TSTP Solution File: SEU048+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU048+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 14:33:43 EDT 2022
% Result : Theorem 59.52s 59.69s
% Output : Refutation 59.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of clauses : 43 ( 8 unt; 19 nHn; 43 RR)
% Number of literals : 162 ( 0 equ; 101 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 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('SEU048+1.p',unknown),
[] ).
cnf(2,axiom,
function(skc10),
file('SEU048+1.p',unknown),
[] ).
cnf(3,axiom,
relation(skc10),
file('SEU048+1.p',unknown),
[] ).
cnf(30,axiom,
~ one_to_one(relation_rng_restriction(skc11,skc10)),
file('SEU048+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ relation(u)
| relation(relation_rng_restriction(v,u)) ),
file('SEU048+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ relation(u)
| ~ function(u)
| function(relation_rng_restriction(v,u)) ),
file('SEU048+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ function(u)
| ~ relation(u)
| one_to_one(u)
| in(skf8(u),relation_dom(u)) ),
file('SEU048+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ function(u)
| ~ relation(u)
| one_to_one(u)
| in(skf7(u),relation_dom(u)) ),
file('SEU048+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ function(u)
| ~ relation(u)
| ~ equal(skf8(u),skf7(u))
| one_to_one(u) ),
file('SEU048+1.p',unknown),
[] ).
cnf(56,axiom,
( ~ function(u)
| ~ relation(u)
| one_to_one(u)
| equal(apply(u,skf8(u)),apply(u,skf7(u))) ),
file('SEU048+1.p',unknown),
[] ).
cnf(57,axiom,
( ~ relation(u)
| ~ function(u)
| ~ relation(v)
| ~ function(v)
| ~ in(w,relation_dom(u))
| ~ equal(u,relation_rng_restriction(x,v))
| in(w,relation_dom(v)) ),
file('SEU048+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ relation(u)
| ~ function(u)
| ~ relation(v)
| ~ function(v)
| ~ in(w,relation_dom(u))
| ~ equal(u,relation_rng_restriction(x,v))
| equal(apply(u,w),apply(v,w)) ),
file('SEU048+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ function(u)
| ~ relation(u)
| ~ one_to_one(u)
| ~ in(v,relation_dom(u))
| ~ in(w,relation_dom(u))
| ~ equal(apply(u,v),apply(u,w))
| equal(v,w) ),
file('SEU048+1.p',unknown),
[] ).
cnf(84,plain,
( ~ function(skc10)
| function(relation_rng_restriction(u,skc10)) ),
inference(res,[status(thm),theory(equality)],[3,49]),
[iquote('0:Res:3.0,49.1')] ).
cnf(86,plain,
relation(relation_rng_restriction(u,skc10)),
inference(res,[status(thm),theory(equality)],[3,39]),
[iquote('0:Res:3.0,39.0')] ).
cnf(107,plain,
( ~ relation(skc10)
| ~ function(u)
| ~ relation(u)
| ~ in(v,relation_dom(u))
| ~ equal(u,relation_rng_restriction(w,skc10))
| in(v,relation_dom(skc10)) ),
inference(res,[status(thm),theory(equality)],[2,57]),
[iquote('0:Res:2.0,57.0')] ).
cnf(123,plain,
( ~ relation(skc10)
| ~ function(skc10)
| ~ in(u,relation_dom(skc10))
| ~ in(v,relation_dom(skc10))
| ~ equal(apply(skc10,v),apply(skc10,u))
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[1,60]),
[iquote('0:Res:1.0,60.0')] ).
cnf(129,plain,
function(relation_rng_restriction(u,skc10)),
inference(mrr,[status(thm)],[84,2]),
[iquote('0:MRR:84.0,2.0')] ).
cnf(131,plain,
( ~ relation(u)
| ~ function(u)
| ~ in(v,relation_dom(u))
| ~ equal(u,relation_rng_restriction(w,skc10))
| in(v,relation_dom(skc10)) ),
inference(mrr,[status(thm)],[107,3]),
[iquote('0:MRR:107.0,3.0')] ).
cnf(134,plain,
( ~ in(u,relation_dom(skc10))
| ~ in(v,relation_dom(skc10))
| ~ equal(apply(skc10,u),apply(skc10,v))
| equal(u,v) ),
inference(mrr,[status(thm)],[123,3,2]),
[iquote('0:MRR:123.0,123.1,3.0,2.0')] ).
cnf(405,plain,
( ~ relation(relation_rng_restriction(u,v))
| ~ function(relation_rng_restriction(u,v))
| ~ relation(v)
| ~ function(v)
| ~ in(w,relation_dom(relation_rng_restriction(u,v)))
| equal(apply(relation_rng_restriction(u,v),w),apply(v,w)) ),
inference(eqr,[status(thm),theory(equality)],[59]),
[iquote('0:EqR:59.5')] ).
cnf(406,plain,
( ~ relation(u)
| ~ function(u)
| ~ in(v,relation_dom(relation_rng_restriction(w,u)))
| equal(apply(relation_rng_restriction(w,u),v),apply(u,v)) ),
inference(ssi,[status(thm)],[405,39,49]),
[iquote('0:SSi:405.1,405.0,39.2,49.1,39.2,49.1')] ).
