%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWV822-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:53:13 PM UTC 2026
% Result : Unsatisfiable 70.83s 9.50s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV822-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 09:26:49 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.41 % Drodi V4.1.1
% 70.83/9.50 % Refutation found
% 70.83/9.50 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 70.83/9.50 % SZS output start CNFRefutation for theBenchmark
% 70.83/9.50 fof(f8,axiom,(
% 70.83/9.50 (![V_m,V_n]: (c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f9,axiom,(
% 70.83/9.50 (![V_m,V_l,V_k,V_n]: (( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat)| ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f16,axiom,(
% 70.83/9.50 (![V_m,V_n]: (( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != V_m| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f33,axiom,(
% 70.83/9.50 (![V_n,V_m]: (( c_lessequals(c_Suc(V_n),V_m,tc_nat)| ~ c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f50,axiom,(
% 70.83/9.50 (![V_i,V_m]: (c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_i,tc_nat)),tc_nat) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f55,axiom,(
% 70.83/9.50 (![V_m,V_j,V_i,V_u,V_n]: (( c_HOL_Oord__class_Oless(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat)| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat)| ~ c_lessequals(V_i,V_j,tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f57,axiom,(
% 70.83/9.50 (![V_i,V_j,V_u,V_m,V_n]: (( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat)| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat)| ~ c_lessequals(V_j,V_i,tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f68,axiom,(
% 70.83/9.50 (![V_m,V_n]: (( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)| c_lessequals(V_m,V_n,tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f73,axiom,(
% 70.83/9.50 c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f81,axiom,(
% 70.83/9.50 (![V_n]: (( V_n = c_HOL_Ozero__class_Ozero(tc_nat)| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f88,axiom,(
% 70.83/9.50 (![V_m,V_k,V_n]: (( c_lessequals(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat)| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f89,axiom,(
% 70.83/9.50 (![V_k,V_m,V_n]: (( c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f92,axiom,(
% 70.83/9.50 (![V_m,V_n]: (( c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat)| ~ c_lessequals(V_m,V_n,tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f93,axiom,(
% 70.83/9.50 (![V_m,V_n]: (( c_lessequals(V_m,V_n,tc_nat)| ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f98,axiom,(
% 70.83/9.50 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f101,axiom,(
% 70.83/9.50 (![V_m,V_n]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),c_Suc(V_m),tc_nat) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f112,axiom,(
% 70.83/9.50 (![V_m,V_n,V_k]: (c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f121,axiom,(
% 70.83/9.50 (![V_m]: (~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f123,axiom,(
% 70.83/9.50 (![V_n,V_m]: (( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat)| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f126,axiom,(
% 70.83/9.50 (![V_m]: (c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f132,axiom,(
% 70.83/9.50 (![V_k,V_m,V_n]: (( c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)| V_m = V_n| V_k = c_HOL_Ozero__class_Ozero(tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f134,axiom,(
% 70.83/9.50 (![V_m,V_k,V_n]: (( c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat) != c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat)| V_k = c_HOL_Ozero__class_Ozero(tc_nat)| V_m = V_n ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f143,axiom,(
% 70.83/9.50 (![V_n]: (c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f172,axiom,(
% 70.83/9.50 (![V_m,V_n]: (( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)| V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))| V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f190,axiom,(
% 70.83/9.50 (![V_m,V_n]: (c_HOL_Otimes__class_Otimes(V_m,c_Suc(V_n),tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f191,axiom,(
% 70.83/9.50 (![V_m,V_n]: (c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f209,axiom,(
% 70.83/9.50 c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f219,axiom,(
% 70.83/9.50 (![V_n]: (c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f220,axiom,(
% 70.83/9.50 (![V_m]: (c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f259,axiom,(
% 70.83/9.50 (![V_n,V_m]: (c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f260,axiom,(
% 70.83/9.50 (![V_i,V_j,V_k]: (c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(V_i,c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f270,axiom,(
% 70.83/9.50 (![V_k,V_m,V_n]: (( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f271,axiom,(
% 70.83/9.50 (![V_k,V_m,V_n]: (( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f273,axiom,(
% 70.83/9.50 (![V_m,V_n,V_k]: (( c_lessequals(V_m,V_n,tc_nat)| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f274,axiom,(
% 70.83/9.50 (![V_m,V_n,V_k]: (( c_lessequals(V_m,V_n,tc_nat)| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f288,axiom,(
% 70.83/9.50 (![V_n]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f308,axiom,(
% 70.83/9.50 (![V_k,V_m,V_n]: (c_HOL_Otimes__class_Otimes(V_k,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f317,axiom,(
% 70.83/9.50 (![V_i,V_j,V_k]: (c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_k,tc_nat),V_j,tc_nat) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f328,axiom,(
% 70.83/9.50 (![V_x]: (~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f347,axiom,(
% 70.83/9.50 (![V_n,V_m]: (( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)| c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)| V_m = V_n ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f367,axiom,(
% 70.83/9.50 (![T_a,V_a,V_b]: (( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f422,axiom,(
% 70.83/9.50 (![V_x,V_r,V_c,V_d]: (( c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_c,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_d,tc_nat),tc_nat)| V_c = V_d| V_r = c_HOL_Ozero__class_Ozero(tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f430,axiom,(
% 70.83/9.50 (![V_k,V_m,V_n]: (( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat)| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f448,axiom,(
% 70.83/9.50 (![V_k,V_m,V_n]: (( c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat)| ~ c_lessequals(V_m,V_n,tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f470,axiom,(
% 70.83/9.50 (![V_m,V_n,V_k]: (( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f498,axiom,(
% 70.83/9.50 (![V_x]: (V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f499,axiom,(
% 70.83/9.50 (![V_n]: (c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f624,axiom,(
% 70.83/9.50 (![V_n,V_m]: (( c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat)| ~ c_lessequals(V_n,V_m,tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f625,axiom,(
% 70.83/9.50 (![V_n,V_m]: (( c_lessequals(V_n,V_m,tc_nat)| ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f637,axiom,(
% 70.83/9.50 (![V_n]: (V_n != c_Suc(V_n) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f640,axiom,(
% 70.83/9.50 (![V_m,V_n]: (( c_lessequals(V_m,c_Suc(V_n),tc_nat)| ~ c_lessequals(V_m,V_n,tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f643,axiom,(
% 70.83/9.50 (![V_x]: (c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f645,axiom,(
% 70.83/9.50 (![V_m]: (c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f649,axiom,(
% 70.83/9.50 (![V_n,V_m]: (( V_n = V_m| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)| c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f652,axiom,(
% 70.83/9.50 (![V_m,V_n]: (c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f654,axiom,(
% 70.83/9.50 (![V_nat,V_nat_H]: (( c_Suc(V_nat) != c_Suc(V_nat_H)| V_nat = V_nat_H ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f656,axiom,(
% 70.83/9.50 (![V_P,V_s,V_n,V_s1]: (( c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(V_P),tc_Com_Ocom),V_s,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1),V_s1)| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f661,axiom,(
% 70.83/9.50 (![V_m,V_n]: (c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f662,axiom,(
% 70.83/9.50 (![V_m,V_n]: (c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f670,axiom,(
% 70.83/9.50 (![V_m,V_n]: (( c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat)| c_Suc(V_m) = V_n| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f673,axiom,(
% 70.83/9.50 (![V_pn,V_s0,V_n,V_s1]: (( c_Natural_Oevaln(c_Com_Ocom_OBODY(V_pn),V_s0,c_Suc(V_n),V_s1)| ~ c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_s0,V_n,V_s1) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f676,axiom,(
% 70.83/9.50 (![V_n]: (c_lessequals(c_Suc(V_n),c_Suc(V_n),tc_nat) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f679,axiom,(
% 70.83/9.50 (![V_n,V_P,V_s,V_s1]: (( V_n = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1))| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f683,axiom,(
% 70.83/9.50 (![V_n,V_m]: (( c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f691,negated_conjecture,(
% 70.83/9.50 ( hBOOL(hAPP(hAPP(v_P,v_x),v_xa))| hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ) ),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f695,negated_conjecture,(
% 70.83/9.50 ( c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_Suc(v_n),v_xb)| c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_xa,v_n,v_xb) ) ),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f699,negated_conjecture,(
% 70.83/9.50 ( ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb))| ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb)) ) ),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f700,negated_conjecture,(
% 70.83/9.50 (![V_Za,V_s_Ha,V_sa,V_Z,V_s_H,V_s]: (( hBOOL(hAPP(hAPP(v_Q,V_Za),V_s_Ha))| ~ c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),V_sa,v_n,V_s_Ha)| ~ hBOOL(hAPP(hAPP(v_P,V_Za),V_sa))| hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H))| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),V_s,c_Suc(v_n),V_s_H)| ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s)) ) ))),
% 70.83/9.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 70.83/9.50 fof(f740,plain,(
% 70.83/9.50 ![X0,X1]: (c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)=c_HOL_Oplus__class_Oplus(X1,X0,tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f8])).
% 70.83/9.50 fof(f741,plain,(
% 70.83/9.50 ![V_m,V_n]: ((![V_l,V_k]: (~c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat)=c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat)|~c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)))|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat))),
% 70.83/9.50 inference(miniscoping,[status(thm)],[f9])).
% 70.83/9.50 fof(f742,plain,(
% 70.83/9.50 ![X0,X1,X2,X3]: (~c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)=c_HOL_Oplus__class_Oplus(X2,X3,tc_nat)|~c_HOL_Oord__class_Oless(X2,X1,tc_nat)|c_HOL_Oord__class_Oless(X0,X3,tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f741])).
% 70.83/9.50 fof(f755,plain,(
% 70.83/9.50 ![V_n]: ((![V_m]: ~c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)=V_m)|V_n=c_HOL_Ozero__class_Ozero(tc_nat))),
% 70.83/9.50 inference(miniscoping,[status(thm)],[f16])).
% 70.83/9.50 fof(f756,plain,(
% 70.83/9.50 ![X0,X1]: (~c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)=X0|X1=c_HOL_Ozero__class_Ozero(tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f755])).
% 70.83/9.50 fof(f781,plain,(
% 70.83/9.50 ![X0,X1]: (c_lessequals(c_Suc(X0),X1,tc_nat)|~c_HOL_Oord__class_Oless(X0,X1,tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f33])).
% 70.83/9.50 fof(f811,plain,(
% 70.83/9.50 ![X0,X1]: (c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f50])).
% 70.83/9.50 fof(f817,plain,(
% 70.83/9.50 ![V_j,V_i]: ((![V_m,V_u,V_n]: (c_HOL_Oord__class_Oless(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat)))|~c_lessequals(V_i,V_j,tc_nat))),
% 70.83/9.50 inference(miniscoping,[status(thm)],[f55])).
% 70.83/9.50 fof(f818,plain,(
% 70.83/9.50 ![X0,X1,X2,X3,X4]: (c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),X4,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),tc_nat)|~c_lessequals(X2,X1,tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f817])).
% 70.83/9.50 fof(f821,plain,(
% 70.83/9.50 ![V_i,V_j]: ((![V_u,V_m,V_n]: (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat)))|~c_lessequals(V_j,V_i,tc_nat))),
% 70.83/9.50 inference(miniscoping,[status(thm)],[f57])).
% 70.83/9.50 fof(f822,plain,(
% 70.83/9.50 ![X0,X1,X2,X3,X4]: (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat),X3,tc_nat),X4,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X4,tc_nat),tc_nat)|~c_lessequals(X1,X0,tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f821])).
% 70.83/9.50 fof(f842,plain,(
% 70.83/9.50 ![X0,X1]: (~c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|c_lessequals(X0,X1,tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f68])).
% 70.83/9.50 fof(f851,plain,(
% 70.83/9.50 c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f73])).
% 70.83/9.50 fof(f864,plain,(
% 70.83/9.50 ![X0]: (X0=c_HOL_Ozero__class_Ozero(tc_nat)|~c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f81])).
% 70.83/9.50 fof(f875,plain,(
% 70.83/9.50 ![V_k]: ((![V_m,V_n]: c_lessequals(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat))|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat))),
% 70.83/9.50 inference(miniscoping,[status(thm)],[f88])).
% 70.83/9.50 fof(f876,plain,(
% 70.83/9.50 ![X0,X1,X2]: (c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f875])).
% 70.83/9.50 fof(f877,plain,(
% 70.83/9.50 ![V_k]: ((![V_m,V_n]: c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat))|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat))),
% 70.83/9.50 inference(miniscoping,[status(thm)],[f89])).
% 70.83/9.50 fof(f878,plain,(
% 70.83/9.50 ![X0,X1,X2]: (c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f877])).
% 70.83/9.50 fof(f883,plain,(
% 70.83/9.50 ![X0,X1]: (c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)|~c_lessequals(X0,X1,tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f92])).
% 70.83/9.50 fof(f884,plain,(
% 70.83/9.50 ![X0,X1]: (c_lessequals(X0,X1,tc_nat)|~c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f93])).
% 70.83/9.50 fof(f890,plain,(
% 70.83/9.50 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f98])).
% 70.83/9.50 fof(f894,plain,(
% 70.83/9.50 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(X0),tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f101])).
% 70.83/9.50 fof(f911,plain,(
% 70.83/9.50 ![X0,X1,X2]: (c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)=c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f112])).
% 70.83/9.50 fof(f927,plain,(
% 70.83/9.50 ![X0]: (~c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f121])).
% 70.83/9.50 fof(f929,plain,(
% 70.83/9.50 ![V_n]: (c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat)|(![V_m]: ~c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)))),
% 70.83/9.50 inference(miniscoping,[status(thm)],[f123])).
% 70.83/9.50 fof(f930,plain,(
% 70.83/9.50 ![X0,X1]: (c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)|~c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f929])).
% 70.83/9.50 fof(f935,plain,(
% 70.83/9.50 ![X0]: (c_HOL_Ominus__class_Ominus(X0,X0,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f126])).
% 70.83/9.50 fof(f944,plain,(
% 70.83/9.50 ![V_k]: ((![V_m,V_n]: (~c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)=c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)|V_m=V_n))|V_k=c_HOL_Ozero__class_Ozero(tc_nat))),
% 70.83/9.50 inference(miniscoping,[status(thm)],[f132])).
% 70.83/9.50 fof(f945,plain,(
% 70.83/9.50 ![X0,X1,X2]: (~c_HOL_Otimes__class_Otimes(X0,X1,tc_nat)=c_HOL_Otimes__class_Otimes(X0,X2,tc_nat)|X1=X2|X0=c_HOL_Ozero__class_Ozero(tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f944])).
% 70.83/9.50 fof(f948,plain,(
% 70.83/9.50 ![V_m,V_n]: ((![V_k]: (~c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat)=c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat)|V_k=c_HOL_Ozero__class_Ozero(tc_nat)))|V_m=V_n)),
% 70.83/9.50 inference(miniscoping,[status(thm)],[f134])).
% 70.83/9.50 fof(f949,plain,(
% 70.83/9.50 ![X0,X1,X2]: (~c_HOL_Otimes__class_Otimes(X0,X1,tc_nat)=c_HOL_Otimes__class_Otimes(X2,X1,tc_nat)|X1=c_HOL_Ozero__class_Ozero(tc_nat)|X0=X2)),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f948])).
% 70.83/9.50 fof(f966,plain,(
% 70.83/9.50 ![X0]: (c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f143])).
% 70.83/9.50 fof(f1005,plain,(
% 70.83/9.50 ![V_m]: ((![V_n]: (~c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))))|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))),
% 70.83/9.50 inference(miniscoping,[status(thm)],[f172])).
% 70.83/9.50 fof(f1006,plain,(
% 70.83/9.50 ![X0,X1]: (~c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)|X1=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|X0=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f1005])).
% 70.83/9.50 fof(f1036,plain,(
% 70.83/9.50 ![X0,X1]: (c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)=c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f190])).
% 70.83/9.50 fof(f1037,plain,(
% 70.83/9.50 ![X0,X1]: (c_HOL_Otimes__class_Otimes(c_Suc(X0),X1,tc_nat)=c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f191])).
% 70.83/9.50 fof(f1068,plain,(
% 70.83/9.50 c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f209])).
% 70.83/9.50 fof(f1087,plain,(
% 70.83/9.50 ![X0]: (c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f219])).
% 70.83/9.50 fof(f1088,plain,(
% 70.83/9.50 ![X0]: (c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f220])).
% 70.83/9.50 fof(f1150,plain,(
% 70.83/9.50 ![X0,X1]: (c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f259])).
% 70.83/9.50 fof(f1151,plain,(
% 70.83/9.50 ![X0,X1,X2]: (c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)=c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f260])).
% 70.83/9.50 fof(f1168,plain,(
% 70.83/9.50 ![V_k]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)|(![V_m,V_n]: ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat)))),
% 70.83/9.50 inference(miniscoping,[status(thm)],[f270])).
