%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM468+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 : 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 01:40:38 PM UTC 2026
% Result : Theorem 0.13s 0.64s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 13 unt; 0 def)
% Number of atoms : 111 ( 54 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 121 ( 44 ~; 39 |; 27 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 26 ( 24 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 != sz00
=> ! [W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1) )
=> ( ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0)
| sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
=> W1 = W2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,hypothesis,
( doDivides0(xl,xn)
& ? [W0] :
( xn = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) )
& doDivides0(xl,xm)
& ? [W0] :
( xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,conjecture,
( xl != sz00
=> ( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( ( xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& aNaturalNumber0(sdtsldt0(xn,xl)) )
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
~ ( xl != sz00
=> ( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( ( xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& aNaturalNumber0(sdtsldt0(xn,xl)) )
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f64,plain,
! [W0,W1,W2] :
( ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f65,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f70,plain,
! [W0] :
( ! [W1,W2] :
( W1 = W2
| ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0)
& sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1) )
| W0 = sz00
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f71,plain,
! [X0,X1,X2] :
( X1 = X2
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f132,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f135,plain,
( doDivides0(xl,xn)
& xn = sdtasdt0(xl,sK3_skl)
& aNaturalNumber0(sK3_skl)
& doDivides0(xl,xm)
& xm = sdtasdt0(xl,sK2_skl)
& aNaturalNumber0(sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(W0,sK2_skl),skolemize(W0,sK3_skl)],[f34]) ).
fof(f139,plain,
aNaturalNumber0(sK3_skl),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f140,plain,
xn = sdtasdt0(xl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f142,plain,
( sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
& xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& aNaturalNumber0(sdtsldt0(xn,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl))
& xl != sz00 ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f143,plain,
xl != sz00,
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f144,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f145,plain,
xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f146,plain,
aNaturalNumber0(sdtsldt0(xn,xl)),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f147,plain,
xn = sdtasdt0(xl,sdtsldt0(xn,xl)),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f148,plain,
sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f189,plain,
! [X0] :
( sdtasdt0(xl,sdtpldt0(X0,sK3_skl)) = sdtpldt0(sdtasdt0(xl,X0),xn)
| ~ aNaturalNumber0(sK3_skl)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xl) ),
inference(paramodulation,[status(thm)],[f140,f65]) ).
fof(f197,plain,
! [X0] :
( sdtasdt0(xl,sdtpldt0(X0,sK3_skl)) = sdtpldt0(sdtasdt0(xl,X0),xn)
| ~ aNaturalNumber0(sK3_skl)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f189,f132]) ).
fof(f320,plain,
! [X0] :
( sK3_skl = X0
| xn != sdtasdt0(xl,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK3_skl)
| xl = sz00
| ~ aNaturalNumber0(xl) ),
inference(paramodulation,[status(thm)],[f140,f71]) ).
fof(f335,plain,
! [X0] :
( sK3_skl = X0
| xn != sdtasdt0(xl,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK3_skl)
| xl = sz00 ),
inference(forward_subsumption_resolution,[status(thm)],[f320,f132]) ).
fof(f700,plain,
! [X0] :
( sK3_skl = X0
| xn != sdtasdt0(xl,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f335,f143]) ).
fof(f702,plain,
( sK3_skl = sdtsldt0(xn,xl)
| ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(sK3_skl) ),
inference(resolution,[status(thm)],[f700,f147]) ).
fof(f712,plain,
( sK3_skl = sdtsldt0(xn,xl)
| ~ aNaturalNumber0(sdtsldt0(xn,xl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f702,f139]) ).
fof(f756,plain,
sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sK3_skl)),
inference(backward_demodulation,[status(thm)],[f759,f148]) ).
fof(f759,plain,
sK3_skl = sdtsldt0(xn,xl),
inference(forward_subsumption_resolution,[status(thm)],[f712,f146]) ).
fof(f1101,plain,
! [X0] :
( sdtasdt0(xl,sdtpldt0(X0,sK3_skl)) = sdtpldt0(sdtasdt0(xl,X0),xn)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f197,f139]) ).
fof(f1111,plain,
( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sK3_skl)) = sdtpldt0(xm,xn)
| ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(paramodulation,[status(thm)],[f145,f1101]) ).
fof(f1114,plain,
sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sK3_skl)) = sdtpldt0(xm,xn),
inference(forward_subsumption_resolution,[status(thm)],[f1111,f144]) ).
fof(f1179,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1114,f756]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM468+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.55 % Computer : n018.cluster.edu
% 0.08/0.55 % Model : x86_64 x86_64
% 0.08/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.55 % Memory : 8046.5625MB
% 0.08/0.55 % OS : Linux 6.8.0-71-generic
% 0.08/0.55 % CPULimit : 300
% 0.08/0.55 % WCLimit : 300
% 0.08/0.55 % DateTime : Mon Sep 21 02:34:59 UTC 2026
% 0.08/0.55 % CPUTime :
% 0.13/0.56 % Drodi V4.1.1
% 0.13/0.64 % Refutation found
% 0.13/0.64 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.67 % Elapsed time: 0.098654 seconds
% 0.13/0.67 % CPU time: 0.568912 seconds
% 0.13/0.67 % Total memory used: 112.896 MB
% 0.13/0.67 % Net memory used: 111.762 MB
%------------------------------------------------------------------------------