TSTP Solution File: HEN008-2 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : HEN008-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.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 12:12:49 EDT 2023
% Result : Unsatisfiable 0.10s 0.36s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 19
% Syntax : Number of formulae : 83 ( 31 unt; 0 def)
% Number of atoms : 185 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 204 ( 102 ~; 100 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 155 (; 155 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : less_equal(zero,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,X)
| X = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] : quotient(X,Y,divide(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z,W] :
( ~ quotient(X,Y,Z)
| ~ quotient(X,Y,W)
| Z = W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] : quotient(zero,X,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : quotient(X,X,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X] : quotient(X,zero,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y,Z] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,Z)
| less_equal(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y,W1,Z,W2] :
( ~ quotient(X,Y,W1)
| ~ less_equal(W1,Z)
| ~ quotient(X,Z,W2)
| less_equal(W2,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y,Z,W1,W2] :
( ~ less_equal(X,Y)
| ~ quotient(Z,Y,W1)
| ~ quotient(Z,X,W2)
| less_equal(W1,W2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
less_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
quotient(a,c,aQc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
quotient(b,c,bQc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ less_equal(aQc,bQc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| quotient(X0,X1,zero) ),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f23,plain,
! [X,Z] :
( ! [Y] : ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
inference(miniscoping,[status(esa)],[f3]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ quotient(X0,X1,X2)
| less_equal(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f25,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(f26,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)],[f25]) ).
fof(f27,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f28,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f30,plain,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f31,plain,
! [Z,W] :
( ! [X,Y] :
( ~ quotient(X,Y,Z)
| ~ quotient(X,Y,W) )
| Z = W ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( ~ quotient(X0,X1,X2)
| ~ quotient(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f34,plain,
! [X0] : quotient(zero,X0,zero),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f35,plain,
! [X0] : quotient(X0,X0,zero),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f36,plain,
! [X0] : quotient(X0,zero,X0),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f37,plain,
! [X,Z] :
( ! [Y] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,Z) )
| less_equal(X,Z) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X2)
| less_equal(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f37]) ).
fof(f39,plain,
! [Y,W2] :
( ! [X,Z] :
( ! [W1] :
( ~ quotient(X,Y,W1)
| ~ less_equal(W1,Z) )
| ~ quotient(X,Z,W2) )
| less_equal(W2,Y) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f40,plain,
! [X0,X1,X2,X3,X4] :
( ~ quotient(X0,X1,X2)
| ~ less_equal(X2,X3)
| ~ quotient(X0,X3,X4)
| less_equal(X4,X1) ),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f41,plain,
! [W1,W2] :
( ! [X,Z] :
( ! [Y] :
( ~ less_equal(X,Y)
| ~ quotient(Z,Y,W1) )
| ~ quotient(Z,X,W2) )
| less_equal(W1,W2) ),
inference(miniscoping,[status(esa)],[f16]) ).
fof(f42,plain,
! [X0,X1,X2,X3,X4] :
( ~ less_equal(X0,X1)
| ~ quotient(X2,X1,X3)
| ~ quotient(X2,X0,X4)
| less_equal(X3,X4) ),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f43,plain,
less_equal(a,b),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f44,plain,
quotient(a,c,aQc),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f45,plain,
quotient(b,c,bQc),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f46,plain,
~ less_equal(aQc,bQc),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f48,plain,
less_equal(aQc,a),
inference(resolution,[status(thm)],[f24,f44]) ).
fof(f50,plain,
! [X0,X1,X2,X3,X4] :
( ~ quotient(c,X0,X1)
| ~ quotient(a,X0,X2)
| ~ quotient(X2,X1,X3)
| ~ quotient(aQc,X0,X4)
| less_equal(X3,X4) ),
inference(resolution,[status(thm)],[f26,f44]) ).
fof(f67,plain,
! [X0] :
( ~ less_equal(a,X0)
| less_equal(aQc,X0) ),
inference(resolution,[status(thm)],[f38,f48]) ).
fof(f83,plain,
! [X0,X1,X2,X3] :
( ~ quotient(X0,X1,X2)
| ~ quotient(X0,zero,X3)
| less_equal(X2,X3) ),
inference(resolution,[status(thm)],[f27,f42]) ).
fof(f85,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[status(thm)],[f27,f28]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ~ quotient(a,c,X0)
| ~ quotient(X0,zero,X1)
| ~ quotient(aQc,c,X2)
| less_equal(X1,X2) ),
inference(resolution,[status(thm)],[f35,f50]) ).
fof(f132,plain,
! [X0] : less_equal(X0,X0),
inference(resolution,[status(thm)],[f36,f24]) ).
fof(f136,plain,
less_equal(aQc,b),
inference(resolution,[status(thm)],[f43,f67]) ).
fof(f182,plain,
! [X0,X1,X2,X3] :
( ~ less_equal(divide(X0,X1),X2)
| ~ quotient(X0,X2,X3)
| less_equal(X3,X1) ),
inference(resolution,[status(thm)],[f30,f40]) ).
fof(f183,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)],[f30,f26]) ).
fof(f184,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[status(thm)],[f30,f24]) ).
fof(f196,plain,
quotient(aQc,b,zero),
inference(resolution,[status(thm)],[f21,f136]) ).
fof(f213,plain,
! [X0] :
( ~ quotient(aQc,b,X0)
| zero = X0 ),
inference(resolution,[status(thm)],[f196,f32]) ).
fof(f262,plain,
! [X0,X1] :
( ~ quotient(X0,zero,X1)
| less_equal(X0,X1) ),
inference(resolution,[status(thm)],[f83,f36]) ).
