%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU296+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 14:35:57 EDT 2022
% Result : Theorem 0.54s 0.78s
% Output : Refutation 0.54s
% 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(skc17),
file('SEU296+1.p',unknown),
[] ).
cnf(2,axiom,
function(skc16),
file('SEU296+1.p',unknown),
[] ).
cnf(3,axiom,
relation(skc16),
file('SEU296+1.p',unknown),
[] ).
cnf(56,axiom,
relation(skf6(u)),
file('SEU296+1.p',unknown),
[] ).
cnf(73,axiom,
subset(u,u),
file('SEU296+1.p',unknown),
[] ).
cnf(76,axiom,
~ finite(relation_image(skc16,skc17)),
file('SEU296+1.p',unknown),
[] ).
cnf(91,axiom,
subset(set_intersection2(u,v),u),
file('SEU296+1.p',unknown),
[] ).
cnf(97,axiom,
( ~ finite(u)
| function(skf6(u)) ),
file('SEU296+1.p',unknown),
[] ).
cnf(106,axiom,
( ~ finite(u)
| finite(set_intersection2(v,u)) ),
file('SEU296+1.p',unknown),
[] ).
cnf(116,axiom,
( ~ finite(u)
| equal(relation_rng(skf6(u)),u) ),
file('SEU296+1.p',unknown),
[] ).
cnf(117,axiom,
( ~ finite(u)
| in(relation_dom(skf6(u)),omega) ),
file('SEU296+1.p',unknown),
[] ).
cnf(119,axiom,
( ~ subset(u,v)
| element(u,powerset(v)) ),
file('SEU296+1.p',unknown),
[] ).
cnf(127,axiom,
( ~ finite(u)
| ~ element(v,powerset(u))
| finite(v) ),
file('SEU296+1.p',unknown),
[] ).
cnf(128,axiom,
( ~ relation(u)
| ~ relation(v)
| relation(relation_composition(v,u)) ),
file('SEU296+1.p',unknown),
[] ).
cnf(137,axiom,
( ~ relation(u)
| equal(relation_image(u,set_intersection2(relation_dom(u),v)),relation_image(u,v)) ),
file('SEU296+1.p',unknown),
[] ).
cnf(138,axiom,
( ~ relation(u)
| ~ relation(v)
| equal(relation_image(u,relation_rng(v)),relation_rng(relation_composition(v,u))) ),
file('SEU296+1.p',unknown),
[] ).
cnf(140,axiom,
( ~ relation(u)
| ~ function(u)
| ~ function(v)
| ~ relation(v)
| function(relation_composition(v,u)) ),
file('SEU296+1.p',unknown),
[] ).
cnf(141,axiom,
( ~ function(u)
| ~ relation(u)
| ~ equal(relation_rng(u),v)
| ~ in(relation_dom(u),omega)
| finite(v) ),
file('SEU296+1.p',unknown),
[] ).
cnf(142,axiom,
( ~ relation(u)
| ~ relation(v)
| ~ subset(relation_rng(v),relation_dom(u))
| equal(relation_dom(relation_composition(v,u)),relation_dom(v)) ),
file('SEU296+1.p',unknown),
[] ).
cnf(149,plain,
equal(relation_image(skc16,set_intersection2(relation_dom(skc16),u)),relation_image(skc16,u)),
inference(res,[status(thm),theory(equality)],[3,137]),
[iquote('0:Res:3.0,137.0')] ).
cnf(154,plain,
( ~ relation(u)
| ~ subset(relation_rng(u),relation_dom(skc16))
| equal(relation_dom(relation_composition(u,skc16)),relation_dom(u)) ),
inference(res,[status(thm),theory(equality)],[3,142]),
[iquote('0:Res:3.0,142.1')] ).
cnf(155,plain,
( ~ relation(u)
| ~ function(u)
| ~ function(skc16)
| function(relation_composition(u,skc16)) ),
inference(res,[status(thm),theory(equality)],[3,140]),
[iquote('0:Res:3.0,140.3')] ).
cnf(156,plain,
( ~ relation(u)
| equal(relation_image(skc16,relation_rng(u)),relation_rng(relation_composition(u,skc16))) ),
inference(res,[status(thm),theory(equality)],[3,138]),
[iquote('0:Res:3.0,138.1')] ).
cnf(157,plain,
( ~ relation(u)
| relation(relation_composition(u,skc16)) ),
inference(res,[status(thm),theory(equality)],[3,128]),
[iquote('0:Res:3.0,128.1')] ).
cnf(169,plain,
finite(set_intersection2(u,skc17)),
inference(res,[status(thm),theory(equality)],[1,106]),
[iquote('0:Res:1.0,106.0')] ).
cnf(174,plain,
( ~ finite(u)
| ~ element(relation_image(skc16,skc17),powerset(u)) ),
inference(res,[status(thm),theory(equality)],[127,76]),
[iquote('0:Res:127.2,76.0')] ).
cnf(176,plain,
( ~ function(u)
| ~ relation(u)
| function(relation_composition(u,skc16)) ),
inference(mrr,[status(thm)],[155,2]),
[iquote('0:MRR:155.2,2.0')] ).
cnf(598,plain,
( ~ finite(u)
| ~ subset(relation_image(skc16,skc17),u) ),
inference(res,[status(thm),theory(equality)],[119,174]),
[iquote('0:Res:119.1,174.1')] ).
cnf(605,plain,
~ finite(relation_image(skc16,skc17)),
inference(res,[status(thm),theory(equality)],[73,598]),
[iquote('0:Res:73.0,598.1')] ).
