TSTP Solution File: SEU351+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU351+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 14:36:31 EDT 2022
% Result : Theorem 3.52s 3.71s
% Output : Refutation 3.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU351+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jun 19 19:03:32 EDT 2022
% 0.14/0.35 % CPUTime :
% 3.52/3.71
% 3.52/3.71 SPASS V 3.9
% 3.52/3.71 SPASS beiseite: Proof found.
% 3.52/3.71 % SZS status Theorem
% 3.52/3.71 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.52/3.71 SPASS derived 6926 clauses, backtracked 139 clauses, performed 5 splits and kept 2407 clauses.
% 3.52/3.71 SPASS allocated 106776 KBytes.
% 3.52/3.71 SPASS spent 0:00:03.35 on the problem.
% 3.52/3.71 0:00:00.03 for the input.
% 3.52/3.71 0:00:00.04 for the FLOTTER CNF translation.
% 3.52/3.71 0:00:00.18 for inferences.
% 3.52/3.71 0:00:00.05 for the backtracking.
% 3.52/3.71 0:00:02.96 for the reduction.
% 3.52/3.71
% 3.52/3.71
% 3.52/3.71 Here is a proof with depth 7, length 161 :
% 3.52/3.71 % SZS output start Refutation
% 3.52/3.71 1[0:Inp] || -> lattice(skc11)*.
% 3.52/3.71 2[0:Inp] || -> complete_latt_str(skc11)*.
% 3.52/3.71 3[0:Inp] || -> latt_str(skc11)*.
% 3.52/3.71 11[0:Inp] || empty_carrier(skc11)* -> .
% 3.52/3.71 14[0:Inp] || -> element(skc14,the_carrier(skc11))*.
% 3.52/3.71 15[0:Inp] || -> element(skc12,the_carrier(skc11))*.
% 3.52/3.71 19[0:Inp] latt_str(u) || -> meet_semilatt_str(u)*.
% 3.52/3.71 20[0:Inp] latt_str(u) || -> join_semilatt_str(u)*.
% 3.52/3.71 22[0:Inp] || -> element(skf5(u,v,w),the_carrier(w))*.
% 3.52/3.71 23[0:Inp] || -> element(skf6(u,v,w),the_carrier(w))*.
% 3.52/3.71 24[0:Inp] || -> element(skf7(u,v,w),the_carrier(w))*.
% 3.52/3.71 28[0:Inp] || -> equal(meet_of_latt_set(skc11,skc13),skc12) latt_set_smaller(skc11,skc12,skc13)*.
% 3.52/3.71 32[0:Inp] lattice(u) latt_str(u) || -> empty_carrier(u)* join_commutative(u).
% 3.52/3.71 33[0:Inp] lattice(u) latt_str(u) || -> empty_carrier(u)* join_associative(u).
% 3.52/3.71 34[0:Inp] lattice(u) latt_str(u) || -> empty_carrier(u)* meet_commutative(u).
% 3.52/3.71 35[0:Inp] lattice(u) latt_str(u) || -> empty_carrier(u)* meet_associative(u).
% 3.52/3.71 36[0:Inp] lattice(u) latt_str(u) || -> empty_carrier(u)* meet_absorbing(u).
% 3.52/3.71 37[0:Inp] lattice(u) latt_str(u) || -> empty_carrier(u)* join_absorbing(u).
% 3.52/3.71 38[0:Inp] latt_str(u) || -> empty_carrier(u) element(join_of_latt_set(u,v),the_carrier(u))*.
% 3.52/3.71 42[0:Inp] latt_str(u) || -> empty_carrier(u) equal(join_of_latt_set(u,a_2_2_lattice3(u,v)),meet_of_latt_set(u,v))**.
% 3.52/3.71 43[0:Inp] || equal(meet_of_latt_set(skc11,skc13),skc12) latt_set_smaller(skc11,skc12,skc13) -> latt_set_smaller(skc11,skc14,skc13)*.
% 3.52/3.71 45[0:Inp] latt_str(u) || in(v,a_2_2_lattice3(u,w))* -> empty_carrier(u) latt_set_smaller(u,v,w).
% 3.52/3.71 46[0:Inp] || equal(meet_of_latt_set(skc11,skc13),skc12) latt_set_smaller(skc11,skc12,skc13) below_refl(skc11,skc14,skc12)* -> .
% 3.52/3.71 47[0:Inp] || element(u,the_carrier(skc11)) latt_set_smaller(skc11,u,skc13) -> equal(meet_of_latt_set(skc11,skc13),skc12) below_refl(skc11,u,skc12)*.
