TSTP Solution File: GEO500+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GEO500+1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n003.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 20:18:09 EDT 2024
% Result : Theorem 151.60s 19.44s
% Output : CNFRefutation 152.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 22 unt; 0 def)
% Number of atoms : 107 ( 55 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 103 ( 52 ~; 44 |; 7 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 138 ( 132 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,axiom,
! [Xp,Xa] : s_m(Xp,Xa,s(Xa,Xp)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f99,axiom,
! [Xa,Xp] : s(Xa,s(Xa,Xp)) = Xp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f100,axiom,
! [Xa,Xp,Xr,Xq] :
( s(Xa,Xp) != Xr
| s(Xa,Xq) != Xr
| Xp = Xq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f102,axiom,
! [Xa,Xp] :
( s(Xa,Xp) != Xp
| Xp = Xa ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f103,axiom,
! [Xa,Xp] :
( s(Xa,Xp) = Xp
| Xp != Xa ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f104,axiom,
! [Xp,Xq,Xa] : s_e(Xp,Xq,s(Xa,Xp),s(Xa,Xq)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f105,axiom,
! [Xp,Xq,Xr,Xa] :
( ~ s_t(Xp,Xq,Xr)
| s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f107,axiom,
! [Xp,Xq,Xr,Xcs,Xa] :
( ~ s_e(Xp,Xq,Xr,Xcs)
| s_e(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr),s(Xa,Xcs)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f109,axiom,
! [Xp,Xa,Xq,Xb] :
( ~ s_m(Xp,Xa,Xq)
| ~ s_m(Xp,Xb,Xq)
| Xa = Xb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f110,axiom,
! [Xa,Xp,Xb] :
( s(Xa,Xp) != s(Xb,Xp)
| Xa = Xb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f111,conjecture,
! [Xa,Xb,Xp] :
( s(Xa,s(Xb,Xp)) != s(Xb,s(Xa,Xp))
| Xa = Xb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f112,negated_conjecture,
~ ! [Xa,Xb,Xp] :
( s(Xa,s(Xb,Xp)) != s(Xb,s(Xa,Xp))
| Xa = Xb ),
inference(negated_conjecture,[status(cth)],[f111]) ).
fof(f121,axiom,
! [Xa,Xm,Xb] :
( ( ~ s_m(Xa,Xm,Xb)
| s_t(Xa,Xm,Xb) )
& ( ~ s_m(Xa,Xm,Xb)
| s_e(Xm,Xa,Xm,Xb) )
& ( ~ s_t(Xa,Xm,Xb)
| ~ s_e(Xm,Xa,Xm,Xb)
| s_m(Xa,Xm,Xb) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f283,plain,
! [X0,X1] : s_m(X0,X1,s(X1,X0)),
inference(cnf_transformation,[status(esa)],[f96]) ).
fof(f287,plain,
! [X0,X1] : s(X0,s(X0,X1)) = X1,
inference(cnf_transformation,[status(esa)],[f99]) ).
fof(f288,plain,
! [Xp,Xq] :
( ! [Xa,Xr] :
( s(Xa,Xp) != Xr
| s(Xa,Xq) != Xr )
| Xp = Xq ),
inference(miniscoping,[status(esa)],[f100]) ).
fof(f289,plain,
! [X0,X1,X2,X3] :
( s(X0,X1) != X2
| s(X0,X3) != X2
| X1 = X3 ),
inference(cnf_transformation,[status(esa)],[f288]) ).
fof(f292,plain,
! [X0,X1] :
( s(X0,X1) != X1
| X1 = X0 ),
inference(cnf_transformation,[status(esa)],[f102]) ).
fof(f293,plain,
! [X0,X1] :
( s(X0,X1) = X1
| X1 != X0 ),
inference(cnf_transformation,[status(esa)],[f103]) ).
fof(f294,plain,
! [X0,X1,X2] : s_e(X0,X1,s(X2,X0),s(X2,X1)),
inference(cnf_transformation,[status(esa)],[f104]) ).
fof(f295,plain,
! [Xp,Xq,Xr] :
( ~ s_t(Xp,Xq,Xr)
| ! [Xa] : s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr)) ),
inference(miniscoping,[status(esa)],[f105]) ).
