TSTP Solution File: SCT045-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SCT045-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 : Mon Jul 18 22:13:11 EDT 2022
% Result : Unsatisfiable 34.24s 34.42s
% Output : Refutation 34.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SCT045-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.11/0.32 % Computer : n016.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sat Jul 2 09:31:13 EDT 2022
% 0.11/0.32 % CPUTime :
% 34.24/34.42
% 34.24/34.42 SPASS V 3.9
% 34.24/34.42 SPASS beiseite: Proof found.
% 34.24/34.42 % SZS status Theorem
% 34.24/34.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.24/34.42 SPASS derived 25410 clauses, backtracked 804 clauses, performed 7 splits and kept 15572 clauses.
% 34.24/34.42 SPASS allocated 105471 KBytes.
% 34.24/34.42 SPASS spent 0:0:34.06 on the problem.
% 34.24/34.42 0:00:00.07 for the input.
% 34.24/34.42 0:00:00.00 for the FLOTTER CNF translation.
% 34.24/34.42 0:00:00.31 for inferences.
% 34.24/34.42 0:00:01.97 for the backtracking.
% 34.24/34.42 0:0:31.30 for the reduction.
% 34.24/34.42
% 34.24/34.42
% 34.24/34.42 Here is a proof with depth 14, length 164 :
% 34.24/34.42 % SZS output start Refutation
% 34.24/34.42 18[0:Inp] || -> equal(hAPP(c_Fun_Ofun__upd(u,v,w,x,y),v),w)**.
% 34.24/34.42 161[0:Inp] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),u)),w),c_Set_Oinsert(v,w,u))**.
% 34.24/34.42 184[0:Inp] || c_lessequals(u,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool))* -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))).
% 34.24/34.42 185[0:Inp] || -> equal(c_Collect(hAPP(c_COMBB(c_Not,tc_bool,tc_bool,u),v),u),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),c_Collect(v,u)))**.
% 34.24/34.42 186[0:Inp] || -> equal(c_Set_Ovimage(u,c_Collect(v,w),x,w),c_Collect(hAPP(c_COMBB(v,w,tc_bool,x),u),x))*.
% 34.24/34.42 212[0:Inp] || -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),tc_fun(v,tc_bool))*.
% 34.24/34.42 309[0:Inp] || -> equal(c_Collect(u,v),u)**.
% 34.24/34.42 312[0:Inp] || equal(c_Set_Oinsert(u,v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 34.24/34.42 369[0:Inp] || -> equal(hAPP(c_COMBK(u,v,w),x),u)**.
% 34.24/34.42 390[0:Inp] || -> equal(c_Set_Ovimage(u,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(v,tc_bool)),w),x,v),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(x,tc_bool)),c_Set_Ovimage(u,w,x,v)))*.
% 34.24/34.42 421[0:Inp] || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),v)),v)**.
% 34.24/34.42 423[0:Inp] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(u),hAPP(c_HOL_Ouminus__class_Ouminus(u),v)),v)**.
% 34.24/34.42 472[0:Inp] || hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v))* -> .
% 34.24/34.42 485[0:Inp] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_HOL_Ouminus__class_Ouminus(u),v),hAPP(c_HOL_Ouminus__class_Ouminus(u),w))* -> equal(v,w).
% 34.24/34.42 505[0:Inp] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_Set_Ovimage(c_COMBK(v,u,x),w,x,u),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))**.
% 34.24/34.42 511[0:Inp] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Set_Oinsert(v,w,u))* -> .
% 34.24/34.42 529[0:Inp] || -> equal(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(u,tc_bool)),v),v),v)**.
% 34.24/34.42 542[0:Inp] || hBOOL(hAPP(c_Set_Ovimage(u,v,w,x),y))* -> hBOOL(hAPP(v,hAPP(u,y))).
% 34.24/34.42 547[0:Inp] || -> equal(c_Set_Oinsert(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),v),c_Collect(hAPP(c_fequal(v),u),v))**.
% 34.24/34.42 548[0:Inp] || -> 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)))**.
% 34.24/34.42 549[0:Inp] || -> equal(c_Collect(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),u),v)**.
% 34.24/34.42 564[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),w)))* -> .
% 34.24/34.42 618[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(c_Set_Oinsert(v,w,u),w).
% 34.24/34.42 656[0:Inp] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),v),u))*.
