%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW215+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 : n001.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 0.22s 0.53s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 10 unt; 0 def)
% Number of atoms : 43 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 44 ( 21 ~; 16 |; 4 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 24 ( 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),v_da____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f61,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
<=> ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1278,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1279,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(negated_conjecture,[status(cth)],[f1278]) ).
fof(f1284,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f1285,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),v_da____),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f1304,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)],[f12]) ).
fof(f1305,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)],[f1304]) ).
fof(f1306,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)],[f1305]) ).
fof(f1475,plain,
! [V_y_2,V_x_2] :
( ( ( V_x_2 != V_y_2
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
inference(NNF_transformation,[status(thm)],[f61]) ).
fof(f1476,plain,
( ! [V_y_2,V_x_2] :
( ( V_x_2 != V_y_2
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) )
| c_Orderings_Oord__class_Oless__eq(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(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
inference(miniscoping,[status(thm)],[f1475]) ).
fof(f1478,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1476]) ).
fof(f4895,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[status(thm)],[f1279]) ).
fof(f5141,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),X0) ),
inference(resolution,[status(thm)],[f1306,f4895]) ).
fof(f5202,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),X0) ),
inference(resolution,[status(thm)],[f1478,f5141]) ).
fof(f5234,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(resolution,[status(thm)],[f5202,f1285]) ).
fof(f5235,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(resolution,[status(thm)],[f5234,f1478]) ).
fof(f5238,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5235,f1284]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW215+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 09:47:17 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.22/0.47 % Drodi V4.1.1
% 0.22/0.53 % Refutation found
% 0.22/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.56 % Elapsed time: 0.195440 seconds
% 0.22/0.56 % CPU time: 0.579533 seconds
% 0.22/0.56 % Total memory used: 212.253 MB
% 0.22/0.56 % Net memory used: 210.656 MB
%------------------------------------------------------------------------------