TSTP Solution File: ALG349-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG349-1 : TPTP v8.1.0. Released v4.1.0.
% 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 : Thu Jul 14 18:03:25 EDT 2022
% Result : Unsatisfiable 14.26s 14.44s
% Output : Refutation 14.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 47
% Syntax : Number of clauses : 105 ( 55 unt; 7 nHn; 105 RR)
% Number of literals : 179 ( 0 equ; 88 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 22 ( 21 usr; 1 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 12 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(40,axiom,
( ~ class_OrderedGroup_Ogroup__add(u)
| ~ equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(w,u))
| equal(v,w) ),
file('ALG349-1.p',unknown),
[] ).
cnf(42,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(u)
| ~ c_lessequals(v,w,u)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(w,u),c_HOL_Ouminus__class_Ouminus(v,u),u) ),
file('ALG349-1.p',unknown),
[] ).
cnf(50,axiom,
( ~ class_OrderedGroup_Ogroup__add(u)
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),v) ),
file('ALG349-1.p',unknown),
[] ).
cnf(52,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(u)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(w,u),v,u) ),
file('ALG349-1.p',unknown),
[] ).
cnf(54,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(u)
| ~ c_lessequals(v,c_HOL_Ouminus__class_Ouminus(w,u),u)
| c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u) ),
file('ALG349-1.p',unknown),
[] ).
cnf(91,axiom,
( ~ class_Lattices_Oupper__semilattice(u)
| ~ c_lessequals(v,w,u)
| c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w),u) ),
file('ALG349-1.p',unknown),
[] ).
cnf(98,axiom,
equal(c_Set_Ovimage(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,v),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),
file('ALG349-1.p',unknown),
[] ).
cnf(124,axiom,
equal(c_Set_Ovimage(u,c_Collect(v,w),x,w),c_Collect(c_COMBB(v,u,w,tc_bool,x),x)),
file('ALG349-1.p',unknown),
[] ).
cnf(157,axiom,
equal(hAPP(c_COMBB(u,v,w,x,y),z),hAPP(u,hAPP(v,z))),
file('ALG349-1.p',unknown),
[] ).
cnf(158,axiom,
equal(hAPP(c_COMBI(u),v),v),
file('ALG349-1.p',unknown),
[] ).
cnf(159,axiom,
equal(hAPP(c_COMBK(u,v,w),x),u),
file('ALG349-1.p',unknown),
[] ).
cnf(246,axiom,
( ~ class_Orderings_Obot(u)
| equal(hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x),c_Orderings_Obot__class_Obot(u)) ),
file('ALG349-1.p',unknown),
[] ).
cnf(260,axiom,
( ~ class_Lattices_Oupper__semilattice(u)
| ~ c_lessequals(v,w,u)
| equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v),w) ),
file('ALG349-1.p',unknown),
[] ).
cnf(262,axiom,
( hBOOL(c_in(u,v,w))
| equal(c_Set_Ovimage(c_COMBK(u,w,x),v,x,w),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))) ),
file('ALG349-1.p',unknown),
[] ).
cnf(277,axiom,
( ~ class_Orderings_Opreorder(u)
| c_lessequals(v,v,u) ),
file('ALG349-1.p',unknown),
[] ).
cnf(289,axiom,
( ~ class_Orderings_Opreorder(u)
| ~ c_lessequals(v,w,u)
| ~ c_lessequals(w,x,u)
| c_lessequals(v,x,u) ),
file('ALG349-1.p',unknown),
[] ).
cnf(301,axiom,
( ~ hBOOL(c_in(u,v,w))
| equal(c_Set_Ovimage(c_COMBK(u,w,x),v,x,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))) ),
file('ALG349-1.p',unknown),
[] ).
cnf(303,axiom,
( ~ class_Orderings_Olinorder(u)
| c_lessequals(v,w,u)
| c_lessequals(w,v,u) ),
file('ALG349-1.p',unknown),
[] ).
