TSTP Solution File: SWW178+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWW178+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.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 93.35s 12.16s
% Output : CNFRefutation 93.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 22
% Syntax : Number of formulae : 92 ( 36 unt; 0 def)
% Number of atoms : 155 ( 40 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 120 ( 57 ~; 50 |; 0 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 119 ( 119 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [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)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [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 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [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 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_RealVector_Onorm__class_Onorm(T_a,V_x) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f62,axiom,
! [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 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,axiom,
! [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) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,axiom,
! [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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f77,axiom,
! [V_r] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f82,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f87,axiom,
! [V_a,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)) = c_RealVector_Onorm__class_Onorm(T_a,V_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f89,axiom,
! [V_y,V_x] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_x,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,V_y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f102,axiom,
! [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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1109,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1137,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1149,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1169,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1189,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1200,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1201,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z))),
inference(negated_conjecture,[status(cth)],[f1200]) ).
fof(f1205,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z))),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f1212,plain,
! [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)) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f1213,plain,
! [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)) ),
inference(miniscoping,[status(esa)],[f1212]) ).
fof(f1214,plain,
! [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)) ),
inference(cnf_transformation,[status(esa)],[f1213]) ).
fof(f1240,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f1299,plain,
! [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 ),
inference(pre_NNF_transformation,[status(esa)],[f28]) ).
fof(f1300,plain,
! [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 ),
inference(miniscoping,[status(esa)],[f1299]) ).
fof(f1301,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ogroup__add(X0)
| c_Groups_Ominus__class_Ominus(X0,c_Groups_Oplus__class_Oplus(X0,X1,X2),X2) = X1 ),
inference(cnf_transformation,[status(esa)],[f1300]) ).
fof(f1302,plain,
! [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 ),
inference(pre_NNF_transformation,[status(esa)],[f29]) ).
fof(f1303,plain,
! [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 ),
inference(miniscoping,[status(esa)],[f1302]) ).
fof(f1304,plain,
! [X0,X1,X2] :
( ~ class_Groups_Ogroup__add(X0)
| c_Groups_Oplus__class_Oplus(X0,c_Groups_Ominus__class_Ominus(X0,X1,X2),X2) = X1 ),
inference(cnf_transformation,[status(esa)],[f1303]) ).
fof(f1320,plain,
! [V_x,T_a] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_RealVector_Onorm__class_Onorm(T_a,V_x) ),
inference(pre_NNF_transformation,[status(esa)],[f35]) ).
fof(f1321,plain,
! [T_a] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ! [V_x] : c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_RealVector_Onorm__class_Onorm(T_a,V_x) ),
inference(miniscoping,[status(esa)],[f1320]) ).
fof(f1322,plain,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ouminus__class_Ouminus(X0,X1)) = c_RealVector_Onorm__class_Onorm(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1321]) ).
fof(f1413,plain,
! [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 ),
inference(pre_NNF_transformation,[status(esa)],[f62]) ).
fof(f1414,plain,
! [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 ),
inference(cnf_transformation,[status(esa)],[f1413]) ).
fof(f1415,plain,
! [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) ),
inference(pre_NNF_transformation,[status(esa)],[f63]) ).
fof(f1416,plain,
! [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) ) ),
inference(miniscoping,[status(esa)],[f1415]) ).
fof(f1417,plain,
! [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) ),
inference(cnf_transformation,[status(esa)],[f1416]) ).
fof(f1418,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f1457,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(cnf_transformation,[status(esa)],[f77]) ).
fof(f1468,plain,
! [V_a,T_a] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) ),
inference(pre_NNF_transformation,[status(esa)],[f82]) ).
fof(f1469,plain,
! [T_a] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ! [V_a] : c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) ),
inference(miniscoping,[status(esa)],[f1468]) ).
fof(f1470,plain,
! [X0,X1] :
( ~ class_Groups_Oordered__ab__group__add__abs(X0)
| c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Oabs__class_Oabs(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f1469]) ).
fof(f1483,plain,
! [V_a,T_a] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)) = c_RealVector_Onorm__class_Onorm(T_a,V_a) ),
inference(pre_NNF_transformation,[status(esa)],[f87]) ).
fof(f1484,plain,
! [T_a] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ! [V_a] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)) = c_RealVector_Onorm__class_Onorm(T_a,V_a) ),
inference(miniscoping,[status(esa)],[f1483]) ).
fof(f1485,plain,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1)) = c_RealVector_Onorm__class_Onorm(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1484]) ).
fof(f1487,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),
inference(cnf_transformation,[status(esa)],[f89]) ).
