TSTP Solution File: LCL901+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : LCL901+1 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n017.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 20:28:21 EDT 2024
% Result : Theorem 1.79s 0.60s
% Output : CNFRefutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 14
% Syntax : Number of formulae : 100 ( 65 unt; 0 def)
% Number of atoms : 142 ( 53 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 82 ( 40 ~; 34 |; 3 &)
% ( 1 <=>; 4 =>; 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 : 184 ( 183 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : '+'('+'(A,B),C) = '+'(A,'+'(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(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,B] : '==>'('==>'(A,B),B) = '==>'('==>'(B,A),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] : '+'(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,conjecture,
! [X17] : '==>'('==>'('==>'(X17,'1'),X17),X17) = '0',
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ! [X17] : '==>'('==>'('==>'(X17,'1'),X17),X17) = '0',
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] : '+'('+'(X0,X1),X2) = '+'(X0,'+'(X1,X2)),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f18,plain,
! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f19,plain,
! [X0] : '+'(X0,'0') = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f20,plain,
! [X0] : '>='(X0,X0),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f24,plain,
! [X3,X4] :
( ~ '>='(X3,X4)
| ~ '>='(X4,X3)
| X3 = X4 ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f25,plain,
! [X0,X1] :
( ~ '>='(X0,X1)
| ~ '>='(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f26,plain,
! [X5,X6,X7] :
( ( ~ '>='('+'(X5,X6),X7)
| '>='(X6,'==>'(X5,X7)) )
& ( '>='('+'(X5,X6),X7)
| ~ '>='(X6,'==>'(X5,X7)) ) ),
inference(NNF_transformation,[status(esa)],[f7]) ).
fof(f27,plain,
( ! [X5,X6,X7] :
( ~ '>='('+'(X5,X6),X7)
| '>='(X6,'==>'(X5,X7)) )
& ! [X5,X6,X7] :
( '>='('+'(X5,X6),X7)
| ~ '>='(X6,'==>'(X5,X7)) ) ),
inference(miniscoping,[status(esa)],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ '>='('+'(X0,X1),X2)
| '>='(X1,'==>'(X0,X2)) ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( '>='('+'(X0,X1),X2)
| ~ '>='(X1,'==>'(X0,X2)) ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f30,plain,
! [X0] : '>='(X0,'0'),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f31,plain,
! [X8,X9,X10] :
( ~ '>='(X8,X9)
| '>='('+'(X8,X10),'+'(X9,X10)) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f32,plain,
! [X8,X9] :
( ~ '>='(X8,X9)
| ! [X10] : '>='('+'(X8,X10),'+'(X9,X10)) ),
inference(miniscoping,[status(esa)],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ '>='(X0,X1)
| '>='('+'(X0,X2),'+'(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f34,plain,
! [X11,X12,X13] :
( ~ '>='(X11,X12)
| '>='('==>'(X12,X13),'==>'(X11,X13)) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f35,plain,
! [X11,X12] :
( ~ '>='(X11,X12)
| ! [X13] : '>='('==>'(X12,X13),'==>'(X11,X13)) ),
inference(miniscoping,[status(esa)],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ~ '>='(X0,X1)
| '>='('==>'(X1,X2),'==>'(X0,X2)) ),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f37,plain,
! [X14,X15,X16] :
( ~ '>='(X14,X15)
| '>='('==>'(X16,X14),'==>'(X16,X15)) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f38,plain,
! [X14,X15] :
( ~ '>='(X14,X15)
| ! [X16] : '>='('==>'(X16,X14),'==>'(X16,X15)) ),
inference(miniscoping,[status(esa)],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ '>='(X0,X1)
| '>='('==>'(X2,X0),'==>'(X2,X1)) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f40,plain,
! [X0] : '+'(X0,'1') = '1',
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f41,plain,
! [X0,X1] : '==>'('==>'(X0,X1),X1) = '==>'('==>'(X1,X0),X0),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f42,plain,
! [X0] : '+'(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f43,plain,
? [X17] : '==>'('==>'('==>'(X17,'1'),X17),X17) != '0',
inference(pre_NNF_transformation,[status(esa)],[f16]) ).
