TSTP Solution File: ALG371-1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : ALG371-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n015.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 20:11:26 EDT 2024
% Result : Unsatisfiable 6.69s 1.30s
% Output : CNFRefutation 6.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 18
% Syntax : Number of formulae : 65 ( 12 unt; 0 def)
% Number of atoms : 135 ( 13 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 121 ( 51 ~; 62 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f370,axiom,
! [V_w,V_z] :
( c_lessequals(V_w,V_z,tc_RealDef_Oreal)
| c_lessequals(V_z,V_w,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f381,axiom,
! [V_i,V_k,V_j] :
( c_lessequals(V_i,V_k,tc_RealDef_Oreal)
| ~ c_lessequals(V_j,V_k,tc_RealDef_Oreal)
| ~ c_lessequals(V_i,V_j,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f385,axiom,
! [V_x,V_y] :
( c_lessequals(V_x,V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f389,axiom,
! [V_x] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f393,axiom,
! [T_a,V_x] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f400,axiom,
! [V_x,V_y] :
( c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
| V_x = V_y
| ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f412,axiom,
! [V_z,V_w] :
( V_z = V_w
| ~ c_lessequals(V_w,V_z,tc_RealDef_Oreal)
| ~ c_lessequals(V_z,V_w,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f428,negated_conjecture,
c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f429,negated_conjecture,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f489,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1155,plain,
! [X0,X1] :
( c_lessequals(X0,X1,tc_RealDef_Oreal)
| c_lessequals(X1,X0,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(esa)],[f370]) ).
fof(f1172,plain,
! [V_i,V_j] :
( ! [V_k] :
( c_lessequals(V_i,V_k,tc_RealDef_Oreal)
| ~ c_lessequals(V_j,V_k,tc_RealDef_Oreal) )
| ~ c_lessequals(V_i,V_j,tc_RealDef_Oreal) ),
inference(miniscoping,[status(esa)],[f381]) ).
fof(f1173,plain,
! [X0,X1,X2] :
( c_lessequals(X0,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X0,X2,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(esa)],[f1172]) ).
fof(f1179,plain,
! [X0,X1] :
( c_lessequals(X0,X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(esa)],[f385]) ).
fof(f1184,plain,
! [X0] : ~ c_HOL_Oord__class_Oless(X0,X0,tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f389]) ).
fof(f1190,plain,
! [T_a] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ! [V_x] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal) ),
inference(miniscoping,[status(esa)],[f393]) ).
fof(f1191,plain,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0),tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(esa)],[f1190]) ).
fof(f1200,plain,
! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal)
| X0 = X1
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(esa)],[f400]) ).
fof(f1214,plain,
! [X0,X1] :
( X0 = X1
| ~ c_lessequals(X1,X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(esa)],[f412]) ).
fof(f1233,plain,
c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f428]) ).
fof(f1234,plain,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f429]) ).
fof(f1294,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(esa)],[f489]) ).
fof(f1324,plain,
c_lessequals(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolution,[status(thm)],[f1179,f1233]) ).
fof(f1328,plain,
( spl0_3
<=> v_r = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
introduced(split_symbol_definition) ).
fof(f1329,plain,
( v_r = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f1328]) ).
fof(f1333,plain,
( spl0_4
<=> c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
introduced(split_symbol_definition) ).
fof(f1334,plain,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f1333]) ).
fof(f1336,plain,
( spl0_5
<=> c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex) = v_r ),
introduced(split_symbol_definition) ).
fof(f1337,plain,
( c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex) = v_r
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f1336]) ).
fof(f1339,plain,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex) = v_r ),
inference(resolution,[status(thm)],[f1200,f1234]) ).
fof(f1340,plain,
( spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f1339,f1333,f1336]) ).
fof(f1342,plain,
( spl0_6
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
introduced(split_symbol_definition) ).
fof(f1344,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)
| spl0_6 ),
inference(component_clause,[status(thm)],[f1342]) ).
fof(f1345,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1214,f1324]) ).
fof(f1346,plain,
( spl0_3
| ~ spl0_6 ),
inference(split_clause,[status(thm)],[f1345,f1328,f1342]) ).
fof(f1399,plain,
( c_HOL_Oord__class_Oless(v_r,v_r,tc_RealDef_Oreal)
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f1329,f1233]) ).
