TSTP Solution File: SEU221+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU221+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 0.18s 0.54s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of clauses : 40 ( 9 unt; 15 nHn; 40 RR)
% Number of literals : 134 ( 0 equ; 80 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc9),
file('SEU221+1.p',unknown),
[] ).
cnf(2,axiom,
function(skc9),
file('SEU221+1.p',unknown),
[] ).
cnf(3,axiom,
one_to_one(skc9),
file('SEU221+1.p',unknown),
[] ).
cnf(26,axiom,
~ one_to_one(function_inverse(skc9)),
file('SEU221+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ function(u)
| ~ relation(u)
| relation(function_inverse(u)) ),
file('SEU221+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ function(u)
| ~ relation(u)
| function(function_inverse(u)) ),
file('SEU221+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ function(u)
| ~ relation(u)
| one_to_one(u)
| in(skf8(u),relation_dom(u)) ),
file('SEU221+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ function(u)
| ~ relation(u)
| one_to_one(u)
| in(skf7(u),relation_dom(u)) ),
file('SEU221+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ function(u)
| ~ relation(u)
| ~ equal(skf8(u),skf7(u))
| one_to_one(u) ),
file('SEU221+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ function(u)
| ~ relation(u)
| one_to_one(u)
| equal(apply(u,skf8(u)),apply(u,skf7(u))) ),
file('SEU221+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ relation(u)
| ~ function(u)
| ~ one_to_one(u)
| ~ in(v,relation_rng(u))
| equal(apply(u,apply(function_inverse(u),v)),v) ),
file('SEU221+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ function(u)
| ~ relation(u)
| ~ one_to_one(v)
| ~ function(v)
| ~ relation(v)
| ~ equal(u,function_inverse(v))
| equal(relation_dom(u),relation_rng(v)) ),
file('SEU221+1.p',unknown),
[] ).
cnf(80,plain,
( ~ function(skc9)
| ~ relation(skc9)
| ~ in(u,relation_rng(skc9))
| equal(apply(skc9,apply(function_inverse(skc9),u)),u) ),
inference(res,[status(thm),theory(equality)],[3,61]),
[iquote('0:Res:3.0,61.0')] ).
cnf(97,plain,
( ~ relation(skc9)
| relation(function_inverse(skc9)) ),
inference(res,[status(thm),theory(equality)],[2,38]),
[iquote('0:Res:2.0,38.1')] ).
cnf(98,plain,
( ~ relation(skc9)
| function(function_inverse(skc9)) ),
inference(res,[status(thm),theory(equality)],[2,39]),
[iquote('0:Res:2.0,39.1')] ).
cnf(113,plain,
( ~ function(skc9)
| ~ one_to_one(skc9)
| ~ relation(u)
| ~ function(u)
| ~ equal(u,function_inverse(skc9))
| equal(relation_dom(u),relation_rng(skc9)) ),
inference(res,[status(thm),theory(equality)],[1,64]),
[iquote('0:Res:1.0,64.0')] ).
cnf(140,plain,
relation(function_inverse(skc9)),
inference(mrr,[status(thm)],[97,1]),
[iquote('0:MRR:97.0,1.0')] ).
cnf(141,plain,
function(function_inverse(skc9)),
inference(mrr,[status(thm)],[98,1]),
[iquote('0:MRR:98.0,1.0')] ).
cnf(144,plain,
( ~ in(u,relation_rng(skc9))
| equal(apply(skc9,apply(function_inverse(skc9),u)),u) ),
inference(mrr,[status(thm)],[80,2,1]),
[iquote('0:MRR:80.0,80.1,2.0,1.0')] ).
cnf(149,plain,
( ~ function(u)
| ~ relation(u)
| ~ equal(u,function_inverse(skc9))
| equal(relation_dom(u),relation_rng(skc9)) ),
inference(mrr,[status(thm)],[113,2,3]),
[iquote('0:MRR:113.0,113.1,2.0,3.0')] ).
