TSTP Solution File: SEU053+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU053+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 14:33:44 EDT 2022
% Result : Theorem 3.14s 3.49s
% Output : Refutation 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 17
% Syntax : Number of clauses : 58 ( 23 unt; 9 nHn; 58 RR)
% Number of literals : 116 ( 0 equ; 52 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc9),
file('SEU053+1.p',unknown),
[] ).
cnf(2,axiom,
function(skc9),
file('SEU053+1.p',unknown),
[] ).
cnf(23,axiom,
~ one_to_one(skc9),
file('SEU053+1.p',unknown),
[] ).
cnf(30,axiom,
~ empty(singleton(u)),
file('SEU053+1.p',unknown),
[] ).
cnf(33,axiom,
equal(set_intersection2(u,u),u),
file('SEU053+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ disjoint_nonempty(u,u)
| empty(u) ),
file('SEU053+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ relation(u)
| equal(relation_image(u,empty_set),empty_set) ),
file('SEU053+1.p',unknown),
[] ).
cnf(48,axiom,
( equal(u,v)
| disjoint(singleton(u),singleton(v)) ),
file('SEU053+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ disjoint(u,v)
| equal(set_intersection2(u,v),empty_set) ),
file('SEU053+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ equal(set_intersection2(u,v),empty_set)
| disjoint(u,v) ),
file('SEU053+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ disjoint(u,v)
| empty(v)
| empty(u)
| disjoint_nonempty(u,v) ),
file('SEU053+1.p',unknown),
[] ).
cnf(66,axiom,
equal(set_intersection2(relation_image(skc9,u),relation_image(skc9,v)),relation_image(skc9,set_intersection2(u,v))),
file('SEU053+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ function(u)
| ~ relation(u)
| one_to_one(u)
| in(skf8(u),relation_dom(u)) ),
file('SEU053+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ function(u)
| ~ relation(u)
| one_to_one(u)
| in(skf7(u),relation_dom(u)) ),
file('SEU053+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ function(u)
| ~ relation(u)
| ~ equal(skf8(u),skf7(u))
| one_to_one(u) ),
file('SEU053+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ function(u)
| ~ relation(u)
| one_to_one(u)
| equal(apply(u,skf8(u)),apply(u,skf7(u))) ),
file('SEU053+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ relation(u)
| ~ function(u)
| ~ in(v,relation_dom(u))
| equal(relation_image(u,singleton(v)),singleton(apply(u,v))) ),
file('SEU053+1.p',unknown),
[] ).
cnf(76,plain,
( ~ relation(skc9)
| ~ in(u,relation_dom(skc9))
| equal(relation_image(skc9,singleton(u)),singleton(apply(skc9,u))) ),
inference(res,[status(thm),theory(equality)],[2,72]),
[iquote('0:Res:2.0,72.0')] ).
cnf(77,plain,
( ~ relation(skc9)
| equal(apply(skc9,skf8(skc9)),apply(skc9,skf7(skc9)))
| one_to_one(skc9) ),
inference(res,[status(thm),theory(equality)],[2,71]),
[iquote('0:Res:2.0,71.1')] ).
cnf(78,plain,
( ~ relation(skc9)
| ~ equal(skf8(skc9),skf7(skc9))
| one_to_one(skc9) ),
inference(res,[status(thm),theory(equality)],[2,70]),
[iquote('0:Res:2.0,70.1')] ).
cnf(79,plain,
( ~ relation(skc9)
| in(skf8(skc9),relation_dom(skc9))
| one_to_one(skc9) ),
inference(res,[status(thm),theory(equality)],[2,67]),
[iquote('0:Res:2.0,67.1')] ).
cnf(80,plain,
( ~ relation(skc9)
| in(skf7(skc9),relation_dom(skc9))
| one_to_one(skc9) ),
inference(res,[status(thm),theory(equality)],[2,68]),
[iquote('0:Res:2.0,68.1')] ).
cnf(89,plain,
equal(relation_image(skc9,empty_set),empty_set),
inference(res,[status(thm),theory(equality)],[1,47]),
[iquote('0:Res:1.0,47.0')] ).