cnf(928,plain,
( ~ relation(relation_rng_restriction(u,skc10))
| ~ function(relation_rng_restriction(u,skc10))
| ~ in(v,relation_dom(relation_rng_restriction(u,skc10)))
| in(v,relation_dom(skc10)) ),
inference(eqr,[status(thm),theory(equality)],[131]),
[iquote('0:EqR:131.3')] ).
cnf(930,plain,
( ~ in(u,relation_dom(relation_rng_restriction(v,skc10)))
| in(u,relation_dom(skc10)) ),
inference(ssi,[status(thm)],[928,129,86]),
[iquote('0:SSi:928.1,928.0,129.0,86.0,129.0,86.0')] ).
cnf(934,plain,
( ~ function(relation_rng_restriction(u,skc10))
| ~ relation(relation_rng_restriction(u,skc10))
| one_to_one(relation_rng_restriction(u,skc10))
| in(skf7(relation_rng_restriction(u,skc10)),relation_dom(skc10)) ),
inference(res,[status(thm),theory(equality)],[54,930]),
[iquote('0:Res:54.3,930.0')] ).
cnf(935,plain,
( ~ function(relation_rng_restriction(u,skc10))
| ~ relation(relation_rng_restriction(u,skc10))
| one_to_one(relation_rng_restriction(u,skc10))
| in(skf8(relation_rng_restriction(u,skc10)),relation_dom(skc10)) ),
inference(res,[status(thm),theory(equality)],[53,930]),
[iquote('0:Res:53.3,930.0')] ).
cnf(951,plain,
( one_to_one(relation_rng_restriction(u,skc10))
| in(skf8(relation_rng_restriction(u,skc10)),relation_dom(skc10)) ),
inference(ssi,[status(thm)],[935,129,86]),
[iquote('0:SSi:935.1,935.0,129.0,86.0,129.0,86.0')] ).
cnf(952,plain,
( one_to_one(relation_rng_restriction(u,skc10))
| in(skf7(relation_rng_restriction(u,skc10)),relation_dom(skc10)) ),
inference(ssi,[status(thm)],[934,129,86]),
[iquote('0:SSi:934.1,934.0,129.0,86.0,129.0,86.0')] ).
cnf(1116,plain,
( ~ function(relation_rng_restriction(u,v))
| ~ relation(relation_rng_restriction(u,v))
| ~ relation(v)
| ~ function(v)
| one_to_one(relation_rng_restriction(u,v))
| equal(apply(relation_rng_restriction(u,v),skf7(relation_rng_restriction(u,v))),apply(v,skf7(relation_rng_restriction(u,v)))) ),
inference(res,[status(thm),theory(equality)],[54,406]),
[iquote('0:Res:54.3,406.2')] ).
cnf(1117,plain,
( ~ function(relation_rng_restriction(u,v))
| ~ relation(relation_rng_restriction(u,v))
| ~ relation(v)
| ~ function(v)
| one_to_one(relation_rng_restriction(u,v))
| equal(apply(relation_rng_restriction(u,v),skf8(relation_rng_restriction(u,v))),apply(v,skf8(relation_rng_restriction(u,v)))) ),
inference(res,[status(thm),theory(equality)],[53,406]),
[iquote('0:Res:53.3,406.2')] ).
cnf(1137,plain,
( ~ function(relation_rng_restriction(u,v))
| ~ relation(relation_rng_restriction(u,v))
| ~ relation(v)
| ~ function(v)
| one_to_one(relation_rng_restriction(u,v))
| equal(apply(relation_rng_restriction(u,v),skf7(relation_rng_restriction(u,v))),apply(v,skf8(relation_rng_restriction(u,v)))) ),
inference(rew,[status(thm),theory(equality)],[56,1117]),
[iquote('0:Rew:56.3,1117.5')] ).
cnf(1138,plain,
( ~ relation(u)
| ~ function(u)
| one_to_one(relation_rng_restriction(v,u))
| equal(apply(relation_rng_restriction(v,u),skf7(relation_rng_restriction(v,u))),apply(u,skf8(relation_rng_restriction(v,u)))) ),
inference(ssi,[status(thm)],[1137,39,49]),
[iquote('0:SSi:1137.1,1137.0,39.2,49.1,39.2,49.1')] ).
cnf(1139,plain,
( ~ function(relation_rng_restriction(u,v))
| ~ relation(relation_rng_restriction(u,v))
| ~ relation(v)
| ~ function(v)
| one_to_one(relation_rng_restriction(u,v))
| equal(apply(v,skf8(relation_rng_restriction(u,v))),apply(v,skf7(relation_rng_restriction(u,v)))) ),
inference(rew,[status(thm),theory(equality)],[1138,1116]),
[iquote('0:Rew:1138.3,1116.5')] ).
cnf(1140,plain,
( ~ relation(u)
| ~ function(u)
| one_to_one(relation_rng_restriction(v,u))
| equal(apply(u,skf8(relation_rng_restriction(v,u))),apply(u,skf7(relation_rng_restriction(v,u)))) ),
inference(ssi,[status(thm)],[1139,39,49]),
[iquote('0:SSi:1139.1,1139.0,39.2,49.1,39.2,49.1')] ).
