%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW234+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 : n018.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 03:07:29 PM UTC 2026
% Result : Theorem 20.15s 3.09s
% Output : CNFRefutation 17.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 48 ( 20 unt; 4 def)
% Number of atoms : 96 ( 2 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 91 ( 43 ~; 38 |; 0 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 49 ( 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,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(f15,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,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(f40,axiom,
! [V_a,V_b,V_c,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1120,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1122,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1274,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1275,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(negated_conjecture,[status(cth)],[f1274]) ).
fof(f1286,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f1287,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f1289,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)],[f9]) ).
fof(f1290,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)],[f1289]) ).
fof(f1291,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)],[f1290]) ).
fof(f1309,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f1310,plain,
! [T_a] :
( ! [V_a] : c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(miniscoping,[status(thm)],[f1309]) ).
fof(f1311,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oabs__class_Oabs(X0,X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f1310]) ).
fof(f1316,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f1401,plain,
! [V_a,V_b,V_c,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f1402,plain,
! [T_a] :
( ! [V_c] :
( ! [V_a,V_b] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) )
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(miniscoping,[status(thm)],[f1401]) ).
fof(f1403,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Oplus__class_Oplus(X0,X3,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ class_Groups_Oordered__comm__monoid__add(X0) ),
inference(cnf_transformation,[status(thm)],[f1402]) ).
fof(f4568,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f1120]) ).
fof(f4570,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f1122]) ).
fof(f4782,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(cnf_transformation,[status(thm)],[f1275]) ).
fof(f4805,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(backward_demodulation,[status(thm)],[f1316,f1286]) ).
fof(f5102,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) ),
inference(resolution,[status(thm)],[f1291,f4782]) ).
fof(f5636,definition,
( sQ42_spl
<=> class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f5638,plain,
( sQ42_spl
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f5636]) ).
fof(f5656,plain,
( sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5638,f4570]) ).
fof(f5657,plain,
sQ42_spl,
inference(contradiction_clause,[status(thm)],[f5656]) ).
fof(f6660,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)),
inference(resolution,[status(thm)],[f4568,f1311]) ).
fof(f6666,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)),
inference(forward_demodulation,[status(thm)],[f1316,f6660]) ).
fof(f6819,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(resolution,[status(thm)],[f5102,f1403]) ).
fof(f6827,definition,
! [X0,X1] :
( sQ133_spl
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f6828,plain,
! [X0,X1] :
( ~ sQ133_spl
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(component_clause,[status(thm)],[f6827]) ).
fof(f6830,plain,
( ~ sQ42_spl
| sQ133_spl ),
inference(split_clause,[status(thm)],[f6819,f6827,f5636]) ).
fof(f6989,definition,
( sQ139_spl
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f6991,plain,
( sQ139_spl
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(component_clause,[status(thm)],[f6989]) ).
fof(f9664,definition,
( sQ253_spl
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_r____)) ),
introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition]) ).
fof(f9666,plain,
( sQ253_spl
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_r____)) ),
inference(component_clause,[status(thm)],[f9664]) ).
fof(f9671,plain,
( sQ253_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9666,f6666]) ).
fof(f9672,plain,
sQ253_spl,
inference(contradiction_clause,[status(thm)],[f9671]) ).
fof(f10545,plain,
( ~ sQ133_spl
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_r____)) ),
inference(resolution,[status(thm)],[f6828,f4805]) ).
fof(f10549,plain,
( ~ sQ133_spl
| ~ sQ139_spl
| ~ sQ253_spl ),
inference(split_clause,[status(thm)],[f10545,f9664,f6989,f6827]) ).
fof(f10550,plain,
( sQ139_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6991,f1287]) ).
fof(f10551,plain,
sQ139_spl,
inference(contradiction_clause,[status(thm)],[f10550]) ).
fof(f10552,plain,
$false,
inference(sat_refutation,[status(thm)],[f5657,f6830,f9672,f10549,f10551]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW234+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 09:44:59 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.45 % Drodi V4.1.1
% 20.15/3.09 % Refutation found
% 20.15/3.09 % SZS status Theorem for theBenchmark: Theorem is valid
% 20.15/3.09 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 17.15/3.16 % Elapsed time: 2.794491 seconds
% 17.15/3.16 % CPU time: 21.153904 seconds
% 17.15/3.16 % Total memory used: 381.258 MB
% 17.15/3.16 % Net memory used: 368.775 MB
%------------------------------------------------------------------------------