%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM421+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 01:40:28 PM UTC 2026
% Result : Theorem 2.82s 0.79s
% Output : CNFRefutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 60 ( 22 unt; 0 def)
% Number of atoms : 126 ( 57 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 113 ( 47 ~; 42 |; 16 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 53 ( 53 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [W0,W1,W2] :
( ( aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [W0] :
( aInteger0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [W0] :
( aInteger0(W0)
=> ( sz00 = sdtpldt0(smndt0(W0),W0)
& sdtpldt0(W0,smndt0(W0)) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [W0] :
( aInteger0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [W0,W1,W2] :
( ( aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
aInteger0(xa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,conjecture,
( sz00 = sdtasdt0(sz00,xa)
& sdtasdt0(xa,sz00) = sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
~ ( sz00 = sdtasdt0(sz00,xa)
& sdtasdt0(xa,sz00) = sz00 ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f21,plain,
aInteger0(sz00),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f22,plain,
aInteger0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f23,plain,
! [W0] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f24,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f27,plain,
! [W0,W1] :
( aInteger0(sdtasdt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f28,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [W0,W1,W2] :
( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f30,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f33,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f34,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0] :
( X0 = sdtpldt0(sz00,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f36,plain,
! [W0] :
( ( sz00 = sdtpldt0(smndt0(W0),W0)
& sdtpldt0(W0,smndt0(W0)) = sz00 )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f38,plain,
! [X0] :
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f41,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f42,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f44,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f46,plain,
! [W0,W1,W2] :
( ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f47,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,plain,
aInteger0(xa),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( sz00 != sdtasdt0(sz00,xa)
| sdtasdt0(xa,sz00) != sz00 ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f51,plain,
( sz00 != sdtasdt0(sz00,xa)
| sdtasdt0(xa,sz00) != sz00 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f53,plain,
aInteger0(smndt0(xa)),
inference(resolution,[status(thm)],[f24,f49]) ).
fof(f64,plain,
sdtpldt0(sz10,sz00) = sz10,
inference(resolution,[status(thm)],[f34,f22]) ).
fof(f70,plain,
! [X0] :
( aInteger0(sdtasdt0(xa,X0))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f28,f49]) ).
fof(f84,plain,
! [X0,X1] :
( sdtpldt0(X0,sdtpldt0(xa,X1)) = sdtpldt0(sdtpldt0(X0,xa),X1)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f30,f49]) ).
fof(f96,plain,
sdtasdt0(xa,sz10) = xa,
inference(resolution,[status(thm)],[f44,f49]) ).
fof(f107,plain,
aInteger0(sdtasdt0(xa,sz00)),
inference(resolution,[status(thm)],[f70,f21]) ).
fof(f135,plain,
sdtasdt0(xa,sz00) = sdtpldt0(sz00,sdtasdt0(xa,sz00)),
inference(resolution,[status(thm)],[f107,f35]) ).
fof(f145,plain,
sz00 = sdtpldt0(smndt0(xa),xa),
inference(resolution,[status(thm)],[f38,f49]) ).
fof(f221,plain,
! [X0] :
( sdtasdt0(X0,xa) = sdtasdt0(xa,X0)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f42,f49]) ).
fof(f261,plain,
sdtasdt0(sz00,xa) = sdtasdt0(xa,sz00),
inference(resolution,[status(thm)],[f221,f21]) ).
fof(f276,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtpldt0(sz10,X1)) = sdtpldt0(sdtasdt0(X0,sz10),sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f47,f22]) ).
fof(f326,plain,
( sz00 != sdtasdt0(xa,sz00)
| sdtasdt0(xa,sz00) != sz00 ),
inference(forward_demodulation,[status(thm)],[f261,f51]) ).
fof(f327,plain,
sdtasdt0(xa,sz00) != sz00,
inference(duplicate_literals_removal,[status(thm)],[f326]) ).
fof(f392,plain,
! [X0] :
( sdtpldt0(X0,sdtpldt0(xa,sdtasdt0(xa,sz00))) = sdtpldt0(sdtpldt0(X0,xa),sdtasdt0(xa,sz00))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f84,f107]) ).
fof(f462,plain,
! [X0] :
( sdtasdt0(X0,sdtpldt0(sz10,sz00)) = sdtpldt0(sdtasdt0(X0,sz10),sdtasdt0(X0,sz00))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f276,f21]) ).
fof(f463,plain,
! [X0] :
( sdtasdt0(X0,sz10) = sdtpldt0(sdtasdt0(X0,sz10),sdtasdt0(X0,sz00))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f64,f462]) ).
fof(f471,plain,
sdtasdt0(xa,sz10) = sdtpldt0(sdtasdt0(xa,sz10),sdtasdt0(xa,sz00)),
inference(resolution,[status(thm)],[f463,f49]) ).
fof(f473,plain,
xa = sdtpldt0(sdtasdt0(xa,sz10),sdtasdt0(xa,sz00)),
inference(forward_demodulation,[status(thm)],[f96,f471]) ).
fof(f474,plain,
xa = sdtpldt0(xa,sdtasdt0(xa,sz00)),
inference(forward_demodulation,[status(thm)],[f96,f473]) ).
fof(f1212,plain,
! [X0] :
( sdtpldt0(X0,xa) = sdtpldt0(sdtpldt0(X0,xa),sdtasdt0(xa,sz00))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f474,f392]) ).
fof(f1224,plain,
sdtpldt0(smndt0(xa),xa) = sdtpldt0(sdtpldt0(smndt0(xa),xa),sdtasdt0(xa,sz00)),
inference(resolution,[status(thm)],[f1212,f53]) ).
fof(f1228,plain,
sz00 = sdtpldt0(sdtpldt0(smndt0(xa),xa),sdtasdt0(xa,sz00)),
inference(forward_demodulation,[status(thm)],[f145,f1224]) ).
fof(f1229,plain,
sz00 = sdtpldt0(sz00,sdtasdt0(xa,sz00)),
inference(forward_demodulation,[status(thm)],[f145,f1228]) ).
fof(f1230,plain,
sz00 = sdtasdt0(xa,sz00),
inference(forward_demodulation,[status(thm)],[f135,f1229]) ).
fof(f1231,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1230,f327]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM421+1 : 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 : n001.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
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 02:32:58 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 2.82/0.79 % Refutation found
% 2.82/0.79 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.82/0.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.82/0.82 % Elapsed time: 0.462595 seconds
% 2.82/0.82 % CPU time: 3.451135 seconds
% 2.82/0.82 % Total memory used: 97.422 MB
% 2.82/0.82 % Net memory used: 89.550 MB
%------------------------------------------------------------------------------