% 3.52/3.71 48[0:Inp] latt_str(u) || element(v,the_carrier(u)) latt_set_smaller(u,v,w) -> empty_carrier(u) in(v,a_2_2_lattice3(u,w))*.
% 3.52/3.71 49[0:Inp] latt_str(u) || element(v,the_carrier(u)) -> empty_carrier(u) in(skf6(v,w,u),w)* latt_element_smaller(u,v,w).
% 3.52/3.71 50[0:Inp] latt_str(u) || element(v,the_carrier(u)) -> empty_carrier(u) in(skf5(v,w,u),w)* latt_set_smaller(u,v,w).
% 3.52/3.71 53[0:Inp] latt_str(u) || element(v,the_carrier(u)) below(u,skf6(v,w,u),v)* -> empty_carrier(u) latt_element_smaller(u,v,w).
% 3.52/3.71 54[0:Inp] latt_str(u) || element(v,the_carrier(u)) below(u,v,skf5(v,w,u))* -> empty_carrier(u) latt_set_smaller(u,v,w).
% 3.52/3.71 58[0:Inp] complete_latt_str(u) lattice(u) latt_str(u) || element(v,the_carrier(u)) equal(v,join_of_latt_set(u,w)) -> empty_carrier(u) latt_element_smaller(u,v,w)*.
% 3.52/3.71 59[0:Inp] latt_str(u) || in(v,w)* element(x,the_carrier(u))+ element(v,the_carrier(u)) latt_element_smaller(u,x,w)* -> empty_carrier(u) below(u,v,x)*.
% 3.52/3.71 60[0:Inp] latt_str(u) || in(v,w)* element(x,the_carrier(u))+ element(v,the_carrier(u)) latt_set_smaller(u,x,w)* -> empty_carrier(u) below(u,x,v)*.
% 3.52/3.71 61[0:Inp] latt_str(u) join_absorbing(u) meet_absorbing(u) meet_commutative(u) || element(v,the_carrier(u)) element(w,the_carrier(u)) below(u,w,v) -> empty_carrier(u) below_refl(u,w,v)*.
% 3.52/3.71 62[0:Inp] latt_str(u) join_absorbing(u) meet_absorbing(u) meet_commutative(u) || element(v,the_carrier(u)) element(w,the_carrier(u)) below_refl(u,w,v)* -> empty_carrier(u) below(u,w,v).
% 3.52/3.71 63[0:Inp] complete_latt_str(u) lattice(u) latt_str(u) || element(v,the_carrier(u)) latt_element_smaller(u,v,w) -> empty_carrier(u) equal(v,join_of_latt_set(u,w)) latt_element_smaller(u,skf7(v,w,u),w)*.
% 3.52/3.71 64[0:Inp] complete_latt_str(u) lattice(u) latt_str(u) || element(v,the_carrier(u)) latt_element_smaller(u,v,w) below(u,v,skf7(v,w,u))* -> empty_carrier(u) equal(v,join_of_latt_set(u,w)).
% 3.52/3.71 65[0:Inp] complete_latt_str(u) lattice(u) latt_str(u) || element(v,the_carrier(u)) element(w,the_carrier(u)) equal(v,join_of_latt_set(u,x))*+ latt_element_smaller(u,w,x)* -> empty_carrier(u) below(u,v,w)*.
% 3.52/3.71 69[0:Res:3.0,62.3] meet_commutative(skc11) meet_absorbing(skc11) join_absorbing(skc11) || element(u,the_carrier(skc11)) element(v,the_carrier(skc11)) below_refl(skc11,u,v)* -> below(skc11,u,v) empty_carrier(skc11).
% 3.52/3.71 77[0:Res:3.0,54.0] || below(skc11,u,skf5(u,v,skc11))* element(u,the_carrier(skc11)) -> latt_set_smaller(skc11,u,v) empty_carrier(skc11).
% 3.52/3.71 78[0:Res:3.0,53.0] || below(skc11,skf6(u,v,skc11),u)* element(u,the_carrier(skc11)) -> latt_element_smaller(skc11,u,v) empty_carrier(skc11).
% 3.52/3.71 82[0:Res:3.0,49.0] || element(u,the_carrier(skc11)) -> in(skf6(u,v,skc11),v)* latt_element_smaller(skc11,u,v) empty_carrier(skc11).
% 3.52/3.71 83[0:Res:3.0,48.0] || element(u,the_carrier(skc11)) latt_set_smaller(skc11,u,v) -> in(u,a_2_2_lattice3(skc11,v))* empty_carrier(skc11).
% 3.52/3.71 85[0:Res:3.0,45.0] || in(u,a_2_2_lattice3(skc11,v))* -> latt_set_smaller(skc11,u,v) empty_carrier(skc11).
