TSTP Solution File: SWW179+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWW179+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:49:47 EDT 2024
% Result : Theorem 16.95s 2.59s
% Output : CNFRefutation 17.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW179+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 29 23:39:55 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.20/0.43 % Drodi V3.6.0
% 16.95/2.59 % Refutation found
% 16.95/2.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 16.95/2.59 % SZS output start CNFRefutation for theBenchmark
% 16.95/2.59 fof(f2,axiom,(
% 16.95/2.59 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)) ),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f3,axiom,(
% 16.95/2.59 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))) ),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f6,axiom,(
% 16.95/2.59 (! [V_s,V_y,V_r,V_x,T_a] :( class_RealVector_Oreal__normed__vector(T_a)=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,V_s)) ) ) ) )),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f14,axiom,(
% 16.95/2.59 (! [V_x,T_a] :( class_RealVector_Oreal__normed__vector(T_a)=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f15,axiom,(
% 16.95/2.59 (! [V_x_2] :( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2))<=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f18,axiom,(
% 16.95/2.59 (! [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) ) ) )),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f19,axiom,(
% 16.95/2.59 (! [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)=> V_z = V_w ) ) )),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f20,axiom,(
% 16.95/2.59 (! [V_y_2,V_x_2] :( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)| V_x_2 = V_y_2 ) ) )),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f21,axiom,(
% 16.95/2.59 (! [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 ) ) )),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f22,axiom,(
% 16.95/2.59 (! [V_r] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) )),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f23,axiom,(
% 16.95/2.59 (! [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)) ) )),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f95,axiom,(
% 16.95/2.59 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f96,axiom,(
% 16.95/2.59 (! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z) = V_z )),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f259,axiom,(
% 16.95/2.59 (! [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) ) )),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f381,axiom,(
% 16.95/2.59 (! [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)) )),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f456,axiom,(
% 16.95/2.59 (! [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 ) )),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f457,axiom,(
% 16.95/2.59 (! [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 ) )),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f492,axiom,(
% 16.95/2.59 (! [V_b_2,V_a_2,T_a] :( class_Groups_Ogroup__add(T_a)=> ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)<=> c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) )),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f513,axiom,(
% 16.95/2.59 (! [V_y_2,V_x_2] :( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<=> V_y_2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2) ) )),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f514,axiom,(
% 16.95/2.59 (! [V_a_2,V_x_2] :( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<=> V_x_2 = V_a_2 ) )),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f539,axiom,(
% 16.95/2.59 (! [V_a] :( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a) )& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = V_a ) ) )),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f1129,axiom,(
% 16.95/2.59 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f1148,axiom,(
% 16.95/2.59 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f1160,axiom,(
% 16.95/2.59 class_Groups_Ogroup__add(tc_RealDef_Oreal) ),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f1275,conjecture,(
% 16.95/2.59 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))) ),
% 16.95/2.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.95/2.59 fof(f1276,negated_conjecture,(
% 16.95/2.59 ~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))) )),
% 16.95/2.59 inference(negated_conjecture,[status(cth)],[f1275])).
% 16.95/2.59 fof(f1280,plain,(
% 16.95/2.59 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f2])).
% 16.95/2.59 fof(f1281,plain,(
% 16.95/2.59 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f3])).
% 16.95/2.59 fof(f1284,plain,(
% 16.95/2.59 ![V_s,V_y,V_r,V_x,T_a]: (~class_RealVector_Oreal__normed__vector(T_a)|(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)|(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,V_s)))))),
% 16.95/2.59 inference(pre_NNF_transformation,[status(esa)],[f6])).
% 16.95/2.59 fof(f1285,plain,(
% 16.95/2.59 ![T_a]: (~class_RealVector_Oreal__normed__vector(T_a)|(![V_r,V_x]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)|(![V_s,V_y]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,V_s)))))))),
% 16.95/2.59 inference(miniscoping,[status(esa)],[f1284])).
% 16.95/2.59 fof(f1286,plain,(
% 16.95/2.59 ![X0,X1,X2,X3,X4]: (~class_RealVector_Oreal__normed__vector(X0)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1),X2)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X3),X4)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,c_Groups_Oplus__class_Oplus(X0,X1,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X4)))),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f1285])).
% 16.95/2.59 fof(f1313,plain,(
% 16.95/2.59 ![V_x,T_a]: (~class_RealVector_Oreal__normed__vector(T_a)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))),
% 16.95/2.59 inference(pre_NNF_transformation,[status(esa)],[f14])).
% 16.95/2.59 fof(f1314,plain,(
% 16.95/2.59 ![T_a]: (~class_RealVector_Oreal__normed__vector(T_a)|(![V_x]: ~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))),
% 16.95/2.59 inference(miniscoping,[status(esa)],[f1313])).
% 16.95/2.59 fof(f1315,plain,(
% 16.95/2.59 ![X0,X1]: (~class_RealVector_Oreal__normed__vector(X0)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f1314])).
% 16.95/2.59 fof(f1316,plain,(
% 16.95/2.59 ![V_x_2]: ((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2))|V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))&(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2))|~V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))),
% 16.95/2.59 inference(NNF_transformation,[status(esa)],[f15])).
% 16.95/2.59 fof(f1317,plain,(
% 16.95/2.59 (![V_x_2]: (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2))|V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))&(![V_x_2]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2))|~V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))),
% 16.95/2.59 inference(miniscoping,[status(esa)],[f1316])).
% 16.95/2.59 fof(f1318,plain,(
% 16.95/2.59 ![X0]: (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0))|X0=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f1317])).
% 16.95/2.59 fof(f1322,plain,(
% 16.95/2.59 ![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)))),
% 16.95/2.59 inference(pre_NNF_transformation,[status(esa)],[f18])).
% 16.95/2.59 fof(f1323,plain,(
% 16.95/2.59 ![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))))),
% 16.95/2.59 inference(miniscoping,[status(esa)],[f1322])).
% 16.95/2.59 fof(f1324,plain,(
% 16.95/2.59 ![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))),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f1323])).
