TSTP Solution File: FLD041-4 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : FLD041-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n002.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 20:16:28 EDT 2024
% Result : Unsatisfiable 8.07s 1.49s
% Output : CNFRefutation 8.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 30
% Syntax : Number of formulae : 103 ( 34 unt; 0 def)
% Number of atoms : 223 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 223 ( 103 ~; 111 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 10 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 125 ( 125 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,V,W,Y,U,Z] :
( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [U,Z,W,X,Y,V] :
( sum(U,Z,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(X,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] :
( sum(additive_identity,X,X)
| ~ defined(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( sum(additive_inverse(X),X,additive_identity)
| ~ defined(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y,X,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f11,axiom,
! [C,D,B,X,Y,A,Z] :
( sum(C,D,B)
| ~ sum(X,Y,A)
| ~ product(A,Z,B)
| ~ product(X,Z,C)
| ~ product(Y,Z,D) ),
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(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(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
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,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
sum(additive_identity,c,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,plain,
! [W,U,Z] :
( ! [V,Y] :
( ! [X] :
( sum(X,V,W)
| ~ sum(X,Y,U) )
| ~ sum(Y,Z,V) )
| ~ sum(U,Z,W) ),
inference(miniscoping,[status(esa)],[f1]) ).
fof(f35,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X1,X2)
| ~ sum(X0,X3,X4)
| ~ sum(X3,X5,X1)
| ~ sum(X4,X5,X2) ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f36,plain,
! [W,X,V] :
( ! [Z,Y] :
( ! [U] :
( sum(U,Z,W)
| ~ sum(X,Y,U) )
| ~ sum(Y,Z,V) )
| ~ sum(X,V,W) ),
inference(miniscoping,[status(esa)],[f2]) ).
fof(f37,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X1,X2)
| ~ sum(X3,X4,X0)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X5,X2) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
! [X0] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f39,plain,
! [X0] :
( sum(additive_inverse(X0),X0,additive_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f40,plain,
! [X0,X1,X2] :
( sum(X0,X1,X2)
| ~ sum(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f41,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(f42,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)],[f41]) ).
fof(f45,plain,
! [X0] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f46,plain,
! [X0] :
( product(multiplicative_inverse(X0),X0,multiplicative_identity)
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f47,plain,
! [X0,X1,X2] :
( product(X0,X1,X2)
| ~ product(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f48,plain,
! [D,Y,Z] :
( ! [C,X] :
( ! [B,A] :
( sum(C,D,B)
| ~ sum(X,Y,A)
| ~ product(A,Z,B) )
| ~ product(X,Z,C) )
| ~ product(Y,Z,D) ),
inference(miniscoping,[status(esa)],[f11]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( sum(X0,X1,X2)
| ~ sum(X3,X4,X5)
| ~ product(X5,X6,X2)
| ~ product(X3,X6,X0)
| ~ product(X4,X6,X1) ),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f54,plain,
defined(additive_identity),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f58,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f67,plain,
! [Y] :
( ! [X] :
( less_or_equal(X,Y)
| less_or_equal(Y,X)
| ~ defined(X) )
| ~ defined(Y) ),
inference(miniscoping,[status(esa)],[f23]) ).
fof(f68,plain,
! [X0,X1] :
( less_or_equal(X0,X1)
| less_or_equal(X1,X0)
| ~ defined(X0)
| ~ defined(X1) ),
inference(cnf_transformation,[status(esa)],[f67]) ).
fof(f72,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f73,plain,
defined(a),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f74,plain,
defined(b),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f75,plain,
defined(c),
inference(cnf_transformation,[status(esa)],[f29]) ).
fof(f76,plain,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f77,plain,
~ sum(additive_identity,b,additive_identity),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f78,plain,
product(a,b,c),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f79,plain,
sum(additive_identity,c,additive_identity),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f81,plain,
sum(additive_identity,c,c),
inference(resolution,[status(thm)],[f38,f75]) ).
fof(f85,plain,
sum(c,additive_identity,additive_identity),
inference(resolution,[status(thm)],[f40,f79]) ).
