TSTP Solution File: SET504-6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET504-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 05:26:39 EDT 2022
% Result : Unsatisfiable 4.32s 4.51s
% Output : Refutation 4.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET504-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.11/0.34 % Computer : n003.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 600
% 0.11/0.34 % DateTime : Sun Jul 10 14:15:44 EDT 2022
% 0.11/0.34 % CPUTime :
% 4.32/4.51
% 4.32/4.51 SPASS V 3.9
% 4.32/4.51 SPASS beiseite: Proof found.
% 4.32/4.51 % SZS status Theorem
% 4.32/4.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.32/4.51 SPASS derived 14210 clauses, backtracked 611 clauses, performed 5 splits and kept 6330 clauses.
% 4.32/4.51 SPASS allocated 89522 KBytes.
% 4.32/4.51 SPASS spent 0:00:04.15 on the problem.
% 4.32/4.51 0:00:00.04 for the input.
% 4.32/4.51 0:00:00.00 for the FLOTTER CNF translation.
% 4.32/4.51 0:00:00.14 for inferences.
% 4.32/4.51 0:00:00.27 for the backtracking.
% 4.32/4.51 0:00:03.61 for the reduction.
% 4.32/4.51
% 4.32/4.51
% 4.32/4.51 Here is a proof with depth 12, length 132 :
% 4.32/4.51 % SZS output start Refutation
% 4.32/4.51 1[0:Inp] || -> member(ordered_pair(x__dfg,universal_class),cross_product(universal_class,universal_class))*.
% 4.32/4.51 2[0:Inp] || member(u,v)*+ subclass(v,w)* -> member(u,w)*.
% 4.32/4.51 3[0:Inp] || -> subclass(u,v) member(not_subclass_element(u,v),u)*.
% 4.32/4.51 4[0:Inp] || member(not_subclass_element(u,v),v)* -> subclass(u,v).
% 4.32/4.51 5[0:Inp] || -> subclass(u,universal_class)*.
% 4.32/4.51 7[0:Inp] || equal(u,v) -> subclass(v,u)*.
% 4.32/4.51 8[0:Inp] || subclass(u,v)*+ subclass(v,u)* -> equal(v,u).
% 4.32/4.51 9[0:Inp] || member(u,unordered_pair(v,w))* -> equal(u,w) equal(u,v).
% 4.32/4.51 11[0:Inp] || member(u,universal_class) -> member(u,unordered_pair(v,u))*.
% 4.32/4.51 12[0:Inp] || -> member(unordered_pair(u,v),universal_class)*.
% 4.32/4.51 13[0:Inp] || -> equal(unordered_pair(u,u),singleton(u))**.
% 4.32/4.51 16[0:Inp] || member(ordered_pair(u,v),cross_product(w,x))* -> member(v,x).
% 4.32/4.51 22[0:Inp] || member(u,intersection(v,w))* -> member(u,v).
% 4.32/4.51 23[0:Inp] || member(u,intersection(v,w))* -> member(u,w).
% 4.32/4.51 24[0:Inp] || member(u,v) member(u,w) -> member(u,intersection(w,v))*.
% 4.32/4.51 25[0:Inp] || member(u,v) member(u,complement(v))* -> .
% 4.32/4.51 26[0:Inp] || member(u,universal_class) -> member(u,v) member(u,complement(v))*.
% 4.32/4.51 27[0:Inp] || -> equal(complement(intersection(complement(u),complement(v))),union(u,v))**.
% 4.32/4.51 28[0:Inp] || -> equal(intersection(complement(intersection(u,v)),complement(intersection(complement(u),complement(v)))),symmetric_difference(u,v))**.
% 4.32/4.51 44[0:Inp] || -> equal(union(u,singleton(u)),successor(u))**.
% 4.32/4.51 67[0:Inp] || -> equal(u,null_class) member(regular(u),u)*.
% 4.32/4.51 68[0:Inp] || -> equal(u,null_class) equal(intersection(u,regular(u)),null_class)**.
% 4.32/4.51 71[0:Inp] || member(u,universal_class) -> equal(u,null_class) member(apply(choice,u),u)*.
