TSTP Solution File: SWW180+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWW180+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:49:47 EDT 2024
% Result : Theorem 22.79s 3.31s
% Output : CNFRefutation 23.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWW180+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 23:33:28 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.22/0.44 % Drodi V3.6.0
% 22.79/3.31 % Refutation found
% 22.79/3.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 22.79/3.31 % SZS output start CNFRefutation for theBenchmark
% 22.79/3.31 fof(f64,axiom,(
% 22.79/3.31 (! [V_x,V_y,T_a] :( class_Orderings_Olinorder(T_a)=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)=> c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) )),
% 22.79/3.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.31 fof(f93,axiom,(
% 22.79/3.31 (! [V_r] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) )),
% 22.79/3.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.31 fof(f151,axiom,(
% 22.79/3.31 (! [V_c,V_b,V_a,T_a] :( class_Rings_Ocomm__semiring__1(T_a)=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b) ) )),
% 22.79/3.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.31 fof(f156,axiom,(
% 22.79/3.31 (! [V_c,V_a,T_a] :( class_Rings_Ocomm__semiring__1(T_a)=> c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )),
% 22.79/3.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.31 fof(f191,axiom,(
% 22.79/3.31 (! [V_x] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x) )),
% 22.79/3.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.31 fof(f199,axiom,(
% 22.79/3.31 (! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w) )),
% 22.79/3.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.31 fof(f200,axiom,(
% 22.79/3.31 (! [V_w,V_z] :( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z) ) )),
% 22.79/3.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.31 fof(f201,axiom,(
% 22.79/3.31 (! [V_k,V_j,V_i] :( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j)=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k) ) ) )),
% 22.79/3.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.31 fof(f216,axiom,(
% 22.79/3.31 (! [V_y_2,V_x_2] :( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)& V_x_2 != V_y_2 ) ) )),
% 22.79/3.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.31 fof(f221,axiom,(
% 22.79/3.31 (! [V_z,V_y,V_x] :( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y)) ) )),
% 22.79/3.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.31 fof(f548,axiom,(
% 22.79/3.31 (! [V_r] :( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_r) )& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = V_r ) ) )),
% 22.79/3.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.31 fof(f797,axiom,(
% 22.79/3.31 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
% 22.79/3.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.31 fof(f914,axiom,(
% 22.79/3.31 (! [V_b,V_a,T_a] :( class_Groups_Ogroup__add(T_a)=> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) )),
% 22.79/3.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.31 fof(f915,axiom,(
% 22.79/3.31 (! [V_b,V_a,T_a] :( class_Groups_Ogroup__add(T_a)=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) )),
% 22.79/3.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.31 fof(f984,axiom,(
% 22.79/3.31 (! [V_y,V_x] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y)) )),
% 22.79/3.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.31 fof(f1014,axiom,(
% 22.79/3.31 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ),
% 22.79/3.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.33 fof(f1016,axiom,(
% 22.79/3.33 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
% 22.79/3.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.33 fof(f1036,axiom,(
% 22.79/3.33 class_Rings_Olinordered__idom(tc_Int_Oint) ),
% 22.79/3.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.33 fof(f1043,axiom,(
% 22.79/3.33 class_Orderings_Opreorder(tc_Int_Oint) ),
% 22.79/3.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.33 fof(f1046,axiom,(
% 22.79/3.33 class_Rings_Ocomm__ring__1(tc_Int_Oint) ),
% 22.79/3.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.33 fof(f1052,axiom,(
% 22.79/3.33 class_Orderings_Oorder(tc_Int_Oint) ),
% 22.79/3.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.33 fof(f1090,axiom,(
% 22.79/3.33 class_Orderings_Opreorder(tc_Nat_Onat) ),
% 22.79/3.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.33 fof(f1096,axiom,(
% 22.79/3.33 class_Orderings_Oorder(tc_Nat_Onat) ),
% 22.79/3.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.33 fof(f1115,axiom,(
% 22.79/3.33 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ),
% 22.79/3.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.33 fof(f1117,axiom,(
% 22.79/3.33 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ),
% 22.79/3.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.33 fof(f1119,axiom,(
% 22.79/3.33 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
% 22.79/3.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.33 fof(f1120,axiom,(
% 22.79/3.33 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ),
% 22.79/3.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.33 fof(f1122,axiom,(
% 22.79/3.33 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ),
% 22.79/3.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.33 fof(f1143,axiom,(
% 22.79/3.33 class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
% 22.79/3.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.33 fof(f1144,axiom,(
% 22.79/3.33 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ),
% 22.79/3.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.33 fof(f1150,axiom,(
% 22.79/3.33 class_Orderings_Opreorder(tc_RealDef_Oreal) ),
% 22.79/3.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.33 fof(f1151,axiom,(
% 22.79/3.33 class_Orderings_Olinorder(tc_RealDef_Oreal) ),
% 22.79/3.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.33 fof(f1153,axiom,(
% 22.79/3.33 class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) ),
% 22.79/3.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.33 fof(f1156,axiom,(
% 22.79/3.33 class_Groups_Ogroup__add(tc_RealDef_Oreal) ),
% 22.79/3.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.33 fof(f1159,axiom,(
% 22.79/3.33 class_Orderings_Oorder(tc_RealDef_Oreal) ),
% 22.79/3.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.33 fof(f1275,conjecture,(
% 22.79/3.33 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))) ),
% 22.79/3.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.79/3.33 fof(f1276,negated_conjecture,(
% 22.79/3.33 ~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))) )),
% 22.79/3.33 inference(negated_conjecture,[status(cth)],[f1275])).
