%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM845+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 : n013.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 01:41:48 PM UTC 2026
% Result : Theorem 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 17 unt; 0 def)
% Number of atoms : 67 ( 66 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 43 ( 18 ~; 14 |; 2 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 23 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [Vd416] :
( vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416)
=> vmul(vsucc(vd411),vsucc(Vd416)) = vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [Vd416] :
( vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416)
=> vmul(vsucc(vd411),vsucc(Vd416)) = vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
! [Vd413] :
( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)
=> vplus(vplus(vmul(vd411,Vd413),vd411),vsucc(Vd413)) = vplus(vmul(vd411,vsucc(Vd413)),vsucc(Vd413)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [Vd413] :
( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)
=> vplus(vmul(vd411,Vd413),vplus(vd411,vsucc(Vd413))) = vplus(vplus(vmul(vd411,Vd413),vd411),vsucc(Vd413)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Vd413] :
( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)
=> vplus(vmul(vd411,Vd413),vsucc(vplus(vd411,Vd413))) = vplus(vmul(vd411,Vd413),vplus(vd411,vsucc(Vd413))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Vd413] :
( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)
=> vplus(vmul(vd411,Vd413),vplus(vsucc(vd411),Vd413)) = vplus(vmul(vd411,Vd413),vsucc(vplus(vd411,Vd413))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [Vd413] :
( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)
=> vplus(vmul(vd411,Vd413),vplus(Vd413,vsucc(vd411))) = vplus(vmul(vd411,Vd413),vplus(vsucc(vd411),Vd413)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Vd413] :
( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)
=> vplus(vplus(vmul(vd411,Vd413),Vd413),vsucc(vd411)) = vplus(vmul(vd411,Vd413),vplus(Vd413,vsucc(vd411))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Vd413] :
( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)
=> vmul(vsucc(vd411),vsucc(Vd413)) = vplus(vmul(vsucc(vd411),Vd413),vsucc(vd411)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,plain,
? [Vd416] :
( vmul(vsucc(vd411),vsucc(Vd416)) != vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416))
& vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f61,plain,
( vmul(vsucc(vd411),vsucc(sK0_skl)) != vplus(vmul(vd411,vsucc(sK0_skl)),vsucc(sK0_skl))
& vmul(vsucc(vd411),sK0_skl) = vplus(vmul(vd411,sK0_skl),sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Vd416,sK0_skl)],[f60]) ).
fof(f62,plain,
vmul(vsucc(vd411),sK0_skl) = vplus(vmul(vd411,sK0_skl),sK0_skl),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
vmul(vsucc(vd411),vsucc(sK0_skl)) != vplus(vmul(vd411,vsucc(sK0_skl)),vsucc(sK0_skl)),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f64,plain,
! [Vd413] :
( vplus(vplus(vmul(vd411,Vd413),vd411),vsucc(Vd413)) = vplus(vmul(vd411,vsucc(Vd413)),vsucc(Vd413))
| vmul(vsucc(vd411),Vd413) != vplus(vmul(vd411,Vd413),Vd413) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f65,plain,
! [X0] :
( vplus(vplus(vmul(vd411,X0),vd411),vsucc(X0)) = vplus(vmul(vd411,vsucc(X0)),vsucc(X0))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [Vd413] :
( vplus(vmul(vd411,Vd413),vplus(vd411,vsucc(Vd413))) = vplus(vplus(vmul(vd411,Vd413),vd411),vsucc(Vd413))
| vmul(vsucc(vd411),Vd413) != vplus(vmul(vd411,Vd413),Vd413) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f67,plain,
! [X0] :
( vplus(vmul(vd411,X0),vplus(vd411,vsucc(X0))) = vplus(vplus(vmul(vd411,X0),vd411),vsucc(X0))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
! [Vd413] :
( vplus(vmul(vd411,Vd413),vsucc(vplus(vd411,Vd413))) = vplus(vmul(vd411,Vd413),vplus(vd411,vsucc(Vd413)))
| vmul(vsucc(vd411),Vd413) != vplus(vmul(vd411,Vd413),Vd413) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f69,plain,
! [X0] :
( vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))) = vplus(vmul(vd411,X0),vplus(vd411,vsucc(X0)))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,plain,
! [Vd413] :
( vplus(vmul(vd411,Vd413),vplus(vsucc(vd411),Vd413)) = vplus(vmul(vd411,Vd413),vsucc(vplus(vd411,Vd413)))
| vmul(vsucc(vd411),Vd413) != vplus(vmul(vd411,Vd413),Vd413) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f71,plain,
! [X0] :
( vplus(vmul(vd411,X0),vplus(vsucc(vd411),X0)) = vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0)))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
! [Vd413] :
( vplus(vmul(vd411,Vd413),vplus(Vd413,vsucc(vd411))) = vplus(vmul(vd411,Vd413),vplus(vsucc(vd411),Vd413))
| vmul(vsucc(vd411),Vd413) != vplus(vmul(vd411,Vd413),Vd413) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f73,plain,
! [X0] :
( vplus(vmul(vd411,X0),vplus(X0,vsucc(vd411))) = vplus(vmul(vd411,X0),vplus(vsucc(vd411),X0))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f74,plain,
! [Vd413] :
( vplus(vplus(vmul(vd411,Vd413),Vd413),vsucc(vd411)) = vplus(vmul(vd411,Vd413),vplus(Vd413,vsucc(vd411)))
| vmul(vsucc(vd411),Vd413) != vplus(vmul(vd411,Vd413),Vd413) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f75,plain,
! [X0] :
( vplus(vplus(vmul(vd411,X0),X0),vsucc(vd411)) = vplus(vmul(vd411,X0),vplus(X0,vsucc(vd411)))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f78,plain,
! [Vd413] :
( vmul(vsucc(vd411),vsucc(Vd413)) = vplus(vmul(vsucc(vd411),Vd413),vsucc(vd411))
| vmul(vsucc(vd411),Vd413) != vplus(vmul(vd411,Vd413),Vd413) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f79,plain,
! [X0] :
( vmul(vsucc(vd411),vsucc(X0)) = vplus(vmul(vsucc(vd411),X0),vsucc(vd411))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f195,plain,
vplus(vplus(vmul(vd411,sK0_skl),vd411),vsucc(sK0_skl)) = vplus(vmul(vd411,vsucc(sK0_skl)),vsucc(sK0_skl)),
inference(resolution,[status(thm)],[f65,f62]) ).