cnf(318,axiom,
equal(c_Collect(u,v),u),
file('ALG349-1.p',unknown),
[] ).
cnf(322,axiom,
equal(c_Collect(c_COMBK(c_True,tc_bool,u),u),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),
file('ALG349-1.p',unknown),
[] ).
cnf(341,axiom,
( ~ class_HOL_Oord(u)
| ~ c_lessequals(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v,w,u),w,u)
| hBOOL(hAPP(c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u),w)) ),
file('ALG349-1.p',unknown),
[] ).
cnf(367,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('ALG349-1.p',unknown),
[] ).
cnf(368,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('ALG349-1.p',unknown),
[] ).
cnf(369,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('ALG349-1.p',unknown),
[] ).
cnf(370,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('ALG349-1.p',unknown),
[] ).
cnf(371,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('ALG349-1.p',unknown),
[] ).
cnf(372,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('ALG349-1.p',unknown),
[] ).
cnf(373,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
file('ALG349-1.p',unknown),
[] ).
cnf(374,axiom,
class_Orderings_Opreorder(tc_bool),
file('ALG349-1.p',unknown),
[] ).
cnf(375,axiom,
class_Lattices_Olattice(tc_bool),
file('ALG349-1.p',unknown),
[] ).
cnf(376,axiom,
class_Orderings_Oorder(tc_bool),
file('ALG349-1.p',unknown),
[] ).
cnf(377,axiom,
class_Orderings_Otop(tc_bool),
file('ALG349-1.p',unknown),
[] ).
cnf(378,axiom,
class_Orderings_Obot(tc_bool),
file('ALG349-1.p',unknown),
[] ).
cnf(379,axiom,
class_HOL_Oord(tc_bool),
file('ALG349-1.p',unknown),
[] ).
cnf(380,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('ALG349-1.p',unknown),
[] ).
cnf(381,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file('ALG349-1.p',unknown),
[] ).
cnf(382,axiom,
class_RealVector_Otopological__space(tc_RealDef_Oreal),
file('ALG349-1.p',unknown),
[] ).
cnf(383,axiom,
class_Lattices_Oupper__semilattice(tc_RealDef_Oreal),
file('ALG349-1.p',unknown),
[] ).
cnf(384,axiom,
class_Lattices_Olower__semilattice(tc_RealDef_Oreal),
file('ALG349-1.p',unknown),
[] ).
cnf(385,axiom,
class_Lattices_Odistrib__lattice(tc_RealDef_Oreal),
file('ALG349-1.p',unknown),
[] ).
cnf(386,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('ALG349-1.p',unknown),
[] ).
cnf(387,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('ALG349-1.p',unknown),
[] ).
cnf(388,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('ALG349-1.p',unknown),
[] ).
cnf(389,axiom,
class_Lattices_Olattice(tc_RealDef_Oreal),
file('ALG349-1.p',unknown),
[] ).
cnf(390,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('ALG349-1.p',unknown),
[] ).
cnf(391,axiom,
class_HOL_Oord(tc_RealDef_Oreal),
file('ALG349-1.p',unknown),
[] ).
cnf(394,axiom,
~ hBOOL(hAPP(c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_bool)),c_Collect(v_P,tc_RealDef_Oreal),tc_RealDef_Oreal),u)),
file('ALG349-1.p',unknown),
[] ).
cnf(396,plain,
equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_COMBK(c_True,tc_bool,u)),
inference(rew,[status(thm),theory(equality)],[318,322]),
[iquote('0:Rew:318.0,322.0')] ).
cnf(408,plain,
~ hBOOL(hAPP(c_Lubs_OisUb(c_COMBK(c_True,tc_bool,tc_RealDef_Oreal),v_P,tc_RealDef_Oreal),u)),
inference(rew,[status(thm),theory(equality)],[396,394,318]),
[iquote('0:Rew:396.0,394.0,318.0,394.0')] ).