% 3.52/3.71 86[0:Res:3.0,42.0] || -> empty_carrier(skc11) equal(join_of_latt_set(skc11,a_2_2_lattice3(skc11,u)),meet_of_latt_set(skc11,u))**.
% 3.52/3.71 87[0:Res:3.0,38.0] || -> element(join_of_latt_set(skc11,u),the_carrier(skc11))* empty_carrier(skc11).
% 3.52/3.71 89[0:Res:3.0,32.0] lattice(skc11) || -> join_commutative(skc11) empty_carrier(skc11)*.
% 3.52/3.71 90[0:Res:3.0,33.0] lattice(skc11) || -> join_associative(skc11) empty_carrier(skc11)*.
% 3.52/3.71 91[0:Res:3.0,34.0] lattice(skc11) || -> meet_commutative(skc11) empty_carrier(skc11)*.
% 3.52/3.71 92[0:Res:3.0,35.0] lattice(skc11) || -> meet_associative(skc11) empty_carrier(skc11)*.
% 3.52/3.71 93[0:Res:3.0,36.0] lattice(skc11) || -> meet_absorbing(skc11) empty_carrier(skc11)*.
% 3.52/3.71 94[0:Res:3.0,37.0] lattice(skc11) || -> join_absorbing(skc11) empty_carrier(skc11)*.
% 3.52/3.71 95[0:Res:3.0,19.0] || -> meet_semilatt_str(skc11)*.
% 3.52/3.71 96[0:Res:3.0,20.0] || -> join_semilatt_str(skc11)*.
% 3.52/3.71 104[0:Res:1.0,65.1] latt_str(skc11) complete_latt_str(skc11) || element(u,the_carrier(skc11)) latt_element_smaller(skc11,u,v)* equal(w,join_of_latt_set(skc11,v))* element(w,the_carrier(skc11)) -> below(skc11,w,u)* empty_carrier(skc11).
% 3.52/3.71 105[0:Res:1.0,64.1] latt_str(skc11) complete_latt_str(skc11) || latt_element_smaller(skc11,u,v) below(skc11,u,skf7(u,v,skc11))* element(u,the_carrier(skc11)) -> equal(u,join_of_latt_set(skc11,v)) empty_carrier(skc11).
% 3.52/3.71 106[0:Res:1.0,63.1] latt_str(skc11) complete_latt_str(skc11) || latt_element_smaller(skc11,u,v) element(u,the_carrier(skc11)) -> latt_element_smaller(skc11,skf7(u,v,skc11),v)* equal(u,join_of_latt_set(skc11,v)) empty_carrier(skc11).
% 3.52/3.71 107[0:Res:1.0,58.1] latt_str(skc11) complete_latt_str(skc11) || equal(u,join_of_latt_set(skc11,v)) element(u,the_carrier(skc11)) -> latt_element_smaller(skc11,u,v)* empty_carrier(skc11).
% 3.52/3.71 147[0:MRR:89.0,89.2,1.0,11.0] || -> join_commutative(skc11)*.
% 3.52/3.71 148[0:MRR:90.0,90.2,1.0,11.0] || -> join_associative(skc11)*.
% 3.52/3.71 149[0:MRR:91.0,91.2,1.0,11.0] || -> meet_commutative(skc11)*.
% 3.52/3.71 150[0:MRR:92.0,92.2,1.0,11.0] || -> meet_associative(skc11)*.
% 3.52/3.71 151[0:MRR:93.0,93.2,1.0,11.0] || -> meet_absorbing(skc11)*.
% 3.52/3.71 152[0:MRR:94.0,94.2,1.0,11.0] || -> join_absorbing(skc11)*.
% 3.52/3.71 153[0:MRR:87.1,11.0] || -> element(join_of_latt_set(skc11,u),the_carrier(skc11))*.
% 3.52/3.71 155[0:MRR:86.0,11.0] || -> equal(join_of_latt_set(skc11,a_2_2_lattice3(skc11,u)),meet_of_latt_set(skc11,u))**.
% 3.52/3.71 157[0:MRR:85.2,11.0] || in(u,a_2_2_lattice3(skc11,v))* -> latt_set_smaller(skc11,u,v).
% 3.52/3.71 159[0:MRR:82.3,11.0] || element(u,the_carrier(skc11)) -> in(skf6(u,v,skc11),v)* latt_element_smaller(skc11,u,v).
% 3.52/3.71 160[0:MRR:83.3,11.0] || element(u,the_carrier(skc11)) latt_set_smaller(skc11,u,v) -> in(u,a_2_2_lattice3(skc11,v))*.
% 3.52/3.71 163[0:MRR:77.3,11.0] || element(u,the_carrier(skc11)) below(skc11,u,skf5(u,v,skc11))* -> latt_set_smaller(skc11,u,v).
