%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO270+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 12:24:48 PM UTC 2026
% Result : Theorem 0.12s 0.41s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 9 unt; 0 def)
% Number of atoms : 145 ( 79 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 193 ( 84 ~; 80 |; 20 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-6 aty)
% Number of variables : 64 ( 62 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [Vd1052] :
( rpoint(Vd1052)
& vf(vd1047,vd1049) = vf(vd1049,Vd1052)
& vf(vd1049,Vd1052) = vf(Vd1052,vd1047) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ? [Vd1052] :
( rpoint(Vd1052)
& vf(vd1047,vd1049) = vf(vd1049,Vd1052)
& vf(vd1049,Vd1052) = vf(Vd1052,vd1047) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
( rpoint(vd1048)
& vd1047 = vd1048
& rpoint(vd1050)
& vd1047 != vd1049
& vd1049 = vd1050 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [Vd1055,Vd1056,Vd1057,Vd1058] :
( ( rpoint(Vd1056)
& Vd1055 = Vd1056
& rpoint(Vd1058)
& Vd1055 != Vd1057
& Vd1057 = Vd1058 )
=> ! [Vd1060] :
( Vd1060 = vskolem1061(Vd1055,Vd1056,Vd1057,Vd1058)
=> ! [Vd1062] :
( Vd1062 = vskolem1063(Vd1060,Vd1055,Vd1056,Vd1057,Vd1058)
=> vf(Vd1057,vskolem1064(Vd1062,Vd1060,Vd1055,Vd1056,Vd1057,Vd1058)) = vf(vskolem1064(Vd1062,Vd1060,Vd1055,Vd1056,Vd1057,Vd1058),Vd1055) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Vd1055,Vd1056,Vd1057,Vd1058] :
( ( rpoint(Vd1056)
& Vd1055 = Vd1056
& rpoint(Vd1058)
& Vd1055 != Vd1057
& Vd1057 = Vd1058 )
=> ! [Vd1060] :
( Vd1060 = vskolem1061(Vd1055,Vd1056,Vd1057,Vd1058)
=> ! [Vd1062] :
( Vd1062 = vskolem1063(Vd1060,Vd1055,Vd1056,Vd1057,Vd1058)
=> vf(Vd1055,Vd1057) = vf(Vd1057,vskolem1064(Vd1062,Vd1060,Vd1055,Vd1056,Vd1057,Vd1058)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Vd1055,Vd1056,Vd1057,Vd1058] :
( ( rpoint(Vd1056)
& Vd1055 = Vd1056
& rpoint(Vd1058)
& Vd1055 != Vd1057
& Vd1057 = Vd1058 )
=> ! [Vd1060] :
( Vd1060 = vskolem1061(Vd1055,Vd1056,Vd1057,Vd1058)
=> ! [Vd1062] :
( Vd1062 = vskolem1063(Vd1060,Vd1055,Vd1056,Vd1057,Vd1058)
=> rpoint(vskolem1064(Vd1062,Vd1060,Vd1055,Vd1056,Vd1057,Vd1058)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f118,plain,
! [Vd1052] :
( ~ rpoint(Vd1052)
| vf(vd1047,vd1049) != vf(vd1049,Vd1052)
| vf(vd1049,Vd1052) != vf(Vd1052,vd1047) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f119,plain,
! [X0] :
( ~ rpoint(X0)
| vf(vd1047,vd1049) != vf(vd1049,X0)
| vf(vd1049,X0) != vf(X0,vd1047) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f120,plain,
vd1049 = vd1050,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f121,plain,
vd1047 != vd1049,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f122,plain,
rpoint(vd1050),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f123,plain,