% 34.24/34.42 663[0:Inp] class_Complete__Lattice_Ocomplete__lattice(u) || -> class_Complete__Lattice_Ocomplete__lattice(tc_fun(v,u))*.
% 34.24/34.42 664[0:Inp] class_Lattices_Olattice(u) || -> class_Lattices_Oupper__semilattice(tc_fun(v,u))*.
% 34.24/34.42 665[0:Inp] class_Lattices_Olattice(u) || -> class_Lattices_Olower__semilattice(tc_fun(v,u))*.
% 34.24/34.42 666[0:Inp] class_Lattices_Odistrib__lattice(u) || -> class_Lattices_Odistrib__lattice(tc_fun(v,u))*.
% 34.24/34.42 667[0:Inp] class_Lattices_Obounded__lattice(u) || -> class_Lattices_Obounded__lattice(tc_fun(v,u))*.
% 34.24/34.42 668[0:Inp] class_Lattices_Oboolean__algebra(u) || -> class_Lattices_Oboolean__algebra(tc_fun(v,u))*.
% 34.24/34.42 670[0:Inp] class_Orderings_Opreorder(u) || -> class_Orderings_Opreorder(tc_fun(v,u))*.
% 34.24/34.42 671[0:Inp] class_Lattices_Olattice(u) || -> class_Lattices_Olattice(tc_fun(v,u))*.
% 34.24/34.42 672[0:Inp] class_Orderings_Oorder(u) || -> class_Orderings_Oorder(tc_fun(v,u))*.
% 34.24/34.42 673[0:Inp] class_Orderings_Obot(u) || -> class_Orderings_Obot(tc_fun(v,u))*.
% 34.24/34.42 674[0:Inp] class_HOL_Oord(u) || -> class_HOL_Oord(tc_fun(v,u))*.
% 34.24/34.42 688[0:Inp] || -> class_Complete__Lattice_Ocomplete__lattice(tc_bool)*.
% 34.24/34.42 689[0:Inp] || -> class_Lattices_Oupper__semilattice(tc_bool)*.
% 34.24/34.42 690[0:Inp] || -> class_Lattices_Olower__semilattice(tc_bool)*.
% 34.24/34.42 691[0:Inp] || -> class_Lattices_Odistrib__lattice(tc_bool)*.
% 34.24/34.42 692[0:Inp] || -> class_Lattices_Obounded__lattice(tc_bool)*.
% 34.24/34.42 693[0:Inp] || -> class_Lattices_Oboolean__algebra(tc_bool)*.
% 34.24/34.42 694[0:Inp] || -> class_Finite__Set_Ofinite_Ofinite(tc_bool)*.
% 34.24/34.42 695[0:Inp] || -> class_Orderings_Opreorder(tc_bool)*.
% 34.24/34.42 696[0:Inp] || -> class_Lattices_Olattice(tc_bool)*.
% 34.24/34.42 697[0:Inp] || -> class_Orderings_Oorder(tc_bool)*.
% 34.24/34.42 698[0:Inp] || -> class_Orderings_Obot(tc_bool)*.
% 34.24/34.42 699[0:Inp] || -> class_HOL_Oord(tc_bool)*.
% 34.24/34.42 700[0:Inp] || -> equal(hAPP(hAPP(c_COMBC(u,v,w,x),y),z),hAPP(hAPP(u,z),y))**.
% 34.24/34.42 701[0:Inp] || -> equal(hAPP(hAPP(c_COMBB(u,v,w,x),y),z),hAPP(u,hAPP(y,z)))**.
% 34.24/34.42 702[0:Inp] || -> hBOOL(hAPP(hAPP(c_fequal(u),v),v))*.
% 34.24/34.42 707[0:Rew:309.0,549.0] || -> equal(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),v)**.
% 34.24/34.42 708[0:Rew:309.0,547.0] || -> equal(c_Set_Oinsert(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),v),hAPP(c_fequal(v),u))**.
% 34.24/34.42 713[0:Rew:309.0,186.0,309.0,186.0] || -> equal(hAPP(c_COMBB(u,v,tc_bool,w),x),c_Set_Ovimage(x,u,w,v))**.
% 34.24/34.42 716[0:Rew:309.0,185.0,713.0,185.0,309.0,185.0] || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),v),c_Set_Ovimage(v,c_Not,u,tc_bool))**.
% 34.24/34.42 718[0:Rew:716.0,421.0] || -> equal(c_Set_Ovimage(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),v),c_Not,u,tc_bool),v)**.
