%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU220+1 : TPTP v8.1.0. Released v3.3.0.
% 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 14:35:09 EDT 2022
% Result : Theorem 0.49s 0.66s
% Output : Refutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 30 ( 9 unt; 0 nHn; 30 RR)
% Number of literals : 94 ( 0 equ; 72 neg)
% Maximal clause size : 7 ( 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+1.p',unknown),
[] ).
cnf(2,axiom,
function(skc10),
file('SEU220+1.p',unknown),
[] ).
cnf(3,axiom,
relation(skc10),
file('SEU220+1.p',unknown),
[] ).
cnf(26,axiom,
in(skc11,relation_rng(skc10)),
file('SEU220+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ function(u)
| ~ relation(u)
| relation(function_inverse(u)) ),
file('SEU220+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ function(u)
| ~ relation(u)
| function(function_inverse(u)) ),
file('SEU220+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ one_to_one(u)
| ~ function(u)
| ~ relation(u)
| equal(relation_dom(function_inverse(u)),relation_rng(u)) ),
file('SEU220+1.p',unknown),
[] ).
cnf(57,axiom,
( ~ equal(apply(skc10,apply(function_inverse(skc10),skc11)),skc11)
| ~ equal(apply(relation_composition(function_inverse(skc10),skc10),skc11),skc11) ),
file('SEU220+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ in(u,relation_rng(v))
| ~ equal(w,apply(x,u))
| ~ skP0(x,w,v,u)
| equal(u,apply(v,w)) ),
file('SEU220+1.p',unknown),
[] ).
cnf(60,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+1.p',unknown),
[] ).
cnf(62,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+1.p',unknown),
[] ).
cnf(78,plain,
( ~ function(skc10)
| ~ one_to_one(skc10)
| equal(relation_dom(function_inverse(skc10)),relation_rng(skc10)) ),
inference(res,[status(thm),theory(equality)],[3,52]),
[iquote('0:Res:3.0,52.0')] ).
cnf(81,plain,
( ~ function(skc10)
| relation(function_inverse(skc10)) ),
inference(res,[status(thm),theory(equality)],[3,38]),
[iquote('0:Res:3.0,38.0')] ).
cnf(82,plain,
( ~ function(skc10)
| function(function_inverse(skc10)) ),
inference(res,[status(thm),theory(equality)],[3,39]),
[iquote('0:Res:3.0,39.0')] ).
cnf(127,plain,
( ~ relation(skc10)
| ~ function(skc10)
| ~ relation(u)
| ~ function(u)
| ~ equal(u,function_inverse(skc10))
| skP0(u,v,skc10,w) ),
inference(res,[status(thm),theory(equality)],[1,60]),
[iquote('0:Res:1.0,60.2')] ).
cnf(130,plain,
( ~ equal(u,apply(v,skc11))
| ~ skP0(v,u,skc10,skc11)
| equal(apply(skc10,u),skc11) ),
inference(res,[status(thm),theory(equality)],[26,59]),
[iquote('0:Res:26.0,59.1')] ).
cnf(136,plain,
relation(function_inverse(skc10)),
inference(mrr,[status(thm)],[81,2]),
[iquote('0:MRR:81.0,2.0')] ).
cnf(137,plain,
function(function_inverse(skc10)),
inference(mrr,[status(thm)],[82,2]),
[iquote('0:MRR:82.0,2.0')] ).
cnf(138,plain,
equal(relation_dom(function_inverse(skc10)),relation_rng(skc10)),
inference(mrr,[status(thm)],[78,2,1]),
[iquote('0:MRR:78.0,78.1,2.0,1.0')] ).
cnf(142,plain,
( ~ function(u)
| ~ relation(u)
| ~ equal(u,function_inverse(skc10))
| skP0(u,v,skc10,w) ),
inference(mrr,[status(thm)],[127,3,2]),
[iquote('0:MRR:127.0,127.1,3.0,2.0')] ).
cnf(445,plain,
( ~ function(u)
| ~ relation(u)
| ~ equal(u,function_inverse(skc10))
| ~ equal(v,apply(u,skc11))
| equal(apply(skc10,v),skc11) ),
inference(res,[status(thm),theory(equality)],[142,130]),
[iquote('0:Res:142.3,130.1')] ).
cnf(554,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)],[62,57]),
[iquote('0:SpL:62.5,57.1')] ).
cnf(563,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)],[554]),
[iquote('0:Obv:554.5')] ).
cnf(564,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)],[138,563]),
[iquote('0:Rew:138.0,563.4')] ).
cnf(565,plain,
( ~ in(skc11,relation_rng(skc10))
| ~ equal(apply(skc10,apply(function_inverse(skc10),skc11)),skc11) ),
inference(ssi,[status(thm)],[564,1,2,3,137,136]),
[iquote('0:SSi:564.3,564.2,564.1,564.0,1.0,2.0,3.0,1.0,2.0,3.0,137.0,136.0,137.0,136.0')] ).
cnf(566,plain,
~ equal(apply(skc10,apply(function_inverse(skc10),skc11)),skc11),
inference(mrr,[status(thm)],[565,26]),
[iquote('0:MRR:565.0,26.0')] ).
cnf(1234,plain,
( ~ function(u)
| ~ relation(u)
| ~ equal(u,function_inverse(skc10))
| equal(apply(skc10,apply(u,skc11)),skc11) ),
inference(eqr,[status(thm),theory(equality)],[445]),
[iquote('0:EqR:445.3')] ).
cnf(1345,plain,
( ~ function(function_inverse(skc10))
| ~ relation(function_inverse(skc10))
| ~ equal(function_inverse(skc10),function_inverse(skc10))
| ~ equal(skc11,skc11) ),
inference(spl,[status(thm),theory(equality)],[1234,566]),
[iquote('0:SpL:1234.3,566.0')] ).
cnf(1349,plain,
( ~ function(function_inverse(skc10))
| ~ relation(function_inverse(skc10)) ),
inference(obv,[status(thm),theory(equality)],[1345]),
[iquote('0:Obv:1345.3')] ).
cnf(1350,plain,
$false,
inference(ssi,[status(thm)],[1349,137,136]),
[iquote('0:SSi:1349.1,1349.0,137.0,136.0,137.0,136.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU220+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n021.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 Jun 20 01:30:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.49/0.66
% 0.49/0.66 SPASS V 3.9
% 0.49/0.66 SPASS beiseite: Proof found.
% 0.49/0.66 % SZS status Theorem
% 0.49/0.66 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.49/0.66 SPASS derived 899 clauses, backtracked 0 clauses, performed 1 splits and kept 352 clauses.
% 0.49/0.66 SPASS allocated 99101 KBytes.
% 0.49/0.66 SPASS spent 0:00:00.29 on the problem.
% 0.49/0.66 0:00:00.03 for the input.
% 0.49/0.66 0:00:00.05 for the FLOTTER CNF translation.
% 0.49/0.66 0:00:00.02 for inferences.
% 0.49/0.66 0:00:00.00 for the backtracking.
% 0.49/0.66 0:00:00.16 for the reduction.
% 0.49/0.66
% 0.49/0.66
% 0.49/0.66 Here is a proof with depth 4, length 30 :
% 0.49/0.66 % SZS output start Refutation
% See solution above
% 0.49/0.66 Formulae used in the proof : t57_funct_1 dt_k2_funct_1 t55_funct_1 t54_funct_1 t23_funct_1
% 0.49/0.66
%------------------------------------------------------------------------------