TSTP Solution File: NUM926+5 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM926+5 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n024.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 20:36:09 EDT 2024
% Result : Theorem 0.20s 0.40s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 49 ( 19 unt; 0 def)
% Number of atoms : 89 ( 44 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 75 ( 35 ~; 28 |; 5 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-3 aty)
% Number of variables : 44 ( 32 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f28,axiom,
ord_less_eq(int,one_one(int),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
( t = one_one(int)
=> ? [X,Y] : plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
( ord_less(int,one_one(int),t)
=> ? [X,Y] : plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [Z_1,W_1] :
( ord_less(int,Z_1,W_1)
<=> ( ord_less_eq(int,Z_1,W_1)
& Z_1 != W_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,axiom,
! [Z,W] : times_times(int,Z,W) = times_times(int,W,Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,axiom,
! [K_1] : number_number_of(int,K_1) = K_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f117,axiom,
! [Z,W] : plus_plus(int,Z,W) = plus_plus(int,W,Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f142,conjecture,
? [X,Y] : plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f143,negated_conjecture,
~ ? [X,Y] : plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
inference(negated_conjecture,[status(cth)],[f142]) ).
fof(f216,plain,
ord_less_eq(int,one_one(int),t),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f217,plain,
( t != one_one(int)
| ? [X,Y] : plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
inference(pre_NNF_transformation,[status(esa)],[f29]) ).
fof(f218,plain,
( t != one_one(int)
| plus_plus(int,power_power(int,sk0_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_1,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
inference(skolemization,[status(esa)],[f217]) ).
fof(f219,plain,
( t != one_one(int)
| plus_plus(int,power_power(int,sk0_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_1,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
inference(cnf_transformation,[status(esa)],[f218]) ).
fof(f220,plain,
( ~ ord_less(int,one_one(int),t)
| ? [X,Y] : plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
inference(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f221,plain,
( ~ ord_less(int,one_one(int),t)
| plus_plus(int,power_power(int,sk0_2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_3,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
inference(skolemization,[status(esa)],[f220]) ).
fof(f222,plain,
( ~ ord_less(int,one_one(int),t)
| plus_plus(int,power_power(int,sk0_2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_3,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
inference(cnf_transformation,[status(esa)],[f221]) ).
fof(f253,plain,
! [Z_1,W_1] :
( ( ~ ord_less(int,Z_1,W_1)
| ( ord_less_eq(int,Z_1,W_1)
& Z_1 != W_1 ) )
& ( ord_less(int,Z_1,W_1)
| ~ ord_less_eq(int,Z_1,W_1)
| Z_1 = W_1 ) ),
inference(NNF_transformation,[status(esa)],[f50]) ).
fof(f254,plain,
( ! [Z_1,W_1] :
( ~ ord_less(int,Z_1,W_1)
| ( ord_less_eq(int,Z_1,W_1)
& Z_1 != W_1 ) )
& ! [Z_1,W_1] :
( ord_less(int,Z_1,W_1)
| ~ ord_less_eq(int,Z_1,W_1)
| Z_1 = W_1 ) ),
inference(miniscoping,[status(esa)],[f253]) ).
fof(f257,plain,
! [X0,X1] :
( ord_less(int,X0,X1)
| ~ ord_less_eq(int,X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f254]) ).
fof(f433,plain,
! [X0,X1] : times_times(int,X0,X1) = times_times(int,X1,X0),
inference(cnf_transformation,[status(esa)],[f113]) ).
fof(f434,plain,
! [X0] : number_number_of(int,X0) = X0,
inference(cnf_transformation,[status(esa)],[f114]) ).
fof(f437,plain,
! [X0,X1] : plus_plus(int,X0,X1) = plus_plus(int,X1,X0),
inference(cnf_transformation,[status(esa)],[f117]) ).
fof(f486,plain,
! [X,Y] : plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
inference(pre_NNF_transformation,[status(esa)],[f143]) ).