% 16.95/2.59 fof(f1325,plain,(
% 16.95/2.59 ![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)|V_z=V_w))),
% 16.95/2.59 inference(pre_NNF_transformation,[status(esa)],[f19])).
% 16.95/2.59 fof(f1326,plain,(
% 16.95/2.59 ![X0,X1]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)|X0=X1)),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f1325])).
% 16.95/2.59 fof(f1327,plain,(
% 16.95/2.59 ![V_y_2,V_x_2]: ((~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)|(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)|V_x_2=V_y_2))&(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)|(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)&~V_x_2=V_y_2)))),
% 16.95/2.59 inference(NNF_transformation,[status(esa)],[f20])).
% 16.95/2.59 fof(f1328,plain,(
% 16.95/2.59 (![V_y_2,V_x_2]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)|(c_Orderings_Oord__class_Oless(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__eq(tc_RealDef_Oreal,V_x_2,V_y_2)|(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)&~V_x_2=V_y_2)))),
% 16.95/2.59 inference(miniscoping,[status(esa)],[f1327])).
% 16.95/2.59 fof(f1329,plain,(
% 16.95/2.59 ![X0,X1]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)|X0=X1)),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f1328])).
% 16.95/2.59 fof(f1330,plain,(
% 16.95/2.59 ![X0,X1]: (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1))),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f1328])).
% 16.95/2.59 fof(f1332,plain,(
% 16.95/2.59 ![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)))),
% 16.95/2.59 inference(NNF_transformation,[status(esa)],[f21])).
% 16.95/2.59 fof(f1333,plain,(
% 16.95/2.59 (![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)))),
% 16.95/2.59 inference(miniscoping,[status(esa)],[f1332])).
% 16.95/2.59 fof(f1335,plain,(
% 16.95/2.59 ![X0,X1]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)|~X0=X1)),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f1333])).
% 16.95/2.59 fof(f1337,plain,(
% 16.95/2.59 ![X0]: (c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0))),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f22])).
% 16.95/2.59 fof(f1338,plain,(
% 16.95/2.59 ![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)))),
% 16.95/2.59 inference(pre_NNF_transformation,[status(esa)],[f23])).
% 16.95/2.59 fof(f1339,plain,(
% 16.95/2.59 ![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))))),
% 16.95/2.59 inference(miniscoping,[status(esa)],[f1338])).
% 16.95/2.59 fof(f1340,plain,(
% 16.95/2.59 ![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)))),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f1339])).
% 16.95/2.59 fof(f1580,plain,(
% 16.95/2.59 ~c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f95])).
% 16.95/2.59 fof(f1581,plain,(
% 16.95/2.59 ![X0]: (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0)=X0)),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f96])).
% 16.95/2.59 fof(f2138,plain,(
% 16.95/2.59 ![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))),
% 16.95/2.59 inference(pre_NNF_transformation,[status(esa)],[f259])).
% 16.95/2.59 fof(f2139,plain,(
% 16.95/2.59 ![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)))),
% 16.95/2.59 inference(miniscoping,[status(esa)],[f2138])).
% 16.95/2.59 fof(f2140,plain,(
% 16.95/2.59 ![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))),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f2139])).
% 16.95/2.59 fof(f2568,plain,(
% 16.95/2.59 ![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)))),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f381])).
% 16.95/2.59 fof(f2824,plain,(
% 16.95/2.59 ![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)),
% 16.95/2.59 inference(pre_NNF_transformation,[status(esa)],[f456])).
% 16.95/2.59 fof(f2825,plain,(
% 16.95/2.59 ![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))),
% 16.95/2.59 inference(miniscoping,[status(esa)],[f2824])).
% 16.95/2.59 fof(f2826,plain,(
% 16.95/2.59 ![X0,X1,X2]: (~class_Groups_Ogroup__add(X0)|c_Groups_Oplus__class_Oplus(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2),X2)=X1)),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f2825])).
% 16.95/2.59 fof(f2827,plain,(
% 16.95/2.59 ![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)),
% 16.95/2.59 inference(pre_NNF_transformation,[status(esa)],[f457])).
% 16.95/2.59 fof(f2828,plain,(
% 16.95/2.59 ![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))),
% 16.95/2.59 inference(miniscoping,[status(esa)],[f2827])).
% 16.95/2.59 fof(f2829,plain,(
% 16.95/2.59 ![X0,X1,X2]: (~class_Groups_Ogroup__add(X0)|c_Groups_Ominus__class_Ominus(X0,c_Groups_Oplus__class_Oplus(X0,X1,X2),X2)=X1)),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f2828])).
% 16.95/2.59 fof(f2956,plain,(
% 16.95/2.59 ![V_b_2,V_a_2,T_a]: (~class_Groups_Ogroup__add(T_a)|(V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)<=>c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)))),
% 16.95/2.59 inference(pre_NNF_transformation,[status(esa)],[f492])).
% 16.95/2.59 fof(f2957,plain,(
% 16.95/2.59 ![V_b_2,V_a_2,T_a]: (~class_Groups_Ogroup__add(T_a)|((~V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a))&(V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|~c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a))))),
% 16.95/2.59 inference(NNF_transformation,[status(esa)],[f2956])).
% 16.95/2.59 fof(f2958,plain,(
% 16.95/2.59 ![T_a]: (~class_Groups_Ogroup__add(T_a)|((![V_b_2,V_a_2]: (~V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)))&(![V_b_2,V_a_2]: (V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|~c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)))))),
% 16.95/2.59 inference(miniscoping,[status(esa)],[f2957])).
% 16.95/2.59 fof(f2959,plain,(
% 16.95/2.59 ![X0,X1,X2]: (~class_Groups_Ogroup__add(X0)|~X1=c_Groups_Ouminus__class_Ouminus(X0,X2)|c_Groups_Oplus__class_Oplus(X0,X1,X2)=c_Groups_Ozero__class_Ozero(X0))),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f2958])).