% 4.32/4.51 114[0:Rew:27.0,28.0] || -> equal(intersection(complement(intersection(u,v)),union(u,v)),symmetric_difference(u,v))**.
% 4.32/4.51 119[0:Res:1.0,16.0] || -> member(universal_class,universal_class)*.
% 4.32/4.51 134[0:SpR:13.0,12.0] || -> member(singleton(u),universal_class)*.
% 4.32/4.51 159[0:SpR:13.0,11.1] || member(u,universal_class) -> member(u,singleton(u))*.
% 4.32/4.51 165[0:Res:67.1,25.1] || member(regular(complement(u)),u)* -> equal(complement(u),null_class).
% 4.32/4.51 174[0:Res:3.1,23.0] || -> subclass(intersection(u,v),w) member(not_subclass_element(intersection(u,v),w),v)*.
% 4.32/4.51 180[0:Res:67.1,22.0] || -> equal(intersection(u,v),null_class) member(regular(intersection(u,v)),u)*.
% 4.32/4.51 181[0:Res:3.1,22.0] || -> subclass(intersection(u,v),w) member(not_subclass_element(intersection(u,v),w),u)*.
% 4.32/4.51 282[0:Res:26.2,4.0] || member(not_subclass_element(u,complement(v)),universal_class)*+ -> member(not_subclass_element(u,complement(v)),v)* subclass(u,complement(v)).
% 4.32/4.51 328[0:Res:5.0,8.0] || subclass(universal_class,u)* -> equal(universal_class,u).
% 4.32/4.51 358[0:Res:119.0,2.0] || subclass(universal_class,u)* -> member(universal_class,u).
% 4.32/4.51 370[0:Res:67.1,2.0] || subclass(u,v) -> equal(u,null_class) member(regular(u),v)*.
% 4.32/4.51 371[0:Res:3.1,2.0] || subclass(u,v) -> subclass(u,w) member(not_subclass_element(u,w),v)*.
% 4.32/4.51 397[0:Res:7.1,358.0] || equal(u,universal_class) -> member(universal_class,u)*.
% 4.32/4.51 424[0:Res:397.1,25.1] || equal(complement(u),universal_class) member(universal_class,u)* -> .
% 4.32/4.51 547[0:Res:159.1,424.1] || member(universal_class,universal_class) equal(complement(singleton(universal_class)),universal_class)** -> .
% 4.32/4.51 554[0:MRR:547.0,119.0] || equal(complement(singleton(universal_class)),universal_class)** -> .
% 4.32/4.51 558[0:SpL:13.0,9.0] || member(u,singleton(v))* -> equal(u,v) equal(u,v).
% 4.32/4.51 572[0:Obv:558.1] || member(u,singleton(v))* -> equal(u,v).
% 4.32/4.51 577[0:Res:67.1,572.0] || -> equal(singleton(u),null_class) equal(regular(singleton(u)),u)**.
% 4.32/4.51 578[0:Res:3.1,572.0] || -> subclass(singleton(u),v) equal(not_subclass_element(singleton(u),v),u)**.
% 4.32/4.51 584[0:Res:71.2,572.0] || member(singleton(u),universal_class) -> equal(singleton(u),null_class) equal(apply(choice,singleton(u)),u)**.
% 4.32/4.51 588[0:MRR:584.0,134.0] || -> equal(singleton(u),null_class) equal(apply(choice,singleton(u)),u)**.
% 4.32/4.51 728[0:SpR:577.1,67.1] || -> equal(singleton(u),null_class) equal(singleton(u),null_class) member(u,singleton(u))*.
% 4.32/4.51 729[0:SpR:577.1,68.1] || -> equal(singleton(u),null_class) equal(singleton(u),null_class) equal(intersection(singleton(u),u),null_class)**.
% 4.32/4.51 731[0:Obv:728.0] || -> equal(singleton(u),null_class) member(u,singleton(u))*.
% 4.32/4.51 732[0:Obv:729.0] || -> equal(singleton(u),null_class) equal(intersection(singleton(u),u),null_class)**.
% 4.32/4.51 778[0:Res:24.2,2.0] || member(u,v)* member(u,w)* subclass(intersection(w,v),x)*+ -> member(u,x)*.
