TSTP Solution File: LCL896+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : LCL896+1 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n013.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 252.80s 32.21s
% Output : CNFRefutation 253.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 11
% Syntax : Number of formulae : 73 ( 48 unt; 0 def)
% Number of atoms : 105 ( 38 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 61 ( 29 ~; 25 |; 3 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 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 : 164 ( 162 !; 2 ?)
% 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(f11,axiom,
! [X14,X15,X16] :
( '>='(X14,X15)
=> '>='('==>'(X16,X14),'==>'(X16,X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B,C] : '+'('+'(A,'==>'(A,B)),'==>'('+'(A,'==>'(A,B)),C)) = '+'(A,'==>'(A,'+'(B,'==>'(B,C)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [X17,X18] : '+'(X17,'==>'(X17,X18)) = '+'(X18,'==>'(X18,X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [X17,X18] : '+'(X17,'==>'(X17,X18)) = '+'(X18,'==>'(X18,X17)),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] : '+'('+'(X0,X1),X2) = '+'(X0,'+'(X1,X2)),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f16,plain,
! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f17,plain,
! [X0] : '+'(X0,'0') = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f18,plain,
! [X0] : '>='(X0,X0),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f22,plain,
! [X3,X4] :
( ~ '>='(X3,X4)
| ~ '>='(X4,X3)
| X3 = X4 ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f23,plain,
! [X0,X1] :
( ~ '>='(X0,X1)
| ~ '>='(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f24,plain,
! [X5,X6,X7] :
( ( ~ '>='('+'(X5,X6),X7)
| '>='(X6,'==>'(X5,X7)) )
& ( '>='('+'(X5,X6),X7)
| ~ '>='(X6,'==>'(X5,X7)) ) ),
inference(NNF_transformation,[status(esa)],[f7]) ).
fof(f25,plain,
( ! [X5,X6,X7] :
( ~ '>='('+'(X5,X6),X7)
| '>='(X6,'==>'(X5,X7)) )
& ! [X5,X6,X7] :
( '>='('+'(X5,X6),X7)
| ~ '>='(X6,'==>'(X5,X7)) ) ),
inference(miniscoping,[status(esa)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ~ '>='('+'(X0,X1),X2)
| '>='(X1,'==>'(X0,X2)) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( '>='('+'(X0,X1),X2)
| ~ '>='(X1,'==>'(X0,X2)) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f28,plain,
! [X0] : '>='(X0,'0'),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f29,plain,
! [X8,X9,X10] :
( ~ '>='(X8,X9)
| '>='('+'(X8,X10),'+'(X9,X10)) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f30,plain,
! [X8,X9] :
( ~ '>='(X8,X9)
| ! [X10] : '>='('+'(X8,X10),'+'(X9,X10)) ),
inference(miniscoping,[status(esa)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ~ '>='(X0,X1)
| '>='('+'(X0,X2),'+'(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f35,plain,
! [X14,X15,X16] :
( ~ '>='(X14,X15)
| '>='('==>'(X16,X14),'==>'(X16,X15)) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f36,plain,
! [X14,X15] :
( ~ '>='(X14,X15)
| ! [X16] : '>='('==>'(X16,X14),'==>'(X16,X15)) ),
inference(miniscoping,[status(esa)],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ '>='(X0,X1)
| '>='('==>'(X2,X0),'==>'(X2,X1)) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] : '+'('+'(X0,'==>'(X0,X1)),'==>'('+'(X0,'==>'(X0,X1)),X2)) = '+'(X0,'==>'(X0,'+'(X1,'==>'(X1,X2)))),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f39,plain,
? [X17,X18] : '+'(X17,'==>'(X17,X18)) != '+'(X18,'==>'(X18,X17)),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f40,plain,
'+'(sk0_0,'==>'(sk0_0,sk0_1)) != '+'(sk0_1,'==>'(sk0_1,sk0_0)),
inference(skolemization,[status(esa)],[f39]) ).
fof(f41,plain,
'+'(sk0_0,'==>'(sk0_0,sk0_1)) != '+'(sk0_1,'==>'(sk0_1,sk0_0)),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f42,plain,
! [X0,X1,X2] : '+'(X0,'+'('==>'(X0,X1),'==>'('+'(X0,'==>'(X0,X1)),X2))) = '+'(X0,'==>'(X0,'+'(X1,'==>'(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f15,f38]) ).