% 22.79/3.33 fof(f1478,plain,(
% 22.79/3.33 ![V_x,V_y,T_a]: (~class_Orderings_Olinorder(T_a)|(c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)))),
% 22.79/3.33 inference(pre_NNF_transformation,[status(esa)],[f64])).
% 22.79/3.33 fof(f1479,plain,(
% 22.79/3.33 ![T_a]: (~class_Orderings_Olinorder(T_a)|(![V_x,V_y]: (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y))))),
% 22.79/3.33 inference(miniscoping,[status(esa)],[f1478])).
% 22.79/3.33 fof(f1480,plain,(
% 22.79/3.33 ![X0,X1,X2]: (~class_Orderings_Olinorder(X0)|c_Orderings_Oord__class_Oless__eq(X0,X1,X2)|c_Orderings_Oord__class_Oless(X0,X2,X1))),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1479])).
% 22.79/3.33 fof(f1586,plain,(
% 22.79/3.33 ![X0]: (c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0))),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f93])).
% 22.79/3.33 fof(f1780,plain,(
% 22.79/3.33 ![V_c,V_b,V_a,T_a]: (~class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b))),
% 22.79/3.33 inference(pre_NNF_transformation,[status(esa)],[f151])).
% 22.79/3.33 fof(f1781,plain,(
% 22.79/3.33 ![T_a]: (~class_Rings_Ocomm__semiring__1(T_a)|(![V_c,V_b,V_a]: c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b)))),
% 22.79/3.33 inference(miniscoping,[status(esa)],[f1780])).
% 22.79/3.33 fof(f1782,plain,(
% 22.79/3.33 ![X0,X1,X2,X3]: (~class_Rings_Ocomm__semiring__1(X0)|c_Groups_Oplus__class_Oplus(X0,c_Groups_Oplus__class_Oplus(X0,X1,X2),X3)=c_Groups_Oplus__class_Oplus(X0,c_Groups_Oplus__class_Oplus(X0,X1,X3),X2))),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1781])).
% 22.79/3.33 fof(f1795,plain,(
% 22.79/3.33 ![V_c,V_a,T_a]: (~class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a))),
% 22.79/3.33 inference(pre_NNF_transformation,[status(esa)],[f156])).
% 22.79/3.33 fof(f1796,plain,(
% 22.79/3.33 ![T_a]: (~class_Rings_Ocomm__semiring__1(T_a)|(![V_c,V_a]: c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)))),
% 22.79/3.33 inference(miniscoping,[status(esa)],[f1795])).
% 22.79/3.33 fof(f1797,plain,(
% 22.79/3.33 ![X0,X1,X2]: (~class_Rings_Ocomm__semiring__1(X0)|c_Groups_Oplus__class_Oplus(X0,X1,X2)=c_Groups_Oplus__class_Oplus(X0,X2,X1))),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1796])).
% 22.79/3.33 fof(f1906,plain,(
% 22.79/3.33 ![X0]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0))),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f191])).
% 22.79/3.33 fof(f1938,plain,(
% 22.79/3.33 ![X0]: (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0))),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f199])).
% 22.79/3.33 fof(f1939,plain,(
% 22.79/3.33 ![X0,X1]: (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0))),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f200])).
% 22.79/3.33 fof(f1940,plain,(
% 22.79/3.33 ![V_k,V_j,V_i]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j)|(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k)))),
% 22.79/3.33 inference(pre_NNF_transformation,[status(esa)],[f201])).
% 22.79/3.33 fof(f1941,plain,(
% 22.79/3.33 ![V_j,V_i]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j)|(![V_k]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k))))),
% 22.79/3.33 inference(miniscoping,[status(esa)],[f1940])).
% 22.79/3.33 fof(f1942,plain,(
% 22.79/3.33 ![X0,X1,X2]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X2))),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1941])).
% 22.79/3.33 fof(f1981,plain,(
% 22.79/3.33 ![V_y_2,V_x_2]: ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)|(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)&~V_x_2=V_y_2))&(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)|(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)|V_x_2=V_y_2)))),
% 22.79/3.33 inference(NNF_transformation,[status(esa)],[f216])).
% 22.79/3.33 fof(f1982,plain,(
% 22.79/3.33 (![V_y_2,V_x_2]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)|(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)&~V_x_2=V_y_2)))&(![V_y_2,V_x_2]: (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)|(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)|V_x_2=V_y_2)))),
% 22.79/3.33 inference(miniscoping,[status(esa)],[f1981])).
% 22.79/3.33 fof(f1984,plain,(
% 22.79/3.33 ![X0,X1]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)|~X0=X1)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1982])).
% 22.79/3.33 fof(f2003,plain,(
% 22.79/3.33 ![V_z,V_y,V_x]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y)))),
% 22.79/3.33 inference(pre_NNF_transformation,[status(esa)],[f221])).
% 22.79/3.33 fof(f2004,plain,(
% 22.79/3.33 ![V_y,V_x]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)|(![V_z]: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y))))),
% 22.79/3.33 inference(miniscoping,[status(esa)],[f2003])).
% 22.79/3.33 fof(f2005,plain,(
% 22.79/3.33 ![X0,X1,X2]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X0),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1)))),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f2004])).
% 22.79/3.33 fof(f3097,plain,(
% 22.79/3.33 ![V_r]: ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_r))&(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)=V_r))),
% 22.79/3.33 inference(pre_NNF_transformation,[status(esa)],[f548])).
