TSTP Solution File: HEN009-2 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : HEN009-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n004.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 20:21:47 EDT 2024
% Result : Unsatisfiable 0.16s 0.45s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 68 ( 21 unt; 0 def)
% Number of atoms : 140 ( 7 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 138 ( 66 ~; 66 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 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 : 85 ( 85 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X,Y,Z] :
( ~ quotient(X,Y,Z)
| less_equal(Z,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(f7,axiom,
! [X] : less_equal(X,identity),
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(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(f17,axiom,
! [X,Y,Z,W1,W2] :
( ~ less_equal(X,Y)
| ~ quotient(X,Z,W1)
| ~ quotient(Y,Z,W2)
| less_equal(W1,W2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
quotient(identity,a,idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
idQa != idQ__idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,plain,
! [X,Z] :
( ! [Y] : ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
inference(miniscoping,[status(esa)],[f3]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ~ quotient(X0,X1,X2)
| less_equal(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f29,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f30,plain,
! [X0] : less_equal(X0,identity),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f31,plain,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f37,plain,
! [X0] : quotient(X0,zero,X0),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f38,plain,
! [X,Z] :
( ! [Y] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,Z) )
| less_equal(X,Z) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X2)
| less_equal(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f40,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(f41,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)],[f40]) ).
fof(f44,plain,
! [W1,W2] :
( ! [Y,Z] :
( ! [X] :
( ~ less_equal(X,Y)
| ~ quotient(X,Z,W1) )
| ~ quotient(Y,Z,W2) )
| less_equal(W1,W2) ),
inference(miniscoping,[status(esa)],[f17]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4] :
( ~ less_equal(X0,X1)
| ~ quotient(X0,X2,X3)
| ~ quotient(X1,X2,X4)
| less_equal(X3,X4) ),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f46,plain,
quotient(identity,a,idQa),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f47,plain,
quotient(identity,idQa,idQ_idQa),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f48,plain,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f49,plain,
idQa != idQ__idQ_idQa,
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f57,plain,
! [X0] : less_equal(X0,X0),
inference(resolution,[status(thm)],[f25,f37]) ).
fof(f115,plain,
! [X0,X1] :
( ~ less_equal(idQ_idQa,X0)
| ~ quotient(identity,X0,X1)
| less_equal(X1,idQa) ),
inference(resolution,[status(thm)],[f41,f47]) ).
fof(f116,plain,
! [X0,X1] :
( ~ less_equal(idQa,X0)
| ~ quotient(identity,X0,X1)
| less_equal(X1,a) ),
inference(resolution,[status(thm)],[f41,f46]) ).
fof(f120,plain,
! [X0,X1,X2,X3] :
( ~ less_equal(divide(X0,X1),X2)
| ~ quotient(X0,X2,X3)
| less_equal(X3,X1) ),
inference(resolution,[status(thm)],[f41,f31]) ).
fof(f130,plain,
( spl0_0
<=> less_equal(idQ__idQ_idQa,idQa) ),
introduced(split_symbol_definition) ).
fof(f131,plain,
( less_equal(idQ__idQ_idQa,idQa)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,plain,
( spl0_1
<=> less_equal(idQ_idQa,idQ_idQa) ),
introduced(split_symbol_definition) ).
fof(f135,plain,
( ~ less_equal(idQ_idQa,idQ_idQa)
| spl0_1 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f380,plain,
! [X0,X1,X2,X3] :
( ~ quotient(X0,X1,X2)
| ~ quotient(identity,X1,X3)
| less_equal(X2,X3) ),
inference(resolution,[status(thm)],[f45,f30]) ).
fof(f872,plain,
! [X0,X1,X2] :
( ~ quotient(identity,X0,X1)
| less_equal(divide(X2,X0),X1) ),
inference(resolution,[status(thm)],[f380,f31]) ).
fof(f980,plain,
! [X0] : less_equal(divide(X0,idQ_idQa),idQ__idQ_idQa),
inference(resolution,[status(thm)],[f872,f48]) ).
fof(f1160,plain,
( ~ less_equal(idQ_idQa,idQ_idQa)
| less_equal(idQ__idQ_idQa,idQa) ),
inference(resolution,[status(thm)],[f115,f48]) ).
fof(f1161,plain,
( ~ spl0_1
| spl0_0 ),
inference(split_clause,[status(thm)],[f1160,f133,f130]) ).
fof(f1164,plain,
( spl0_33
<=> less_equal(idQ_idQa,a) ),
introduced(split_symbol_definition) ).