% 34.24/34.42 720[0:Rew:716.0,718.0] || -> equal(c_Set_Ovimage(c_Set_Ovimage(u,c_Not,v,tc_bool),c_Not,v,tc_bool),u)**.
% 34.24/34.42 722[0:Rew:716.0,184.0] || c_lessequals(u,c_Set_Ovimage(u,c_Not,v,tc_bool),tc_fun(v,tc_bool))* -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))).
% 34.24/34.42 726[0:Rew:708.0,161.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_fequal(u),v)),w),c_Set_Oinsert(v,w,u))**.
% 34.24/34.42 732[0:Rew:716.0,390.0,716.0,390.0] || -> equal(c_Set_Ovimage(u,c_Set_Ovimage(v,c_Not,w,tc_bool),x,w),c_Set_Ovimage(c_Set_Ovimage(u,v,x,w),c_Not,x,tc_bool))*.
% 34.24/34.42 733[0:Rew:732.0,720.0] || -> equal(c_Set_Ovimage(u,c_Set_Ovimage(c_Not,c_Not,tc_bool,tc_bool),v,tc_bool),u)**.
% 34.24/34.42 735[0:Rew:716.0,564.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),v),c_Set_Ovimage(w,c_Not,u,tc_bool)))* -> .
% 34.24/34.42 942[0:SpL:708.0,511.0] || equal(hAPP(c_fequal(u),v),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> .
% 34.24/34.42 1146[0:Res:656.1,618.0] || hBOOL(hAPP(u,v)) -> equal(c_Set_Oinsert(v,u,w),u)**.
% 34.24/34.42 1357[0:SpL:733.0,542.0] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(c_Set_Ovimage(c_Not,c_Not,tc_bool,tc_bool),hAPP(u,v)))*.
% 34.24/34.42 1388[0:SpR:369.0,1357.1] || hBOOL(hAPP(c_COMBK(u,v,w),x))* -> hBOOL(hAPP(c_Set_Ovimage(c_Not,c_Not,tc_bool,tc_bool),u))*.
% 34.24/34.42 1400[0:Rew:369.0,1388.0] || hBOOL(u) -> hBOOL(hAPP(c_Set_Ovimage(c_Not,c_Not,tc_bool,tc_bool),u))*.
% 34.24/34.42 1442[0:SpR:707.0,700.0] || -> equal(hAPP(hAPP(c_in(u),v),w),hAPP(w,v))**.
% 34.24/34.42 1570[0:Rew:1442.0,735.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(c_Set_Ovimage(w,c_Not,u,tc_bool),v))* -> .
% 34.24/34.42 1629[0:Rew:1442.0,505.0] || -> hBOOL(hAPP(u,v)) equal(c_Set_Ovimage(c_COMBK(v,w,x),u,x,w),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))**.
% 34.24/34.42 1634[0:Rew:1442.0,1570.0] || hBOOL(hAPP(u,v)) hBOOL(hAPP(c_Set_Ovimage(u,c_Not,w,tc_bool),v))* -> .
% 34.24/34.42 1742[0:Res:1400.1,1634.1] || hBOOL(u) hBOOL(hAPP(c_Not,u))* -> .
% 34.24/34.42 1855[0:SpR:713.0,701.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w,x),y),hAPP(v,hAPP(u,y)))**.
% 34.24/34.42 1921[0:SpR:733.0,1855.0] || -> equal(hAPP(c_Set_Ovimage(c_Not,c_Not,tc_bool,tc_bool),hAPP(u,v)),hAPP(u,v))**.
% 34.24/34.42 1922[0:SpR:548.0,1855.0] || -> 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)))*.
% 34.24/34.42 1924[0:Rew:1855.0,1921.0] || -> equal(hAPP(c_Not,hAPP(c_Not,hAPP(u,v))),hAPP(u,v))**.
% 34.24/34.42 1933[0:SpR:529.0,1924.0] || -> equal(hAPP(c_Not,hAPP(c_Not,u)),u)**.
% 34.24/34.42 2085[0:SpR:18.0,1922.0] || -> 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))*.
% 34.24/34.42 2321[0:SpR:726.0,212.0] || -> c_lessequals(hAPP(c_fequal(u),v),c_Set_Oinsert(v,w,u),tc_fun(u,tc_bool))*.
