TSTP Solution File: SEU296+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU296+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 14:35:58 EDT 2022
% Result : Theorem 0.60s 0.80s
% Output : Refutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of clauses : 42 ( 12 unt; 0 nHn; 42 RR)
% Number of literals : 104 ( 0 equ; 66 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
finite(skc24),
file('SEU296+3.p',unknown),
[] ).
cnf(2,axiom,
function(skc23),
file('SEU296+3.p',unknown),
[] ).
cnf(3,axiom,
relation(skc23),
file('SEU296+3.p',unknown),
[] ).
cnf(81,axiom,
relation(skf6(u)),
file('SEU296+3.p',unknown),
[] ).
cnf(102,axiom,
subset(u,u),
file('SEU296+3.p',unknown),
[] ).
cnf(105,axiom,
~ finite(relation_image(skc23,skc24)),
file('SEU296+3.p',unknown),
[] ).
cnf(120,axiom,
subset(set_intersection2(u,v),u),
file('SEU296+3.p',unknown),
[] ).
cnf(126,axiom,
( ~ finite(u)
| function(skf6(u)) ),
file('SEU296+3.p',unknown),
[] ).
cnf(135,axiom,
( ~ finite(u)
| finite(set_intersection2(v,u)) ),
file('SEU296+3.p',unknown),
[] ).
cnf(145,axiom,
( ~ finite(u)
| equal(relation_rng(skf6(u)),u) ),
file('SEU296+3.p',unknown),
[] ).
cnf(146,axiom,
( ~ finite(u)
| in(relation_dom(skf6(u)),omega) ),
file('SEU296+3.p',unknown),
[] ).
cnf(148,axiom,
( ~ subset(u,v)
| element(u,powerset(v)) ),
file('SEU296+3.p',unknown),
[] ).
cnf(159,axiom,
( ~ finite(u)
| ~ element(v,powerset(u))
| finite(v) ),
file('SEU296+3.p',unknown),
[] ).
cnf(160,axiom,
( ~ relation(u)
| ~ relation(v)
| relation(relation_composition(v,u)) ),
file('SEU296+3.p',unknown),
[] ).
cnf(173,axiom,
( ~ relation(u)
| equal(relation_image(u,set_intersection2(relation_dom(u),v)),relation_image(u,v)) ),
file('SEU296+3.p',unknown),
[] ).
cnf(174,axiom,
( ~ relation(u)
| ~ relation(v)
| equal(relation_image(u,relation_rng(v)),relation_rng(relation_composition(v,u))) ),
file('SEU296+3.p',unknown),
[] ).
cnf(176,axiom,
( ~ relation(u)
| ~ function(u)
| ~ function(v)
| ~ relation(v)
| function(relation_composition(v,u)) ),
file('SEU296+3.p',unknown),
[] ).
cnf(177,axiom,
( ~ function(u)
| ~ relation(u)
| ~ equal(relation_rng(u),v)
| ~ in(relation_dom(u),omega)
| finite(v) ),
file('SEU296+3.p',unknown),
[] ).
cnf(181,axiom,
( ~ relation(u)
| ~ relation(v)
| ~ subset(relation_rng(v),relation_dom(u))
| equal(relation_dom(relation_composition(v,u)),relation_dom(v)) ),
file('SEU296+3.p',unknown),
[] ).
cnf(189,plain,
equal(relation_image(skc23,set_intersection2(relation_dom(skc23),u)),relation_image(skc23,u)),
inference(res,[status(thm),theory(equality)],[3,173]),
[iquote('0:Res:3.0,173.0')] ).
cnf(199,plain,
( ~ relation(u)
| ~ subset(relation_rng(u),relation_dom(skc23))
| equal(relation_dom(relation_composition(u,skc23)),relation_dom(u)) ),
inference(res,[status(thm),theory(equality)],[3,181]),
[iquote('0:Res:3.0,181.1')] ).
cnf(200,plain,
( ~ relation(u)
| ~ function(u)
| ~ function(skc23)
| function(relation_composition(u,skc23)) ),
inference(res,[status(thm),theory(equality)],[3,176]),
[iquote('0:Res:3.0,176.3')] ).
cnf(201,plain,
( ~ relation(u)
| equal(relation_image(skc23,relation_rng(u)),relation_rng(relation_composition(u,skc23))) ),
inference(res,[status(thm),theory(equality)],[3,174]),
[iquote('0:Res:3.0,174.1')] ).
cnf(202,plain,
( ~ relation(u)
| relation(relation_composition(u,skc23)) ),
inference(res,[status(thm),theory(equality)],[3,160]),
[iquote('0:Res:3.0,160.1')] ).
cnf(220,plain,
finite(set_intersection2(u,skc24)),
inference(res,[status(thm),theory(equality)],[1,135]),
[iquote('0:Res:1.0,135.0')] ).
cnf(225,plain,
( ~ finite(u)
| ~ element(relation_image(skc23,skc24),powerset(u)) ),
inference(res,[status(thm),theory(equality)],[159,105]),
[iquote('0:Res:159.2,105.0')] ).
cnf(231,plain,
( ~ function(u)
| ~ relation(u)
| function(relation_composition(u,skc23)) ),
inference(mrr,[status(thm)],[200,2]),
[iquote('0:MRR:200.2,2.0')] ).
cnf(848,plain,
( ~ function(u)
| ~ relation(u)
| ~ in(relation_dom(u),omega)
| finite(relation_rng(u)) ),
inference(eqr,[status(thm),theory(equality)],[177]),
[iquote('0:EqR:177.2')] ).
cnf(1036,plain,
( ~ finite(u)
| ~ subset(relation_image(skc23,skc24),u) ),
inference(res,[status(thm),theory(equality)],[148,225]),
[iquote('0:Res:148.1,225.1')] ).
