TSTP Solution File: GRP067-1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRP067-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 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 : Wed May 31 12:10:06 EDT 2023
% Result : Unsatisfiable 0.16s 0.36s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 8
% Syntax : Number of formulae : 58 ( 43 unt; 0 def)
% Number of atoms : 76 ( 54 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 15 ~; 15 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 73 (; 73 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : divide(divide(divide(X,X),divide(X,divide(Y,divide(divide(identity,X),Z)))),Z) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = divide(X,divide(identity,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : inverse(X) = divide(identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : identity = divide(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : divide(divide(divide(X0,X0),divide(X0,divide(X1,divide(divide(identity,X0),X2)))),X2) = X1,
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f7,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,divide(identity,X1)),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f8,plain,
! [X0] : inverse(X0) = divide(identity,X0),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f9,plain,
! [X0] : identity = divide(X0,X0),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f10,plain,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f11,plain,
( spl0_0
<=> multiply(inverse(a1),a1) = identity ),
introduced(split_symbol_definition) ).
fof(f13,plain,
( multiply(inverse(a1),a1) != identity
| spl0_0 ),
inference(component_clause,[status(thm)],[f11]) ).
fof(f14,plain,
( spl0_1
<=> multiply(identity,a2) = a2 ),
introduced(split_symbol_definition) ).
fof(f16,plain,
( multiply(identity,a2) != a2
| spl0_1 ),
inference(component_clause,[status(thm)],[f14]) ).
fof(f17,plain,
( spl0_2
<=> multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(split_symbol_definition) ).
fof(f19,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| spl0_2 ),
inference(component_clause,[status(thm)],[f17]) ).
fof(f20,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f10,f11,f14,f17]) ).
fof(f21,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f9,f8]) ).
fof(f23,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f8,f7]) ).
fof(f24,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f23]) ).
fof(f25,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(paramodulation,[status(thm)],[f9,f23]) ).
fof(f26,plain,
! [X0] : multiply(X0,identity) = divide(X0,identity),
inference(paramodulation,[status(thm)],[f21,f23]) ).
fof(f29,plain,
! [X0,X1,X2] : divide(divide(identity,divide(X0,divide(X1,divide(divide(identity,X0),X2)))),X2) = X1,
inference(forward_demodulation,[status(thm)],[f9,f6]) ).
fof(f30,plain,
! [X0,X1,X2] : divide(inverse(divide(X0,divide(X1,divide(divide(identity,X0),X2)))),X2) = X1,
inference(forward_demodulation,[status(thm)],[f8,f29]) ).
fof(f31,plain,
! [X0,X1,X2] : divide(inverse(divide(X0,divide(X1,divide(inverse(X0),X2)))),X2) = X1,
inference(forward_demodulation,[status(thm)],[f8,f30]) ).
fof(f34,plain,
! [X0,X1] : divide(inverse(inverse(divide(X0,divide(inverse(identity),X1)))),X1) = X0,
inference(paramodulation,[status(thm)],[f8,f31]) ).
fof(f35,plain,
! [X0,X1] : divide(inverse(inverse(divide(X0,divide(identity,X1)))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f21,f34]) ).
fof(f36,plain,
! [X0,X1] : divide(inverse(inverse(divide(X0,inverse(X1)))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f8,f35]) ).
fof(f37,plain,
! [X0,X1] : divide(inverse(inverse(multiply(X0,X1))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f23,f36]) ).
fof(f45,plain,
! [X0,X1] : divide(inverse(divide(X0,divide(X1,identity))),inverse(X0)) = X1,
inference(paramodulation,[status(thm)],[f9,f31]) ).
fof(f46,plain,
! [X0,X1] : multiply(inverse(divide(X0,divide(X1,identity))),X0) = X1,
inference(forward_demodulation,[status(thm)],[f23,f45]) ).
fof(f51,plain,
! [X0,X1,X2] : multiply(inverse(divide(X0,divide(X1,divide(inverse(X0),inverse(X2))))),X2) = X1,
inference(paramodulation,[status(thm)],[f31,f23]) ).
