TSTP Solution File: HEN010-2 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% 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 : n020.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 12:12:51 EDT 2023
% Result : Unsatisfiable 2.22s 0.63s
% Output : CNFRefutation 2.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 83 ( 25 unt; 0 def)
% Number of atoms : 180 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 188 ( 91 ~; 91 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 115 (; 115 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(f9,axiom,
! [X,Y,Z,W] :
( ~ quotient(X,Y,Z)
| ~ quotient(X,Y,W)
| Z = W ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : quotient(X,X,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X] : quotient(X,zero,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y,Z] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,Z)
| less_equal(X,Z) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
quotient(identity,a,idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f37,plain,
! [X0] : quotient(X0,X0,zero),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f38,plain,
! [X0] : quotient(X0,zero,X0),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f39,plain,
! [X,Z] :
( ! [Y] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,Z) )
| less_equal(X,Z) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X2)
| less_equal(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f39]) ).
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(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(f58,plain,
less_equal(idQa_Q__idQ_idQa,idQa),
inference(resolution,[status(thm)],[f26,f51]) ).
fof(f60,plain,
! [X0] : less_equal(X0,X0),
inference(resolution,[status(thm)],[f26,f38]) ).
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(f78,plain,
( spl0_1
<=> idQa_Q__idQ_idQa = idQa ),
introduced(split_symbol_definition) ).
fof(f79,plain,
( idQa_Q__idQ_idQa = idQa
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f81,plain,
( ~ less_equal(idQa,idQa_Q__idQ_idQa)
| idQa_Q__idQ_idQa = idQa ),
inference(resolution,[status(thm)],[f30,f58]) ).
fof(f82,plain,
( ~ spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f81,f75,f78]) ).
fof(f96,plain,
! [X0,X1] :
( ~ quotient(X0,zero,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f34,f38]) ).
fof(f98,plain,
! [X0,X1] :
( ~ quotient(X0,X0,X1)
| zero = X1 ),
inference(resolution,[status(thm)],[f34,f37]) ).
fof(f100,plain,
! [X0] : X0 = divide(X0,zero),
inference(resolution,[status(thm)],[f96,f32]) ).
fof(f104,plain,
! [X0] : zero = divide(X0,X0),
inference(resolution,[status(thm)],[f98,f32]) ).
fof(f112,plain,
! [X0,X1,X2,X3,X4] :
( ~ quotient(a,X0,X1)
| ~ quotient(identity,X0,X2)
| ~ quotient(X2,X1,X3)
| ~ quotient(idQa,X0,X4)
| less_equal(X3,X4) ),
inference(resolution,[status(thm)],[f28,f49]) ).
fof(f120,plain,
! [X0] :
( ~ less_equal(idQa,X0)
| less_equal(idQa_Q__idQ_idQa,X0) ),
inference(resolution,[status(thm)],[f40,f58]) ).
fof(f128,plain,
! [X0,X1] :
( ~ less_equal(idQa,X0)
| ~ quotient(identity,X0,X1)
| less_equal(X1,a) ),
inference(resolution,[status(thm)],[f42,f49]) ).
fof(f131,plain,
! [X0,X1] :
( ~ less_equal(idQa_Q__idQ_idQa,X0)
| ~ quotient(idQa,X0,X1)
| less_equal(X1,idQ_idQa) ),
inference(resolution,[status(thm)],[f42,f51]) ).
fof(f134,plain,
! [X0,X1,X2,X3] :
( ~ less_equal(divide(X0,X1),X2)
| ~ quotient(X0,X2,X3)
| less_equal(X3,X1) ),
inference(resolution,[status(thm)],[f42,f32]) ).
fof(f229,plain,
! [X0] :
( ~ less_equal(idQa_Q__idQ_idQa,X0)
| less_equal(divide(idQa,X0),idQ_idQa) ),
inference(resolution,[status(thm)],[f131,f32]) ).
fof(f431,plain,
less_equal(divide(idQa,idQa_Q__idQ_idQa),idQ_idQa),
inference(resolution,[status(thm)],[f229,f60]) ).
fof(f435,plain,
! [X0] :
( ~ less_equal(idQ_idQa,X0)
| less_equal(divide(idQa,idQa_Q__idQ_idQa),X0) ),
inference(resolution,[status(thm)],[f431,f40]) ).
fof(f927,plain,
! [X0,X1,X2,X3] :
( ~ quotient(identity,X0,X1)
| ~ quotient(X1,divide(a,X0),X2)
| ~ quotient(idQa,X0,X3)
| less_equal(X2,X3) ),
inference(resolution,[status(thm)],[f112,f32]) ).
fof(f1302,plain,
( spl0_38
<=> less_equal(idQ_idQa,a) ),
introduced(split_symbol_definition) ).
fof(f1303,plain,
( less_equal(idQ_idQa,a)
| ~ spl0_38 ),
inference(component_clause,[status(thm)],[f1302]) ).
fof(f1305,plain,
( spl0_39
<=> less_equal(idQa,idQa) ),
introduced(split_symbol_definition) ).
fof(f1307,plain,
( ~ less_equal(idQa,idQa)
| spl0_39 ),
inference(component_clause,[status(thm)],[f1305]) ).
