TSTP Solution File: HEN004-2 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : HEN004-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n013.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 20:21:42 EDT 2024
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 21 unt; 0 def)
% Number of atoms : 73 ( 7 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 74 ( 38 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 84 ( 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y] :
( ~ quotient(X,Y,zero)
| less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,V1,Z,V2,V3,V4,V5] :
( ~ quotient(X,Y,V1)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Z,V3)
| ~ quotient(V3,V2,V4)
| ~ quotient(V1,Z,V5)
| less_equal(V4,V5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : less_equal(zero,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,X)
| X = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] : quotient(X,Y,divide(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] : quotient(zero,X,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : quotient(X,X,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ quotient(x,zero,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,plain,
! [X0,X1] :
( ~ quotient(X0,X1,zero)
| less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f16,plain,
! [X,Z] :
( ! [Y] : ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
inference(miniscoping,[status(esa)],[f3]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ quotient(X0,X1,X2)
| less_equal(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f18,plain,
! [V4,V5] :
( ! [V1,Z] :
( ! [V2,V3] :
( ! [X] :
( ! [Y] :
( ~ quotient(X,Y,V1)
| ~ quotient(Y,Z,V2) )
| ~ quotient(X,Z,V3) )
| ~ quotient(V3,V2,V4) )
| ~ quotient(V1,Z,V5) )
| less_equal(V4,V5) ),
inference(miniscoping,[status(esa)],[f4]) ).
fof(f19,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ quotient(X0,X1,X2)
| ~ quotient(X1,X3,X4)
| ~ quotient(X0,X3,X5)
| ~ quotient(X5,X4,X6)
| ~ quotient(X2,X3,X7)
| less_equal(X6,X7) ),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f20,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f21,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f23,plain,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f27,plain,
! [X0] : quotient(zero,X0,zero),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f28,plain,
! [X0] : quotient(X0,X0,zero),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f29,plain,
~ quotient(x,zero,x),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f51,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[status(thm)],[f17,f23]) ).
fof(f71,plain,
! [X0,X1] :
( ~ less_equal(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[status(thm)],[f21,f51]) ).
fof(f72,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[status(thm)],[f21,f20]) ).
fof(f100,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ quotient(X0,X1,X2)
| ~ quotient(X3,X1,X4)
| ~ quotient(X4,X2,X5)
| ~ quotient(divide(X3,X0),X1,X6)
| less_equal(X5,X6) ),
inference(resolution,[status(thm)],[f19,f23]) ).
fof(f118,plain,
! [X0,X1,X2,X3,X4] :
( ~ quotient(X0,X1,X2)
| ~ quotient(X2,zero,X3)
| ~ quotient(divide(X0,zero),X1,X4)
| less_equal(X3,X4) ),
inference(resolution,[status(thm)],[f100,f27]) ).
fof(f424,plain,
! [X0,X1,X2,X3] :
( ~ quotient(divide(X0,X1),zero,X2)
| ~ quotient(divide(X0,zero),X1,X3)
| less_equal(X2,X3) ),
inference(resolution,[status(thm)],[f118,f23]) ).
fof(f436,plain,
! [X0,X1,X2] :
( ~ quotient(divide(X0,zero),X1,X2)
| less_equal(divide(divide(X0,X1),zero),X2) ),
inference(resolution,[status(thm)],[f424,f23]) ).
fof(f451,plain,
! [X0] : less_equal(divide(divide(X0,divide(X0,zero)),zero),zero),
inference(resolution,[status(thm)],[f436,f28]) ).
fof(f459,plain,
! [X0] : zero = divide(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[f451,f72]) ).
fof(f530,plain,
! [X0] : quotient(divide(X0,divide(X0,zero)),zero,zero),
inference(paramodulation,[status(thm)],[f459,f23]) ).
fof(f534,plain,
! [X0] : less_equal(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[f530,f15]) ).
fof(f581,plain,
! [X0] : zero = divide(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[f534,f72]) ).
fof(f644,plain,
! [X0] : quotient(X0,divide(X0,zero),zero),
inference(paramodulation,[status(thm)],[f581,f23]) ).
fof(f665,plain,
! [X0] : less_equal(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[f644,f15]) ).
fof(f685,plain,
! [X0] : divide(X0,zero) = X0,
inference(resolution,[status(thm)],[f665,f71]) ).
fof(f727,plain,
! [X0] : quotient(X0,zero,X0),
inference(paramodulation,[status(thm)],[f685,f23]) ).
fof(f728,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f29,f727]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : HEN004-2 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 29 20:03:04 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.6.0
% 0.12/0.36 % Refutation found
% 0.12/0.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.37 % Elapsed time: 0.027983 seconds
% 0.12/0.37 % CPU time: 0.108474 seconds
% 0.12/0.37 % Total memory used: 6.976 MB
% 0.12/0.37 % Net memory used: 6.706 MB
%------------------------------------------------------------------------------