TSTP Solution File: SEU055+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU055+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 14:33:45 EDT 2022
% Result : Theorem 1.36s 1.59s
% Output : Refutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 27
% Syntax : Number of clauses : 67 ( 32 unt; 13 nHn; 67 RR)
% Number of literals : 125 ( 0 equ; 53 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc9),
file('SEU055+1.p',unknown),
[] ).
cnf(2,axiom,
function(skc9),
file('SEU055+1.p',unknown),
[] ).
cnf(5,axiom,
relation_empty_yielding(empty_set),
file('SEU055+1.p',unknown),
[] ).
cnf(7,axiom,
empty(empty_set),
file('SEU055+1.p',unknown),
[] ).
cnf(8,axiom,
relation(empty_set),
file('SEU055+1.p',unknown),
[] ).
cnf(15,axiom,
empty(skc23),
file('SEU055+1.p',unknown),
[] ).
cnf(16,axiom,
function(skc23),
file('SEU055+1.p',unknown),
[] ).
cnf(23,axiom,
~ one_to_one(skc9),
file('SEU055+1.p',unknown),
[] ).
cnf(27,axiom,
subset(u,u),
file('SEU055+1.p',unknown),
[] ).
cnf(28,axiom,
element(skf9(u),u),
file('SEU055+1.p',unknown),
[] ).
cnf(30,axiom,
~ empty(singleton(u)),
file('SEU055+1.p',unknown),
[] ).
cnf(35,axiom,
equal(set_difference(u,empty_set),u),
file('SEU055+1.p',unknown),
[] ).
cnf(36,axiom,
equal(set_difference(empty_set,u),empty_set),
file('SEU055+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ empty(u)
| equal(u,empty_set) ),
file('SEU055+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ subset(u,v)
| element(u,powerset(v)) ),
file('SEU055+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ element(u,v)
| empty(v)
| in(u,v) ),
file('SEU055+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ equal(set_difference(u,v),empty_set)
| subset(u,v) ),
file('SEU055+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ subset(u,v)
| equal(set_difference(u,v),empty_set) ),
file('SEU055+1.p',unknown),
[] ).
cnf(53,axiom,
( equal(u,v)
| equal(set_difference(singleton(u),singleton(v)),singleton(u)) ),
file('SEU055+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('SEU055+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ empty(u)
| ~ in(v,w)
| ~ element(w,powerset(u)) ),
file('SEU055+1.p',unknown),
[] ).
cnf(59,axiom,
equal(set_difference(relation_image(skc9,u),relation_image(skc9,v)),relation_image(skc9,set_difference(u,v))),
file('SEU055+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ function(u)
| ~ relation(u)
| one_to_one(u)
| in(skf8(u),relation_dom(u)) ),
file('SEU055+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ function(u)
| ~ relation(u)
| one_to_one(u)
| in(skf7(u),relation_dom(u)) ),
file('SEU055+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ function(u)
| ~ relation(u)
| ~ equal(skf8(u),skf7(u))
| one_to_one(u) ),
file('SEU055+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ function(u)
| ~ relation(u)
| one_to_one(u)
| equal(apply(u,skf8(u)),apply(u,skf7(u))) ),
file('SEU055+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ relation(u)
| ~ function(u)
| ~ in(v,relation_dom(u))
| equal(relation_image(u,singleton(v)),singleton(apply(u,v))) ),
file('SEU055+1.p',unknown),
[] ).
cnf(71,plain,
( ~ relation(skc9)
| equal(apply(skc9,skf8(skc9)),apply(skc9,skf7(skc9)))
| one_to_one(skc9) ),
inference(res,[status(thm),theory(equality)],[2,65]),
[iquote('0:Res:2.0,65.1')] ).
cnf(72,plain,
( ~ relation(skc9)
| ~ equal(skf8(skc9),skf7(skc9))
| one_to_one(skc9) ),
inference(res,[status(thm),theory(equality)],[2,64]),
[iquote('0:Res:2.0,64.1')] ).
cnf(73,plain,
( ~ relation(skc9)
| in(skf8(skc9),relation_dom(skc9))
| one_to_one(skc9) ),
inference(res,[status(thm),theory(equality)],[2,60]),
[iquote('0:Res:2.0,60.1')] ).
cnf(74,plain,
( ~ relation(skc9)
| in(skf7(skc9),relation_dom(skc9))
| one_to_one(skc9) ),
inference(res,[status(thm),theory(equality)],[2,61]),
[iquote('0:Res:2.0,61.1')] ).
cnf(94,plain,
in(skf8(skc9),relation_dom(skc9)),
inference(mrr,[status(thm)],[73,1,23]),
[iquote('0:MRR:73.0,73.2,1.0,23.0')] ).
cnf(95,plain,
in(skf7(skc9),relation_dom(skc9)),
inference(mrr,[status(thm)],[74,1,23]),
[iquote('0:MRR:74.0,74.2,1.0,23.0')] ).
cnf(96,plain,
~ equal(skf8(skc9),skf7(skc9)),
inference(mrr,[status(thm)],[72,1,23]),
[iquote('0:MRR:72.0,72.2,1.0,23.0')] ).