% 3.52/3.71 164[0:MRR:78.3,11.0] || element(u,the_carrier(skc11)) below(skc11,skf6(u,v,skc11),u)* -> latt_element_smaller(skc11,u,v).
% 3.52/3.71 167[0:MRR:107.0,107.1,107.5,3.0,2.0,11.0] || element(u,the_carrier(skc11)) equal(u,join_of_latt_set(skc11,v)) -> latt_element_smaller(skc11,u,v)*.
% 3.52/3.71 170[0:MRR:106.0,106.1,106.6,3.0,2.0,11.0] || element(u,the_carrier(skc11)) latt_element_smaller(skc11,u,v) -> equal(u,join_of_latt_set(skc11,v)) latt_element_smaller(skc11,skf7(u,v,skc11),v)*.
% 3.52/3.71 172[0:MRR:69.0,69.1,69.2,69.7,149.0,151.0,152.0,11.0] || element(u,the_carrier(skc11)) element(v,the_carrier(skc11)) below_refl(skc11,v,u)* -> below(skc11,v,u).
% 3.52/3.71 173[0:MRR:105.0,105.1,105.6,3.0,2.0,11.0] || element(u,the_carrier(skc11)) latt_element_smaller(skc11,u,v) below(skc11,u,skf7(u,v,skc11))* -> equal(u,join_of_latt_set(skc11,v)).
% 3.52/3.71 174[0:MRR:104.0,104.1,104.7,3.0,2.0,11.0] || element(u,the_carrier(skc11)) element(v,the_carrier(skc11)) equal(u,join_of_latt_set(skc11,w))*+ latt_element_smaller(skc11,v,w)* -> below(skc11,u,v)*.
% 3.52/3.71 175[1:Spt:47.0,47.1,47.3] || element(u,the_carrier(skc11)) latt_set_smaller(skc11,u,skc13) -> below_refl(skc11,u,skc12)*.
% 3.52/3.71 176[2:Spt:28.0] || -> equal(meet_of_latt_set(skc11,skc13),skc12)**.
% 3.52/3.71 177[2:Rew:176.0,46.0] || equal(skc12,skc12) latt_set_smaller(skc11,skc12,skc13) below_refl(skc11,skc14,skc12)* -> .
% 3.52/3.71 178[2:Rew:176.0,43.0] || equal(skc12,skc12) latt_set_smaller(skc11,skc12,skc13) -> latt_set_smaller(skc11,skc14,skc13)*.
% 3.52/3.71 179[2:Obv:178.0] || latt_set_smaller(skc11,skc12,skc13) -> latt_set_smaller(skc11,skc14,skc13)*.
% 3.52/3.71 180[2:Obv:177.0] || latt_set_smaller(skc11,skc12,skc13) below_refl(skc11,skc14,skc12)* -> .
% 3.52/3.71 210[2:Res:175.2,180.1] || element(skc14,the_carrier(skc11)) latt_set_smaller(skc11,skc14,skc13)* latt_set_smaller(skc11,skc12,skc13) -> .
% 3.52/3.71 211[2:MRR:210.0,210.1,14.0,179.1] || latt_set_smaller(skc11,skc12,skc13)* -> .
% 3.52/3.71 332[0:Res:159.1,157.0] || element(u,the_carrier(skc11)) -> latt_element_smaller(skc11,u,a_2_2_lattice3(skc11,v)) latt_set_smaller(skc11,skf6(u,a_2_2_lattice3(skc11,v),skc11),v)*.
% 3.52/3.71 352[0:Res:49.3,45.1] latt_str(u) latt_str(v) || element(w,the_carrier(u)) -> empty_carrier(u) latt_element_smaller(u,w,a_2_2_lattice3(v,x)) empty_carrier(v) latt_set_smaller(v,skf6(w,a_2_2_lattice3(v,x),u),x)*.
% 3.52/3.71 414[1:Res:175.2,172.2] || element(u,the_carrier(skc11)) latt_set_smaller(skc11,u,skc13) element(skc12,the_carrier(skc11)) element(u,the_carrier(skc11)) -> below(skc11,u,skc12)*.
% 3.52/3.71 419[1:Obv:414.0] || latt_set_smaller(skc11,u,skc13) element(skc12,the_carrier(skc11)) element(u,the_carrier(skc11)) -> below(skc11,u,skc12)*.
% 3.52/3.71 420[1:MRR:419.1,15.0] || latt_set_smaller(skc11,u,skc13) element(u,the_carrier(skc11)) -> below(skc11,u,skc12)*.