fof(f207,plain,
vplus(vmul(vd411,sK0_skl),vplus(vd411,vsucc(sK0_skl))) = vplus(vplus(vmul(vd411,sK0_skl),vd411),vsucc(sK0_skl)),
inference(resolution,[status(thm)],[f67,f62]) ).
fof(f213,plain,
vplus(vmul(vd411,sK0_skl),vsucc(vplus(vd411,sK0_skl))) = vplus(vmul(vd411,sK0_skl),vplus(vd411,vsucc(sK0_skl))),
inference(resolution,[status(thm)],[f69,f62]) ).
fof(f219,plain,
vplus(vmul(vd411,sK0_skl),vplus(vsucc(vd411),sK0_skl)) = vplus(vmul(vd411,sK0_skl),vsucc(vplus(vd411,sK0_skl))),
inference(resolution,[status(thm)],[f71,f62]) ).
fof(f225,plain,
vplus(vmul(vd411,sK0_skl),vplus(sK0_skl,vsucc(vd411))) = vplus(vmul(vd411,sK0_skl),vplus(vsucc(vd411),sK0_skl)),
inference(resolution,[status(thm)],[f73,f62]) ).
fof(f231,plain,
vplus(vplus(vmul(vd411,sK0_skl),sK0_skl),vsucc(vd411)) = vplus(vmul(vd411,sK0_skl),vplus(sK0_skl,vsucc(vd411))),
inference(resolution,[status(thm)],[f75,f62]) ).
fof(f233,plain,
vplus(vmul(vsucc(vd411),sK0_skl),vsucc(vd411)) = vplus(vmul(vd411,sK0_skl),vplus(sK0_skl,vsucc(vd411))),
inference(forward_demodulation,[status(thm)],[f62,f231]) ).
fof(f245,plain,
vmul(vsucc(vd411),vsucc(sK0_skl)) = vplus(vmul(vsucc(vd411),sK0_skl),vsucc(vd411)),
inference(resolution,[status(thm)],[f79,f62]) ).
fof(f304,plain,
vplus(vmul(vd411,sK0_skl),vplus(vd411,vsucc(sK0_skl))) = vplus(vmul(vd411,vsucc(sK0_skl)),vsucc(sK0_skl)),
inference(forward_demodulation,[status(thm)],[f195,f207]) ).
fof(f307,plain,
vplus(vmul(vd411,sK0_skl),vsucc(vplus(vd411,sK0_skl))) = vplus(vmul(vd411,vsucc(sK0_skl)),vsucc(sK0_skl)),
inference(forward_demodulation,[status(thm)],[f304,f213]) ).
fof(f311,plain,
vmul(vsucc(vd411),vsucc(sK0_skl)) = vplus(vmul(vd411,sK0_skl),vplus(sK0_skl,vsucc(vd411))),
inference(forward_demodulation,[status(thm)],[f245,f233]) ).
fof(f313,plain,
vplus(vmul(vd411,sK0_skl),vplus(vsucc(vd411),sK0_skl)) = vplus(vmul(vd411,vsucc(sK0_skl)),vsucc(sK0_skl)),
inference(forward_demodulation,[status(thm)],[f307,f219]) ).
fof(f316,plain,
vmul(vsucc(vd411),vsucc(sK0_skl)) = vplus(vmul(vd411,vsucc(sK0_skl)),vsucc(sK0_skl)),
inference(backward_demodulation,[status(thm)],[f317,f313]) ).
fof(f317,plain,
vmul(vsucc(vd411),vsucc(sK0_skl)) = vplus(vmul(vd411,sK0_skl),vplus(vsucc(vd411),sK0_skl)),
inference(forward_demodulation,[status(thm)],[f311,f225]) ).
fof(f319,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f316,f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM845+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 03:12:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.063764 seconds
% 0.14/0.43 % CPU time: 0.272470 seconds
% 0.14/0.43 % Total memory used: 84.803 MB
% 0.14/0.43 % Net memory used: 84.510 MB
%------------------------------------------------------------------------------