vd1047 = vd1048,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f124,plain,
rpoint(vd1048),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f125,plain,
! [Vd1055,Vd1056,Vd1057,Vd1058] :
( ! [Vd1060] :
( ! [Vd1062] :
( vf(Vd1057,vskolem1064(Vd1062,Vd1060,Vd1055,Vd1056,Vd1057,Vd1058)) = vf(vskolem1064(Vd1062,Vd1060,Vd1055,Vd1056,Vd1057,Vd1058),Vd1055)
| Vd1062 != vskolem1063(Vd1060,Vd1055,Vd1056,Vd1057,Vd1058) )
| Vd1060 != vskolem1061(Vd1055,Vd1056,Vd1057,Vd1058) )
| ~ rpoint(Vd1056)
| Vd1055 != Vd1056
| ~ rpoint(Vd1058)
| Vd1055 = Vd1057
| Vd1057 != Vd1058 ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f126,plain,
! [X0,X1,X2,X3,X4,X5] :
( vf(X0,vskolem1064(X5,X4,X2,X3,X0,X1)) = vf(vskolem1064(X5,X4,X2,X3,X0,X1),X2)
| X5 != vskolem1063(X4,X2,X3,X0,X1)
| X4 != vskolem1061(X2,X3,X0,X1)
| ~ rpoint(X3)
| X2 != X3
| ~ rpoint(X1)
| X2 = X0
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
! [Vd1055,Vd1056,Vd1057,Vd1058] :
( ! [Vd1060] :
( ! [Vd1062] :
( vf(Vd1055,Vd1057) = vf(Vd1057,vskolem1064(Vd1062,Vd1060,Vd1055,Vd1056,Vd1057,Vd1058))
| Vd1062 != vskolem1063(Vd1060,Vd1055,Vd1056,Vd1057,Vd1058) )
| Vd1060 != vskolem1061(Vd1055,Vd1056,Vd1057,Vd1058) )
| ~ rpoint(Vd1056)
| Vd1055 != Vd1056
| ~ rpoint(Vd1058)
| Vd1055 = Vd1057
| Vd1057 != Vd1058 ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f128,plain,
! [X0,X1,X2,X3,X4,X5] :
( vf(X2,X0) = vf(X0,vskolem1064(X5,X4,X2,X3,X0,X1))
| X5 != vskolem1063(X4,X2,X3,X0,X1)
| X4 != vskolem1061(X2,X3,X0,X1)
| ~ rpoint(X3)
| X2 != X3
| ~ rpoint(X1)
| X2 = X0
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f137,plain,
! [Vd1055,Vd1056,Vd1057,Vd1058] :
( ! [Vd1060] :
( ! [Vd1062] :
( rpoint(vskolem1064(Vd1062,Vd1060,Vd1055,Vd1056,Vd1057,Vd1058))
| Vd1062 != vskolem1063(Vd1060,Vd1055,Vd1056,Vd1057,Vd1058) )
| Vd1060 != vskolem1061(Vd1055,Vd1056,Vd1057,Vd1058) )
| ~ rpoint(Vd1056)
| Vd1055 != Vd1056
| ~ rpoint(Vd1058)
| Vd1055 = Vd1057
| Vd1057 != Vd1058 ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f138,plain,
! [X0,X1,X2,X3,X4,X5] :
( rpoint(vskolem1064(X5,X4,X2,X3,X0,X1))
| X5 != vskolem1063(X4,X2,X3,X0,X1)
| X4 != vskolem1061(X2,X3,X0,X1)
| ~ rpoint(X3)
| X2 != X3
| ~ rpoint(X1)
| X2 = X0
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f638,plain,
! [X0,X1] :
( vf(X1,vskolem1064(vskolem1063(vskolem1061(X0,X0,X1,X1),X0,X0,X1,X1),vskolem1061(X0,X0,X1,X1),X0,X0,X1,X1)) = vf(vskolem1064(vskolem1063(vskolem1061(X0,X0,X1,X1),X0,X0,X1,X1),vskolem1061(X0,X0,X1,X1),X0,X0,X1,X1),X0)
| ~ rpoint(X0)
| ~ rpoint(X1)
| X0 = X1 ),
inference(destructive_equality_resolution,[status(thm)],[f126]) ).
fof(f639,plain,
! [X0,X1] :
( vf(X0,X1) = vf(X1,vskolem1064(vskolem1063(vskolem1061(X0,X0,X1,X1),X0,X0,X1,X1),vskolem1061(X0,X0,X1,X1),X0,X0,X1,X1))
| ~ rpoint(X0)
| ~ rpoint(X1)
| X0 = X1 ),
inference(destructive_equality_resolution,[status(thm)],[f128]) ).
