TSTP Solution File: SWW208+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWW208+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n014.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 : Wed May 31 12:44:29 EDT 2023
% Result : Theorem 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 32
% Syntax : Number of formulae : 110 ( 32 unt; 0 def)
% Number of atoms : 246 ( 26 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 228 ( 92 ~; 101 |; 8 &)
% ( 17 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 21 ( 19 usr; 15 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 73 (; 72 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,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(f4,axiom,
! [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,B_n)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [V_x] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2)))
<=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( V_x != V_y
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,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(f33,axiom,
! [V_w] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_w)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,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(f64,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1021,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1074,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1112,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1121,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1123,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1149,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1269,conjecture,
( 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),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
& ! [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)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1270,negated_conjecture,
~ ( 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),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
& ! [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)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(negated_conjecture,[status(cth)],[f1269]) ).
fof(f1274,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)],[f2]) ).
fof(f1276,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)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f1280,plain,
! [X0] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X0)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f1286,plain,
! [V_b,V_a,T_a] :
( ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f1287,plain,
! [T_a] :
( ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ! [V_a] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ! [V_b] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ),
inference(miniscoping,[status(esa)],[f1286]) ).
fof(f1288,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__comm__monoid__add(X0)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X2))) ),
inference(cnf_transformation,[status(esa)],[f1287]) ).
fof(f1298,plain,
! [V_b,V_a,T_a] :
( ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f1299,plain,
! [T_a] :
( ~ class_Groups_Oordered__comm__monoid__add(T_a)
| ! [V_a] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ! [V_b] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
inference(miniscoping,[status(esa)],[f1298]) ).
fof(f1300,plain,
! [X0,X1,X2] :
( ~ class_Groups_Oordered__comm__monoid__add(X0)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,X1),c_Groups_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,X2),c_Groups_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X2)),c_Groups_Ozero__class_Ozero(X0))) ),
inference(cnf_transformation,[status(esa)],[f1299]) ).
fof(f1307,plain,
! [V_a_2,T_a] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2)))
<=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f1308,plain,
! [V_a_2,T_a] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2)))
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2)))
| V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(NNF_transformation,[status(esa)],[f1307]) ).
fof(f1309,plain,
! [T_a] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ( ! [V_a_2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2)))
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ! [V_a_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2)))
| V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
inference(miniscoping,[status(esa)],[f1308]) ).
fof(f1310,plain,
! [X0,X1] :
( ~ class_Groups_Oordered__ab__group__add__abs(X0)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0)),c_Groups_Oabs__class_Oabs(X0,X1)))
| X1 != c_Groups_Ozero__class_Ozero(X0) ),
inference(cnf_transformation,[status(esa)],[f1309]) ).
fof(f1319,plain,
! [V_y,V_x,T_a] :
( ~ class_Rings_Olinordered__idom(T_a)
| V_x = V_y
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ),
inference(pre_NNF_transformation,[status(esa)],[f22]) ).
fof(f1320,plain,
! [T_a] :
( ~ class_Rings_Olinordered__idom(T_a)
| ! [V_y,V_x] :
( V_x = V_y
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ),
inference(miniscoping,[status(esa)],[f1319]) ).
fof(f1321,plain,
! [X0,X1,X2] :
( ~ class_Rings_Olinordered__idom(X0)
| X1 = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,X2),X1)) ),
inference(cnf_transformation,[status(esa)],[f1320]) ).
fof(f1354,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)],[f32]) ).
fof(f1355,plain,
! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X0)),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f1443,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)],[f60]) ).
fof(f1444,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)],[f1443]) ).
fof(f1445,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,X0),X1))
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f1444]) ).
fof(f1458,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f4306,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(cnf_transformation,[status(esa)],[f1021]) ).
fof(f4359,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(cnf_transformation,[status(esa)],[f1074]) ).
fof(f4397,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f1112]) ).
fof(f4406,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f1121]) ).
fof(f4408,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f1123]) ).
fof(f4434,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f1149]) ).
fof(f4607,plain,
( ~ 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),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ? [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)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(pre_NNF_transformation,[status(esa)],[f1270]) ).
fof(f4608,plain,
( ~ 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),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ 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)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(skolemization,[status(esa)],[f4607]) ).
