TSTP Solution File: GRP069-1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GRP069-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n023.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 0.14s 0.31s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 8
% Syntax : Number of formulae : 67 ( 52 unt; 0 def)
% Number of atoms : 85 ( 63 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 15 ~; 15 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 103 ( 103 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : divide(X,divide(divide(divide(divide(X,X),Y),Z),divide(divide(identity,X),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(X0,divide(divide(divide(divide(X0,X0),X1),X2),divide(divide(identity,X0),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] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f22,plain,
! [X0,X1,X2] : divide(X0,divide(divide(divide(divide(X0,X0),X1),X2),divide(inverse(X0),X2))) = X1,
inference(backward_demodulation,[status(thm)],[f8,f6]) ).
fof(f23,plain,
! [X0,X1,X2] : divide(X0,divide(divide(divide(identity,X1),X2),divide(inverse(X0),X2))) = X1,
inference(forward_demodulation,[status(thm)],[f9,f22]) ).
fof(f24,plain,
! [X0,X1,X2] : divide(X0,divide(divide(inverse(X1),X2),divide(inverse(X0),X2))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f23]) ).
fof(f27,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f21]) ).
fof(f28,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(paramodulation,[status(thm)],[f9,f21]) ).
fof(f39,plain,
! [X0] : divide(X0,identity) = X0,
inference(paramodulation,[status(thm)],[f9,f24]) ).
fof(f40,plain,
! [X0,X1,X2,X3] : divide(X0,divide(X1,divide(inverse(X0),divide(divide(inverse(X1),X2),divide(inverse(inverse(X3)),X2))))) = X3,
inference(paramodulation,[status(thm)],[f24,f24]) ).
fof(f41,plain,
! [X0,X1,X2,X3] : divide(X0,divide(X1,divide(inverse(X0),divide(divide(inverse(X1),X2),divide(multiply(identity,X3),X2))))) = X3,
inference(forward_demodulation,[status(thm)],[f27,f40]) ).
fof(f44,plain,
! [X0,X1] : divide(X0,divide(identity,divide(inverse(X0),inverse(X1)))) = X1,
inference(paramodulation,[status(thm)],[f9,f24]) ).
fof(f45,plain,
! [X0,X1] : divide(X0,inverse(divide(inverse(X0),inverse(X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f44]) ).
fof(f46,plain,
! [X0,X1] : multiply(X0,divide(inverse(X0),inverse(X1))) = X1,
inference(forward_demodulation,[status(thm)],[f21,f45]) ).
fof(f47,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[status(thm)],[f21,f46]) ).
fof(f54,plain,
! [X0,X1] : divide(X0,divide(divide(inverse(X1),inverse(X0)),identity)) = X1,
inference(paramodulation,[status(thm)],[f9,f24]) ).
fof(f55,plain,
! [X0,X1] : divide(X0,divide(inverse(X1),inverse(X0))) = X1,
inference(forward_demodulation,[status(thm)],[f39,f54]) ).
fof(f56,plain,
! [X0,X1] : divide(X0,multiply(inverse(X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f21,f55]) ).
fof(f75,plain,
! [X0] : multiply(X0,identity) = X0,
inference(paramodulation,[status(thm)],[f28,f47]) ).
fof(f80,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(paramodulation,[status(thm)],[f75,f47]) ).
fof(f83,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f80,f47]) ).
fof(f84,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f75,f83]) ).
fof(f85,plain,
! [X0] : X0 = multiply(identity,X0),
inference(forward_demodulation,[status(thm)],[f27,f84]) ).
fof(f88,plain,
! [X0,X1,X2,X3] : divide(X0,divide(X1,divide(inverse(X0),divide(divide(inverse(X1),X2),divide(X3,X2))))) = X3,
inference(backward_demodulation,[status(thm)],[f85,f41]) ).
fof(f97,plain,
! [X0] : inverse(multiply(inverse(X0),identity)) = X0,
inference(paramodulation,[status(thm)],[f8,f56]) ).
fof(f98,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f75,f97]) ).