% 4.32/4.51 2393[0:SpR:732.1,24.2] || member(u,v) member(u,singleton(v))* -> equal(singleton(v),null_class) member(u,null_class).
% 4.32/4.51 3401[0:Res:370.2,165.0] || subclass(complement(u),u)* -> equal(complement(u),null_class) equal(complement(u),null_class).
% 4.32/4.51 3415[0:Obv:3401.1] || subclass(complement(u),u)* -> equal(complement(u),null_class).
% 4.32/4.51 3425[0:Res:5.0,3415.0] || -> equal(complement(universal_class),null_class)**.
% 4.32/4.51 3436[0:SpR:3425.0,27.0] || -> equal(complement(intersection(null_class,complement(u))),union(universal_class,u))**.
% 4.32/4.51 3438[0:SpR:3425.0,27.0] || -> equal(complement(intersection(complement(u),null_class)),union(u,universal_class))**.
% 4.32/4.51 3450[0:SpL:3425.0,25.1] || member(u,universal_class) member(u,null_class)* -> .
% 4.32/4.51 3671[0:SpR:578.1,3.1] || -> subclass(singleton(u),v)* subclass(singleton(u),v)* member(u,singleton(u))*.
% 4.32/4.51 3675[0:Obv:3671.0] || -> subclass(singleton(u),v)* member(u,singleton(u))*.
% 4.32/4.51 3676[0:Rew:731.0,3675.0] || -> subclass(null_class,u)* member(v,singleton(v))*.
% 4.32/4.51 3682[1:Spt:3676.0] || -> subclass(null_class,u)*.
% 4.32/4.51 3688[1:Res:3682.0,8.0] || subclass(u,null_class)* -> equal(u,null_class).
% 4.32/4.51 4380[0:Res:174.1,4.0] || -> subclass(intersection(u,v),v)* subclass(intersection(u,v),v)*.
% 4.32/4.51 4382[0:Obv:4380.0] || -> subclass(intersection(u,v),v)*.
% 4.32/4.51 4413[1:Res:4382.0,3688.0] || -> equal(intersection(u,null_class),null_class)**.
% 4.32/4.51 4417[1:Rew:4413.0,3438.0] || -> equal(union(u,universal_class),complement(null_class))**.
% 4.32/4.51 4618[1:SpR:4413.0,114.0] || -> equal(intersection(complement(null_class),union(u,null_class)),symmetric_difference(u,null_class))**.
% 4.32/4.51 4641[1:SpL:4413.0,22.0] || member(u,null_class)* -> member(u,v)*.
% 4.32/4.51 4659[1:MRR:3450.0,4641.1] || member(u,null_class)* -> .
% 4.32/4.51 4693[1:Res:180.1,4659.0] || -> equal(intersection(null_class,u),null_class)**.
% 4.32/4.51 4711[1:Rew:4693.0,3436.0] || -> equal(union(universal_class,u),complement(null_class))**.
% 4.32/4.51 4776[1:SpR:4417.0,114.0] || -> equal(intersection(complement(intersection(u,universal_class)),complement(null_class)),symmetric_difference(u,universal_class))**.
% 4.32/4.51 4818[1:SpR:4711.0,44.0] || -> equal(complement(null_class),successor(universal_class))**.
% 4.32/4.51 4826[1:Rew:4818.0,4711.0] || -> equal(union(universal_class,u),successor(universal_class))**.
% 4.32/4.51 4850[1:Rew:4818.0,4618.0] || -> equal(intersection(successor(universal_class),union(u,null_class)),symmetric_difference(u,null_class))**.
% 4.32/4.51 4852[1:Rew:4818.0,4776.0] || -> equal(intersection(complement(intersection(u,universal_class)),successor(universal_class)),symmetric_difference(u,universal_class))**.
% 4.32/4.51 5557[0:Res:181.1,4.0] || -> subclass(intersection(u,v),u)* subclass(intersection(u,v),u)*.
% 4.32/4.51 5561[0:Obv:5557.0] || -> subclass(intersection(u,v),u)*.