fof(f644,plain,
! [X0,X1] :
( rpoint(vskolem1064(vskolem1063(vskolem1061(X0,X0,X1,X1),X0,X0,X1,X1),vskolem1061(X0,X0,X1,X1),X0,X0,X1,X1))
| ~ rpoint(X0)
| ~ rpoint(X1)
| X0 = X1 ),
inference(destructive_equality_resolution,[status(thm)],[f138]) ).
fof(f874,plain,
rpoint(vd1049),
inference(forward_demodulation,[status(thm)],[f120,f122]) ).
fof(f876,plain,
rpoint(vd1047),
inference(forward_demodulation,[status(thm)],[f123,f124]) ).
fof(f878,plain,
( ~ rpoint(vskolem1064(vskolem1063(vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049),vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049))
| vf(vd1049,vskolem1064(vskolem1063(vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049),vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049)) != vf(vskolem1064(vskolem1063(vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049),vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049),vd1047)
| ~ rpoint(vd1047)
| ~ rpoint(vd1049)
| vd1047 = vd1049 ),
inference(resolution,[status(thm)],[f639,f119]) ).
fof(f879,plain,
( ~ rpoint(vskolem1064(vskolem1063(vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049),vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049))
| vf(vd1049,vskolem1064(vskolem1063(vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049),vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049)) != vf(vskolem1064(vskolem1063(vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049),vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049),vd1047)
| ~ rpoint(vd1047)
| ~ rpoint(vd1049) ),
inference(forward_subsumption_resolution,[status(thm)],[f878,f121]) ).
fof(f880,plain,
( ~ rpoint(vskolem1064(vskolem1063(vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049),vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049))
| vf(vd1049,vskolem1064(vskolem1063(vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049),vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049)) != vf(vskolem1064(vskolem1063(vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049),vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049),vd1047)
| ~ rpoint(vd1047) ),
inference(forward_subsumption_resolution,[status(thm)],[f879,f874]) ).
fof(f881,plain,
( ~ rpoint(vd1047)
| ~ rpoint(vd1049)
| vd1047 = vd1049
| ~ rpoint(vskolem1064(vskolem1063(vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049),vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049))
| ~ rpoint(vd1047) ),
inference(resolution,[status(thm)],[f880,f638]) ).
fof(f882,plain,
( ~ rpoint(vd1049)
| vd1047 = vd1049
| ~ rpoint(vskolem1064(vskolem1063(vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049),vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049))
| ~ rpoint(vd1047) ),
inference(duplicate_literals_removal,[status(thm)],[f881]) ).
fof(f883,plain,
( ~ rpoint(vd1049)
| vd1047 = vd1049
| ~ rpoint(vskolem1064(vskolem1063(vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049),vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049)) ),
inference(forward_subsumption_resolution,[status(thm)],[f882,f876]) ).
fof(f884,plain,
( ~ rpoint(vd1049)
| ~ rpoint(vskolem1064(vskolem1063(vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049),vskolem1061(vd1047,vd1047,vd1049,vd1049),vd1047,vd1047,vd1049,vd1049)) ),
inference(forward_subsumption_resolution,[status(thm)],[f883,f121]) ).
fof(f885,plain,
( ~ rpoint(vd1049)
| ~ rpoint(vd1047)
| ~ rpoint(vd1049)
| vd1047 = vd1049 ),
inference(resolution,[status(thm)],[f644,f884]) ).
fof(f886,plain,
( ~ rpoint(vd1047)
| ~ rpoint(vd1049)
| vd1047 = vd1049 ),
inference(duplicate_literals_removal,[status(thm)],[f885]) ).
fof(f887,plain,
( ~ rpoint(vd1047)
| ~ rpoint(vd1049) ),
inference(forward_subsumption_resolution,[status(thm)],[f886,f121]) ).
fof(f889,plain,
~ rpoint(vd1047),
inference(forward_subsumption_resolution,[status(thm)],[f887,f874]) ).
fof(f890,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f876,f889]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO270+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 14:59:20 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.38 % Drodi V4.1.1
% 0.12/0.41 % Refutation found
% 0.12/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.073653 seconds
% 0.12/0.43 % CPU time: 0.211957 seconds
% 0.12/0.43 % Total memory used: 78.509 MB
% 0.12/0.43 % Net memory used: 78.246 MB
%------------------------------------------------------------------------------