% 22.79/3.33 fof(f3098,plain,(
% 22.79/3.33 (![V_r]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_r)))&(![V_r]: (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)=V_r))),
% 22.79/3.33 inference(miniscoping,[status(esa)],[f3097])).
% 22.79/3.33 fof(f3100,plain,(
% 22.79/3.33 ![X0]: (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)=X0)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f3098])).
% 22.79/3.33 fof(f3853,plain,(
% 22.79/3.33 ~c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Groups_Oone__class_Oone(tc_Int_Oint)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f797])).
% 22.79/3.33 fof(f4198,plain,(
% 22.79/3.33 ![V_b,V_a,T_a]: (~class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b)=V_a)),
% 22.79/3.33 inference(pre_NNF_transformation,[status(esa)],[f914])).
% 22.79/3.33 fof(f4199,plain,(
% 22.79/3.33 ![T_a]: (~class_Groups_Ogroup__add(T_a)|(![V_b,V_a]: c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b)=V_a))),
% 22.79/3.33 inference(miniscoping,[status(esa)],[f4198])).
% 22.79/3.33 fof(f4200,plain,(
% 22.79/3.33 ![X0,X1,X2]: (~class_Groups_Ogroup__add(X0)|c_Groups_Ominus__class_Ominus(X0,c_Groups_Oplus__class_Oplus(X0,X1,X2),X2)=X1)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f4199])).
% 22.79/3.33 fof(f4201,plain,(
% 22.79/3.33 ![V_b,V_a,T_a]: (~class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b)=V_a)),
% 22.79/3.33 inference(pre_NNF_transformation,[status(esa)],[f915])).
% 22.79/3.33 fof(f4202,plain,(
% 22.79/3.33 ![T_a]: (~class_Groups_Ogroup__add(T_a)|(![V_b,V_a]: c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b)=V_a))),
% 22.79/3.33 inference(miniscoping,[status(esa)],[f4201])).
% 22.79/3.33 fof(f4203,plain,(
% 22.79/3.33 ![X0,X1,X2]: (~class_Groups_Ogroup__add(X0)|c_Groups_Oplus__class_Oplus(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2),X2)=X1)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f4202])).
% 22.79/3.33 fof(f4440,plain,(
% 22.79/3.33 ![X0,X1]: (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)))),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f984])).
% 22.79/3.33 fof(f4491,plain,(
% 22.79/3.33 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1014])).
% 22.79/3.33 fof(f4493,plain,(
% 22.79/3.33 class_Groups_Olinordered__ab__group__add(tc_Int_Oint)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1016])).
% 22.79/3.33 fof(f4513,plain,(
% 22.79/3.33 class_Rings_Olinordered__idom(tc_Int_Oint)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1036])).
% 22.79/3.33 fof(f4520,plain,(
% 22.79/3.33 class_Orderings_Opreorder(tc_Int_Oint)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1043])).
% 22.79/3.33 fof(f4523,plain,(
% 22.79/3.33 class_Rings_Ocomm__ring__1(tc_Int_Oint)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1046])).
% 22.79/3.33 fof(f4529,plain,(
% 22.79/3.33 class_Orderings_Oorder(tc_Int_Oint)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1052])).
% 22.79/3.33 fof(f4567,plain,(
% 22.79/3.33 class_Orderings_Opreorder(tc_Nat_Onat)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1090])).
% 22.79/3.33 fof(f4573,plain,(
% 22.79/3.33 class_Orderings_Oorder(tc_Nat_Onat)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1096])).
% 22.79/3.33 fof(f4592,plain,(
% 22.79/3.33 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1115])).
% 22.79/3.33 fof(f4594,plain,(
% 22.79/3.33 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1117])).
% 22.79/3.33 fof(f4596,plain,(
% 22.79/3.33 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1119])).
% 22.79/3.33 fof(f4597,plain,(
% 22.79/3.33 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1120])).
% 22.79/3.33 fof(f4599,plain,(
% 22.79/3.33 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1122])).
% 22.79/3.33 fof(f4620,plain,(
% 22.79/3.33 class_Rings_Olinordered__idom(tc_RealDef_Oreal)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1143])).
% 22.79/3.33 fof(f4621,plain,(
% 22.79/3.33 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1144])).
% 22.79/3.33 fof(f4627,plain,(
% 22.79/3.33 class_Orderings_Opreorder(tc_RealDef_Oreal)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1150])).
% 22.79/3.33 fof(f4628,plain,(
% 22.79/3.33 class_Orderings_Olinorder(tc_RealDef_Oreal)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1151])).
% 22.79/3.33 fof(f4630,plain,(
% 22.79/3.33 class_Rings_Ocomm__ring__1(tc_RealDef_Oreal)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1153])).
% 22.79/3.33 fof(f4633,plain,(
% 22.79/3.33 class_Groups_Ogroup__add(tc_RealDef_Oreal)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1156])).
% 22.79/3.33 fof(f4636,plain,(
% 22.79/3.33 class_Orderings_Oorder(tc_RealDef_Oreal)),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1159])).
% 22.79/3.33 fof(f4812,plain,(
% 22.79/3.33 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))),
% 22.79/3.33 inference(cnf_transformation,[status(esa)],[f1276])).
% 22.79/3.33 fof(f4851,plain,(
% 22.79/3.33 ![X0]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0))),
% 22.79/3.33 inference(forward_demodulation,[status(thm)],[f1586,f1906])).
