%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW217+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:07:27 PM UTC 2026
% Result : Theorem 0.12s 0.51s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 13 unt; 0 def)
% Number of atoms : 70 ( 18 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 70 ( 32 ~; 28 |; 5 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 35 ( 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____),v_e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f120,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(f121,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(f132,axiom,
! [V_y_2,V_x_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) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1260,conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),v_e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1261,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),v_e),
inference(negated_conjecture,[status(cth)],[f1260]) ).
fof(f1268,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____),v_e),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f1276,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f1599,plain,
! [V_w,V_z] :
( V_z = V_w
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w) ),
inference(pre_NNF_transformation,[status(thm)],[f120]) ).
fof(f1600,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1599]) ).
fof(f1601,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,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_j) ),
inference(pre_NNF_transformation,[status(thm)],[f121]) ).
fof(f1602,plain,
! [V_j,V_i] :
( ! [V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,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_j) ),
inference(miniscoping,[status(thm)],[f1601]) ).
fof(f1603,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1602]) ).
fof(f1630,plain,
! [V_y_2,V_x_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
& 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) ) ),
inference(NNF_transformation,[status(thm)],[f132]) ).
fof(f1631,plain,
( ! [V_y_2,V_x_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_y_2,V_x_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) ) ),
inference(miniscoping,[status(thm)],[f1630]) ).
fof(f1632,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1631]) ).
fof(f1633,plain,
! [X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1631]) ).
fof(f1634,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1631]) ).
fof(f4748,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),v_e),
inference(cnf_transformation,[status(thm)],[f1261]) ).
fof(f4836,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f1633]) ).
fof(f5061,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) = v_e
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),v_e) ),
inference(resolution,[status(thm)],[f1634,f4748]) ).
fof(f5069,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,v_e)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),X0)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) = v_e ),
inference(resolution,[status(thm)],[f5061,f1603]) ).
fof(f5112,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,v_e)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),X0)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) = v_e ),
inference(resolution,[status(thm)],[f5069,f1632]) ).
fof(f5117,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) = v_e ),
inference(resolution,[status(thm)],[f5112,f1268]) ).
fof(f5120,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) = v_e,
inference(forward_subsumption_resolution,[status(thm)],[f5117,f1276]) ).
fof(f5176,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____)),
inference(backward_demodulation,[status(thm)],[f5120,f1276]) ).
fof(f5191,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____) = v_e
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____),v_e) ),
inference(resolution,[status(thm)],[f5176,f1600]) ).
fof(f5252,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____),v_e)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____) = v_e ),
inference(resolution,[status(thm)],[f5191,f1632]) ).
fof(f5256,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____) = v_e,
inference(forward_subsumption_resolution,[status(thm)],[f5252,f1268]) ).
fof(f5260,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e,v_e),
inference(backward_demodulation,[status(thm)],[f5256,f1268]) ).
fof(f5274,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5260,f4836]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW217+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n012.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 09:41:36 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.45 % Drodi V4.1.1
% 0.12/0.51 % Refutation found
% 0.12/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.56 % Elapsed time: 0.192836 seconds
% 0.12/0.56 % CPU time: 0.478557 seconds
% 0.12/0.56 % Total memory used: 159.805 MB
% 0.12/0.56 % Net memory used: 158.822 MB
%------------------------------------------------------------------------------