% 16.95/2.59 fof(f3035,plain,(
% 16.95/2.59 ![V_y_2,V_x_2]: ((~c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_y_2=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2))&(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|~V_y_2=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)))),
% 16.95/2.59 inference(NNF_transformation,[status(esa)],[f513])).
% 16.95/2.59 fof(f3036,plain,(
% 16.95/2.59 (![V_y_2,V_x_2]: (~c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_y_2=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)))&(![V_y_2,V_x_2]: (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|~V_y_2=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)))),
% 16.95/2.59 inference(miniscoping,[status(esa)],[f3035])).
% 16.95/2.59 fof(f3038,plain,(
% 16.95/2.59 ![X0,X1]: (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|~X1=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0))),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f3036])).
% 16.95/2.59 fof(f3039,plain,(
% 16.95/2.59 ![V_a_2,V_x_2]: ((~c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2=V_a_2)&(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|~V_x_2=V_a_2))),
% 16.95/2.59 inference(NNF_transformation,[status(esa)],[f514])).
% 16.95/2.59 fof(f3040,plain,(
% 16.95/2.59 (![V_a_2,V_x_2]: (~c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2=V_a_2))&(![V_a_2,V_x_2]: (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|~V_x_2=V_a_2))),
% 16.95/2.59 inference(miniscoping,[status(esa)],[f3039])).
% 16.95/2.59 fof(f3042,plain,(
% 16.95/2.59 ![X0,X1]: (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|~X0=X1)),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f3040])).
% 16.95/2.59 fof(f3134,plain,(
% 16.95/2.59 ![V_a]: ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a))&(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a)=V_a))),
% 16.95/2.59 inference(pre_NNF_transformation,[status(esa)],[f539])).
% 16.95/2.59 fof(f3135,plain,(
% 16.95/2.59 (![V_a]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a)))&(![V_a]: (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a)=V_a))),
% 16.95/2.59 inference(miniscoping,[status(esa)],[f3134])).
% 16.95/2.59 fof(f3137,plain,(
% 16.95/2.59 ![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)),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f3135])).
% 16.95/2.59 fof(f4650,plain,(
% 16.95/2.59 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f1129])).
% 16.95/2.59 fof(f4669,plain,(
% 16.95/2.59 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f1148])).
% 16.95/2.59 fof(f4681,plain,(
% 16.95/2.59 class_Groups_Ogroup__add(tc_RealDef_Oreal)),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f1160])).
% 16.95/2.59 fof(f4856,plain,(
% 16.95/2.59 ~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))),
% 16.95/2.59 inference(cnf_transformation,[status(esa)],[f1276])).
% 16.95/2.59 fof(f4899,plain,(
% 16.95/2.59 ![X0]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X0))),
% 16.95/2.59 inference(destructive_equality_resolution,[status(esa)],[f1335])).
% 16.95/2.59 fof(f4969,plain,(
% 16.95/2.59 ![X0,X1]: (~class_Groups_Ogroup__add(X0)|c_Groups_Oplus__class_Oplus(X0,c_Groups_Ouminus__class_Ouminus(X0,X1),X1)=c_Groups_Ozero__class_Ozero(X0))),
% 16.95/2.59 inference(destructive_equality_resolution,[status(esa)],[f2959])).
% 16.95/2.59 fof(f4975,plain,(
% 16.95/2.59 ![X0]: (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
% 16.95/2.59 inference(destructive_equality_resolution,[status(esa)],[f3038])).
% 16.95/2.59 fof(f4977,plain,(
% 16.95/2.59 ![X0,X1]: (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|~X0=X1)),
% 16.95/2.59 inference(forward_demodulation,[status(thm)],[f2568,f3042])).
% 16.95/2.59 fof(f4978,plain,(
% 16.95/2.59 ![X0]: (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X0)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
% 16.95/2.59 inference(destructive_equality_resolution,[status(esa)],[f4977])).
% 16.95/2.59 fof(f4990,plain,(
% 16.95/2.59 ![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)),
% 16.95/2.59 inference(forward_demodulation,[status(thm)],[f1337,f3137])).
% 16.95/2.59 fof(f5143,plain,(
% 16.95/2.59 ~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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____))))),
% 16.95/2.59 inference(forward_demodulation,[status(thm)],[f1337,f4856])).
% 16.95/2.59 fof(f5146,plain,(
% 16.95/2.59 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
% 16.95/2.59 inference(backward_demodulation,[status(thm)],[f1337,f1281])).
% 16.95/2.59 fof(f5207,plain,(
% 16.95/2.59 c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
% 16.95/2.59 inference(resolution,[status(thm)],[f4899,f4990])).
% 16.95/2.59 fof(f5210,plain,(
% 16.95/2.59 spl0_0 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f5212,plain,(
% 16.95/2.59 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|spl0_0),
% 16.95/2.59 inference(component_clause,[status(thm)],[f5210])).
% 16.95/2.59 fof(f5213,plain,(
% 16.95/2.59 spl0_1 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f5215,plain,(
% 16.95/2.59 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|spl0_1),
% 16.95/2.59 inference(component_clause,[status(thm)],[f5213])).
% 16.95/2.59 fof(f5216,plain,(
% 16.95/2.59 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
% 16.95/2.59 inference(resolution,[status(thm)],[f1326,f1580])).
% 16.95/2.59 fof(f5217,plain,(
% 16.95/2.59 ~spl0_0|~spl0_1),
% 16.95/2.59 inference(split_clause,[status(thm)],[f5216,f5210,f5213])).
% 16.95/2.59 fof(f5223,plain,(
% 16.95/2.59 ~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|spl0_0),
% 16.95/2.59 inference(resolution,[status(thm)],[f5212,f1330])).
% 16.95/2.59 fof(f5255,plain,(
% 16.95/2.59 spl0_5 <=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f5256,plain,(
% 16.95/2.59 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|~spl0_5),
% 16.95/2.59 inference(component_clause,[status(thm)],[f5255])).
% 16.95/2.59 fof(f5268,plain,(
% 16.95/2.59 spl0_8 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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____))))),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f5270,plain,(
% 16.95/2.59 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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____))))|spl0_8),
% 16.95/2.59 inference(component_clause,[status(thm)],[f5268])).