% 70.83/9.50 fof(f1169,plain,(
% 70.83/9.50 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),c_HOL_Otimes__class_Otimes(X2,X0,tc_nat),tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f1168])).
% 70.83/9.50 fof(f1170,plain,(
% 70.83/9.50 ![V_k]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)|(![V_m,V_n]: ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)))),
% 70.83/9.50 inference(miniscoping,[status(thm)],[f271])).
% 70.83/9.50 fof(f1171,plain,(
% 70.83/9.50 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f1170])).
% 70.83/9.50 fof(f1173,plain,(
% 70.83/9.50 ![X0,X1,X2]: (c_lessequals(X0,X1,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)|~c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f273])).
% 70.83/9.50 fof(f1174,plain,(
% 70.83/9.50 ![X0,X1,X2]: (c_lessequals(X0,X1,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)|~c_lessequals(c_HOL_Otimes__class_Otimes(X2,X0,tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f274])).
% 70.83/9.50 fof(f1196,plain,(
% 70.83/9.50 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X0),tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f288])).
% 70.83/9.50 fof(f1232,plain,(
% 70.83/9.50 ![X0,X1,X2]: (c_HOL_Otimes__class_Otimes(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f308])).
% 70.83/9.50 fof(f1248,plain,(
% 70.83/9.50 ![X0,X1,X2]: (c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f317])).
% 70.83/9.50 fof(f1265,plain,(
% 70.83/9.50 ![X0]: (~c_HOL_Oord__class_Oless(X0,X0,tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f328])).
% 70.83/9.50 fof(f1291,plain,(
% 70.83/9.50 ![X0,X1]: (~c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|~c_HOL_Ominus__class_Ominus(X1,X0,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|X1=X0)),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f347])).
% 70.83/9.50 fof(f1316,plain,(
% 70.83/9.50 ![X0,X1,X2]: (~class_OrderedGroup_Opordered__ab__group__add(X0)|c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)|~c_HOL_Oord__class_Oless(X1,X2,X0))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f367])).
% 70.83/9.50 fof(f1410,plain,(
% 70.83/9.50 ![V_r]: ((![V_c,V_d]: ((![V_x]: ~c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_c,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_d,tc_nat),tc_nat))|V_c=V_d))|V_r=c_HOL_Ozero__class_Ozero(tc_nat))),
% 70.83/9.50 inference(miniscoping,[status(thm)],[f422])).
% 70.83/9.50 fof(f1411,plain,(
% 70.83/9.50 ![X0,X1,X2,X3]: (~c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)|X2=X3|X1=c_HOL_Ozero__class_Ozero(tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f1410])).
% 70.83/9.50 fof(f1426,plain,(
% 70.83/9.50 ![V_m,V_n]: ((![V_k]: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat))|~c_HOL_Oord__class_Oless(V_m,V_n,tc_nat))),
% 70.83/9.50 inference(miniscoping,[status(thm)],[f430])).
% 70.83/9.50 fof(f1427,plain,(
% 70.83/9.50 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X0),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X0),X2,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(X1,X2,tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f1426])).
% 70.83/9.50 fof(f1460,plain,(
% 70.83/9.50 ![V_m,V_n]: ((![V_k]: c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat))|~c_lessequals(V_m,V_n,tc_nat))),
% 70.83/9.50 inference(miniscoping,[status(thm)],[f448])).
% 70.83/9.50 fof(f1461,plain,(
% 70.83/9.50 ![X0,X1,X2]: (c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X0),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X0),X2,tc_nat),tc_nat)|~c_lessequals(X1,X2,tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f1460])).
% 70.83/9.50 fof(f1498,plain,(
% 70.83/9.50 ![V_k]: ((![V_m,V_n]: (c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)))|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat))),
% 70.83/9.50 inference(miniscoping,[status(thm)],[f470])).
% 70.83/9.50 fof(f1499,plain,(
% 70.83/9.50 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(X0,X1,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f1498])).
% 70.83/9.50 fof(f1552,plain,(
% 70.83/9.50 ![X0]: (X0=c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f498])).
% 70.83/9.50 fof(f1553,plain,(
% 70.83/9.50 ![X0]: (c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)=X0)),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f499])).
% 70.83/9.50 fof(f1755,plain,(
% 70.83/9.50 ![X0,X1]: (c_lessequals(c_Suc(X0),c_Suc(X1),tc_nat)|~c_lessequals(X0,X1,tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f624])).
% 70.83/9.50 fof(f1756,plain,(
% 70.83/9.50 ![X0,X1]: (c_lessequals(X0,X1,tc_nat)|~c_lessequals(c_Suc(X0),c_Suc(X1),tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f625])).
% 70.83/9.50 fof(f1770,plain,(
% 70.83/9.50 ![X0]: (~X0=c_Suc(X0))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f637])).
% 70.83/9.50 fof(f1773,plain,(
% 70.83/9.50 ![X0,X1]: (c_lessequals(X0,c_Suc(X1),tc_nat)|~c_lessequals(X0,X1,tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f640])).
% 70.83/9.50 fof(f1777,plain,(
% 70.83/9.50 ![X0]: (c_HOL_Oord__class_Oless(X0,c_Suc(X0),tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f643])).
% 70.83/9.50 fof(f1779,plain,(
% 70.83/9.50 ![X0]: (~c_Suc(X0)=c_HOL_Ozero__class_Ozero(tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f645])).
% 70.83/9.50 fof(f1783,plain,(
% 70.83/9.50 ![X0,X1]: (X0=X1|~c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)|c_HOL_Oord__class_Oless(X0,X1,tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f649])).
% 70.83/9.50 fof(f1786,plain,(
% 70.83/9.50 ![X0,X1]: (c_HOL_Ominus__class_Ominus(c_Suc(X0),c_Suc(X1),tc_nat)=c_HOL_Ominus__class_Ominus(X0,X1,tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f652])).
% 70.83/9.50 fof(f1788,plain,(
% 70.83/9.50 ![X0,X1]: (~c_Suc(X0)=c_Suc(X1)|X0=X1)),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f654])).
% 70.83/9.50 fof(f1790,plain,(
% 70.83/9.50 ![X0,X1,X2,X3]: (c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(X0),tc_Com_Ocom),X1,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X0,X2,X1,X3),X3)|~c_Natural_Oevaln(c_Com_Ocom_OBODY(X0),X1,X2,X3))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f656])).
% 70.83/9.50 fof(f1797,plain,(
% 70.83/9.50 ![X0,X1]: (c_HOL_Oplus__class_Oplus(c_Suc(X0),X1,tc_nat)=c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f661])).
% 70.83/9.50 fof(f1798,plain,(
% 70.83/9.50 ![X0,X1]: (c_HOL_Oplus__class_Oplus(X0,c_Suc(X1),tc_nat)=c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f662])).
% 70.83/9.50 fof(f1807,plain,(
% 70.83/9.50 ![X0,X1]: (c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat)|c_Suc(X0)=X1|~c_HOL_Oord__class_Oless(X0,X1,tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f670])).
% 70.83/9.50 fof(f1810,plain,(
% 70.83/9.50 ![X0,X1,X2,X3]: (c_Natural_Oevaln(c_Com_Ocom_OBODY(X0),X1,c_Suc(X2),X3)|~c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(X0),tc_Com_Ocom),X1,X2,X3))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f673])).
% 70.83/9.50 fof(f1813,plain,(
% 70.83/9.50 ![X0]: (c_lessequals(c_Suc(X0),c_Suc(X0),tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f676])).
% 70.83/9.50 fof(f1816,plain,(
% 70.83/9.50 ![X0,X1,X2,X3]: (X0=c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X1,X0,X2,X3))|~c_Natural_Oevaln(c_Com_Ocom_OBODY(X1),X2,X0,X3))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f679])).
% 70.83/9.50 fof(f1820,plain,(
% 70.83/9.50 ![X0,X1]: (c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)|c_HOL_Oord__class_Oless(X1,X0,tc_nat))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f683])).
% 70.83/9.50 fof(f1831,plain,(
% 70.83/9.50 hBOOL(hAPP(hAPP(v_P,v_x),v_xa))|hBOOL(hAPP(hAPP(v_P,v_x),v_xa))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f691])).
% 70.83/9.50 fof(f1835,plain,(
% 70.83/9.50 c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_Suc(v_n),v_xb)|c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_xa,v_n,v_xb)),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f695])).
% 70.83/9.50 fof(f1839,plain,(
% 70.83/9.50 ~hBOOL(hAPP(hAPP(v_Q,v_x),v_xb))|~hBOOL(hAPP(hAPP(v_Q,v_x),v_xb))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f699])).
% 70.83/9.50 fof(f1840,plain,(
% 70.83/9.50 ![V_Z,V_s]: ((![V_s_H]: (((![V_Za,V_sa]: ((![V_s_Ha]: (hBOOL(hAPP(hAPP(v_Q,V_Za),V_s_Ha))|~c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),V_sa,v_n,V_s_Ha)))|~hBOOL(hAPP(hAPP(v_P,V_Za),V_sa))))|hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H)))|~c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),V_s,c_Suc(v_n),V_s_H)))|~hBOOL(hAPP(hAPP(v_P,V_Z),V_s)))),
% 70.83/9.50 inference(miniscoping,[status(thm)],[f700])).
% 70.83/9.50 fof(f1841,plain,(
% 70.83/9.50 ![X0,X1,X2,X3,X4,X5]: (hBOOL(hAPP(hAPP(v_Q,X0),X1))|~c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),X2,v_n,X1)|~hBOOL(hAPP(hAPP(v_P,X0),X2))|hBOOL(hAPP(hAPP(v_Q,X3),X4))|~c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),X5,c_Suc(v_n),X4)|~hBOOL(hAPP(hAPP(v_P,X3),X5)))),
% 70.83/9.50 inference(cnf_transformation,[status(thm)],[f1840])).
% 70.83/9.50 fof(f1869,definition,(
% 70.83/9.50 sQ0_spl <=> (hBOOL(hAPP(hAPP(v_P,v_x),v_xa)))),
% 70.83/9.50 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 70.83/9.50 fof(f1870,plain,(
% 70.83/9.50 hBOOL(hAPP(hAPP(v_P,v_x),v_xa))|~sQ0_spl),
% 70.83/9.50 inference(component_clause,[status(thm)],[f1869])).
% 70.83/9.50 fof(f1872,plain,(
% 70.83/9.50 sQ0_spl),
% 70.83/9.50 inference(split_clause,[status(thm)],[f1831,f1869])).
% 70.83/9.50 fof(f1873,definition,(
% 70.83/9.50 sQ1_spl <=> (c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_Suc(v_n),v_xb))),
% 70.83/9.50 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 70.83/9.50 fof(f1874,plain,(
% 70.83/9.50 c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_Suc(v_n),v_xb)|~sQ1_spl),
% 70.83/9.50 inference(component_clause,[status(thm)],[f1873])).
% 70.83/9.50 fof(f1877,definition,(
% 70.83/9.50 sQ2_spl <=> (hBOOL(hAPP(hAPP(v_Q,v_x),v_xb)))),
% 70.83/9.50 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 70.83/9.50 fof(f1879,plain,(
% 70.83/9.50 ~hBOOL(hAPP(hAPP(v_Q,v_x),v_xb))|sQ2_spl),
% 70.83/9.50 inference(component_clause,[status(thm)],[f1877])).
% 70.83/9.50 fof(f1881,definition,(
% 70.83/9.50 sQ3_spl <=> (c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_xa,v_n,v_xb))),
% 70.83/9.50 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 70.83/9.50 fof(f1882,plain,(
% 70.83/9.50 c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_xa,v_n,v_xb)|~sQ3_spl),
% 70.83/9.50 inference(component_clause,[status(thm)],[f1881])).
% 70.83/9.50 fof(f1883,plain,(
% 70.83/9.50 ~c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_xa,v_n,v_xb)|sQ3_spl),
% 70.83/9.50 inference(component_clause,[status(thm)],[f1881])).
% 70.83/9.50 fof(f1885,plain,(
% 70.83/9.50 sQ1_spl|sQ3_spl),
% 70.83/9.50 inference(split_clause,[status(thm)],[f1835,f1873,f1881])).
% 70.83/9.50 fof(f1889,plain,(
% 70.83/9.50 ~sQ2_spl),
% 70.83/9.50 inference(split_clause,[status(thm)],[f1839,f1877])).
% 70.83/9.50 fof(f1890,definition,(
% 70.83/9.50 ![X0,X1,X2]: (sQ4_spl <=> (hBOOL(hAPP(hAPP(v_Q,X0),X1))|~c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),X2,v_n,X1)|~hBOOL(hAPP(hAPP(v_P,X0),X2))))),
% 70.83/9.50 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 70.83/9.50 fof(f1891,plain,(
% 70.83/9.50 ![X0,X1,X2]: (hBOOL(hAPP(hAPP(v_Q,X0),X1))|~c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),X2,v_n,X1)|~hBOOL(hAPP(hAPP(v_P,X0),X2))|~sQ4_spl)),
% 70.83/9.50 inference(component_clause,[status(thm)],[f1890])).
% 70.83/9.50 fof(f1893,definition,(
% 70.83/9.50 ![X3,X4,X5]: (sQ5_spl <=> (hBOOL(hAPP(hAPP(v_Q,X3),X4))|~c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),X5,c_Suc(v_n),X4)|~hBOOL(hAPP(hAPP(v_P,X3),X5))))),
% 70.83/9.50 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 70.83/9.50 fof(f1894,plain,(
% 70.83/9.50 ![X0,X1,X2]: (hBOOL(hAPP(hAPP(v_Q,X0),X1))|~c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),X2,c_Suc(v_n),X1)|~hBOOL(hAPP(hAPP(v_P,X0),X2))|~sQ5_spl)),
% 70.83/9.50 inference(component_clause,[status(thm)],[f1893])).
% 70.83/9.50 fof(f1896,plain,(
% 70.83/9.50 sQ4_spl|sQ5_spl),
% 70.83/9.50 inference(split_clause,[status(thm)],[f1841,f1890,f1893])).
% 70.83/9.50 fof(f2011,plain,(
% 70.83/9.50 ![X0]: (c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat))),
% 70.83/9.50 inference(resolution,[status(thm)],[f894,f864])).
% 70.83/9.50 fof(f2087,plain,(
% 70.83/9.50 c_HOL_Ozero__class_Ozero(tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
% 70.83/9.50 inference(resolution,[status(thm)],[f1006,f851])).
% 70.83/9.50 fof(f2089,definition,(
% 70.83/9.50 sQ30_spl <=> (c_HOL_Ozero__class_Ozero(tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))),
% 70.83/9.50 introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition])).
% 70.83/9.50 fof(f2090,plain,(
% 70.83/9.50 c_HOL_Ozero__class_Ozero(tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|~sQ30_spl),
% 70.83/9.50 inference(component_clause,[status(thm)],[f2089])).
% 70.83/9.50 fof(f2092,definition,(
% 70.83/9.50 sQ31_spl <=> (c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))),
% 70.83/9.50 introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 70.83/9.50 fof(f2095,plain,(
% 70.83/9.50 sQ30_spl|sQ31_spl),
% 70.83/9.50 inference(split_clause,[status(thm)],[f2087,f2089,f2092])).
% 70.83/9.50 fof(f2097,plain,(
% 70.83/9.50 $false|~sQ30_spl),
% 70.83/9.50 inference(forward_subsumption_resolution,[status(thm)],[f2090,f1770])).
% 70.83/9.50 fof(f2098,plain,(
% 70.83/9.50 ~sQ30_spl),
% 70.83/9.50 inference(contradiction_clause,[status(thm)],[f2097])).
% 70.83/9.50 fof(f2101,definition,(
% 70.83/9.50 sQ32_spl <=> (c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat))),
% 70.83/9.50 introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition])).
% 70.83/9.50 fof(f2165,plain,(
% 70.83/9.50 c_Suc(v_n)=c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_Suc(v_n),v_xa,v_xb))|~sQ1_spl),
% 70.83/9.50 inference(resolution,[status(thm)],[f1816,f1874])).
% 70.83/9.50 fof(f2210,plain,(
% 70.83/9.50 ![X0,X1]: (~c_HOL_Oord__class_Oless(X0,X0,tc_nat)|c_HOL_Oord__class_Oless(X1,X1,tc_nat))),
% 70.83/9.50 inference(resolution,[status(thm)],[f742,f740])).
% 70.83/9.50 fof(f2221,definition,(
% 70.83/9.50 ![X0]: (sQ38_spl <=> (~c_HOL_Oord__class_Oless(X0,X0,tc_nat)))),
% 70.83/9.50 introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition])).
% 70.83/9.50 fof(f2224,definition,(
% 70.83/9.50 ![X1]: (sQ39_spl <=> (c_HOL_Oord__class_Oless(X1,X1,tc_nat)))),
% 70.83/9.50 introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition])).
