TSTP Solution File: HEN010-2 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : HEN010-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n010.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 20:21:48 EDT 2024
% Result : Unsatisfiable 2.79s 0.75s
% Output : CNFRefutation 2.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of formulae : 75 ( 19 unt; 0 def)
% Number of atoms : 183 ( 21 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 213 ( 105 ~; 104 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 133 ( 133 !; 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(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(f13,axiom,
! [X] : quotient(X,zero,X),
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(f18,axiom,
! [X,Y1,Y2,Y3] :
( ~ quotient(identity,X,Y1)
| ~ quotient(identity,Y1,Y2)
| ~ quotient(identity,Y2,Y3)
| Y1 = Y3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
quotient(identity,a,idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| quotient(X0,X1,zero) ),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f25,plain,
! [X,Z] :
( ! [Y] : ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
inference(miniscoping,[status(esa)],[f3]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ~ quotient(X0,X1,X2)
| less_equal(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f27,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(f28,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)],[f27]) ).
fof(f30,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f32,plain,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f33,plain,
! [Z,W] :
( ! [X,Y] :
( ~ quotient(X,Y,Z)
| ~ quotient(X,Y,W) )
| Z = W ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f34,plain,
! [X0,X1,X2,X3] :
( ~ quotient(X0,X1,X2)
| ~ quotient(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f38,plain,
! [X0] : quotient(X0,zero,X0),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f41,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(f42,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)],[f41]) ).
fof(f43,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(f44,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)],[f43]) ).
fof(f47,plain,
! [Y1,Y3] :
( ! [Y2] :
( ! [X] : ~ quotient(identity,X,Y1)
| ~ quotient(identity,Y1,Y2)
| ~ quotient(identity,Y2,Y3) )
| Y1 = Y3 ),
inference(miniscoping,[status(esa)],[f18]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( ~ quotient(identity,X0,X1)
| ~ quotient(identity,X1,X2)
| ~ quotient(identity,X2,X3)
| X1 = X3 ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f49,plain,
quotient(identity,a,idQa),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f50,plain,
quotient(identity,idQa,idQ_idQa),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f51,plain,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f52,plain,
idQa != idQa_Q__idQ_idQa,
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f60,plain,
! [X0] : less_equal(X0,X0),
inference(resolution,[status(thm)],[f26,f38]) ).
fof(f61,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[status(thm)],[f26,f32]) ).
fof(f74,plain,
! [X0,X1] :
( ~ less_equal(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[status(thm)],[f30,f61]) ).
fof(f75,plain,
( spl0_0
<=> less_equal(idQa,idQa_Q__idQ_idQa) ),
introduced(split_symbol_definition) ).
fof(f77,plain,
( ~ less_equal(idQa,idQa_Q__idQ_idQa)
| spl0_0 ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f94,plain,
! [X0] :
( ~ quotient(idQa,idQ_idQa,X0)
| idQa_Q__idQ_idQa = X0 ),
inference(resolution,[status(thm)],[f34,f51]) ).
fof(f118,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)],[f28,f32]) ).
fof(f129,plain,
! [X0,X1] :
( ~ less_equal(idQa,X0)
| ~ quotient(identity,X0,X1)
| less_equal(X1,a) ),
inference(resolution,[status(thm)],[f42,f49]) ).
fof(f141,plain,
idQa_Q__idQ_idQa = divide(idQa,idQ_idQa),
inference(resolution,[status(thm)],[f94,f32]) ).
fof(f643,plain,
( spl0_23
<=> divide(idQa,idQ_idQa) = idQa ),
introduced(split_symbol_definition) ).
fof(f644,plain,
( divide(idQa,idQ_idQa) = idQa
| ~ spl0_23 ),
inference(component_clause,[status(thm)],[f643]) ).
fof(f646,plain,
( ~ less_equal(idQa,idQa_Q__idQ_idQa)
| divide(idQa,idQ_idQa) = idQa ),
inference(paramodulation,[status(thm)],[f141,f74]) ).
fof(f647,plain,
( ~ spl0_0
| spl0_23 ),
inference(split_clause,[status(thm)],[f646,f75,f643]) ).
fof(f712,plain,
! [X0,X1] :
( ~ quotient(identity,idQa,X0)
| ~ quotient(identity,X0,X1)
| idQa = X1 ),
inference(resolution,[status(thm)],[f48,f49]) ).
fof(f2789,plain,
( spl0_66
<=> less_equal(idQ_idQa,a) ),
introduced(split_symbol_definition) ).
fof(f2790,plain,
( less_equal(idQ_idQa,a)
| ~ spl0_66 ),
inference(component_clause,[status(thm)],[f2789]) ).
fof(f2792,plain,
( spl0_67
<=> less_equal(idQa,idQa) ),
introduced(split_symbol_definition) ).
fof(f2794,plain,
( ~ less_equal(idQa,idQa)
| spl0_67 ),
inference(component_clause,[status(thm)],[f2792]) ).
