TSTP Solution File: LCL903+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : LCL903+1 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n025.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 12:20:49 EDT 2023
% Result : Theorem 14.84s 2.30s
% Output : CNFRefutation 15.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 89 ( 41 unt; 0 def)
% Number of atoms : 152 ( 46 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 121 ( 58 ~; 53 |; 4 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 166 (; 165 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : '+'(A,B) = '+'(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : '+'(A,'0') = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : '>='(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( '>='(X0,X1)
& '>='(X1,X2) )
=> '>='(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X3,X4] :
( ( '>='(X3,X4)
& '>='(X4,X3) )
=> X3 = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X5,X6,X7] :
( '>='('+'(X5,X6),X7)
<=> '>='(X6,'==>'(X5,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] : '>='(A,'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X8,X9,X10] :
( '>='(X8,X9)
=> '>='('+'(X8,X10),'+'(X9,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X11,X12,X13] :
( '>='(X11,X12)
=> '>='('==>'(X12,X13),'==>'(X11,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X14,X15,X16] :
( '>='(X14,X15)
=> '>='('==>'(X16,X14),'==>'(X16,X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] : '+'(A,'1') = '1',
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] : '==>'('==>'('==>'(A,'1'),A),A) = '0',
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,conjecture,
! [X17] : '+'(X17,X17) = X17,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [X17] : '+'(X17,X17) = X17,
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f17,plain,
! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f18,plain,
! [X0] : '+'(X0,'0') = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f19,plain,
! [X0] : '>='(X0,X0),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ '>='(X0,X1)
| ~ '>='(X1,X2)
| '>='(X0,X2) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f21,plain,
! [X0,X2] :
( ! [X1] :
( ~ '>='(X0,X1)
| ~ '>='(X1,X2) )
| '>='(X0,X2) ),
inference(miniscoping,[status(esa)],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ~ '>='(X0,X1)
| ~ '>='(X1,X2)
| '>='(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f23,plain,
! [X3,X4] :
( ~ '>='(X3,X4)
| ~ '>='(X4,X3)
| X3 = X4 ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f24,plain,
! [X0,X1] :
( ~ '>='(X0,X1)
| ~ '>='(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f25,plain,
! [X5,X6,X7] :
( ( ~ '>='('+'(X5,X6),X7)
| '>='(X6,'==>'(X5,X7)) )
& ( '>='('+'(X5,X6),X7)
| ~ '>='(X6,'==>'(X5,X7)) ) ),
inference(NNF_transformation,[status(esa)],[f7]) ).
fof(f26,plain,
( ! [X5,X6,X7] :
( ~ '>='('+'(X5,X6),X7)
| '>='(X6,'==>'(X5,X7)) )
& ! [X5,X6,X7] :
( '>='('+'(X5,X6),X7)
| ~ '>='(X6,'==>'(X5,X7)) ) ),
inference(miniscoping,[status(esa)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ '>='('+'(X0,X1),X2)
| '>='(X1,'==>'(X0,X2)) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( '>='('+'(X0,X1),X2)
| ~ '>='(X1,'==>'(X0,X2)) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f29,plain,
! [X0] : '>='(X0,'0'),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f30,plain,
! [X8,X9,X10] :
( ~ '>='(X8,X9)
| '>='('+'(X8,X10),'+'(X9,X10)) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f31,plain,
! [X8,X9] :
( ~ '>='(X8,X9)
| ! [X10] : '>='('+'(X8,X10),'+'(X9,X10)) ),
inference(miniscoping,[status(esa)],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ~ '>='(X0,X1)
| '>='('+'(X0,X2),'+'(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f33,plain,
! [X11,X12,X13] :
( ~ '>='(X11,X12)
| '>='('==>'(X12,X13),'==>'(X11,X13)) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f34,plain,
! [X11,X12] :
( ~ '>='(X11,X12)
| ! [X13] : '>='('==>'(X12,X13),'==>'(X11,X13)) ),
inference(miniscoping,[status(esa)],[f33]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ~ '>='(X0,X1)
| '>='('==>'(X1,X2),'==>'(X0,X2)) ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f36,plain,
! [X14,X15,X16] :
( ~ '>='(X14,X15)
| '>='('==>'(X16,X14),'==>'(X16,X15)) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f37,plain,
! [X14,X15] :
( ~ '>='(X14,X15)
| ! [X16] : '>='('==>'(X16,X14),'==>'(X16,X15)) ),
inference(miniscoping,[status(esa)],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ~ '>='(X0,X1)
| '>='('==>'(X2,X0),'==>'(X2,X1)) ),
inference(cnf_transformation,[status(esa)],[f37]) ).
fof(f39,plain,
! [X0] : '+'(X0,'1') = '1',
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f40,plain,
! [X0] : '==>'('==>'('==>'(X0,'1'),X0),X0) = '0',
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f41,plain,
? [X17] : '+'(X17,X17) != X17,
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f42,plain,
'+'(sk0_0,sk0_0) != sk0_0,
inference(skolemization,[status(esa)],[f41]) ).