cnf(292,plain,
( ~ function(u)
| ~ relation(u)
| ~ function(u)
| ~ relation(u)
| ~ equal(u,function_inverse(skc9))
| one_to_one(u)
| in(skf7(u),relation_rng(skc9)) ),
inference(spr,[status(thm),theory(equality)],[149,53]),
[iquote('0:SpR:149.3,53.3')] ).
cnf(293,plain,
( ~ function(u)
| ~ relation(u)
| ~ function(u)
| ~ relation(u)
| ~ equal(u,function_inverse(skc9))
| one_to_one(u)
| in(skf8(u),relation_rng(skc9)) ),
inference(spr,[status(thm),theory(equality)],[149,52]),
[iquote('0:SpR:149.3,52.3')] ).
cnf(303,plain,
( ~ function(u)
| ~ relation(u)
| ~ equal(u,function_inverse(skc9))
| one_to_one(u)
| in(skf8(u),relation_rng(skc9)) ),
inference(obv,[status(thm),theory(equality)],[293]),
[iquote('0:Obv:293.1')] ).
cnf(304,plain,
( ~ function(u)
| ~ relation(u)
| ~ equal(u,function_inverse(skc9))
| one_to_one(u)
| in(skf7(u),relation_rng(skc9)) ),
inference(obv,[status(thm),theory(equality)],[292]),
[iquote('0:Obv:292.1')] ).
cnf(327,plain,
( ~ function(function_inverse(skc9))
| ~ relation(function_inverse(skc9))
| ~ in(skf8(function_inverse(skc9)),relation_rng(skc9))
| one_to_one(function_inverse(skc9))
| equal(apply(skc9,apply(function_inverse(skc9),skf7(function_inverse(skc9)))),skf8(function_inverse(skc9))) ),
inference(spr,[status(thm),theory(equality)],[58,144]),
[iquote('0:SpR:58.3,144.1')] ).
cnf(329,plain,
( ~ in(skf8(function_inverse(skc9)),relation_rng(skc9))
| one_to_one(function_inverse(skc9))
| equal(apply(skc9,apply(function_inverse(skc9),skf7(function_inverse(skc9)))),skf8(function_inverse(skc9))) ),
inference(ssi,[status(thm)],[327,141,140]),
[iquote('0:SSi:327.1,327.0,141.0,140.0,141.0,140.0')] ).
cnf(330,plain,
( ~ in(skf8(function_inverse(skc9)),relation_rng(skc9))
| equal(apply(skc9,apply(function_inverse(skc9),skf7(function_inverse(skc9)))),skf8(function_inverse(skc9))) ),
inference(mrr,[status(thm)],[329,26]),
[iquote('0:MRR:329.1,26.0')] ).
cnf(392,plain,
( ~ in(skf8(function_inverse(skc9)),relation_rng(skc9))
| ~ in(skf7(function_inverse(skc9)),relation_rng(skc9))
| equal(skf8(function_inverse(skc9)),skf7(function_inverse(skc9))) ),
inference(spr,[status(thm),theory(equality)],[330,144]),
[iquote('0:SpR:330.1,144.1')] ).
cnf(422,plain,
( ~ function(function_inverse(skc9))
| ~ relation(function_inverse(skc9))
| ~ equal(function_inverse(skc9),function_inverse(skc9))
| ~ in(skf7(function_inverse(skc9)),relation_rng(skc9))
| one_to_one(function_inverse(skc9))
| equal(skf8(function_inverse(skc9)),skf7(function_inverse(skc9))) ),
inference(res,[status(thm),theory(equality)],[303,392]),
[iquote('0:Res:303.4,392.0')] ).
cnf(423,plain,
( ~ function(function_inverse(skc9))
| ~ relation(function_inverse(skc9))
| ~ in(skf7(function_inverse(skc9)),relation_rng(skc9))
| one_to_one(function_inverse(skc9))
| equal(skf8(function_inverse(skc9)),skf7(function_inverse(skc9))) ),
inference(obv,[status(thm),theory(equality)],[422]),
[iquote('0:Obv:422.2')] ).
