TSTP Solution File: GRP066-1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GRP066-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n028.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 20:19:08 EDT 2024
% Result : Unsatisfiable 0.16s 0.39s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 8
% Syntax : Number of formulae : 66 ( 51 unt; 0 def)
% Number of atoms : 84 ( 62 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 : 8 ( 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 : 95 ( 95 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : divide(divide(identity,divide(X,divide(Y,divide(divide(divide(X,X),X),Z)))),Z) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = divide(X,divide(identity,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : inverse(X) = divide(identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : identity = divide(X,X),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : divide(divide(identity,divide(X0,divide(X1,divide(divide(divide(X0,X0),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,
! [X0,X1,X2] : divide(inverse(divide(X0,divide(X1,divide(divide(divide(X0,X0),X0),X2)))),X2) = X1,
inference(backward_demodulation,[status(thm)],[f8,f6]) ).
fof(f22,plain,
! [X0,X1,X2] : divide(inverse(divide(X0,divide(X1,divide(divide(identity,X0),X2)))),X2) = X1,
inference(forward_demodulation,[status(thm)],[f9,f21]) ).
fof(f23,plain,
! [X0,X1,X2] : divide(inverse(divide(X0,divide(X1,divide(inverse(X0),X2)))),X2) = X1,
inference(forward_demodulation,[status(thm)],[f8,f22]) ).
fof(f24,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f25,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f9,f8]) ).
fof(f27,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f24]) ).
fof(f28,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(paramodulation,[status(thm)],[f9,f24]) ).
fof(f29,plain,
! [X0] : multiply(X0,identity) = divide(X0,identity),
inference(paramodulation,[status(thm)],[f25,f24]) ).
fof(f37,plain,
! [X0,X1] : divide(inverse(inverse(divide(X0,divide(inverse(identity),X1)))),X1) = X0,
inference(paramodulation,[status(thm)],[f8,f23]) ).
fof(f38,plain,
! [X0,X1] : divide(multiply(identity,divide(X0,divide(inverse(identity),X1))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f27,f37]) ).
fof(f39,plain,
! [X0,X1] : divide(multiply(identity,divide(X0,divide(identity,X1))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f25,f38]) ).
fof(f40,plain,
! [X0,X1] : divide(multiply(identity,divide(X0,inverse(X1))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f8,f39]) ).
fof(f41,plain,
! [X0,X1] : divide(multiply(identity,multiply(X0,X1)),X1) = X0,
inference(forward_demodulation,[status(thm)],[f24,f40]) ).
fof(f49,plain,
! [X0,X1] : divide(inverse(divide(X0,divide(X1,identity))),inverse(X0)) = X1,
inference(paramodulation,[status(thm)],[f9,f23]) ).
fof(f50,plain,
! [X0,X1] : multiply(inverse(divide(X0,divide(X1,identity))),X0) = X1,
inference(forward_demodulation,[status(thm)],[f24,f49]) ).
fof(f70,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,multiply(identity,X1)),
inference(paramodulation,[status(thm)],[f27,f24]) ).
fof(f77,plain,
! [X0,X1] : multiply(multiply(identity,multiply(X0,multiply(identity,X1))),inverse(X1)) = X0,
inference(paramodulation,[status(thm)],[f41,f70]) ).
fof(f109,plain,
! [X0] : divide(multiply(identity,divide(X0,identity)),identity) = X0,
inference(paramodulation,[status(thm)],[f29,f41]) ).
fof(f136,plain,
! [X0] : multiply(inverse(identity),divide(X0,identity)) = X0,
inference(paramodulation,[status(thm)],[f9,f50]) ).
fof(f137,plain,
! [X0] : multiply(identity,divide(X0,identity)) = X0,
inference(forward_demodulation,[status(thm)],[f25,f136]) ).
fof(f149,plain,
! [X0,X1] : divide(multiply(identity,X0),X1) = inverse(divide(X1,divide(X0,identity))),
inference(paramodulation,[status(thm)],[f50,f41]) ).
fof(f150,plain,
! [X0] : divide(X0,identity) = X0,
inference(backward_demodulation,[status(thm)],[f137,f109]) ).
fof(f156,plain,
! [X0,X1] : divide(multiply(identity,X0),X1) = inverse(divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f150,f149]) ).