fof(f43,plain,
'+'(sk0_0,sk0_0) != sk0_0,
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f848,plain,
! [X0,X1] : '>='('+'(X0,X1),'+'('0',X1)),
inference(resolution,[status(thm)],[f29,f32]) ).
fof(f850,plain,
! [X0] : '+'('0',X0) = X0,
inference(paramodulation,[status(thm)],[f17,f18]) ).
fof(f945,plain,
! [X0] : '+'('1',X0) = '1',
inference(paramodulation,[status(thm)],[f17,f39]) ).
fof(f1086,plain,
! [X0] :
( ~ '>='('0',X0)
| '0' = X0 ),
inference(resolution,[status(thm)],[f24,f29]) ).
fof(f1092,plain,
! [X0,X1,X2] :
( ~ '>='('+'(X0,X1),X2)
| ~ '>='('==>'(X0,X2),X1)
| '==>'(X0,X2) = X1 ),
inference(resolution,[status(thm)],[f27,f24]) ).
fof(f1093,plain,
! [X0,X1,X2,X3] :
( ~ '>='('+'(X0,X1),X2)
| '>='('+'(X1,X3),'+'('==>'(X0,X2),X3)) ),
inference(resolution,[status(thm)],[f27,f32]) ).
fof(f1094,plain,
! [X0,X1] : '>='('+'(X0,'==>'(X0,X1)),X1),
inference(resolution,[status(thm)],[f28,f19]) ).
fof(f1097,plain,
! [X0,X1] : '>='('+'(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f850,f848]) ).
fof(f1103,plain,
! [X0] : '>='('1',X0),
inference(paramodulation,[status(thm)],[f945,f1097]) ).
fof(f1120,plain,
! [X0,X1] : '>='('+'(X0,X1),X0),
inference(paramodulation,[status(thm)],[f17,f1097]) ).
fof(f1125,plain,
! [X0] :
( ~ '>='(X0,'1')
| X0 = '1' ),
inference(resolution,[status(thm)],[f1103,f24]) ).
fof(f1129,plain,
! [X0,X1,X2] :
( ~ '>='(X0,'+'(X1,X2))
| '>='(X0,X1) ),
inference(resolution,[status(thm)],[f1120,f22]) ).
fof(f1130,plain,
! [X0,X1] :
( ~ '>='(X0,'+'(X0,X1))
| X0 = '+'(X0,X1) ),
inference(resolution,[status(thm)],[f1120,f24]) ).
fof(f1273,plain,
! [X0,X1] :
( ~ '>='('0','+'(X0,X1))
| '0' = X0 ),
inference(resolution,[status(thm)],[f1129,f1086]) ).
fof(f1340,plain,
! [X0] :
( ~ '>='('0',X0)
| '0' = X0 ),
inference(paramodulation,[status(thm)],[f18,f1273]) ).
fof(f1365,plain,
! [X0,X1,X2] : '>='('+'(X0,X1),'+'('==>'(X2,'+'(X2,X0)),X1)),
inference(resolution,[status(thm)],[f1093,f19]) ).
fof(f2239,plain,
! [X0,X1] :
( '0' = '==>'(X0,X1)
| ~ '>='('+'(X0,'0'),X1) ),
inference(resolution,[status(thm)],[f1340,f27]) ).
fof(f2240,plain,
! [X0,X1] :
( '0' = '==>'(X0,X1)
| ~ '>='(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f18,f2239]) ).
fof(f2813,plain,
! [X0] : '+'(X0,'==>'(X0,'1')) = '1',
inference(resolution,[status(thm)],[f1094,f1125]) ).
fof(f2820,plain,
! [X0] : '>='('==>'('0',X0),X0),
inference(paramodulation,[status(thm)],[f850,f1094]) ).
fof(f2948,plain,
! [X0,X1] :
( ~ '>='(X0,'+'(X1,X0))
| X0 = '+'(X0,X1) ),
inference(paramodulation,[status(thm)],[f17,f1130]) ).
fof(f3084,plain,
! [X0,X1,X2] :
( ~ '>='(X0,X1)
| ~ '>='('==>'(X0,X2),'==>'(X1,X2))
| '==>'(X0,X2) = '==>'(X1,X2) ),
inference(resolution,[status(thm)],[f35,f24]) ).
fof(f3103,plain,
! [X0] : '>='('+'('==>'('==>'(X0,'1'),X0),'0'),X0),
inference(paramodulation,[status(thm)],[f40,f1094]) ).
fof(f3104,plain,
! [X0] : '>='('==>'('==>'(X0,'1'),X0),X0),
inference(forward_demodulation,[status(thm)],[f18,f3103]) ).