cnf(424,plain,
( ~ in(skf7(function_inverse(skc9)),relation_rng(skc9))
| one_to_one(function_inverse(skc9))
| equal(skf8(function_inverse(skc9)),skf7(function_inverse(skc9))) ),
inference(ssi,[status(thm)],[423,141,140]),
[iquote('0:SSi:423.1,423.0,141.0,140.0,141.0,140.0')] ).
cnf(425,plain,
( ~ in(skf7(function_inverse(skc9)),relation_rng(skc9))
| equal(skf8(function_inverse(skc9)),skf7(function_inverse(skc9))) ),
inference(mrr,[status(thm)],[424,26]),
[iquote('0:MRR:424.1,26.0')] ).
cnf(462,plain,
( ~ function(function_inverse(skc9))
| ~ relation(function_inverse(skc9))
| ~ equal(function_inverse(skc9),function_inverse(skc9))
| one_to_one(function_inverse(skc9))
| equal(skf8(function_inverse(skc9)),skf7(function_inverse(skc9))) ),
inference(res,[status(thm),theory(equality)],[304,425]),
[iquote('0:Res:304.4,425.0')] ).
cnf(463,plain,
( ~ function(function_inverse(skc9))
| ~ relation(function_inverse(skc9))
| one_to_one(function_inverse(skc9))
| equal(skf8(function_inverse(skc9)),skf7(function_inverse(skc9))) ),
inference(obv,[status(thm),theory(equality)],[462]),
[iquote('0:Obv:462.2')] ).
cnf(464,plain,
( one_to_one(function_inverse(skc9))
| equal(skf8(function_inverse(skc9)),skf7(function_inverse(skc9))) ),
inference(ssi,[status(thm)],[463,141,140]),
[iquote('0:SSi:463.1,463.0,141.0,140.0,141.0,140.0')] ).
cnf(465,plain,
equal(skf8(function_inverse(skc9)),skf7(function_inverse(skc9))),
inference(mrr,[status(thm)],[464,26]),
[iquote('0:MRR:464.0,26.0')] ).
cnf(472,plain,
( ~ function(function_inverse(skc9))
| ~ relation(function_inverse(skc9))
| ~ equal(skf7(function_inverse(skc9)),skf7(function_inverse(skc9)))
| one_to_one(function_inverse(skc9)) ),
inference(spl,[status(thm),theory(equality)],[465,54]),
[iquote('0:SpL:465.0,54.2')] ).
cnf(475,plain,
( ~ function(function_inverse(skc9))
| ~ relation(function_inverse(skc9))
| one_to_one(function_inverse(skc9)) ),
inference(obv,[status(thm),theory(equality)],[472]),
[iquote('0:Obv:472.2')] ).
cnf(476,plain,
one_to_one(function_inverse(skc9)),
inference(ssi,[status(thm)],[475,141,140]),
[iquote('0:SSi:475.1,475.0,141.0,140.0,141.0,140.0')] ).
cnf(477,plain,
$false,
inference(mrr,[status(thm)],[476,26]),
[iquote('0:MRR:476.0,26.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU221+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 18:40:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.18/0.54
% 0.18/0.54 SPASS V 3.9
% 0.18/0.54 SPASS beiseite: Proof found.
% 0.18/0.54 % SZS status Theorem
% 0.18/0.54 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.54 SPASS derived 300 clauses, backtracked 0 clauses, performed 2 splits and kept 177 clauses.
% 0.18/0.54 SPASS allocated 98290 KBytes.
% 0.18/0.54 SPASS spent 0:00:00.18 on the problem.
% 0.18/0.54 0:00:00.04 for the input.
% 0.18/0.54 0:00:00.09 for the FLOTTER CNF translation.
% 0.18/0.54 0:00:00.00 for inferences.
% 0.18/0.54 0:00:00.00 for the backtracking.
% 0.18/0.54 0:00:00.02 for the reduction.
% 0.18/0.54
% 0.18/0.54
% 0.18/0.54 Here is a proof with depth 6, length 40 :
% 0.18/0.54 % SZS output start Refutation
% See solution above
% 0.18/0.54 Formulae used in the proof : t62_funct_1 dt_k2_funct_1 d8_funct_1 t57_funct_1 t54_funct_1
% 0.18/0.54
%------------------------------------------------------------------------------