% 4.32/4.51 5579[0:SpR:114.0,5561.0] || -> subclass(symmetric_difference(u,v),complement(intersection(u,v)))*.
% 4.32/4.51 6319[1:SpR:4826.0,4850.0] || -> equal(intersection(successor(universal_class),successor(universal_class)),symmetric_difference(universal_class,null_class))**.
% 4.32/4.51 6393[1:SpR:6319.0,24.2] || member(u,successor(universal_class)) member(u,successor(universal_class)) -> member(u,symmetric_difference(universal_class,null_class))*.
% 4.32/4.51 6413[1:Obv:6393.0] || member(u,successor(universal_class)) -> member(u,symmetric_difference(universal_class,null_class))*.
% 4.32/4.51 6800[1:Res:6413.1,4.0] || member(not_subclass_element(u,symmetric_difference(universal_class,null_class)),successor(universal_class))* -> subclass(u,symmetric_difference(universal_class,null_class)).
% 4.41/4.59 7985[0:Res:371.2,282.0] || subclass(u,universal_class) -> subclass(u,complement(v)) member(not_subclass_element(u,complement(v)),v)* subclass(u,complement(v)).
% 4.41/4.59 7989[0:Obv:7985.1] || subclass(u,universal_class) -> member(not_subclass_element(u,complement(v)),v)* subclass(u,complement(v)).
% 4.41/4.59 7990[0:MRR:7989.0,5.0] || -> member(not_subclass_element(u,complement(v)),v)* subclass(u,complement(v)).
% 4.41/4.59 8078[1:Res:7990.0,4659.0] || -> subclass(u,complement(null_class))*.
% 4.41/4.59 8083[1:Rew:4818.0,8078.0] || -> subclass(u,successor(universal_class))*.
% 4.41/4.59 8159[1:Res:8083.0,328.0] || -> equal(successor(universal_class),universal_class)**.
% 4.41/4.59 8172[1:Rew:8159.0,4818.0] || -> equal(complement(null_class),universal_class)**.
% 4.41/4.59 8208[1:Rew:8159.0,6319.0] || -> equal(intersection(universal_class,universal_class),symmetric_difference(universal_class,null_class))**.
% 4.41/4.59 8267[1:Rew:8159.0,4852.0] || -> equal(intersection(complement(intersection(u,universal_class)),universal_class),symmetric_difference(u,universal_class))**.
% 4.41/4.59 8534[1:Rew:8159.0,6800.0] || member(not_subclass_element(u,symmetric_difference(universal_class,null_class)),universal_class)* -> subclass(u,symmetric_difference(universal_class,null_class)).
% 4.41/4.59 9863[0:Res:5.0,778.2] || member(u,v)* member(u,w)* -> member(u,universal_class)*.
% 4.41/4.59 9873[0:Con:9863.1] || member(u,v)*+ -> member(u,universal_class)*.
% 4.41/4.59 9933[0:Res:3.1,9873.0] || -> subclass(u,v) member(not_subclass_element(u,v),universal_class)*.
% 4.41/4.59 10049[1:MRR:8534.0,9933.1] || -> subclass(u,symmetric_difference(universal_class,null_class))*.
% 4.41/4.59 10233[1:Res:10049.0,328.0] || -> equal(symmetric_difference(universal_class,null_class),universal_class)**.
% 4.41/4.59 10243[1:Rew:10233.0,8208.0] || -> equal(intersection(universal_class,universal_class),universal_class)**.
% 4.41/4.59 10998[1:SpR:732.1,8267.0] || -> equal(singleton(universal_class),null_class) equal(intersection(complement(null_class),universal_class),symmetric_difference(singleton(universal_class),universal_class))**.
% 4.41/4.59 11026[1:Rew:10243.0,10998.1,8172.0,10998.1] || -> equal(singleton(universal_class),null_class) equal(symmetric_difference(singleton(universal_class),universal_class),universal_class)**.
% 4.41/4.59 11040[2:Spt:11026.0] || -> equal(singleton(universal_class),null_class)**.
% 4.41/4.59 11041[2:Rew:11040.0,554.0] || equal(complement(null_class),universal_class)** -> .