fof(f5293,plain,
! [X0] :
( ~ '>='('+'('==>'(X0,'1'),X0),X0)
| '==>'('==>'(X0,'1'),X0) = X0 ),
inference(resolution,[status(thm)],[f1092,f3104]) ).
fof(f5294,plain,
! [X0] :
( ~ '>='('+'(X0,'==>'(X0,'1')),X0)
| '==>'('==>'(X0,'1'),X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f17,f5293]) ).
fof(f5295,plain,
! [X0] :
( ~ '>='('1',X0)
| '==>'('==>'(X0,'1'),X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f2813,f5294]) ).
fof(f5296,plain,
! [X0] : '==>'('==>'(X0,'1'),X0) = X0,
inference(forward_subsumption_resolution,[status(thm)],[f5295,f1103]) ).
fof(f5301,plain,
! [X0] :
( ~ '>='('+'('0',X0),X0)
| '==>'('0',X0) = X0 ),
inference(resolution,[status(thm)],[f1092,f2820]) ).
fof(f5302,plain,
! [X0] :
( ~ '>='(X0,X0)
| '==>'('0',X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f850,f5301]) ).
fof(f5303,plain,
! [X0] : '==>'('0',X0) = X0,
inference(forward_subsumption_resolution,[status(thm)],[f5302,f19]) ).
fof(f5384,plain,
! [X0,X1] :
( ~ '>='(X0,'0')
| '>='(X1,'==>'(X0,X1)) ),
inference(paramodulation,[status(thm)],[f5303,f35]) ).
fof(f5385,plain,
! [X0,X1] : '>='(X0,'==>'(X1,X0)),
inference(forward_subsumption_resolution,[status(thm)],[f5384,f29]) ).
fof(f7421,plain,
! [X0,X1] :
( ~ '>='('==>'(X0,'1'),X1)
| ~ '>='(X0,'==>'(X1,X0))
| '==>'('==>'(X0,'1'),X0) = '==>'(X1,X0) ),
inference(paramodulation,[status(thm)],[f5296,f3084]) ).
fof(f7422,plain,
! [X0,X1] :
( ~ '>='('==>'(X0,'1'),X1)
| ~ '>='(X0,'==>'(X1,X0))
| X0 = '==>'(X1,X0) ),
inference(forward_demodulation,[status(thm)],[f5296,f7421]) ).
fof(f7423,plain,
! [X0,X1] :
( ~ '>='('==>'(X0,'1'),X1)
| X0 = '==>'(X1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f7422,f5385]) ).
fof(f9088,plain,
! [X0,X1] :
( X0 = '==>'('==>'(X0,X1),X0)
| ~ '>='('1',X1) ),
inference(resolution,[status(thm)],[f7423,f38]) ).
fof(f9089,plain,
! [X0,X1] : X0 = '==>'('==>'(X0,X1),X0),
inference(forward_subsumption_resolution,[status(thm)],[f9088,f1103]) ).
fof(f9191,plain,
! [X0,X1] :
( '0' = X0
| ~ '>='('==>'(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f9089,f2240]) ).
fof(f9194,plain,
! [X0,X1] :
( '0' = '==>'(X0,X1)
| ~ '>='(X0,'==>'(X0,X1)) ),
inference(resolution,[status(thm)],[f9191,f35]) ).
fof(f11514,plain,
! [X0,X1] : '>='(X0,'+'('==>'(X1,'+'(X1,X0)),'0')),
inference(paramodulation,[status(thm)],[f18,f1365]) ).
fof(f11515,plain,
! [X0,X1] : '>='(X0,'==>'(X1,'+'(X1,X0))),
inference(forward_demodulation,[status(thm)],[f18,f11514]) ).
fof(f11695,plain,
! [X0] : '0' = '==>'(X0,'+'(X0,X0)),
inference(resolution,[status(thm)],[f11515,f9194]) ).
fof(f11885,plain,
! [X0] : '>='('+'(X0,'0'),'+'(X0,X0)),
inference(paramodulation,[status(thm)],[f11695,f1094]) ).
fof(f11886,plain,
! [X0] : '>='(X0,'+'(X0,X0)),
inference(forward_demodulation,[status(thm)],[f18,f11885]) ).
fof(f11927,plain,
! [X0] : X0 = '+'(X0,X0),
inference(resolution,[status(thm)],[f11886,f2948]) ).
fof(f11994,plain,
sk0_0 != sk0_0,
inference(backward_demodulation,[status(thm)],[f11927,f43]) ).
fof(f11995,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f11994]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL903+1 : TPTP v8.1.2. Released v5.5.0.
% 0.04/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 09:57:27 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 14.84/2.30 % Refutation found
% 14.84/2.30 % SZS status Theorem for theBenchmark: Theorem is valid
% 14.84/2.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 15.55/2.35 % Elapsed time: 1.985784 seconds
% 15.55/2.35 % CPU time: 15.572081 seconds
% 15.55/2.35 % Memory used: 102.012 MB
%------------------------------------------------------------------------------