cnf(419,plain,
equal(c_COMBB(u,v,w,tc_bool,x),c_Set_Ovimage(v,u,x,w)),
inference(rew,[status(thm),theory(equality)],[318,124]),
[iquote('0:Rew:318.0,124.0,318.0,124.0')] ).
cnf(422,plain,
( ~ hBOOL(c_in(u,v,w))
| equal(c_Set_Ovimage(c_COMBK(u,w,x),v,x,w),c_COMBK(c_True,tc_bool,x)) ),
inference(rew,[status(thm),theory(equality)],[396,301]),
[iquote('0:Rew:396.0,301.1')] ).
cnf(429,plain,
( ~ class_HOL_Oord(u)
| ~ c_lessequals(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v,w,u),w,u)
| hBOOL(hAPP(c_Lubs_OisUb(c_COMBK(c_True,tc_bool,u),v,u),w)) ),
inference(rew,[status(thm),theory(equality)],[396,341]),
[iquote('0:Rew:396.0,341.2')] ).
cnf(464,plain,
( ~ class_HOL_Oord(tc_RealDef_Oreal)
| ~ c_lessequals(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,u,tc_RealDef_Oreal),u,tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[429,408]),
[iquote('0:Res:429.2,408.0')] ).
cnf(469,plain,
~ c_lessequals(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,u,tc_RealDef_Oreal),u,tc_RealDef_Oreal),
inference(mrr,[status(thm)],[464,391]),
[iquote('0:MRR:464.0,391.0')] ).
cnf(531,plain,
( ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_lessequals(u,c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,u,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[303,469]),
[iquote('0:Res:303.1,469.0')] ).
cnf(533,plain,
c_lessequals(u,c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,u,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(ssi,[status(thm)],[531,388,386,381,380,387,390,385,382,383,391,384,389]),
[iquote('0:SSi:531.0,388.0,386.0,381.0,380.0,387.0,390.0,385.0,382.0,383.0,391.0,384.0,389.0')] ).
cnf(1026,plain,
( ~ class_OrderedGroup_Ogroup__add(u)
| ~ class_OrderedGroup_Ogroup__add(u)
| ~ equal(v,c_HOL_Ouminus__class_Ouminus(w,u))
| equal(c_HOL_Ouminus__class_Ouminus(v,u),w) ),
inference(spl,[status(thm),theory(equality)],[50,40]),
[iquote('0:SpL:50.1,40.1')] ).
cnf(1035,plain,
( ~ class_OrderedGroup_Ogroup__add(u)
| ~ equal(v,c_HOL_Ouminus__class_Ouminus(w,u))
| equal(c_HOL_Ouminus__class_Ouminus(v,u),w) ),
inference(obv,[status(thm),theory(equality)],[1026]),
[iquote('0:Obv:1026.0')] ).
cnf(2077,plain,
equal(hAPP(c_Set_Ovimage(u,v,w,x),y),hAPP(v,hAPP(u,y))),
inference(spr,[status(thm),theory(equality)],[419,157]),
[iquote('0:SpR:419.0,157.0')] ).
cnf(2149,plain,
equal(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v),hAPP(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),hAPP(x,v))),
inference(spr,[status(thm),theory(equality)],[98,2077]),
[iquote('0:SpR:98.0,2077.0')] ).
cnf(2419,plain,
( ~ class_OrderedGroup_Ogroup__add(u)
| ~ class_OrderedGroup_Ogroup__add(u)
| ~ equal(v,w)
| equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(w,u)) ),
inference(spl,[status(thm),theory(equality)],[50,1035]),
[iquote('0:SpL:50.1,1035.1')] ).
cnf(2424,plain,
( ~ class_OrderedGroup_Ogroup__add(u)
| ~ equal(v,w)
| equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(w,u)) ),
inference(obv,[status(thm),theory(equality)],[2419]),
[iquote('0:Obv:2419.0')] ).
cnf(2803,plain,
equal(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v),hAPP(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x)),
inference(spr,[status(thm),theory(equality)],[159,2149]),
[iquote('0:SpR:159.0,2149.0')] ).