fof(f44,plain,
'==>'('==>'('==>'(sk0_0,'1'),sk0_0),sk0_0) != '0',
inference(skolemization,[status(esa)],[f43]) ).
fof(f45,plain,
'==>'('==>'('==>'(sk0_0,'1'),sk0_0),sk0_0) != '0',
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f48,plain,
! [X0,X1] :
( ~ '>='(X0,X1)
| '>='('0','==>'(X0,X1)) ),
inference(paramodulation,[status(thm)],[f19,f28]) ).
fof(f61,plain,
! [X0,X1] : '>='('==>'('0',X0),'==>'(X1,X0)),
inference(resolution,[status(thm)],[f36,f30]) ).
fof(f62,plain,
! [X0,X1] : '>='('+'(X0,'==>'('0',X1)),X1),
inference(resolution,[status(thm)],[f61,f29]) ).
fof(f78,plain,
! [X0,X1,X2] :
( '>='('+'('==>'(X0,X1),X2),X1)
| ~ '>='(X2,'==>'('==>'(X1,X0),X0)) ),
inference(paramodulation,[status(thm)],[f41,f29]) ).
fof(f102,plain,
! [X0,X1] : '>='(X0,'==>'(X1,'+'(X1,X0))),
inference(resolution,[status(thm)],[f20,f28]) ).
fof(f103,plain,
! [X0,X1] : '>='('+'('==>'(X0,X1),'==>'('==>'(X1,X0),X0)),X1),
inference(resolution,[status(thm)],[f20,f78]) ).
fof(f104,plain,
! [X0,X1] : '>='('+'(X0,'==>'(X0,X1)),X1),
inference(resolution,[status(thm)],[f20,f29]) ).
fof(f107,plain,
! [X0] : '>='('0','==>'(X0,X0)),
inference(resolution,[status(thm)],[f20,f48]) ).
fof(f108,plain,
! [X0] : '>='('==>'('0',X0),X0),
inference(paramodulation,[status(thm)],[f42,f62]) ).
fof(f110,plain,
! [X0] : '1' = '+'('1',X0),
inference(paramodulation,[status(thm)],[f40,f18]) ).
fof(f111,plain,
! [X0] : X0 = '+'('0',X0),
inference(paramodulation,[status(thm)],[f19,f18]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ~ '>='('+'(X0,X1),X2)
| '>='(X0,'==>'(X1,X2)) ),
inference(paramodulation,[status(thm)],[f18,f28]) ).
fof(f130,plain,
! [X0] : '>='('1',X0),
inference(paramodulation,[status(thm)],[f110,f62]) ).
fof(f140,plain,
! [X0] : '>='('0','==>'('1',X0)),
inference(resolution,[status(thm)],[f130,f48]) ).
fof(f189,plain,
! [X0] :
( ~ '>='('==>'(X0,X0),'0')
| '0' = '==>'(X0,X0) ),
inference(resolution,[status(thm)],[f25,f107]) ).
fof(f190,plain,
! [X0] : '0' = '==>'(X0,X0),
inference(forward_subsumption_resolution,[status(thm)],[f189,f30]) ).
fof(f191,plain,
! [X0] :
( ~ '>='(X0,'1')
| '1' = X0 ),
inference(resolution,[status(thm)],[f25,f130]) ).
fof(f198,plain,
! [X0] :
( ~ '>='('0',X0)
| X0 = '0' ),
inference(resolution,[status(thm)],[f25,f30]) ).
fof(f213,plain,
! [X0,X1] :
( '>='('+'(X0,X1),X0)
| ~ '>='(X1,'0') ),
inference(paramodulation,[status(thm)],[f190,f29]) ).
fof(f214,plain,
! [X0,X1] : '>='('+'(X0,X1),X0),
inference(forward_subsumption_resolution,[status(thm)],[f213,f30]) ).
fof(f229,plain,
! [X0,X1] : '>='('+'(X0,X1),X1),
inference(paramodulation,[status(thm)],[f18,f214]) ).
