality)],[551,490]),
[iquote('0:SpL:551.7,490.0')] ).
cnf(1197,plain,
( ~ function(function_inverse(skc10))
| ~ relation(function_inverse(skc10))
| ~ one_to_one(skc10)
| ~ function(skc10)
| ~ relation(skc10)
| ~ in(skc11,relation_dom(skc10)) ),
inference(obv,[status(thm),theory(equality)],[1192]),
[iquote('0:Obv:1192.7')] ).
cnf(1198,plain,
~ in(skc11,relation_dom(skc10)),
inference(ssi,[status(thm)],[1197,1,2,3,143,142]),
[iquote('0:SSi:1197.4,1197.3,1197.2,1197.1,1197.0,1.0,2.0,3.0,1.0,2.0,3.0,1.0,2.0,3.0,143.0,142.0,143.0,142.0')] ).
cnf(1199,plain,
$false,
inference(mrr,[status(thm)],[1198,28]),
[iquote('0:MRR:1198.0,28.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU023+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n020.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 : Sat Jun 18 23:02:48 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.47/0.64
% 0.47/0.64 SPASS V 3.9
% 0.47/0.64 SPASS beiseite: Proof found.
% 0.47/0.64 % SZS status Theorem
% 0.47/0.64 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.64 SPASS derived 949 clauses, backtracked 0 clauses, performed 1 splits and kept 557 clauses.
% 0.47/0.64 SPASS allocated 98881 KBytes.
% 0.47/0.64 SPASS spent 0:00:00.28 on the problem.
% 0.47/0.64 0:00:00.03 for the input.
% 0.47/0.64 0:00:00.05 for the FLOTTER CNF translation.
% 0.47/0.64 0:00:00.02 for inferences.
% 0.47/0.64 0:00:00.00 for the backtracking.
% 0.47/0.64 0:00:00.14 for the reduction.
% 0.47/0.64
% 0.47/0.64
% 0.47/0.64 Here is a proof with depth 2, length 22 :
% 0.47/0.64 % SZS output start Refutation
% See solution above
% 0.47/0.64 Formulae used in the proof : t56_funct_1 dt_k2_funct_1 t23_funct_1 t54_funct_1
% 0.47/0.64
%------------------------------------------------------------------------------