% 16.95/2.59 fof(f5271,plain,(
% 16.95/2.59 spl0_9 <=> c_Groups_Ozero__class_Ozero(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____)))),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f5272,plain,(
% 16.95/2.59 c_Groups_Ozero__class_Ozero(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____)))|~spl0_9),
% 16.95/2.59 inference(component_clause,[status(thm)],[f5271])).
% 16.95/2.59 fof(f5274,plain,(
% 16.95/2.59 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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_Groups_Ozero__class_Ozero(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____)))),
% 16.95/2.59 inference(resolution,[status(thm)],[f1329,f5143])).
% 16.95/2.59 fof(f5275,plain,(
% 16.95/2.59 ~spl0_8|spl0_9),
% 16.95/2.59 inference(split_clause,[status(thm)],[f5274,f5268,f5271])).
% 16.95/2.59 fof(f5276,plain,(
% 16.95/2.59 ![X0]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),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____))))|spl0_8)),
% 16.95/2.59 inference(resolution,[status(thm)],[f5270,f1324])).
% 16.95/2.59 fof(f5313,plain,(
% 16.95/2.59 spl0_12 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f5314,plain,(
% 16.95/2.59 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|~spl0_12),
% 16.95/2.59 inference(component_clause,[status(thm)],[f5313])).
% 16.95/2.59 fof(f5316,plain,(
% 16.95/2.59 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Groups_Oone__class_Oone(tc_RealDef_Oreal)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f1581,f1318])).
% 16.95/2.59 fof(f5317,plain,(
% 16.95/2.59 spl0_12|spl0_5),
% 16.95/2.59 inference(split_clause,[status(thm)],[f5316,f5313,f5255])).
% 16.95/2.59 fof(f5318,plain,(
% 16.95/2.59 $false|spl0_0|~spl0_12),
% 16.95/2.59 inference(forward_subsumption_resolution,[status(thm)],[f5314,f5223])).
% 16.95/2.59 fof(f5319,plain,(
% 16.95/2.59 spl0_0|~spl0_12),
% 16.95/2.59 inference(contradiction_clause,[status(thm)],[f5318])).
% 16.95/2.59 fof(f5320,plain,(
% 16.95/2.59 $false|~spl0_5),
% 16.95/2.59 inference(forward_subsumption_resolution,[status(thm)],[f5256,f1580])).
% 16.95/2.59 fof(f5321,plain,(
% 16.95/2.59 ~spl0_5),
% 16.95/2.59 inference(contradiction_clause,[status(thm)],[f5320])).
% 16.95/2.59 fof(f5349,plain,(
% 16.95/2.59 spl0_13 <=> class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f5351,plain,(
% 16.95/2.59 ~class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)|spl0_13),
% 16.95/2.59 inference(component_clause,[status(thm)],[f5349])).
% 16.95/2.59 fof(f5367,plain,(
% 16.95/2.59 $false|spl0_13),
% 16.95/2.59 inference(forward_subsumption_resolution,[status(thm)],[f5351,f4650])).
% 16.95/2.59 fof(f5368,plain,(
% 16.95/2.59 spl0_13),
% 16.95/2.59 inference(contradiction_clause,[status(thm)],[f5367])).
% 16.95/2.59 fof(f5953,plain,(
% 16.95/2.59 spl0_75 <=> class_Groups_Ogroup__add(tc_RealDef_Oreal)),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f5955,plain,(
% 16.95/2.59 ~class_Groups_Ogroup__add(tc_RealDef_Oreal)|spl0_75),
% 16.95/2.59 inference(component_clause,[status(thm)],[f5953])).
% 16.95/2.59 fof(f5956,plain,(
% 16.95/2.59 spl0_76 <=> c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)=X0),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f5957,plain,(
% 16.95/2.59 ![X0]: (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)=X0|~spl0_76)),
% 16.95/2.59 inference(component_clause,[status(thm)],[f5956])).
% 16.95/2.59 fof(f5959,plain,(
% 16.95/2.59 ![X0]: (~class_Groups_Ogroup__add(tc_RealDef_Oreal)|c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)=X0)),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f4978,f2826])).
% 16.95/2.59 fof(f5960,plain,(
% 16.95/2.59 ~spl0_75|spl0_76),
% 16.95/2.59 inference(split_clause,[status(thm)],[f5959,f5953,f5956])).
% 16.95/2.59 fof(f5961,plain,(
% 16.95/2.59 $false|spl0_75),
% 16.95/2.59 inference(forward_subsumption_resolution,[status(thm)],[f5955,f4681])).
% 16.95/2.59 fof(f5962,plain,(
% 16.95/2.59 spl0_75),
% 16.95/2.59 inference(contradiction_clause,[status(thm)],[f5961])).
% 16.95/2.59 fof(f5977,plain,(
% 16.95/2.59 spl0_77 <=> class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f5979,plain,(
% 16.95/2.59 ~class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)|spl0_77),
% 16.95/2.59 inference(component_clause,[status(thm)],[f5977])).
% 16.95/2.59 fof(f6006,plain,(
% 16.95/2.59 spl0_82 <=> c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=X0),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f6007,plain,(
% 16.95/2.59 ![X0]: (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=X0|~spl0_82)),
% 16.95/2.59 inference(component_clause,[status(thm)],[f6006])).
% 16.95/2.59 fof(f6009,plain,(
% 16.95/2.59 ![X0]: (~class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)|c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=X0|~spl0_76)),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f5957,f2140])).
% 16.95/2.59 fof(f6010,plain,(
% 16.95/2.59 ~spl0_77|spl0_82|~spl0_76),
% 16.95/2.59 inference(split_clause,[status(thm)],[f6009,f5977,f6006,f5956])).
% 16.95/2.59 fof(f6015,plain,(
% 16.95/2.59 $false|spl0_77),
% 16.95/2.59 inference(forward_subsumption_resolution,[status(thm)],[f5979,f4669])).