cnf(99,plain,
in(skf8(skc9),relation_dom(skc9)),
inference(mrr,[status(thm)],[79,1,23]),
[iquote('0:MRR:79.0,79.2,1.0,23.0')] ).
cnf(100,plain,
in(skf7(skc9),relation_dom(skc9)),
inference(mrr,[status(thm)],[80,1,23]),
[iquote('0:MRR:80.0,80.2,1.0,23.0')] ).
cnf(101,plain,
~ equal(skf8(skc9),skf7(skc9)),
inference(mrr,[status(thm)],[78,1,23]),
[iquote('0:MRR:78.0,78.2,1.0,23.0')] ).
cnf(102,plain,
equal(apply(skc9,skf8(skc9)),apply(skc9,skf7(skc9))),
inference(mrr,[status(thm)],[77,1,23]),
[iquote('0:MRR:77.0,77.2,1.0,23.0')] ).
cnf(103,plain,
( ~ in(u,relation_dom(skc9))
| equal(relation_image(skc9,singleton(u)),singleton(apply(skc9,u))) ),
inference(mrr,[status(thm)],[76,1]),
[iquote('0:MRR:76.0,1.0')] ).
cnf(187,plain,
( ~ equal(u,empty_set)
| disjoint(u,u) ),
inference(spl,[status(thm),theory(equality)],[33,52]),
[iquote('0:SpL:33.0,52.0')] ).
cnf(249,plain,
( ~ disjoint(u,u)
| empty(u)
| empty(u)
| empty(u) ),
inference(res,[status(thm),theory(equality)],[59,39]),
[iquote('0:Res:59.3,39.0')] ).
cnf(251,plain,
( ~ disjoint(u,u)
| empty(u) ),
inference(obv,[status(thm),theory(equality)],[249]),
[iquote('0:Obv:249.2')] ).
cnf(254,plain,
( ~ equal(u,empty_set)
| empty(u) ),
inference(res,[status(thm),theory(equality)],[187,251]),
[iquote('0:Res:187.1,251.0')] ).
cnf(267,plain,
~ equal(singleton(u),empty_set),
inference(res,[status(thm),theory(equality)],[254,30]),
[iquote('0:Res:254.1,30.0')] ).
cnf(477,plain,
( ~ relation(skc9)
| ~ function(skc9)
| ~ in(u,relation_dom(skc9))
| equal(set_intersection2(relation_image(skc9,v),singleton(apply(skc9,u))),relation_image(skc9,set_intersection2(v,singleton(u)))) ),
inference(spr,[status(thm),theory(equality)],[72,66]),
[iquote('0:SpR:72.3,66.0')] ).
cnf(478,plain,
( ~ relation(skc9)
| ~ function(skc9)
| ~ in(u,relation_dom(skc9))
| equal(set_intersection2(singleton(apply(skc9,u)),relation_image(skc9,v)),relation_image(skc9,set_intersection2(singleton(u),v))) ),
inference(spr,[status(thm),theory(equality)],[72,66]),
[iquote('0:SpR:72.3,66.0')] ).
cnf(480,plain,
( ~ in(u,relation_dom(skc9))
| equal(set_intersection2(singleton(apply(skc9,u)),relation_image(skc9,v)),relation_image(skc9,set_intersection2(singleton(u),v))) ),
inference(ssi,[status(thm)],[478,2,1]),
[iquote('0:SSi:478.1,478.0,2.0,1.0,2.0,1.0')] ).
cnf(481,plain,
( ~ in(u,relation_dom(skc9))
| equal(set_intersection2(relation_image(skc9,v),singleton(apply(skc9,u))),relation_image(skc9,set_intersection2(v,singleton(u)))) ),
inference(ssi,[status(thm)],[477,2,1]),
[iquote('0:SSi:477.1,477.0,2.0,1.0,2.0,1.0')] ).