% 22.79/3.33 fof(f4856,plain,(
% 22.79/3.33 ![X0]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X0))),
% 22.79/3.33 inference(destructive_equality_resolution,[status(esa)],[f1984])).
% 22.79/3.33 fof(f4918,plain,(
% 22.79/3.33 ![X0]: (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)=X0)),
% 22.79/3.33 inference(forward_demodulation,[status(thm)],[f1586,f3100])).
% 22.79/3.33 fof(f5023,plain,(
% 22.79/3.33 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))),
% 22.79/3.33 inference(forward_demodulation,[status(thm)],[f1586,f4812])).
% 22.79/3.33 fof(f5077,plain,(
% 22.79/3.33 c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
% 22.79/3.33 inference(resolution,[status(thm)],[f4918,f4856])).
% 22.79/3.33 fof(f5150,plain,(
% 22.79/3.33 spl0_6 <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Groups_Oone__class_Oone(tc_Int_Oint)),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f5151,plain,(
% 22.79/3.33 c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Groups_Oone__class_Oone(tc_Int_Oint)|~spl0_6),
% 22.79/3.33 inference(component_clause,[status(thm)],[f5150])).
% 22.79/3.33 fof(f5160,plain,(
% 22.79/3.33 spl0_8 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f5163,plain,(
% 22.79/3.33 spl0_9 <=> c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f5164,plain,(
% 22.79/3.33 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))|~spl0_9),
% 22.79/3.33 inference(component_clause,[status(thm)],[f5163])).
% 22.79/3.33 fof(f5812,plain,(
% 22.79/3.33 ![X0]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),X0)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))))),
% 22.79/3.33 inference(resolution,[status(thm)],[f1942,f5023])).
% 22.79/3.33 fof(f5960,plain,(
% 22.79/3.33 spl0_35 <=> class_Orderings_Olinorder(tc_RealDef_Oreal)),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f5962,plain,(
% 22.79/3.33 ~class_Orderings_Olinorder(tc_RealDef_Oreal)|spl0_35),
% 22.79/3.33 inference(component_clause,[status(thm)],[f5960])).
% 22.79/3.33 fof(f6004,plain,(
% 22.79/3.33 $false|spl0_35),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f5962,f4628])).
% 22.79/3.33 fof(f6005,plain,(
% 22.79/3.33 spl0_35),
% 22.79/3.33 inference(contradiction_clause,[status(thm)],[f6004])).
% 22.79/3.33 fof(f6006,plain,(
% 22.79/3.33 spl0_41 <=> class_Orderings_Opreorder(tc_Nat_Onat)),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f6008,plain,(
% 22.79/3.33 ~class_Orderings_Opreorder(tc_Nat_Onat)|spl0_41),
% 22.79/3.33 inference(component_clause,[status(thm)],[f6006])).
% 22.79/3.33 fof(f6015,plain,(
% 22.79/3.33 spl0_42 <=> class_Orderings_Opreorder(tc_Int_Oint)),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f6017,plain,(
% 22.79/3.33 ~class_Orderings_Opreorder(tc_Int_Oint)|spl0_42),
% 22.79/3.33 inference(component_clause,[status(thm)],[f6015])).
% 22.79/3.33 fof(f6020,plain,(
% 22.79/3.33 spl0_43 <=> class_Orderings_Opreorder(tc_RealDef_Oreal)),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f6022,plain,(
% 22.79/3.33 ~class_Orderings_Opreorder(tc_RealDef_Oreal)|spl0_43),
% 22.79/3.33 inference(component_clause,[status(thm)],[f6020])).
% 22.79/3.33 fof(f6045,plain,(
% 22.79/3.33 spl0_44 <=> class_Orderings_Oorder(tc_Nat_Onat)),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f6047,plain,(
% 22.79/3.33 ~class_Orderings_Oorder(tc_Nat_Onat)|spl0_44),
% 22.79/3.33 inference(component_clause,[status(thm)],[f6045])).
% 22.79/3.33 fof(f6054,plain,(
% 22.79/3.33 spl0_45 <=> class_Orderings_Oorder(tc_Int_Oint)),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f6056,plain,(
% 22.79/3.33 ~class_Orderings_Oorder(tc_Int_Oint)|spl0_45),
% 22.79/3.33 inference(component_clause,[status(thm)],[f6054])).
% 22.79/3.33 fof(f6059,plain,(
% 22.79/3.33 spl0_46 <=> class_Orderings_Oorder(tc_RealDef_Oreal)),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f6061,plain,(
% 22.79/3.33 ~class_Orderings_Oorder(tc_RealDef_Oreal)|spl0_46),
% 22.79/3.33 inference(component_clause,[status(thm)],[f6059])).
% 22.79/3.33 fof(f6122,plain,(
% 22.79/3.33 spl0_53 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f6123,plain,(
% 22.79/3.33 ![X0]: (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|~spl0_53)),
% 22.79/3.33 inference(component_clause,[status(thm)],[f6122])).
% 22.79/3.33 fof(f6125,plain,(
% 22.79/3.33 ![X0]: (~class_Orderings_Olinorder(tc_RealDef_Oreal)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))),
% 22.79/3.33 inference(resolution,[status(thm)],[f1480,f4851])).
% 22.79/3.33 fof(f6126,plain,(
% 22.79/3.33 ~spl0_35|spl0_53),
% 22.79/3.33 inference(split_clause,[status(thm)],[f6125,f5960,f6122])).