% 16.95/2.59 fof(f6016,plain,(
% 16.95/2.59 spl0_77),
% 16.95/2.59 inference(contradiction_clause,[status(thm)],[f6015])).
% 16.95/2.59 fof(f6018,plain,(
% 16.95/2.59 ![X0,X1]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))|~spl0_82)),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f6007,f1340])).
% 16.95/2.59 fof(f6019,plain,(
% 16.95/2.59 spl0_83 <=> c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=X0),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f6020,plain,(
% 16.95/2.59 ![X0]: (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=X0|~spl0_83)),
% 16.95/2.59 inference(component_clause,[status(thm)],[f6019])).
% 16.95/2.59 fof(f6022,plain,(
% 16.95/2.59 ![X0]: (~class_Groups_Ogroup__add(tc_RealDef_Oreal)|c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=X0|~spl0_82)),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f6007,f2826])).
% 16.95/2.59 fof(f6023,plain,(
% 16.95/2.59 ~spl0_75|spl0_83|~spl0_82),
% 16.95/2.59 inference(split_clause,[status(thm)],[f6022,f5953,f6019,f6006])).
% 16.95/2.59 fof(f6147,plain,(
% 16.95/2.59 spl0_96 <=> c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f6148,plain,(
% 16.95/2.59 c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|~spl0_96),
% 16.95/2.59 inference(component_clause,[status(thm)],[f6147])).
% 16.95/2.59 fof(f6253,plain,(
% 16.95/2.59 ~class_Groups_Ogroup__add(tc_RealDef_Oreal)|c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|~spl0_82),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f6007,f4969])).
% 16.95/2.59 fof(f6254,plain,(
% 16.95/2.59 ~spl0_75|spl0_96|~spl0_82),
% 16.95/2.59 inference(split_clause,[status(thm)],[f6253,f5953,f6147,f6006])).
% 16.95/2.59 fof(f6332,plain,(
% 16.95/2.59 spl0_115 <=> c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0))=X0),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f6333,plain,(
% 16.95/2.59 ![X0]: (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0))=X0|~spl0_115)),
% 16.95/2.59 inference(component_clause,[status(thm)],[f6332])).
% 16.95/2.59 fof(f6335,plain,(
% 16.95/2.59 ![X0]: (~class_Groups_Ogroup__add(tc_RealDef_Oreal)|c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0))=X0)),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f4975,f2829])).
% 16.95/2.59 fof(f6336,plain,(
% 16.95/2.59 ~spl0_75|spl0_115),
% 16.95/2.59 inference(split_clause,[status(thm)],[f6335,f5953,f6332])).
% 16.95/2.59 fof(f7300,plain,(
% 16.95/2.59 ![X0]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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____)),X0))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))|spl0_8)),
% 16.95/2.59 inference(resolution,[status(thm)],[f5276,f1340])).
% 16.95/2.59 fof(f7441,plain,(
% 16.95/2.59 spl0_245 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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____)))),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f7443,plain,(
% 16.95/2.59 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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____)))|spl0_245),
% 16.95/2.59 inference(component_clause,[status(thm)],[f7441])).
% 16.95/2.59 fof(f7444,plain,(
% 16.95/2.59 spl0_246 <=> 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f7446,plain,(
% 16.95/2.59 ~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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))|spl0_246),
% 16.95/2.59 inference(component_clause,[status(thm)],[f7444])).
% 16.95/2.59 fof(f7447,plain,(
% 16.95/2.59 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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____)))|spl0_8|~spl0_82),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f6007,f7300])).
% 16.95/2.59 fof(f7448,plain,(
% 16.95/2.59 ~spl0_245|~spl0_246|spl0_8|~spl0_82),
% 16.95/2.59 inference(split_clause,[status(thm)],[f7447,f7441,f7444,f5268,f6006])).
% 16.95/2.59 fof(f7451,plain,(
% 16.95/2.59 ![X0]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,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____)))|spl0_245)),
% 16.95/2.59 inference(resolution,[status(thm)],[f7443,f1324])).
% 16.95/2.59 fof(f7461,plain,(
% 16.95/2.59 $false|spl0_246),
% 16.95/2.59 inference(forward_subsumption_resolution,[status(thm)],[f7446,f5146])).
% 16.95/2.59 fof(f7462,plain,(
% 16.95/2.59 spl0_246),
% 16.95/2.59 inference(contradiction_clause,[status(thm)],[f7461])).
% 16.95/2.59 fof(f7488,plain,(
% 16.95/2.59 ![X0]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))|spl0_245)),
% 16.95/2.59 inference(resolution,[status(thm)],[f7451,f1340])).
% 16.95/2.59 fof(f7526,plain,(
% 16.95/2.59 spl0_252 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f7528,plain,(
% 16.95/2.59 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))|spl0_252),
% 16.95/2.59 inference(component_clause,[status(thm)],[f7526])).
% 16.95/2.59 fof(f7529,plain,(
% 16.95/2.59 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))|spl0_245|~spl0_82),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f6007,f7488])).
% 16.95/2.59 fof(f7530,plain,(
% 16.95/2.59 ~spl0_0|~spl0_252|spl0_245|~spl0_82),
% 16.95/2.59 inference(split_clause,[status(thm)],[f7529,f5210,f7526,f7441,f6006])).
% 16.95/2.59 fof(f7531,plain,(
% 16.95/2.59 $false|spl0_252),
% 16.95/2.59 inference(forward_subsumption_resolution,[status(thm)],[f7528,f1280])).
% 16.95/2.59 fof(f7532,plain,(
% 16.95/2.59 spl0_252),
% 16.95/2.59 inference(contradiction_clause,[status(thm)],[f7531])).
% 16.95/2.59 fof(f7679,plain,(
% 16.95/2.59 ![X0,X1,X2]: (~class_RealVector_Oreal__normed__vector(X0)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1),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_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X2),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(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,c_Groups_Oplus__class_Oplus(X0,X1,X2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~spl0_9)),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f5272,f1286])).