% 70.83/9.50 fof(f2225,plain,(
% 70.83/9.50 ![X0]: (c_HOL_Oord__class_Oless(X0,X0,tc_nat)|~sQ39_spl)),
% 70.83/9.50 inference(component_clause,[status(thm)],[f2224])).
% 70.83/9.50 fof(f2227,plain,(
% 70.83/9.50 sQ38_spl|sQ39_spl),
% 70.83/9.50 inference(split_clause,[status(thm)],[f2210,f2221,f2224])).
% 70.83/9.50 fof(f2286,plain,(
% 70.83/9.50 c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1068,f1037])).
% 71.57/9.52 fof(f2287,plain,(
% 71.57/9.52 c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)=c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1068,f1036])).
% 71.57/9.52 fof(f2293,definition,(
% 71.57/9.52 sQ42_spl <=> (c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f2349,plain,(
% 71.57/9.52 ![X0]: (c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))),
% 71.57/9.52 inference(resolution,[status(thm)],[f1196,f884])).
% 71.57/9.52 fof(f2350,plain,(
% 71.57/9.52 ![X0]: (c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(X0),tc_nat))),
% 71.57/9.52 inference(resolution,[status(thm)],[f1196,f781])).
% 71.57/9.52 fof(f2423,plain,(
% 71.57/9.52 ~c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f851,f756])).
% 71.57/9.52 fof(f2424,plain,(
% 71.57/9.52 ![X0,X1]: (~c_HOL_Otimes__class_Otimes(c_Suc(X0),X1,tc_nat)=X1|c_HOL_Otimes__class_Otimes(X0,X1,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1037,f756])).
% 71.57/9.52 fof(f2425,plain,(
% 71.57/9.52 ![X0,X1]: (~c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)=X0|c_HOL_Otimes__class_Otimes(X0,X1,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1036,f756])).
% 71.57/9.52 fof(f2429,plain,(
% 71.57/9.52 ~sQ31_spl|sQ32_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f2423,f2092,f2101])).
% 71.57/9.52 fof(f2438,definition,(
% 71.57/9.52 sQ57_spl <=> (c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f2440,plain,(
% 71.57/9.52 ~c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|sQ57_spl),
% 71.57/9.52 inference(component_clause,[status(thm)],[f2438])).
% 71.57/9.52 fof(f2448,definition,(
% 71.57/9.52 ![X0]: (sQ59_spl <=> (c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)|~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f2452,definition,(
% 71.57/9.52 ![X0]: (sQ60_spl <=> (c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f2653,plain,(
% 71.57/9.52 ![X0]: (c_lessequals(X0,X0,tc_nat))),
% 71.57/9.52 inference(resolution,[status(thm)],[f1756,f1813])).
% 71.57/9.52 fof(f2724,plain,(
% 71.57/9.52 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2,tc_nat),tc_nat)|~c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1068,f818])).
% 71.57/9.52 fof(f2729,plain,(
% 71.57/9.52 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X0,tc_nat),c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat),tc_nat)|~c_lessequals(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1068,f818])).
% 71.57/9.52 fof(f2740,plain,(
% 71.57/9.52 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1,tc_nat),X2,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2,tc_nat),tc_nat)|~c_lessequals(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1068,f822])).
% 71.57/9.52 fof(f2745,plain,(
% 71.57/9.52 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1,tc_nat),X2,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat),tc_nat)|~c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1068,f822])).
% 71.57/9.52 fof(f2790,plain,(
% 71.57/9.52 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X0),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X0),c_Suc(X1),tc_nat),tc_nat))),
% 71.57/9.52 inference(resolution,[status(thm)],[f1777,f1427])).
% 71.57/9.52 fof(f2837,plain,(
% 71.57/9.52 ![X0,X1]: (c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)=X0|c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat))),
% 71.57/9.52 inference(resolution,[status(thm)],[f1783,f894])).
% 71.57/9.52 fof(f2838,plain,(
% 71.57/9.52 ![X0,X1]: (X0=c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)|c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat))),
% 71.57/9.52 inference(resolution,[status(thm)],[f1783,f811])).
% 71.57/9.52 fof(f2953,plain,(
% 71.57/9.52 ![X0,X1]: (~c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|c_lessequals(c_Suc(X0),c_Suc(X1),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1786,f842])).
% 71.57/9.52 fof(f2978,plain,(
% 71.57/9.52 ![X0,X1]: (c_HOL_Oplus__class_Oplus(X0,c_Suc(X1),tc_nat)=c_Suc(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f740,f1797])).
% 71.57/9.52 fof(f2988,plain,(
% 71.57/9.52 ![X0,X1,X2,X3]: (~c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)=c_Suc(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat))|~c_HOL_Oord__class_Oless(c_Suc(X2),X1,tc_nat)|c_HOL_Oord__class_Oless(X0,X3,tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1797,f742])).
% 71.57/9.52 fof(f3043,plain,(
% 71.57/9.52 ![X0,X1]: (c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat))),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1798,f811])).
% 71.57/9.52 fof(f3099,plain,(
% 71.57/9.52 ![X0,X1]: (c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),c_Suc(X0),tc_nat)|c_Suc(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat))=c_Suc(X0))),
% 71.57/9.52 inference(resolution,[status(thm)],[f1807,f894])).
% 71.57/9.52 fof(f3111,plain,(
% 71.57/9.52 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)|c_lessequals(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X2,X0,tc_nat)),tc_nat))),
% 71.57/9.52 inference(resolution,[status(thm)],[f876,f1773])).
% 71.57/9.52 fof(f3112,plain,(
% 71.57/9.52 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)|c_lessequals(c_Suc(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat)),c_Suc(c_HOL_Otimes__class_Otimes(X2,X0,tc_nat)),tc_nat))),
% 71.57/9.52 inference(resolution,[status(thm)],[f876,f1755])).
% 71.57/9.52 fof(f3113,plain,(
% 71.57/9.52 ![X0,X1,X2,X3]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)|c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X1),c_HOL_Otimes__class_Otimes(X2,X0,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),c_HOL_Otimes__class_Otimes(X3,X0,tc_nat),tc_nat),tc_nat))),
% 71.57/9.52 inference(resolution,[status(thm)],[f876,f1461])).
% 71.57/9.52 fof(f3115,plain,(
% 71.57/9.52 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X2,X0,tc_nat)),tc_nat))),
% 71.57/9.52 inference(resolution,[status(thm)],[f876,f883])).
% 71.57/9.52 fof(f3140,definition,(
% 71.57/9.52 sQ132_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f3142,plain,(
% 71.57/9.52 ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|sQ132_spl),
% 71.57/9.52 inference(component_clause,[status(thm)],[f3140])).
% 71.57/9.52 fof(f3152,plain,(
% 71.57/9.52 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)|c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat)),tc_nat))),
% 71.57/9.52 inference(resolution,[status(thm)],[f878,f1773])).
% 71.57/9.52 fof(f3153,plain,(
% 71.57/9.52 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)|c_lessequals(c_Suc(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat)),c_Suc(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat)),tc_nat))),
% 71.57/9.52 inference(resolution,[status(thm)],[f878,f1755])).
% 71.57/9.52 fof(f3154,plain,(
% 71.57/9.52 ![X0,X1,X2,X3]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)|c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X1),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),c_HOL_Otimes__class_Otimes(X0,X3,tc_nat),tc_nat),tc_nat))),
% 71.57/9.52 inference(resolution,[status(thm)],[f878,f1461])).
% 71.57/9.52 fof(f3156,plain,(
% 71.57/9.52 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat)),tc_nat))),
% 71.57/9.52 inference(resolution,[status(thm)],[f878,f883])).
% 71.57/9.52 fof(f3382,definition,(
% 71.57/9.52 sQ155_spl <=> (c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f3384,plain,(
% 71.57/9.52 ~c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|sQ155_spl),
% 71.57/9.52 inference(component_clause,[status(thm)],[f3382])).
% 71.57/9.52 fof(f3688,definition,(
% 71.57/9.52 ![X0]: (sQ170_spl <=> (c_HOL_Oord__class_Oless(X0,c_Suc(X0),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f4403,definition,(
% 71.57/9.52 sQ206_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f4404,plain,(
% 71.57/9.52 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ206_spl),
% 71.57/9.52 inference(component_clause,[status(thm)],[f4403])).
% 71.57/9.52 fof(f4412,plain,(
% 71.57/9.52 ![X0]: (~c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|c_lessequals(X0,X0,tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f935,f842])).
% 71.57/9.52 fof(f4419,definition,(
% 71.57/9.52 ![X0]: (sQ207_spl <=> (c_lessequals(X0,X0,tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f4422,plain,(
% 71.57/9.52 ~sQ32_spl|sQ207_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f4412,f2101,f4419])).
% 71.57/9.52 fof(f4469,plain,(
% 71.57/9.52 ![X0]: (~c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)|c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=X0|c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1068,f945])).
% 71.57/9.52 fof(f4476,definition,(
% 71.57/9.52 ![X0]: (sQ213_spl <=> (~c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)|c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=X0))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f4479,plain,(
% 71.57/9.52 sQ213_spl|sQ30_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f4469,f4476,f2089])).
% 71.57/9.52 fof(f4490,plain,(
% 71.57/9.52 ![X0]: (~c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat)|c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=X0)),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1068,f949])).
% 71.57/9.52 fof(f4497,definition,(
% 71.57/9.52 ![X0]: (sQ216_spl <=> (~c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=X0))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f4500,plain,(
% 71.57/9.52 sQ216_spl|sQ30_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f4490,f4497,f2089])).
% 71.57/9.52 fof(f4830,plain,(
% 71.57/9.52 ![X0]: (~c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f2011,f842])).
% 71.57/9.52 fof(f4837,definition,(
% 71.57/9.52 ![X0]: (sQ247_spl <=> (c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f4840,plain,(
% 71.57/9.52 ~sQ32_spl|sQ247_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f4830,f2101,f4837])).
% 71.57/9.52 fof(f5015,definition,(
% 71.57/9.52 sQ265_spl <=> (c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f5342,definition,(
% 71.57/9.52 sQ314_spl <=> (c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ314_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f7075,definition,(
% 71.57/9.52 sQ487_spl <=> (c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ487_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f7266,plain,(
% 71.57/9.52 c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.52 inference(forward_demodulation,[status(thm)],[f1797,f2286])).
% 71.57/9.52 fof(f7267,plain,(
% 71.57/9.52 c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.52 inference(forward_demodulation,[status(thm)],[f1798,f7266])).
% 71.57/9.52 fof(f7268,plain,(
% 71.57/9.52 c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))),
% 71.57/9.52 inference(forward_demodulation,[status(thm)],[f890,f7267])).
% 71.57/9.52 fof(f7297,plain,(
% 71.57/9.52 ![X0]: (~c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))|c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat)|X0=c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f7268,f949])).
% 71.57/9.52 fof(f7299,plain,(
% 71.57/9.52 ![X0]: (~c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X0,tc_nat)=c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))|X0=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_HOL_Ozero__class_Ozero(tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f7268,f945])).
% 71.57/9.52 fof(f7314,plain,(
% 71.57/9.52 c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|~c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f7268,f930])).
% 71.57/9.52 fof(f7353,definition,(
% 71.57/9.52 sQ509_spl <=> (c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_HOL_Ozero__class_Ozero(tc_nat))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ509_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f7354,plain,(
% 71.57/9.52 c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_HOL_Ozero__class_Ozero(tc_nat)|~sQ509_spl),
% 71.57/9.52 inference(component_clause,[status(thm)],[f7353])).
% 71.57/9.52 fof(f7356,definition,(
% 71.57/9.52 sQ510_spl <=> (c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ510_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f7375,definition,(
% 71.57/9.52 ![X0]: (sQ511_spl <=> (~c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))|X0=c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ511_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f7378,plain,(
% 71.57/9.52 sQ511_spl|sQ30_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f7297,f7375,f2089])).
% 71.57/9.52 fof(f7380,definition,(
% 71.57/9.52 ![X0]: (sQ512_spl <=> (~c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X0,tc_nat)=c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))|X0=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ512_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f7383,plain,(
% 71.57/9.52 sQ512_spl|sQ509_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f7299,f7380,f7353])).
% 71.57/9.52 fof(f7388,definition,(
% 71.57/9.52 sQ514_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ514_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f7390,plain,(
% 71.57/9.52 ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)|sQ514_spl),
% 71.57/9.52 inference(component_clause,[status(thm)],[f7388])).
% 71.57/9.52 fof(f7412,definition,(
% 71.57/9.52 sQ518_spl <=> (c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ518_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f7414,plain,(
% 71.57/9.52 ~c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)|sQ518_spl),
% 71.57/9.52 inference(component_clause,[status(thm)],[f7412])).
% 71.57/9.52 fof(f7425,plain,(
% 71.57/9.52 sQ42_spl|~sQ518_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f7314,f2293,f7412])).
% 71.57/9.52 fof(f7477,definition,(
% 71.57/9.52 sQ530_spl <=> (c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ530_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f7479,plain,(
% 71.57/9.52 ~c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)|sQ530_spl),
% 71.57/9.52 inference(component_clause,[status(thm)],[f7477])).
% 71.57/9.52 fof(f7505,plain,(
% 71.57/9.52 $false|~sQ509_spl),
% 71.57/9.52 inference(forward_subsumption_resolution,[status(thm)],[f7354,f1779])).
% 71.57/9.52 fof(f7506,plain,(
% 71.57/9.52 ~sQ509_spl),
% 71.57/9.52 inference(contradiction_clause,[status(thm)],[f7505])).
% 71.57/9.52 fof(f7641,plain,(
% 71.57/9.52 c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)=c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.52 inference(forward_demodulation,[status(thm)],[f1797,f2287])).
% 71.57/9.52 fof(f7642,plain,(
% 71.57/9.52 c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)=c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.52 inference(forward_demodulation,[status(thm)],[f1798,f7641])).
% 71.57/9.52 fof(f7643,plain,(
% 71.57/9.52 c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)=c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))),
% 71.57/9.52 inference(forward_demodulation,[status(thm)],[f890,f7642])).
% 71.57/9.52 fof(f7674,plain,(
% 71.57/9.52 ![X0]: (~c_HOL_Otimes__class_Otimes(X0,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)=c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))|c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_HOL_Ozero__class_Ozero(tc_nat)|X0=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f7643,f949])).
% 71.57/9.52 fof(f7676,plain,(
% 71.57/9.52 ![X0]: (~c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)=c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))|X0=c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))|c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f7643,f945])).
% 71.57/9.52 fof(f7718,definition,(
% 71.57/9.52 sQ536_spl <=> (c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ536_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f7749,definition,(
% 71.57/9.52 ![X0]: (sQ537_spl <=> (~c_HOL_Otimes__class_Otimes(X0,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)=c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))|X0=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ537_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f7752,plain,(
% 71.57/9.52 sQ537_spl|sQ509_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f7674,f7749,f7353])).
% 71.57/9.52 fof(f7754,definition,(
% 71.57/9.52 ![X0]: (sQ538_spl <=> (~c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)=c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))|X0=c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ538_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f7757,plain,(
% 71.57/9.52 sQ538_spl|sQ30_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f7676,f7754,f2089])).
% 71.57/9.52 fof(f7906,definition,(
% 71.57/9.52 sQ559_spl <=> (c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ559_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f7907,plain,(
% 71.57/9.52 c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|~sQ559_spl),
% 71.57/9.52 inference(component_clause,[status(thm)],[f7906])).
% 71.57/9.52 fof(f7914,definition,(
% 71.57/9.52 sQ561_spl <=> (c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ561_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f7915,plain,(
% 71.57/9.52 c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|~sQ561_spl),
% 71.57/9.52 inference(component_clause,[status(thm)],[f7914])).
% 71.57/9.52 fof(f7932,definition,(
% 71.57/9.52 sQ562_spl <=> (c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ562_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f7933,plain,(
% 71.57/9.52 c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|~sQ562_spl),
% 71.57/9.52 inference(component_clause,[status(thm)],[f7932])).
% 71.57/9.52 fof(f7936,definition,(
% 71.57/9.52 sQ563_spl <=> (c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ563_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f7937,plain,(
% 71.57/9.52 c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|~sQ563_spl),
% 71.57/9.52 inference(component_clause,[status(thm)],[f7936])).
% 71.57/9.52 fof(f7982,plain,(
% 71.57/9.52 ![X0]: (c_lessequals(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1087,f878])).
% 71.57/9.52 fof(f7983,plain,(
% 71.57/9.52 ![X0]: (c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1087,f878])).
% 71.57/9.52 fof(f8035,definition,(
% 71.57/9.52 ![X0]: (sQ565_spl <=> (c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ565_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f8059,definition,(
% 71.57/9.52 ![X0]: (sQ567_spl <=> (c_lessequals(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ567_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f8062,plain,(
% 71.57/9.52 sQ567_spl|sQ206_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f7982,f8059,f4403])).
