%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM849+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 : n018.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 01:41:49 PM UTC 2026
% Result : Theorem 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 22 unt; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 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 : 21 ( 20 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [Vd454] :
( vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454))
=> vmul(vmul(vd448,vd449),vsucc(Vd454)) = vmul(vd448,vmul(vd449,vsucc(Vd454))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [Vd454] :
( vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454))
=> vmul(vmul(vd448,vd449),vsucc(Vd454)) = vmul(vd448,vmul(vd449,vsucc(Vd454))) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f8,axiom,
! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Vd408,Vd409] : vmul(vsucc(Vd408),Vd409) = vplus(vmul(Vd408,Vd409),Vd409),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,plain,
? [Vd454] :
( vmul(vmul(vd448,vd449),vsucc(Vd454)) != vmul(vd448,vmul(vd449,vsucc(Vd454)))
& vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454)) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f15,plain,
( vmul(vmul(vd448,vd449),vsucc(sK0_skl)) != vmul(vd448,vmul(vd449,vsucc(sK0_skl)))
& vmul(vmul(vd448,vd449),sK0_skl) = vmul(vd448,vmul(vd449,sK0_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Vd454,sK0_skl)],[f14]) ).
fof(f16,plain,
vmul(vmul(vd448,vd449),sK0_skl) = vmul(vd448,vmul(vd449,sK0_skl)),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
vmul(vmul(vd448,vd449),vsucc(sK0_skl)) != vmul(vd448,vmul(vd449,vsucc(sK0_skl))),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f27,plain,
! [X0,X1,X2] : vmul(X0,vplus(X1,X2)) = vplus(vmul(X0,X1),vmul(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f28,plain,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f29,plain,
! [X0,X1] : vmul(vsucc(X0),X1) = vplus(vmul(X0,X1),X1),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f44,plain,
vmul(vd448,vmul(vd449,sK0_skl)) = vmul(sK0_skl,vmul(vd448,vd449)),
inference(paramodulation,[status(thm)],[f16,f28]) ).
fof(f51,plain,
vmul(vmul(vd449,vd448),sK0_skl) = vmul(vd448,vmul(vd449,sK0_skl)),
inference(paramodulation,[status(thm)],[f28,f16]) ).
fof(f52,plain,
vmul(vsucc(sK0_skl),vmul(vd448,vd449)) != vmul(vd448,vmul(vd449,vsucc(sK0_skl))),
inference(paramodulation,[status(thm)],[f28,f17]) ).
fof(f59,plain,
vmul(vmul(vd449,vd448),sK0_skl) = vmul(sK0_skl,vmul(vd448,vd449)),
inference(forward_demodulation,[status(thm)],[f44,f51]) ).
fof(f61,plain,
! [X0,X1] : vmul(vsucc(X0),X1) = vplus(vmul(X1,X0),X1),
inference(paramodulation,[status(thm)],[f28,f29]) ).
fof(f174,plain,
! [X0] : vmul(vd448,vplus(vmul(vd449,sK0_skl),X0)) = vplus(vmul(sK0_skl,vmul(vd448,vd449)),vmul(vd448,X0)),
inference(paramodulation,[status(thm)],[f44,f27]) ).
fof(f199,plain,
vmul(sK0_skl,vmul(vd449,vd448)) = vmul(sK0_skl,vmul(vd448,vd449)),
inference(paramodulation,[status(thm)],[f28,f59]) ).
fof(f211,plain,
! [X0] : vmul(vd448,vplus(vmul(vd449,sK0_skl),X0)) = vplus(vmul(sK0_skl,vmul(vd449,vd448)),vmul(vd448,X0)),
inference(backward_demodulation,[status(thm)],[f199,f174]) ).
fof(f226,plain,
vmul(vsucc(sK0_skl),vmul(vd448,vd449)) = vplus(vmul(sK0_skl,vmul(vd449,vd448)),vmul(vd448,vd449)),
inference(paramodulation,[status(thm)],[f199,f29]) ).
fof(f232,plain,
vmul(vsucc(sK0_skl),vmul(vd448,vd449)) = vmul(vd448,vplus(vmul(vd449,sK0_skl),vd449)),
inference(forward_demodulation,[status(thm)],[f211,f226]) ).
fof(f233,plain,
vmul(vd448,vmul(vsucc(sK0_skl),vd449)) != vmul(vd448,vmul(vd449,vsucc(sK0_skl))),
inference(backward_demodulation,[status(thm)],[f234,f52]) ).
fof(f234,plain,
vmul(vsucc(sK0_skl),vmul(vd448,vd449)) = vmul(vd448,vmul(vsucc(sK0_skl),vd449)),
inference(forward_demodulation,[status(thm)],[f61,f232]) ).
fof(f245,plain,
vmul(vd448,vmul(vd449,vsucc(sK0_skl))) != vmul(vd448,vmul(vd449,vsucc(sK0_skl))),
inference(paramodulation,[status(thm)],[f28,f233]) ).
fof(f247,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM849+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n018.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 03:15:13 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.14/0.38 % Refutation found
% 0.14/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.40 % Elapsed time: 0.036122 seconds
% 0.14/0.40 % CPU time: 0.100585 seconds
% 0.14/0.40 % Total memory used: 15.646 MB
% 0.14/0.40 % Net memory used: 15.614 MB
%------------------------------------------------------------------------------