% 3.52/3.71 423[1:Res:420.2,164.1] || latt_set_smaller(skc11,skf6(skc12,u,skc11),skc13)* element(skf6(skc12,u,skc11),the_carrier(skc11)) element(skc12,the_carrier(skc11)) -> latt_element_smaller(skc11,skc12,u).
% 3.52/3.71 424[1:MRR:423.1,423.2,23.0,15.0] || latt_set_smaller(skc11,skf6(skc12,u,skc11),skc13)* -> latt_element_smaller(skc11,skc12,u).
% 3.52/3.71 429[1:Res:332.2,424.0] || element(skc12,the_carrier(skc11)) -> latt_element_smaller(skc11,skc12,a_2_2_lattice3(skc11,skc13))* latt_element_smaller(skc11,skc12,a_2_2_lattice3(skc11,skc13))*.
% 3.52/3.71 430[1:Obv:429.1] || element(skc12,the_carrier(skc11)) -> latt_element_smaller(skc11,skc12,a_2_2_lattice3(skc11,skc13))*.
% 3.52/3.71 431[1:MRR:430.0,15.0] || -> latt_element_smaller(skc11,skc12,a_2_2_lattice3(skc11,skc13))*.
% 3.52/3.71 444[0:Res:15.0,59.2] latt_str(skc11) || in(u,v)* element(u,the_carrier(skc11)) latt_element_smaller(skc11,skc12,v)* -> empty_carrier(skc11) below(skc11,u,skc12)*.
% 3.52/3.71 454[0:Res:24.0,59.2] latt_str(u) || in(v,w)* element(v,the_carrier(u)) latt_element_smaller(u,skf7(x,y,u),w)*+ -> empty_carrier(u) below(u,v,skf7(x,y,u))*.
% 3.52/3.71 464[0:SSi:444.0,2.0,1.0,3.0,150.0,148.0,147.0,96.0,95.0,152.0,151.0,149.0] || in(u,v)* element(u,the_carrier(skc11)) latt_element_smaller(skc11,skc12,v)* -> empty_carrier(skc11) below(skc11,u,skc12)*.
% 3.52/3.71 465[0:MRR:464.3,11.0] || in(u,v)* element(u,the_carrier(skc11))+ latt_element_smaller(skc11,skc12,v)* -> below(skc11,u,skc12)*.
% 3.52/3.71 525[0:Res:23.0,60.2] latt_str(u) || in(v,w)* element(v,the_carrier(u)) latt_set_smaller(u,skf6(x,y,u),w)*+ -> empty_carrier(u) below(u,skf6(x,y,u),v)*.
% 3.52/3.71 607[0:Res:14.0,465.1] || in(skc14,u) latt_element_smaller(skc11,skc12,u)* -> below(skc11,skc14,skc12).
% 3.52/3.71 634[0:Res:167.2,607.1] || element(skc12,the_carrier(skc11)) equal(join_of_latt_set(skc11,u),skc12)** in(skc14,u) -> below(skc11,skc14,skc12)*.
% 3.52/3.71 640[0:MRR:634.0,15.0] || equal(join_of_latt_set(skc11,u),skc12)**+ in(skc14,u) -> below(skc11,skc14,skc12)*.
% 3.52/3.71 645[0:SpL:155.0,640.0] || equal(meet_of_latt_set(skc11,u),skc12) in(skc14,a_2_2_lattice3(skc11,u))* -> below(skc11,skc14,skc12).
% 3.52/3.71 647[0:Res:160.2,645.1] || element(skc14,the_carrier(skc11)) latt_set_smaller(skc11,skc14,u)* equal(meet_of_latt_set(skc11,u),skc12) -> below(skc11,skc14,skc12)*.
% 3.52/3.71 649[0:MRR:647.0,14.0] || latt_set_smaller(skc11,skc14,u)* equal(meet_of_latt_set(skc11,u),skc12)+ -> below(skc11,skc14,skc12)*.
% 3.52/3.71 1055[0:EqR:174.2] || element(join_of_latt_set(skc11,u),the_carrier(skc11)) element(v,the_carrier(skc11)) latt_element_smaller(skc11,v,u) -> below(skc11,join_of_latt_set(skc11,u),v)*.
% 3.52/3.71 1058[0:MRR:1055.0,153.0] || element(u,the_carrier(skc11)) latt_element_smaller(skc11,u,v) -> below(skc11,join_of_latt_set(skc11,v),u)*.
% 3.52/3.71 1068[0:Res:1058.2,163.1] || element(skf5(join_of_latt_set(skc11,u),v,skc11),the_carrier(skc11)) latt_element_smaller(skc11,skf5(join_of_latt_set(skc11,u),v,skc11),u)* element(join_of_latt_set(skc11,u),the_carrier(skc11)) -> latt_set_smaller(skc11,join_of_latt_set(skc11,u),v).
