TSTP Solution File: GRP109-1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GRP109-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n014.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 20:19:15 EDT 2024
% Result : Unsatisfiable 0.20s 0.47s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 58 ( 34 unt; 0 def)
% Number of atoms : 88 ( 54 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 55 ( 25 ~; 26 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 74 ( 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : double_divide(inverse(double_divide(X,inverse(double_divide(inverse(Y),double_divide(X,Z))))),Z) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = inverse(double_divide(Y,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : double_divide(inverse(double_divide(X0,inverse(double_divide(inverse(X1),double_divide(X0,X2))))),X2) = X1,
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f5,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f6,plain,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4) ),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f7,plain,
( spl0_0
<=> multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
introduced(split_symbol_definition) ).
fof(f9,plain,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| spl0_0 ),
inference(component_clause,[status(thm)],[f7]) ).
fof(f10,plain,
( spl0_1
<=> multiply(multiply(inverse(b2),b2),a2) = a2 ),
introduced(split_symbol_definition) ).
fof(f12,plain,
( multiply(multiply(inverse(b2),b2),a2) != a2
| spl0_1 ),
inference(component_clause,[status(thm)],[f10]) ).
fof(f13,plain,
( spl0_2
<=> multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(split_symbol_definition) ).
fof(f15,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| spl0_2 ),
inference(component_clause,[status(thm)],[f13]) ).
fof(f16,plain,
( spl0_3
<=> multiply(a4,b4) = multiply(b4,a4) ),
introduced(split_symbol_definition) ).
fof(f18,plain,
( multiply(a4,b4) != multiply(b4,a4)
| spl0_3 ),
inference(component_clause,[status(thm)],[f16]) ).
fof(f19,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f6,f7,f10,f13,f16]) ).
fof(f20,plain,
! [X0,X1,X2] : double_divide(inverse(double_divide(X0,multiply(double_divide(X0,X1),inverse(X2)))),X1) = X2,
inference(backward_demodulation,[status(thm)],[f5,f4]) ).
fof(f21,plain,
! [X0,X1,X2] : double_divide(multiply(multiply(double_divide(X0,X1),inverse(X2)),X0),X1) = X2,
inference(forward_demodulation,[status(thm)],[f5,f20]) ).
fof(f22,plain,
! [X0,X1,X2,X3] : double_divide(multiply(multiply(X0,inverse(X1)),multiply(multiply(double_divide(X2,X3),inverse(X0)),X2)),X3) = X1,
inference(paramodulation,[status(thm)],[f21,f21]) ).
fof(f24,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(double_divide(X1,X0),inverse(X2)),X1)) = inverse(X2),
inference(paramodulation,[status(thm)],[f21,f5]) ).
fof(f26,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(double_divide(X1,X0),multiply(X2,X3)),X1)) = inverse(double_divide(X3,X2)),
inference(paramodulation,[status(thm)],[f5,f24]) ).
fof(f27,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(double_divide(X1,X0),multiply(X2,X3)),X1)) = multiply(X2,X3),
inference(forward_demodulation,[status(thm)],[f5,f26]) ).
fof(f48,plain,
! [X0,X1] : double_divide(inverse(X0),multiply(X0,inverse(X1))) = X1,
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f66,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X1)),inverse(X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f48,f5]) ).
fof(f67,plain,
! [X0,X1] : multiply(inverse(X0),inverse(multiply(X1,inverse(X0)))) = inverse(X1),
inference(paramodulation,[status(thm)],[f66,f66]) ).
fof(f71,plain,
! [X0,X1] : double_divide(inverse(multiply(X0,inverse(X1))),inverse(X1)) = X0,
inference(paramodulation,[status(thm)],[f66,f48]) ).
fof(f84,plain,
! [X0,X1] : double_divide(inverse(inverse(X0)),inverse(X1)) = multiply(X1,inverse(X0)),
inference(paramodulation,[status(thm)],[f67,f48]) ).