cnf(783,plain,
( ~ function(u)
| ~ relation(u)
| ~ in(relation_dom(u),omega)
| finite(relation_rng(u)) ),
inference(eqr,[status(thm),theory(equality)],[141]),
[iquote('0:EqR:141.2')] ).
cnf(1196,plain,
( ~ finite(u)
| ~ relation(skf6(u))
| equal(relation_rng(relation_composition(skf6(u),skc16)),relation_image(skc16,u)) ),
inference(spr,[status(thm),theory(equality)],[116,156]),
[iquote('0:SpR:116.1,156.1')] ).
cnf(1203,plain,
( ~ finite(u)
| equal(relation_rng(relation_composition(skf6(u),skc16)),relation_image(skc16,u)) ),
inference(ssi,[status(thm)],[1196,56,97]),
[iquote('0:SSi:1196.1,56.1,97.0')] ).
cnf(1601,plain,
( ~ finite(u)
| ~ relation(skf6(u))
| ~ subset(u,relation_dom(skc16))
| equal(relation_dom(relation_composition(skf6(u),skc16)),relation_dom(skf6(u))) ),
inference(spl,[status(thm),theory(equality)],[116,154]),
[iquote('0:SpL:116.1,154.1')] ).
cnf(1610,plain,
( ~ finite(u)
| ~ subset(u,relation_dom(skc16))
| equal(relation_dom(relation_composition(skf6(u),skc16)),relation_dom(skf6(u))) ),
inference(ssi,[status(thm)],[1601,56,97]),
[iquote('0:SSi:1601.1,56.1,97.0')] ).
cnf(2447,plain,
( ~ finite(u)
| ~ function(relation_composition(skf6(u),skc16))
| ~ relation(relation_composition(skf6(u),skc16))
| ~ subset(u,relation_dom(skc16))
| ~ in(relation_dom(skf6(u)),omega)
| finite(relation_rng(relation_composition(skf6(u),skc16))) ),
inference(spl,[status(thm),theory(equality)],[1610,783]),
[iquote('0:SpL:1610.2,783.2')] ).
cnf(2457,plain,
( ~ finite(u)
| ~ function(relation_composition(skf6(u),skc16))
| ~ relation(relation_composition(skf6(u),skc16))
| ~ subset(u,relation_dom(skc16))
| ~ in(relation_dom(skf6(u)),omega)
| finite(relation_image(skc16,u)) ),
inference(rew,[status(thm),theory(equality)],[1203,2447]),
[iquote('0:Rew:1203.1,2447.5')] ).
cnf(2458,plain,
( ~ finite(u)
| ~ subset(u,relation_dom(skc16))
| ~ in(relation_dom(skf6(u)),omega)
| finite(relation_image(skc16,u)) ),
inference(ssi,[status(thm)],[2457,157,56,97,176]),
[iquote('0:SSi:2457.2,2457.1,157.1,56.0,97.2,176.1,56.0,97.1,157.1,56.0,97.2,176.1,56.0,97.1')] ).
cnf(2459,plain,
( ~ finite(u)
| ~ subset(u,relation_dom(skc16))
| finite(relation_image(skc16,u)) ),
inference(mrr,[status(thm)],[2458,117]),
[iquote('0:MRR:2458.2,117.1')] ).
cnf(3507,plain,
( ~ finite(set_intersection2(relation_dom(skc16),u))
| finite(relation_image(skc16,set_intersection2(relation_dom(skc16),u))) ),
inference(res,[status(thm),theory(equality)],[91,2459]),
[iquote('0:Res:91.0,2459.1')] ).
cnf(3529,plain,
( ~ finite(set_intersection2(relation_dom(skc16),u))
| finite(relation_image(skc16,u)) ),
inference(rew,[status(thm),theory(equality)],[149,3507]),
[iquote('0:Rew:149.0,3507.1')] ).
cnf(3555,plain,
finite(relation_image(skc16,skc17)),
inference(sor,[status(thm)],[3529,169]),
[iquote('0:SoR:3529.0,169.0')] ).
cnf(3557,plain,
$false,
inference(mrr,[status(thm)],[3555,605]),
[iquote('0:MRR:3555.0,605.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : SEU296+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.12 % Command : run_spass %d %s
% 0.09/0.32 % Computer : n032.cluster.edu
% 0.09/0.32 % Model : x86_64 x86_64
% 0.09/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.32 % Memory : 8042.1875MB
% 0.09/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.32 % CPULimit : 300
% 0.09/0.32 % WCLimit : 600
% 0.09/0.32 % DateTime : Sun Jun 19 09:10:03 EDT 2022
% 0.09/0.32 % CPUTime :
% 0.54/0.78
% 0.54/0.78 SPASS V 3.9
% 0.54/0.78 SPASS beiseite: Proof found.
% 0.54/0.78 % SZS status Theorem
% 0.54/0.78 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.54/0.78 SPASS derived 2667 clauses, backtracked 10 clauses, performed 3 splits and kept 1137 clauses.
% 0.54/0.78 SPASS allocated 100409 KBytes.
% 0.54/0.78 SPASS spent 0:00:00.42 on the problem.
% 0.54/0.78 0:00:00.03 for the input.
% 0.54/0.78 0:00:00.03 for the FLOTTER CNF translation.
% 0.54/0.78 0:00:00.05 for inferences.
% 0.54/0.78 0:00:00.00 for the backtracking.
% 0.54/0.78 0:00:00.28 for the reduction.
% 0.54/0.78
% 0.54/0.78
% 0.54/0.78 Here is a proof with depth 5, length 42 :
% 0.54/0.78 % SZS output start Refutation
% See solution above
% 0.54/0.78 Formulae used in the proof : t17_finset_1 d1_finset_1 rc4_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
% 0.54/0.78
%------------------------------------------------------------------------------