cnf(2848,plain,
( ~ class_Orderings_Obot(tc_bool)
| equal(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v),c_Orderings_Obot__class_Obot(tc_bool)) ),
inference(spr,[status(thm),theory(equality)],[2803,246]),
[iquote('0:SpR:2803.0,246.1')] ).
cnf(2858,plain,
equal(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v),c_Orderings_Obot__class_Obot(tc_bool)),
inference(ssi,[status(thm)],[2848,378,377,373,374,376,370,367,372,371,368,379,369,375]),
[iquote('0:SSi:2848.0,378.0,377.0,373.0,374.0,376.0,370.0,367.0,372.0,371.0,368.0,379.0,369.0,375.0')] ).
cnf(4427,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),u,tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[533,52]),
[iquote('0:Res:533.0,52.1')] ).
cnf(4436,plain,
c_lessequals(c_HOL_Ouminus__class_Ouminus(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),u,tc_RealDef_Oreal),
inference(ssi,[status(thm)],[4427,388,386,381,380,387,390,385,382,383,391,384,389]),
[iquote('0:SSi:4427.0,388.0,386.0,381.0,380.0,387.0,390.0,385.0,382.0,383.0,391.0,384.0,389.0')] ).
cnf(4451,plain,
( ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,u,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(spr,[status(thm),theory(equality)],[50,4436]),
[iquote('0:SpR:50.1,4436.0')] ).
cnf(4461,plain,
c_lessequals(c_HOL_Ouminus__class_Ouminus(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,u,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(ssi,[status(thm)],[4451,388,386,381,380,387,390,385,382,383,391,384,389]),
[iquote('0:SSi:4451.0,388.0,386.0,381.0,380.0,387.0,390.0,385.0,382.0,383.0,391.0,384.0,389.0')] ).
cnf(4507,plain,
( ~ class_Orderings_Opreorder(u)
| ~ class_OrderedGroup_Opordered__ab__group__add(u)
| c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u) ),
inference(res,[status(thm),theory(equality)],[277,54]),
[iquote('0:Res:277.1,54.1')] ).
cnf(4527,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal)
| c_lessequals(u,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,u,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[4461,54]),
[iquote('0:Res:4461.0,54.1')] ).
cnf(4528,plain,
c_lessequals(u,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,u,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(ssi,[status(thm)],[4527,388,386,381,380,387,390,385,382,383,391,384,389]),
[iquote('0:SSi:4527.0,388.0,386.0,381.0,380.0,387.0,390.0,385.0,382.0,383.0,391.0,384.0,389.0')] ).
cnf(7519,plain,
( ~ class_Lattices_Oupper__semilattice(tc_RealDef_Oreal)
| ~ c_lessequals(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_RealDef_Oreal),u),v),tc_RealDef_Oreal),v,tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[91,469]),
[iquote('0:Res:91.2,469.0')] ).
cnf(7528,plain,
~ c_lessequals(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_RealDef_Oreal),u),v),tc_RealDef_Oreal),v,tc_RealDef_Oreal),
inference(ssi,[status(thm)],[7519,388,386,381,380,387,390,385,382,383,391,384,389]),
[iquote('0:SSi:7519.0,388.0,386.0,381.0,380.0,387.0,390.0,385.0,382.0,383.0,391.0,384.0,389.0')] ).
cnf(7573,plain,
( ~ class_Lattices_Oupper__semilattice(tc_RealDef_Oreal)
| ~ c_lessequals(u,v,tc_RealDef_Oreal)
| ~ c_lessequals(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,v,tc_RealDef_Oreal),u,tc_RealDef_Oreal) ),
inference(spl,[status(thm),theory(equality)],[260,7528]),
[iquote('0:SpL:260.2,7528.0')] ).
cnf(7583,plain,
( ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_lessequals(u,c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_RealDef_Oreal),v),u),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[303,7528]),
[iquote('0:Res:303.2,7528.0')] ).