% 4.41/4.59 11043[2:Rew:8172.0,11041.0] || equal(universal_class,universal_class)* -> .
% 4.41/4.59 11044[2:Obv:11043.0] || -> .
% 4.41/4.59 11045[2:Spt:11044.0,11026.0,11040.0] || equal(singleton(universal_class),null_class)** -> .
% 4.41/4.59 11046[2:Spt:11044.0,11026.1] || -> equal(symmetric_difference(singleton(universal_class),universal_class),universal_class)**.
% 4.41/4.59 11048[2:SpR:11046.0,5579.0] || -> subclass(universal_class,complement(intersection(singleton(universal_class),universal_class)))*.
% 4.41/4.59 11062[2:Res:11048.0,328.0] || -> equal(complement(intersection(singleton(universal_class),universal_class)),universal_class)**.
% 4.41/4.59 11119[2:SpL:11062.0,25.1] || member(u,intersection(singleton(universal_class),universal_class))* member(u,universal_class) -> .
% 4.41/4.59 11142[2:MRR:11119.1,23.1] || member(u,intersection(singleton(universal_class),universal_class))* -> .
% 4.41/4.59 11207[2:Res:24.2,11142.0] || member(u,universal_class) member(u,singleton(universal_class))* -> .
% 4.41/4.59 11250[2:MRR:11207.0,9873.1] || member(u,singleton(universal_class))* -> .
% 4.41/4.59 11271[2:Res:71.2,11250.0] || member(singleton(universal_class),universal_class)* -> equal(singleton(universal_class),null_class).
% 4.41/4.59 11296[2:MRR:11271.0,11271.1,134.0,11045.0] || -> .
% 4.41/4.59 11297[1:Spt:11296.0,3676.1] || -> member(u,singleton(u))*.
% 4.41/4.59 11298[0:MRR:3450.0,9873.1] || member(u,null_class)* -> .
% 4.41/4.59 11482[0:MRR:2393.3,11298.0] || member(u,v) member(u,singleton(v))* -> equal(singleton(v),null_class).
% 4.41/4.59 11532[1:Res:11297.0,9873.0] || -> member(u,universal_class)*.
% 4.41/4.59 11533[1:Res:11297.0,2.0] || subclass(singleton(u),v)* -> member(u,v).
% 4.41/4.59 11538[1:MRR:71.0,11532.0] || -> equal(u,null_class) member(apply(choice,u),u)*.
% 4.41/4.59 11864[0:Res:371.2,11298.0] || subclass(u,null_class)*+ -> subclass(u,v)*.
% 4.41/4.59 12745[0:Res:7.1,11864.0] || equal(null_class,u) -> subclass(u,v)*.
% 4.41/4.59 13387[1:Res:12745.1,11533.0] || equal(singleton(u),null_class) -> member(u,v)*.
% 4.41/4.59 13431[1:Res:13387.1,11298.0] || equal(singleton(u),null_class)** -> .
% 4.41/4.59 13441[1:MRR:588.0,13431.0] || -> equal(apply(choice,singleton(u)),u)**.
% 4.41/4.59 13445[1:MRR:11482.2,13431.0] || member(u,v) member(u,singleton(v))* -> .
% 4.41/4.59 17437[1:Res:11538.1,13445.1] || member(apply(choice,singleton(u)),u)* -> equal(singleton(u),null_class).
% 4.41/4.59 17455[1:Rew:13441.0,17437.0] || member(u,u)* -> equal(singleton(u),null_class).
% 4.41/4.59 17456[1:MRR:17455.1,13431.0] || member(u,u)* -> .
% 4.41/4.59 17457[1:UnC:17456.0,11532.0] || -> .
% 4.41/4.59 % SZS output end Refutation
% 4.41/4.59 Formulae used in the proof : prove_corollary_1_to_universal_class_not_set_1 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets equal_implies_subclass2 subclass_implies_equal unordered_pair_member unordered_pair3 unordered_pairs_in_universal singleton_set cartesian_product2 intersection1 intersection2 intersection3 complement1 complement2 union symmetric_difference successor regularity1 regularity2 choice2
% 4.41/4.59
%------------------------------------------------------------------------------