fof(f4609,plain,
( ~ 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),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ 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)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(cnf_transformation,[status(esa)],[f4608]) ).
fof(f4646,plain,
( spl0_0
<=> 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),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
introduced(split_symbol_definition) ).
fof(f4648,plain,
( ~ 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),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| spl0_0 ),
inference(component_clause,[status(thm)],[f4646]) ).
fof(f4649,plain,
( spl0_1
<=> 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)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
introduced(split_symbol_definition) ).
fof(f4651,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)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| spl0_1 ),
inference(component_clause,[status(thm)],[f4649]) ).
fof(f4652,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f4609,f4646,f4649]) ).
fof(f4653,plain,
! [X0] :
( ~ class_Groups_Oordered__ab__group__add__abs(X0)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0)),c_Groups_Oabs__class_Oabs(X0,c_Groups_Ozero__class_Ozero(X0)))) ),
inference(destructive_equality_resolution,[status(esa)],[f1310]) ).
fof(f4830,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X1))
| X0 = X1
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) ),
inference(resolution,[status(thm)],[f1445,f1354]) ).
fof(f4870,plain,
( spl0_12
<=> class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(split_symbol_definition) ).
fof(f4872,plain,
( ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
| spl0_12 ),
inference(component_clause,[status(thm)],[f4870]) ).
fof(f4921,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f4651,f1276]) ).
fof(f4922,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f4921]) ).
fof(f4938,plain,
( spl0_26
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)) ),
introduced(split_symbol_definition) ).
fof(f4940,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
| spl0_26 ),
inference(component_clause,[status(thm)],[f4938]) ).
fof(f4941,plain,
( spl0_27
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
introduced(split_symbol_definition) ).
fof(f4944,plain,
( ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
| ~ hBOOL(hAPP(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 ),
inference(resolution,[status(thm)],[f4648,f1288]) ).
fof(f4945,plain,
( ~ spl0_12
| ~ spl0_26
| ~ spl0_27
| spl0_0 ),
inference(split_clause,[status(thm)],[f4944,f4870,f4938,f4941,f4646]) ).
fof(f4948,plain,
( $false
| spl0_26 ),
inference(forward_subsumption_resolution,[status(thm)],[f4940,f1274]) ).
fof(f4949,plain,
spl0_26,
inference(contradiction_clause,[status(thm)],[f4948]) ).
fof(f5615,plain,
( spl0_111
<=> class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(split_symbol_definition) ).
fof(f5617,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| spl0_111 ),
inference(component_clause,[status(thm)],[f5615]) ).
fof(f5890,plain,
( spl0_137
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(split_symbol_definition) ).
fof(f5891,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl0_137 ),
inference(component_clause,[status(thm)],[f5890]) ).
fof(f5893,plain,
( spl0_138
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
introduced(split_symbol_definition) ).
fof(f5895,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| spl0_138 ),
inference(component_clause,[status(thm)],[f5893]) ).
fof(f5896,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(resolution,[status(thm)],[f4653,f4830]) ).
fof(f5897,plain,
( ~ spl0_111
| spl0_137
| spl0_138 ),
inference(split_clause,[status(thm)],[f5896,f5615,f5890,f5893]) ).
fof(f6034,plain,
( spl0_158
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
introduced(split_symbol_definition) ).
fof(f6036,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| spl0_158 ),
inference(component_clause,[status(thm)],[f6034]) ).
fof(f6200,plain,
( spl0_176
<=> class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
introduced(split_symbol_definition) ).
fof(f6202,plain,
( ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| spl0_176 ),
inference(component_clause,[status(thm)],[f6200]) ).
fof(f6488,plain,
( spl0_209
<=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
introduced(split_symbol_definition) ).
fof(f6489,plain,
( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ spl0_209 ),
inference(component_clause,[status(thm)],[f6488]) ).
fof(f6493,plain,
( ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| hBOOL(hAPP(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_158 ),
inference(resolution,[status(thm)],[f6036,f1321]) ).
fof(f6494,plain,
( ~ spl0_176
| spl0_209
| spl0_27
| spl0_158 ),
inference(split_clause,[status(thm)],[f6493,f6200,f6488,f4941,f6034]) ).