cnf(929,plain,
( ~ in(skf8(skc9),relation_dom(skc9))
| equal(set_intersection2(singleton(apply(skc9,skf7(skc9))),relation_image(skc9,u)),relation_image(skc9,set_intersection2(singleton(skf8(skc9)),u))) ),
inference(spr,[status(thm),theory(equality)],[102,480]),
[iquote('0:SpR:102.0,480.1')] ).
cnf(937,plain,
equal(set_intersection2(singleton(apply(skc9,skf7(skc9))),relation_image(skc9,u)),relation_image(skc9,set_intersection2(singleton(skf8(skc9)),u))),
inference(mrr,[status(thm)],[929,99]),
[iquote('0:MRR:929.0,99.0')] ).
cnf(966,plain,
( ~ in(skf8(skc9),relation_dom(skc9))
| equal(set_intersection2(relation_image(skc9,u),singleton(apply(skc9,skf7(skc9)))),relation_image(skc9,set_intersection2(u,singleton(skf8(skc9))))) ),
inference(spr,[status(thm),theory(equality)],[102,481]),
[iquote('0:SpR:102.0,481.1')] ).
cnf(980,plain,
equal(set_intersection2(relation_image(skc9,u),singleton(apply(skc9,skf7(skc9)))),relation_image(skc9,set_intersection2(u,singleton(skf8(skc9))))),
inference(mrr,[status(thm)],[966,99]),
[iquote('0:MRR:966.0,99.0')] ).
cnf(1526,plain,
( ~ in(skf7(skc9),relation_dom(skc9))
| equal(relation_image(skc9,set_intersection2(singleton(skf8(skc9)),u)),relation_image(skc9,set_intersection2(singleton(skf7(skc9)),u))) ),
inference(spr,[status(thm),theory(equality)],[937,480]),
[iquote('0:SpR:937.0,480.1')] ).
cnf(1550,plain,
equal(relation_image(skc9,set_intersection2(singleton(skf8(skc9)),u)),relation_image(skc9,set_intersection2(singleton(skf7(skc9)),u))),
inference(mrr,[status(thm)],[1526,100]),
[iquote('0:MRR:1526.0,100.0')] ).
cnf(1617,plain,
( ~ in(skf7(skc9),relation_dom(skc9))
| equal(relation_image(skc9,set_intersection2(u,singleton(skf8(skc9)))),relation_image(skc9,set_intersection2(u,singleton(skf7(skc9))))) ),
inference(spr,[status(thm),theory(equality)],[980,481]),
[iquote('0:SpR:980.0,481.1')] ).
cnf(1641,plain,
equal(relation_image(skc9,set_intersection2(u,singleton(skf8(skc9)))),relation_image(skc9,set_intersection2(u,singleton(skf7(skc9))))),
inference(mrr,[status(thm)],[1617,100]),
[iquote('0:MRR:1617.0,100.0')] ).
cnf(2807,plain,
equal(relation_image(skc9,set_intersection2(singleton(skf7(skc9)),singleton(skf8(skc9)))),relation_image(skc9,singleton(skf8(skc9)))),
inference(spr,[status(thm),theory(equality)],[33,1550]),
[iquote('0:SpR:33.0,1550.0')] ).
cnf(2808,plain,
( ~ disjoint(singleton(skf8(skc9)),u)
| equal(relation_image(skc9,set_intersection2(singleton(skf7(skc9)),u)),relation_image(skc9,empty_set)) ),
inference(spr,[status(thm),theory(equality)],[51,1550]),
[iquote('0:SpR:51.1,1550.0')] ).
cnf(2827,plain,
equal(relation_image(skc9,set_intersection2(singleton(skf7(skc9)),singleton(skf7(skc9)))),relation_image(skc9,singleton(skf8(skc9)))),
inference(rew,[status(thm),theory(equality)],[1641,2807]),
[iquote('0:Rew:1641.0,2807.0')] ).
cnf(2828,plain,
equal(relation_image(skc9,singleton(skf8(skc9))),relation_image(skc9,singleton(skf7(skc9)))),
inference(rew,[status(thm),theory(equality)],[33,2827]),
[iquote('0:Rew:33.0,2827.0')] ).