% 22.79/3.33 fof(f6276,plain,(
% 22.79/3.33 spl0_69 <=> class_Groups_Ogroup__add(tc_RealDef_Oreal)),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f6278,plain,(
% 22.79/3.33 ~class_Groups_Ogroup__add(tc_RealDef_Oreal)|spl0_69),
% 22.79/3.33 inference(component_clause,[status(thm)],[f6276])).
% 22.79/3.33 fof(f6295,plain,(
% 22.79/3.33 $false|spl0_69),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f6278,f4633])).
% 22.79/3.33 fof(f6296,plain,(
% 22.79/3.33 spl0_69),
% 22.79/3.33 inference(contradiction_clause,[status(thm)],[f6295])).
% 22.79/3.33 fof(f6302,plain,(
% 22.79/3.33 spl0_72 <=> class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f6304,plain,(
% 22.79/3.33 ~class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)|spl0_72),
% 22.79/3.33 inference(component_clause,[status(thm)],[f6302])).
% 22.79/3.33 fof(f6324,plain,(
% 22.79/3.33 $false|spl0_72),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f6304,f4621])).
% 22.79/3.33 fof(f6325,plain,(
% 22.79/3.33 spl0_72),
% 22.79/3.33 inference(contradiction_clause,[status(thm)],[f6324])).
% 22.79/3.33 fof(f6513,plain,(
% 22.79/3.33 $false|~spl0_6),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f5151,f3853])).
% 22.79/3.33 fof(f6514,plain,(
% 22.79/3.33 ~spl0_6),
% 22.79/3.33 inference(contradiction_clause,[status(thm)],[f6513])).
% 22.79/3.33 fof(f6562,plain,(
% 22.79/3.33 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))|~spl0_9),
% 22.79/3.33 inference(backward_demodulation,[status(thm)],[f5164,f5023])).
% 22.79/3.33 fof(f6563,plain,(
% 22.79/3.33 $false|~spl0_9),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f6562,f1938])).
% 22.79/3.33 fof(f6564,plain,(
% 22.79/3.33 ~spl0_9),
% 22.79/3.33 inference(contradiction_clause,[status(thm)],[f6563])).
% 22.79/3.33 fof(f6565,plain,(
% 22.79/3.33 spl0_101 <=> class_Rings_Olinordered__idom(tc_Int_Oint)),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f6567,plain,(
% 22.79/3.33 ~class_Rings_Olinordered__idom(tc_Int_Oint)|spl0_101),
% 22.79/3.33 inference(component_clause,[status(thm)],[f6565])).
% 22.79/3.33 fof(f6583,plain,(
% 22.79/3.33 spl0_103 <=> class_Rings_Olinordered__idom(tc_RealDef_Oreal)),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f6585,plain,(
% 22.79/3.33 ~class_Rings_Olinordered__idom(tc_RealDef_Oreal)|spl0_103),
% 22.79/3.33 inference(component_clause,[status(thm)],[f6583])).
% 22.79/3.33 fof(f6718,plain,(
% 22.79/3.33 $false|spl0_101),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f6567,f4513])).
% 22.79/3.33 fof(f6719,plain,(
% 22.79/3.33 spl0_101),
% 22.79/3.33 inference(contradiction_clause,[status(thm)],[f6718])).
% 22.79/3.33 fof(f6720,plain,(
% 22.79/3.33 $false|spl0_103),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f6585,f4620])).
% 22.79/3.33 fof(f6721,plain,(
% 22.79/3.33 spl0_103),
% 22.79/3.33 inference(contradiction_clause,[status(thm)],[f6720])).
% 22.79/3.33 fof(f6761,plain,(
% 22.79/3.33 spl0_130 <=> class_Rings_Ocomm__ring__1(tc_RealDef_Oreal)),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f6763,plain,(
% 22.79/3.33 ~class_Rings_Ocomm__ring__1(tc_RealDef_Oreal)|spl0_130),
% 22.79/3.33 inference(component_clause,[status(thm)],[f6761])).
% 22.79/3.33 fof(f6769,plain,(
% 22.79/3.33 spl0_132 <=> class_Rings_Ocomm__ring__1(tc_Int_Oint)),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f6771,plain,(
% 22.79/3.33 ~class_Rings_Ocomm__ring__1(tc_Int_Oint)|spl0_132),
% 22.79/3.33 inference(component_clause,[status(thm)],[f6769])).
% 22.79/3.33 fof(f6777,plain,(
% 22.79/3.33 $false|spl0_130),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f6763,f4630])).
% 22.79/3.33 fof(f6778,plain,(
% 22.79/3.33 spl0_130),
% 22.79/3.33 inference(contradiction_clause,[status(thm)],[f6777])).
% 22.79/3.33 fof(f6779,plain,(
% 22.79/3.33 $false|spl0_132),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f6771,f4523])).
% 22.79/3.33 fof(f6780,plain,(
% 22.79/3.33 spl0_132),
% 22.79/3.33 inference(contradiction_clause,[status(thm)],[f6779])).
% 22.79/3.33 fof(f6954,plain,(
% 22.79/3.33 spl0_165 <=> class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal)),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f6956,plain,(
% 22.79/3.33 ~class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal)|spl0_165),
% 22.79/3.33 inference(component_clause,[status(thm)],[f6954])).
% 22.79/3.33 fof(f6996,plain,(
% 22.79/3.33 $false|spl0_165),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f6956,f4597])).
% 22.79/3.33 fof(f6997,plain,(
% 22.79/3.33 spl0_165),
% 22.79/3.33 inference(contradiction_clause,[status(thm)],[f6996])).
