TSTP Solution File: GRP004-2 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRP004-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n008.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 12:09:40 EDT 2023
% Result : Unsatisfiable 0.19s 0.37s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 13 unt; 0 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 54 ( 28 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 68 (; 68 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : product(identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : product(inverse(X),X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z,W] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| equalish(Z,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,U,Z,V,W] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W)
| product(X,V,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,W,Z] :
( ~ equalish(X,Y)
| ~ product(W,Z,X)
| product(W,Z,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ product(a,inverse(a),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f10,plain,
! [X0] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f11,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f12,plain,
! [Z,W] :
( ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) )
| equalish(Z,W) ),
inference(miniscoping,[status(esa)],[f4]) ).
fof(f13,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| equalish(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f14,plain,
! [X,V,W] :
( ! [U,Z] :
( ! [Y] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V) )
| ~ product(U,Z,W) )
| product(X,V,W) ),
inference(miniscoping,[status(esa)],[f5]) ).
fof(f15,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X1,X3,X4)
| ~ product(X2,X3,X5)
| product(X0,X4,X5) ),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f18,plain,
! [Y,W,Z] :
( ! [X] :
( ~ equalish(X,Y)
| ~ product(W,Z,X) )
| product(W,Z,Y) ),
inference(miniscoping,[status(esa)],[f7]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( ~ equalish(X0,X1)
| ~ product(X2,X3,X0)
| product(X2,X3,X1) ),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f20,plain,
~ product(a,inverse(a),identity),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,identity)
| ~ product(X1,X2,X3)
| product(X0,X3,X2) ),
inference(resolution,[status(thm)],[f15,f9]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| product(inverse(X0),X2,X1) ),
inference(resolution,[status(thm)],[f26,f10]) ).
fof(f73,plain,
! [X0,X1] : product(inverse(X0),multiply(X0,X1),X1),
inference(resolution,[status(thm)],[f11,f59]) ).
fof(f132,plain,
! [X0,X1] : product(inverse(inverse(X0)),X1,multiply(X0,X1)),
inference(resolution,[status(thm)],[f73,f59]) ).
fof(f233,plain,
! [X0,X1] :
( ~ product(inverse(X0),X0,X1)
| equalish(X1,identity) ),
inference(resolution,[status(thm)],[f13,f10]) ).
fof(f253,plain,
! [X0,X1,X2] :
( ~ equalish(multiply(X0,X1),X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f19,f11]) ).
fof(f291,plain,
! [X0] : equalish(multiply(X0,inverse(X0)),identity),
inference(resolution,[status(thm)],[f233,f132]) ).
fof(f839,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(resolution,[status(thm)],[f253,f291]) ).
fof(f843,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f20,f839]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP004-2 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 11:29:38 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.35 % Drodi V3.5.1
% 0.19/0.37 % Refutation found
% 0.19/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.38 % Elapsed time: 0.039828 seconds
% 0.19/0.38 % CPU time: 0.176299 seconds
% 0.19/0.38 % Memory used: 10.129 MB
%------------------------------------------------------------------------------