%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO500+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:25:08 PM UTC 2026
% Result : Theorem 239.95s 36.53s
% Output : CNFRefutation 239.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 22 unt; 0 def)
% Number of atoms : 84 ( 30 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 74 ( 36 ~; 31 |; 7 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 105 ( 99 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,axiom,
! [Xp,Xa] : s_m(Xp,Xa,s(Xa,Xp)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f99,axiom,
! [Xa,Xp] : s(Xa,s(Xa,Xp)) = Xp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f102,axiom,
! [Xa,Xp] :
( Xp = Xa
| s(Xa,Xp) != Xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f103,axiom,
! [Xa,Xp] :
( Xp != Xa
| s(Xa,Xp) = Xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f104,axiom,
! [Xp,Xq,Xa] : s_e(Xp,Xq,s(Xa,Xp),s(Xa,Xq)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f105,axiom,
! [Xp,Xq,Xr,Xa] :
( s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr))
| ~ s_t(Xp,Xq,Xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f107,axiom,
! [Xp,Xq,Xr,Xcs,Xa] :
( s_e(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr),s(Xa,Xcs))
| ~ s_e(Xp,Xq,Xr,Xcs) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f109,axiom,
! [Xp,Xa,Xq,Xb] :
( Xa = Xb
| ~ s_m(Xp,Xb,Xq)
| ~ s_m(Xp,Xa,Xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f111,conjecture,
! [Xa,Xb,Xp] :
( Xa = Xb
| s(Xa,s(Xb,Xp)) != s(Xb,s(Xa,Xp)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f112,negated_conjecture,
~ ! [Xa,Xb,Xp] :
( Xa = Xb
| s(Xa,s(Xb,Xp)) != s(Xb,s(Xa,Xp)) ),
inference(negated_conjecture,[status(cth)],[f111]) ).
fof(f121,axiom,
! [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) )
& ( s_t(Xa,Xm,Xb)
| ~ s_m(Xa,Xm,Xb) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f283,plain,
! [X0,X1] : s_m(X0,X1,s(X1,X0)),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f287,plain,
! [X0,X1] : X0 = s(X1,s(X1,X0)),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f292,plain,
! [X0,X1] :
( s(X0,X1) != X1
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f293,plain,
! [X0,X1] :
( X1 != X0
| s(X0,X1) = X1 ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f294,plain,
! [X0,X1,X2] : s_e(X0,X1,s(X2,X0),s(X2,X1)),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f295,plain,
! [Xp,Xq,Xr] :
( ! [Xa] : s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr))
| ~ s_t(Xp,Xq,Xr) ),
inference(miniscoping,[status(thm)],[f105]) ).
fof(f296,plain,
! [X0,X1,X2,X3] :
( ~ s_t(X1,X2,X3)
| s_t(s(X0,X1),s(X0,X2),s(X0,X3)) ),
inference(cnf_transformation,[status(thm)],[f295]) ).
fof(f299,plain,
! [Xp,Xq,Xr,Xcs] :
( ! [Xa] : s_e(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr),s(Xa,Xcs))
| ~ s_e(Xp,Xq,Xr,Xcs) ),
inference(miniscoping,[status(thm)],[f107]) ).
fof(f300,plain,
! [X0,X1,X2,X3,X4] :
( ~ s_e(X1,X2,X3,X4)
| s_e(s(X0,X1),s(X0,X2),s(X0,X3),s(X0,X4)) ),
inference(cnf_transformation,[status(thm)],[f299]) ).
fof(f303,plain,
! [Xa,Xb] :
( Xa = Xb
| ! [Xp,Xq] :
( ~ s_m(Xp,Xb,Xq)
| ~ s_m(Xp,Xa,Xq) ) ),
inference(miniscoping,[status(thm)],[f109]) ).
fof(f304,plain,
! [X0,X1,X2,X3] :
( X1 = X3
| ~ s_m(X0,X3,X2)
| ~ s_m(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f303]) ).
fof(f307,plain,
? [Xa,Xb,Xp] :
( Xa != Xb
& s(Xa,s(Xb,Xp)) = s(Xb,s(Xa,Xp)) ),
inference(pre_NNF_transformation,[status(thm)],[f112]) ).
fof(f308,plain,
? [Xa,Xb] :
( Xa != Xb
& ? [Xp] : s(Xa,s(Xb,Xp)) = s(Xb,s(Xa,Xp)) ),
inference(miniscoping,[status(thm)],[f307]) ).
fof(f309,plain,
( sK0_skl != sK1_skl
& s(sK0_skl,s(sK1_skl,sK2_skl)) = s(sK1_skl,s(sK0_skl,sK2_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(Xa,sK0_skl),skolemize(Xb,sK1_skl),skolemize(Xp,sK2_skl)],[f308]) ).