fof(f2812,plain,
( ~ less_equal(idQa,idQa)
| less_equal(idQ_idQa,a) ),
inference(resolution,[status(thm)],[f129,f50]) ).
fof(f2813,plain,
( ~ spl0_67
| spl0_66 ),
inference(split_clause,[status(thm)],[f2812,f2792,f2789]) ).
fof(f2834,plain,
( $false
| spl0_67 ),
inference(forward_subsumption_resolution,[status(thm)],[f2794,f60]) ).
fof(f2835,plain,
spl0_67,
inference(contradiction_clause,[status(thm)],[f2834]) ).
fof(f3054,plain,
! [X0,X1,X2] :
( ~ quotient(X0,a,X1)
| ~ quotient(X0,idQ_idQa,X2)
| less_equal(X1,X2)
| ~ spl0_66 ),
inference(resolution,[status(thm)],[f2790,f44]) ).
fof(f3065,plain,
( quotient(idQ_idQa,a,zero)
| ~ spl0_66 ),
inference(resolution,[status(thm)],[f2790,f23]) ).
fof(f3086,plain,
! [X0,X1,X2,X3] :
( ~ quotient(X0,a,X1)
| ~ quotient(X1,zero,X2)
| ~ quotient(divide(X0,idQ_idQa),a,X3)
| less_equal(X2,X3)
| ~ spl0_66 ),
inference(resolution,[status(thm)],[f3065,f118]) ).
fof(f3286,plain,
! [X0,X1] :
( ~ quotient(X0,idQ_idQa,X1)
| less_equal(divide(X0,a),X1)
| ~ spl0_66 ),
inference(resolution,[status(thm)],[f3054,f32]) ).
fof(f3725,plain,
! [X0] :
( ~ quotient(identity,idQ_idQa,X0)
| idQa = X0 ),
inference(resolution,[status(thm)],[f712,f50]) ).
fof(f4452,plain,
idQa = divide(identity,idQ_idQa),
inference(resolution,[status(thm)],[f3725,f32]) ).
fof(f4748,plain,
! [X0,X1] :
( ~ quotient(idQa,zero,X0)
| ~ quotient(divide(identity,idQ_idQa),a,X1)
| less_equal(X0,X1)
| ~ spl0_66 ),
inference(resolution,[status(thm)],[f3086,f49]) ).
fof(f4749,plain,
! [X0,X1] :
( ~ quotient(idQa,zero,X0)
| ~ quotient(idQa,a,X1)
| less_equal(X0,X1)
| ~ spl0_66 ),
inference(forward_demodulation,[status(thm)],[f4452,f4748]) ).
fof(f5263,plain,
( less_equal(divide(idQa,a),idQa_Q__idQ_idQa)
| ~ spl0_66 ),
inference(resolution,[status(thm)],[f3286,f51]) ).
fof(f9732,plain,
! [X0] :
( ~ quotient(idQa,a,X0)
| less_equal(idQa,X0)
| ~ spl0_66 ),
inference(resolution,[status(thm)],[f4749,f38]) ).
fof(f10931,plain,
( less_equal(idQa,divide(idQa,a))
| ~ spl0_66 ),
inference(resolution,[status(thm)],[f9732,f32]) ).
fof(f10939,plain,
( divide(idQa,a) = idQa
| ~ spl0_66 ),
inference(resolution,[status(thm)],[f10931,f74]) ).
fof(f11000,plain,
( less_equal(idQa,idQa_Q__idQ_idQa)
| ~ spl0_66 ),
inference(backward_demodulation,[status(thm)],[f10939,f5263]) ).
fof(f11001,plain,
( $false
| spl0_0
| ~ spl0_66 ),
inference(forward_subsumption_resolution,[status(thm)],[f11000,f77]) ).
fof(f11002,plain,
( spl0_0
| ~ spl0_66 ),
inference(contradiction_clause,[status(thm)],[f11001]) ).
fof(f11073,plain,
( idQa_Q__idQ_idQa = idQa
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f141,f644]) ).
fof(f11074,plain,
( $false
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[status(thm)],[f11073,f52]) ).
fof(f11075,plain,
~ spl0_23,
inference(contradiction_clause,[status(thm)],[f11074]) ).
fof(f11076,plain,
$false,
inference(sat_refutation,[status(thm)],[f647,f2813,f2835,f11002,f11075]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HEN010-2 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 29 19:56:35 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Drodi V3.6.0
% 2.79/0.75 % Refutation found
% 2.79/0.75 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.79/0.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.79/0.76 % Elapsed time: 0.413565 seconds
% 2.79/0.76 % CPU time: 3.199128 seconds
% 2.79/0.76 % Total memory used: 69.448 MB
% 2.79/0.76 % Net memory used: 63.589 MB
%------------------------------------------------------------------------------