fof(f52,plain,
! [X0,X1,X2] : multiply(inverse(divide(X0,divide(X1,multiply(inverse(X0),X2)))),X2) = X1,
inference(forward_demodulation,[status(thm)],[f23,f51]) ).
fof(f68,plain,
! [X0,X1] : divide(multiply(identity,multiply(X0,X1)),X1) = X0,
inference(forward_demodulation,[status(thm)],[f24,f37]) ).
fof(f103,plain,
! [X0] : multiply(inverse(identity),divide(X0,identity)) = X0,
inference(paramodulation,[status(thm)],[f9,f46]) ).
fof(f104,plain,
! [X0] : multiply(identity,divide(X0,identity)) = X0,
inference(forward_demodulation,[status(thm)],[f21,f103]) ).
fof(f177,plain,
! [X0] : multiply(identity,X0) = multiply(identity,multiply(X0,identity)),
inference(paramodulation,[status(thm)],[f68,f104]) ).
fof(f178,plain,
! [X0] : multiply(identity,X0) = multiply(identity,divide(X0,identity)),
inference(forward_demodulation,[status(thm)],[f26,f177]) ).
fof(f179,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[status(thm)],[f104,f178]) ).
fof(f190,plain,
! [X0] : divide(X0,identity) = X0,
inference(backward_demodulation,[status(thm)],[f179,f104]) ).
fof(f191,plain,
! [X0,X1] : divide(multiply(X0,X1),X1) = X0,
inference(backward_demodulation,[status(thm)],[f179,f68]) ).
fof(f193,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(backward_demodulation,[status(thm)],[f179,f24]) ).
fof(f198,plain,
! [X0,X1] : multiply(inverse(divide(X0,X1)),X0) = X1,
inference(backward_demodulation,[status(thm)],[f190,f46]) ).
fof(f272,plain,
! [X0,X1] : divide(X0,X1) = inverse(divide(X1,X0)),
inference(paramodulation,[status(thm)],[f198,f191]) ).
fof(f584,plain,
! [X0,X1,X2] : multiply(divide(divide(X0,multiply(inverse(X1),X2)),X1),X2) = X0,
inference(forward_demodulation,[status(thm)],[f272,f52]) ).
fof(f596,plain,
! [X0,X1,X2] : multiply(multiply(divide(X0,multiply(inverse(inverse(X1)),X2)),X1),X2) = X0,
inference(paramodulation,[status(thm)],[f23,f584]) ).
fof(f597,plain,
! [X0,X1,X2] : multiply(multiply(divide(X0,multiply(X1,X2)),X1),X2) = X0,
inference(forward_demodulation,[status(thm)],[f193,f596]) ).
fof(f1346,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f191,f597]) ).
fof(f2410,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| spl0_2 ),
inference(backward_demodulation,[status(thm)],[f1346,f19]) ).
fof(f2411,plain,
( $false
| spl0_2 ),
inference(trivial_equality_resolution,[status(esa)],[f2410]) ).
fof(f2412,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f2411]) ).
fof(f2467,plain,
( identity != identity
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f25,f13]) ).
fof(f2468,plain,
( $false
| spl0_0 ),
inference(trivial_equality_resolution,[status(esa)],[f2467]) ).
fof(f2469,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f2468]) ).
fof(f2470,plain,
( a2 != a2
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f179,f16]) ).
fof(f2471,plain,
( $false
| spl0_1 ),
inference(trivial_equality_resolution,[status(esa)],[f2470]) ).
fof(f2472,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f2471]) ).
fof(f2473,plain,
$false,
inference(sat_refutation,[status(thm)],[f20,f2412,f2469,f2472]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : GRP067-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 0.08/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n002.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue May 30 11:45:58 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.32 % Drodi V3.5.1
% 0.16/0.36 % Refutation found
% 0.16/0.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.38 % Elapsed time: 0.070023 seconds
% 0.16/0.38 % CPU time: 0.119594 seconds
% 0.16/0.38 % Memory used: 18.415 MB
%------------------------------------------------------------------------------