fof(f487,plain,
! [X0,X1] : plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
inference(cnf_transformation,[status(esa)],[f486]) ).
fof(f488,plain,
( spl0_0
<=> t = one_one(int) ),
introduced(split_symbol_definition) ).
fof(f491,plain,
( spl0_1
<=> plus_plus(int,power_power(int,sk0_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_1,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
introduced(split_symbol_definition) ).
fof(f492,plain,
( plus_plus(int,power_power(int,sk0_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_1,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f491]) ).
fof(f494,plain,
( ~ spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f219,f488,f491]) ).
fof(f495,plain,
( spl0_2
<=> ord_less(int,one_one(int),t) ),
introduced(split_symbol_definition) ).
fof(f498,plain,
( spl0_3
<=> plus_plus(int,power_power(int,sk0_2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_3,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
introduced(split_symbol_definition) ).
fof(f499,plain,
( plus_plus(int,power_power(int,sk0_2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_3,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f501,plain,
( ~ spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f222,f495,f498]) ).
fof(f503,plain,
! [X0,X1] : plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int)),
inference(backward_demodulation,[status(thm)],[f434,f487]) ).
fof(f512,plain,
! [X0,X1] : plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int)),
inference(paramodulation,[status(thm)],[f437,f503]) ).
fof(f513,plain,
! [X0,X1] : plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,one_one(int),times_times(int,bit0(bit0(bit1(pls))),m)),
inference(forward_demodulation,[status(thm)],[f437,f512]) ).
fof(f514,plain,
! [X0,X1] : plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))),
inference(forward_demodulation,[status(thm)],[f433,f513]) ).
fof(f1029,plain,
( ord_less(int,one_one(int),t)
| one_one(int) = t ),
inference(resolution,[status(thm)],[f257,f216]) ).
fof(f1030,plain,
( spl0_2
| spl0_0 ),
inference(split_clause,[status(thm)],[f1029,f495,f488]) ).
fof(f1033,plain,
( plus_plus(int,power_power(int,sk0_2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_3,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,one_one(int),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m))
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f437,f499]) ).
fof(f1034,plain,
( plus_plus(int,power_power(int,sk0_2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_3,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,one_one(int),times_times(int,m,number_number_of(int,bit0(bit0(bit1(pls))))))
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f433,f1033]) ).
fof(f1035,plain,
( plus_plus(int,power_power(int,sk0_2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_3,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f434,f1034]) ).
fof(f1036,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f1035,f514]) ).
fof(f1037,plain,
~ spl0_3,
inference(contradiction_clause,[status(thm)],[f1036]) ).
fof(f1038,plain,
( plus_plus(int,power_power(int,sk0_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_1,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,one_one(int),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m))
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f437,f492]) ).
fof(f1039,plain,
( plus_plus(int,power_power(int,sk0_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_1,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,one_one(int),times_times(int,m,number_number_of(int,bit0(bit0(bit1(pls))))))
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f433,f1038]) ).
fof(f1040,plain,
( plus_plus(int,power_power(int,sk0_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sk0_1,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f434,f1039]) ).
fof(f1041,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f1040,f514]) ).
fof(f1042,plain,
~ spl0_1,
inference(contradiction_clause,[status(thm)],[f1041]) ).
fof(f1043,plain,
$false,
inference(sat_refutation,[status(thm)],[f494,f501,f1030,f1037,f1042]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM926+5 : TPTP v8.1.2. Released v5.3.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 29 20:54:36 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.36 % Drodi V3.6.0
% 0.20/0.40 % Refutation found
% 0.20/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.42 % Elapsed time: 0.069368 seconds
% 0.20/0.42 % CPU time: 0.388819 seconds
% 0.20/0.42 % Total memory used: 72.177 MB
% 0.20/0.42 % Net memory used: 72.056 MB
%------------------------------------------------------------------------------