TSTP Solution File: NUM926+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM926+1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n006.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 12:31:02 EDT 2023
% Result : Theorem 0.14s 0.32s
% Output : CNFRefutation 0.15s
% 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 ( 3 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 44 (; 32 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
ord_less_eq_int(one_one_int,t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,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(f3,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(f29,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(f91,axiom,
! [A_6,B_3] : times_times_int(A_6,B_3) = times_times_int(B_3,A_6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f103,axiom,
! [A,C] : plus_plus_int(A,C) = plus_plus_int(C,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f112,axiom,
! [K_1] : number_number_of_int(K_1) = K_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f124,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(f125,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)],[f124]) ).
fof(f126,plain,
ord_less_eq_int(one_one_int,t),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f127,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)],[f2]) ).
fof(f128,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)],[f127]) ).
fof(f129,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)],[f128]) ).
fof(f130,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)],[f3]) ).
fof(f131,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)],[f130]) ).
fof(f132,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)],[f131]) ).
fof(f160,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)],[f29]) ).
fof(f161,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)],[f160]) ).
fof(f164,plain,
! [X0,X1] :
( ord_less_int(X0,X1)
| ~ ord_less_eq_int(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f161]) ).
fof(f308,plain,
! [X0,X1] : times_times_int(X0,X1) = times_times_int(X1,X0),
inference(cnf_transformation,[status(esa)],[f91]) ).
fof(f320,plain,
! [X0,X1] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
inference(cnf_transformation,[status(esa)],[f103]) ).
fof(f344,plain,
! [X0] : number_number_of_int(X0) = X0,
inference(cnf_transformation,[status(esa)],[f112]) ).
fof(f380,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)],[f125]) ).
fof(f381,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)],[f380]) ).
fof(f382,plain,
( spl0_0
<=> t = one_one_int ),
introduced(split_symbol_definition) ).
fof(f385,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(f386,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)],[f385]) ).
fof(f388,plain,
( ~ spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f129,f382,f385]) ).
fof(f389,plain,
( spl0_2
<=> ord_less_int(one_one_int,t) ),
introduced(split_symbol_definition) ).
fof(f392,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(f393,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)],[f392]) ).
fof(f395,plain,
( ~ spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f132,f389,f392]) ).
fof(f397,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)],[f344,f381]) ).
fof(f398,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)],[f320,f397]) ).
fof(f399,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)],[f320,f398]) ).
fof(f400,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)],[f308,f399]) ).
fof(f428,plain,
( ord_less_int(one_one_int,t)
| one_one_int = t ),
inference(resolution,[status(thm)],[f164,f126]) ).
fof(f429,plain,
( spl0_2
| spl0_0 ),
inference(split_clause,[status(thm)],[f428,f389,f382]) ).
fof(f431,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)],[f320,f393]) ).
fof(f432,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)],[f308,f431]) ).
fof(f433,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)],[f344,f432]) ).
fof(f434,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f433,f400]) ).
fof(f435,plain,
~ spl0_3,
inference(contradiction_clause,[status(thm)],[f434]) ).
fof(f436,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)],[f320,f386]) ).
fof(f437,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)],[f308,f436]) ).
fof(f438,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)],[f344,f437]) ).
fof(f439,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f438,f400]) ).
fof(f440,plain,
~ spl0_1,
inference(contradiction_clause,[status(thm)],[f439]) ).
fof(f441,plain,
$false,
inference(sat_refutation,[status(thm)],[f388,f395,f429,f435,f440]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09 % Problem : NUM926+1 : TPTP v8.1.2. Released v5.3.0.
% 0.08/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n006.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 09:47:32 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.14/0.31 % Drodi V3.5.1
% 0.14/0.32 % Refutation found
% 0.14/0.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.54 % Elapsed time: 0.018270 seconds
% 0.15/0.54 % CPU time: 0.018646 seconds
% 0.15/0.54 % Memory used: 4.118 MB
%------------------------------------------------------------------------------