cnf(2831,plain,
( ~ disjoint(singleton(skf8(skc9)),u)
| equal(relation_image(skc9,set_intersection2(singleton(skf7(skc9)),u)),empty_set) ),
inference(rew,[status(thm),theory(equality)],[89,2808]),
[iquote('0:Rew:89.0,2808.1')] ).
cnf(2878,plain,
( ~ in(skf8(skc9),relation_dom(skc9))
| equal(relation_image(skc9,singleton(skf7(skc9))),singleton(apply(skc9,skf8(skc9)))) ),
inference(spr,[status(thm),theory(equality)],[2828,103]),
[iquote('0:SpR:2828.0,103.1')] ).
cnf(2894,plain,
( ~ in(skf8(skc9),relation_dom(skc9))
| equal(relation_image(skc9,singleton(skf7(skc9))),singleton(apply(skc9,skf7(skc9)))) ),
inference(rew,[status(thm),theory(equality)],[102,2878]),
[iquote('0:Rew:102.0,2878.1')] ).
cnf(2895,plain,
equal(relation_image(skc9,singleton(skf7(skc9))),singleton(apply(skc9,skf7(skc9)))),
inference(mrr,[status(thm)],[2894,99]),
[iquote('0:MRR:2894.0,99.0')] ).
cnf(8754,plain,
( ~ disjoint(singleton(skf8(skc9)),singleton(skf7(skc9)))
| equal(relation_image(skc9,singleton(skf7(skc9))),empty_set) ),
inference(spr,[status(thm),theory(equality)],[33,2831]),
[iquote('0:SpR:33.0,2831.1')] ).
cnf(8784,plain,
( ~ disjoint(singleton(skf8(skc9)),singleton(skf7(skc9)))
| equal(singleton(apply(skc9,skf7(skc9))),empty_set) ),
inference(rew,[status(thm),theory(equality)],[2895,8754]),
[iquote('0:Rew:2895.0,8754.1')] ).
cnf(8785,plain,
~ disjoint(singleton(skf8(skc9)),singleton(skf7(skc9))),
inference(mrr,[status(thm)],[8784,267]),
[iquote('0:MRR:8784.1,267.0')] ).
cnf(8957,plain,
equal(skf8(skc9),skf7(skc9)),
inference(res,[status(thm),theory(equality)],[48,8785]),
[iquote('0:Res:48.1,8785.0')] ).
cnf(8958,plain,
$false,
inference(mrr,[status(thm)],[8957,101]),
[iquote('0:MRR:8957.0,101.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU053+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.10/0.34 % Computer : n011.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8042.1875MB
% 0.10/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 600
% 0.10/0.34 % DateTime : Sun Jun 19 01:47:08 EDT 2022
% 0.10/0.34 % CPUTime :
% 3.14/3.49
% 3.14/3.49 SPASS V 3.9
% 3.14/3.49 SPASS beiseite: Proof found.
% 3.14/3.49 % SZS status Theorem
% 3.14/3.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.14/3.49 SPASS derived 6816 clauses, backtracked 0 clauses, performed 3 splits and kept 2080 clauses.
% 3.14/3.49 SPASS allocated 105513 KBytes.
% 3.14/3.49 SPASS spent 0:00:03.06 on the problem.
% 3.14/3.49 0:00:00.03 for the input.
% 3.14/3.49 0:00:00.04 for the FLOTTER CNF translation.
% 3.14/3.49 0:00:00.20 for inferences.
% 3.14/3.49 0:00:00.01 for the backtracking.
% 3.14/3.49 0:00:02.73 for the reduction.
% 3.14/3.49
% 3.14/3.49
% 3.14/3.49 Here is a proof with depth 6, length 58 :
% 3.14/3.49 % SZS output start Refutation
% See solution above
% 3.14/3.49 Formulae used in the proof : t122_funct_1 fc2_subset_1 idempotence_k3_xboole_0 irreflexivity_r1_subset_1 t149_relat_1 t17_zfmisc_1 d7_xboole_0 redefinition_r1_subset_1 d8_funct_1 t117_funct_1
% 3.14/3.49
%------------------------------------------------------------------------------