TSTP Solution File: SWV050+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWV050+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n004.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 12:40:33 EDT 2023
% Result : Theorem 0.16s 0.42s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 75 ( 53 unt; 0 def)
% Number of atoms : 108 ( 81 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 54 ( 21 ~; 20 |; 8 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 17 con; 0-3 aty)
% Number of variables : 28 (; 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [Body] : sum(n0,tptp_minus_1,Body) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
succ(tptp_minus_1) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X] : plus(X,n1) = succ(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [X] : plus(X,n3) = succ(succ(succ(X))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [X] : plus(n3,X) = succ(succ(succ(X))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [X] : plus(X,n4) = succ(succ(succ(succ(X)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [X] : plus(n4,X) = succ(succ(succ(succ(X)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [X] : plus(X,n5) = succ(succ(succ(succ(succ(X))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [X] : minus(X,n1) = pred(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [X] : pred(succ(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
( ( pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
& pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) )
=> ( n0 = sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
& pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ( ( pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
& pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) )
=> ( n0 = sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
& pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f83,axiom,
succ(succ(succ(succ(succ(n0))))) = n5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,axiom,
succ(n0) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,plain,
! [X0] : sum(n0,tptp_minus_1,X0) = n0,
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f199,plain,
succ(tptp_minus_1) = n0,
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f200,plain,
! [X0] : plus(X0,n1) = succ(X0),
inference(cnf_transformation,[status(esa)],[f29]) ).
fof(f204,plain,
! [X0] : plus(X0,n3) = succ(succ(succ(X0))),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f205,plain,
! [X0] : plus(n3,X0) = succ(succ(succ(X0))),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f206,plain,
! [X0] : plus(X0,n4) = succ(succ(succ(succ(X0)))),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f207,plain,
! [X0] : plus(n4,X0) = succ(succ(succ(succ(X0)))),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f208,plain,
! [X0] : plus(X0,n5) = succ(succ(succ(succ(succ(X0))))),
inference(cnf_transformation,[status(esa)],[f37]) ).
fof(f210,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f211,plain,
! [X0] : pred(succ(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f244,plain,
( pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
& pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
& ( n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
| pv86 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
| pv88 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ) ),
inference(pre_NNF_transformation,[status(esa)],[f54]) ).
fof(f245,plain,
pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))),
inference(cnf_transformation,[status(esa)],[f244]) ).
fof(f246,plain,
pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))),
inference(cnf_transformation,[status(esa)],[f244]) ).
fof(f247,plain,
( n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
| pv86 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
| pv88 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ),
inference(cnf_transformation,[status(esa)],[f244]) ).
fof(f282,plain,
succ(succ(succ(succ(succ(n0))))) = n5,
inference(cnf_transformation,[status(esa)],[f83]) ).
fof(f283,plain,
succ(n0) = n1,
inference(cnf_transformation,[status(esa)],[f84]) ).
fof(f313,plain,
( spl0_0
<=> n0 = sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) ),
introduced(split_symbol_definition) ).
fof(f315,plain,
( n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
| spl0_0 ),
inference(component_clause,[status(thm)],[f313]) ).
fof(f316,plain,
( spl0_1
<=> pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) ),
introduced(split_symbol_definition) ).
fof(f318,plain,
( pv86 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
| spl0_1 ),
inference(component_clause,[status(thm)],[f316]) ).
fof(f319,plain,
( spl0_2
<=> pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ),
introduced(split_symbol_definition) ).
fof(f321,plain,
( pv88 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
| spl0_2 ),
inference(component_clause,[status(thm)],[f319]) ).
fof(f322,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f247,f313,f316,f319]) ).
fof(f324,plain,
! [X0] : plus(n3,X0) = plus(X0,n3),
inference(forward_demodulation,[status(thm)],[f204,f205]) ).
fof(f325,plain,
! [X0] : plus(X0,n4) = plus(succ(X0),n3),
inference(forward_demodulation,[status(thm)],[f204,f206]) ).
fof(f326,plain,
! [X0] : plus(X0,n4) = plus(n3,succ(X0)),
inference(forward_demodulation,[status(thm)],[f324,f325]) ).
fof(f327,plain,
! [X0] : plus(n4,X0) = plus(succ(X0),n3),
inference(forward_demodulation,[status(thm)],[f204,f207]) ).
fof(f328,plain,
! [X0] : plus(n4,X0) = plus(n3,succ(X0)),
inference(forward_demodulation,[status(thm)],[f324,f327]) ).