fof(f43,plain,
! [X0,X1,X2] : '+'(X0,'+'(X1,X2)) = '+'(X1,'+'(X2,X0)),
inference(paramodulation,[status(thm)],[f16,f15]) ).
fof(f48,plain,
! [X0,X1,X2] : '+'('+'(X0,X1),X2) = '+'(X1,'+'(X0,X2)),
inference(paramodulation,[status(thm)],[f16,f15]) ).
fof(f49,plain,
! [X0,X1,X2] : '+'(X0,'+'(X1,X2)) = '+'(X1,'+'(X0,X2)),
inference(forward_demodulation,[status(thm)],[f15,f48]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ '>='('+'(X0,X1),X2)
| '>='(X0,'==>'(X1,X2)) ),
inference(paramodulation,[status(thm)],[f16,f26]) ).
fof(f105,plain,
! [X0,X1,X2] : '+'(X0,'+'(X1,X2)) = '+'(X0,'+'(X2,X1)),
inference(paramodulation,[status(thm)],[f43,f49]) ).
fof(f2450,plain,
! [X0,X1] : '>='(X0,'==>'(X1,'+'(X1,X0))),
inference(resolution,[status(thm)],[f18,f26]) ).
fof(f2451,plain,
! [X0,X1] : '>='('+'(X0,'==>'(X0,X1)),X1),
inference(resolution,[status(thm)],[f18,f27]) ).
fof(f2458,plain,
! [X0] : '+'('0',X0) = X0,
inference(paramodulation,[status(thm)],[f16,f17]) ).
fof(f2655,plain,
! [X0] : '>='('0','==>'(X0,X0)),
inference(paramodulation,[status(thm)],[f17,f2450]) ).
fof(f2677,plain,
! [X0,X1] : '>='(X0,'==>'(X1,'+'(X0,X1))),
inference(paramodulation,[status(thm)],[f16,f2450]) ).
fof(f2690,plain,
! [X0,X1] : '>='('+'(X0,X1),'+'(X1,X0)),
inference(resolution,[status(thm)],[f2677,f27]) ).
fof(f2720,plain,
! [X0,X1,X2] : '>='('==>'(X0,'+'(X1,X2)),'==>'(X0,'+'(X2,X1))),
inference(resolution,[status(thm)],[f2690,f37]) ).
fof(f2857,plain,
! [X0,X1] : '>='('+'('0',X0),'+'('==>'(X1,X1),X0)),
inference(resolution,[status(thm)],[f31,f2655]) ).
fof(f2858,plain,
! [X0,X1] : '>='(X0,'+'('==>'(X1,X1),X0)),
inference(forward_demodulation,[status(thm)],[f2458,f2857]) ).
fof(f2863,plain,
! [X0,X1] : '>='('+'(X0,X1),'+'('0',X1)),
inference(resolution,[status(thm)],[f31,f28]) ).
fof(f2864,plain,
! [X0,X1] : '>='('+'(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f2458,f2863]) ).
fof(f3057,plain,
! [X0,X1,X2] :
( ~ '>='('==>'(X0,'+'(X1,X2)),'==>'(X0,'+'(X2,X1)))
| '==>'(X0,'+'(X1,X2)) = '==>'(X0,'+'(X2,X1)) ),
inference(resolution,[status(thm)],[f23,f2720]) ).
fof(f3058,plain,
! [X0,X1,X2] : '==>'(X0,'+'(X1,X2)) = '==>'(X0,'+'(X2,X1)),
inference(forward_subsumption_resolution,[status(thm)],[f3057,f2720]) ).
fof(f3060,plain,
! [X0,X1] :
( ~ '>='('+'('==>'(X0,X0),X1),X1)
| '+'('==>'(X0,X0),X1) = X1 ),
inference(resolution,[status(thm)],[f23,f2858]) ).
fof(f3061,plain,
! [X0,X1] : '+'('==>'(X0,X0),X1) = X1,
inference(forward_subsumption_resolution,[status(thm)],[f3060,f2864]) ).
fof(f3067,plain,
! [X0] :
( ~ '>='('0',X0)
| '0' = X0 ),
inference(resolution,[status(thm)],[f23,f28]) ).
fof(f3175,plain,
! [X0] : '==>'(X0,X0) = '0',
inference(paramodulation,[status(thm)],[f17,f3061]) ).
