TSTP Solution File: GRP132-2.002 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRP132-2.002 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n019.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 : Wed May 31 12:10:40 EDT 2023
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 67 ( 7 unt; 0 def)
% Number of atoms : 169 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 205 ( 103 ~; 94 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 9 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 62 (; 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
! [X1,Y1,Z1,X2,Y2,Z2] :
( ~ product(X1,Y1,Z1)
| ~ product(X2,Y2,Z1)
| ~ product(Z2,X1,Y1)
| ~ product(Z2,X2,Y2)
| equalish(Y1,Y2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f19,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f20,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f22,plain,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2) ),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f25,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f10]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f27,plain,
! [W,Z] :
( ! [Y,X] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f11]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| equalish(X0,X3) ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f31,plain,
! [Y1,Y2] :
( ! [X2,Z2] :
( ! [X1] :
( ! [Z1] :
( ~ product(X1,Y1,Z1)
| ~ product(X2,Y2,Z1) )
| ~ product(Z2,X1,Y1) )
| ~ product(Z2,X2,Y2) )
| equalish(Y1,Y2) ),
inference(miniscoping,[status(esa)],[f13]) ).
fof(f32,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X3,X4,X2)
| ~ product(X5,X0,X1)
| ~ product(X5,X3,X4)
| equalish(X1,X4) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( ~ product(e_1,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f20,f28]) ).
fof(f34,plain,
! [X0,X1] :
( ~ product(X0,e_1,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f20,f26]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,e_1,X1)
| ~ product(X2,e_2,X1)
| ~ product(X3,X0,e_1)
| ~ product(X3,X2,e_2) ),
inference(resolution,[status(thm)],[f20,f32]) ).
fof(f43,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_2,e_1)
| product(X0,e_2,e_2) ),
inference(resolution,[status(thm)],[f22,f19]) ).
fof(f44,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_1,e_1)
| product(X0,e_1,e_2) ),
inference(resolution,[status(thm)],[f22,f18]) ).
fof(f45,plain,
( spl0_0
<=> product(e_2,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f46,plain,
( product(e_2,e_2,e_1)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,plain,
( spl0_1
<=> product(e_2,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f49,plain,
( product(e_2,e_2,e_2)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f48]) ).
fof(f51,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f43,f19]) ).
fof(f52,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f51,f45,f48]) ).
fof(f53,plain,
( spl0_2
<=> product(e_1,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f54,plain,
( product(e_1,e_2,e_1)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,plain,
( spl0_3
<=> product(e_1,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f57,plain,
( product(e_1,e_2,e_2)
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[f43,f18]) ).
fof(f60,plain,
( spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f59,f53,f56]) ).
fof(f61,plain,
( spl0_4
<=> product(e_2,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f62,plain,
( product(e_2,e_1,e_1)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,plain,
( spl0_5
<=> product(e_2,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f65,plain,
( product(e_2,e_1,e_2)
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f64]) ).
fof(f67,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[f44,f19]) ).
fof(f68,plain,
( spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f67,f61,f64]) ).
fof(f69,plain,
( spl0_6
<=> product(e_1,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f70,plain,
( product(e_1,e_1,e_1)
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( spl0_7
<=> product(e_1,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f73,plain,
( product(e_1,e_1,e_2)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f75,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f44,f18]) ).
fof(f76,plain,
( spl0_6
| spl0_7 ),
inference(split_clause,[status(thm)],[f75,f69,f72]) ).
fof(f77,plain,
! [X0,X1] :
( ~ product(X0,e_1,e_1)
| ~ product(X1,X0,e_1)
| ~ product(X1,e_1,e_2)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f54,f36]) ).
fof(f78,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f54,f34]) ).
fof(f79,plain,
( $false
| ~ spl0_6
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f78,f70]) ).
fof(f80,plain,
( ~ spl0_6
| ~ spl0_2 ),
inference(contradiction_clause,[status(thm)],[f79]) ).
fof(f84,plain,
( ~ product(e_2,e_1,e_1)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f46,f34]) ).
fof(f85,plain,
( $false
| ~ spl0_4
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f62]) ).
fof(f86,plain,
( ~ spl0_4
| ~ spl0_0 ),
inference(contradiction_clause,[status(thm)],[f85]) ).
fof(f88,plain,
! [X0,X1] :
( ~ product(X0,e_1,e_2)
| ~ product(X1,X0,e_1)
| ~ product(X1,e_1,e_2)
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f57,f36]) ).
fof(f94,plain,
! [X0] :
( ~ product(X0,e_1,e_2)
| ~ product(e_2,X0,e_1)
| ~ spl0_5
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f65,f88]) ).
fof(f97,plain,
( ~ product(e_1,e_2,e_2)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f49,f33]) ).
fof(f98,plain,
( $false
| ~ spl0_3
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f97,f57]) ).
fof(f99,plain,
( ~ spl0_3
| ~ spl0_1 ),
inference(contradiction_clause,[status(thm)],[f98]) ).
fof(f100,plain,
( ~ product(e_1,e_1,e_2)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f65,f33]) ).
fof(f101,plain,
( ~ spl0_7
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f100,f72,f64]) ).
fof(f103,plain,
( ~ product(e_2,e_1,e_2)
| ~ spl0_0
| ~ spl0_5
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f46,f94]) ).
fof(f104,plain,
( $false
| ~ spl0_0
| ~ spl0_5
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f103,f65]) ).
fof(f105,plain,
( ~ spl0_0
| ~ spl0_5
| ~ spl0_3 ),
inference(contradiction_clause,[status(thm)],[f104]) ).
fof(f110,plain,
! [X0] :
( ~ product(X0,e_1,e_1)
| ~ product(e_1,X0,e_1)
| ~ spl0_7
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f73,f77]) ).
fof(f113,plain,
( ~ product(e_1,e_2,e_1)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f62,f110]) ).
fof(f114,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(split_clause,[status(thm)],[f113,f53,f61,f72]) ).
fof(f116,plain,
$false,
inference(sat_refutation,[status(thm)],[f52,f60,f68,f76,f80,f86,f99,f101,f105,f114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP132-2.002 : TPTP v8.1.2. Released v1.2.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue May 30 11:31:25 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.12/0.35 % Drodi V3.5.1
% 0.12/0.36 % Refutation found
% 0.12/0.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.58 % Elapsed time: 0.014207 seconds
% 0.20/0.58 % CPU time: 0.037437 seconds
% 0.20/0.58 % Memory used: 1.991 MB
%------------------------------------------------------------------------------