fof(f91,plain,
! [X0,X1,X2] : double_divide(inverse(multiply(X0,X1)),inverse(X2)) = multiply(X2,inverse(double_divide(X1,X0))),
inference(paramodulation,[status(thm)],[f5,f84]) ).
fof(f92,plain,
! [X0,X1,X2] : double_divide(inverse(multiply(X0,X1)),inverse(X2)) = multiply(X2,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f5,f91]) ).
fof(f100,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X0))) = X1,
inference(backward_demodulation,[status(thm)],[f92,f71]) ).
fof(f105,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,inverse(double_divide(X2,X0))),
inference(paramodulation,[status(thm)],[f100,f27]) ).
fof(f106,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X0,X2)),
inference(forward_demodulation,[status(thm)],[f5,f105]) ).
fof(f117,plain,
! [X0,X1] : X0 = multiply(X0,multiply(X1,inverse(X1))),
inference(paramodulation,[status(thm)],[f100,f106]) ).
fof(f166,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,multiply(X2,inverse(X2)))) = multiply(X1,X0),
inference(paramodulation,[status(thm)],[f117,f106]) ).
fof(f167,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f117,f166]) ).
fof(f172,plain,
( $false
| spl0_3 ),
inference(backward_subsumption_resolution,[status(thm)],[f18,f167]) ).
fof(f173,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f172]) ).
fof(f174,plain,
( multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f167,f15]) ).
fof(f175,plain,
( multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3))
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f106,f174]) ).
fof(f176,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f167,f175]) ).
fof(f177,plain,
( $false
| spl0_2 ),
inference(trivial_equality_resolution,[status(esa)],[f176]) ).
fof(f178,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f177]) ).
fof(f179,plain,
( multiply(a1,inverse(a1)) != multiply(inverse(b1),b1)
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f167,f9]) ).
fof(f180,plain,
( multiply(a1,inverse(a1)) != multiply(b1,inverse(b1))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f167,f179]) ).
fof(f214,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f167,f100]) ).
fof(f227,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X2,X0)),
inference(paramodulation,[status(thm)],[f167,f106]) ).
fof(f450,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f117,f214]) ).
fof(f453,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(paramodulation,[status(thm)],[f117,f214]) ).
fof(f467,plain,
! [X0,X1] : double_divide(X0,inverse(X1)) = multiply(X1,inverse(X0)),
inference(backward_demodulation,[status(thm)],[f450,f84]) ).
fof(f497,plain,
( $false
| spl0_0 ),
inference(backward_subsumption_resolution,[status(thm)],[f180,f453]) ).
fof(f498,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f497]) ).
fof(f500,plain,
! [X0,X1] : multiply(X0,double_divide(X0,inverse(X1))) = X1,
inference(backward_demodulation,[status(thm)],[f467,f100]) ).
fof(f599,plain,
( multiply(a2,multiply(inverse(b2),b2)) != a2
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f167,f12]) ).
fof(f600,plain,
( multiply(b2,multiply(a2,inverse(b2))) != a2
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f227,f599]) ).
fof(f601,plain,
( multiply(b2,double_divide(b2,inverse(a2))) != a2
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f467,f600]) ).
fof(f602,plain,
( a2 != a2
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f500,f601]) ).
fof(f603,plain,
( $false
| spl0_1 ),
inference(trivial_equality_resolution,[status(esa)],[f602]) ).
fof(f604,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f603]) ).
fof(f605,plain,
$false,
inference(sat_refutation,[status(thm)],[f19,f173,f178,f498,f604]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP109-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 00:20:04 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % Drodi V3.6.0
% 0.20/0.47 % Refutation found
% 0.20/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.49 % Elapsed time: 0.135984 seconds
% 0.20/0.49 % CPU time: 0.958207 seconds
% 0.20/0.49 % Total memory used: 57.119 MB
% 0.20/0.49 % Net memory used: 55.928 MB
%------------------------------------------------------------------------------