TSTP Solution File: FLD029-3 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : FLD029-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n026.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 20:16:24 EDT 2024
% Result : Unsatisfiable 18.05s 2.73s
% Output : CNFRefutation 18.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 28
% Syntax : Number of formulae : 104 ( 36 unt; 0 def)
% Number of atoms : 216 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 200 ( 88 ~; 102 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 11 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 65 ( 65 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X,V,W,Y,U,Z] :
( product(X,V,W)
| ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] :
( product(multiplicative_identity,X,X)
| ~ defined(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] :
( product(multiplicative_inverse(X),X,multiplicative_identity)
| sum(additive_identity,X,additive_identity)
| ~ defined(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Y,X,Z] :
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X] :
( defined(multiplicative_inverse(X))
| ~ defined(X)
| sum(additive_identity,X,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X,Y] :
( product(X,Y,multiply(X,Y))
| ~ defined(X)
| ~ defined(Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X,Y] :
( less_or_equal(X,Y)
| less_or_equal(Y,X)
| ~ defined(X)
| ~ defined(Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,hypothesis,
defined(u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,hypothesis,
defined(v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
product(a,u,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
product(a,v,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ product(multiplicative_identity,u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,plain,
! [W,U,Z] :
( ! [V,Y] :
( ! [X] :
( product(X,V,W)
| ~ product(X,Y,U) )
| ~ product(Y,Z,V) )
| ~ product(U,Z,W) ),
inference(miniscoping,[status(esa)],[f6]) ).
fof(f43,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ product(X3,X5,X1)
| ~ product(X4,X5,X2) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f46,plain,
! [X0] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f47,plain,
! [X0] :
( product(multiplicative_inverse(X0),X0,multiplicative_identity)
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f48,plain,
! [X0,X1,X2] :
( product(X0,X1,X2)
| ~ product(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f55,plain,
defined(additive_identity),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f59,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f60,plain,
! [X0] :
( defined(multiplicative_inverse(X0))
| ~ defined(X0)
| sum(additive_identity,X0,additive_identity) ),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f63,plain,
! [Y] :
( ! [X] :
( product(X,Y,multiply(X,Y))
| ~ defined(X) )
| ~ defined(Y) ),
inference(miniscoping,[status(esa)],[f20]) ).
fof(f64,plain,
! [X0,X1] :
( product(X0,X1,multiply(X0,X1))
| ~ defined(X0)
| ~ defined(X1) ),
inference(cnf_transformation,[status(esa)],[f63]) ).
fof(f68,plain,
! [Y] :
( ! [X] :
( less_or_equal(X,Y)
| less_or_equal(Y,X)
| ~ defined(X) )
| ~ defined(Y) ),
inference(miniscoping,[status(esa)],[f23]) ).
fof(f69,plain,
! [X0,X1] :
( less_or_equal(X0,X1)
| less_or_equal(X1,X0)
| ~ defined(X0)
| ~ defined(X1) ),
inference(cnf_transformation,[status(esa)],[f68]) ).
fof(f73,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f74,plain,
defined(a),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f75,plain,
defined(b),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f76,plain,
defined(u),
inference(cnf_transformation,[status(esa)],[f29]) ).
fof(f77,plain,
defined(v),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f78,plain,
~ sum(additive_identity,b,additive_identity),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f79,plain,
product(a,u,b),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f80,plain,
product(a,v,b),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f81,plain,
~ product(multiplicative_identity,u,v),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f88,plain,
product(multiplicative_identity,v,v),
inference(resolution,[status(thm)],[f46,f77]) ).
fof(f89,plain,
product(multiplicative_identity,u,u),
inference(resolution,[status(thm)],[f46,f76]) ).
fof(f92,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(resolution,[status(thm)],[f46,f59]) ).
fof(f94,plain,
product(v,a,b),
inference(resolution,[status(thm)],[f48,f80]) ).
fof(f95,plain,
product(u,a,b),
inference(resolution,[status(thm)],[f48,f79]) ).
fof(f206,plain,
( spl0_4
<=> product(multiplicative_inverse(b),b,multiplicative_identity) ),
introduced(split_symbol_definition) ).
fof(f207,plain,
( product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f209,plain,
( spl0_5
<=> sum(additive_identity,b,additive_identity) ),
introduced(split_symbol_definition) ).
fof(f210,plain,
( sum(additive_identity,b,additive_identity)
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f212,plain,
( product(multiplicative_inverse(b),b,multiplicative_identity)
| sum(additive_identity,b,additive_identity) ),
inference(resolution,[status(thm)],[f47,f75]) ).