fof(f1400,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f1399,f1184]) ).
fof(f1401,plain,
~ spl0_3,
inference(contradiction_clause,[status(thm)],[f1400]) ).
fof(f1405,plain,
( c_lessequals(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| spl0_6 ),
inference(resolution,[status(thm)],[f1344,f1155]) ).
fof(f1406,plain,
! [X0] :
( c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X0,v_r,tc_RealDef_Oreal)
| spl0_6 ),
inference(resolution,[status(thm)],[f1405,f1173]) ).
fof(f1795,plain,
( spl0_43
<=> c_lessequals(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(split_symbol_definition) ).
fof(f1796,plain,
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_43 ),
inference(component_clause,[status(thm)],[f1795]) ).
fof(f1797,plain,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| spl0_43 ),
inference(component_clause,[status(thm)],[f1795]) ).
fof(f1983,plain,
( spl0_58
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex) ),
introduced(split_symbol_definition) ).
fof(f1984,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex)
| ~ spl0_58 ),
inference(component_clause,[status(thm)],[f1983]) ).
fof(f1986,plain,
( spl0_59
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(split_symbol_definition) ).
fof(f1988,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| spl0_59 ),
inference(component_clause,[status(thm)],[f1986]) ).
fof(f1989,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_43 ),
inference(resolution,[status(thm)],[f1796,f1214]) ).
fof(f1990,plain,
( spl0_58
| ~ spl0_59
| ~ spl0_43 ),
inference(split_clause,[status(thm)],[f1989,f1983,f1986,f1795]) ).
fof(f2216,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)
| ~ spl0_58 ),
inference(backward_demodulation,[status(thm)],[f1984,f1234]) ).
fof(f2217,plain,
( $false
| spl0_6
| ~ spl0_58 ),
inference(forward_subsumption_resolution,[status(thm)],[f2216,f1344]) ).
fof(f2218,plain,
( spl0_6
| ~ spl0_58 ),
inference(contradiction_clause,[status(thm)],[f2217]) ).
fof(f2219,plain,
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f1334,f1179]) ).
fof(f2305,plain,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| spl0_43
| spl0_6 ),
inference(resolution,[status(thm)],[f1797,f1406]) ).
fof(f2306,plain,
( $false
| ~ spl0_4
| spl0_43
| spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f2305,f2219]) ).
fof(f2307,plain,
( ~ spl0_4
| spl0_43
| spl0_6 ),
inference(contradiction_clause,[status(thm)],[f2306]) ).
fof(f8085,plain,
( spl0_483
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
introduced(split_symbol_definition) ).
fof(f8087,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| spl0_483 ),
inference(component_clause,[status(thm)],[f8085]) ).
fof(f8088,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)
| ~ spl0_5 ),
inference(paramodulation,[status(thm)],[f1337,f1191]) ).
fof(f8089,plain,
( ~ spl0_483
| spl0_6
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f8088,f8085,f1342,f1336]) ).
fof(f8090,plain,
( $false
| spl0_483 ),
inference(forward_subsumption_resolution,[status(thm)],[f8087,f1294]) ).
fof(f8091,plain,
spl0_483,
inference(contradiction_clause,[status(thm)],[f8090]) ).
fof(f8498,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| spl0_59 ),
inference(resolution,[status(thm)],[f1988,f1191]) ).
fof(f8499,plain,
( ~ spl0_483
| spl0_59 ),
inference(split_clause,[status(thm)],[f8498,f8085,f1986]) ).
fof(f8507,plain,
$false,
inference(sat_refutation,[status(thm)],[f1340,f1346,f1401,f1990,f2218,f2307,f8089,f8091,f8499]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ALG371-1 : TPTP v8.1.2. Released v4.1.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 23:52:02 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.40 % Drodi V3.6.0
% 6.69/1.30 % Refutation found
% 6.69/1.30 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 6.69/1.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.38/1.33 % Elapsed time: 0.966941 seconds
% 7.38/1.33 % CPU time: 7.231114 seconds
% 7.38/1.33 % Total memory used: 148.195 MB
% 7.38/1.33 % Net memory used: 146.121 MB
%------------------------------------------------------------------------------