%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM613+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 0.07s 15.40s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 11 unt; 0 def)
% Number of atoms : 50 ( 27 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 43 ( 15 ~; 13 |; 12 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 10 ( 10 !; 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(f99,hypothesis,
( aElementOf0(xQ,slbdtsldtrb0(xO,xK))
& sbrdtbr0(xQ) = xK
& aSubsetOf0(xQ,xO)
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSet0(xQ) ),
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(f406,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f407,plain,
szszuzczcdt0(xk) = xK,
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f599,plain,
( aElementOf0(xQ,slbdtsldtrb0(xO,xK))
& sbrdtbr0(xQ) = xK
& aSubsetOf0(xQ,xO)
& ! [W0] :
( aElementOf0(W0,xO)
| ~ aElementOf0(W0,xQ) )
& aSet0(xQ) ),
inference(pre_NNF_transformation,[status(thm)],[f99]) ).
fof(f603,plain,
sbrdtbr0(xQ) = xK,
inference(cnf_transformation,[status(thm)],[f599]) ).
fof(f644,plain,
szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f645,plain,
aElementOf0(sbrdtbr0(xP),szNzAzT0),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f646,plain,
sbrdtbr0(xP) != xk,
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f1063,plain,
szszuzczcdt0(sbrdtbr0(xP)) = xK,
inference(backward_demodulation,[status(thm)],[f603,f644]) ).
fof(f1361,plain,
! [X0] :
( X0 = xk
| szszuzczcdt0(X0) != szszuzczcdt0(xk)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[f195,f406]) ).
fof(f1365,plain,
! [X0] :
( X0 = xk
| szszuzczcdt0(X0) != xK
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_demodulation,[status(thm)],[f407,f1361]) ).
fof(f1376,plain,
( sbrdtbr0(xP) = xk
| szszuzczcdt0(sbrdtbr0(xP)) != xK ),
inference(resolution,[status(thm)],[f1365,f645]) ).
fof(f1380,plain,
( sbrdtbr0(xP) = xk
| xK != xK ),
inference(forward_demodulation,[status(thm)],[f1063,f1376]) ).
fof(f1381,plain,
sbrdtbr0(xP) = xk,
inference(trivial_equality_resolution,[status(thm)],[f1380]) ).
fof(f1382,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1381,f646]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM613+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/15.31 % CPULimit : 300
% 0.07/15.31 % WCLimit : 300
% 0.07/15.31 % DateTime : Mon Sep 21 02:47:32 UTC 2026
% 0.07/15.31 % CPUTime :
% 0.07/15.34 % Drodi V4.1.1
% 0.07/15.40 % Refutation found
% 0.07/15.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/15.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/15.43 % Elapsed time: 0.108017 seconds
% 0.21/15.43 % CPU time: 0.360839 seconds
% 0.21/15.43 % Total memory used: 128.496 MB
% 0.21/15.43 % Net memory used: 127.895 MB
%------------------------------------------------------------------------------