fof(f6495,plain,
( $false
| ~ spl0_209 ),
inference(forward_subsumption_resolution,[status(thm)],[f6489,f1458]) ).
fof(f6496,plain,
~ spl0_209,
inference(contradiction_clause,[status(thm)],[f6495]) ).
fof(f7143,plain,
( $false
| spl0_111 ),
inference(forward_subsumption_resolution,[status(thm)],[f4406,f5617]) ).
fof(f7144,plain,
spl0_111,
inference(contradiction_clause,[status(thm)],[f7143]) ).
fof(f7630,plain,
( ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(resolution,[status(thm)],[f1280,f1300]) ).
fof(f7631,plain,
( ~ spl0_12
| ~ spl0_138
| ~ spl0_158 ),
inference(split_clause,[status(thm)],[f7630,f4870,f5893,f6034]) ).
fof(f7718,plain,
( $false
| spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f4408,f4872]) ).
fof(f7719,plain,
spl0_12,
inference(contradiction_clause,[status(thm)],[f7718]) ).
fof(f8103,plain,
( $false
| spl0_176 ),
inference(forward_subsumption_resolution,[status(thm)],[f4434,f6202]) ).
fof(f8104,plain,
spl0_176,
inference(contradiction_clause,[status(thm)],[f8103]) ).
fof(f8195,plain,
( spl0_336
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
introduced(split_symbol_definition) ).
fof(f8197,plain,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat)
| spl0_336 ),
inference(component_clause,[status(thm)],[f8195]) ).
fof(f8231,plain,
( spl0_342
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
introduced(split_symbol_definition) ).
fof(f8233,plain,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
| spl0_342 ),
inference(component_clause,[status(thm)],[f8231]) ).
fof(f8259,plain,
( spl0_348
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(split_symbol_definition) ).
fof(f8261,plain,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint)
| spl0_348 ),
inference(component_clause,[status(thm)],[f8259]) ).
fof(f8340,plain,
( $false
| spl0_348 ),
inference(forward_subsumption_resolution,[status(thm)],[f8261,f4306]) ).
fof(f8341,plain,
spl0_348,
inference(contradiction_clause,[status(thm)],[f8340]) ).
fof(f8342,plain,
( $false
| spl0_342 ),
inference(forward_subsumption_resolution,[status(thm)],[f8233,f4397]) ).
fof(f8343,plain,
spl0_342,
inference(contradiction_clause,[status(thm)],[f8342]) ).
fof(f8344,plain,
( $false
| spl0_336 ),
inference(forward_subsumption_resolution,[status(thm)],[f8197,f4359]) ).
fof(f8345,plain,
spl0_336,
inference(contradiction_clause,[status(thm)],[f8344]) ).
fof(f8359,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ spl0_137
| spl0_138 ),
inference(forward_demodulation,[status(thm)],[f5891,f5895]) ).
fof(f8360,plain,
( $false
| ~ spl0_137
| spl0_138 ),
inference(forward_subsumption_resolution,[status(thm)],[f8359,f1355]) ).
fof(f8361,plain,
( ~ spl0_137
| spl0_138 ),
inference(contradiction_clause,[status(thm)],[f8360]) ).
fof(f8362,plain,
$false,
inference(sat_refutation,[status(thm)],[f4652,f4922,f4945,f4949,f5897,f6494,f6496,f7144,f7631,f7719,f8104,f8341,f8343,f8345,f8361]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08 % Problem : SWW208+1 : TPTP v8.1.2. Released v5.2.0.
% 0.04/0.09 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.28 % Computer : n014.cluster.edu
% 0.07/0.28 % Model : x86_64 x86_64
% 0.07/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.28 % Memory : 8042.1875MB
% 0.07/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.28 % CPULimit : 300
% 0.07/0.28 % WCLimit : 300
% 0.07/0.28 % DateTime : Tue May 30 10:51:03 EDT 2023
% 0.07/0.28 % CPUTime :
% 0.12/0.33 % Drodi V3.5.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.45 % Elapsed time: 0.167320 seconds
% 0.12/0.45 % CPU time: 0.626536 seconds
% 0.12/0.45 % Memory used: 126.685 MB
%------------------------------------------------------------------------------