cnf(7604,plain,
c_lessequals(u,c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_RealDef_Oreal),v),u),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(ssi,[status(thm)],[7583,388,386,381,380,387,390,385,382,383,391,384,389]),
[iquote('0:SSi:7583.0,388.0,386.0,381.0,380.0,387.0,390.0,385.0,382.0,383.0,391.0,384.0,389.0')] ).
cnf(7607,plain,
( ~ c_lessequals(u,v,tc_RealDef_Oreal)
| ~ c_lessequals(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,v,tc_RealDef_Oreal),u,tc_RealDef_Oreal) ),
inference(ssi,[status(thm)],[7573,388,386,381,380,387,390,385,382,383,391,384,389]),
[iquote('0:SSi:7573.0,388.0,386.0,381.0,380.0,387.0,390.0,385.0,382.0,383.0,391.0,384.0,389.0')] ).
cnf(8786,plain,
~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,u,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),u,tc_RealDef_Oreal),
inference(res,[status(thm),theory(equality)],[4528,7607]),
[iquote('0:Res:4528.0,7607.1')] ).
cnf(8793,plain,
( ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,u,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),u,tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[4507,7607]),
[iquote('0:Res:4507.2,7607.1')] ).
cnf(8806,plain,
~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,u,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),u,tc_RealDef_Oreal),
inference(ssi,[status(thm)],[8793,388,386,381,380,387,390,385,382,383,391,384,389]),
[iquote('0:SSi:8793.1,8793.0,388.0,386.0,381.0,380.0,387.0,390.0,385.0,382.0,383.0,391.0,384.0,389.0,388.0,386.0,381.0,380.0,387.0,390.0,385.0,382.0,383.0,391.0,384.0,389.0')] ).
cnf(8836,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal)
| ~ c_lessequals(u,c_HOL_Ouminus__class_Ouminus(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[42,8806]),
[iquote('0:Res:42.2,8806.0')] ).
cnf(8853,plain,
~ c_lessequals(u,c_HOL_Ouminus__class_Ouminus(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(ssi,[status(thm)],[8836,388,386,381,380,387,390,385,382,383,391,384,389]),
[iquote('0:SSi:8836.0,388.0,386.0,381.0,380.0,387.0,390.0,385.0,382.0,383.0,391.0,384.0,389.0')] ).
cnf(8888,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal)
| ~ c_lessequals(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),u,tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[42,8853]),
[iquote('0:Res:42.2,8853.0')] ).
cnf(8899,plain,
~ c_lessequals(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),u,tc_RealDef_Oreal),
inference(ssi,[status(thm)],[8888,388,386,381,380,387,390,385,382,383,391,384,389]),
[iquote('0:SSi:8888.0,388.0,386.0,381.0,380.0,387.0,390.0,385.0,382.0,383.0,391.0,384.0,389.0')] ).
cnf(8979,plain,
( ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_lessequals(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,u,tc_RealDef_Oreal),v,tc_RealDef_Oreal)
| c_lessequals(u,v,tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[533,289]),
[iquote('0:Res:533.0,289.1')] ).
cnf(9032,plain,
( ~ c_lessequals(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,u,tc_RealDef_Oreal),v,tc_RealDef_Oreal)
| c_lessequals(u,v,tc_RealDef_Oreal) ),
inference(ssi,[status(thm)],[8979,388,386,381,380,387,390,385,382,383,391,384,389]),
[iquote('0:SSi:8979.0,388.0,386.0,381.0,380.0,387.0,390.0,385.0,382.0,383.0,391.0,384.0,389.0')] ).
cnf(9078,plain,
( ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| ~ equal(u,v)
| ~ c_lessequals(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),u,tc_RealDef_Oreal) ),
inference(spl,[status(thm),theory(equality)],[2424,8899]),
[iquote('0:SpL:2424.2,8899.0')] ).