cnf(97,plain,
equal(apply(skc9,skf8(skc9)),apply(skc9,skf7(skc9))),
inference(mrr,[status(thm)],[71,1,23]),
[iquote('0:MRR:71.0,71.2,1.0,23.0')] ).
cnf(110,plain,
equal(skc23,empty_set),
inference(ems,[status(thm)],[40,15]),
[iquote('0:EmS:40.0,15.0')] ).
cnf(114,plain,
function(empty_set),
inference(rew,[status(thm),theory(equality)],[110,16]),
[iquote('0:Rew:110.0,16.0')] ).
cnf(154,plain,
( ~ equal(u,empty_set)
| subset(u,empty_set) ),
inference(spl,[status(thm),theory(equality)],[35,48]),
[iquote('0:SpL:35.0,48.0')] ).
cnf(169,plain,
( empty(u)
| in(skf9(u),u) ),
inference(res,[status(thm),theory(equality)],[28,47]),
[iquote('0:Res:28.0,47.0')] ).
cnf(209,plain,
( ~ empty(u)
| ~ subset(v,u)
| ~ in(w,v) ),
inference(res,[status(thm),theory(equality)],[45,58]),
[iquote('0:Res:45.1,58.2')] ).
cnf(245,plain,
( ~ in(u,singleton(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[55]),
[iquote('0:EqR:55.1')] ).
cnf(252,plain,
( empty(singleton(u))
| equal(skf9(singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[169,245]),
[iquote('0:Res:169.1,245.0')] ).
cnf(253,plain,
equal(skf9(singleton(u)),u),
inference(mrr,[status(thm)],[252,30]),
[iquote('0:MRR:252.0,30.0')] ).
cnf(255,plain,
( empty(singleton(u))
| in(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[253,169]),
[iquote('0:SpR:253.0,169.1')] ).
cnf(258,plain,
in(u,singleton(u)),
inference(mrr,[status(thm)],[255,30]),
[iquote('0:MRR:255.0,30.0')] ).
cnf(295,plain,
( ~ subset(relation_image(skc9,u),relation_image(skc9,v))
| equal(relation_image(skc9,set_difference(u,v)),empty_set) ),
inference(spr,[status(thm),theory(equality)],[59,49]),
[iquote('0:SpR:59.0,49.1')] ).
cnf(431,plain,
( ~ relation(skc9)
| ~ function(skc9)
| ~ in(u,relation_dom(skc9))
| equal(set_difference(singleton(apply(skc9,u)),relation_image(skc9,v)),relation_image(skc9,set_difference(singleton(u),v))) ),
inference(spr,[status(thm),theory(equality)],[66,59]),
[iquote('0:SpR:66.3,59.0')] ).
cnf(433,plain,
( ~ in(u,relation_dom(skc9))
| equal(set_difference(singleton(apply(skc9,u)),relation_image(skc9,v)),relation_image(skc9,set_difference(singleton(u),v))) ),
inference(ssi,[status(thm)],[431,2,1]),
[iquote('0:SSi:431.1,431.0,2.0,1.0,2.0,1.0')] ).
cnf(513,plain,
( ~ empty(empty_set)
| ~ equal(u,empty_set)
| ~ in(v,u) ),
inference(res,[status(thm),theory(equality)],[154,209]),
[iquote('0:Res:154.1,209.1')] ).
cnf(522,plain,
( ~ equal(u,empty_set)
| ~ in(v,u) ),
inference(ssi,[status(thm)],[513,5,8,7,114]),
[iquote('0:SSi:513.0,5.0,8.0,7.0,114.0')] ).
cnf(539,plain,
~ equal(singleton(u),empty_set),
inference(res,[status(thm),theory(equality)],[258,522]),
[iquote('0:Res:258.0,522.1')] ).
cnf(791,plain,
equal(relation_image(skc9,set_difference(u,u)),empty_set),
inference(res,[status(thm),theory(equality)],[27,295]),
[iquote('0:Res:27.0,295.0')] ).
cnf(827,plain,
equal(relation_image(skc9,empty_set),empty_set),
inference(spr,[status(thm),theory(equality)],[36,791]),
[iquote('0:SpR:36.0,791.0')] ).
cnf(913,plain,
( ~ in(skf8(skc9),relation_dom(skc9))
| equal(set_difference(singleton(apply(skc9,skf7(skc9))),relation_image(skc9,u)),relation_image(skc9,set_difference(singleton(skf8(skc9)),u))) ),
inference(spr,[status(thm),theory(equality)],[97,433]),
[iquote('0:SpR:97.0,433.1')] ).
cnf(921,plain,
equal(set_difference(singleton(apply(skc9,skf7(skc9))),relation_image(skc9,u)),relation_image(skc9,set_difference(singleton(skf8(skc9)),u))),
inference(mrr,[status(thm)],[913,94]),
[iquote('0:MRR:913.0,94.0')] ).
cnf(1123,plain,
( ~ in(skf7(skc9),relation_dom(skc9))
| equal(relation_image(skc9,set_difference(singleton(skf8(skc9)),u)),relation_image(skc9,set_difference(singleton(skf7(skc9)),u))) ),
inference(spr,[status(thm),theory(equality)],[921,433]),
[iquote('0:SpR:921.0,433.1')] ).