% 3.52/3.71 1070[0:MRR:1068.0,1068.2,22.0,153.0] || latt_element_smaller(skc11,skf5(join_of_latt_set(skc11,u),v,skc11),u)* -> latt_set_smaller(skc11,join_of_latt_set(skc11,u),v).
% 3.52/3.71 1072[0:SpL:155.0,1070.0] || latt_element_smaller(skc11,skf5(meet_of_latt_set(skc11,u),v,skc11),a_2_2_lattice3(skc11,u))* -> latt_set_smaller(skc11,join_of_latt_set(skc11,a_2_2_lattice3(skc11,u)),v).
% 3.52/3.71 1079[0:Rew:155.0,1072.1] || latt_element_smaller(skc11,skf5(meet_of_latt_set(skc11,u),v,skc11),a_2_2_lattice3(skc11,u))* -> latt_set_smaller(skc11,meet_of_latt_set(skc11,u),v).
% 3.52/3.71 1198[2:SpL:176.0,1079.0] || latt_element_smaller(skc11,skf5(skc12,u,skc11),a_2_2_lattice3(skc11,skc13))* -> latt_set_smaller(skc11,meet_of_latt_set(skc11,skc13),u).
% 3.52/3.71 1203[2:Rew:176.0,1198.1] || latt_element_smaller(skc11,skf5(skc12,u,skc11),a_2_2_lattice3(skc11,skc13))* -> latt_set_smaller(skc11,skc12,u).
% 3.52/3.71 1573[0:Res:170.3,454.3] latt_str(skc11) || element(u,the_carrier(skc11)) latt_element_smaller(skc11,u,v) in(w,v) element(w,the_carrier(skc11)) -> equal(u,join_of_latt_set(skc11,v)) empty_carrier(skc11) below(skc11,w,skf7(u,v,skc11))*.
% 3.52/3.71 1577[0:SSi:1573.0,2.0,1.0,3.0,150.0,148.0,147.0,96.0,95.0,152.0,151.0,149.0] || element(u,the_carrier(skc11)) latt_element_smaller(skc11,u,v) in(w,v) element(w,the_carrier(skc11)) -> equal(u,join_of_latt_set(skc11,v)) empty_carrier(skc11) below(skc11,w,skf7(u,v,skc11))*.
% 3.52/3.71 1578[0:MRR:1577.5,11.0] || element(u,the_carrier(skc11)) latt_element_smaller(skc11,u,v) in(w,v) element(w,the_carrier(skc11)) -> equal(u,join_of_latt_set(skc11,v)) below(skc11,w,skf7(u,v,skc11))*.
% 3.52/3.71 1889[0:Res:352.6,525.3] latt_str(u) latt_str(u) latt_str(u) || element(v,the_carrier(u)) in(w,x) element(w,the_carrier(u)) -> empty_carrier(u) latt_element_smaller(u,v,a_2_2_lattice3(u,x)) empty_carrier(u) empty_carrier(u) below(u,skf6(v,a_2_2_lattice3(u,x),u),w)*.
% 3.52/3.71 1891[0:Obv:1889.8] latt_str(u) || element(v,the_carrier(u)) in(w,x) element(w,the_carrier(u)) -> latt_element_smaller(u,v,a_2_2_lattice3(u,x)) empty_carrier(u) below(u,skf6(v,a_2_2_lattice3(u,x),u),w)*.
% 3.52/3.71 4597[0:Res:1578.5,173.2] || element(u,the_carrier(skc11)) latt_element_smaller(skc11,u,v)* in(u,v) element(u,the_carrier(skc11)) element(u,the_carrier(skc11)) latt_element_smaller(skc11,u,v)* -> equal(u,join_of_latt_set(skc11,v)) equal(u,join_of_latt_set(skc11,v)).
% 3.52/3.71 4598[0:Obv:4597.6] || in(u,v) element(u,the_carrier(skc11)) latt_element_smaller(skc11,u,v)* -> equal(u,join_of_latt_set(skc11,v)).
% 3.52/3.71 4610[1:Res:431.0,4598.2] || in(skc12,a_2_2_lattice3(skc11,skc13)) element(skc12,the_carrier(skc11)) -> equal(join_of_latt_set(skc11,a_2_2_lattice3(skc11,skc13)),skc12)**.
% 3.52/3.71 9361[0:Res:1891.6,164.1] latt_str(skc11) || element(u,the_carrier(skc11)) in(u,v) element(u,the_carrier(skc11)) element(u,the_carrier(skc11)) -> latt_element_smaller(skc11,u,a_2_2_lattice3(skc11,v))* empty_carrier(skc11) latt_element_smaller(skc11,u,a_2_2_lattice3(skc11,v))*.