% 71.57/9.52 fof(f8063,definition,(
% 71.57/9.52 ![X0]: (sQ568_spl <=> (c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ568_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f8066,plain,(
% 71.57/9.52 sQ568_spl|sQ206_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f7983,f8063,f4403])).
% 71.57/9.52 fof(f8226,plain,(
% 71.57/9.52 ![X0]: (c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1088,f876])).
% 71.57/9.52 fof(f8227,plain,(
% 71.57/9.52 ![X0]: (c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1088,f876])).
% 71.57/9.52 fof(f8298,definition,(
% 71.57/9.52 ![X0]: (sQ597_spl <=> (c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ597_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f8328,definition,(
% 71.57/9.52 ![X0]: (sQ599_spl <=> (c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ599_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f8331,plain,(
% 71.57/9.52 sQ599_spl|sQ206_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f8226,f8328,f4403])).
% 71.57/9.52 fof(f8332,definition,(
% 71.57/9.52 ![X0]: (sQ600_spl <=> (c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ600_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f8335,plain,(
% 71.57/9.52 sQ600_spl|sQ206_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f8227,f8332,f4403])).
% 71.57/9.52 fof(f8425,plain,(
% 71.57/9.52 $false|~sQ206_spl),
% 71.57/9.52 inference(forward_subsumption_resolution,[status(thm)],[f4404,f927])).
% 71.57/9.52 fof(f8426,plain,(
% 71.57/9.52 ~sQ206_spl),
% 71.57/9.52 inference(contradiction_clause,[status(thm)],[f8425])).
% 71.57/9.52 fof(f9106,plain,(
% 71.57/9.52 ~c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f7643,f2424])).
% 71.57/9.52 fof(f9107,plain,(
% 71.57/9.52 ~c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1068,f2424])).
% 71.57/9.52 fof(f9108,plain,(
% 71.57/9.52 ![X0]: (~c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1088,f2424])).
% 71.57/9.52 fof(f9119,definition,(
% 71.57/9.52 sQ670_spl <=> (c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ670_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f9121,plain,(
% 71.57/9.52 ~c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))|sQ670_spl),
% 71.57/9.52 inference(component_clause,[status(thm)],[f9119])).
% 71.57/9.52 fof(f9122,plain,(
% 71.57/9.52 ~sQ670_spl|sQ536_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f9106,f9119,f7718])).
% 71.57/9.52 fof(f9123,plain,(
% 71.57/9.52 ~sQ31_spl|sQ487_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f9107,f2092,f7075])).
% 71.57/9.52 fof(f9124,plain,(
% 71.57/9.52 ~sQ32_spl|sQ597_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f9108,f2101,f8298])).
% 71.57/9.52 fof(f9295,plain,(
% 71.57/9.52 ![X0]: (~c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1087,f2425])).
% 71.57/9.52 fof(f9296,plain,(
% 71.57/9.52 ~c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))|c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f7268,f2425])).
% 71.57/9.52 fof(f9298,plain,(
% 71.57/9.52 ~c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1068,f2425])).
% 71.57/9.52 fof(f9308,plain,(
% 71.57/9.52 ~sQ32_spl|sQ565_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f9295,f2101,f8035])).
% 71.57/9.52 fof(f9309,plain,(
% 71.57/9.52 ~sQ670_spl|sQ510_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f9296,f9119,f7356])).
% 71.57/9.52 fof(f9311,plain,(
% 71.57/9.52 ~sQ31_spl|sQ314_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f9298,f2092,f5342])).
% 71.57/9.52 fof(f9872,plain,(
% 71.57/9.52 ![X0,X1]: (~c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|c_lessequals(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1150,f842])).
% 71.57/9.52 fof(f9889,definition,(
% 71.57/9.52 ![X0,X1]: (sQ738_spl <=> (c_lessequals(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ738_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f9892,plain,(
% 71.57/9.52 ~sQ32_spl|sQ738_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f9872,f2101,f9889])).
% 71.57/9.52 fof(f10013,definition,(
% 71.57/9.52 ![X0]: (sQ752_spl <=> (~c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ominus__class_Ominus(X0,X0,tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ752_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f10014,plain,(
% 71.57/9.52 ![X0]: (~c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ominus__class_Ominus(X0,X0,tc_nat)|~sQ752_spl)),
% 71.57/9.52 inference(component_clause,[status(thm)],[f10013])).
% 71.57/9.52 fof(f10105,plain,(
% 71.57/9.52 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1088,f1169])).
% 71.57/9.52 fof(f10112,plain,(
% 71.57/9.52 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1088,f1169])).
% 71.57/9.52 fof(f10127,definition,(
% 71.57/9.52 ![X0]: (sQ765_spl <=> (~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ765_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f10130,plain,(
% 71.57/9.52 sQ206_spl|sQ765_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f10105,f4403,f10127])).
% 71.57/9.52 fof(f10143,definition,(
% 71.57/9.52 ![X0]: (sQ769_spl <=> (~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ769_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f10146,plain,(
% 71.57/9.52 sQ206_spl|sQ769_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f10112,f4403,f10143])).
% 71.57/9.52 fof(f10309,plain,(
% 71.57/9.52 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1087,f1171])).
% 71.57/9.52 fof(f10316,plain,(
% 71.57/9.52 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1087,f1171])).
% 71.57/9.52 fof(f10323,definition,(
% 71.57/9.52 ![X0]: (sQ776_spl <=> (~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ776_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f10326,plain,(
% 71.57/9.52 sQ206_spl|sQ776_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f10309,f4403,f10323])).
% 71.57/9.52 fof(f10339,definition,(
% 71.57/9.52 ![X0]: (sQ780_spl <=> (~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ780_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f10342,plain,(
% 71.57/9.52 sQ206_spl|sQ780_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f10316,f4403,f10339])).
% 71.57/9.52 fof(f10360,plain,(
% 71.57/9.52 ![X0]: (c_lessequals(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X0,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|~c_lessequals(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f7268,f1173])).
% 71.57/9.52 fof(f10361,plain,(
% 71.57/9.52 ![X0]: (c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)|~c_lessequals(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Otimes__class_Otimes(X0,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f7643,f1173])).
% 71.57/9.52 fof(f10362,plain,(
% 71.57/9.52 ![X0]: (c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|~c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1068,f1173])).
% 71.57/9.52 fof(f10367,plain,(
% 71.57/9.52 ![X0]: (c_lessequals(X0,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|~c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f7268,f1173])).
% 71.57/9.52 fof(f10368,plain,(
% 71.57/9.52 ![X0]: (c_lessequals(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)|~c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f7643,f1173])).
% 71.57/9.52 fof(f10369,plain,(
% 71.57/9.52 ![X0]: (c_lessequals(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|~c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1068,f1173])).
% 71.57/9.52 fof(f10381,definition,(
% 71.57/9.52 ![X0]: (sQ786_spl <=> (c_lessequals(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X0,tc_nat)|~c_lessequals(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ786_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f10384,plain,(
% 71.57/9.52 sQ786_spl|~sQ132_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f10360,f10381,f3140])).
% 71.57/9.52 fof(f10385,definition,(
% 71.57/9.52 ![X0]: (sQ787_spl <=> (c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)|~c_lessequals(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Otimes__class_Otimes(X0,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ787_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f10388,plain,(
% 71.57/9.52 sQ787_spl|~sQ514_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f10361,f10385,f7388])).
% 71.57/9.52 fof(f10389,definition,(
% 71.57/9.52 ![X0]: (sQ788_spl <=> (c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)|~c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ788_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f10392,plain,(
% 71.57/9.52 sQ788_spl|~sQ132_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f10362,f10389,f3140])).
% 71.57/9.52 fof(f10397,definition,(
% 71.57/9.52 ![X0]: (sQ790_spl <=> (c_lessequals(X0,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)|~c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ790_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f10400,plain,(
% 71.57/9.52 sQ790_spl|~sQ132_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f10367,f10397,f3140])).
% 71.57/9.52 fof(f10401,definition,(
% 71.57/9.52 ![X0]: (sQ791_spl <=> (c_lessequals(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|~c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ791_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f10404,plain,(
% 71.57/9.52 sQ791_spl|~sQ514_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f10368,f10401,f7388])).
% 71.57/9.52 fof(f10405,definition,(
% 71.57/9.52 ![X0]: (sQ792_spl <=> (c_lessequals(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|~c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ792_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f10408,plain,(
% 71.57/9.52 sQ792_spl|~sQ132_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f10369,f10405,f3140])).
% 71.57/9.52 fof(f10413,plain,(
% 71.57/9.52 $false|sQ132_spl),
% 71.57/9.52 inference(forward_subsumption_resolution,[status(thm)],[f3142,f1196])).
% 71.57/9.52 fof(f10414,plain,(
% 71.57/9.52 sQ132_spl),
% 71.57/9.52 inference(contradiction_clause,[status(thm)],[f10413])).
% 71.57/9.52 fof(f10418,plain,(
% 71.57/9.52 ![X0]: (c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)|~c_lessequals(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X0,tc_nat),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f7268,f1174])).
% 71.57/9.52 fof(f10419,plain,(
% 71.57/9.52 ![X0]: (c_lessequals(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X0,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|~c_lessequals(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f7643,f1174])).
% 71.57/9.52 fof(f10420,plain,(
% 71.57/9.52 ![X0]: (c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|~c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1068,f1174])).
% 71.57/9.52 fof(f10425,plain,(
% 71.57/9.52 ![X0]: (c_lessequals(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)|~c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X0,tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f7268,f1174])).
% 71.57/9.52 fof(f10426,plain,(
% 71.57/9.52 ![X0]: (c_lessequals(X0,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|~c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f7643,f1174])).
% 71.57/9.52 fof(f10427,plain,(
% 71.57/9.52 ![X0]: (c_lessequals(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|~c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.52 inference(paramodulation,[status(thm)],[f1068,f1174])).
% 71.57/9.52 fof(f10437,definition,(
% 71.57/9.52 ![X0]: (sQ795_spl <=> (c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)|~c_lessequals(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X0,tc_nat),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ795_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f10440,plain,(
% 71.57/9.52 sQ795_spl|~sQ514_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f10418,f10437,f7388])).
% 71.57/9.52 fof(f10441,definition,(
% 71.57/9.52 ![X0]: (sQ796_spl <=> (c_lessequals(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X0,tc_nat)|~c_lessequals(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ796_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f10444,plain,(
% 71.57/9.52 sQ796_spl|~sQ132_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f10419,f10441,f3140])).
% 71.57/9.52 fof(f10445,definition,(
% 71.57/9.52 ![X0]: (sQ797_spl <=> (c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)|~c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ797_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f10448,plain,(
% 71.57/9.52 sQ797_spl|~sQ132_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f10420,f10445,f3140])).
% 71.57/9.52 fof(f10453,definition,(
% 71.57/9.52 ![X0]: (sQ799_spl <=> (c_lessequals(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|~c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X0,tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ799_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f10456,plain,(
% 71.57/9.52 sQ799_spl|~sQ514_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f10425,f10453,f7388])).
% 71.57/9.52 fof(f10457,definition,(
% 71.57/9.52 ![X0]: (sQ800_spl <=> (c_lessequals(X0,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)|~c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ800_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f10460,plain,(
% 71.57/9.52 sQ800_spl|~sQ132_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f10426,f10457,f3140])).
% 71.57/9.52 fof(f10461,definition,(
% 71.57/9.52 ![X0]: (sQ801_spl <=> (c_lessequals(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|~c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ801_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f10464,plain,(
% 71.57/9.52 sQ801_spl|~sQ132_spl),
% 71.57/9.52 inference(split_clause,[status(thm)],[f10427,f10461,f3140])).
% 71.57/9.52 fof(f10465,plain,(
% 71.57/9.52 $false|sQ514_spl),
% 71.57/9.52 inference(forward_subsumption_resolution,[status(thm)],[f7390,f1196])).
% 71.57/9.52 fof(f10466,plain,(
% 71.57/9.52 sQ514_spl),
% 71.57/9.52 inference(contradiction_clause,[status(thm)],[f10465])).
% 71.57/9.52 fof(f10915,definition,(
% 71.57/9.52 sQ844_spl <=> (v_n=c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_Suc(v_n),v_xa,v_xb))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ844_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f10916,plain,(
% 71.57/9.52 v_n=c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_Suc(v_n),v_xa,v_xb)|~sQ844_spl),
% 71.57/9.52 inference(component_clause,[status(thm)],[f10915])).
% 71.57/9.52 fof(f10922,plain,(
% 71.57/9.52 $false|sQ57_spl),
% 71.57/9.52 inference(forward_subsumption_resolution,[status(thm)],[f2440,f2349])).
% 71.57/9.52 fof(f10923,plain,(
% 71.57/9.52 sQ57_spl),
% 71.57/9.52 inference(contradiction_clause,[status(thm)],[f10922])).
% 71.57/9.52 fof(f10924,plain,(
% 71.57/9.52 $false|sQ530_spl),
% 71.57/9.52 inference(forward_subsumption_resolution,[status(thm)],[f7479,f2349])).
% 71.57/9.52 fof(f10925,plain,(
% 71.57/9.52 sQ530_spl),
% 71.57/9.52 inference(contradiction_clause,[status(thm)],[f10924])).
% 71.57/9.52 fof(f10936,plain,(
% 71.57/9.52 ~c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|~sQ752_spl),
% 71.57/9.52 inference(forward_demodulation,[status(thm)],[f935,f10014])).
% 71.57/9.52 fof(f10937,plain,(
% 71.57/9.52 $false|~sQ752_spl),
% 71.57/9.52 inference(trivial_equality_resolution,[status(thm)],[f10936])).
% 71.57/9.52 fof(f10938,plain,(
% 71.57/9.52 ~sQ752_spl),
% 71.57/9.52 inference(contradiction_clause,[status(thm)],[f10937])).
% 71.57/9.52 fof(f10939,plain,(
% 71.57/9.52 $false|sQ670_spl),
% 71.57/9.52 inference(trivial_equality_resolution,[status(thm)],[f9121])).
% 71.57/9.52 fof(f10940,plain,(
% 71.57/9.52 sQ670_spl),
% 71.57/9.52 inference(contradiction_clause,[status(thm)],[f10939])).
% 71.57/9.52 fof(f10947,plain,(
% 71.57/9.52 c_HOL_Ozero__class_Ozero(tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|~sQ562_spl),
% 71.57/9.52 inference(forward_demodulation,[status(thm)],[f1088,f7933])).
% 71.57/9.52 fof(f10948,plain,(
% 71.57/9.52 $false|~sQ562_spl),
% 71.57/9.52 inference(forward_subsumption_resolution,[status(thm)],[f10947,f1770])).
% 71.57/9.52 fof(f10949,plain,(
% 71.57/9.52 ~sQ562_spl),
% 71.57/9.52 inference(contradiction_clause,[status(thm)],[f10948])).
% 71.57/9.52 fof(f10950,plain,(
% 71.57/9.52 c_HOL_Ozero__class_Ozero(tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|~sQ559_spl),
% 71.57/9.52 inference(forward_demodulation,[status(thm)],[f1087,f7907])).
% 71.57/9.52 fof(f10951,plain,(
% 71.57/9.52 $false|~sQ559_spl),
% 71.57/9.52 inference(forward_subsumption_resolution,[status(thm)],[f10950,f1770])).
% 71.57/9.52 fof(f10952,plain,(
% 71.57/9.52 ~sQ559_spl),
% 71.57/9.52 inference(contradiction_clause,[status(thm)],[f10951])).
% 71.57/9.52 fof(f11066,definition,(
% 71.57/9.52 ![X1]: (sQ846_spl <=> (~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ846_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f11067,plain,(
% 71.57/9.52 ![X0]: (~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X0),tc_nat)|~sQ846_spl)),
% 71.57/9.52 inference(component_clause,[status(thm)],[f11066])).
% 71.57/9.52 fof(f11126,plain,(
% 71.57/9.52 $false|~sQ846_spl),
% 71.57/9.52 inference(forward_subsumption_resolution,[status(thm)],[f11067,f1196])).
% 71.57/9.52 fof(f11127,plain,(
% 71.57/9.52 ~sQ846_spl),
% 71.57/9.52 inference(contradiction_clause,[status(thm)],[f11126])).
% 71.57/9.52 fof(f11176,definition,(
% 71.57/9.52 ![X2]: (sQ859_spl <=> (~c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X2),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ859_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f11177,plain,(
% 71.57/9.52 ![X0]: (~c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X0),tc_nat)|~sQ859_spl)),
% 71.57/9.52 inference(component_clause,[status(thm)],[f11176])).
% 71.57/9.52 fof(f11222,plain,(
% 71.57/9.52 $false|~sQ859_spl),
% 71.57/9.52 inference(forward_subsumption_resolution,[status(thm)],[f11177,f2349])).
