TSTP Solution File: SWW207+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWW207+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n008.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 20:49:50 EDT 2024
% Result : Theorem 0.19s 0.55s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of formulae : 84 ( 19 unt; 0 def)
% Number of atoms : 198 ( 39 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 195 ( 81 ~; 92 |; 11 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-2 aty)
% Number of variables : 87 ( 84 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,B_n))),v_r)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
& V_x_2 != V_y_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
| V_x_2 = V_y_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [V_w,V_z] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z))
=> V_z = V_w ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_j))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j),V_k))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_k)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [V_w,V_z] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f133,axiom,
! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f203,axiom,
hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f570,axiom,
! [V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)) = c_RealDef_Oreal(tc_Nat_Onat,V_x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1269,conjecture,
? [B_K] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
& ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,B_n)))))),B_K)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1270,negated_conjecture,
~ ? [B_K] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
& ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,B_n)))))),B_K)) ),
inference(negated_conjecture,[status(cth)],[f1269]) ).
fof(f1276,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f1302,plain,
! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X0))),v_r)),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f1303,plain,
! [V_y_2,V_x_2] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
& V_x_2 != V_y_2 ) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
| V_x_2 = V_y_2 ) ),
inference(NNF_transformation,[status(esa)],[f13]) ).
fof(f1304,plain,
( ! [V_y_2,V_x_2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
| ( hBOOL(hAPP(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] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
| V_x_2 = V_y_2 ) ),
inference(miniscoping,[status(esa)],[f1303]) ).
fof(f1305,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1)) ),
inference(cnf_transformation,[status(esa)],[f1304]) ).
fof(f1306,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X1))
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f1304]) ).
fof(f1307,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f1304]) ).
fof(f1308,plain,
! [V_y_2,V_x_2] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
| V_x_2 = V_y_2 )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
& V_x_2 != V_y_2 ) ) ),
inference(NNF_transformation,[status(esa)],[f14]) ).
fof(f1309,plain,
( ! [V_y_2,V_x_2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
| hBOOL(hAPP(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] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
& V_x_2 != V_y_2 ) ) ),
inference(miniscoping,[status(esa)],[f1308]) ).
fof(f1312,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f1309]) ).
fof(f1452,plain,
! [V_w,V_z] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z))
| V_z = V_w ),
inference(pre_NNF_transformation,[status(esa)],[f56]) ).
fof(f1453,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0))
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f1452]) ).
fof(f1454,plain,
! [V_k,V_j,V_i] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_j))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j),V_k))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_k)) ),
inference(pre_NNF_transformation,[status(esa)],[f57]) ).
fof(f1455,plain,
! [V_j,V_i] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_j))
| ! [V_k] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j),V_k))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_k)) ) ),
inference(miniscoping,[status(esa)],[f1454]) ).
fof(f1456,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X2)) ),
inference(cnf_transformation,[status(esa)],[f1455]) ).
fof(f1457,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) ),
inference(cnf_transformation,[status(esa)],[f58]) ).
fof(f1549,plain,
! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X0))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0))),
inference(cnf_transformation,[status(esa)],[f84]) ).
fof(f1713,plain,
! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)))),
inference(cnf_transformation,[status(esa)],[f133]) ).
fof(f1907,plain,
hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f203]) ).
fof(f3033,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0)) = c_RealDef_Oreal(tc_Nat_Onat,X0),
inference(cnf_transformation,[status(esa)],[f570]) ).
fof(f4607,plain,
! [B_K] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
| ? [B_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,B_n)))))),B_K)) ),
inference(pre_NNF_transformation,[status(esa)],[f1270]) ).
fof(f4608,plain,
! [B_K] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(B_K))))))),B_K)) ),
inference(skolemization,[status(esa)],[f4607]) ).
fof(f4609,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(X0))))))),X0)) ),
inference(cnf_transformation,[status(esa)],[f4608]) ).
fof(f4648,plain,
! [X0] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X0)),
inference(destructive_equality_resolution,[status(esa)],[f1306]) ).
fof(f4649,plain,
! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X0)),
inference(destructive_equality_resolution,[status(esa)],[f1312]) ).
fof(f4779,plain,
( spl0_0
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)) ),
introduced(split_symbol_definition) ).
fof(f4780,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f4779]) ).
fof(f4782,plain,
( spl0_1
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r ),
introduced(split_symbol_definition) ).
fof(f4783,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f4782]) ).
fof(f4785,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r ),
inference(resolution,[status(thm)],[f1276,f1307]) ).
fof(f4786,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f4785,f4779,f4782]) ).
fof(f4809,plain,
( hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = v_r
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f4783,f1907]) ).
fof(f4812,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(X0))))))),X0))
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f4783,f4609]) ).
fof(f4818,plain,
! [X0] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(X0))))))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ),
inference(resolution,[status(thm)],[f1457,f4609]) ).
fof(f4819,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X0))
| X1 = X0 ),
inference(resolution,[status(thm)],[f1457,f1307]) ).