fof(f232,plain,
! [X0,X1] : '>='(X0,'==>'(X1,X0)),
inference(resolution,[status(thm)],[f229,f28]) ).
fof(f235,plain,
! [X0,X1] :
( ~ '>='(X0,'+'(X1,X0))
| '+'(X1,X0) = X0 ),
inference(resolution,[status(thm)],[f229,f25]) ).
fof(f237,plain,
! [X0,X1,X2] : '>='('==>'(X0,'+'(X1,X2)),'==>'(X0,X2)),
inference(resolution,[status(thm)],[f229,f39]) ).
fof(f252,plain,
! [X0,X1] :
( ~ '>='('==>'(X0,X1),X1)
| X1 = '==>'(X0,X1) ),
inference(resolution,[status(thm)],[f232,f25]) ).
fof(f262,plain,
! [X0,X1] :
( ~ '>='('==>'(X0,'+'(X0,X1)),X1)
| X1 = '==>'(X0,'+'(X0,X1)) ),
inference(resolution,[status(thm)],[f102,f25]) ).
fof(f329,plain,
! [X0] : '==>'('1',X0) = '0',
inference(resolution,[status(thm)],[f140,f198]) ).
fof(f359,plain,
! [X0] : '1' = '+'(X0,'==>'(X0,'1')),
inference(resolution,[status(thm)],[f104,f191]) ).
fof(f366,plain,
! [X0,X1] : '>='('0','==>'('+'(X0,'==>'(X0,X1)),X1)),
inference(resolution,[status(thm)],[f104,f48]) ).
fof(f536,plain,
! [X0,X1,X2] : '>='('+'(X0,X1),'+'('==>'(X2,X0),X1)),
inference(resolution,[status(thm)],[f33,f232]) ).
fof(f558,plain,
! [X0,X1] :
( ~ '>='('1',X0)
| '>='(X1,'==>'('==>'(X1,'1'),X0)) ),
inference(paramodulation,[status(thm)],[f359,f117]) ).
fof(f559,plain,
! [X0,X1] : '>='(X0,'==>'('==>'(X0,'1'),X1)),
inference(forward_subsumption_resolution,[status(thm)],[f558,f130]) ).
fof(f2118,plain,
! [X0,X1] :
( ~ '>='(X0,'+'(X0,X1))
| '+'(X1,X0) = X0 ),
inference(paramodulation,[status(thm)],[f18,f235]) ).
fof(f2121,plain,
! [X0] : X0 = '==>'('0',X0),
inference(resolution,[status(thm)],[f252,f108]) ).
fof(f2941,plain,
! [X0] : '>='('+'('0','==>'('==>'(X0,'1'),'1')),X0),
inference(paramodulation,[status(thm)],[f329,f103]) ).
fof(f2942,plain,
! [X0] : '>='('==>'('==>'(X0,'1'),'1'),X0),
inference(forward_demodulation,[status(thm)],[f111,f2941]) ).
fof(f3019,plain,
! [X0] :
( ~ '>='(X0,'==>'('==>'(X0,'1'),'1'))
| '==>'('==>'(X0,'1'),'1') = X0 ),
inference(resolution,[status(thm)],[f2942,f25]) ).
fof(f3020,plain,
! [X0] : '==>'('==>'(X0,'1'),'1') = X0,
inference(forward_subsumption_resolution,[status(thm)],[f3019,f559]) ).
fof(f3868,plain,
! [X0,X1] : '>='(X0,'+'('==>'(X1,X0),X0)),
inference(paramodulation,[status(thm)],[f42,f536]) ).
fof(f3869,plain,
! [X0,X1] : '>='(X0,'+'(X0,'==>'(X1,X0))),
inference(forward_demodulation,[status(thm)],[f18,f3868]) ).
fof(f3922,plain,
! [X0,X1] : '+'('==>'(X0,X1),X1) = X1,
inference(resolution,[status(thm)],[f3869,f2118]) ).
fof(f3923,plain,
! [X0,X1] : '+'(X0,'==>'(X1,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f18,f3922]) ).