fof(f103,plain,
product(multiplicative_identity,b,b),
inference(resolution,[status(thm)],[f45,f74]) ).
fof(f108,plain,
sum(additive_inverse(b),b,additive_identity),
inference(resolution,[status(thm)],[f39,f74]) ).
fof(f181,plain,
( spl0_5
<=> sum(additive_identity,b,additive_identity) ),
introduced(split_symbol_definition) ).
fof(f182,plain,
( sum(additive_identity,b,additive_identity)
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f186,plain,
( spl0_6
<=> product(multiplicative_inverse(a),a,multiplicative_identity) ),
introduced(split_symbol_definition) ).
fof(f187,plain,
( product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,plain,
( spl0_7
<=> sum(additive_identity,a,additive_identity) ),
introduced(split_symbol_definition) ).
fof(f190,plain,
( sum(additive_identity,a,additive_identity)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,plain,
( product(multiplicative_inverse(a),a,multiplicative_identity)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[f46,f73]) ).
fof(f193,plain,
( spl0_6
| spl0_7 ),
inference(split_clause,[status(thm)],[f192,f186,f189]) ).
fof(f209,plain,
! [X0,X1,X2] :
( product(multiplicative_inverse(a),X0,X1)
| ~ product(a,X2,X0)
| ~ product(multiplicative_identity,X2,X1)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f187,f42]) ).
fof(f212,plain,
! [X0] :
( product(multiplicative_inverse(a),c,X0)
| ~ product(multiplicative_identity,b,X0)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f209,f78]) ).
fof(f259,plain,
! [X0,X1,X2] :
( sum(c,X0,X1)
| ~ sum(additive_identity,X2,X0)
| ~ sum(additive_identity,X2,X1) ),
inference(resolution,[status(thm)],[f85,f35]) ).
fof(f286,plain,
! [X0] :
( sum(c,c,X0)
| ~ sum(additive_identity,c,X0) ),
inference(resolution,[status(thm)],[f259,f81]) ).
fof(f289,plain,
sum(c,c,c),
inference(resolution,[status(thm)],[f286,f81]) ).
fof(f378,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f190,f76]) ).
fof(f379,plain,
~ spl0_7,
inference(contradiction_clause,[status(thm)],[f378]) ).
fof(f380,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f182,f77]) ).
fof(f381,plain,
~ spl0_5,
inference(contradiction_clause,[status(thm)],[f380]) ).
fof(f384,plain,
! [X0] :
( less_or_equal(multiplicative_identity,X0)
| less_or_equal(X0,multiplicative_identity)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f68,f58]) ).
fof(f385,plain,
! [X0] :
( less_or_equal(c,X0)
| less_or_equal(X0,c)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f68,f75]) ).
fof(f386,plain,
! [X0] :
( less_or_equal(b,X0)
| less_or_equal(X0,b)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f68,f74]) ).
fof(f387,plain,
! [X0] :
( less_or_equal(a,X0)
| less_or_equal(X0,a)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f68,f73]) ).
fof(f388,plain,
! [X0] :
( less_or_equal(additive_identity,X0)
| less_or_equal(X0,additive_identity)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f68,f54]) ).
fof(f561,plain,
! [X0,X1,X2,X3] :
( sum(X0,X1,X2)
| ~ product(c,X3,X2)
| ~ product(c,X3,X0)
| ~ product(c,X3,X1) ),
inference(resolution,[status(thm)],[f289,f49]) ).
fof(f747,plain,
( spl0_37
<=> less_or_equal(additive_identity,additive_identity) ),
introduced(split_symbol_definition) ).
fof(f1275,plain,
( product(multiplicative_inverse(a),c,b)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f103,f212]) ).
fof(f1656,plain,
! [X0,X1,X2] :
( sum(additive_identity,X0,X1)
| ~ sum(b,X0,X2)
| ~ sum(additive_inverse(b),X2,X1) ),
inference(resolution,[status(thm)],[f108,f37]) ).
fof(f1705,plain,
( product(c,multiplicative_inverse(a),b)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f1275,f47]) ).