% 16.95/2.59 fof(f7680,plain,(
% 16.95/2.59 ![X0,X1,X2]: (~class_RealVector_Oreal__normed__vector(X0)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1),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_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X2),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))|~spl0_9)),
% 16.95/2.59 inference(forward_subsumption_resolution,[status(thm)],[f7679,f1315])).
% 16.95/2.59 fof(f7720,plain,(
% 16.95/2.59 ![X0,X1,X2,X3]: (~class_RealVector_Oreal__normed__vector(X0)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))|~class_RealVector_Oreal__normed__vector(X0)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X3),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))|~spl0_9)),
% 16.95/2.59 inference(resolution,[status(thm)],[f7680,f1286])).
% 16.95/2.59 fof(f7721,plain,(
% 16.95/2.59 ![X0,X1,X2,X3]: (~class_RealVector_Oreal__normed__vector(X0)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1),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(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X3),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))|~spl0_9)),
% 16.95/2.59 inference(duplicate_literals_removal,[status(esa)],[f7720])).
% 16.95/2.59 fof(f7765,plain,(
% 16.95/2.59 spl0_267 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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____)))),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f7767,plain,(
% 16.95/2.59 ~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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____)))|spl0_267),
% 16.95/2.59 inference(component_clause,[status(thm)],[f7765])).
% 16.95/2.59 fof(f7826,plain,(
% 16.95/2.59 spl0_280 <=> ~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f7827,plain,(
% 16.95/2.59 ![X0]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|~spl0_280)),
% 16.95/2.59 inference(component_clause,[status(thm)],[f7826])).
% 16.95/2.59 fof(f7829,plain,(
% 16.95/2.59 spl0_281 <=> ~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X2),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f7830,plain,(
% 16.95/2.59 ![X0]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))|~spl0_281)),
% 16.95/2.59 inference(component_clause,[status(thm)],[f7829])).
% 16.95/2.59 fof(f7836,plain,(
% 16.95/2.59 ![X0,X1]: (~class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))|~spl0_9)),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f5207,f7721])).
% 16.95/2.59 fof(f7837,plain,(
% 16.95/2.59 ~spl0_13|~spl0_267|spl0_280|spl0_281|~spl0_9),
% 16.95/2.59 inference(split_clause,[status(thm)],[f7836,f5349,f7765,f7826,f7829,f5271])).
% 16.95/2.59 fof(f8515,plain,(
% 16.95/2.59 ![X0]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~spl0_82)),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f4975,f6018])).
% 16.95/2.59 fof(f8842,plain,(
% 16.95/2.59 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|~spl0_82|spl0_1),
% 16.95/2.59 inference(resolution,[status(thm)],[f8515,f5215])).
% 16.95/2.59 fof(f11077,plain,(
% 16.95/2.59 ![X0]: (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)|~spl0_76)),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f5957,f2568])).
% 16.95/2.59 fof(f11097,plain,(
% 16.95/2.59 spl0_416 <=> 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),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f11098,plain,(
% 16.95/2.59 ![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_416)),
% 16.95/2.59 inference(component_clause,[status(thm)],[f11097])).
% 16.95/2.59 fof(f11100,plain,(
% 16.95/2.59 ![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)),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f2568,f2826])).
% 16.95/2.59 fof(f11101,plain,(
% 16.95/2.59 ~spl0_75|spl0_416),
% 16.95/2.59 inference(split_clause,[status(thm)],[f11100,f5953,f11097])).
% 16.95/2.59 fof(f11118,plain,(
% 16.95/2.59 spl0_419 <=> 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),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f11119,plain,(
% 16.95/2.59 ![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_419)),
% 16.95/2.59 inference(component_clause,[status(thm)],[f11118])).
% 16.95/2.59 fof(f11121,plain,(
% 16.95/2.59 ![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)),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f2568,f2829])).
% 16.95/2.59 fof(f11122,plain,(
% 16.95/2.59 ~spl0_75|spl0_419),
% 16.95/2.59 inference(split_clause,[status(thm)],[f11121,f5953,f11118])).
% 16.95/2.59 fof(f11123,plain,(
% 16.95/2.59 spl0_420 <=> c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0),X1)=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0)),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f11124,plain,(
% 16.95/2.59 ![X0,X1]: (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0),X1)=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0)|~spl0_420)),
% 16.95/2.59 inference(component_clause,[status(thm)],[f11123])).
% 16.95/2.59 fof(f11131,plain,(
% 16.95/2.59 ![X0]: (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0))=X0|~spl0_76|~spl0_115)),
% 16.95/2.59 inference(backward_demodulation,[status(thm)],[f11077,f6333])).
% 16.95/2.59 fof(f11134,plain,(
% 16.95/2.59 ![X0,X1]: (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)|~spl0_76|~spl0_115)),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f11131,f2568])).
% 16.95/2.59 fof(f11147,plain,(
% 16.95/2.59 ![X0,X1]: (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1),X1)=X0|~spl0_76|~spl0_115|~spl0_419)),
% 16.95/2.59 inference(backward_demodulation,[status(thm)],[f11134,f11119])).
% 16.95/2.59 fof(f11148,plain,(
% 16.95/2.59 ![X0,X1]: (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),X1)=X0|~spl0_76|~spl0_115|~spl0_416)),
% 16.95/2.59 inference(backward_demodulation,[status(thm)],[f11134,f11098])).
% 16.95/2.59 fof(f11182,plain,(
% 16.95/2.59 spl0_424 <=> c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0))=X1),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f11183,plain,(
% 16.95/2.59 ![X0,X1]: (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0))=X1|~spl0_424)),
% 16.95/2.59 inference(component_clause,[status(thm)],[f11182])).
% 16.95/2.59 fof(f11185,plain,(
% 16.95/2.59 ![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_76|~spl0_115|~spl0_419)),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f11147,f2140])).
% 16.95/2.59 fof(f11186,plain,(
% 16.95/2.59 ~spl0_77|spl0_424|~spl0_76|~spl0_115|~spl0_419),
% 16.95/2.59 inference(split_clause,[status(thm)],[f11185,f5977,f11182,f5956,f6332,f11118])).