cnf(1066,plain,
~ finite(relation_image(skc23,skc24)),
inference(res,[status(thm),theory(equality)],[102,1036]),
[iquote('0:Res:102.0,1036.1')] ).
cnf(1351,plain,
( ~ finite(u)
| ~ relation(skf6(u))
| equal(relation_rng(relation_composition(skf6(u),skc23)),relation_image(skc23,u)) ),
inference(spr,[status(thm),theory(equality)],[145,201]),
[iquote('0:SpR:145.1,201.1')] ).
cnf(1358,plain,
( ~ finite(u)
| equal(relation_rng(relation_composition(skf6(u),skc23)),relation_image(skc23,u)) ),
inference(ssi,[status(thm)],[1351,81,126]),
[iquote('0:SSi:1351.1,81.1,126.0')] ).
cnf(1830,plain,
( ~ finite(u)
| ~ relation(skf6(u))
| ~ subset(u,relation_dom(skc23))
| equal(relation_dom(relation_composition(skf6(u),skc23)),relation_dom(skf6(u))) ),
inference(spl,[status(thm),theory(equality)],[145,199]),
[iquote('0:SpL:145.1,199.1')] ).
cnf(1839,plain,
( ~ finite(u)
| ~ subset(u,relation_dom(skc23))
| equal(relation_dom(relation_composition(skf6(u),skc23)),relation_dom(skf6(u))) ),
inference(ssi,[status(thm)],[1830,81,126]),
[iquote('0:SSi:1830.1,81.1,126.0')] ).
cnf(2699,plain,
( ~ finite(u)
| ~ function(relation_composition(skf6(u),skc23))
| ~ relation(relation_composition(skf6(u),skc23))
| ~ subset(u,relation_dom(skc23))
| ~ in(relation_dom(skf6(u)),omega)
| finite(relation_rng(relation_composition(skf6(u),skc23))) ),
inference(spl,[status(thm),theory(equality)],[1839,848]),
[iquote('0:SpL:1839.2,848.2')] ).
cnf(2709,plain,
( ~ finite(u)
| ~ function(relation_composition(skf6(u),skc23))
| ~ relation(relation_composition(skf6(u),skc23))
| ~ subset(u,relation_dom(skc23))
| ~ in(relation_dom(skf6(u)),omega)
| finite(relation_image(skc23,u)) ),
inference(rew,[status(thm),theory(equality)],[1358,2699]),
[iquote('0:Rew:1358.1,2699.5')] ).
cnf(2710,plain,
( ~ finite(u)
| ~ subset(u,relation_dom(skc23))
| ~ in(relation_dom(skf6(u)),omega)
| finite(relation_image(skc23,u)) ),
inference(ssi,[status(thm)],[2709,202,81,126,231]),
[iquote('0:SSi:2709.2,2709.1,202.1,81.0,126.2,231.1,81.0,126.1,202.1,81.0,126.2,231.1,81.0,126.1')] ).
cnf(2711,plain,
( ~ finite(u)
| ~ subset(u,relation_dom(skc23))
| finite(relation_image(skc23,u)) ),
inference(mrr,[status(thm)],[2710,146]),
[iquote('0:MRR:2710.2,146.1')] ).
cnf(3901,plain,
( ~ finite(set_intersection2(relation_dom(skc23),u))
| finite(relation_image(skc23,set_intersection2(relation_dom(skc23),u))) ),
inference(res,[status(thm),theory(equality)],[120,2711]),
[iquote('0:Res:120.0,2711.1')] ).
cnf(3923,plain,
( ~ finite(set_intersection2(relation_dom(skc23),u))
| finite(relation_image(skc23,u)) ),
inference(rew,[status(thm),theory(equality)],[189,3901]),
[iquote('0:Rew:189.0,3901.1')] ).
cnf(3949,plain,
finite(relation_image(skc23,skc24)),
inference(sor,[status(thm)],[3923,220]),
[iquote('0:SoR:3923.0,220.0')] ).
cnf(3951,plain,
$false,
inference(mrr,[status(thm)],[3949,1066]),
[iquote('0:MRR:3949.0,1066.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : SEU296+3 : TPTP v8.1.0. Released v3.2.0.
% 0.05/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 19 20:36:45 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.60/0.80
% 0.60/0.80 SPASS V 3.9
% 0.60/0.80 SPASS beiseite: Proof found.
% 0.60/0.80 % SZS status Theorem
% 0.60/0.80 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.60/0.80 SPASS derived 2948 clauses, backtracked 10 clauses, performed 3 splits and kept 1317 clauses.
% 0.60/0.80 SPASS allocated 100761 KBytes.
% 0.60/0.80 SPASS spent 0:00:00.42 on the problem.
% 0.60/0.80 0:00:00.03 for the input.
% 0.60/0.80 0:00:00.04 for the FLOTTER CNF translation.
% 0.60/0.80 0:00:00.04 for inferences.
% 0.60/0.80 0:00:00.00 for the backtracking.
% 0.60/0.80 0:00:00.26 for the reduction.
% 0.60/0.80
% 0.60/0.80
% 0.60/0.80 Here is a proof with depth 5, length 42 :
% 0.60/0.80 % SZS output start Refutation
% See solution above
% 0.60/0.80 Formulae used in the proof : t17_finset_1 d1_finset_1 rc5_funct_1 reflexivity_r1_tarski t17_xboole_1 fc10_finset_1 t3_subset cc2_finset_1 dt_k5_relat_1 t145_relat_1 t160_relat_1 fc1_funct_1 t46_relat_1
% 0.60/0.80
%------------------------------------------------------------------------------