fof(f296,plain,
! [X0,X1,X2,X3] :
( ~ s_t(X0,X1,X2)
| s_t(s(X3,X0),s(X3,X1),s(X3,X2)) ),
inference(cnf_transformation,[status(esa)],[f295]) ).
fof(f299,plain,
! [Xp,Xq,Xr,Xcs] :
( ~ s_e(Xp,Xq,Xr,Xcs)
| ! [Xa] : s_e(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr),s(Xa,Xcs)) ),
inference(miniscoping,[status(esa)],[f107]) ).
fof(f300,plain,
! [X0,X1,X2,X3,X4] :
( ~ s_e(X0,X1,X2,X3)
| s_e(s(X4,X0),s(X4,X1),s(X4,X2),s(X4,X3)) ),
inference(cnf_transformation,[status(esa)],[f299]) ).
fof(f303,plain,
! [Xa,Xb] :
( ! [Xp,Xq] :
( ~ s_m(Xp,Xa,Xq)
| ~ s_m(Xp,Xb,Xq) )
| Xa = Xb ),
inference(miniscoping,[status(esa)],[f109]) ).
fof(f304,plain,
! [X0,X1,X2,X3] :
( ~ s_m(X0,X1,X2)
| ~ s_m(X0,X3,X2)
| X1 = X3 ),
inference(cnf_transformation,[status(esa)],[f303]) ).
fof(f305,plain,
! [Xa,Xb] :
( ! [Xp] : s(Xa,Xp) != s(Xb,Xp)
| Xa = Xb ),
inference(miniscoping,[status(esa)],[f110]) ).
fof(f306,plain,
! [X0,X1,X2] :
( s(X0,X1) != s(X2,X1)
| X0 = X2 ),
inference(cnf_transformation,[status(esa)],[f305]) ).
fof(f307,plain,
? [Xa,Xb,Xp] :
( s(Xa,s(Xb,Xp)) = s(Xb,s(Xa,Xp))
& Xa != Xb ),
inference(pre_NNF_transformation,[status(esa)],[f112]) ).
fof(f308,plain,
? [Xa,Xb] :
( ? [Xp] : s(Xa,s(Xb,Xp)) = s(Xb,s(Xa,Xp))
& Xa != Xb ),
inference(miniscoping,[status(esa)],[f307]) ).
fof(f309,plain,
( s(sk0_0,s(sk0_1,sk0_2)) = s(sk0_1,s(sk0_0,sk0_2))
& sk0_0 != sk0_1 ),
inference(skolemization,[status(esa)],[f308]) ).
fof(f310,plain,
s(sk0_0,s(sk0_1,sk0_2)) = s(sk0_1,s(sk0_0,sk0_2)),
inference(cnf_transformation,[status(esa)],[f309]) ).
fof(f311,plain,
sk0_0 != sk0_1,
inference(cnf_transformation,[status(esa)],[f309]) ).
fof(f355,plain,
( ! [Xa,Xm,Xb] :
( ~ s_m(Xa,Xm,Xb)
| s_t(Xa,Xm,Xb) )
& ! [Xa,Xm,Xb] :
( ~ s_m(Xa,Xm,Xb)
| s_e(Xm,Xa,Xm,Xb) )
& ! [Xa,Xm,Xb] :
( ~ s_t(Xa,Xm,Xb)
| ~ s_e(Xm,Xa,Xm,Xb)
| s_m(Xa,Xm,Xb) ) ),
inference(miniscoping,[status(esa)],[f121]) ).
fof(f356,plain,
! [X0,X1,X2] :
( ~ s_m(X0,X1,X2)
| s_t(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f355]) ).
fof(f358,plain,
! [X0,X1,X2] :
( ~ s_t(X0,X1,X2)
| ~ s_e(X1,X0,X1,X2)
| s_m(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f355]) ).
fof(f371,plain,
! [X0,X1,X2] :
( s(X0,X1) != s(X0,X2)
| X2 = X1 ),
inference(destructive_equality_resolution,[status(esa)],[f289]) ).
fof(f372,plain,
! [X0] : s(X0,X0) = X0,
inference(destructive_equality_resolution,[status(esa)],[f293]) ).
