TSTP Solution File: LCL902+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : LCL902+1 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.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 0.21s 0.45s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 36 unt; 0 def)
% Number of atoms : 81 ( 26 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 51 ( 25 ~; 20 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 88 ( 87 !; 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(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(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,'1'),'1') = X17,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [X17] : '==>'('==>'(X17,'1'),'1') = 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(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(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,'1'),'1') != X17,
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f42,plain,
'==>'('==>'(sk0_0,'1'),'1') != sk0_0,
inference(skolemization,[status(esa)],[f41]) ).
fof(f43,plain,
'==>'('==>'(sk0_0,'1'),'1') != sk0_0,
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f46,plain,
! [X0,X1] : '>='(X0,'==>'(X1,'+'(X1,X0))),
inference(resolution,[status(thm)],[f19,f27]) ).
fof(f47,plain,
! [X0,X1] : '>='('+'(X0,'==>'(X0,X1)),X1),
inference(resolution,[status(thm)],[f19,f28]) ).
fof(f101,plain,
! [X0] : '>='('0','==>'(X0,X0)),
inference(paramodulation,[status(thm)],[f18,f46]) ).
fof(f104,plain,
! [X0] : '1' = '+'('1',X0),
inference(paramodulation,[status(thm)],[f39,f17]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ~ '>='('+'(X0,X1),X2)
| '>='(X0,'==>'(X1,X2)) ),
inference(paramodulation,[status(thm)],[f17,f27]) ).
fof(f134,plain,
! [X0] : '>='('1',X0),
inference(paramodulation,[status(thm)],[f104,f47]) ).
fof(f144,plain,
! [X0,X1] : '>='('==>'(X0,'1'),'==>'(X0,X1)),
inference(resolution,[status(thm)],[f134,f38]) ).
fof(f198,plain,
! [X0] :
( ~ '>='('==>'(X0,X0),'0')
| '0' = '==>'(X0,X0) ),
inference(resolution,[status(thm)],[f24,f101]) ).
fof(f199,plain,
! [X0] : '0' = '==>'(X0,X0),
inference(forward_subsumption_resolution,[status(thm)],[f198,f29]) ).
fof(f205,plain,
! [X0] :
( ~ '>='(X0,'1')
| '1' = X0 ),
inference(resolution,[status(thm)],[f24,f134]) ).
fof(f223,plain,
! [X0,X1] :
( '>='('+'(X0,X1),X0)
| ~ '>='(X1,'0') ),
inference(paramodulation,[status(thm)],[f199,f28]) ).
fof(f224,plain,
! [X0,X1] : '>='('+'(X0,X1),X0),
inference(forward_subsumption_resolution,[status(thm)],[f223,f29]) ).
fof(f237,plain,
! [X0,X1] : '>='('+'(X0,X1),X1),
inference(paramodulation,[status(thm)],[f17,f224]) ).
fof(f239,plain,
! [X0,X1] : '>='(X0,'==>'(X1,X0)),
inference(resolution,[status(thm)],[f237,f27]) ).
fof(f260,plain,
! [X0] : '1' = '+'(X0,'==>'(X0,'1')),
inference(resolution,[status(thm)],[f205,f47]) ).
fof(f627,plain,
! [X0] : '>='('+'('==>'('==>'(X0,'1'),X0),'0'),X0),
inference(paramodulation,[status(thm)],[f40,f47]) ).
fof(f628,plain,
! [X0] : '>='('==>'('==>'(X0,'1'),X0),X0),
inference(forward_demodulation,[status(thm)],[f18,f627]) ).
fof(f652,plain,
! [X0,X1] :
( ~ '>='('1',X0)
| '>='(X1,'==>'('==>'(X1,'1'),X0)) ),
inference(paramodulation,[status(thm)],[f260,f113]) ).
fof(f653,plain,
! [X0,X1] : '>='(X0,'==>'('==>'(X0,'1'),X1)),
inference(forward_subsumption_resolution,[status(thm)],[f652,f134]) ).
fof(f1119,plain,
! [X0] :
( ~ '>='(X0,'==>'('==>'(X0,'1'),X0))
| '==>'('==>'(X0,'1'),X0) = X0 ),
inference(resolution,[status(thm)],[f628,f24]) ).
fof(f1120,plain,
! [X0] : '==>'('==>'(X0,'1'),X0) = X0,
inference(forward_subsumption_resolution,[status(thm)],[f1119,f239]) ).
fof(f1170,plain,
! [X0] : '>='('==>'('==>'(X0,'1'),'1'),X0),
inference(paramodulation,[status(thm)],[f1120,f144]) ).
fof(f2105,plain,
! [X0] :
( ~ '>='(X0,'==>'('==>'(X0,'1'),'1'))
| '==>'('==>'(X0,'1'),'1') = X0 ),
inference(resolution,[status(thm)],[f1170,f24]) ).
fof(f2106,plain,
! [X0] : '==>'('==>'(X0,'1'),'1') = X0,
inference(forward_subsumption_resolution,[status(thm)],[f2105,f653]) ).
fof(f2130,plain,
sk0_0 != sk0_0,
inference(backward_demodulation,[status(thm)],[f2106,f43]) ).
fof(f2131,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f2130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LCL902+1 : TPTP v8.1.2. Released v5.5.0.
% 0.08/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 20:33:35 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 0.21/0.45 % Refutation found
% 0.21/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.48 % Elapsed time: 0.112470 seconds
% 0.21/0.48 % CPU time: 0.787942 seconds
% 0.21/0.48 % Total memory used: 48.581 MB
% 0.21/0.48 % Net memory used: 47.570 MB
%------------------------------------------------------------------------------