fof(f4823,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(v_r))))))))
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f4818,f4780]) ).
fof(f4824,plain,
( spl0_6
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(v_r))))))),v_r)) ),
introduced(split_symbol_definition) ).
fof(f4826,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(v_r))))))),v_r))
| spl0_6 ),
inference(component_clause,[status(thm)],[f4824]) ).
fof(f4827,plain,
( spl0_7
<=> v_r = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(v_r)))))) ),
introduced(split_symbol_definition) ).
fof(f4828,plain,
( v_r = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(v_r))))))
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f4827]) ).
fof(f4830,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(v_r))))))),v_r))
| v_r = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(v_r))))))
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f4823,f1453]) ).
fof(f4831,plain,
( ~ spl0_6
| spl0_7
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f4830,f4824,f4827,f4779]) ).
fof(f4845,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X0))),X1)) ),
inference(resolution,[status(thm)],[f1549,f1456]) ).
fof(f4908,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f1907,f4809]) ).
fof(f4910,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),X0))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(X0))))))))
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f4812,f1457]) ).
fof(f4972,plain,
( spl0_26
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),v_r)) ),
introduced(split_symbol_definition) ).
fof(f4974,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),v_r))
| spl0_26 ),
inference(component_clause,[status(thm)],[f4972]) ).
fof(f4975,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),v_r))
| ~ spl0_7 ),
inference(paramodulation,[status(thm)],[f4828,f4609]) ).
fof(f4976,plain,
( ~ spl0_0
| ~ spl0_26
| ~ spl0_7 ),
inference(split_clause,[status(thm)],[f4975,f4779,f4972,f4827]) ).
fof(f4985,plain,
( $false
| spl0_26 ),
inference(forward_subsumption_resolution,[status(thm)],[f4974,f4649]) ).
fof(f4986,plain,
spl0_26,
inference(contradiction_clause,[status(thm)],[f4985]) ).
fof(f5021,plain,
! [X0] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),v_r))
| v_r = X0
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(X0))))))))
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f4819,f4910]) ).
fof(f5066,plain,
! [X0] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0))))
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f4908,f1713]) ).
fof(f5068,plain,
! [X0] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0))))
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f5066,f1305]) ).
fof(f5069,plain,
! [X0] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X0))))
| ~ spl0_1 ),
inference(paramodulation,[status(thm)],[f3033,f5066]) ).
fof(f5099,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),v_r))
| v_r = X0
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(X0))))))),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f5021,f1456]) ).
fof(f5102,plain,
! [X0] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),v_r))
| v_r = X0
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(X0)))))))
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f5099,f1549]) ).
fof(f5110,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),v_r))
| v_r = X0
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(X0)))))),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f5102,f1456]) ).
fof(f5158,plain,
! [X0] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X0))))
| ~ spl0_1 ),
inference(paramodulation,[status(thm)],[f3033,f5068]) ).
fof(f5670,plain,
! [X0] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),v_r))
| v_r = X0
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),v_r))
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f1302,f5110]) ).
fof(f5671,plain,
! [X0] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),v_r))
| v_r = X0
| ~ spl0_1 ),
inference(duplicate_literals_removal,[status(esa)],[f5670]) ).
fof(f5672,plain,
! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X0)))),v_r)),
inference(resolution,[status(thm)],[f1302,f4845]) ).
fof(f5685,plain,
! [X0] :
( v_r = X0
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),X0))
| X0 = v_r
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f5671,f1453]) ).
fof(f5686,plain,
! [X0] :
( v_r = X0
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),X0))
| ~ spl0_1 ),
inference(duplicate_literals_removal,[status(esa)],[f5685]) ).
fof(f5691,plain,
! [X0] :
( v_r = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X0))
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f5686,f5158]) ).
fof(f5713,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),v_r))
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f5691,f5069]) ).
fof(f5714,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f5713,f4648]) ).
fof(f5715,plain,
~ spl0_1,
inference(contradiction_clause,[status(thm)],[f5714]) ).
fof(f5945,plain,
( $false
| spl0_6 ),
inference(backward_subsumption_resolution,[status(thm)],[f4826,f5672]) ).
fof(f5946,plain,
spl0_6,
inference(contradiction_clause,[status(thm)],[f5945]) ).
fof(f5947,plain,
$false,
inference(sat_refutation,[status(thm)],[f4786,f4831,f4976,f4986,f5715,f5946]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SWW207+1 : TPTP v8.1.2. Released v5.2.0.
% 0.09/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Apr 29 23:09:42 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.43 % Drodi V3.6.0
% 0.19/0.55 % Refutation found
% 0.19/0.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.58 % Elapsed time: 0.236212 seconds
% 0.19/0.58 % CPU time: 1.075763 seconds
% 0.19/0.58 % Total memory used: 174.297 MB
% 0.19/0.58 % Net memory used: 173.345 MB
%------------------------------------------------------------------------------