% 71.57/9.52 fof(f11223,plain,(
% 71.57/9.52 ~sQ859_spl),
% 71.57/9.52 inference(contradiction_clause,[status(thm)],[f11222])).
% 71.57/9.52 fof(f11404,plain,(
% 71.57/9.52 ![X0]: (hBOOL(hAPP(hAPP(v_Q,X0),v_xb))|~hBOOL(hAPP(hAPP(v_P,X0),v_xa))|~sQ3_spl|~sQ4_spl)),
% 71.57/9.52 inference(resolution,[status(thm)],[f1882,f1891])).
% 71.57/9.52 fof(f11405,plain,(
% 71.57/9.52 c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_Suc(v_n),v_xb)|~sQ3_spl),
% 71.57/9.52 inference(resolution,[status(thm)],[f1882,f1810])).
% 71.57/9.52 fof(f11422,definition,(
% 71.57/9.52 sQ884_spl <=> (c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ884_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f11423,plain,(
% 71.57/9.52 c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|~sQ884_spl),
% 71.57/9.52 inference(component_clause,[status(thm)],[f11422])).
% 71.57/9.52 fof(f12357,plain,(
% 71.57/9.52 c_HOL_Ozero__class_Ozero(tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|~sQ563_spl),
% 71.57/9.52 inference(forward_demodulation,[status(thm)],[f1088,f7937])).
% 71.57/9.52 fof(f12358,plain,(
% 71.57/9.52 $false|~sQ563_spl),
% 71.57/9.52 inference(forward_subsumption_resolution,[status(thm)],[f12357,f1770])).
% 71.57/9.52 fof(f12359,plain,(
% 71.57/9.52 ~sQ563_spl),
% 71.57/9.52 inference(contradiction_clause,[status(thm)],[f12358])).
% 71.57/9.52 fof(f12360,plain,(
% 71.57/9.52 c_HOL_Ozero__class_Ozero(tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|~sQ561_spl),
% 71.57/9.52 inference(forward_demodulation,[status(thm)],[f1087,f7915])).
% 71.57/9.52 fof(f12361,plain,(
% 71.57/9.52 $false|~sQ561_spl),
% 71.57/9.52 inference(forward_subsumption_resolution,[status(thm)],[f12360,f1770])).
% 71.57/9.52 fof(f12362,plain,(
% 71.57/9.52 ~sQ561_spl),
% 71.57/9.52 inference(contradiction_clause,[status(thm)],[f12361])).
% 71.57/9.52 fof(f12411,plain,(
% 71.57/9.52 $false|sQ518_spl),
% 71.57/9.52 inference(forward_subsumption_resolution,[status(thm)],[f7414,f2350])).
% 71.57/9.52 fof(f12412,plain,(
% 71.57/9.52 sQ518_spl),
% 71.57/9.52 inference(contradiction_clause,[status(thm)],[f12411])).
% 71.57/9.52 fof(f12545,plain,(
% 71.57/9.52 $false|~sQ39_spl),
% 71.57/9.52 inference(forward_subsumption_resolution,[status(thm)],[f2225,f1265])).
% 71.57/9.52 fof(f12546,plain,(
% 71.57/9.52 ~sQ39_spl),
% 71.57/9.52 inference(contradiction_clause,[status(thm)],[f12545])).
% 71.57/9.52 fof(f12549,plain,(
% 71.57/9.52 hBOOL(hAPP(hAPP(v_Q,v_x),v_xb))|~sQ3_spl|~sQ4_spl|~sQ0_spl),
% 71.57/9.52 inference(resolution,[status(thm)],[f11404,f1870])).
% 71.57/9.52 fof(f12550,plain,(
% 71.57/9.52 $false|sQ2_spl|~sQ3_spl|~sQ4_spl|~sQ0_spl),
% 71.57/9.52 inference(forward_subsumption_resolution,[status(thm)],[f12549,f1879])).
% 71.57/9.52 fof(f12551,plain,(
% 71.57/9.52 sQ2_spl|~sQ3_spl|~sQ4_spl|~sQ0_spl),
% 71.57/9.52 inference(contradiction_clause,[status(thm)],[f12550])).
% 71.57/9.52 fof(f12607,plain,(
% 71.57/9.52 ![X0]: (hBOOL(hAPP(hAPP(v_Q,X0),v_xb))|~hBOOL(hAPP(hAPP(v_P,X0),v_xa))|~sQ1_spl|~sQ5_spl)),
% 71.57/9.52 inference(resolution,[status(thm)],[f1874,f1894])).
% 71.57/9.52 fof(f12609,plain,(
% 71.57/9.52 c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_xa,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_Suc(v_n),v_xa,v_xb),v_xb)|~sQ1_spl),
% 71.57/9.52 inference(resolution,[status(thm)],[f1874,f1790])).
% 71.57/9.52 fof(f12678,definition,(
% 71.57/9.52 ![X0]: (sQ995_spl <=> (c_lessequals(c_Suc(X0),c_Suc(X0),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ995_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f13319,plain,(
% 71.57/9.52 ![X0,X1,X2]: (c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat))),
% 71.57/9.52 inference(forward_demodulation,[status(thm)],[f1151,f1248])).
% 71.57/9.52 fof(f13588,definition,(
% 71.57/9.52 ![X0]: (sQ1092_spl <=> (c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ1092_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f13598,plain,(
% 71.57/9.52 $false|sQ155_spl),
% 71.57/9.52 inference(forward_subsumption_resolution,[status(thm)],[f3384,f2349])).
% 71.57/9.52 fof(f13599,plain,(
% 71.57/9.52 sQ155_spl),
% 71.57/9.52 inference(contradiction_clause,[status(thm)],[f13598])).
% 71.57/9.52 fof(f15781,definition,(
% 71.57/9.52 ![X0]: (sQ1270_spl <=> (c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ1270_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f15782,plain,(
% 71.57/9.52 ![X0]: (c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1270_spl)),
% 71.57/9.52 inference(component_clause,[status(thm)],[f15781])).
% 71.57/9.52 fof(f15791,definition,(
% 71.57/9.52 ![X0]: (sQ1272_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X0),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ1272_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f15792,plain,(
% 71.57/9.52 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X0),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1272_spl)),
% 71.57/9.52 inference(component_clause,[status(thm)],[f15791])).
% 71.57/9.52 fof(f15796,definition,(
% 71.57/9.52 sQ1273_spl <=> (c_Suc(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat))),
% 71.57/9.52 introduced(definition,[new_symbols(definition,[sQ1273_spl])],[split_symbol_definition])).
% 71.57/9.52 fof(f15797,plain,(
% 71.57/9.52 c_Suc(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat)|~sQ1273_spl),
% 71.57/9.53 inference(component_clause,[status(thm)],[f15796])).
% 71.57/9.53 fof(f15939,definition,(
% 71.57/9.53 sQ1308_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))),
% 71.57/9.53 introduced(definition,[new_symbols(definition,[sQ1308_spl])],[split_symbol_definition])).
% 71.57/9.53 fof(f15940,plain,(
% 71.57/9.53 c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1308_spl),
% 71.57/9.53 inference(component_clause,[status(thm)],[f15939])).
% 71.57/9.53 fof(f16135,plain,(
% 71.57/9.53 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1308_spl),
% 71.57/9.53 inference(forward_demodulation,[status(thm)],[f890,f15940])).
% 71.57/9.53 fof(f16136,plain,(
% 71.57/9.53 $false|~sQ1308_spl),
% 71.57/9.53 inference(forward_subsumption_resolution,[status(thm)],[f16135,f927])).
% 71.57/9.53 fof(f16137,plain,(
% 71.57/9.53 ~sQ1308_spl),
% 71.57/9.53 inference(contradiction_clause,[status(thm)],[f16136])).
% 71.57/9.53 fof(f16157,plain,(
% 71.57/9.53 c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat)|~sQ1273_spl),
% 71.57/9.53 inference(forward_demodulation,[status(thm)],[f2011,f15797])).
% 71.57/9.53 fof(f16158,plain,(
% 71.57/9.53 $false|~sQ1273_spl),
% 71.57/9.53 inference(forward_subsumption_resolution,[status(thm)],[f16157,f1779])).
% 71.57/9.53 fof(f16159,plain,(
% 71.57/9.53 ~sQ1273_spl),
% 71.57/9.53 inference(contradiction_clause,[status(thm)],[f16158])).
% 71.57/9.53 fof(f16160,plain,(
% 71.57/9.53 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1272_spl),
% 71.57/9.53 inference(forward_demodulation,[status(thm)],[f2011,f15792])).
% 71.57/9.53 fof(f16161,plain,(
% 71.57/9.53 $false|~sQ1272_spl),
% 71.57/9.53 inference(forward_subsumption_resolution,[status(thm)],[f16160,f927])).
% 71.57/9.53 fof(f16162,plain,(
% 71.57/9.53 ~sQ1272_spl),
% 71.57/9.53 inference(contradiction_clause,[status(thm)],[f16161])).
% 71.57/9.53 fof(f16165,plain,(
% 71.57/9.53 $false|~sQ1270_spl),
% 71.57/9.53 inference(forward_subsumption_resolution,[status(thm)],[f15782,f927])).
% 71.57/9.54 fof(f16166,plain,(
% 71.57/9.54 ~sQ1270_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f16165])).
% 71.57/9.54 fof(f16180,plain,(
% 71.57/9.54 ![X0]: (~c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|~c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Ozero__class_Ozero(tc_nat)=X0)),
% 71.57/9.54 inference(paramodulation,[status(thm)],[f2011,f1291])).
% 71.57/9.54 fof(f16185,plain,(
% 71.57/9.54 ![X0,X1]: (~c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|~c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|X0=c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),
% 71.57/9.54 inference(paramodulation,[status(thm)],[f1150,f1291])).
% 71.57/9.54 fof(f16187,plain,(
% 71.57/9.54 ![X0]: (~c_HOL_Ominus__class_Ominus(X0,X0,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|~c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|X0=X0)),
% 71.57/9.54 inference(paramodulation,[status(thm)],[f935,f1291])).
% 71.57/9.54 fof(f16188,definition,(
% 71.57/9.54 sQ1335_spl <=> (c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1335_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f16190,plain,(
% 71.57/9.54 ~c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|sQ1335_spl),
% 71.57/9.54 inference(component_clause,[status(thm)],[f16188])).
% 71.57/9.54 fof(f16197,definition,(
% 71.57/9.54 ![X0]: (sQ1336_spl <=> (~c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Ozero__class_Ozero(tc_nat)=X0))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1336_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f16200,plain,(
% 71.57/9.54 sQ1336_spl|~sQ32_spl),
% 71.57/9.54 inference(split_clause,[status(thm)],[f16180,f16197,f2101])).
% 71.57/9.54 fof(f16202,definition,(
% 71.57/9.54 ![X0,X1]: (sQ1337_spl <=> (~c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|X0=c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1337_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f16205,plain,(
% 71.57/9.54 sQ1337_spl|~sQ32_spl),
% 71.57/9.54 inference(split_clause,[status(thm)],[f16185,f16202,f2101])).
% 71.57/9.54 fof(f16206,definition,(
% 71.57/9.54 ![X0]: (sQ1338_spl <=> (~c_HOL_Ominus__class_Ominus(X0,X0,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|X0=X0))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1338_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f16209,plain,(
% 71.57/9.54 sQ1338_spl|~sQ32_spl),
% 71.57/9.54 inference(split_clause,[status(thm)],[f16187,f16206,f2101])).
% 71.57/9.54 fof(f16210,plain,(
% 71.57/9.54 ~c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|sQ1335_spl),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f2011,f16190])).
% 71.57/9.54 fof(f16211,plain,(
% 71.57/9.54 $false|sQ1335_spl),
% 71.57/9.54 inference(trivial_equality_resolution,[status(thm)],[f16210])).
% 71.57/9.54 fof(f16212,plain,(
% 71.57/9.54 sQ1335_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f16211])).
% 71.57/9.54 fof(f16292,definition,(
% 71.57/9.54 sQ1351_spl <=> (class_OrderedGroup_Opordered__ab__group__add(tc_nat))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1351_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f16602,plain,(
% 71.57/9.54 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2,tc_nat),tc_nat)|~c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat))),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f1797,f2724])).
% 71.57/9.54 fof(f16623,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)),c_HOL_Oplus__class_Oplus(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X1,tc_nat),tc_nat)|~c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat))),
% 71.57/9.54 inference(paramodulation,[status(thm)],[f7268,f16602])).
% 71.57/9.54 fof(f16624,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)),c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat),tc_nat)|~c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.54 inference(paramodulation,[status(thm)],[f1068,f16602])).
% 71.57/9.54 fof(f16639,definition,(
% 71.57/9.54 ![X0,X1]: (sQ1374_spl <=> (c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)),c_HOL_Oplus__class_Oplus(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X1,tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1374_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f16642,plain,(
% 71.57/9.54 sQ1374_spl|~sQ518_spl),
% 71.57/9.54 inference(split_clause,[status(thm)],[f16623,f16639,f7412])).
% 71.57/9.54 fof(f16643,definition,(
% 71.57/9.54 ![X0,X1]: (sQ1375_spl <=> (c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)),c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1375_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f16646,plain,(
% 71.57/9.54 sQ1375_spl|~sQ42_spl),
% 71.57/9.54 inference(split_clause,[status(thm)],[f16624,f16643,f2293])).
% 71.57/9.54 fof(f16769,plain,(
% 71.57/9.54 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X0,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)),tc_nat)|~c_lessequals(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f1797,f2729])).
% 71.57/9.54 fof(f16784,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)),tc_nat)|~c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.54 inference(paramodulation,[status(thm)],[f1087,f16769])).
% 71.57/9.54 fof(f16786,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)),tc_nat)|~c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.54 inference(paramodulation,[status(thm)],[f1068,f16769])).
% 71.57/9.54 fof(f16803,definition,(
% 71.57/9.54 ![X0,X1]: (sQ1376_spl <=> (c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1376_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f16806,plain,(
% 71.57/9.54 sQ1376_spl|~sQ57_spl),
% 71.57/9.54 inference(split_clause,[status(thm)],[f16784,f16803,f2438])).
% 71.57/9.54 fof(f16811,definition,(
% 71.57/9.54 ![X0,X1]: (sQ1378_spl <=> (c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1378_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f16814,plain,(
% 71.57/9.54 sQ1378_spl|~sQ42_spl),
% 71.57/9.54 inference(split_clause,[status(thm)],[f16786,f16811,f2293])).
% 71.57/9.54 fof(f17534,plain,(
% 71.57/9.54 ![X0]: (~class_OrderedGroup_Opordered__ab__group__add(tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X0),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))),
% 71.57/9.54 inference(resolution,[status(thm)],[f1316,f1196])).
% 71.57/9.54 fof(f17554,definition,(
% 71.57/9.54 ![X0,X1,X2]: (sQ1453_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X0),c_Suc(X1),tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1453_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f17555,plain,(
% 71.57/9.54 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X0),c_Suc(X1),tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1453_spl)),
% 71.57/9.54 inference(component_clause,[status(thm)],[f17554])).
% 71.57/9.54 fof(f17558,definition,(
% 71.57/9.54 ![X0,X1,X2]: (sQ1454_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Suc(X0),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1454_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f17559,plain,(
% 71.57/9.54 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Suc(X0),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1454_spl)),
% 71.57/9.54 inference(component_clause,[status(thm)],[f17558])).
% 71.57/9.54 fof(f17562,definition,(
% 71.57/9.54 ![X0,X1,X2]: (sQ1455_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Suc(X0),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1455_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f17563,plain,(
% 71.57/9.54 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Suc(X0),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1455_spl)),
% 71.57/9.54 inference(component_clause,[status(thm)],[f17562])).
% 71.57/9.54 fof(f17566,definition,(
% 71.57/9.54 ![X0,X1]: (sQ1456_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(X0),X1,tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1456_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f17567,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(X0),X1,tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1456_spl)),
% 71.57/9.54 inference(component_clause,[status(thm)],[f17566])).
% 71.57/9.54 fof(f17570,definition,(
% 71.57/9.54 ![X0,X1]: (sQ1457_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1457_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f17571,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1457_spl)),
% 71.57/9.54 inference(component_clause,[status(thm)],[f17570])).
% 71.57/9.54 fof(f17574,definition,(
% 71.57/9.54 ![X0,X1]: (sQ1458_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X0),c_Suc(X1),tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1458_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f17575,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X0),c_Suc(X1),tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1458_spl)),
% 71.57/9.54 inference(component_clause,[status(thm)],[f17574])).
% 71.57/9.54 fof(f17578,plain,(
% 71.57/9.54 ~sQ1351_spl|sQ1272_spl),
% 71.57/9.54 inference(split_clause,[status(thm)],[f17534,f16292,f15791])).