% 22.79/3.33 fof(f7005,plain,(
% 22.79/3.33 spl0_173 <=> class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal)),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f7007,plain,(
% 22.79/3.33 ~class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal)|spl0_173),
% 22.79/3.33 inference(component_clause,[status(thm)],[f7005])).
% 22.79/3.33 fof(f7010,plain,(
% 22.79/3.33 $false|spl0_173),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f7007,f4594])).
% 22.79/3.33 fof(f7011,plain,(
% 22.79/3.33 spl0_173),
% 22.79/3.33 inference(contradiction_clause,[status(thm)],[f7010])).
% 22.79/3.33 fof(f7014,plain,(
% 22.79/3.33 spl0_174 <=> class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal)),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f7016,plain,(
% 22.79/3.33 ~class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal)|spl0_174),
% 22.79/3.33 inference(component_clause,[status(thm)],[f7014])).
% 22.79/3.33 fof(f7037,plain,(
% 22.79/3.33 $false|spl0_174),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f7016,f4592])).
% 22.79/3.33 fof(f7038,plain,(
% 22.79/3.33 spl0_174),
% 22.79/3.33 inference(contradiction_clause,[status(thm)],[f7037])).
% 22.79/3.33 fof(f7044,plain,(
% 22.79/3.33 spl0_179 <=> class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f7046,plain,(
% 22.79/3.33 ~class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)|spl0_179),
% 22.79/3.33 inference(component_clause,[status(thm)],[f7044])).
% 22.79/3.33 fof(f7062,plain,(
% 22.79/3.33 spl0_183 <=> class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint)),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f7064,plain,(
% 22.79/3.33 ~class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint)|spl0_183),
% 22.79/3.33 inference(component_clause,[status(thm)],[f7062])).
% 22.79/3.33 fof(f7125,plain,(
% 22.79/3.33 $false|spl0_183),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f7064,f4491])).
% 22.79/3.33 fof(f7126,plain,(
% 22.79/3.33 spl0_183),
% 22.79/3.33 inference(contradiction_clause,[status(thm)],[f7125])).
% 22.79/3.33 fof(f7127,plain,(
% 22.79/3.33 $false|spl0_179),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f7046,f4596])).
% 22.79/3.33 fof(f7128,plain,(
% 22.79/3.33 spl0_179),
% 22.79/3.33 inference(contradiction_clause,[status(thm)],[f7127])).
% 22.79/3.33 fof(f7711,plain,(
% 22.79/3.33 ![X0]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),X0)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))),X0))),
% 22.79/3.33 inference(resolution,[status(thm)],[f5812,f1939])).
% 22.79/3.33 fof(f7813,plain,(
% 22.79/3.33 $false|spl0_42),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f6017,f4520])).
% 22.79/3.33 fof(f7814,plain,(
% 22.79/3.33 spl0_42),
% 22.79/3.33 inference(contradiction_clause,[status(thm)],[f7813])).
% 22.79/3.33 fof(f7815,plain,(
% 22.79/3.33 $false|spl0_45),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f6056,f4529])).
% 22.79/3.33 fof(f7816,plain,(
% 22.79/3.33 spl0_45),
% 22.79/3.33 inference(contradiction_clause,[status(thm)],[f7815])).
% 22.79/3.33 fof(f7817,plain,(
% 22.79/3.33 $false|spl0_46),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f6061,f4636])).
% 22.79/3.33 fof(f7818,plain,(
% 22.79/3.33 spl0_46),
% 22.79/3.33 inference(contradiction_clause,[status(thm)],[f7817])).
% 22.79/3.33 fof(f7819,plain,(
% 22.79/3.33 $false|spl0_43),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f6022,f4627])).
% 22.79/3.33 fof(f7820,plain,(
% 22.79/3.33 spl0_43),
% 22.79/3.33 inference(contradiction_clause,[status(thm)],[f7819])).
% 22.79/3.33 fof(f7821,plain,(
% 22.79/3.33 $false|spl0_41),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f6008,f4567])).
% 22.79/3.33 fof(f7822,plain,(
% 22.79/3.33 spl0_41),
% 22.79/3.33 inference(contradiction_clause,[status(thm)],[f7821])).
% 22.79/3.33 fof(f7823,plain,(
% 22.79/3.33 $false|spl0_44),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f6047,f4573])).
% 22.79/3.33 fof(f7824,plain,(
% 22.79/3.33 spl0_44),
% 22.79/3.33 inference(contradiction_clause,[status(thm)],[f7823])).
% 22.79/3.33 fof(f9327,plain,(
% 22.79/3.33 spl0_484 <=> c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),X1)=X0),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f9328,plain,(
% 22.79/3.33 ![X0,X1]: (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),X1)=X0|~spl0_484)),
% 22.79/3.33 inference(component_clause,[status(thm)],[f9327])).
% 22.79/3.33 fof(f9330,plain,(
% 22.79/3.33 ![X0,X1]: (~class_Groups_Ogroup__add(tc_RealDef_Oreal)|c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),X1)=X0)),
% 22.79/3.33 inference(paramodulation,[status(thm)],[f4440,f4203])).
% 22.79/3.33 fof(f9331,plain,(
% 22.79/3.33 ~spl0_69|spl0_484),
% 22.79/3.33 inference(split_clause,[status(thm)],[f9330,f6276,f9327])).
% 22.79/3.33 fof(f9352,plain,(
% 22.79/3.33 spl0_489 <=> c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))=X0),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f9353,plain,(
% 22.79/3.33 ![X0,X1]: (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))=X0|~spl0_489)),
% 22.79/3.33 inference(component_clause,[status(thm)],[f9352])).