fof(f1165,plain,
( less_equal(idQ_idQa,a)
| ~ spl0_33 ),
inference(component_clause,[status(thm)],[f1164]) ).
fof(f1167,plain,
( spl0_34
<=> less_equal(idQa,idQa) ),
introduced(split_symbol_definition) ).
fof(f1169,plain,
( ~ less_equal(idQa,idQa)
| spl0_34 ),
inference(component_clause,[status(thm)],[f1167]) ).
fof(f1187,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f135,f57]) ).
fof(f1188,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f1187]) ).
fof(f1195,plain,
( spl0_37
<=> less_equal(idQa,idQ__idQ_idQa) ),
introduced(split_symbol_definition) ).
fof(f1197,plain,
( ~ less_equal(idQa,idQ__idQ_idQa)
| spl0_37 ),
inference(component_clause,[status(thm)],[f1195]) ).
fof(f1198,plain,
( spl0_38
<=> idQ__idQ_idQa = idQa ),
introduced(split_symbol_definition) ).
fof(f1199,plain,
( idQ__idQ_idQa = idQa
| ~ spl0_38 ),
inference(component_clause,[status(thm)],[f1198]) ).
fof(f1201,plain,
( ~ less_equal(idQa,idQ__idQ_idQa)
| idQ__idQ_idQa = idQa
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f131,f29]) ).
fof(f1202,plain,
( ~ spl0_37
| spl0_38
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f1201,f1195,f1198,f130]) ).
fof(f1374,plain,
( ~ less_equal(idQa,idQa)
| less_equal(idQ_idQa,a) ),
inference(resolution,[status(thm)],[f116,f47]) ).
fof(f1375,plain,
( ~ spl0_34
| spl0_33 ),
inference(split_clause,[status(thm)],[f1374,f1167,f1164]) ).
fof(f1396,plain,
( $false
| spl0_34 ),
inference(forward_subsumption_resolution,[status(thm)],[f1169,f57]) ).
fof(f1397,plain,
spl0_34,
inference(contradiction_clause,[status(thm)],[f1396]) ).
fof(f1401,plain,
! [X0,X1] :
( ~ quotient(X0,idQ__idQ_idQa,X1)
| less_equal(X1,idQ_idQa) ),
inference(resolution,[status(thm)],[f120,f980]) ).
fof(f1671,plain,
! [X0] : less_equal(divide(X0,idQ__idQ_idQa),idQ_idQa),
inference(resolution,[status(thm)],[f1401,f31]) ).
fof(f1679,plain,
! [X0,X1] :
( ~ less_equal(idQ_idQa,X0)
| less_equal(divide(X1,idQ__idQ_idQa),X0) ),
inference(resolution,[status(thm)],[f1671,f39]) ).
fof(f2604,plain,
! [X0] :
( less_equal(divide(X0,idQ__idQ_idQa),a)
| ~ spl0_33 ),
inference(resolution,[status(thm)],[f1679,f1165]) ).
fof(f2611,plain,
! [X0,X1] :
( ~ quotient(X0,a,X1)
| less_equal(X1,idQ__idQ_idQa)
| ~ spl0_33 ),
inference(resolution,[status(thm)],[f2604,f120]) ).
fof(f2631,plain,
( less_equal(idQa,idQ__idQ_idQa)
| ~ spl0_33 ),
inference(resolution,[status(thm)],[f2611,f46]) ).
fof(f2632,plain,
( $false
| spl0_37
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[status(thm)],[f2631,f1197]) ).
fof(f2633,plain,
( spl0_37
| ~ spl0_33 ),
inference(contradiction_clause,[status(thm)],[f2632]) ).
fof(f2636,plain,
( $false
| ~ spl0_38 ),
inference(forward_subsumption_resolution,[status(thm)],[f1199,f49]) ).
fof(f2637,plain,
~ spl0_38,
inference(contradiction_clause,[status(thm)],[f2636]) ).
fof(f2638,plain,
$false,
inference(sat_refutation,[status(thm)],[f1161,f1188,f1202,f1375,f1397,f2633,f2637]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : HEN009-2 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n004.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Mon Apr 29 20:02:48 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.33 % Drodi V3.6.0
% 0.16/0.45 % Refutation found
% 0.16/0.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.47 % Elapsed time: 0.137874 seconds
% 0.16/0.47 % CPU time: 0.974252 seconds
% 0.16/0.47 % Total memory used: 33.954 MB
% 0.16/0.47 % Net memory used: 31.397 MB
%------------------------------------------------------------------------------