fof(f213,plain,
( spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f212,f206,f209]) ).
fof(f253,plain,
( product(b,multiplicative_inverse(b),multiplicative_identity)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f207,f48]) ).
fof(f305,plain,
! [X0,X1,X2] :
( product(v,X0,X1)
| ~ product(a,X2,X0)
| ~ product(b,X2,X1) ),
inference(resolution,[status(thm)],[f94,f43]) ).
fof(f312,plain,
! [X0,X1,X2] :
( product(u,X0,X1)
| ~ product(a,X2,X0)
| ~ product(b,X2,X1) ),
inference(resolution,[status(thm)],[f95,f43]) ).
fof(f430,plain,
! [X0] :
( product(a,X0,multiply(a,X0))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f64,f74]) ).
fof(f483,plain,
( spl0_17
<=> defined(multiplicative_inverse(b)) ),
introduced(split_symbol_definition) ).
fof(f484,plain,
( defined(multiplicative_inverse(b))
| ~ spl0_17 ),
inference(component_clause,[status(thm)],[f483]) ).
fof(f486,plain,
( defined(multiplicative_inverse(b))
| sum(additive_identity,b,additive_identity) ),
inference(resolution,[status(thm)],[f60,f75]) ).
fof(f487,plain,
( spl0_17
| spl0_5 ),
inference(split_clause,[status(thm)],[f486,f483,f209]) ).
fof(f503,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f210,f78]) ).
fof(f504,plain,
~ spl0_5,
inference(contradiction_clause,[status(thm)],[f503]) ).
fof(f514,plain,
( product(a,multiplicative_inverse(b),multiply(a,multiplicative_inverse(b)))
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f484,f430]) ).
fof(f1027,plain,
! [X0] :
( less_or_equal(v,X0)
| less_or_equal(X0,v)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f69,f77]) ).
fof(f1028,plain,
! [X0] :
( less_or_equal(u,X0)
| less_or_equal(X0,u)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f69,f76]) ).
fof(f1029,plain,
! [X0] :
( less_or_equal(b,X0)
| less_or_equal(X0,b)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f69,f75]) ).
fof(f1030,plain,
! [X0] :
( less_or_equal(a,X0)
| less_or_equal(X0,a)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f69,f74]) ).
fof(f1031,plain,
! [X0] :
( less_or_equal(multiplicative_identity,X0)
| less_or_equal(X0,multiplicative_identity)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f69,f59]) ).
fof(f1032,plain,
! [X0] :
( less_or_equal(additive_identity,X0)
| less_or_equal(X0,additive_identity)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f69,f55]) ).
fof(f1081,plain,
! [X0] :
( product(u,multiply(a,multiplicative_inverse(b)),X0)
| ~ product(b,multiplicative_inverse(b),X0)
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f514,f312]) ).
fof(f1083,plain,
! [X0] :
( product(v,multiply(a,multiplicative_inverse(b)),X0)
| ~ product(b,multiplicative_inverse(b),X0)
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f514,f305]) ).
fof(f1277,plain,
! [X0,X1,X2] :
( product(multiplicative_identity,X0,X1)
| ~ product(multiplicative_identity,X2,X0)
| ~ product(multiplicative_identity,X2,X1) ),
inference(resolution,[status(thm)],[f92,f43]) ).
fof(f1280,plain,
( spl0_53
<=> less_or_equal(additive_identity,additive_identity) ),
introduced(split_symbol_definition) ).
fof(f1296,plain,
( product(u,multiply(a,multiplicative_inverse(b)),multiplicative_identity)
| ~ spl0_17
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f1081,f253]) ).
fof(f1306,plain,
( product(multiply(a,multiplicative_inverse(b)),u,multiplicative_identity)
| ~ spl0_17
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f1296,f48]) ).
fof(f1573,plain,
( spl0_77
<=> less_or_equal(v,v) ),
introduced(split_symbol_definition) ).
fof(f1576,plain,
( less_or_equal(v,v)
| less_or_equal(v,v) ),
inference(resolution,[status(thm)],[f1027,f77]) ).
fof(f1577,plain,
spl0_77,
inference(split_clause,[status(thm)],[f1576,f1573]) ).
fof(f1631,plain,
( product(v,multiply(a,multiplicative_inverse(b)),multiplicative_identity)
| ~ spl0_17
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f1083,f253]) ).