% 3.69/3.92 9364[0:Obv:9361.5] latt_str(skc11) || in(u,v) element(u,the_carrier(skc11)) -> empty_carrier(skc11) latt_element_smaller(skc11,u,a_2_2_lattice3(skc11,v))*.
% 3.69/3.92 9365[0:SSi:9364.0,2.0,1.0,3.0,150.0,148.0,147.0,96.0,95.0,152.0,151.0,149.0] || in(u,v) element(u,the_carrier(skc11)) -> empty_carrier(skc11) latt_element_smaller(skc11,u,a_2_2_lattice3(skc11,v))*.
% 3.69/3.92 9366[0:MRR:9365.2,11.0] || in(u,v) element(u,the_carrier(skc11)) -> latt_element_smaller(skc11,u,a_2_2_lattice3(skc11,v))*.
% 3.69/3.92 9395[2:Res:9366.2,1203.0] || in(skf5(skc12,u,skc11),skc13) element(skf5(skc12,u,skc11),the_carrier(skc11))* -> latt_set_smaller(skc11,skc12,u).
% 3.69/3.92 9408[2:MRR:9395.1,22.0] || in(skf5(skc12,u,skc11),skc13)* -> latt_set_smaller(skc11,skc12,u).
% 3.69/3.92 9430[2:Res:50.3,9408.0] latt_str(skc11) || element(skc12,the_carrier(skc11)) -> empty_carrier(skc11) latt_set_smaller(skc11,skc12,skc13)* latt_set_smaller(skc11,skc12,skc13)*.
% 3.69/3.92 9433[2:Obv:9430.3] latt_str(skc11) || element(skc12,the_carrier(skc11)) -> empty_carrier(skc11) latt_set_smaller(skc11,skc12,skc13)*.
% 3.69/3.92 9434[2:SSi:9433.0,2.0,1.0,3.0,150.0,148.0,147.0,96.0,95.0,152.0,151.0,149.0] || element(skc12,the_carrier(skc11)) -> empty_carrier(skc11) latt_set_smaller(skc11,skc12,skc13)*.
% 3.69/3.92 9435[2:MRR:9434.0,9434.1,9434.2,15.0,11.0,211.0] || -> .
% 3.69/3.92 9436[2:Spt:9435.0,28.0,176.0] || equal(meet_of_latt_set(skc11,skc13),skc12)** -> .
% 3.69/3.92 9437[2:Spt:9435.0,28.1] || -> latt_set_smaller(skc11,skc12,skc13)*.
% 3.69/3.92 9441[1:Rew:155.0,4610.2] || in(skc12,a_2_2_lattice3(skc11,skc13))* element(skc12,the_carrier(skc11)) -> equal(meet_of_latt_set(skc11,skc13),skc12).
% 3.69/3.92 9442[1:MRR:9441.1,15.0] || in(skc12,a_2_2_lattice3(skc11,skc13))* -> equal(meet_of_latt_set(skc11,skc13),skc12).
% 3.69/3.92 9443[2:MRR:9442.1,9436.0] || in(skc12,a_2_2_lattice3(skc11,skc13))* -> .
% 3.69/3.92 9467[2:Res:48.4,9443.0] latt_str(skc11) || element(skc12,the_carrier(skc11)) latt_set_smaller(skc11,skc12,skc13)* -> empty_carrier(skc11).
% 3.69/3.92 9470[2:SSi:9467.0,2.0,1.0,3.0,150.0,148.0,147.0,96.0,95.0,152.0,151.0,149.0] || element(skc12,the_carrier(skc11)) latt_set_smaller(skc11,skc12,skc13)* -> empty_carrier(skc11).
% 3.69/3.92 9471[2:MRR:9470.0,9470.1,9470.2,15.0,9437.0,11.0] || -> .
% 3.69/3.92 9472[1:Spt:9471.0,47.2] || -> equal(meet_of_latt_set(skc11,skc13),skc12)**.
% 3.69/3.92 9473[1:Rew:9472.0,43.0] || equal(skc12,skc12) latt_set_smaller(skc11,skc12,skc13) -> latt_set_smaller(skc11,skc14,skc13)*.
% 3.69/3.92 9474[1:Obv:9473.0] || latt_set_smaller(skc11,skc12,skc13) -> latt_set_smaller(skc11,skc14,skc13)*.
% 3.69/3.92 9475[1:Rew:9472.0,46.0] || equal(skc12,skc12) latt_set_smaller(skc11,skc12,skc13) below_refl(skc11,skc14,skc12)* -> .