% 16.95/2.59 fof(f11206,plain,(
% 16.95/2.59 ![X0,X1]: (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)|~spl0_424|~spl0_76|~spl0_115|~spl0_416)),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f11148,f11183])).
% 16.95/2.59 fof(f11213,plain,(
% 16.95/2.59 ![X0,X1]: (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1))=X1|~spl0_76|~spl0_115|~spl0_416|~spl0_424)),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f11183,f11148])).
% 16.95/2.59 fof(f11258,plain,(
% 16.95/2.59 ![X0,X1]: (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),X0)=X1|~spl0_424|~spl0_76|~spl0_115|~spl0_416)),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f11206,f11148])).
% 16.95/2.59 fof(f11374,plain,(
% 16.95/2.59 c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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_424|~spl0_76|~spl0_115|~spl0_416|~spl0_9),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f5272,f11258])).
% 16.95/2.59 fof(f11375,plain,(
% 16.95/2.59 c_Groups_Ouminus__class_Ouminus(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_424|~spl0_76|~spl0_115|~spl0_416|~spl0_9),
% 16.95/2.59 inference(forward_demodulation,[status(thm)],[f11077,f11374])).
% 16.95/2.59 fof(f11376,plain,(
% 16.95/2.59 c_Groups_Ouminus__class_Ouminus(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_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))|~spl0_424|~spl0_76|~spl0_115|~spl0_416|~spl0_9),
% 16.95/2.59 inference(forward_demodulation,[status(thm)],[f11206,f11375])).
% 16.95/2.59 fof(f11378,plain,(
% 16.95/2.59 ![X0,X1]: (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1),X0)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)|~spl0_424|~spl0_76|~spl0_115|~spl0_416)),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f2568,f11258])).
% 16.95/2.59 fof(f11658,plain,(
% 16.95/2.59 ![X0,X1]: (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0),X1)=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0)|~spl0_420)),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f2568,f11124])).
% 16.95/2.59 fof(f11742,plain,(
% 16.95/2.59 ![X0,X1]: (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1))=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)|~spl0_416|~spl0_424|~spl0_76|~spl0_115)),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f11134,f11213])).
% 16.95/2.59 fof(f11775,plain,(
% 16.95/2.59 ![X0,X1]: (~class_Groups_Ogroup__add(tc_RealDef_Oreal)|c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0),X1)=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0)|~spl0_424|~spl0_76|~spl0_115|~spl0_416)),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f11378,f2826])).
% 16.95/2.59 fof(f11776,plain,(
% 16.95/2.59 ~spl0_75|spl0_420|~spl0_424|~spl0_76|~spl0_115|~spl0_416),
% 16.95/2.59 inference(split_clause,[status(thm)],[f11775,f5953,f11123,f11182,f5956,f6332,f11097])).
% 16.95/2.59 fof(f11924,plain,(
% 16.95/2.59 ![X0,X1]: (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0),X1)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))|~spl0_416|~spl0_424|~spl0_76|~spl0_115)),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f11742,f11378])).
% 16.95/2.59 fof(f11935,plain,(
% 16.95/2.59 c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(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_424|~spl0_76|~spl0_115|~spl0_416|~spl0_9),
% 16.95/2.59 inference(backward_demodulation,[status(thm)],[f11924,f11376])).
% 16.95/2.59 fof(f11936,plain,(
% 16.95/2.59 c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(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_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))|~spl0_420|~spl0_424|~spl0_76|~spl0_115|~spl0_416|~spl0_9),
% 16.95/2.59 inference(forward_demodulation,[status(thm)],[f11658,f11935])).
% 16.95/2.59 fof(f13162,plain,(
% 16.95/2.59 ~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|~spl0_280),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f5207,f7827])).
% 16.95/2.59 fof(f13163,plain,(
% 16.95/2.59 $false|~spl0_12|~spl0_280),
% 16.95/2.59 inference(forward_subsumption_resolution,[status(thm)],[f13162,f5314])).
% 16.95/2.59 fof(f13164,plain,(
% 16.95/2.59 ~spl0_12|~spl0_280),
% 16.95/2.59 inference(contradiction_clause,[status(thm)],[f13163])).
% 16.95/2.59 fof(f13165,plain,(
% 16.95/2.59 ![X0]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))|c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)=c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)|~spl0_281)),
% 16.95/2.59 inference(resolution,[status(thm)],[f7830,f1329])).
% 16.95/2.59 fof(f13193,plain,(
% 16.95/2.59 spl0_632 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f13195,plain,(
% 16.95/2.59 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))|spl0_632),
% 16.95/2.59 inference(component_clause,[status(thm)],[f13193])).
% 16.95/2.59 fof(f13196,plain,(
% 16.95/2.59 spl0_633 <=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f13197,plain,(
% 16.95/2.59 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)|~spl0_633),
% 16.95/2.59 inference(component_clause,[status(thm)],[f13196])).
% 16.95/2.59 fof(f13199,plain,(
% 16.95/2.59 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)|~spl0_281),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f5207,f13165])).
% 16.95/2.59 fof(f13200,plain,(
% 16.95/2.59 ~spl0_632|spl0_633|~spl0_281),
% 16.95/2.59 inference(split_clause,[status(thm)],[f13199,f13193,f13196,f7829])).
% 16.95/2.59 fof(f13201,plain,(
% 16.95/2.59 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))|spl0_632),
% 16.95/2.59 inference(forward_demodulation,[status(thm)],[f5207,f13195])).
% 16.95/2.59 fof(f13202,plain,(
% 16.95/2.59 $false|spl0_632),
% 16.95/2.59 inference(forward_subsumption_resolution,[status(thm)],[f13201,f1280])).
% 16.95/2.59 fof(f13203,plain,(
% 16.95/2.59 spl0_632),
% 16.95/2.59 inference(contradiction_clause,[status(thm)],[f13202])).