% 34.24/34.42 2331[0:SpR:1146.1,2321.0] || hBOOL(hAPP(u,v)) -> c_lessequals(hAPP(c_fequal(w),v),u,tc_fun(w,tc_bool))*.
% 34.24/34.42 2753[0:SpL:423.1,485.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oboolean__algebra(u) || equal(v,hAPP(c_HOL_Ouminus__class_Ouminus(u),w))* -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(u),v),w)*.
% 34.24/34.42 2762[0:Obv:2753.0] class_Lattices_Oboolean__algebra(u) || equal(v,hAPP(c_HOL_Ouminus__class_Ouminus(u),w))*+ -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(u),v),w)*.
% 34.24/34.42 3217[0:SpL:423.1,2762.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oboolean__algebra(u) || equal(v,w) -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(u),v),hAPP(c_HOL_Ouminus__class_Ouminus(u),w))*.
% 34.24/34.42 3221[0:Obv:3217.0] class_Lattices_Oboolean__algebra(u) || equal(v,w) -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(u),v),hAPP(c_HOL_Ouminus__class_Ouminus(u),w))*.
% 34.24/34.42 3422[0:SpR:3221.2,716.0] class_Lattices_Oboolean__algebra(tc_fun(u,tc_bool)) || equal(v,w) -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),v),c_Set_Ovimage(w,c_Not,u,tc_bool))*.
% 34.24/34.42 3458[0:Rew:716.0,3422.2] class_Lattices_Oboolean__algebra(tc_fun(u,tc_bool)) || equal(v,w) -> equal(c_Set_Ovimage(v,c_Not,u,tc_bool),c_Set_Ovimage(w,c_Not,u,tc_bool))*.
% 34.24/34.42 3459[0:SSi:3458.0,673.0,698.0,688.0,699.0,694.0,691.0,692.0,693.0,697.0,695.0,690.0,689.0,696.1,663.0,698.0,688.0,699.0,694.0,691.0,692.0,693.0,697.0,695.0,690.0,689.0,696.1,674.0,698.0,688.0,699.0,694.0,691.0,692.0,693.0,697.0,695.0,690.0,689.0,696.1,666.0,698.0,688.0,699.0,694.0,691.0,692.0,693.0,697.0,695.0,690.0,689.0,696.1,667.0,698.0,688.0,699.0,694.0,691.0,692.0,693.0,697.0,695.0,690.0,689.0,696.1,668.0,698.0,688.0,699.0,694.0,691.0,692.0,693.0,697.0,695.0,690.0,689.0,696.1,672.0,698.0,688.0,699.0,694.0,691.0,692.0,693.0,697.0,695.0,690.0,689.0,696.1,670.0,698.0,688.0,699.0,694.0,691.0,692.0,693.0,697.0,695.0,690.0,689.0,696.1,665.0,698.0,688.0,699.0,694.0,691.0,692.0,693.0,697.0,695.0,690.0,689.0,696.1,664.0,698.0,688.0,699.0,694.0,691.0,692.0,693.0,697.0,695.0,690.0,689.0,696.1,671.0,698.0,688.0,699.0,694.0,691.0,692.0,693.0,697.0,695.0,690.0,689.0,696.1] || equal(u,v) -> equal(c_Set_Ovimage(u,c_Not,w,tc_bool),c_Set_Ovimage(v,c_Not,w,tc_bool))*.
% 34.24/34.42 3519[0:SpR:3459.1,1855.0] || equal(u,v) -> equal(hAPP(c_Set_Ovimage(v,c_Not,w,tc_bool),x),hAPP(c_Not,hAPP(u,x)))*.
% 34.24/34.42 3538[0:Rew:1855.0,3519.1] || equal(u,v) -> equal(hAPP(c_Not,hAPP(v,w)),hAPP(c_Not,hAPP(u,w)))*.
% 34.24/34.42 3551[0:SpR:3538.1,1933.0] || equal(u,v) -> equal(hAPP(c_Not,hAPP(c_Not,hAPP(u,w))),hAPP(v,w))*.
% 34.24/34.42 3554[0:SpR:3538.1,1933.0] || equal(u,c_Not) -> equal(hAPP(c_Not,hAPP(u,v)),v)**.
% 34.24/34.42 3700[0:Rew:1933.0,3551.1] || equal(u,v) -> equal(hAPP(u,w),hAPP(v,w))*.
% 34.24/34.42 3737[0:SpR:2085.0,3554.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Not)** -> equal(hAPP(c_Not,hAPP(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w)),x)*.
