%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM480+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 01:40:41 PM UTC 2026
% Result : Theorem 0.16s 0.45s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 10 unt; 0 def)
% Number of atoms : 50 ( 22 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 46 ( 17 ~; 14 |; 12 &)
% ( 0 <=>; 3 =>; 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 : 9 ( 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p') ).
fof(f36,hypothesis,
( aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
aNaturalNumber0(xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( 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)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,conjecture,
( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl)
| sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
~ ( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl)
| sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f61,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(f62,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)],[f61]) ).
fof(f143,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f150,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f154,plain,
sdtasdt0(xn,xm) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f155,plain,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f156,plain,
( sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtsldt0(sdtasdt0(xn,xm),xl)
& sdtasdt0(xn,xm) != sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f157,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f159,plain,
sdtasdt0(xn,xm) != sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f186,plain,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xn,xm),
inference(forward_demodulation,[status(thm)],[f154,f155]) ).
fof(f187,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl) ),
inference(paramodulation,[status(thm)],[f186,f62]) ).
fof(f190,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[status(thm)],[f187,f143]) ).
fof(f202,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))
| ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f190,f150]) ).
fof(f203,plain,
~ aNaturalNumber0(sdtsldt0(xm,xl)),
inference(resolution,[status(thm)],[f202,f159]) ).
fof(f204,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f203,f157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM480+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n015.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 02:36:50 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 0.16/0.45 % Refutation found
% 0.16/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.51 % Elapsed time: 0.085010 seconds
% 0.16/0.51 % CPU time: 0.135240 seconds
% 0.16/0.51 % Total memory used: 23.297 MB
% 0.16/0.51 % Net memory used: 23.260 MB
%------------------------------------------------------------------------------