TSTP Solution File: NUM925+6 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM925+6 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n019.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 20:36:07 EDT 2024
% Result : Theorem 2.99s 0.85s
% Output : CNFRefutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 26 unt; 0 def)
% Number of atoms : 58 ( 45 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 22 ~; 15 |; 2 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-4 aty)
% Number of variables : 41 ( 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f39,axiom,
! [X_a,B_1_1,B_2] : hAPP(X_a,X_a,B_1_1,ti(X_a,B_2)) = hAPP(X_a,X_a,B_1_1,B_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f78,axiom,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f89,axiom,
! [K_2,L_1] :
( hAPP(int,int,bit0,K_2) = hAPP(int,int,bit0,L_1)
<=> K_2 = L_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f119,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f121,axiom,
! [K] : hAPP(int,int,plus_plus(int,K),pls) = K,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f138,axiom,
! [K] : hAPP(int,int,bit1,K) = hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),K)),K),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f210,axiom,
! [X_a] :
( ring_11004092258visors(X_a)
=> ! [N,A_1] :
( ti(X_a,A_1) != zero_zero(X_a)
=> hAPP(nat,X_a,power_power(X_a,A_1),N) != zero_zero(X_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f554,axiom,
ring_11004092258visors(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f660,conjecture,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f661,negated_conjecture,
~ ( hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int) ),
inference(negated_conjecture,[status(cth)],[f660]) ).
fof(f738,plain,
! [X0,X1,X2] : hAPP(X0,X0,X1,ti(X0,X2)) = hAPP(X0,X0,X1,X2),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f748,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f816,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
inference(cnf_transformation,[status(esa)],[f78]) ).
fof(f850,plain,
! [K_2,L_1] :
( ( hAPP(int,int,bit0,K_2) != hAPP(int,int,bit0,L_1)
| K_2 = L_1 )
& ( hAPP(int,int,bit0,K_2) = hAPP(int,int,bit0,L_1)
| K_2 != L_1 ) ),
inference(NNF_transformation,[status(esa)],[f89]) ).
fof(f851,plain,
( ! [K_2,L_1] :
( hAPP(int,int,bit0,K_2) != hAPP(int,int,bit0,L_1)
| K_2 = L_1 )
& ! [K_2,L_1] :
( hAPP(int,int,bit0,K_2) = hAPP(int,int,bit0,L_1)
| K_2 != L_1 ) ),
inference(miniscoping,[status(esa)],[f850]) ).
fof(f852,plain,
! [X0,X1] :
( hAPP(int,int,bit0,X0) != hAPP(int,int,bit0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f851]) ).
fof(f944,plain,
pls = zero_zero(int),
inference(cnf_transformation,[status(esa)],[f119]) ).
fof(f946,plain,
! [X0] : hAPP(int,int,plus_plus(int,X0),pls) = X0,
inference(cnf_transformation,[status(esa)],[f121]) ).
fof(f976,plain,
! [X0] : hAPP(int,int,bit1,X0) = hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),X0)),X0),
inference(cnf_transformation,[status(esa)],[f138]) ).
fof(f1181,plain,
! [X_a] :
( ~ ring_11004092258visors(X_a)
| ! [N,A_1] :
( ti(X_a,A_1) = zero_zero(X_a)
| hAPP(nat,X_a,power_power(X_a,A_1),N) != zero_zero(X_a) ) ),
inference(pre_NNF_transformation,[status(esa)],[f210]) ).
fof(f1182,plain,
! [X_a] :
( ~ ring_11004092258visors(X_a)
| ! [A_1] :
( ti(X_a,A_1) = zero_zero(X_a)
| ! [N] : hAPP(nat,X_a,power_power(X_a,A_1),N) != zero_zero(X_a) ) ),
inference(miniscoping,[status(esa)],[f1181]) ).
fof(f1183,plain,
! [X0,X1,X2] :
( ~ ring_11004092258visors(X0)
| ti(X0,X1) = zero_zero(X0)
| hAPP(nat,X0,power_power(X0,X1),X2) != zero_zero(X0) ),
inference(cnf_transformation,[status(esa)],[f1182]) ).
fof(f2255,plain,
ring_11004092258visors(int),
inference(cnf_transformation,[status(esa)],[f554]) ).
fof(f2361,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(cnf_transformation,[status(esa)],[f661]) ).
fof(f2418,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = pls,
inference(backward_demodulation,[status(thm)],[f944,f2361]) ).
fof(f2427,plain,
hAPP(int,int,bit1,pls) = hAPP(int,int,plus_plus(int,one_one(int)),pls),
inference(paramodulation,[status(thm)],[f976,f946]) ).
fof(f2428,plain,
hAPP(int,int,bit1,pls) = one_one(int),
inference(forward_demodulation,[status(thm)],[f946,f2427]) ).
fof(f2437,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = pls,
inference(backward_demodulation,[status(thm)],[f2428,f2418]) ).
fof(f2441,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(forward_demodulation,[status(thm)],[f944,f748]) ).
fof(f2823,plain,
! [X0] : ti(int,X0) = X0,
inference(resolution,[status(thm)],[f738,f852]) ).
fof(f2920,plain,
! [X0,X1] :
( ti(int,X0) = zero_zero(int)
| hAPP(nat,int,power_power(int,X0),X1) != zero_zero(int) ),
inference(resolution,[status(thm)],[f2255,f1183]) ).
fof(f2921,plain,
! [X0,X1] :
( ti(int,X0) = pls
| hAPP(nat,int,power_power(int,X0),X1) != zero_zero(int) ),
inference(forward_demodulation,[status(thm)],[f944,f2920]) ).
fof(f2922,plain,
! [X0,X1] :
( ti(int,X0) = pls
| hAPP(nat,int,power_power(int,X0),X1) != pls ),
inference(forward_demodulation,[status(thm)],[f944,f2921]) ).
fof(f3138,plain,
! [X0,X1] :
( X0 = pls
| hAPP(nat,int,power_power(int,X0),X1) != pls ),
inference(forward_demodulation,[status(thm)],[f2823,f2922]) ).
fof(f3139,plain,
hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)) = pls,
inference(resolution,[status(thm)],[f3138,f2437]) ).
fof(f3779,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
inference(backward_demodulation,[status(thm)],[f3139,f2441]) ).
fof(f3780,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3779,f816]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM925+6 : TPTP v8.1.2. Released v5.3.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n019.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 20:54:29 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.42 % Drodi V3.6.0
% 2.99/0.85 % Refutation found
% 2.99/0.85 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.99/0.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.48/0.88 % Elapsed time: 0.528820 seconds
% 3.48/0.88 % CPU time: 3.608536 seconds
% 3.48/0.88 % Total memory used: 168.905 MB
% 3.48/0.88 % Net memory used: 167.203 MB
%------------------------------------------------------------------------------