cnf(9116,plain,
( ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| ~ equal(u,v)
| ~ c_lessequals(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,v,tc_RealDef_Oreal),u,tc_RealDef_Oreal) ),
inference(rew,[status(thm),theory(equality)],[50,9078]),
[iquote('0:Rew:50.1,9078.2')] ).
cnf(9117,plain,
( ~ equal(u,v)
| ~ c_lessequals(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,v,tc_RealDef_Oreal),u,tc_RealDef_Oreal) ),
inference(ssi,[status(thm)],[9116,388,386,381,380,387,390,385,382,383,391,384,389]),
[iquote('0:SSi:9116.0,388.0,386.0,381.0,380.0,387.0,390.0,385.0,382.0,383.0,391.0,384.0,389.0')] ).
cnf(9149,plain,
c_lessequals(u,c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_RealDef_Oreal),v),c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,u,tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(res,[status(thm),theory(equality)],[7604,9032]),
[iquote('0:Res:7604.0,9032.0')] ).
cnf(9422,plain,
( ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal)
| ~ equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,u,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),u) ),
inference(res,[status(thm),theory(equality)],[4507,9117]),
[iquote('0:Res:4507.2,9117.1')] ).
cnf(9449,plain,
~ equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,u,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),u),
inference(ssi,[status(thm)],[9422,388,386,381,380,387,390,385,382,383,391,384,389]),
[iquote('0:SSi:9422.1,9422.0,388.0,386.0,381.0,380.0,387.0,390.0,385.0,382.0,383.0,391.0,384.0,389.0,388.0,386.0,381.0,380.0,387.0,390.0,385.0,382.0,383.0,391.0,384.0,389.0')] ).
cnf(11017,plain,
( hBOOL(c_in(u,v,w))
| equal(hAPP(v,hAPP(c_COMBK(u,w,x),y)),hAPP(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),y)) ),
inference(spr,[status(thm),theory(equality)],[262,2077]),
[iquote('0:SpR:262.1,2077.0')] ).
cnf(11021,plain,
( hBOOL(c_in(u,v,w))
| equal(hAPP(v,u),c_Orderings_Obot__class_Obot(tc_bool)) ),
inference(rew,[status(thm),theory(equality)],[159,11017,2858]),
[iquote('0:Rew:159.0,11017.1,2858.0,11017.1')] ).
cnf(15834,plain,
( ~ hBOOL(c_in(u,v,w))
| equal(hAPP(v,hAPP(c_COMBK(u,w,x),y)),hAPP(c_COMBK(c_True,tc_bool,x),y)) ),
inference(spr,[status(thm),theory(equality)],[422,2077]),
[iquote('0:SpR:422.1,2077.0')] ).
cnf(15840,plain,
( ~ hBOOL(c_in(u,v,w))
| equal(hAPP(v,u),c_True) ),
inference(rew,[status(thm),theory(equality)],[159,15834]),
[iquote('0:Rew:159.0,15834.1,159.0,15834.1')] ).
cnf(28025,plain,
( equal(hAPP(u,v),c_Orderings_Obot__class_Obot(tc_bool))
| equal(hAPP(u,v),c_True) ),
inference(res,[status(thm),theory(equality)],[11021,15840]),
[iquote('0:Res:11021.0,15840.0')] ).
cnf(28315,plain,
( equal(hAPP(c_COMBI(u),v),c_True)
| equal(c_Orderings_Obot__class_Obot(tc_bool),v) ),
inference(spr,[status(thm),theory(equality)],[28025,158]),
[iquote('0:SpR:28025.0,158.0')] ).
cnf(28888,plain,
( equal(u,c_True)
| equal(c_Orderings_Obot__class_Obot(tc_bool),u) ),
inference(rew,[status(thm),theory(equality)],[158,28315]),
[iquote('0:Rew:158.0,28315.0')] ).
cnf(33225,plain,
( ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),u,tc_RealDef_Oreal)
| equal(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,u,tc_RealDef_Oreal),c_True) ),
inference(spl,[status(thm),theory(equality)],[28888,469]),
[iquote('0:SpL:28888.1,469.0')] ).