fof(f273,plain,
zero = divide(aQc,b),
inference(resolution,[status(thm)],[f213,f30]) ).
fof(f289,plain,
! [X0] : less_equal(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[f262,f30]) ).
fof(f300,plain,
! [X0] :
( ~ less_equal(divide(X0,zero),X0)
| X0 = divide(X0,zero) ),
inference(resolution,[status(thm)],[f289,f28]) ).
fof(f301,plain,
! [X0] : X0 = divide(X0,zero),
inference(forward_subsumption_resolution,[status(thm)],[f300,f184]) ).
fof(f583,plain,
! [X0,X1,X2] :
( ~ quotient(X0,divide(X0,X1),X2)
| less_equal(X2,X1) ),
inference(resolution,[status(thm)],[f182,f132]) ).
fof(f604,plain,
! [X0,X1,X2,X3] :
( ~ quotient(X0,c,X1)
| ~ quotient(X1,bQc,X2)
| ~ quotient(divide(X0,b),c,X3)
| less_equal(X2,X3) ),
inference(resolution,[status(thm)],[f183,f45]) ).
fof(f761,plain,
! [X0,X1] :
( ~ quotient(aQc,zero,X0)
| ~ quotient(aQc,c,X1)
| less_equal(X0,X1) ),
inference(resolution,[status(thm)],[f91,f44]) ).
fof(f1079,plain,
! [X0,X1] : less_equal(divide(X0,divide(X0,X1)),X1),
inference(resolution,[status(thm)],[f583,f30]) ).
fof(f9930,plain,
! [X0] :
( ~ quotient(aQc,c,X0)
| less_equal(aQc,X0) ),
inference(resolution,[status(thm)],[f761,f36]) ).
fof(f9933,plain,
less_equal(aQc,divide(aQc,c)),
inference(resolution,[status(thm)],[f9930,f30]) ).
fof(f9943,plain,
( spl0_120
<=> less_equal(divide(aQc,c),aQc) ),
introduced(split_symbol_definition) ).
fof(f9945,plain,
( ~ less_equal(divide(aQc,c),aQc)
| spl0_120 ),
inference(component_clause,[status(thm)],[f9943]) ).
fof(f9946,plain,
( spl0_121
<=> aQc = divide(aQc,c) ),
introduced(split_symbol_definition) ).
fof(f9947,plain,
( aQc = divide(aQc,c)
| ~ spl0_121 ),
inference(component_clause,[status(thm)],[f9946]) ).
fof(f9949,plain,
( ~ less_equal(divide(aQc,c),aQc)
| aQc = divide(aQc,c) ),
inference(resolution,[status(thm)],[f9933,f28]) ).
fof(f9950,plain,
( ~ spl0_120
| spl0_121 ),
inference(split_clause,[status(thm)],[f9949,f9943,f9946]) ).
fof(f9951,plain,
( $false
| spl0_120 ),
inference(forward_subsumption_resolution,[status(thm)],[f9945,f184]) ).
fof(f9952,plain,
spl0_120,
inference(contradiction_clause,[status(thm)],[f9951]) ).
fof(f10050,plain,
( quotient(aQc,c,aQc)
| ~ spl0_121 ),
inference(paramodulation,[status(thm)],[f9947,f30]) ).
fof(f10056,plain,
! [X0,X1] :
( ~ quotient(aQc,bQc,X0)
| ~ quotient(divide(aQc,b),c,X1)
| less_equal(X0,X1)
| ~ spl0_121 ),
inference(resolution,[status(thm)],[f10050,f604]) ).
fof(f10057,plain,
! [X0,X1] :
( ~ quotient(aQc,bQc,X0)
| ~ quotient(zero,c,X1)
| less_equal(X0,X1)
| ~ spl0_121 ),
inference(forward_demodulation,[status(thm)],[f273,f10056]) ).
fof(f11933,plain,
! [X0] :
( ~ quotient(zero,c,X0)
| less_equal(divide(aQc,bQc),X0)
| ~ spl0_121 ),
inference(resolution,[status(thm)],[f10057,f30]) ).
fof(f11953,plain,
( less_equal(divide(aQc,bQc),zero)
| ~ spl0_121 ),
inference(resolution,[status(thm)],[f11933,f34]) ).
fof(f11959,plain,
( zero = divide(aQc,bQc)
| ~ spl0_121 ),
inference(resolution,[status(thm)],[f11953,f85]) ).
fof(f12068,plain,
( less_equal(divide(aQc,zero),bQc)
| ~ spl0_121 ),
inference(paramodulation,[status(thm)],[f11959,f1079]) ).
fof(f12069,plain,
( less_equal(aQc,bQc)
| ~ spl0_121 ),
inference(forward_demodulation,[status(thm)],[f301,f12068]) ).
fof(f12070,plain,
( $false
| ~ spl0_121 ),
inference(forward_subsumption_resolution,[status(thm)],[f12069,f46]) ).
fof(f12071,plain,
~ spl0_121,
inference(contradiction_clause,[status(thm)],[f12070]) ).
fof(f12072,plain,
$false,
inference(sat_refutation,[status(thm)],[f9950,f9952,f12071]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : HEN008-2 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.06/0.25 % Computer : n029.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Tue May 30 09:48:36 EDT 2023
% 0.06/0.25 % CPUTime :
% 0.06/0.26 % Drodi V3.5.1
% 0.10/0.36 % Refutation found
% 0.10/0.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.38 % Elapsed time: 0.120381 seconds
% 0.10/0.38 % CPU time: 0.849062 seconds
% 0.10/0.38 % Memory used: 27.098 MB
%------------------------------------------------------------------------------