TSTP Solution File: SEU098+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU098+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 14:33:57 EDT 2022
% Result : Theorem 0.37s 0.54s
% Output : Refutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of clauses : 41 ( 22 unt; 1 nHn; 41 RR)
% Number of literals : 76 ( 0 equ; 39 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc22),
file('SEU098+1.p',unknown),
[] ).
cnf(2,axiom,
function(skc22),
file('SEU098+1.p',unknown),
[] ).
cnf(97,axiom,
relation(first_projection(u,v)),
file('SEU098+1.p',unknown),
[] ).
cnf(98,axiom,
function(first_projection(u,v)),
file('SEU098+1.p',unknown),
[] ).
cnf(102,axiom,
( finite(skc22)
| finite(relation_dom(skc22)) ),
file('SEU098+1.p',unknown),
[] ).
cnf(128,axiom,
( ~ finite(skc22)
| ~ finite(relation_dom(skc22)) ),
file('SEU098+1.p',unknown),
[] ).
cnf(129,axiom,
equal(first_projection_as_func_of(u,v),first_projection(u,v)),
file('SEU098+1.p',unknown),
[] ).
cnf(137,axiom,
quasi_total(first_projection_as_func_of(u,v),cartesian_product2(u,v),u),
file('SEU098+1.p',unknown),
[] ).
cnf(138,axiom,
relation_of2_as_subset(first_projection_as_func_of(u,v),cartesian_product2(u,v),u),
file('SEU098+1.p',unknown),
[] ).
cnf(151,axiom,
( ~ relation_of2_as_subset(u,v,w)
| relation_of2(u,v,w) ),
file('SEU098+1.p',unknown),
[] ).
cnf(153,axiom,
( ~ finite(u)
| ~ subset(v,u)
| finite(v) ),
file('SEU098+1.p',unknown),
[] ).
cnf(158,axiom,
( ~ finite(u)
| ~ finite(v)
| finite(cartesian_product2(v,u)) ),
file('SEU098+1.p',unknown),
[] ).
cnf(159,axiom,
( ~ relation(u)
| subset(u,cartesian_product2(relation_dom(u),relation_rng(u))) ),
file('SEU098+1.p',unknown),
[] ).
cnf(169,axiom,
( ~ relation(u)
| ~ function(u)
| ~ finite(v)
| finite(relation_image(u,v)) ),
file('SEU098+1.p',unknown),
[] ).
cnf(170,axiom,
( ~ function(u)
| ~ relation(u)
| ~ finite(relation_dom(u))
| finite(relation_rng(u)) ),
file('SEU098+1.p',unknown),
[] ).
cnf(172,axiom,
( ~ function(u)
| ~ relation_of2(u,v,w)
| ~ quasi_total(u,v,w)
| equal(function_image(v,w,u,x),relation_image(u,x)) ),
file('SEU098+1.p',unknown),
[] ).
cnf(173,axiom,
( ~ relation(u)
| ~ function(u)
| equal(function_image(cartesian_product2(relation_dom(u),relation_rng(u)),relation_dom(u),first_projection_as_func_of(relation_dom(u),relation_rng(u)),u),relation_dom(u)) ),
file('SEU098+1.p',unknown),
[] ).
cnf(175,plain,
relation_of2_as_subset(first_projection(u,v),cartesian_product2(u,v),u),
inference(rew,[status(thm),theory(equality)],[129,138]),
[iquote('0:Rew:129.0,138.0')] ).
cnf(176,plain,
quasi_total(first_projection(u,v),cartesian_product2(u,v),u),
inference(rew,[status(thm),theory(equality)],[129,137]),
[iquote('0:Rew:129.0,137.0')] ).
cnf(180,plain,
( ~ function(u)
| ~ relation(u)
| equal(function_image(cartesian_product2(relation_dom(u),relation_rng(u)),relation_dom(u),first_projection(relation_dom(u),relation_rng(u)),u),relation_dom(u)) ),
inference(rew,[status(thm),theory(equality)],[129,173]),
[iquote('0:Rew:129.0,173.2')] ).
cnf(184,plain,
( ~ relation(skc22)
| ~ finite(relation_dom(skc22))
| finite(relation_rng(skc22)) ),
inference(res,[status(thm),theory(equality)],[2,170]),
[iquote('0:Res:2.0,170.1')] ).
cnf(190,plain,
( ~ function(skc22)
| equal(function_image(cartesian_product2(relation_dom(skc22),relation_rng(skc22)),relation_dom(skc22),first_projection(relation_dom(skc22),relation_rng(skc22)),skc22),relation_dom(skc22)) ),
inference(res,[status(thm),theory(equality)],[1,180]),
[iquote('0:Res:1.0,180.0')] ).
cnf(196,plain,
subset(skc22,cartesian_product2(relation_dom(skc22),relation_rng(skc22))),
inference(res,[status(thm),theory(equality)],[1,159]),
[iquote('0:Res:1.0,159.0')] ).
cnf(204,plain,
( ~ finite(relation_dom(skc22))
| finite(relation_rng(skc22)) ),
inference(mrr,[status(thm)],[184,1]),
[iquote('0:MRR:184.0,1.0')] ).
cnf(206,plain,
equal(function_image(cartesian_product2(relation_dom(skc22),relation_rng(skc22)),relation_dom(skc22),first_projection(relation_dom(skc22),relation_rng(skc22)),skc22),relation_dom(skc22)),
inference(mrr,[status(thm)],[190,2]),
[iquote('0:MRR:190.0,2.0')] ).
cnf(207,plain,
finite(relation_dom(skc22)),
inference(spt,[spt(split,[position(s1)])],[102]),
[iquote('1:Spt:102.1')] ).