% 71.57/9.54 fof(f17579,definition,(
% 71.57/9.54 ![X0,X1]: (sQ1459_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat),c_Suc(X0),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1459_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f17580,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat),c_Suc(X0),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1459_spl)),
% 71.57/9.54 inference(component_clause,[status(thm)],[f17579])).
% 71.57/9.54 fof(f17583,definition,(
% 71.57/9.54 ![X0,X1]: (sQ1460_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(c_Suc(X0)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1460_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f17584,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(c_Suc(X0)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1460_spl)),
% 71.57/9.54 inference(component_clause,[status(thm)],[f17583])).
% 71.57/9.54 fof(f17587,definition,(
% 71.57/9.54 ![X0,X1,X2]: (sQ1461_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1461_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f17588,plain,(
% 71.57/9.54 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1461_spl)),
% 71.57/9.54 inference(component_clause,[status(thm)],[f17587])).
% 71.57/9.54 fof(f17591,definition,(
% 71.57/9.54 ![X0,X1,X2]: (sQ1462_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1462_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f17592,plain,(
% 71.57/9.54 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1462_spl)),
% 71.57/9.54 inference(component_clause,[status(thm)],[f17591])).
% 71.57/9.54 fof(f17595,definition,(
% 71.57/9.54 ![X0,X1]: (sQ1463_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(X0),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1463_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f17596,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(X0),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1463_spl)),
% 71.57/9.54 inference(component_clause,[status(thm)],[f17595])).
% 71.57/9.54 fof(f17599,definition,(
% 71.57/9.54 ![X0,X1]: (sQ1464_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1464_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f17600,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1464_spl)),
% 71.57/9.54 inference(component_clause,[status(thm)],[f17599])).
% 71.57/9.54 fof(f17603,definition,(
% 71.57/9.54 ![X0,X1]: (sQ1465_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat))),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1465_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f17604,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat))),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1465_spl)),
% 71.57/9.54 inference(component_clause,[status(thm)],[f17603])).
% 71.57/9.54 fof(f17607,definition,(
% 71.57/9.54 ![X0,X1]: (sQ1466_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1466_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f17608,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1466_spl)),
% 71.57/9.54 inference(component_clause,[status(thm)],[f17607])).
% 71.57/9.54 fof(f17611,definition,(
% 71.57/9.54 ![X0,X1]: (sQ1467_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1467_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f17612,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1467_spl)),
% 71.57/9.54 inference(component_clause,[status(thm)],[f17611])).
% 71.57/9.54 fof(f17615,definition,(
% 71.57/9.54 ![X0,X1,X2]: (sQ1468_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1468_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f17616,plain,(
% 71.57/9.54 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1468_spl)),
% 71.57/9.54 inference(component_clause,[status(thm)],[f17615])).
% 71.57/9.54 fof(f17619,definition,(
% 71.57/9.54 ![X0,X1,X2]: (sQ1469_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1469_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f17620,plain,(
% 71.57/9.54 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1469_spl)),
% 71.57/9.54 inference(component_clause,[status(thm)],[f17619])).
% 71.57/9.54 fof(f17623,definition,(
% 71.57/9.54 ![X0,X1]: (sQ1470_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1470_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f17624,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1470_spl)),
% 71.57/9.54 inference(component_clause,[status(thm)],[f17623])).
% 71.57/9.54 fof(f17627,definition,(
% 71.57/9.54 ![X0,X1]: (sQ1471_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1471_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f17628,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1471_spl)),
% 71.57/9.54 inference(component_clause,[status(thm)],[f17627])).
% 71.57/9.54 fof(f17635,definition,(
% 71.57/9.54 ![X0]: (sQ1473_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(X0),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1473_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f17636,plain,(
% 71.57/9.54 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(X0),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1473_spl)),
% 71.57/9.54 inference(component_clause,[status(thm)],[f17635])).
% 71.57/9.54 fof(f17650,plain,(
% 71.57/9.54 $false|~sQ1473_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f17636,f927])).
% 71.57/9.54 fof(f17651,plain,(
% 71.57/9.54 ~sQ1473_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f17650])).
% 71.57/9.54 fof(f17653,plain,(
% 71.57/9.54 $false|~sQ1471_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f17628,f927])).
% 71.57/9.54 fof(f17654,plain,(
% 71.57/9.54 ~sQ1471_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f17653])).
% 71.57/9.54 fof(f17655,plain,(
% 71.57/9.54 $false|~sQ1470_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f17624,f927])).
% 71.57/9.54 fof(f17656,plain,(
% 71.57/9.54 ~sQ1470_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f17655])).
% 71.57/9.54 fof(f17657,plain,(
% 71.57/9.54 $false|~sQ1469_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f17620,f927])).
% 71.57/9.54 fof(f17658,plain,(
% 71.57/9.54 ~sQ1469_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f17657])).
% 71.57/9.54 fof(f17659,plain,(
% 71.57/9.54 $false|~sQ1468_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f17616,f927])).
% 71.57/9.54 fof(f17660,plain,(
% 71.57/9.54 ~sQ1468_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f17659])).
% 71.57/9.54 fof(f17661,plain,(
% 71.57/9.54 $false|~sQ1467_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f17612,f927])).
% 71.57/9.54 fof(f17662,plain,(
% 71.57/9.54 ~sQ1467_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f17661])).
% 71.57/9.54 fof(f17663,plain,(
% 71.57/9.54 $false|~sQ1466_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f17608,f927])).
% 71.57/9.54 fof(f17664,plain,(
% 71.57/9.54 ~sQ1466_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f17663])).
% 71.57/9.54 fof(f17665,plain,(
% 71.57/9.54 $false|~sQ1465_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f17604,f927])).
% 71.57/9.54 fof(f17666,plain,(
% 71.57/9.54 ~sQ1465_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f17665])).
% 71.57/9.54 fof(f17667,plain,(
% 71.57/9.54 $false|~sQ1464_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f17600,f927])).
% 71.57/9.54 fof(f17668,plain,(
% 71.57/9.54 ~sQ1464_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f17667])).
% 71.57/9.54 fof(f17669,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(c_Suc(X0),X1,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1463_spl)),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f13319,f17596])).
% 71.57/9.54 fof(f17670,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1463_spl)),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f1797,f17669])).
% 71.57/9.54 fof(f17671,plain,(
% 71.57/9.54 $false|~sQ1463_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f17670,f927])).
% 71.57/9.54 fof(f17672,plain,(
% 71.57/9.54 ~sQ1463_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f17671])).
% 71.57/9.54 fof(f17673,plain,(
% 71.57/9.54 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X2,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1462_spl)),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f13319,f17592])).
% 71.57/9.54 fof(f17674,plain,(
% 71.57/9.54 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X2,tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1462_spl)),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f1797,f17673])).
% 71.57/9.54 fof(f17675,plain,(
% 71.57/9.54 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1462_spl)),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f911,f17674])).
% 71.57/9.54 fof(f17676,plain,(
% 71.57/9.54 $false|~sQ1462_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f17675,f927])).
% 71.57/9.54 fof(f17677,plain,(
% 71.57/9.54 ~sQ1462_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f17676])).
% 71.57/9.54 fof(f17678,plain,(
% 71.57/9.54 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X2,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1461_spl)),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f13319,f17588])).
% 71.57/9.54 fof(f17679,plain,(
% 71.57/9.54 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1461_spl)),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f1797,f17678])).
% 71.57/9.54 fof(f17680,plain,(
% 71.57/9.54 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1461_spl)),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f911,f17679])).
% 71.57/9.54 fof(f17681,plain,(
% 71.57/9.54 $false|~sQ1461_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f17680,f927])).
% 71.57/9.54 fof(f17682,plain,(
% 71.57/9.54 ~sQ1461_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f17681])).
% 71.57/9.54 fof(f17683,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(c_Suc(c_Suc(X0)),X1,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1460_spl)),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f13319,f17584])).
% 71.57/9.54 fof(f17684,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Oplus__class_Oplus(c_Suc(X0),X1,tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1460_spl)),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f1797,f17683])).
% 71.57/9.54 fof(f17685,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1460_spl)),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f1797,f17684])).
% 71.57/9.54 fof(f17686,plain,(
% 71.57/9.54 $false|~sQ1460_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f17685,f927])).
% 71.57/9.54 fof(f17687,plain,(
% 71.57/9.54 ~sQ1460_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f17686])).
% 71.57/9.54 fof(f17688,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_Suc(X0),X1,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1459_spl)),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f13319,f17580])).
% 71.57/9.54 fof(f17689,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1459_spl)),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f1797,f17688])).
% 71.57/9.54 fof(f17690,plain,(
% 71.57/9.54 $false|~sQ1459_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f17689,f927])).
% 71.57/9.54 fof(f17691,plain,(
% 71.57/9.54 ~sQ1459_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f17690])).
% 71.57/9.54 fof(f17692,plain,(
% 71.57/9.54 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1458_spl),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f2011,f17575])).
% 71.57/9.54 fof(f17693,plain,(
% 71.57/9.54 $false|~sQ1458_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f17692,f927])).
% 71.57/9.54 fof(f17694,plain,(
% 71.57/9.54 ~sQ1458_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f17693])).
% 71.57/9.54 fof(f17695,plain,(
% 71.57/9.54 $false|~sQ1457_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f17571,f927])).
% 71.57/9.54 fof(f17696,plain,(
% 71.57/9.54 ~sQ1457_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f17695])).
% 71.57/9.54 fof(f17697,plain,(
% 71.57/9.54 $false|~sQ1456_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f17567,f927])).
% 71.57/9.54 fof(f17698,plain,(
% 71.57/9.54 ~sQ1456_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f17697])).
% 71.57/9.54 fof(f17699,plain,(
% 71.57/9.54 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1455_spl)),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f1232,f17563])).
% 71.57/9.54 fof(f17700,plain,(
% 71.57/9.54 $false|~sQ1455_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f17699,f927])).
% 71.57/9.54 fof(f17701,plain,(
% 71.57/9.54 ~sQ1455_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f17700])).
% 71.57/9.54 fof(f17702,plain,(
% 71.57/9.54 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1454_spl)),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f1232,f17559])).
% 71.57/9.54 fof(f17703,plain,(
% 71.57/9.54 $false|~sQ1454_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f17702,f927])).
% 71.57/9.54 fof(f17704,plain,(
% 71.57/9.54 ~sQ1454_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f17703])).
% 71.57/9.54 fof(f17705,plain,(
% 71.57/9.54 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1453_spl)),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f1232,f17555])).
% 71.57/9.54 fof(f17706,plain,(
% 71.57/9.54 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat),tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1453_spl)),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f13319,f17705])).
% 71.57/9.54 fof(f17707,plain,(
% 71.57/9.54 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1453_spl)),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f1797,f17706])).
% 71.57/9.54 fof(f17708,plain,(
% 71.57/9.54 $false|~sQ1453_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f17707,f927])).
% 71.57/9.54 fof(f17709,plain,(
% 71.57/9.54 ~sQ1453_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f17708])).
% 71.57/9.54 fof(f18148,definition,(
% 71.57/9.54 sQ1541_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat),tc_nat))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1541_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f18149,plain,(
% 71.57/9.54 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat),tc_nat)|~sQ1541_spl),
% 71.57/9.54 inference(component_clause,[status(thm)],[f18148])).
% 71.57/9.54 fof(f18155,plain,(
% 71.57/9.54 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1541_spl),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f966,f18149])).
% 71.57/9.54 fof(f18156,plain,(
% 71.57/9.54 $false|~sQ1541_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f18155,f927])).
% 71.57/9.54 fof(f18157,plain,(
% 71.57/9.54 ~sQ1541_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f18156])).
% 71.57/9.54 fof(f18248,definition,(
% 71.57/9.54 ![X0]: (sQ1550_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Oord__class_Omax(v_n,X0,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1550_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f18249,plain,(
% 71.57/9.54 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Oord__class_Omax(v_n,X0,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1550_spl)),
% 71.57/9.54 inference(component_clause,[status(thm)],[f18248])).
% 71.57/9.54 fof(f18313,plain,(
% 71.57/9.54 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1550_spl),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f2011,f18249])).
% 71.57/9.54 fof(f18314,plain,(
% 71.57/9.54 $false|~sQ1550_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f18313,f927])).
% 71.57/9.54 fof(f18315,plain,(
% 71.57/9.54 ~sQ1550_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f18314])).
% 71.57/9.54 fof(f18521,plain,(
% 71.57/9.54 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1,tc_nat),X2,tc_nat)|~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2,tc_nat),tc_nat)|~c_lessequals(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f1797,f2740])).
% 71.57/9.54 fof(f18541,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X0,tc_nat),X1,tc_nat)|~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),tc_nat)|~c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.54 inference(paramodulation,[status(thm)],[f1087,f18521])).
% 71.57/9.54 fof(f18543,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X0,tc_nat),X1,tc_nat)|~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)),c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat),tc_nat)|~c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.54 inference(paramodulation,[status(thm)],[f1068,f18521])).
% 71.57/9.54 fof(f18553,definition,(
% 71.57/9.54 ![X0,X1]: (sQ1564_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X0,tc_nat),X1,tc_nat)|~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1564_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f18556,plain,(
% 71.57/9.54 sQ1564_spl|~sQ57_spl),
% 71.57/9.54 inference(split_clause,[status(thm)],[f18541,f18553,f2438])).
% 71.57/9.54 fof(f18561,definition,(
% 71.57/9.54 ![X0,X1]: (sQ1566_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X0,tc_nat),X1,tc_nat)|~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)),c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1566_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f18564,plain,(
% 71.57/9.54 sQ1566_spl|~sQ42_spl),
% 71.57/9.54 inference(split_clause,[status(thm)],[f18543,f18561,f2293])).
% 71.57/9.54 fof(f18677,plain,(
% 71.57/9.54 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1,tc_nat),X2,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)),tc_nat)|~c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat))),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f1797,f2745])).
% 71.57/9.54 fof(f18693,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X0,tc_nat),X1,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X0,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)),tc_nat)|~c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat))),
% 71.57/9.54 inference(paramodulation,[status(thm)],[f7268,f18677])).
% 71.57/9.54 fof(f18694,plain,(
% 71.57/9.54 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X0,tc_nat),X1,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)),tc_nat)|~c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.54 inference(paramodulation,[status(thm)],[f1068,f18677])).
% 71.57/9.54 fof(f18713,definition,(
% 71.57/9.54 ![X0,X1]: (sQ1568_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X0,tc_nat),X1,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X0,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1568_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f18716,plain,(
% 71.57/9.54 sQ1568_spl|~sQ518_spl),
% 71.57/9.54 inference(split_clause,[status(thm)],[f18693,f18713,f7412])).
% 71.57/9.54 fof(f18717,definition,(
% 71.57/9.54 ![X0,X1]: (sQ1569_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X0,tc_nat),X1,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1569_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f18720,plain,(
% 71.57/9.54 sQ1569_spl|~sQ42_spl),
% 71.57/9.54 inference(split_clause,[status(thm)],[f18694,f18717,f2293])).
% 71.57/9.54 fof(f19261,definition,(
% 71.57/9.54 ![X0]: (sQ1594_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Oord__class_Omax(X0,v_n,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1594_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f19262,plain,(
% 71.57/9.54 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Oord__class_Omax(X0,v_n,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1594_spl)),
% 71.57/9.54 inference(component_clause,[status(thm)],[f19261])).
% 71.57/9.54 fof(f19326,plain,(
% 71.57/9.54 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1594_spl),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f2011,f19262])).
% 71.57/9.54 fof(f19327,plain,(
% 71.57/9.54 $false|~sQ1594_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f19326,f927])).
% 71.57/9.54 fof(f19328,plain,(
% 71.57/9.54 ~sQ1594_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f19327])).
% 71.57/9.54 fof(f20755,definition,(
% 71.57/9.54 sQ1731_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat),tc_nat))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1731_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f20756,plain,(
% 71.57/9.54 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat),tc_nat)|~sQ1731_spl),
% 71.57/9.54 inference(component_clause,[status(thm)],[f20755])).
% 71.57/9.54 fof(f20762,plain,(
% 71.57/9.54 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1731_spl),
% 71.57/9.54 inference(forward_demodulation,[status(thm)],[f1087,f20756])).
% 71.57/9.54 fof(f20763,plain,(
% 71.57/9.54 $false|~sQ1731_spl),
% 71.57/9.54 inference(forward_subsumption_resolution,[status(thm)],[f20762,f927])).
% 71.57/9.54 fof(f20764,plain,(
% 71.57/9.54 ~sQ1731_spl),
% 71.57/9.54 inference(contradiction_clause,[status(thm)],[f20763])).
% 71.57/9.54 fof(f20861,definition,(
% 71.57/9.54 sQ1739_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))),
% 71.57/9.54 introduced(definition,[new_symbols(definition,[sQ1739_spl])],[split_symbol_definition])).