cnf(33347,plain,
( ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),u,tc_RealDef_Oreal)
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,u,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_True) ),
inference(spl,[status(thm),theory(equality)],[28888,8786]),
[iquote('0:SpL:28888.1,8786.0')] ).
cnf(33922,plain,
( ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),u,tc_RealDef_Oreal)
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(v_P,c_True,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_True) ),
inference(rew,[status(thm),theory(equality)],[33225,33347]),
[iquote('0:Rew:33225.1,33347.1')] ).
cnf(33923,plain,
~ c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),u,tc_RealDef_Oreal),
inference(mrr,[status(thm)],[33922,9449]),
[iquote('0:MRR:33922.1,9449.0')] ).
cnf(33924,plain,
$false,
inference(unc,[status(thm)],[33923,9149]),
[iquote('0:UnC:33923.0,9149.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG349-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n024.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 08:44:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 14.26/14.44
% 14.26/14.44 SPASS V 3.9
% 14.26/14.44 SPASS beiseite: Proof found.
% 14.26/14.44 % SZS status Theorem
% 14.26/14.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.26/14.44 SPASS derived 25096 clauses, backtracked 2561 clauses, performed 37 splits and kept 10361 clauses.
% 14.26/14.44 SPASS allocated 102736 KBytes.
% 14.26/14.44 SPASS spent 0:0:14.07 on the problem.
% 14.26/14.44 0:00:00.05 for the input.
% 14.26/14.44 0:00:00.00 for the FLOTTER CNF translation.
% 14.26/14.44 0:00:00.34 for inferences.
% 14.26/14.44 0:00:00.59 for the backtracking.
% 14.26/14.44 0:0:12.95 for the reduction.
% 14.26/14.44
% 14.26/14.44
% 14.26/14.44 Here is a proof with depth 8, length 105 :
% 14.26/14.44 % SZS output start Refutation
% See solution above
% 14.80/15.01 Formulae used in the proof : cls_neg__equal__iff__equal_0 cls_le__imp__neg__le_0 cls_minus__minus_0 cls_minus__le__iff_0 cls_le__minus__iff_0 cls_le__supI2_0 cls_vimage__empty_0 cls_vimage__Collect__eq_0 cls_COMBB__def_0 cls_COMBI__def_0 cls_COMBK__def_0 cls_bot__fun__eq_0 cls_sup__absorb1_0 cls_vimage__const_1 cls_order__eq__refl_0 cls_order__trans_0 cls_vimage__const_0 cls_linorder__linear_0 cls_Collect__def_0 cls_UNIV__def_0 cls_isUb__UNIV__I_1 clsarity_bool__Complete__Lattice_Ocomplete__lattice clsarity_bool__Lattices_Oupper__semilattice clsarity_bool__Lattices_Olower__semilattice clsarity_bool__Lattices_Odistrib__lattice clsarity_bool__Lattices_Obounded__lattice clsarity_bool__Lattices_Oboolean__algebra clsarity_bool__Finite__Set_Ofinite_Ofinite clsarity_bool__Orderings_Opreorder clsarity_bool__Lattices_Olattice clsarity_bool__Orderings_Oorder clsarity_bool__Orderings_Otop clsarity_bool__Orderings_Obot clsarity_bool__HOL_Oord clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add clsarity_RealDef__Oreal__RealVector_Otopological__space clsarity_RealDef__Oreal__Lattices_Oupper__semilattice clsarity_RealDef__Oreal__Lattices_Olower__semilattice clsarity_RealDef__Oreal__Lattices_Odistrib__lattice clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add clsarity_RealDef__Oreal__Orderings_Opreorder clsarity_RealDef__Oreal__Orderings_Olinorder clsarity_RealDef__Oreal__Lattices_Olattice clsarity_RealDef__Oreal__Orderings_Oorder clsarity_RealDef__Oreal__HOL_Oord cls_conjecture_0
% 14.80/15.01
%------------------------------------------------------------------------------