%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM460+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 : n026.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 01:40:36 PM UTC 2026
% Result : Theorem 0.14s 10.66s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 9 unt; 1 def)
% Number of atoms : 136 ( 27 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 161 ( 61 ~; 55 |; 38 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 46 ( 35 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,conjecture,
( ( sdtlseqdt0(xn,xl)
& ? [W0] :
( sdtpldt0(xn,W0) = xl
& aNaturalNumber0(W0) )
& sdtlseqdt0(xm,xn)
& ? [W0] :
( sdtpldt0(xm,W0) = xn
& aNaturalNumber0(W0) ) )
=> ( sdtlseqdt0(xm,xl)
| ? [W0] :
( sdtpldt0(xm,W0) = xl
& aNaturalNumber0(W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
~ ( ( sdtlseqdt0(xn,xl)
& ? [W0] :
( sdtpldt0(xn,W0) = xl
& aNaturalNumber0(W0) )
& sdtlseqdt0(xm,xn)
& ? [W0] :
( sdtpldt0(xm,W0) = xn
& aNaturalNumber0(W0) ) )
=> ( sdtlseqdt0(xm,xl)
| ? [W0] :
( sdtpldt0(xm,W0) = xl
& aNaturalNumber0(W0) ) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f31,plain,
! [W0,W1] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f32,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f37,plain,
! [W0,W1,W2] :
( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f38,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f66,plain,
! [W0,W1] :
( ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f67,plain,
! [W0,W1] :
( ( ( ! [W2] :
( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2) )
| sdtlseqdt0(W0,W1) )
& ( ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
| ~ sdtlseqdt0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
! [W0,W1] :
( ( ( ! [W2] :
( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2) )
| sdtlseqdt0(W0,W1) )
& ( ( sdtpldt0(W0,sK0_skl(W1,W0)) = W1
& aNaturalNumber0(sK0_skl(W1,W0)) )
| ~ sdtlseqdt0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W2,sK0_skl(W1,W0))],[f67]) ).
fof(f71,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f82,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f84,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f85,plain,
( ~ sdtlseqdt0(xm,xl)
& ! [W0] :
( sdtpldt0(xm,W0) != xl
| ~ aNaturalNumber0(W0) )
& sdtlseqdt0(xn,xl)
& ? [W0] :
( sdtpldt0(xn,W0) = xl
& aNaturalNumber0(W0) )
& sdtlseqdt0(xm,xn)
& ? [W0] :
( sdtpldt0(xm,W0) = xn
& aNaturalNumber0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f86,plain,
( ~ sdtlseqdt0(xm,xl)
& ! [W0] :
( sdtpldt0(xm,W0) != xl
| ~ aNaturalNumber0(W0) )
& sdtlseqdt0(xn,xl)
& sdtpldt0(xn,sK2_skl) = xl
& aNaturalNumber0(sK2_skl)
& sdtlseqdt0(xm,xn)
& sdtpldt0(xm,sK1_skl) = xn
& aNaturalNumber0(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(W0,sK1_skl),skolemize(W0,sK2_skl)],[f85]) ).
fof(f87,plain,
aNaturalNumber0(sK1_skl),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f88,plain,
sdtpldt0(xm,sK1_skl) = xn,
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f90,plain,
aNaturalNumber0(sK2_skl),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f91,plain,
sdtpldt0(xn,sK2_skl) = xl,
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f94,plain,
~ sdtlseqdt0(xm,xl),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f119,plain,
! [X0] :
( sdtpldt0(xn,X0) = sdtpldt0(xm,sdtpldt0(sK1_skl,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK1_skl)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f88,f38]) ).
fof(f127,plain,
! [X0] :
( sdtpldt0(xn,X0) = sdtpldt0(xm,sdtpldt0(sK1_skl,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f119,f82]) ).
fof(f329,plain,
! [X0] :
( sdtpldt0(xn,X0) = sdtpldt0(xm,sdtpldt0(sK1_skl,X0))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f127,f87]) ).
fof(f331,plain,
! [X0] :
( ~ aNaturalNumber0(sdtpldt0(sK1_skl,X0))
| sdtlseqdt0(xm,sdtpldt0(xn,X0))
| ~ aNaturalNumber0(sdtpldt0(xn,X0))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f329,f71]) ).
fof(f335,plain,
! [X0] :
( ~ aNaturalNumber0(sdtpldt0(sK1_skl,X0))
| sdtlseqdt0(xm,sdtpldt0(xn,X0))
| ~ aNaturalNumber0(sdtpldt0(xn,X0))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f331,f82]) ).
fof(f346,plain,
( ~ aNaturalNumber0(sdtpldt0(sK1_skl,sK2_skl))
| sdtlseqdt0(xm,xl)
| ~ aNaturalNumber0(sdtpldt0(xn,sK2_skl))
| ~ aNaturalNumber0(sK2_skl) ),
inference(paramodulation,[status(thm)],[f91,f335]) ).
fof(f349,plain,
( ~ aNaturalNumber0(sdtpldt0(sK1_skl,sK2_skl))
| sdtlseqdt0(xm,xl)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f91,f346]) ).
fof(f350,plain,
( ~ aNaturalNumber0(sdtpldt0(sK1_skl,sK2_skl))
| sdtlseqdt0(xm,xl)
| ~ aNaturalNumber0(xl) ),
inference(forward_subsumption_resolution,[status(thm)],[f349,f90]) ).
fof(f351,plain,
( ~ aNaturalNumber0(sdtpldt0(sK1_skl,sK2_skl))
| sdtlseqdt0(xm,xl) ),
inference(forward_subsumption_resolution,[status(thm)],[f350,f84]) ).
fof(f352,plain,
( ~ aNaturalNumber0(sK2_skl)
| ~ aNaturalNumber0(sK1_skl)
| sdtlseqdt0(xm,xl) ),
inference(resolution,[status(thm)],[f351,f32]) ).
fof(f353,plain,
( ~ aNaturalNumber0(sK2_skl)
| ~ aNaturalNumber0(sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f352,f94]) ).
fof(f355,plain,
~ aNaturalNumber0(sK2_skl),
inference(forward_subsumption_resolution,[status(thm)],[f353,f87]) ).
fof(f356,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f90,f355]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM460+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.52 % Computer : n026.cluster.edu
% 0.10/10.52 % Model : x86_64 x86_64
% 0.10/10.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.52 % Memory : 8046.5625MB
% 0.10/10.52 % OS : Linux 6.8.0-71-generic
% 0.10/10.52 % CPULimit : 300
% 0.10/10.52 % WCLimit : 300
% 0.10/10.52 % DateTime : Mon Sep 21 02:35:02 UTC 2026
% 0.10/10.52 % CPUTime :
% 0.10/10.54 % Drodi V4.1.1
% 0.14/10.66 % Refutation found
% 0.14/10.66 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/10.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/10.68 % Elapsed time: 0.137430 seconds
% 0.14/10.68 % CPU time: 0.824465 seconds
% 0.14/10.68 % Total memory used: 114.844 MB
% 0.14/10.68 % Net memory used: 113.807 MB
%------------------------------------------------------------------------------