cnf(3649,plain,
( ~ relation(skc10)
| ~ function(skc10)
| ~ in(skf8(relation_rng_restriction(u,skc10)),relation_dom(skc10))
| ~ in(v,relation_dom(skc10))
| ~ equal(apply(skc10,skf7(relation_rng_restriction(u,skc10))),apply(skc10,v))
| one_to_one(relation_rng_restriction(u,skc10))
| equal(skf8(relation_rng_restriction(u,skc10)),v) ),
inference(spl,[status(thm),theory(equality)],[1140,134]),
[iquote('0:SpL:1140.3,134.2')] ).
cnf(3664,plain,
( ~ in(skf8(relation_rng_restriction(u,skc10)),relation_dom(skc10))
| ~ in(v,relation_dom(skc10))
| ~ equal(apply(skc10,skf7(relation_rng_restriction(u,skc10))),apply(skc10,v))
| one_to_one(relation_rng_restriction(u,skc10))
| equal(skf8(relation_rng_restriction(u,skc10)),v) ),
inference(ssi,[status(thm)],[3649,1,2,3]),
[iquote('0:SSi:3649.1,3649.0,1.0,2.0,3.0,1.0,2.0,3.0')] ).
cnf(3665,plain,
( ~ in(u,relation_dom(skc10))
| ~ equal(apply(skc10,skf7(relation_rng_restriction(v,skc10))),apply(skc10,u))
| one_to_one(relation_rng_restriction(v,skc10))
| equal(skf8(relation_rng_restriction(v,skc10)),u) ),
inference(mrr,[status(thm)],[3664,951]),
[iquote('0:MRR:3664.0,951.1')] ).
cnf(29226,plain,
( ~ in(skf7(relation_rng_restriction(u,skc10)),relation_dom(skc10))
| one_to_one(relation_rng_restriction(u,skc10))
| equal(skf8(relation_rng_restriction(u,skc10)),skf7(relation_rng_restriction(u,skc10))) ),
inference(eqr,[status(thm),theory(equality)],[3665]),
[iquote('0:EqR:3665.1')] ).
cnf(29244,plain,
( one_to_one(relation_rng_restriction(u,skc10))
| equal(skf8(relation_rng_restriction(u,skc10)),skf7(relation_rng_restriction(u,skc10))) ),
inference(mrr,[status(thm)],[29226,952]),
[iquote('0:MRR:29226.0,952.1')] ).
cnf(29279,plain,
( ~ function(relation_rng_restriction(u,skc10))
| ~ relation(relation_rng_restriction(u,skc10))
| ~ equal(skf7(relation_rng_restriction(u,skc10)),skf7(relation_rng_restriction(u,skc10)))
| one_to_one(relation_rng_restriction(u,skc10))
| one_to_one(relation_rng_restriction(u,skc10)) ),
inference(spl,[status(thm),theory(equality)],[29244,55]),
[iquote('0:SpL:29244.1,55.2')] ).
cnf(29294,plain,
( ~ function(relation_rng_restriction(u,skc10))
| ~ relation(relation_rng_restriction(u,skc10))
| one_to_one(relation_rng_restriction(u,skc10)) ),
inference(obv,[status(thm),theory(equality)],[29279]),
[iquote('0:Obv:29279.3')] ).
cnf(29295,plain,
one_to_one(relation_rng_restriction(u,skc10)),
inference(ssi,[status(thm)],[29294,129,86]),
[iquote('0:SSi:29294.1,29294.0,129.0,86.0,129.0,86.0')] ).
cnf(29296,plain,
$false,
inference(unc,[status(thm)],[29295,30]),
[iquote('0:UnC:29295.0,30.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU048+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 07:50:47 EDT 2022
% 0.13/0.34 % CPUTime :
% 59.52/59.69
% 59.52/59.69 SPASS V 3.9
% 59.52/59.69 SPASS beiseite: Proof found.
% 59.52/59.69 % SZS status Theorem
% 59.52/59.69 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 59.52/59.69 SPASS derived 20541 clauses, backtracked 0 clauses, performed 4 splits and kept 9237 clauses.
% 59.52/59.69 SPASS allocated 135087 KBytes.
% 59.52/59.69 SPASS spent 0:0:55.86 on the problem.
% 59.52/59.69 0:00:00.04 for the input.
% 59.52/59.69 0:00:00.07 for the FLOTTER CNF translation.
% 59.52/59.69 0:00:00.47 for inferences.
% 59.52/59.69 0:00:00.06 for the backtracking.
% 59.52/59.69 0:0:54.99 for the reduction.
% 59.52/59.69
% 59.52/59.69
% 59.52/59.69 Here is a proof with depth 5, length 43 :
% 59.52/59.69 % SZS output start Refutation
% See solution above
% 59.52/59.69 Formulae used in the proof : t99_funct_1 dt_k8_relat_1 fc5_funct_1 d8_funct_1 t85_funct_1
% 59.52/59.69
%------------------------------------------------------------------------------