% 16.95/2.59 fof(f13364,plain,(
% 16.95/2.59 spl0_649 <=> c_Groups_Ozero__class_Ozero(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____))),
% 16.95/2.59 introduced(split_symbol_definition)).
% 16.95/2.59 fof(f13365,plain,(
% 16.95/2.59 c_Groups_Ozero__class_Ozero(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____))|~spl0_649),
% 16.95/2.59 inference(component_clause,[status(thm)],[f13364])).
% 16.95/2.59 fof(f13367,plain,(
% 16.95/2.59 ~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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))|c_Groups_Ozero__class_Ozero(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____))|spl0_267),
% 16.95/2.59 inference(resolution,[status(thm)],[f7767,f1329])).
% 16.95/2.59 fof(f13368,plain,(
% 16.95/2.59 ~spl0_246|spl0_649|spl0_267),
% 16.95/2.59 inference(split_clause,[status(thm)],[f13367,f7444,f13364,f7765])).
% 16.95/2.59 fof(f13388,plain,(
% 16.95/2.59 c_Groups_Ozero__class_Ozero(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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~spl0_649|~spl0_9),
% 16.95/2.59 inference(backward_demodulation,[status(thm)],[f13365,f5272])).
% 16.95/2.59 fof(f13389,plain,(
% 16.95/2.59 c_Groups_Ozero__class_Ozero(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____))|~spl0_82|~spl0_649|~spl0_9),
% 16.95/2.59 inference(forward_demodulation,[status(thm)],[f6007,f13388])).
% 16.95/2.59 fof(f13390,plain,(
% 16.95/2.59 c_Groups_Ozero__class_Ozero(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))|~spl0_424|~spl0_76|~spl0_115|~spl0_416|~spl0_82|~spl0_649|~spl0_9),
% 16.95/2.59 inference(forward_demodulation,[status(thm)],[f11206,f13389])).
% 16.95/2.59 fof(f13483,plain,(
% 16.95/2.59 c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|~spl0_424|~spl0_76|~spl0_115|~spl0_416|~spl0_82|~spl0_649|~spl0_9),
% 16.95/2.59 inference(paramodulation,[status(thm)],[f13390,f11742])).
% 16.95/2.59 fof(f13484,plain,(
% 16.95/2.59 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|~spl0_83|~spl0_424|~spl0_76|~spl0_115|~spl0_416|~spl0_82|~spl0_649|~spl0_9),
% 16.95/2.59 inference(forward_demodulation,[status(thm)],[f6020,f13483])).
% 16.95/2.59 fof(f13519,plain,(
% 16.95/2.59 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))|~spl0_83|~spl0_424|~spl0_76|~spl0_115|~spl0_416|~spl0_649|~spl0_9|~spl0_82|spl0_1),
% 16.95/2.59 inference(backward_demodulation,[status(thm)],[f13484,f8842])).
% 16.95/2.59 fof(f13520,plain,(
% 16.95/2.59 ~spl0_252|~spl0_83|~spl0_424|~spl0_76|~spl0_115|~spl0_416|~spl0_649|~spl0_9|~spl0_82|spl0_1),
% 16.95/2.59 inference(split_clause,[status(thm)],[f13519,f7526,f6019,f11182,f5956,f6332,f11097,f13364,f5271,f6006,f5213])).
% 16.95/2.59 fof(f13574,plain,(
% 16.95/2.59 c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(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____))|~spl0_633|~spl0_420|~spl0_424|~spl0_76|~spl0_115|~spl0_416|~spl0_9),
% 16.95/2.59 inference(forward_demodulation,[status(thm)],[f13197,f11936])).
% 16.95/2.59 fof(f13575,plain,(
% 16.95/2.59 c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(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____))|~spl0_96|~spl0_633|~spl0_420|~spl0_424|~spl0_76|~spl0_115|~spl0_416|~spl0_9),
% 16.95/2.59 inference(forward_demodulation,[status(thm)],[f6148,f13574])).
% 16.95/2.59 fof(f13576,plain,(
% 16.95/2.59 c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(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____))|~spl0_96|~spl0_633|~spl0_420|~spl0_424|~spl0_76|~spl0_115|~spl0_416|~spl0_9),
% 17.46/2.64 inference(forward_demodulation,[status(thm)],[f11077,f13575])).
% 17.46/2.64 fof(f13640,plain,(
% 17.46/2.64 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|~spl0_96|~spl0_633|~spl0_420|~spl0_424|~spl0_76|~spl0_115|~spl0_416|~spl0_9),
% 17.46/2.64 inference(forward_demodulation,[status(thm)],[f13576,f5146])).
% 17.46/2.64 fof(f13641,plain,(
% 17.46/2.64 $false|~spl0_82|spl0_1|~spl0_96|~spl0_633|~spl0_420|~spl0_424|~spl0_76|~spl0_115|~spl0_416|~spl0_9),
% 17.46/2.64 inference(forward_subsumption_resolution,[status(thm)],[f13640,f8842])).
% 17.46/2.64 fof(f13642,plain,(
% 17.46/2.64 ~spl0_82|spl0_1|~spl0_96|~spl0_633|~spl0_420|~spl0_424|~spl0_76|~spl0_115|~spl0_416|~spl0_9),
% 17.46/2.64 inference(contradiction_clause,[status(thm)],[f13641])).
% 17.46/2.64 fof(f13643,plain,(
% 17.46/2.64 $false),
% 17.46/2.64 inference(sat_refutation,[status(thm)],[f5217,f5275,f5317,f5319,f5321,f5368,f5960,f5962,f6010,f6016,f6023,f6254,f6336,f7448,f7462,f7530,f7532,f7837,f11101,f11122,f11186,f11776,f13164,f13200,f13203,f13368,f13520,f13642])).
% 17.46/2.64 % SZS output end CNFRefutation for theBenchmark.p
% 17.46/2.65 % Elapsed time: 2.301376 seconds
% 17.46/2.65 % CPU time: 17.454920 seconds
% 17.46/2.65 % Total memory used: 320.756 MB
% 17.46/2.65 % Net memory used: 316.132 MB
%------------------------------------------------------------------------------