cnf(1136,plain,
equal(relation_image(skc9,set_difference(singleton(skf8(skc9)),u)),relation_image(skc9,set_difference(singleton(skf7(skc9)),u))),
inference(mrr,[status(thm)],[1123,95]),
[iquote('0:MRR:1123.0,95.0')] ).
cnf(1137,plain,
equal(set_difference(singleton(apply(skc9,skf7(skc9))),relation_image(skc9,u)),relation_image(skc9,set_difference(singleton(skf7(skc9)),u))),
inference(rew,[status(thm),theory(equality)],[1136,921]),
[iquote('0:Rew:1136.0,921.0')] ).
cnf(1293,plain,
equal(relation_image(skc9,set_difference(singleton(skf7(skc9)),empty_set)),set_difference(singleton(apply(skc9,skf7(skc9))),empty_set)),
inference(spr,[status(thm),theory(equality)],[827,1137]),
[iquote('0:SpR:827.0,1137.0')] ).
cnf(1296,plain,
equal(relation_image(skc9,singleton(skf7(skc9))),singleton(apply(skc9,skf7(skc9)))),
inference(rew,[status(thm),theory(equality)],[35,1293]),
[iquote('0:Rew:35.0,1293.0,35.0,1293.0')] ).
cnf(3076,plain,
( ~ subset(singleton(skf8(skc9)),u)
| equal(relation_image(skc9,set_difference(singleton(skf7(skc9)),u)),relation_image(skc9,empty_set)) ),
inference(spr,[status(thm),theory(equality)],[49,1136]),
[iquote('0:SpR:49.1,1136.0')] ).
cnf(3087,plain,
( ~ subset(singleton(skf8(skc9)),u)
| equal(relation_image(skc9,set_difference(singleton(skf7(skc9)),u)),empty_set) ),
inference(rew,[status(thm),theory(equality)],[827,3076]),
[iquote('0:Rew:827.0,3076.1')] ).
cnf(8456,plain,
( ~ subset(singleton(skf8(skc9)),singleton(u))
| equal(skf7(skc9),u)
| equal(relation_image(skc9,singleton(skf7(skc9))),empty_set) ),
inference(spr,[status(thm),theory(equality)],[53,3087]),
[iquote('0:SpR:53.1,3087.1')] ).
cnf(8487,plain,
( ~ subset(singleton(skf8(skc9)),singleton(u))
| equal(skf7(skc9),u)
| equal(singleton(apply(skc9,skf7(skc9))),empty_set) ),
inference(rew,[status(thm),theory(equality)],[1296,8456]),
[iquote('0:Rew:1296.0,8456.2')] ).
cnf(8488,plain,
( ~ subset(singleton(skf8(skc9)),singleton(u))
| equal(skf7(skc9),u) ),
inference(mrr,[status(thm)],[8487,539]),
[iquote('0:MRR:8487.2,539.0')] ).
cnf(8853,plain,
equal(skf8(skc9),skf7(skc9)),
inference(res,[status(thm),theory(equality)],[27,8488]),
[iquote('0:Res:27.0,8488.0')] ).
cnf(8854,plain,
$false,
inference(mrr,[status(thm)],[8853,96]),
[iquote('0:MRR:8853.0,96.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU055+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.33 % CPULimit : 300
% 0.18/0.33 % WCLimit : 600
% 0.18/0.33 % DateTime : Mon Jun 20 05:41:15 EDT 2022
% 0.18/0.33 % CPUTime :
% 1.36/1.59
% 1.36/1.59 SPASS V 3.9
% 1.36/1.59 SPASS beiseite: Proof found.
% 1.36/1.59 % SZS status Theorem
% 1.36/1.59 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.36/1.59 SPASS derived 5931 clauses, backtracked 112 clauses, performed 4 splits and kept 1487 clauses.
% 1.36/1.59 SPASS allocated 104499 KBytes.
% 1.36/1.59 SPASS spent 0:00:01.21 on the problem.
% 1.36/1.59 0:00:00.03 for the input.
% 1.36/1.59 0:00:00.04 for the FLOTTER CNF translation.
% 1.36/1.59 0:00:00.08 for inferences.
% 1.36/1.59 0:00:00.02 for the backtracking.
% 1.36/1.59 0:00:00.99 for the reduction.
% 1.36/1.59
% 1.36/1.59
% 1.36/1.59 Here is a proof with depth 6, length 67 :
% 1.36/1.59 % SZS output start Refutation
% See solution above
% 1.36/1.59 Formulae used in the proof : t124_funct_1 fc12_relat_1 fc4_relat_1 rc2_funct_1 reflexivity_r1_tarski existence_m1_subset_1 fc2_subset_1 t3_boole t4_boole t6_boole t3_subset t2_subset t37_xboole_1 t20_zfmisc_1 d1_tarski antisymmetry_r2_hidden t5_subset d8_funct_1 t117_funct_1
% 1.36/1.59
%------------------------------------------------------------------------------