% 71.57/9.54 fof(f20862,plain,(
% 71.57/9.54 c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1739_spl),
% 71.57/9.55 inference(component_clause,[status(thm)],[f20861])).
% 71.57/9.55 fof(f20899,plain,(
% 71.57/9.55 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1739_spl),
% 71.57/9.55 inference(forward_demodulation,[status(thm)],[f2011,f20862])).
% 71.57/9.55 fof(f20900,plain,(
% 71.57/9.55 $false|~sQ1739_spl),
% 71.57/9.55 inference(forward_subsumption_resolution,[status(thm)],[f20899,f927])).
% 71.57/9.55 fof(f20901,plain,(
% 71.57/9.55 ~sQ1739_spl),
% 71.57/9.55 inference(contradiction_clause,[status(thm)],[f20900])).
% 71.57/9.55 fof(f20946,definition,(
% 71.57/9.55 ![X0]: (sQ1744_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X0,v_n,tc_nat),v_n,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ1744_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f20947,plain,(
% 71.57/9.55 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X0,v_n,tc_nat),v_n,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1744_spl)),
% 71.57/9.55 inference(component_clause,[status(thm)],[f20946])).
% 71.57/9.55 fof(f21009,plain,(
% 71.57/9.55 $false|~sQ1744_spl),
% 71.57/9.55 inference(forward_subsumption_resolution,[status(thm)],[f20947,f927])).
% 71.57/9.55 fof(f21010,plain,(
% 71.57/9.55 ~sQ1744_spl),
% 71.57/9.55 inference(contradiction_clause,[status(thm)],[f21009])).
% 71.57/9.55 fof(f21199,definition,(
% 71.57/9.55 ![X0]: (sQ1773_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_Suc(X0)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ1773_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f21200,plain,(
% 71.57/9.55 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_Suc(X0)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ1773_spl)),
% 71.57/9.55 inference(component_clause,[status(thm)],[f21199])).
% 71.57/9.55 fof(f21264,plain,(
% 71.57/9.55 $false|~sQ1773_spl),
% 71.57/9.55 inference(forward_subsumption_resolution,[status(thm)],[f21200,f927])).
% 71.57/9.55 fof(f21265,plain,(
% 71.57/9.55 ~sQ1773_spl),
% 71.57/9.55 inference(contradiction_clause,[status(thm)],[f21264])).
% 71.57/9.55 fof(f21563,definition,(
% 71.57/9.55 ![X0,X1,X2]: (sQ1810_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),X2,tc_nat),c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(X2,X0,tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ1810_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f21564,plain,(
% 71.57/9.55 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),X2,tc_nat),c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(X2,X0,tc_nat)|~sQ1810_spl)),
% 71.57/9.55 inference(component_clause,[status(thm)],[f21563])).
% 71.57/9.55 fof(f21570,plain,(
% 71.57/9.55 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),X2,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(X2,X0,tc_nat)|~sQ1810_spl)),
% 71.57/9.55 inference(forward_demodulation,[status(thm)],[f1088,f21564])).
% 71.57/9.55 fof(f21571,plain,(
% 71.57/9.55 ![X0,X1]: (~c_HOL_Oord__class_Oless(X0,X1,tc_nat)|~sQ1810_spl)),
% 71.57/9.55 inference(forward_subsumption_resolution,[status(thm)],[f21570,f927])).
% 71.57/9.55 fof(f21580,plain,(
% 71.57/9.55 ![X0,X1]: (c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)|~sQ1810_spl)),
% 71.57/9.55 inference(backward_subsumption_resolution,[status(thm)],[f1820,f21571])).
% 71.57/9.55 fof(f21608,plain,(
% 71.57/9.55 $false|~sQ1810_spl),
% 71.57/9.55 inference(forward_subsumption_resolution,[status(thm)],[f21580,f21571])).
% 71.57/9.55 fof(f21609,plain,(
% 71.57/9.55 ~sQ1810_spl),
% 71.57/9.55 inference(contradiction_clause,[status(thm)],[f21608])).
% 71.57/9.55 fof(f22364,plain,(
% 71.57/9.55 ![X0]: (c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f2011,f2837])).
% 71.57/9.55 fof(f22481,plain,(
% 71.57/9.55 sQ1092_spl|sQ206_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f22364,f13588,f4403])).
% 71.57/9.55 fof(f22534,plain,(
% 71.57/9.55 c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f890,f2838])).
% 71.57/9.55 fof(f22683,plain,(
% 71.57/9.55 sQ265_spl|sQ206_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f22534,f5015,f4403])).
% 71.57/9.55 fof(f23523,definition,(
% 71.57/9.55 sQ2024_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(v_n),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2024_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f23524,plain,(
% 71.57/9.55 c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(v_n),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ2024_spl),
% 71.57/9.55 inference(component_clause,[status(thm)],[f23523])).
% 71.57/9.55 fof(f23589,plain,(
% 71.57/9.55 c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ2024_spl),
% 71.57/9.55 inference(forward_demodulation,[status(thm)],[f1786,f23524])).
% 71.57/9.55 fof(f23590,plain,(
% 71.57/9.55 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ2024_spl),
% 71.57/9.55 inference(forward_demodulation,[status(thm)],[f2011,f23589])).
% 71.57/9.55 fof(f23591,plain,(
% 71.57/9.55 $false|~sQ2024_spl),
% 71.57/9.55 inference(forward_subsumption_resolution,[status(thm)],[f23590,f1265])).
% 71.57/9.55 fof(f23592,plain,(
% 71.57/9.55 ~sQ2024_spl),
% 71.57/9.55 inference(contradiction_clause,[status(thm)],[f23591])).
% 71.57/9.55 fof(f23687,definition,(
% 71.57/9.55 ![X0]: (sQ2050_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X0),v_n,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2050_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f23688,plain,(
% 71.57/9.55 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X0),v_n,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ2050_spl)),
% 71.57/9.55 inference(component_clause,[status(thm)],[f23687])).
% 71.57/9.55 fof(f23752,plain,(
% 71.57/9.55 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ2050_spl),
% 71.57/9.55 inference(forward_demodulation,[status(thm)],[f2011,f23688])).
% 71.57/9.55 fof(f23753,plain,(
% 71.57/9.55 $false|~sQ2050_spl),
% 71.57/9.55 inference(forward_subsumption_resolution,[status(thm)],[f23752,f1265])).
% 71.57/9.55 fof(f23754,plain,(
% 71.57/9.55 ~sQ2050_spl),
% 71.57/9.55 inference(contradiction_clause,[status(thm)],[f23753])).
% 71.57/9.55 fof(f23760,plain,(
% 71.57/9.55 hBOOL(hAPP(hAPP(v_Q,v_x),v_xb))|~sQ1_spl|~sQ5_spl|~sQ0_spl),
% 71.57/9.55 inference(resolution,[status(thm)],[f12607,f1870])).
% 71.57/9.55 fof(f23761,plain,(
% 71.57/9.55 $false|sQ2_spl|~sQ1_spl|~sQ5_spl|~sQ0_spl),
% 71.57/9.55 inference(forward_subsumption_resolution,[status(thm)],[f23760,f1879])).
% 71.57/9.55 fof(f23762,plain,(
% 71.57/9.55 sQ2_spl|~sQ1_spl|~sQ5_spl|~sQ0_spl),
% 71.57/9.55 inference(contradiction_clause,[status(thm)],[f23761])).
% 71.57/9.55 fof(f23774,plain,(
% 71.57/9.55 ![X0]: (~c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(X0),tc_nat))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f2011,f2953])).
% 71.57/9.55 fof(f23778,plain,(
% 71.57/9.55 ![X0,X1]: (~c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|c_lessequals(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f1150,f2953])).
% 71.57/9.55 fof(f23780,plain,(
% 71.57/9.55 ![X0]: (~c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|c_lessequals(c_Suc(X0),c_Suc(X0),tc_nat))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f935,f2953])).
% 71.57/9.55 fof(f23782,definition,(
% 71.57/9.55 ![X0]: (sQ2064_spl <=> (c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(X0),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2064_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f23785,plain,(
% 71.57/9.55 ~sQ32_spl|sQ2064_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f23774,f2101,f23782])).
% 71.57/9.55 fof(f23786,definition,(
% 71.57/9.55 ![X0,X1]: (sQ2065_spl <=> (c_lessequals(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2065_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f23789,plain,(
% 71.57/9.55 ~sQ32_spl|sQ2065_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f23778,f2101,f23786])).
% 71.57/9.55 fof(f23791,plain,(
% 71.57/9.55 ~sQ32_spl|sQ995_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f23780,f2101,f12678])).
% 71.57/9.55 fof(f24546,definition,(
% 71.57/9.55 ![X0]: (sQ2117_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(v_n,X0,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2117_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f24547,plain,(
% 71.57/9.55 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(v_n,X0,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ2117_spl)),
% 71.57/9.55 inference(component_clause,[status(thm)],[f24546])).
% 71.57/9.55 fof(f24611,plain,(
% 71.57/9.55 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ2117_spl),
% 71.57/9.55 inference(forward_demodulation,[status(thm)],[f2011,f24547])).
% 71.57/9.55 fof(f24612,plain,(
% 71.57/9.55 $false|~sQ2117_spl),
% 71.57/9.55 inference(forward_subsumption_resolution,[status(thm)],[f24611,f1265])).
% 71.57/9.55 fof(f24613,plain,(
% 71.57/9.55 ~sQ2117_spl),
% 71.57/9.55 inference(contradiction_clause,[status(thm)],[f24612])).
% 71.57/9.55 fof(f24716,definition,(
% 71.57/9.55 ![X0]: (sQ2144_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X0,v_n,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2144_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f24717,plain,(
% 71.57/9.55 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X0,v_n,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ2144_spl)),
% 71.57/9.55 inference(component_clause,[status(thm)],[f24716])).
% 71.57/9.55 fof(f24781,plain,(
% 71.57/9.55 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ2144_spl),
% 71.57/9.55 inference(forward_demodulation,[status(thm)],[f2011,f24717])).
% 71.57/9.55 fof(f24782,plain,(
% 71.57/9.55 $false|~sQ2144_spl),
% 71.57/9.55 inference(forward_subsumption_resolution,[status(thm)],[f24781,f1265])).
% 71.57/9.55 fof(f24783,plain,(
% 71.57/9.55 ~sQ2144_spl),
% 71.57/9.55 inference(contradiction_clause,[status(thm)],[f24782])).
% 71.57/9.55 fof(f25356,definition,(
% 71.57/9.55 ![X0]: (sQ2196_spl <=> (~c_Suc(X0)=c_Suc(X0)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2196_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f25357,plain,(
% 71.57/9.55 ![X0]: (~c_Suc(X0)=c_Suc(X0)|~sQ2196_spl)),
% 71.57/9.55 inference(component_clause,[status(thm)],[f25356])).
% 71.57/9.55 fof(f25363,plain,(
% 71.57/9.55 $false|~sQ2196_spl),
% 71.57/9.55 inference(trivial_equality_resolution,[status(thm)],[f25357])).
% 71.57/9.55 fof(f25364,plain,(
% 71.57/9.55 ~sQ2196_spl),
% 71.57/9.55 inference(contradiction_clause,[status(thm)],[f25363])).
% 71.57/9.55 fof(f25380,plain,(
% 71.57/9.55 ![X0,X1]: (~c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|X1=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f1068,f1411])).
% 71.57/9.55 fof(f25467,definition,(
% 71.57/9.55 ![X0,X1]: (sQ2197_spl <=> (~c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|X1=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2197_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f25470,plain,(
% 71.57/9.55 sQ2197_spl|sQ30_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f25380,f25467,f2089])).
% 71.57/9.55 fof(f26172,definition,(
% 71.57/9.55 sQ2270_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_Suc(v_n),v_xa,v_xb),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2270_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f26173,plain,(
% 71.57/9.55 c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_Suc(v_n),v_xa,v_xb),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ2270_spl),
% 71.57/9.55 inference(component_clause,[status(thm)],[f26172])).
% 71.57/9.55 fof(f26237,plain,(
% 71.57/9.55 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~sQ2270_spl),
% 71.57/9.55 inference(forward_demodulation,[status(thm)],[f2011,f26173])).
% 71.57/9.55 fof(f26238,plain,(
% 71.57/9.55 $false|~sQ2270_spl),
% 71.57/9.55 inference(forward_subsumption_resolution,[status(thm)],[f26237,f1265])).
% 71.57/9.55 fof(f26239,plain,(
% 71.57/9.55 ~sQ2270_spl),
% 71.57/9.55 inference(contradiction_clause,[status(thm)],[f26238])).
% 71.57/9.55 fof(f26324,plain,(
% 71.57/9.55 ![X0,X1]: (~c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X0),tc_nat)|c_HOL_Oord__class_Oless(X1,X1,tc_nat))),
% 71.57/9.55 inference(resolution,[status(thm)],[f2988,f2978])).
% 71.57/9.55 fof(f26355,definition,(
% 71.57/9.55 ![X0]: (sQ2286_spl <=> (~c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X0),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2286_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f26358,plain,(
% 71.57/9.55 sQ2286_spl|sQ39_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f26324,f26355,f2224])).
% 71.57/9.55 fof(f26391,definition,(
% 71.57/9.55 ![X1]: (sQ2287_spl <=> (c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X1),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2287_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f26392,plain,(
% 71.57/9.55 ![X0]: (c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X0),tc_nat)|~sQ2287_spl)),
% 71.57/9.55 inference(component_clause,[status(thm)],[f26391])).
% 71.57/9.55 fof(f26395,plain,(
% 71.57/9.55 $false|~sQ2287_spl),
% 71.57/9.55 inference(forward_subsumption_resolution,[status(thm)],[f26392,f1265])).
% 71.57/9.55 fof(f26396,plain,(
% 71.57/9.55 ~sQ2287_spl),
% 71.57/9.55 inference(contradiction_clause,[status(thm)],[f26395])).
% 71.57/9.55 fof(f26453,plain,(
% 71.57/9.55 ![X0,X1]: (c_HOL_Oord__class_Oless(X0,c_Suc(X0),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat))),
% 71.57/9.55 inference(resolution,[status(thm)],[f1499,f2790])).
% 71.57/9.55 fof(f26455,plain,(
% 71.57/9.55 ![X0]: (c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)|~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f1068,f1499])).
% 71.57/9.55 fof(f26460,plain,(
% 71.57/9.55 ![X0]: (c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f1068,f1499])).
% 71.57/9.55 fof(f26465,plain,(
% 71.57/9.55 sQ170_spl|sQ846_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f26453,f3688,f11066])).
% 71.57/9.55 fof(f26469,plain,(
% 71.57/9.55 sQ59_spl|~sQ132_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f26455,f2448,f3140])).
% 71.57/9.55 fof(f26471,plain,(
% 71.57/9.55 sQ60_spl|~sQ132_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f26460,f2452,f3140])).
% 71.57/9.55 fof(f27675,plain,(
% 71.57/9.55 c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_xa,v_n,v_xb)|~sQ844_spl|~sQ1_spl),
% 71.57/9.55 inference(forward_demodulation,[status(thm)],[f10916,f12609])).
% 71.57/9.55 fof(f27676,plain,(
% 71.57/9.55 $false|sQ3_spl|~sQ844_spl|~sQ1_spl),
% 71.57/9.55 inference(forward_subsumption_resolution,[status(thm)],[f27675,f1883])).
% 71.57/9.55 fof(f27677,plain,(
% 71.57/9.55 sQ3_spl|~sQ844_spl|~sQ1_spl),
% 71.57/9.55 inference(contradiction_clause,[status(thm)],[f27676])).
% 71.57/9.55 fof(f28020,plain,(
% 71.57/9.55 ![X0]: (~c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=X0|c_HOL_Ozero__class_Ozero(tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|X0=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f1552,f1006])).
% 71.57/9.55 fof(f28151,definition,(
% 71.57/9.55 ![X0]: (sQ2390_spl <=> (~c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=X0|X0=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2390_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f28154,plain,(
% 71.57/9.55 sQ2390_spl|sQ30_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f28020,f28151,f2089])).
% 71.57/9.55 fof(f28156,definition,(
% 71.57/9.55 ![X0]: (sQ2391_spl <=> (~c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=X0|X0=c_HOL_Ozero__class_Ozero(tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2391_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f28157,plain,(
% 71.57/9.55 ![X0]: (~c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=X0|X0=c_HOL_Ozero__class_Ozero(tc_nat)|~sQ2391_spl)),
% 71.57/9.55 inference(component_clause,[status(thm)],[f28156])).
% 71.57/9.55 fof(f28161,definition,(
% 71.57/9.55 ![X0]: (sQ2392_spl <=> (~c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=X0))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2392_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f28162,plain,(
% 71.57/9.55 ![X0]: (~c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=X0|~sQ2392_spl)),
% 71.57/9.55 inference(component_clause,[status(thm)],[f28161])).