% 3.69/3.92 9476[1:Obv:9475.0] || latt_set_smaller(skc11,skc12,skc13) below_refl(skc11,skc14,skc12)* -> .
% 3.69/3.92 9545[1:SpL:9472.0,649.1] || latt_set_smaller(skc11,skc14,skc13) equal(skc12,skc12) -> below(skc11,skc14,skc12)*.
% 3.69/3.92 9557[1:SpL:9472.0,1079.0] || latt_element_smaller(skc11,skf5(skc12,u,skc11),a_2_2_lattice3(skc11,skc13))* -> latt_set_smaller(skc11,meet_of_latt_set(skc11,skc13),u).
% 3.69/3.92 9595[1:Obv:9545.1] || latt_set_smaller(skc11,skc14,skc13) -> below(skc11,skc14,skc12)*.
% 3.69/3.92 9616[1:Rew:9472.0,9557.1] || latt_element_smaller(skc11,skf5(skc12,u,skc11),a_2_2_lattice3(skc11,skc13))* -> latt_set_smaller(skc11,skc12,u).
% 3.69/3.92 9661[2:Spt:9474.0] || latt_set_smaller(skc11,skc12,skc13)* -> .
% 3.69/3.92 10080[1:Res:9366.2,9616.0] || in(skf5(skc12,u,skc11),skc13) element(skf5(skc12,u,skc11),the_carrier(skc11))* -> latt_set_smaller(skc11,skc12,u).
% 3.69/3.92 10085[1:MRR:10080.1,22.0] || in(skf5(skc12,u,skc11),skc13)* -> latt_set_smaller(skc11,skc12,u).
% 3.69/3.92 10089[1:Res:50.3,10085.0] latt_str(skc11) || element(skc12,the_carrier(skc11)) -> empty_carrier(skc11) latt_set_smaller(skc11,skc12,skc13)* latt_set_smaller(skc11,skc12,skc13)*.
% 3.69/3.92 10092[1:Obv:10089.3] latt_str(skc11) || element(skc12,the_carrier(skc11)) -> empty_carrier(skc11) latt_set_smaller(skc11,skc12,skc13)*.
% 3.69/3.92 10093[1:SSi:10092.0,2.0,1.0,3.0,150.0,148.0,147.0,96.0,95.0,152.0,151.0,149.0] || element(skc12,the_carrier(skc11)) -> empty_carrier(skc11) latt_set_smaller(skc11,skc12,skc13)*.
% 3.69/3.92 10094[2:MRR:10093.0,10093.1,10093.2,15.0,11.0,9661.0] || -> .
% 3.69/3.92 10095[2:Spt:10094.0,9474.0,9661.0] || -> latt_set_smaller(skc11,skc12,skc13)*.
% 3.69/3.92 10096[2:Spt:10094.0,9474.1] || -> latt_set_smaller(skc11,skc14,skc13)*.
% 3.69/3.92 10097[2:MRR:9595.0,10096.0] || -> below(skc11,skc14,skc12)*.
% 3.69/3.92 10098[2:MRR:9476.0,10095.0] || below_refl(skc11,skc14,skc12)* -> .
% 3.69/3.92 10108[2:Res:61.8,10098.0] latt_str(skc11) join_absorbing(skc11) meet_absorbing(skc11) meet_commutative(skc11) || element(skc12,the_carrier(skc11)) element(skc14,the_carrier(skc11)) below(skc11,skc14,skc12)* -> empty_carrier(skc11).
% 3.69/3.92 10110[2:SSi:10108.3,10108.2,10108.1,10108.0,2.0,1.0,3.0,150.0,148.0,147.0,96.0,95.0,152.0,151.0,149.0,2.0,1.0,3.0,150.0,148.0,147.0,96.0,95.0,152.0,151.0,149.0,2.0,1.0,3.0,150.0,148.0,147.0,96.0,95.0,152.0,151.0,149.0,2.0,1.0,3.0,150.0,148.0,147.0,96.0,95.0,152.0,151.0,149.0] || element(skc12,the_carrier(skc11)) element(skc14,the_carrier(skc11)) below(skc11,skc14,skc12)* -> empty_carrier(skc11).
% 3.69/3.92 10111[2:MRR:10110.0,10110.1,10110.2,10110.3,15.0,14.0,10097.0,11.0] || -> .
% 3.69/3.92 % SZS output end Refutation
% 3.69/3.92 Formulae used in the proof : t34_lattice3 existence_m1_subset_1 dt_l3_lattices d16_lattice3 d17_lattice3 d21_lattice3 cc1_lattices dt_k15_lattice3 d22_lattice3 fraenkel_a_2_2_lattice3 redefinition_r3_lattices
% 3.69/3.92
%------------------------------------------------------------------------------