fof(f310,plain,
s(sK1_skl,s(sK0_skl,sK2_skl)) = s(sK0_skl,s(sK1_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f309]) ).
fof(f311,plain,
sK0_skl != sK1_skl,
inference(cnf_transformation,[status(thm)],[f309]) ).
fof(f355,plain,
( ! [Xa,Xm,Xb] :
( s_m(Xa,Xm,Xb)
| ~ s_e(Xm,Xa,Xm,Xb)
| ~ s_t(Xa,Xm,Xb) )
& ! [Xa,Xm,Xb] :
( s_e(Xm,Xa,Xm,Xb)
| ~ s_m(Xa,Xm,Xb) )
& ! [Xa,Xm,Xb] :
( s_t(Xa,Xm,Xb)
| ~ s_m(Xa,Xm,Xb) ) ),
inference(miniscoping,[status(thm)],[f121]) ).
fof(f356,plain,
! [X0,X1,X2] :
( ~ s_m(X0,X1,X2)
| s_t(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f355]) ).
fof(f358,plain,
! [X0,X1,X2] :
( s_m(X1,X0,X2)
| ~ s_t(X1,X0,X2)
| ~ s_e(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f355]) ).
fof(f371,plain,
! [X0] : X0 = s(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f293]) ).
fof(f377,plain,
s(sK1_skl,sK2_skl) = s(sK0_skl,s(sK1_skl,s(sK0_skl,sK2_skl))),
inference(paramodulation,[status(thm)],[f310,f287]) ).
fof(f450,plain,
! [X0,X1] : s_e(X0,X1,X0,s(X0,X1)),
inference(paramodulation,[status(thm)],[f371,f294]) ).
fof(f463,plain,
! [X0,X1,X2] : s_e(s(X0,X1),s(X0,X2),s(X0,X1),s(X0,s(X1,X2))),
inference(resolution,[status(thm)],[f450,f300]) ).
fof(f709,plain,
! [X0,X1] : s_t(X0,X1,s(X1,X0)),
inference(resolution,[status(thm)],[f356,f283]) ).
fof(f715,plain,
! [X0,X1,X2] : s_t(s(X0,X1),s(X0,X2),s(X0,s(X2,X1))),
inference(resolution,[status(thm)],[f709,f296]) ).
fof(f1841,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ s_m(X0,X1,s(X2,X0)) ),
inference(resolution,[status(thm)],[f304,f283]) ).
fof(f2784,plain,
s_e(s(sK0_skl,sK1_skl),s(sK0_skl,s(sK0_skl,sK2_skl)),s(sK0_skl,sK1_skl),s(sK1_skl,sK2_skl)),
inference(paramodulation,[status(thm)],[f377,f463]) ).
fof(f2800,plain,
s_e(s(sK0_skl,sK1_skl),sK2_skl,s(sK0_skl,sK1_skl),s(sK1_skl,sK2_skl)),
inference(forward_demodulation,[status(thm)],[f287,f2784]) ).
fof(f11193,plain,
s_t(s(sK0_skl,s(sK0_skl,sK2_skl)),s(sK0_skl,sK1_skl),s(sK1_skl,sK2_skl)),
inference(paramodulation,[status(thm)],[f377,f715]) ).
fof(f11202,plain,
s_t(sK2_skl,s(sK0_skl,sK1_skl),s(sK1_skl,sK2_skl)),
inference(forward_demodulation,[status(thm)],[f287,f11193]) ).
fof(f29442,plain,
( s_m(sK2_skl,s(sK0_skl,sK1_skl),s(sK1_skl,sK2_skl))
| ~ s_t(sK2_skl,s(sK0_skl,sK1_skl),s(sK1_skl,sK2_skl)) ),
inference(resolution,[status(thm)],[f2800,f358]) ).
fof(f29454,plain,
s_m(sK2_skl,s(sK0_skl,sK1_skl),s(sK1_skl,sK2_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f29442,f11202]) ).
fof(f29501,plain,
sK1_skl = s(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f29454,f1841]) ).
fof(f29578,plain,
sK0_skl = sK1_skl,
inference(resolution,[status(thm)],[f29501,f292]) ).
fof(f30187,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f29578,f311]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO500+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n016.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sun Sep 20 16:58:57 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.39 % Drodi V4.1.1
% 239.95/36.53 % Refutation found
% 239.95/36.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 239.95/36.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 41.91/36.61 % Elapsed time: 31.216750 seconds
% 41.91/36.61 % CPU time: 247.338984 seconds
% 41.91/36.61 % Total memory used: 454.353 MB
% 41.91/36.61 % Net memory used: 384.606 MB
%------------------------------------------------------------------------------