% 22.79/3.33 fof(f9355,plain,(
% 22.79/3.33 ![X0,X1]: (~class_Groups_Ogroup__add(tc_RealDef_Oreal)|c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))=X0)),
% 22.79/3.33 inference(paramodulation,[status(thm)],[f4440,f4200])).
% 22.79/3.33 fof(f9356,plain,(
% 22.79/3.33 ~spl0_69|spl0_489),
% 22.79/3.33 inference(split_clause,[status(thm)],[f9355,f6276,f9352])).
% 22.79/3.33 fof(f9901,plain,(
% 22.79/3.33 spl0_510 <=> c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f9902,plain,(
% 22.79/3.33 ![X0,X1]: (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))|~spl0_510)),
% 22.79/3.33 inference(component_clause,[status(thm)],[f9901])).
% 22.79/3.33 fof(f9904,plain,(
% 22.79/3.33 ![X0,X1]: (~class_Groups_Ogroup__add(tc_RealDef_Oreal)|c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))|~spl0_484)),
% 22.79/3.33 inference(paramodulation,[status(thm)],[f9328,f4203])).
% 22.79/3.33 fof(f9905,plain,(
% 22.79/3.33 ~spl0_69|spl0_510|~spl0_484),
% 22.79/3.33 inference(split_clause,[status(thm)],[f9904,f6276,f9901,f9327])).
% 22.79/3.33 fof(f9906,plain,(
% 22.79/3.33 ![X0,X1]: (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),X1)=X0|~spl0_510|~spl0_484)),
% 22.79/3.33 inference(backward_demodulation,[status(thm)],[f9902,f9328])).
% 22.79/3.33 fof(f9907,plain,(
% 22.79/3.33 ![X0,X1]: (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1),X1)=X0|~spl0_510|~spl0_489)),
% 22.79/3.33 inference(backward_demodulation,[status(thm)],[f9902,f9353])).
% 22.79/3.33 fof(f9965,plain,(
% 22.79/3.33 spl0_517 <=> c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0))=X1),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f9966,plain,(
% 22.79/3.33 ![X0,X1]: (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0))=X1|~spl0_517)),
% 22.79/3.33 inference(component_clause,[status(thm)],[f9965])).
% 22.79/3.33 fof(f9968,plain,(
% 22.79/3.33 ![X0,X1]: (~class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)|c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0))=X1|~spl0_510|~spl0_489)),
% 22.79/3.33 inference(paramodulation,[status(thm)],[f9907,f1797])).
% 22.79/3.33 fof(f9969,plain,(
% 22.79/3.33 ~spl0_72|spl0_517|~spl0_510|~spl0_489),
% 22.79/3.33 inference(split_clause,[status(thm)],[f9968,f6302,f9965,f9901,f9352])).
% 22.79/3.33 fof(f9975,plain,(
% 22.79/3.33 ![X0,X1]: (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)|~spl0_517|~spl0_510|~spl0_484)),
% 22.79/3.33 inference(paramodulation,[status(thm)],[f9906,f9966])).
% 22.79/3.33 fof(f9985,plain,(
% 22.79/3.33 ![X0,X1,X2]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X0),X1)|~spl0_517)),
% 22.79/3.33 inference(paramodulation,[status(thm)],[f9966,f2005])).
% 22.79/3.33 fof(f12519,plain,(
% 22.79/3.33 spl0_735 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f12521,plain,(
% 22.79/3.33 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|spl0_735),
% 22.79/3.33 inference(component_clause,[status(thm)],[f12519])).
% 22.79/3.33 fof(f12543,plain,(
% 22.79/3.33 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|spl0_735),
% 22.79/3.33 inference(forward_demodulation,[status(thm)],[f1586,f12521])).
% 22.79/3.33 fof(f12544,plain,(
% 22.79/3.33 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|spl0_735),
% 22.79/3.33 inference(forward_demodulation,[status(thm)],[f5077,f12543])).
% 22.79/3.33 fof(f12545,plain,(
% 22.79/3.33 $false|spl0_735),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f12544,f1938])).
% 22.79/3.33 fof(f12546,plain,(
% 22.79/3.33 spl0_735),
% 22.79/3.33 inference(contradiction_clause,[status(thm)],[f12545])).
% 22.79/3.33 fof(f12683,plain,(
% 22.79/3.33 spl0_745 <=> class_Groups_Olinordered__ab__group__add(tc_Int_Oint)),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f12685,plain,(
% 22.79/3.33 ~class_Groups_Olinordered__ab__group__add(tc_Int_Oint)|spl0_745),
% 22.79/3.33 inference(component_clause,[status(thm)],[f12683])).
% 22.79/3.33 fof(f12755,plain,(
% 22.79/3.33 spl0_753 <=> class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal)),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f12757,plain,(
% 22.79/3.33 ~class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal)|spl0_753),
% 22.79/3.33 inference(component_clause,[status(thm)],[f12755])).
% 22.79/3.33 fof(f12816,plain,(
% 22.79/3.33 $false|spl0_753),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f12757,f4599])).
% 22.79/3.33 fof(f12817,plain,(
% 22.79/3.33 spl0_753),
% 22.79/3.33 inference(contradiction_clause,[status(thm)],[f12816])).
% 22.79/3.33 fof(f12818,plain,(
% 22.79/3.33 $false|spl0_745),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f12685,f4493])).