fof(f104,plain,
! [X0,X1] : divide(multiply(inverse(inverse(X0)),X1),X1) = X0,
inference(paramodulation,[status(thm)],[f47,f56]) ).
fof(f105,plain,
! [X0,X1] : divide(multiply(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f98,f104]) ).
fof(f113,plain,
! [X0,X1] : divide(X0,multiply(X1,X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f98,f56]) ).
fof(f119,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,X1),
inference(paramodulation,[status(thm)],[f98,f21]) ).
fof(f126,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X1)),X1) = X0,
inference(paramodulation,[status(thm)],[f21,f105]) ).
fof(f127,plain,
! [X0,X1] : multiply(divide(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f119,f126]) ).
fof(f145,plain,
! [X0,X1] : divide(X0,X1) = inverse(divide(X1,X0)),
inference(paramodulation,[status(thm)],[f127,f113]) ).
fof(f300,plain,
! [X0,X1,X2] : multiply(X0,divide(X1,X2)) = divide(X0,divide(X2,X1)),
inference(paramodulation,[status(thm)],[f145,f119]) ).
fof(f326,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = divide(X0,divide(inverse(X2),X1)),
inference(paramodulation,[status(thm)],[f21,f300]) ).
fof(f349,plain,
! [X0,X1,X2,X3] : divide(X0,multiply(X1,multiply(divide(divide(inverse(X1),X2),divide(X3,X2)),X0))) = X3,
inference(backward_demodulation,[status(thm)],[f326,f88]) ).
fof(f386,plain,
! [X0,X1,X2] : divide(X0,multiply(X1,multiply(divide(inverse(X1),divide(X2,identity)),X0))) = X2,
inference(paramodulation,[status(thm)],[f39,f349]) ).
fof(f387,plain,
! [X0,X1,X2] : divide(X0,multiply(X1,multiply(divide(inverse(X1),X2),X0))) = X2,
inference(forward_demodulation,[status(thm)],[f39,f386]) ).
fof(f451,plain,
! [X0,X1,X2] : divide(multiply(inverse(divide(inverse(X0),X1)),X2),multiply(X0,X2)) = X1,
inference(paramodulation,[status(thm)],[f47,f387]) ).
fof(f452,plain,
! [X0,X1,X2] : divide(multiply(divide(X0,inverse(X1)),X2),multiply(X1,X2)) = X0,
inference(forward_demodulation,[status(thm)],[f145,f451]) ).
fof(f453,plain,
! [X0,X1,X2] : divide(multiply(multiply(X0,X1),X2),multiply(X1,X2)) = X0,
inference(forward_demodulation,[status(thm)],[f21,f452]) ).
fof(f526,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(paramodulation,[status(thm)],[f453,f127]) ).
fof(f538,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| spl0_2 ),
inference(backward_demodulation,[status(thm)],[f526,f19]) ).
fof(f539,plain,
( $false
| spl0_2 ),
inference(trivial_equality_resolution,[status(esa)],[f538]) ).
fof(f540,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f539]) ).
fof(f543,plain,
( identity != identity
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f28,f13]) ).
fof(f544,plain,
( $false
| spl0_0 ),
inference(trivial_equality_resolution,[status(esa)],[f543]) ).
fof(f545,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f544]) ).
fof(f546,plain,
( a2 != a2
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f85,f16]) ).
fof(f547,plain,
( $false
| spl0_1 ),
inference(trivial_equality_resolution,[status(esa)],[f546]) ).
fof(f548,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f547]) ).
fof(f549,plain,
$false,
inference(sat_refutation,[status(thm)],[f20,f540,f545,f548]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : GRP069-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 0.02/0.09 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.29 % Computer : n023.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Tue Apr 30 00:43:40 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.09/0.30 % Drodi V3.6.0
% 0.14/0.31 % Refutation found
% 0.14/0.31 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.32 % Elapsed time: 0.031253 seconds
% 0.14/0.32 % CPU time: 0.169516 seconds
% 0.14/0.32 % Total memory used: 26.775 MB
% 0.14/0.32 % Net memory used: 26.399 MB
%------------------------------------------------------------------------------