fof(f3379,plain,
! [X0,X1] : '0' = '==>'('+'(X0,X1),'+'(X1,X0)),
inference(paramodulation,[status(thm)],[f3175,f3058]) ).
fof(f3675,plain,
! [X0,X1,X2] :
( '>='('+'('+'(X0,X1),X2),'+'(X1,X0))
| ~ '>='(X2,'0') ),
inference(paramodulation,[status(thm)],[f3379,f27]) ).
fof(f3676,plain,
! [X0,X1,X2] :
( '>='('+'(X0,'+'(X1,X2)),'+'(X1,X0))
| ~ '>='(X2,'0') ),
inference(forward_demodulation,[status(thm)],[f15,f3675]) ).
fof(f3677,plain,
! [X0,X1,X2] : '>='('+'(X0,'+'(X1,X2)),'+'(X1,X0)),
inference(forward_subsumption_resolution,[status(thm)],[f3676,f28]) ).
fof(f3715,plain,
! [X0,X1,X2] : '>='(X0,'==>'('+'(X1,X2),'+'(X1,X0))),
inference(resolution,[status(thm)],[f3677,f55]) ).
fof(f3857,plain,
! [X0,X1,X2] : '>='(X0,'==>'('+'(X1,X2),'+'(X0,X1))),
inference(paramodulation,[status(thm)],[f3058,f3715]) ).
fof(f6307,plain,
! [X0,X1] :
( ~ '>='(X0,'+'(X1,'==>'(X1,X0)))
| X0 = '+'(X1,'==>'(X1,X0)) ),
inference(resolution,[status(thm)],[f2451,f23]) ).
fof(f7412,plain,
! [X0,X1] : '0' = '==>'('+'(X0,X1),'+'('0',X0)),
inference(resolution,[status(thm)],[f3067,f3857]) ).
fof(f7413,plain,
! [X0,X1] : '0' = '==>'('+'(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f2458,f7412]) ).
fof(f7750,plain,
! [X0,X1] : '+'(X0,'+'('==>'(X0,X1),'0')) = '+'(X0,'==>'(X0,'+'(X1,'==>'(X1,X0)))),
inference(paramodulation,[status(thm)],[f7413,f42]) ).
fof(f7751,plain,
! [X0,X1] : '+'(X0,'+'('0','==>'(X0,X1))) = '+'(X0,'==>'(X0,'+'(X1,'==>'(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f105,f7750]) ).
fof(f7752,plain,
! [X0,X1] : '+'(X0,'==>'(X0,X1)) = '+'(X0,'==>'(X0,'+'(X1,'==>'(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f2458,f7751]) ).
fof(f40129,plain,
! [X0,X1] :
( ~ '>='('+'(X0,'==>'(X0,X1)),'+'(X1,'==>'(X1,X0)))
| '+'(X0,'==>'(X0,X1)) = '+'(X1,'==>'(X1,'+'(X0,'==>'(X0,X1)))) ),
inference(paramodulation,[status(thm)],[f7752,f6307]) ).
fof(f40130,plain,
! [X0,X1] :
( ~ '>='('+'(X0,'==>'(X0,X1)),'+'(X1,'==>'(X1,X0)))
| '+'(X0,'==>'(X0,X1)) = '+'(X1,'==>'(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f7752,f40129]) ).
fof(f40152,plain,
! [X0,X1] : '>='('+'(X0,'==>'(X0,X1)),'+'(X1,'==>'(X1,X0))),
inference(paramodulation,[status(thm)],[f7752,f2451]) ).
fof(f40534,plain,
! [X0,X1] : '+'(X0,'==>'(X0,X1)) = '+'(X1,'==>'(X1,X0)),
inference(backward_subsumption_resolution,[status(thm)],[f40130,f40152]) ).
fof(f40535,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f41,f40534]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LCL896+1 : TPTP v8.1.2. Released v5.5.0.
% 0.08/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n013.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 20:21:49 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 252.80/32.21 % Refutation found
% 252.80/32.21 % SZS status Theorem for theBenchmark: Theorem is valid
% 252.80/32.21 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 254.03/32.39 % Elapsed time: 32.030173 seconds
% 254.03/32.39 % CPU time: 253.787234 seconds
% 254.03/32.39 % Total memory used: 713.043 MB
% 254.03/32.39 % Net memory used: 692.561 MB
%------------------------------------------------------------------------------