%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM479+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 01:40:40 PM UTC 2026
% Result : Theorem 86.40s 12.92s
% Output : CNFRefutation 86.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 17 unt; 0 def)
% Number of atoms : 66 ( 31 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 56 ( 22 ~; 16 |; 12 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,hypothesis,
( aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
aNaturalNumber0(xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,conjecture,
( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( ( sdtasdt0(xn,xm) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl))
& aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xl)) )
=> sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
~ ( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( ( sdtasdt0(xn,xm) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl))
& aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xl)) )
=> sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f58,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f59,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,plain,
! [W0,W1,W2] :
( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f61,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f142,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f143,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f149,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f150,plain,
( sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) != sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl))
& sdtasdt0(xn,xm) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl))
& aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f151,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f152,plain,
xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f154,plain,
sdtasdt0(xn,xm) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f155,plain,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) != sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f170,plain,
! [X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),sdtsldt0(xm,xl)) = sdtasdt0(X0,sdtasdt0(X1,sdtsldt0(xm,xl)))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f61,f151]) ).
fof(f199,plain,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) != sdtasdt0(xn,xm),
inference(forward_demodulation,[status(thm)],[f154,f155]) ).
fof(f225,plain,
! [X0] :
( sdtasdt0(X0,xl) = sdtasdt0(xl,X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f142,f59]) ).
fof(f238,plain,
! [X0] :
( sdtasdt0(X0,xm) = sdtasdt0(xm,X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f143,f59]) ).
fof(f302,plain,
! [X0] :
( sdtasdt0(sdtasdt0(X0,xl),sdtsldt0(xm,xl)) = sdtasdt0(X0,sdtasdt0(xl,sdtsldt0(xm,xl)))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f170,f142]) ).
fof(f307,plain,
! [X0] :
( sdtasdt0(sdtasdt0(X0,xl),sdtsldt0(xm,xl)) = sdtasdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f152,f302]) ).
fof(f567,plain,
sdtasdt0(xn,xl) = sdtasdt0(xl,xn),
inference(resolution,[status(thm)],[f225,f149]) ).
fof(f872,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(resolution,[status(thm)],[f238,f149]) ).
fof(f1212,plain,
sdtasdt0(sdtasdt0(xn,xl),sdtsldt0(xm,xl)) = sdtasdt0(xn,xm),
inference(resolution,[status(thm)],[f307,f149]) ).
fof(f2575,plain,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) != sdtasdt0(xm,xn),
inference(forward_demodulation,[status(thm)],[f872,f199]) ).
fof(f3770,plain,
sdtasdt0(xn,xm) != sdtasdt0(xm,xn),
inference(backward_demodulation,[status(thm)],[f3771,f2575]) ).
fof(f3771,plain,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xn,xm),
inference(forward_demodulation,[status(thm)],[f567,f1212]) ).
fof(f5819,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(resolution,[status(thm)],[f238,f149]) ).
fof(f5824,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5819,f3770]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM479+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 02:34:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 86.40/12.92 % Refutation found
% 86.40/12.92 % SZS status Theorem for theBenchmark: Theorem is valid
% 86.40/12.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 86.40/12.96 % Elapsed time: 12.576785 seconds
% 86.40/12.96 % CPU time: 99.076108 seconds
% 86.40/12.96 % Total memory used: 382.406 MB
% 86.40/12.96 % Net memory used: 352.852 MB
%------------------------------------------------------------------------------