% 34.24/34.42 3789[0:SpL:3554.1,1742.1] || equal(u,c_Not) hBOOL(hAPP(u,v))* hBOOL(v) -> .
% 34.24/34.42 3793[0:AED:312.0,3737.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Not)** -> .
% 34.24/34.42 4115[0:SpR:3700.1,1933.0] || equal(c_Not,u) -> equal(hAPP(u,hAPP(c_Not,v)),v)**.
% 34.24/34.42 4357[0:SpL:3700.1,942.0] || equal(c_fequal(u),v) equal(hAPP(v,w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))* -> .
% 34.24/34.42 4654[0:SpR:4115.1,1442.0] || equal(c_in(u),c_Not)**+ -> equal(hAPP(v,hAPP(c_Not,w)),hAPP(w,v))**.
% 34.24/34.42 4759[0:SpL:4115.1,942.0] || equal(c_fequal(u),c_Not) equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))* -> .
% 34.24/34.42 4806[0:AED:312.0,4759.1] || equal(c_fequal(u),c_Not)** -> .
% 34.24/34.42 5492[0:Res:702.0,3789.1] || equal(hAPP(c_fequal(u),v),c_Not)** hBOOL(v) -> .
% 34.24/34.42 5576[0:SpL:3700.1,5492.0] || equal(u,c_fequal(v))* equal(hAPP(u,w),c_Not)**+ hBOOL(w) -> .
% 34.24/34.42 5723[0:Res:2331.1,722.0] || hBOOL(hAPP(c_Set_Ovimage(hAPP(c_fequal(u),v),c_Not,u,tc_bool),v))* -> equal(hAPP(c_fequal(u),v),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 34.24/34.42 5731[0:Rew:1855.0,5723.0] || hBOOL(hAPP(c_Not,hAPP(hAPP(c_fequal(u),v),v)))* -> equal(hAPP(c_fequal(u),v),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 34.24/34.42 5732[0:MRR:5731.1,942.0] || hBOOL(hAPP(c_Not,hAPP(hAPP(c_fequal(u),v),v)))* -> .
% 34.24/34.42 5733[0:SpL:3700.1,5732.0] || equal(u,c_fequal(v))* hBOOL(hAPP(c_Not,hAPP(hAPP(u,w),w)))*+ -> .
% 34.24/34.42 9788[0:SpL:1442.0,5733.1] || equal(c_in(u),c_fequal(v))* hBOOL(hAPP(c_Not,hAPP(w,w)))*+ -> .
% 34.24/34.42 9898[0:SpL:3554.1,9788.1] || equal(u,c_Not) equal(c_in(v),c_fequal(w))*+ hBOOL(u)* -> .
% 34.24/34.42 11809[0:SpR:1629.1,733.0] || -> hBOOL(hAPP(c_Set_Ovimage(c_Not,c_Not,tc_bool,tc_bool),u))* equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_COMBK(u,tc_bool,v))*.
% 34.24/34.42 11822[0:Rew:1933.0,11809.0,1855.0,11809.0] || -> hBOOL(u) equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_COMBK(u,tc_bool,v))*.
% 34.24/34.42 12164[0:SpR:11822.1,369.0] || -> hBOOL(u)* equal(hAPP(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w),u)*.
% 34.24/34.42 12379[0:SpR:12164.1,12164.1] || -> hBOOL(u)* hBOOL(v)* equal(u,v)*.
% 34.24/34.42 13093[0:SpL:12164.1,4357.1] || equal(c_fequal(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* equal(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))* -> hBOOL(w)*.
% 34.24/34.42 13102[0:SpL:12164.1,5576.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_fequal(v))* equal(w,c_Not) hBOOL(x)* -> hBOOL(w)*.
% 34.24/34.42 15198[0:SpL:12379.2,3793.0] || equal(u,c_Not) -> hBOOL(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* hBOOL(u)*.
% 34.24/34.42 15228[0:SpL:12379.2,4806.0] || equal(u,c_Not)+ -> hBOOL(c_fequal(v))* hBOOL(u)*.
% 34.24/34.42 15523[0:SpL:12379.2,9898.1] || equal(u,c_Not) equal(v,c_fequal(w))* hBOOL(u)* -> hBOOL(c_in(x))* hBOOL(v)*.