fof(f1810,plain,
( spl0_106
<=> less_or_equal(u,u) ),
introduced(split_symbol_definition) ).
fof(f1813,plain,
( less_or_equal(u,u)
| less_or_equal(u,u) ),
inference(resolution,[status(thm)],[f1028,f76]) ).
fof(f1814,plain,
spl0_106,
inference(split_clause,[status(thm)],[f1813,f1810]) ).
fof(f1932,plain,
( spl0_132
<=> less_or_equal(b,b) ),
introduced(split_symbol_definition) ).
fof(f1935,plain,
( less_or_equal(b,b)
| less_or_equal(b,b) ),
inference(resolution,[status(thm)],[f1029,f75]) ).
fof(f1936,plain,
spl0_132,
inference(split_clause,[status(thm)],[f1935,f1932]) ).
fof(f2036,plain,
( spl0_156
<=> less_or_equal(a,a) ),
introduced(split_symbol_definition) ).
fof(f2039,plain,
( less_or_equal(a,a)
| less_or_equal(a,a) ),
inference(resolution,[status(thm)],[f1030,f74]) ).
fof(f2040,plain,
spl0_156,
inference(split_clause,[status(thm)],[f2039,f2036]) ).
fof(f2849,plain,
( spl0_243
<=> less_or_equal(multiplicative_identity,multiplicative_identity) ),
introduced(split_symbol_definition) ).
fof(f2852,plain,
( less_or_equal(multiplicative_identity,multiplicative_identity)
| less_or_equal(multiplicative_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[f1031,f59]) ).
fof(f2853,plain,
spl0_243,
inference(split_clause,[status(thm)],[f2852,f2849]) ).
fof(f2975,plain,
( less_or_equal(additive_identity,additive_identity)
| less_or_equal(additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f1032,f55]) ).
fof(f2976,plain,
spl0_53,
inference(split_clause,[status(thm)],[f2975,f1280]) ).
fof(f6195,plain,
! [X0,X1,X2] :
( product(v,X0,X1)
| ~ product(multiply(a,multiplicative_inverse(b)),X2,X0)
| ~ product(multiplicative_identity,X2,X1)
| ~ spl0_17
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f1631,f43]) ).
fof(f6199,plain,
! [X0] :
( product(v,multiplicative_identity,X0)
| ~ product(multiplicative_identity,u,X0)
| ~ spl0_17
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f6195,f1306]) ).
fof(f6200,plain,
( product(v,multiplicative_identity,u)
| ~ spl0_17
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f6199,f89]) ).
fof(f10092,plain,
( product(multiplicative_identity,v,u)
| ~ spl0_17
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f6200,f48]) ).
fof(f10473,plain,
( spl0_852
<=> sum(additive_identity,additive_identity,multiplicative_identity) ),
introduced(split_symbol_definition) ).
fof(f10474,plain,
( sum(additive_identity,additive_identity,multiplicative_identity)
| ~ spl0_852 ),
inference(component_clause,[status(thm)],[f10473]) ).
fof(f10478,plain,
( $false
| ~ spl0_852 ),
inference(forward_subsumption_resolution,[status(thm)],[f10474,f73]) ).
fof(f10479,plain,
~ spl0_852,
inference(contradiction_clause,[status(thm)],[f10478]) ).
fof(f14403,plain,
! [X0] :
( product(multiplicative_identity,u,X0)
| ~ product(multiplicative_identity,v,X0)
| ~ spl0_17
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f10092,f1277]) ).
fof(f14414,plain,
( product(multiplicative_identity,u,v)
| ~ spl0_17
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f14403,f88]) ).
fof(f14415,plain,
( $false
| ~ spl0_17
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f14414,f81]) ).
fof(f14416,plain,
( ~ spl0_17
| ~ spl0_4 ),
inference(contradiction_clause,[status(thm)],[f14415]) ).
fof(f14417,plain,
$false,
inference(sat_refutation,[status(thm)],[f213,f487,f504,f1577,f1814,f1936,f2040,f2853,f2976,f10479,f14416]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : FLD029-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 23:37:49 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Drodi V3.6.0
% 18.05/2.73 % Refutation found
% 18.05/2.73 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 18.05/2.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 18.79/2.76 % Elapsed time: 2.394789 seconds
% 18.79/2.76 % CPU time: 18.870990 seconds
% 18.79/2.76 % Total memory used: 117.241 MB
% 18.79/2.76 % Net memory used: 111.563 MB
%------------------------------------------------------------------------------