fof(f1523,plain,
! [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) ),
inference(pre_NNF_transformation,[status(esa)],[f102]) ).
fof(f1524,plain,
! [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) ),
inference(miniscoping,[status(esa)],[f1523]) ).
fof(f1525,plain,
! [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) ),
inference(cnf_transformation,[status(esa)],[f1524]) ).
fof(f4406,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f1109]) ).
fof(f4434,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f1137]) ).
fof(f4446,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f1149]) ).
fof(f4466,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(esa)],[f1169]) ).
fof(f4486,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(esa)],[f1189]) ).
fof(f4497,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z))),
inference(cnf_transformation,[status(esa)],[f1201]) ).
fof(f4646,plain,
( spl0_0
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z)))) ),
introduced(split_symbol_definition) ).
fof(f4648,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z))))
| spl0_0 ),
inference(component_clause,[status(thm)],[f4646]) ).
fof(f4649,plain,
( spl0_1
<=> c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z))) ),
introduced(split_symbol_definition) ).
fof(f4650,plain,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z)))
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f4649]) ).
fof(f4652,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z))))
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z))) ),
inference(resolution,[status(thm)],[f1414,f1205]) ).
fof(f4653,plain,
( ~ spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f4652,f4646,f4649]) ).
fof(f5436,plain,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z),v_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z)))
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f1487,f4650]) ).
fof(f7923,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1),X1) = X0,
inference(resolution,[status(thm)],[f1304,f4446]) ).
fof(f8535,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),X1) = X0,
inference(resolution,[status(thm)],[f4486,f1301]) ).
fof(f8862,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0),
inference(resolution,[status(thm)],[f1322,f4466]) ).
fof(f11324,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)),
inference(resolution,[status(thm)],[f1470,f4406]) ).
fof(f11325,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)),
inference(forward_demodulation,[status(thm)],[f1457,f11324]) ).
fof(f11971,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z))) ),
inference(resolution,[status(thm)],[f4497,f1417]) ).
fof(f14367,plain,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1)) = c_RealVector_Onorm__class_Onorm(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f1457,f1485]) ).
fof(f14368,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0),
inference(resolution,[status(thm)],[f14367,f4466]) ).
fof(f15384,plain,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z)))
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f8535,f5436]) ).
fof(f15609,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z)),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z)) ),
inference(resolution,[status(thm)],[f11971,f1214]) ).
fof(f16889,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),
inference(resolution,[status(thm)],[f1525,f4434]) ).
fof(f19245,plain,
! [X0,X1] : X0 = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1)),
inference(paramodulation,[status(thm)],[f7923,f16889]) ).
fof(f21783,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z),v_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f1487,f4648]) ).
fof(f21784,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f8535,f21783]) ).
fof(f30369,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f8862,f21784]) ).
fof(f32400,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z)) ),
inference(paramodulation,[status(thm)],[f19245,f15609]) ).
fof(f37913,plain,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z)))
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f8862,f15384]) ).
fof(f40297,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z)),
inference(resolution,[status(thm)],[f32400,f11325]) ).
fof(f40298,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z)),
inference(forward_demodulation,[status(thm)],[f14368,f40297]) ).
fof(f40312,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z)),
inference(resolution,[status(thm)],[f32400,f1240]) ).
fof(f40317,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_w,v_z)))),
inference(resolution,[status(thm)],[f40298,f1418]) ).
fof(f40318,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f40317,f30369]) ).
fof(f40319,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f40318]) ).
fof(f45765,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z))
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f37913,f40312]) ).
fof(f45766,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f45765,f1240]) ).
fof(f45767,plain,
~ spl0_1,
inference(contradiction_clause,[status(thm)],[f45766]) ).
fof(f45768,plain,
$false,
inference(sat_refutation,[status(thm)],[f4653,f40319,f45767]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : SWW178+1 : TPTP v8.1.2. Released v5.2.0.
% 0.05/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.34 % Computer : n032.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8042.1875MB
% 0.09/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Apr 29 23:09:35 EDT 2024
% 0.09/0.34 % CPUTime :
% 0.14/0.41 % Drodi V3.6.0
% 93.35/12.16 % Refutation found
% 93.35/12.16 % SZS status Theorem for theBenchmark: Theorem is valid
% 93.35/12.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 94.05/12.26 % Elapsed time: 11.910334 seconds
% 94.05/12.26 % CPU time: 93.930787 seconds
% 94.05/12.26 % Total memory used: 563.929 MB
% 94.05/12.26 % Net memory used: 555.212 MB
%------------------------------------------------------------------------------