fof(f329,plain,
! [X0] : plus(n4,X0) = plus(X0,n4),
inference(forward_demodulation,[status(thm)],[f326,f328]) ).
fof(f330,plain,
! [X0] : plus(X0,n5) = plus(succ(succ(X0)),n3),
inference(forward_demodulation,[status(thm)],[f204,f208]) ).
fof(f331,plain,
! [X0] : plus(X0,n5) = plus(n3,succ(succ(X0))),
inference(forward_demodulation,[status(thm)],[f324,f330]) ).
fof(f332,plain,
! [X0] : plus(X0,n5) = plus(succ(X0),n4),
inference(forward_demodulation,[status(thm)],[f326,f331]) ).
fof(f333,plain,
! [X0] : plus(X0,n5) = plus(n4,succ(X0)),
inference(forward_demodulation,[status(thm)],[f329,f332]) ).
fof(f341,plain,
pv86 = sum(n0,pred(n5),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))),
inference(forward_demodulation,[status(thm)],[f210,f245]) ).
fof(f342,plain,
pv88 = sum(n0,pred(n5),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))),
inference(forward_demodulation,[status(thm)],[f210,f246]) ).
fof(f346,plain,
plus(succ(succ(n0)),n3) = n5,
inference(forward_demodulation,[status(thm)],[f204,f282]) ).
fof(f347,plain,
plus(n3,succ(succ(n0))) = n5,
inference(forward_demodulation,[status(thm)],[f324,f346]) ).
fof(f348,plain,
plus(succ(n0),n4) = n5,
inference(forward_demodulation,[status(thm)],[f326,f347]) ).
fof(f349,plain,
plus(n4,succ(n0)) = n5,
inference(forward_demodulation,[status(thm)],[f329,f348]) ).
fof(f350,plain,
plus(n0,n5) = n5,
inference(forward_demodulation,[status(thm)],[f333,f349]) ).
fof(f353,plain,
( pv88 != sum(n0,pred(n5),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f210,f321]) ).
fof(f354,plain,
( pv88 != pv88
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f342,f353]) ).
fof(f355,plain,
( $false
| spl0_2 ),
inference(trivial_equality_resolution,[status(esa)],[f354]) ).
fof(f356,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f355]) ).
fof(f357,plain,
( n0 != sum(n0,pred(n0),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f210,f315]) ).
fof(f361,plain,
plus(n0,n5) = plus(n4,n1),
inference(paramodulation,[status(thm)],[f283,f333]) ).
fof(f362,plain,
n5 = plus(n4,n1),
inference(forward_demodulation,[status(thm)],[f350,f361]) ).
fof(f363,plain,
n5 = succ(n4),
inference(forward_demodulation,[status(thm)],[f200,f362]) ).
fof(f395,plain,
pred(n0) = tptp_minus_1,
inference(paramodulation,[status(thm)],[f199,f211]) ).
fof(f397,plain,
pred(n5) = n4,
inference(paramodulation,[status(thm)],[f363,f211]) ).
fof(f399,plain,
( n0 != sum(n0,tptp_minus_1,divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
| spl0_0 ),
inference(backward_demodulation,[status(thm)],[f395,f357]) ).
fof(f400,plain,
( n0 != n0
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f197,f399]) ).
fof(f401,plain,
( $false
| spl0_0 ),
inference(trivial_equality_resolution,[status(esa)],[f400]) ).
fof(f402,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f401]) ).
fof(f404,plain,
pv86 = sum(n0,n4,divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))),
inference(backward_demodulation,[status(thm)],[f397,f341]) ).
fof(f405,plain,
( pv86 != sum(n0,pred(n5),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f210,f318]) ).
fof(f406,plain,
( pv86 != sum(n0,n4,divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f397,f405]) ).
fof(f407,plain,
( pv86 != pv86
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f404,f406]) ).
fof(f408,plain,
( $false
| spl0_1 ),
inference(trivial_equality_resolution,[status(esa)],[f407]) ).
fof(f409,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f408]) ).
fof(f410,plain,
$false,
inference(sat_refutation,[status(thm)],[f322,f356,f402,f409]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWV050+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.06/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue May 30 11:30:37 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.11/0.33 % Drodi V3.5.1
% 0.16/0.42 % Refutation found
% 0.16/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.44 % Elapsed time: 0.119419 seconds
% 0.16/0.44 % CPU time: 0.366515 seconds
% 0.16/0.44 % Memory used: 58.888 MB
%------------------------------------------------------------------------------