%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM613+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 01:41:12 PM UTC 2026
% Result : Theorem 0.13s 0.62s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 13 unt; 0 def)
% Number of atoms : 40 ( 27 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 14 ~; 12 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 8 ( 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( szszuzczcdt0(W0) = szszuzczcdt0(W1)
=> W0 = W1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f80,hypothesis,
( szszuzczcdt0(xk) = xK
& aElementOf0(xk,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f109,hypothesis,
( aElementOf0(sbrdtbr0(xP),szNzAzT0)
& szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ)
& sbrdtbr0(xQ) = szszuzczcdt0(xk) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f110,conjecture,
sbrdtbr0(xP) = xk,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f111,negated_conjecture,
sbrdtbr0(xP) != xk,
inference(negated_conjecture,[status(cth)],[f110]) ).
fof(f194,plain,
! [W0,W1] :
( W0 = W1
| szszuzczcdt0(W0) != szszuzczcdt0(W1)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f195,plain,
! [X0,X1] :
( X0 = X1
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f384,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f385,plain,
szszuzczcdt0(xk) = xK,
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f454,plain,
sbrdtbr0(xQ) = szszuzczcdt0(xk),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f455,plain,
szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f456,plain,
aElementOf0(sbrdtbr0(xP),szNzAzT0),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f457,plain,
sbrdtbr0(xP) != xk,
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f551,plain,
szszuzczcdt0(sbrdtbr0(xP)) = xK,
inference(backward_demodulation,[status(thm)],[f553,f455]) ).
fof(f552,plain,
xK = szszuzczcdt0(xk),
inference(backward_demodulation,[status(thm)],[f553,f454]) ).
fof(f553,plain,
sbrdtbr0(xQ) = xK,
inference(forward_demodulation,[status(thm)],[f454,f385]) ).
fof(f970,plain,
! [X0] :
( X0 = xk
| szszuzczcdt0(X0) != szszuzczcdt0(xk)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[f195,f384]) ).
fof(f975,plain,
! [X0] :
( X0 = xk
| szszuzczcdt0(X0) != xK
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_demodulation,[status(thm)],[f552,f970]) ).
fof(f984,plain,
( sbrdtbr0(xP) = xk
| szszuzczcdt0(sbrdtbr0(xP)) != xK ),
inference(resolution,[status(thm)],[f975,f456]) ).
fof(f990,plain,
( sbrdtbr0(xP) = xk
| xK != xK ),
inference(forward_demodulation,[status(thm)],[f551,f984]) ).
fof(f991,plain,
sbrdtbr0(xP) = xk,
inference(trivial_equality_resolution,[status(thm)],[f990]) ).
fof(f992,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f991,f457]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM613+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.55 % Computer : n001.cluster.edu
% 0.10/0.55 % Model : x86_64 x86_64
% 0.10/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.55 % Memory : 8046.5625MB
% 0.10/0.55 % OS : Linux 6.8.0-71-generic
% 0.10/0.55 % CPULimit : 300
% 0.10/0.55 % WCLimit : 300
% 0.10/0.55 % DateTime : Mon Sep 21 02:50:14 UTC 2026
% 0.10/0.55 % CPUTime :
% 0.13/0.57 % Drodi V4.1.1
% 0.13/0.62 % Refutation found
% 0.13/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.64 % Elapsed time: 0.079742 seconds
% 0.13/0.64 % CPU time: 0.351300 seconds
% 0.13/0.64 % Total memory used: 104.682 MB
% 0.13/0.64 % Net memory used: 104.342 MB
%------------------------------------------------------------------------------