cnf(208,plain,
finite(relation_rng(skc22)),
inference(mrr,[status(thm)],[204,207]),
[iquote('1:MRR:204.0,207.0')] ).
cnf(209,plain,
~ finite(skc22),
inference(mrr,[status(thm)],[128,207]),
[iquote('1:MRR:128.1,207.0')] ).
cnf(332,plain,
( ~ finite(cartesian_product2(relation_dom(skc22),relation_rng(skc22)))
| finite(skc22) ),
inference(res,[status(thm),theory(equality)],[196,153]),
[iquote('0:Res:196.0,153.1')] ).
cnf(338,plain,
~ finite(cartesian_product2(relation_dom(skc22),relation_rng(skc22))),
inference(mrr,[status(thm)],[332,209]),
[iquote('1:MRR:332.1,209.0')] ).
cnf(377,plain,
relation_of2(first_projection(u,v),cartesian_product2(u,v),u),
inference(res,[status(thm),theory(equality)],[175,151]),
[iquote('0:Res:175.0,151.0')] ).
cnf(398,plain,
( ~ finite(relation_dom(skc22))
| ~ finite(relation_rng(skc22)) ),
inference(sor,[status(thm)],[338,158]),
[iquote('1:SoR:338.0,158.2')] ).
cnf(399,plain,
$false,
inference(ssi,[status(thm)],[398,208,207]),
[iquote('1:SSi:398.1,398.0,208.0,207.0')] ).
cnf(400,plain,
~ finite(relation_dom(skc22)),
inference(spt,[spt(split,[position(sa)])],[399,207]),
[iquote('1:Spt:399.0,102.1,207.0')] ).
cnf(401,plain,
finite(skc22),
inference(spt,[spt(split,[position(s2)])],[102]),
[iquote('1:Spt:399.0,102.0')] ).
cnf(1312,plain,
( ~ function(first_projection(relation_dom(skc22),relation_rng(skc22)))
| ~ relation_of2(first_projection(relation_dom(skc22),relation_rng(skc22)),cartesian_product2(relation_dom(skc22),relation_rng(skc22)),relation_dom(skc22))
| ~ quasi_total(first_projection(relation_dom(skc22),relation_rng(skc22)),cartesian_product2(relation_dom(skc22),relation_rng(skc22)),relation_dom(skc22))
| equal(relation_image(first_projection(relation_dom(skc22),relation_rng(skc22)),skc22),relation_dom(skc22)) ),
inference(spr,[status(thm),theory(equality)],[206,172]),
[iquote('0:SpR:206.0,172.3')] ).
cnf(1320,plain,
( ~ relation_of2(first_projection(relation_dom(skc22),relation_rng(skc22)),cartesian_product2(relation_dom(skc22),relation_rng(skc22)),relation_dom(skc22))
| ~ quasi_total(first_projection(relation_dom(skc22),relation_rng(skc22)),cartesian_product2(relation_dom(skc22),relation_rng(skc22)),relation_dom(skc22))
| equal(relation_image(first_projection(relation_dom(skc22),relation_rng(skc22)),skc22),relation_dom(skc22)) ),
inference(ssi,[status(thm)],[1312,98,97]),
[iquote('0:SSi:1312.0,98.0,97.0')] ).
cnf(1321,plain,
equal(relation_image(first_projection(relation_dom(skc22),relation_rng(skc22)),skc22),relation_dom(skc22)),
inference(mrr,[status(thm)],[1320,377,176]),
[iquote('0:MRR:1320.0,1320.1,377.0,176.0')] ).
cnf(1353,plain,
( ~ relation(first_projection(relation_dom(skc22),relation_rng(skc22)))
| ~ function(first_projection(relation_dom(skc22),relation_rng(skc22)))
| ~ finite(skc22)
| finite(relation_dom(skc22)) ),
inference(spr,[status(thm),theory(equality)],[1321,169]),
[iquote('0:SpR:1321.0,169.3')] ).
cnf(1361,plain,
finite(relation_dom(skc22)),
inference(ssi,[status(thm)],[1353,2,1,401,98,97]),
[iquote('1:SSi:1353.2,1353.1,1353.0,2.0,1.0,401.0,98.0,97.0,98.0,97.0')] ).
cnf(1362,plain,
$false,
inference(mrr,[status(thm)],[1361,400]),
[iquote('1:MRR:1361.0,400.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU098+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n017.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 : Sat Jun 18 22:56:12 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.37/0.54
% 0.37/0.54 SPASS V 3.9
% 0.37/0.54 SPASS beiseite: Proof found.
% 0.37/0.54 % SZS status Theorem
% 0.37/0.54 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.37/0.54 SPASS derived 1027 clauses, backtracked 9 clauses, performed 1 splits and kept 688 clauses.
% 0.37/0.54 SPASS allocated 98675 KBytes.
% 0.37/0.54 SPASS spent 0:00:00.20 on the problem.
% 0.37/0.54 0:00:00.03 for the input.
% 0.37/0.54 0:00:00.03 for the FLOTTER CNF translation.
% 0.37/0.54 0:00:00.02 for inferences.
% 0.37/0.54 0:00:00.00 for the backtracking.
% 0.37/0.54 0:00:00.08 for the reduction.
% 0.37/0.54
% 0.37/0.54
% 0.37/0.54 Here is a proof with depth 3, length 41 :
% 0.37/0.54 % SZS output start Refutation
% See solution above
% 0.37/0.54 Formulae used in the proof : t29_finset_1 dt_k7_funct_3 redefinition_k9_funct_3 dt_k9_funct_3 redefinition_m2_relset_1 t13_finset_1 t19_finset_1 t21_relat_1 t17_finset_1 t26_finset_1 redefinition_k2_funct_2 t100_funct_3
% 0.37/0.54
%------------------------------------------------------------------------------