fof(f2522,plain,
( spl0_188
<=> less_or_equal(c,c) ),
introduced(split_symbol_definition) ).
fof(f2525,plain,
( less_or_equal(c,c)
| less_or_equal(c,c) ),
inference(resolution,[status(thm)],[f385,f75]) ).
fof(f2526,plain,
spl0_188,
inference(split_clause,[status(thm)],[f2525,f2522]) ).
fof(f2720,plain,
( spl0_236
<=> less_or_equal(b,b) ),
introduced(split_symbol_definition) ).
fof(f2723,plain,
( less_or_equal(b,b)
| less_or_equal(b,b) ),
inference(resolution,[status(thm)],[f386,f74]) ).
fof(f2724,plain,
spl0_236,
inference(split_clause,[status(thm)],[f2723,f2720]) ).
fof(f2975,plain,
( spl0_280
<=> less_or_equal(multiplicative_identity,multiplicative_identity) ),
introduced(split_symbol_definition) ).
fof(f2978,plain,
( less_or_equal(multiplicative_identity,multiplicative_identity)
| less_or_equal(multiplicative_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[f384,f58]) ).
fof(f2979,plain,
spl0_280,
inference(split_clause,[status(thm)],[f2978,f2975]) ).
fof(f3460,plain,
( spl0_369
<=> less_or_equal(a,a) ),
introduced(split_symbol_definition) ).
fof(f3463,plain,
( less_or_equal(a,a)
| less_or_equal(a,a) ),
inference(resolution,[status(thm)],[f387,f73]) ).
fof(f3464,plain,
spl0_369,
inference(split_clause,[status(thm)],[f3463,f3460]) ).
fof(f3619,plain,
( less_or_equal(additive_identity,additive_identity)
| less_or_equal(additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f388,f54]) ).
fof(f3620,plain,
spl0_37,
inference(split_clause,[status(thm)],[f3619,f747]) ).
fof(f4723,plain,
! [X0,X1] :
( sum(X0,X1,b)
| ~ product(c,multiplicative_inverse(a),X0)
| ~ product(c,multiplicative_inverse(a),X1)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f1705,f561]) ).
fof(f4794,plain,
! [X0] :
( sum(b,X0,b)
| ~ product(c,multiplicative_inverse(a),X0)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f4723,f1705]) ).
fof(f4796,plain,
( sum(b,b,b)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f4794,f1705]) ).
fof(f6612,plain,
( spl0_716
<=> sum(additive_identity,additive_identity,multiplicative_identity) ),
introduced(split_symbol_definition) ).
fof(f6613,plain,
( sum(additive_identity,additive_identity,multiplicative_identity)
| ~ spl0_716 ),
inference(component_clause,[status(thm)],[f6612]) ).
fof(f6617,plain,
( $false
| ~ spl0_716 ),
inference(forward_subsumption_resolution,[status(thm)],[f6613,f72]) ).
fof(f6618,plain,
~ spl0_716,
inference(contradiction_clause,[status(thm)],[f6617]) ).
fof(f8147,plain,
! [X0] :
( sum(additive_identity,b,X0)
| ~ sum(additive_inverse(b),b,X0)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f4796,f1656]) ).
fof(f8161,plain,
( sum(additive_identity,b,additive_identity)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f8147,f108]) ).
fof(f8162,plain,
( spl0_5
| ~ spl0_6 ),
inference(split_clause,[status(thm)],[f8161,f181,f186]) ).
fof(f8163,plain,
$false,
inference(sat_refutation,[status(thm)],[f193,f379,f381,f2526,f2724,f2979,f3464,f3620,f6618,f8162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : FLD041-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n002.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Mon Apr 29 23:38:54 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % Drodi V3.6.0
% 8.07/1.49 % Refutation found
% 8.07/1.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 8.07/1.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.07/1.53 % Elapsed time: 1.199447 seconds
% 8.07/1.53 % CPU time: 8.197033 seconds
% 8.07/1.53 % Total memory used: 72.517 MB
% 8.07/1.53 % Net memory used: 67.320 MB
%------------------------------------------------------------------------------