%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW238+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 03:07:30 PM UTC 2026
% Result : Theorem 0.46s 1.20s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 10 unt; 0 def)
% Number of atoms : 18 ( 5 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 3 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 18 ( 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [V_z,V_w] : 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f1188,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1272,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)),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_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1273,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)),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_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))),
inference(negated_conjecture,[status(cth)],[f1272]) ).
fof(f1278,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,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,X0,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f1462,plain,
! [V_c,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f66]) ).
fof(f1463,plain,
! [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)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(miniscoping,[status(thm)],[f1462]) ).
fof(f1464,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X0,X1,X2) = c_Groups_Oplus__class_Oplus(X0,X2,X1)
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(thm)],[f1463]) ).
fof(f4768,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f1188]) ).
fof(f4910,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)),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_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))),
inference(cnf_transformation,[status(thm)],[f1273]) ).
fof(f6493,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0),
inference(resolution,[status(thm)],[f1464,f4768]) ).
fof(f10393,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____),v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))),
inference(paramodulation,[status(thm)],[f6493,f4910]) ).
fof(f10408,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f10393,f1278]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW238+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.49 % Computer : n007.cluster.edu
% 0.17/0.49 % Model : x86_64 x86_64
% 0.17/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.49 % Memory : 8046.5625MB
% 0.17/0.49 % OS : Linux 6.8.0-71-generic
% 0.17/0.49 % CPULimit : 300
% 0.17/0.49 % WCLimit : 300
% 0.17/0.49 % DateTime : Mon Sep 21 09:40:36 UTC 2026
% 0.17/0.49 % CPUTime :
% 0.31/0.67 % Drodi V4.1.1
% 0.46/1.20 % Refutation found
% 0.46/1.20 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.46/1.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.46/1.26 % Elapsed time: 0.760374 seconds
% 0.46/1.26 % CPU time: 4.466465 seconds
% 0.46/1.26 % Total memory used: 246.482 MB
% 0.46/1.26 % Net memory used: 243.331 MB
%------------------------------------------------------------------------------