% 22.79/3.33 fof(f12819,plain,(
% 22.79/3.33 spl0_745),
% 22.79/3.33 inference(contradiction_clause,[status(thm)],[f12818])).
% 22.79/3.33 fof(f15867,plain,(
% 22.79/3.33 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))),
% 22.79/3.33 inference(resolution,[status(thm)],[f7711,f5812])).
% 22.79/3.33 fof(f15868,plain,(
% 22.79/3.33 ~spl0_8),
% 22.79/3.33 inference(split_clause,[status(thm)],[f15867,f5160])).
% 22.79/3.33 fof(f17318,plain,(
% 22.79/3.33 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)))|~spl0_517),
% 22.79/3.33 inference(resolution,[status(thm)],[f9985,f5023])).
% 22.79/3.33 fof(f17319,plain,(
% 22.79/3.33 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)))|~spl0_510|~spl0_484|~spl0_517),
% 22.79/3.33 inference(forward_demodulation,[status(thm)],[f9975,f17318])).
% 22.79/3.33 fof(f17320,plain,(
% 22.79/3.33 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)))|~spl0_510|~spl0_484|~spl0_517),
% 22.79/3.33 inference(forward_demodulation,[status(thm)],[f9975,f17319])).
% 22.79/3.33 fof(f18408,plain,(
% 22.79/3.33 spl0_1276 <=> c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),X2)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)),X1)),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f18409,plain,(
% 22.79/3.33 ![X0,X1,X2]: (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),X2)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)),X1)|~spl0_1276)),
% 22.79/3.33 inference(component_clause,[status(thm)],[f18408])).
% 22.79/3.33 fof(f18411,plain,(
% 22.79/3.33 ![X0,X1,X2]: (~class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)|c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),X2)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)),X1))),
% 22.79/3.33 inference(paramodulation,[status(thm)],[f4440,f1782])).
% 22.79/3.33 fof(f18412,plain,(
% 22.79/3.33 ~spl0_72|spl0_1276),
% 22.79/3.33 inference(split_clause,[status(thm)],[f18411,f6302,f18408])).
% 22.79/3.33 fof(f18483,plain,(
% 22.79/3.33 spl0_1289 <=> c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X2))),
% 22.79/3.33 introduced(split_symbol_definition)).
% 22.79/3.33 fof(f18484,plain,(
% 22.79/3.33 ![X0,X1,X2]: (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X2))|~spl0_1289)),
% 22.79/3.33 inference(component_clause,[status(thm)],[f18483])).
% 22.79/3.33 fof(f18486,plain,(
% 22.79/3.33 ![X0,X1,X2]: (~class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)|c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X2))|~spl0_517)),
% 22.79/3.33 inference(paramodulation,[status(thm)],[f9966,f1782])).
% 22.79/3.33 fof(f18487,plain,(
% 22.79/3.33 ~spl0_72|spl0_1289|~spl0_517),
% 22.79/3.33 inference(split_clause,[status(thm)],[f18486,f6302,f18483,f9965])).
% 22.79/3.33 fof(f18678,plain,(
% 22.79/3.33 ![X0,X1,X2]: (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),X2)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X2),X1)|~spl0_1276)),
% 22.79/3.33 inference(forward_demodulation,[status(thm)],[f4440,f18409])).
% 22.79/3.33 fof(f18698,plain,(
% 22.79/3.33 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))|~spl0_1276|~spl0_510|~spl0_484|~spl0_517),
% 22.79/3.33 inference(backward_demodulation,[status(thm)],[f18678,f17320])).
% 22.79/3.33 fof(f18699,plain,(
% 22.79/3.33 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))))|~spl0_1276|~spl0_510|~spl0_484|~spl0_517),
% 22.79/3.33 inference(forward_demodulation,[status(thm)],[f9975,f18698])).
% 22.79/3.33 fof(f18700,plain,(
% 22.79/3.33 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|~spl0_1289|~spl0_1276|~spl0_510|~spl0_484|~spl0_517),
% 22.79/3.33 inference(forward_demodulation,[status(thm)],[f18484,f18699])).
% 22.79/3.33 fof(f18701,plain,(
% 22.79/3.33 $false|~spl0_53|~spl0_1289|~spl0_1276|~spl0_510|~spl0_484|~spl0_517),
% 22.79/3.33 inference(forward_subsumption_resolution,[status(thm)],[f18700,f6123])).
% 23.05/3.37 fof(f18702,plain,(
% 23.05/3.37 ~spl0_53|~spl0_1289|~spl0_1276|~spl0_510|~spl0_484|~spl0_517),
% 23.05/3.37 inference(contradiction_clause,[status(thm)],[f18701])).
% 23.05/3.37 fof(f18703,plain,(
% 23.05/3.37 $false),
% 23.05/3.37 inference(sat_refutation,[status(thm)],[f6005,f6126,f6296,f6325,f6514,f6564,f6719,f6721,f6778,f6780,f6997,f7011,f7038,f7126,f7128,f7814,f7816,f7818,f7820,f7822,f7824,f9331,f9356,f9905,f9969,f12546,f12817,f12819,f15868,f18412,f18487,f18702])).
% 23.05/3.37 % SZS output end CNFRefutation for theBenchmark.p
% 23.05/3.40 % Elapsed time: 3.040198 seconds
% 23.05/3.40 % CPU time: 23.161279 seconds
% 23.05/3.40 % Total memory used: 401.094 MB
% 23.05/3.40 % Net memory used: 391.888 MB
%------------------------------------------------------------------------------