fof(f1502,plain,
( ~ less_equal(idQa,idQa)
| less_equal(idQ_idQa,a) ),
inference(resolution,[status(thm)],[f128,f50]) ).
fof(f1503,plain,
( ~ spl0_39
| spl0_38 ),
inference(split_clause,[status(thm)],[f1502,f1305,f1302]) ).
fof(f1524,plain,
( $false
| spl0_39 ),
inference(forward_subsumption_resolution,[status(thm)],[f1307,f60]) ).
fof(f1525,plain,
spl0_39,
inference(contradiction_clause,[status(thm)],[f1524]) ).
fof(f1680,plain,
( less_equal(divide(idQa,idQa_Q__idQ_idQa),a)
| ~ spl0_38 ),
inference(resolution,[status(thm)],[f1303,f435]) ).
fof(f1761,plain,
! [X0] :
( ~ quotient(idQa,a,X0)
| less_equal(X0,idQa_Q__idQ_idQa)
| ~ spl0_38 ),
inference(resolution,[status(thm)],[f1680,f134]) ).
fof(f1833,plain,
( less_equal(divide(idQa,a),idQa_Q__idQ_idQa)
| ~ spl0_38 ),
inference(resolution,[status(thm)],[f1761,f32]) ).
fof(f1841,plain,
( spl0_52
<=> less_equal(idQa_Q__idQ_idQa,divide(idQa,a)) ),
introduced(split_symbol_definition) ).
fof(f1843,plain,
( ~ less_equal(idQa_Q__idQ_idQa,divide(idQa,a))
| spl0_52 ),
inference(component_clause,[status(thm)],[f1841]) ).
fof(f1844,plain,
( spl0_53
<=> divide(idQa,a) = idQa_Q__idQ_idQa ),
introduced(split_symbol_definition) ).
fof(f1845,plain,
( divide(idQa,a) = idQa_Q__idQ_idQa
| ~ spl0_53 ),
inference(component_clause,[status(thm)],[f1844]) ).
fof(f1847,plain,
( ~ less_equal(idQa_Q__idQ_idQa,divide(idQa,a))
| divide(idQa,a) = idQa_Q__idQ_idQa
| ~ spl0_38 ),
inference(resolution,[status(thm)],[f1833,f30]) ).
fof(f1848,plain,
( ~ spl0_52
| spl0_53
| ~ spl0_38 ),
inference(split_clause,[status(thm)],[f1847,f1841,f1844,f1302]) ).
fof(f4112,plain,
! [X0,X1,X2] :
( ~ quotient(identity,X0,X1)
| ~ quotient(idQa,X0,X2)
| less_equal(divide(X1,divide(a,X0)),X2) ),
inference(resolution,[status(thm)],[f927,f32]) ).
fof(f27204,plain,
! [X0] :
( ~ quotient(idQa,a,X0)
| less_equal(divide(idQa,divide(a,a)),X0) ),
inference(resolution,[status(thm)],[f4112,f49]) ).
fof(f27205,plain,
! [X0] :
( ~ quotient(idQa,a,X0)
| less_equal(divide(idQa,zero),X0) ),
inference(forward_demodulation,[status(thm)],[f104,f27204]) ).
fof(f27206,plain,
! [X0] :
( ~ quotient(idQa,a,X0)
| less_equal(idQa,X0) ),
inference(forward_demodulation,[status(thm)],[f100,f27205]) ).
fof(f27617,plain,
less_equal(idQa,divide(idQa,a)),
inference(resolution,[status(thm)],[f27206,f32]) ).
fof(f27628,plain,
less_equal(idQa_Q__idQ_idQa,divide(idQa,a)),
inference(resolution,[status(thm)],[f27617,f120]) ).
fof(f27629,plain,
( $false
| spl0_52 ),
inference(forward_subsumption_resolution,[status(thm)],[f27628,f1843]) ).
fof(f27630,plain,
spl0_52,
inference(contradiction_clause,[status(thm)],[f27629]) ).
fof(f27669,plain,
( less_equal(idQa,idQa_Q__idQ_idQa)
| ~ spl0_53 ),
inference(backward_demodulation,[status(thm)],[f1845,f27617]) ).
fof(f27670,plain,
( $false
| spl0_0
| ~ spl0_53 ),
inference(forward_subsumption_resolution,[status(thm)],[f27669,f77]) ).
fof(f27671,plain,
( spl0_0
| ~ spl0_53 ),
inference(contradiction_clause,[status(thm)],[f27670]) ).
fof(f27832,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f79,f52]) ).
fof(f27833,plain,
~ spl0_1,
inference(contradiction_clause,[status(thm)],[f27832]) ).
fof(f27834,plain,
$false,
inference(sat_refutation,[status(thm)],[f82,f1503,f1525,f1848,f27630,f27671,f27833]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : HEN010-2 : TPTP v8.1.2. Released v1.0.0.
% 0.09/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue May 30 09:32:58 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.13/0.33 % Drodi V3.5.1
% 2.22/0.63 % Refutation found
% 2.22/0.63 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.22/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.22/0.64 % Elapsed time: 0.306515 seconds
% 2.22/0.64 % CPU time: 2.341748 seconds
% 2.22/0.64 % Memory used: 44.674 MB
%------------------------------------------------------------------------------