fof(f383,plain,
s(sk0_1,s(sk0_0,s(sk0_1,sk0_2))) = s(sk0_0,sk0_2),
inference(paramodulation,[status(thm)],[f310,f287]) ).
fof(f394,plain,
! [X0] :
( s(sk0_0,sk0_2) != s(sk0_1,X0)
| X0 = s(sk0_0,s(sk0_1,sk0_2)) ),
inference(paramodulation,[status(thm)],[f383,f371]) ).
fof(f815,plain,
! [X0,X1] : s_e(X0,X1,X0,s(X0,X1)),
inference(paramodulation,[status(thm)],[f372,f294]) ).
fof(f883,plain,
! [X0,X1,X2] : s_e(s(X0,X1),s(X0,X2),s(X0,X1),s(X0,s(X1,X2))),
inference(resolution,[status(thm)],[f815,f300]) ).
fof(f918,plain,
! [X0,X1] : s_t(X0,X1,s(X1,X0)),
inference(resolution,[status(thm)],[f356,f283]) ).
fof(f928,plain,
! [X0,X1,X2] : s_t(s(X0,X1),s(X0,X2),s(X0,s(X2,X1))),
inference(resolution,[status(thm)],[f918,f296]) ).
fof(f2103,plain,
! [X0,X1,X2] :
( ~ s_m(X0,X1,s(X2,X0))
| X1 = X2 ),
inference(resolution,[status(thm)],[f304,f283]) ).
fof(f11270,plain,
! [X0] :
( s(sk0_0,sk0_2) != s(sk0_1,s(X0,s(sk0_1,sk0_2)))
| X0 = sk0_0 ),
inference(resolution,[status(thm)],[f394,f306]) ).
fof(f11407,plain,
! [X0] :
( s(sk0_0,sk0_2) != s(sk0_1,s(s(X0,sk0_0),s(sk0_1,sk0_2)))
| sk0_0 = X0 ),
inference(resolution,[status(thm)],[f11270,f292]) ).
fof(f15930,plain,
s(sk0_0,sk0_2) != s(sk0_1,s(s(sk0_1,sk0_0),s(sk0_1,sk0_2))),
inference(resolution,[status(thm)],[f11407,f311]) ).
fof(f37454,plain,
! [X0,X1,X2] :
( ~ s_t(s(X0,X1),s(X0,X2),s(X0,s(X2,X1)))
| s_m(s(X0,X1),s(X0,X2),s(X0,s(X2,X1))) ),
inference(resolution,[status(thm)],[f358,f883]) ).
fof(f37455,plain,
! [X0,X1,X2] : s_m(s(X0,X1),s(X0,X2),s(X0,s(X2,X1))),
inference(forward_subsumption_resolution,[status(thm)],[f37454,f928]) ).
fof(f40563,plain,
s_m(s(sk0_1,s(sk0_1,sk0_2)),s(sk0_1,sk0_0),s(sk0_0,sk0_2)),
inference(paramodulation,[status(thm)],[f383,f37455]) ).
fof(f40564,plain,
s_m(sk0_2,s(sk0_1,sk0_0),s(sk0_0,sk0_2)),
inference(forward_demodulation,[status(thm)],[f287,f40563]) ).
fof(f43161,plain,
s(sk0_1,sk0_0) = sk0_0,
inference(resolution,[status(thm)],[f40564,f2103]) ).
fof(f43222,plain,
s(sk0_0,sk0_2) != s(sk0_1,s(sk0_0,s(sk0_1,sk0_2))),
inference(backward_demodulation,[status(thm)],[f43161,f15930]) ).
fof(f43223,plain,
s(sk0_0,sk0_2) != s(sk0_0,sk0_2),
inference(forward_demodulation,[status(thm)],[f383,f43222]) ).
fof(f43224,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f43223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO500+1 : TPTP v8.1.2. Released v7.0.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 30 01:41:03 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 151.60/19.44 % Refutation found
% 151.60/19.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 151.60/19.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 152.66/19.60 % Elapsed time: 19.235271 seconds
% 152.66/19.60 % CPU time: 152.434524 seconds
% 152.66/19.60 % Total memory used: 712.146 MB
% 152.66/19.60 % Net memory used: 674.386 MB
%------------------------------------------------------------------------------