fof(f157,plain,
! [X0] : multiply(identity,X0) = X0,
inference(backward_demodulation,[status(thm)],[f150,f137]) ).
fof(f173,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,X1),
inference(backward_demodulation,[status(thm)],[f157,f70]) ).
fof(f180,plain,
! [X0,X1] : multiply(multiply(X0,multiply(identity,X1)),inverse(X1)) = X0,
inference(backward_demodulation,[status(thm)],[f157,f77]) ).
fof(f181,plain,
! [X0,X1] : divide(multiply(X0,multiply(identity,X1)),X1) = X0,
inference(forward_demodulation,[status(thm)],[f173,f180]) ).
fof(f182,plain,
! [X0,X1] : divide(multiply(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f157,f181]) ).
fof(f186,plain,
! [X0,X1] : divide(X0,X1) = inverse(divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f157,f156]) ).
fof(f195,plain,
! [X0,X1,X2] : divide(divide(divide(X0,divide(inverse(X1),X2)),X1),X2) = X0,
inference(backward_demodulation,[status(thm)],[f186,f23]) ).
fof(f231,plain,
! [X0,X1,X2] : divide(divide(X0,X1),X2) = multiply(X0,divide(inverse(X1),X2)),
inference(paramodulation,[status(thm)],[f182,f195]) ).
fof(f372,plain,
! [X0,X1,X2] : multiply(X0,divide(X1,X2)) = divide(X0,divide(X2,X1)),
inference(paramodulation,[status(thm)],[f186,f173]) ).
fof(f379,plain,
! [X0,X1,X2] : divide(divide(X0,X1),X2) = divide(X0,divide(X2,inverse(X1))),
inference(backward_demodulation,[status(thm)],[f372,f231]) ).
fof(f380,plain,
! [X0,X1,X2] : divide(divide(X0,X1),X2) = divide(X0,multiply(X2,X1)),
inference(forward_demodulation,[status(thm)],[f24,f379]) ).
fof(f454,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = divide(X0,divide(inverse(X2),X1)),
inference(paramodulation,[status(thm)],[f24,f372]) ).
fof(f495,plain,
! [X0,X1,X2] : divide(multiply(X0,X1),X2) = divide(X0,multiply(X2,inverse(X1))),
inference(paramodulation,[status(thm)],[f24,f380]) ).
fof(f496,plain,
! [X0,X1,X2] : divide(multiply(X0,X1),X2) = divide(X0,divide(X2,X1)),
inference(forward_demodulation,[status(thm)],[f173,f495]) ).
fof(f540,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = divide(X0,divide(inverse(X2),X1)),
inference(paramodulation,[status(thm)],[f24,f496]) ).
fof(f541,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(forward_demodulation,[status(thm)],[f454,f540]) ).
fof(f582,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| spl0_2 ),
inference(backward_demodulation,[status(thm)],[f541,f19]) ).
fof(f583,plain,
( $false
| spl0_2 ),
inference(trivial_equality_resolution,[status(esa)],[f582]) ).
fof(f584,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f583]) ).
fof(f586,plain,
( identity != identity
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f28,f13]) ).
fof(f587,plain,
( $false
| spl0_0 ),
inference(trivial_equality_resolution,[status(esa)],[f586]) ).
fof(f588,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f587]) ).
fof(f589,plain,
( a2 != a2
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f157,f16]) ).
fof(f590,plain,
( $false
| spl0_1 ),
inference(trivial_equality_resolution,[status(esa)],[f589]) ).
fof(f591,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f590]) ).
fof(f592,plain,
$false,
inference(sat_refutation,[status(thm)],[f20,f584,f588,f591]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP066-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 0.03/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.34 % Computer : n028.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8042.1875MB
% 0.10/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Tue Apr 30 00:36:14 EDT 2024
% 0.10/0.35 % CPUTime :
% 0.10/0.35 % Drodi V3.6.0
% 0.16/0.39 % Refutation found
% 0.16/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.41 % Elapsed time: 0.056733 seconds
% 0.16/0.41 % CPU time: 0.268484 seconds
% 0.16/0.41 % Total memory used: 42.266 MB
% 0.16/0.41 % Net memory used: 41.328 MB
%------------------------------------------------------------------------------