% 71.57/9.55 fof(f28168,definition,(
% 71.57/9.55 ![X0]: (sQ2393_spl <=> (~X0=c_HOL_Ozero__class_Ozero(tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2393_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f28169,plain,(
% 71.57/9.55 ![X0]: (~X0=c_HOL_Ozero__class_Ozero(tc_nat)|~sQ2393_spl)),
% 71.57/9.55 inference(component_clause,[status(thm)],[f28168])).
% 71.57/9.55 fof(f28174,definition,(
% 71.57/9.55 ![X0]: (sQ2394_spl <=> (~X0=X0))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2394_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f28175,plain,(
% 71.57/9.55 ![X0]: (~X0=X0|~sQ2394_spl)),
% 71.57/9.55 inference(component_clause,[status(thm)],[f28174])).
% 71.57/9.55 fof(f28218,plain,(
% 71.57/9.55 $false|~sQ2394_spl),
% 71.57/9.55 inference(trivial_equality_resolution,[status(thm)],[f28175])).
% 71.57/9.55 fof(f28219,plain,(
% 71.57/9.55 ~sQ2394_spl),
% 71.57/9.55 inference(contradiction_clause,[status(thm)],[f28218])).
% 71.57/9.55 fof(f28220,plain,(
% 71.57/9.55 $false|~sQ2393_spl),
% 71.57/9.55 inference(destructive_equality_resolution,[status(thm)],[f28169])).
% 71.57/9.55 fof(f28221,plain,(
% 71.57/9.55 ~sQ2393_spl),
% 71.57/9.55 inference(contradiction_clause,[status(thm)],[f28220])).
% 71.57/9.55 fof(f28222,plain,(
% 71.57/9.55 $false|~sQ2392_spl),
% 71.57/9.55 inference(destructive_equality_resolution,[status(thm)],[f28162])).
% 71.57/9.55 fof(f28223,plain,(
% 71.57/9.55 ~sQ2392_spl),
% 71.57/9.55 inference(contradiction_clause,[status(thm)],[f28222])).
% 71.57/9.55 fof(f28224,plain,(
% 71.57/9.55 c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat)|~sQ2391_spl),
% 71.57/9.55 inference(destructive_equality_resolution,[status(thm)],[f28157])).
% 71.57/9.55 fof(f28225,plain,(
% 71.57/9.55 $false|~sQ2391_spl),
% 71.57/9.55 inference(forward_subsumption_resolution,[status(thm)],[f28224,f1779])).
% 71.57/9.55 fof(f28226,plain,(
% 71.57/9.55 ~sQ2391_spl),
% 71.57/9.55 inference(contradiction_clause,[status(thm)],[f28225])).
% 71.57/9.55 fof(f28511,definition,(
% 71.57/9.55 ![X0]: (sQ2415_spl <=> (~c_HOL_Oord__class_Oless(X0,c_Suc(X0),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2415_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f28512,plain,(
% 71.57/9.55 ![X0]: (~c_HOL_Oord__class_Oless(X0,c_Suc(X0),tc_nat)|~sQ2415_spl)),
% 71.57/9.55 inference(component_clause,[status(thm)],[f28511])).
% 71.57/9.55 fof(f28609,plain,(
% 71.57/9.55 ![X0]: (c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_Suc(X0)),tc_nat))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f1553,f3043])).
% 71.57/9.55 fof(f28690,plain,(
% 71.57/9.55 $false|~sQ2415_spl),
% 71.57/9.55 inference(forward_subsumption_resolution,[status(thm)],[f28609,f28512])).
% 71.57/9.55 fof(f28691,plain,(
% 71.57/9.55 ~sQ2415_spl),
% 71.57/9.55 inference(contradiction_clause,[status(thm)],[f28690])).
% 71.57/9.55 fof(f29351,plain,(
% 71.57/9.55 ![X0]: (c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|c_Suc(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f2011,f3099])).
% 71.57/9.55 fof(f29435,definition,(
% 71.57/9.55 ![X0]: (sQ2490_spl <=> (c_Suc(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2490_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f29438,plain,(
% 71.57/9.55 sQ884_spl|sQ2490_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f29351,f11422,f29435])).
% 71.57/9.55 fof(f29446,plain,(
% 71.57/9.55 $false|~sQ884_spl),
% 71.57/9.55 inference(forward_subsumption_resolution,[status(thm)],[f11423,f1265])).
% 71.57/9.55 fof(f29447,plain,(
% 71.57/9.55 ~sQ884_spl),
% 71.57/9.55 inference(contradiction_clause,[status(thm)],[f29446])).
% 71.57/9.55 fof(f30511,plain,(
% 71.57/9.55 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),tc_nat))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f1088,f3111])).
% 71.57/9.55 fof(f30516,plain,(
% 71.57/9.55 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f1088,f3111])).
% 71.57/9.55 fof(f30603,definition,(
% 71.57/9.55 ![X0]: (sQ2618_spl <=> (c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2618_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f30606,plain,(
% 71.57/9.55 sQ206_spl|sQ2618_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f30511,f4403,f30603])).
% 71.57/9.55 fof(f30608,definition,(
% 71.57/9.55 ![X0]: (sQ2619_spl <=> (c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2619_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f30611,plain,(
% 71.57/9.55 sQ206_spl|sQ2619_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f30516,f4403,f30608])).
% 71.57/9.55 fof(f30670,plain,(
% 71.57/9.55 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),tc_nat))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f1088,f3112])).
% 71.57/9.55 fof(f30675,plain,(
% 71.57/9.55 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|c_lessequals(c_Suc(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f1088,f3112])).
% 71.57/9.55 fof(f30803,definition,(
% 71.57/9.55 ![X0]: (sQ2638_spl <=> (c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2638_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f30806,plain,(
% 71.57/9.55 sQ206_spl|sQ2638_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f30670,f4403,f30803])).
% 71.57/9.55 fof(f30811,definition,(
% 71.57/9.55 ![X0]: (sQ2640_spl <=> (c_lessequals(c_Suc(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2640_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f30814,plain,(
% 71.57/9.55 sQ206_spl|sQ2640_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f30675,f4403,f30811])).
% 71.57/9.55 fof(f30885,plain,(
% 71.57/9.55 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),tc_nat))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f1088,f3113])).
% 71.57/9.55 fof(f30894,plain,(
% 71.57/9.55 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f1088,f3113])).
% 71.57/9.55 fof(f31018,definition,(
% 71.57/9.55 ![X0,X1]: (sQ2661_spl <=> (c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2661_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f31021,plain,(
% 71.57/9.55 sQ206_spl|sQ2661_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f30885,f4403,f31018])).
% 71.57/9.55 fof(f31029,definition,(
% 71.57/9.55 ![X0,X1]: (sQ2663_spl <=> (c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2663_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f31032,plain,(
% 71.57/9.55 sQ206_spl|sQ2663_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f30894,f4403,f31029])).
% 71.57/9.55 fof(f31218,definition,(
% 71.57/9.55 ![X3,X4]: (sQ2688_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(X4,X3,tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2688_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f31219,plain,(
% 71.57/9.55 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(X1,X0,tc_nat)|~sQ2688_spl)),
% 71.57/9.55 inference(component_clause,[status(thm)],[f31218])).
% 71.57/9.55 fof(f31336,plain,(
% 71.57/9.55 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(X0,X1,tc_nat)|~sQ2688_spl)),
% 71.57/9.55 inference(forward_demodulation,[status(thm)],[f1088,f31219])).
% 71.57/9.55 fof(f31337,plain,(
% 71.57/9.55 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(X0,X1,tc_nat)|~sQ2688_spl)),
% 71.57/9.55 inference(forward_demodulation,[status(thm)],[f1088,f31336])).
% 71.57/9.55 fof(f31338,plain,(
% 71.57/9.55 ![X0,X1]: (~c_HOL_Oord__class_Oless(X0,X1,tc_nat)|~sQ2688_spl)),
% 71.57/9.55 inference(forward_subsumption_resolution,[status(thm)],[f31337,f1265])).
% 71.57/9.55 fof(f31364,plain,(
% 71.57/9.55 $false|~sQ2688_spl),
% 71.57/9.55 inference(backward_subsumption_resolution,[status(thm)],[f3043,f31338])).
% 71.57/9.55 fof(f31368,plain,(
% 71.57/9.55 ~sQ2688_spl),
% 71.57/9.55 inference(contradiction_clause,[status(thm)],[f31364])).
% 71.57/9.55 fof(f31400,plain,(
% 71.57/9.55 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),tc_nat))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f1088,f3115])).
% 71.57/9.55 fof(f31405,plain,(
% 71.57/9.55 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f1088,f3115])).
% 71.57/9.55 fof(f31493,definition,(
% 71.57/9.55 ![X0]: (sQ2727_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2727_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f31496,plain,(
% 71.57/9.55 sQ206_spl|sQ2727_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f31400,f4403,f31493])).
% 71.57/9.55 fof(f31501,definition,(
% 71.57/9.55 ![X0]: (sQ2729_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2729_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f31504,plain,(
% 71.57/9.55 sQ206_spl|sQ2729_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f31405,f4403,f31501])).
% 71.57/9.55 fof(f32431,plain,(
% 71.57/9.55 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)),tc_nat))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f1087,f3152])).
% 71.57/9.55 fof(f32436,plain,(
% 71.57/9.55 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|c_lessequals(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f1087,f3152])).
% 71.57/9.55 fof(f32524,definition,(
% 71.57/9.55 ![X0]: (sQ2865_spl <=> (c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2865_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f32527,plain,(
% 71.57/9.55 sQ206_spl|sQ2865_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f32431,f4403,f32524])).
% 71.57/9.55 fof(f32529,definition,(
% 71.57/9.55 ![X0]: (sQ2866_spl <=> (c_lessequals(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2866_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f32532,plain,(
% 71.57/9.55 sQ206_spl|sQ2866_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f32436,f4403,f32529])).
% 71.57/9.55 fof(f32592,plain,(
% 71.57/9.55 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)),tc_nat))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f1087,f3153])).
% 71.57/9.55 fof(f32597,plain,(
% 71.57/9.55 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|c_lessequals(c_Suc(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f1087,f3153])).
% 71.57/9.55 fof(f32726,definition,(
% 71.57/9.55 ![X0]: (sQ2885_spl <=> (c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2885_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f32729,plain,(
% 71.57/9.55 sQ206_spl|sQ2885_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f32592,f4403,f32726])).
% 71.57/9.55 fof(f32734,definition,(
% 71.57/9.55 ![X0]: (sQ2887_spl <=> (c_lessequals(c_Suc(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2887_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f32737,plain,(
% 71.57/9.55 sQ206_spl|sQ2887_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f32597,f4403,f32734])).
% 71.57/9.55 fof(f32809,plain,(
% 71.57/9.55 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),tc_nat),tc_nat))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f1087,f3154])).
% 71.57/9.55 fof(f32818,plain,(
% 71.57/9.55 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat))),
% 71.57/9.55 inference(paramodulation,[status(thm)],[f1087,f3154])).
% 71.57/9.55 fof(f32942,definition,(
% 71.57/9.55 ![X0,X1]: (sQ2908_spl <=> (c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),tc_nat),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2908_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f32945,plain,(
% 71.57/9.55 sQ206_spl|sQ2908_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f32809,f4403,f32942])).
% 71.57/9.55 fof(f32953,definition,(
% 71.57/9.55 ![X0,X1]: (sQ2910_spl <=> (c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)))),
% 71.57/9.55 introduced(definition,[new_symbols(definition,[sQ2910_spl])],[split_symbol_definition])).
% 71.57/9.55 fof(f32956,plain,(
% 71.57/9.55 sQ206_spl|sQ2910_spl),
% 71.57/9.55 inference(split_clause,[status(thm)],[f32818,f4403,f32953])).
% 71.57/9.55 fof(f33287,plain,(
% 71.57/9.55 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)),tc_nat))),
% 71.57/9.56 inference(paramodulation,[status(thm)],[f1087,f3156])).
% 71.57/9.56 fof(f33292,plain,(
% 71.57/9.56 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))),
% 71.57/9.56 inference(paramodulation,[status(thm)],[f1087,f3156])).
% 71.57/9.56 fof(f33381,definition,(
% 71.57/9.56 ![X0]: (sQ2972_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)),tc_nat)))),
% 71.57/9.56 introduced(definition,[new_symbols(definition,[sQ2972_spl])],[split_symbol_definition])).
% 71.57/9.56 fof(f33384,plain,(
% 71.57/9.56 sQ206_spl|sQ2972_spl),
% 71.57/9.56 inference(split_clause,[status(thm)],[f33287,f4403,f33381])).
% 71.57/9.56 fof(f33389,definition,(
% 71.57/9.56 ![X0]: (sQ2974_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)))),
% 71.57/9.56 introduced(definition,[new_symbols(definition,[sQ2974_spl])],[split_symbol_definition])).
% 71.57/9.56 fof(f33392,plain,(
% 71.57/9.56 sQ206_spl|sQ2974_spl),
% 71.57/9.56 inference(split_clause,[status(thm)],[f33292,f4403,f33389])).
% 71.57/9.56 fof(f34314,definition,(
% 71.57/9.56 ![X2]: (sQ3100_spl <=> (~c_lessequals(X2,X2,tc_nat)))),
% 71.57/9.56 introduced(definition,[new_symbols(definition,[sQ3100_spl])],[split_symbol_definition])).
% 71.57/9.56 fof(f34315,plain,(
% 71.57/9.56 ![X0]: (~c_lessequals(X0,X0,tc_nat)|~sQ3100_spl)),
% 71.57/9.56 inference(component_clause,[status(thm)],[f34314])).
% 71.57/9.56 fof(f34370,plain,(
% 71.57/9.56 $false|~sQ3100_spl),
% 71.57/9.56 inference(forward_subsumption_resolution,[status(thm)],[f34315,f2653])).
% 71.57/9.56 fof(f34371,plain,(
% 71.57/9.56 ~sQ3100_spl),
% 71.57/9.56 inference(contradiction_clause,[status(thm)],[f34370])).
% 71.57/9.56 fof(f36019,plain,(
% 71.57/9.56 v_n=c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_Suc(v_n),v_xa,v_xb)|~sQ1_spl),
% 71.57/9.56 inference(resolution,[status(thm)],[f2165,f1788])).
% 71.57/9.56 fof(f36071,plain,(
% 71.57/9.56 sQ844_spl|~sQ1_spl),
% 71.57/9.56 inference(split_clause,[status(thm)],[f36019,f10915,f1873])).
% 71.57/9.56 fof(f36100,plain,(
% 71.57/9.56 sQ1_spl|~sQ3_spl),
% 71.57/9.56 inference(split_clause,[status(thm)],[f11405,f1873,f1881])).
% 71.57/9.56 fof(f36101,plain,(
% 71.57/9.56 $false),
% 71.57/9.56 inference(sat_refutation,[status(thm)],[f1872,f1885,f1889,f1896,f2095,f2098,f2227,f2429,f4422,f4479,f4500,f4840,f7378,f7383,f7425,f7506,f7752,f7757,f8062,f8066,f8331,f8335,f8426,f9122,f9123,f9124,f9308,f9309,f9311,f9892,f10130,f10146,f10326,f10342,f10384,f10388,f10392,f10400,f10404,f10408,f10414,f10440,f10444,f10448,f10456,f10460,f10464,f10466,f10923,f10925,f10938,f10940,f10949,f10952,f11127,f11223,f12359,f12362,f12412,f12546,f12551,f13599,f16137,f16159,f16162,f16166,f16200,f16205,f16209,f16212,f16642,f16646,f16806,f16814,f17578,f17651,f17654,f17656,f17658,f17660,f17662,f17664,f17666,f17668,f17672,f17677,f17682,f17687,f17691,f17694,f17696,f17698,f17701,f17704,f17709,f18157,f18315,f18556,f18564,f18716,f18720,f19328,f20764,f20901,f21010,f21265,f21609,f22481,f22683,f23592,f23754,f23762,f23785,f23789,f23791,f24613,f24783,f25364,f25470,f26239,f26358,f26396,f26465,f26469,f26471,f27677,f28154,f28219,f28221,f28223,f28226,f28691,f29438,f29447,f30606,f30611,f30806,f30814,f31021,f31032,f31368,f31496,f31504,f32527,f32532,f32729,f32737,f32945,f32956,f33384,f33392,f34371,f36071,f36100])).
% 71.57/9.57 % SZS output end CNFRefutation for theBenchmark.p
% 71.57/9.58 % Elapsed time: 9.205012 seconds
% 71.57/9.58 % CPU time: 72.062369 seconds
% 71.57/9.58 % Total memory used: 481.788 MB
% 71.57/9.58 % Net memory used: 453.745 MB
%------------------------------------------------------------------------------