fof(f3975,plain,
! [X0,X1] : '+'(X0,'==>'('==>'(X0,X1),X1)) = X0,
inference(paramodulation,[status(thm)],[f41,f3923]) ).
fof(f7590,plain,
! [X0,X1] : '==>'('+'(X0,'==>'(X0,X1)),X1) = '0',
inference(resolution,[status(thm)],[f366,f198]) ).
fof(f7824,plain,
! [X0,X1] : '+'('+'(X0,'==>'(X0,X1)),'==>'('0',X1)) = '+'(X0,'==>'(X0,X1)),
inference(paramodulation,[status(thm)],[f7590,f3975]) ).
fof(f7825,plain,
! [X0,X1] : '+'(X0,'+'('==>'(X0,X1),'==>'('0',X1))) = '+'(X0,'==>'(X0,X1)),
inference(forward_demodulation,[status(thm)],[f17,f7824]) ).
fof(f7826,plain,
! [X0,X1] : '+'(X0,'+'('==>'(X0,X1),X1)) = '+'(X0,'==>'(X0,X1)),
inference(forward_demodulation,[status(thm)],[f2121,f7825]) ).
fof(f7827,plain,
! [X0,X1] : '+'(X0,'+'(X1,'==>'(X0,X1))) = '+'(X0,'==>'(X0,X1)),
inference(forward_demodulation,[status(thm)],[f18,f7826]) ).
fof(f7828,plain,
! [X0,X1] : '+'(X0,X1) = '+'(X0,'==>'(X0,X1)),
inference(forward_demodulation,[status(thm)],[f3923,f7827]) ).
fof(f8006,plain,
! [X0,X1] :
( ~ '>='('==>'(X0,'+'(X0,X1)),'==>'(X0,X1))
| '==>'(X0,X1) = '==>'(X0,'+'(X0,'==>'(X0,X1))) ),
inference(paramodulation,[status(thm)],[f7828,f262]) ).
fof(f8007,plain,
! [X0,X1] :
( ~ '>='('==>'(X0,'+'(X0,X1)),'==>'(X0,X1))
| '==>'(X0,X1) = '==>'(X0,'+'(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f7828,f8006]) ).
fof(f8008,plain,
! [X0,X1] : '==>'(X0,X1) = '==>'(X0,'+'(X0,X1)),
inference(forward_subsumption_resolution,[status(thm)],[f8007,f237]) ).
fof(f8093,plain,
! [X0,X1] : '==>'(X0,'==>'(X0,X1)) = '==>'(X0,'+'(X0,X1)),
inference(paramodulation,[status(thm)],[f7828,f8008]) ).
fof(f8094,plain,
! [X0,X1] : '==>'(X0,'==>'(X0,X1)) = '==>'(X0,X1),
inference(forward_demodulation,[status(thm)],[f8008,f8093]) ).
fof(f8215,plain,
! [X0] : '==>'('==>'(X0,'1'),X0) = '==>'('==>'(X0,'1'),'1'),
inference(paramodulation,[status(thm)],[f3020,f8094]) ).
fof(f8216,plain,
! [X0] : '==>'('==>'(X0,'1'),X0) = X0,
inference(forward_demodulation,[status(thm)],[f3020,f8215]) ).
fof(f8312,plain,
'==>'(sk0_0,sk0_0) != '0',
inference(backward_demodulation,[status(thm)],[f8216,f45]) ).
fof(f8313,plain,
'0' != '0',
inference(forward_demodulation,[status(thm)],[f190,f8312]) ).
fof(f8314,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f8313]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL901+1 : TPTP v8.1.2. Released v5.5.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n017.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 : Mon Apr 29 19:56:18 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Drodi V3.6.0
% 1.79/0.60 % Refutation found
% 1.79/0.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.79/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.79/0.62 % Elapsed time: 0.264220 seconds
% 1.79/0.62 % CPU time: 1.999927 seconds
% 1.79/0.62 % Total memory used: 67.364 MB
% 1.79/0.62 % Net memory used: 64.758 MB
%------------------------------------------------------------------------------