% 34.24/34.42 16108[0:Res:12379.0,1742.1] || hBOOL(u)+ -> hBOOL(v)* equal(hAPP(c_Not,u),v)*.
% 34.24/34.42 19477[1:Spt:15228.0,15228.2] || equal(u,c_Not) -> hBOOL(u)*.
% 34.24/34.42 19491[1:MRR:15523.2,19477.1] || equal(u,c_Not)* equal(v,c_fequal(w))* -> hBOOL(c_in(x))* hBOOL(v)*.
% 34.24/34.42 19495[1:AED:312.0,19491.0] || equal(u,c_fequal(v))*+ -> hBOOL(c_in(w))* hBOOL(u)*.
% 34.24/34.42 19531[1:Res:19477.1,1742.1] || equal(hAPP(c_Not,u),c_Not)** hBOOL(u) -> .
% 34.24/34.42 19695[1:SpL:1933.0,19531.0] || equal(u,c_Not) hBOOL(hAPP(c_Not,u))* -> .
% 34.24/34.42 19755[1:Res:19477.1,19695.1] || equal(hAPP(c_Not,u),c_Not)** equal(u,c_Not) -> .
% 34.24/34.42 19901[1:SpL:3554.1,19755.0] || equal(u,c_Not) equal(v,c_Not) equal(hAPP(u,v),c_Not)** -> .
% 34.24/34.42 20090[2:Spt:19495.0,19495.2] || equal(u,c_fequal(v))*+ -> hBOOL(u)*.
% 34.24/34.42 20091[2:EqR:20090.0] || -> hBOOL(c_fequal(u))*.
% 34.24/34.42 20102[2:Res:20091.0,16108.0] || -> hBOOL(u)* equal(hAPP(c_Not,c_fequal(v)),u)*.
% 34.24/34.42 20113[2:SpR:20102.1,1933.0] || -> hBOOL(u) equal(hAPP(c_Not,u),c_fequal(v))*.
% 34.24/34.42 21804[2:SpL:20113.1,4806.0] || equal(hAPP(c_Not,u),c_Not)** -> hBOOL(u).
% 34.24/34.42 21838[2:MRR:21804.1,19531.1] || equal(hAPP(c_Not,u),c_Not)** -> .
% 34.24/34.42 21839[2:UnC:21838.0,1933.0] || -> .
% 34.24/34.42 21866[2:Spt:21839.0,19495.1] || -> hBOOL(c_in(u))*.
% 34.24/34.42 21872[2:Res:21866.0,16108.0] || -> hBOOL(u)* equal(hAPP(c_Not,c_in(v)),u)*.
% 34.24/34.42 22155[2:SpR:21872.1,1933.0] || -> hBOOL(hAPP(c_Not,u))* equal(hAPP(c_Not,hAPP(c_Not,c_in(v))),u)*.
% 34.24/34.42 23206[2:Rew:1933.0,22155.1] || -> hBOOL(hAPP(c_Not,u))* equal(c_in(v),u)*.
% 34.24/34.42 24419[2:SpL:23206.1,4654.0] || equal(u,c_Not) -> hBOOL(hAPP(c_Not,u))* equal(hAPP(v,hAPP(c_Not,w)),hAPP(w,v))**.
% 34.24/34.42 24997[2:MRR:24419.1,19695.1] || equal(u,c_Not)* -> equal(hAPP(v,hAPP(c_Not,w)),hAPP(w,v))**.
% 34.24/34.42 24998[2:Rew:24997.1,4115.1] || equal(c_Not,u) -> equal(hAPP(v,u),v)**.
% 34.24/34.42 25118[2:Rew:24998.1,19901.2] || equal(u,c_Not)* equal(v,c_Not)* equal(u,c_Not)* -> .
% 34.24/34.42 25260[2:Obv:25118.0] || equal(u,c_Not)* equal(v,c_Not)* -> .
% 34.24/34.42 25261[2:Con:25260.1] || equal(u,c_Not)* -> .
% 34.24/34.42 25262[2:AED:312.0,25261.0] || -> .
% 34.24/34.42 25504[1:Spt:25262.0,15228.1] || -> hBOOL(c_fequal(u))*.
% 34.24/34.42 25513[1:Res:25504.0,16108.0] || -> hBOOL(u)* equal(hAPP(c_Not,c_fequal(v)),u)*.
% 34.24/34.42 25523[1:SpR:25513.1,1933.0] || -> hBOOL(u) equal(hAPP(c_Not,u),c_fequal(v))*.
