%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM845+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 0.03s 0.32s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 19 unt; 0 def)
% Number of atoms : 41 ( 40 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 6 ~; 2 |; 6 &)
% ( 0 <=>; 3 =>; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 39 !; 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(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(f12,axiom,
! [Vd396,Vd397] :
( vmul(Vd396,v1) = Vd396
& vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [Vd42,Vd43] :
( vplus(Vd42,v1) = vsucc(Vd42)
& vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,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(f18,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)],[f17]) ).
fof(f19,plain,
vmul(vsucc(vd411),sK0_skl) = vplus(vmul(vd411,sK0_skl),sK0_skl),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
vmul(vsucc(vd411),vsucc(sK0_skl)) != vplus(vmul(vd411,vsucc(sK0_skl)),vsucc(sK0_skl)),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f29,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(f30,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)],[f29]) ).
fof(f38,plain,
( ! [Vd396] : vmul(Vd396,v1) = Vd396
& ! [Vd396,Vd397] : vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f39,plain,
! [X0,X1] : vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f41,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f43,plain,
! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f44,plain,
( ! [Vd42] : vplus(Vd42,v1) = vsucc(Vd42)
& ! [Vd42,Vd43] : vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43)) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f45,plain,
! [X0,X1] : vplus(X0,vsucc(X1)) = vsucc(vplus(X0,X1)),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f57,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)],[f30,f19]) ).
fof(f72,plain,
! [X0,X1] : vplus(X0,vsucc(X1)) = vsucc(vplus(X1,X0)),
inference(paramodulation,[status(thm)],[f41,f45]) ).
fof(f74,plain,
! [X0,X1] : vplus(X0,vsucc(X1)) = vplus(X1,vsucc(X0)),
inference(paramodulation,[status(thm)],[f45,f72]) ).
fof(f81,plain,
! [X0,X1] : vplus(vsucc(X0),X1) = vplus(X0,vsucc(X1)),
inference(paramodulation,[status(thm)],[f41,f74]) ).
fof(f105,plain,
vplus(vmul(vd411,sK0_skl),vplus(sK0_skl,vsucc(vd411))) = vplus(vmul(vd411,sK0_skl),vplus(vd411,vsucc(sK0_skl))),
inference(backward_demodulation,[status(thm)],[f81,f57]) ).
fof(f139,plain,
! [X0] : vplus(vmul(vsucc(vd411),sK0_skl),X0) = vplus(vmul(vd411,sK0_skl),vplus(sK0_skl,X0)),
inference(paramodulation,[status(thm)],[f19,f43]) ).
fof(f140,plain,
! [X0,X1,X2] : vplus(vmul(X0,vsucc(X1)),X2) = vplus(vmul(X0,X1),vplus(X0,X2)),
inference(paramodulation,[status(thm)],[f39,f43]) ).
fof(f155,plain,
vplus(vmul(vsucc(vd411),sK0_skl),vsucc(vd411)) = vplus(vmul(vd411,sK0_skl),vplus(vd411,vsucc(sK0_skl))),
inference(backward_demodulation,[status(thm)],[f139,f105]) ).
fof(f174,plain,
vmul(vsucc(vd411),vsucc(sK0_skl)) = vplus(vmul(vd411,sK0_skl),vplus(vd411,vsucc(sK0_skl))),
inference(forward_demodulation,[status(thm)],[f39,f155]) ).
fof(f175,plain,
vmul(vsucc(vd411),vsucc(sK0_skl)) = vplus(vmul(vd411,vsucc(sK0_skl)),vsucc(sK0_skl)),
inference(forward_demodulation,[status(thm)],[f140,f174]) ).
fof(f176,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f175,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM845+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Mon Sep 21 03:12:36 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 0.03/0.32 % Refutation found
% 0.03/0.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.03/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.33 % Elapsed time: 0.036763 seconds
% 0.07/0.33 % CPU time: 0.088793 seconds
% 0.07/0.33 % Total memory used: 67.447 MB
% 0.07/0.33 % Net memory used: 67.102 MB
%------------------------------------------------------------------------------