% 34.24/34.42 25793[1:SpR:25513.1,1933.0] || -> hBOOL(hAPP(c_Not,u))* equal(hAPP(c_Not,hAPP(c_Not,c_fequal(v))),u)*.
% 34.24/34.42 26781[1:Rew:1933.0,25793.1] || -> hBOOL(hAPP(c_Not,u))* equal(c_fequal(v),u)*.
% 34.24/34.42 27057[1:SpL:25523.1,4806.0] || equal(hAPP(c_Not,u),c_Not)** -> hBOOL(u).
% 34.24/34.42 27347[1:SpL:1933.0,27057.0] || equal(u,c_Not) -> hBOOL(hAPP(c_Not,u))*.
% 34.24/34.42 27387[1:Res:27347.1,1742.1] || equal(u,c_Not) hBOOL(u)* -> .
% 34.71/34.89 27415[1:MRR:13102.3,27387.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_fequal(v))* equal(w,c_Not)* hBOOL(x)* -> .
% 34.71/34.89 27423[1:MRR:15198.2,27387.1] || equal(u,c_Not)* -> hBOOL(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))*.
% 34.71/34.89 27449[1:AED:312.0,27423.0] || -> hBOOL(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))*.
% 34.71/34.89 27541[1:AED:312.0,27415.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_fequal(v))* hBOOL(w)* -> .
% 34.71/34.89 27544[1:MRR:13093.2,27541.1] || equal(c_fequal(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* equal(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))* -> .
% 34.71/34.89 27550[1:AED:312.0,27544.1] || equal(c_fequal(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 34.71/34.89 28052[1:SpL:11822.1,27550.0] || equal(c_fequal(u),c_COMBK(v,tc_bool,w))* -> hBOOL(v).
% 34.71/34.89 28190[1:SpR:26781.1,11822.1] || -> hBOOL(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* hBOOL(v) equal(c_fequal(w),c_COMBK(v,tc_bool,u))*.
% 34.71/34.89 28835[1:SpL:26781.1,472.0] || hBOOL(hAPP(c_fequal(u),v))* -> hBOOL(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))*.
% 34.71/34.89 29249[1:MRR:28190.2,28052.0] || -> hBOOL(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* hBOOL(v)*.
% 34.71/34.89 29250[1:MRR:28835.0,29249.1] || -> hBOOL(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))*.
% 34.71/34.89 29508[1:Res:29250.0,3789.1] || equal(c_Not,c_Not) hBOOL(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))* -> .
% 34.71/34.89 29515[1:Obv:29508.0] || hBOOL(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))* -> .
% 34.71/34.89 29516[1:MRR:29515.0,27449.0] || -> .
% 34.71/34.89 % SZS output end Refutation
% 34.71/34.89 Formulae used in the proof : cls_fun__upd__same_0 cls_insert__is__Un_0 cls_subset__Compl__self__eq_0 cls_Collect__neg__eq_0 cls_vimage__Collect__eq_0 cls_Un__upper1_0 cls_Collect__def_0 cls_insert__not__empty_0 cls_COMBK__def_0 cls_vimage__Compl_0 cls_double__complement_0 cls_double__compl_0 cls_bot1E_0 cls_compl__eq__compl__iff_0 cls_vimage__const_1 cls_empty__not__insert_0 cls_Int__absorb_0 cls_vimage__code_0 cls_singleton__conv2_0 cls_vimage__empty_0 cls_Collect__mem__eq_0 cls_ComplD_0 cls_insert__absorb_0 cls_mem__def_1 clsarity_fun__Complete__Lattice_Ocomplete__lattice clsarity_fun__Lattices_Oupper__semilattice clsarity_fun__Lattices_Olower__semilattice clsarity_fun__Lattices_Odistrib__lattice clsarity_fun__Lattices_Obounded__lattice clsarity_fun__Lattices_Oboolean__algebra clsarity_fun__Orderings_Opreorder clsarity_fun__Lattices_Olattice clsarity_fun__Orderings_Oorder clsarity_fun__Orderings_Obot clsarity_fun__HOL_Oord 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_Obot clsarity_bool__HOL_Oord cls_ATP__Linkup_OCOMBC__def_0 cls_ATP__Linkup_OCOMBB__def_0 cls_ATP__Linkup_Oequal__imp__fequal_0
% 34.71/34.89
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