%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM422+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 : n006.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 25.30s 3.97s
% Output : CNFRefutation 27.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 76 ( 33 unt; 0 def)
% Number of atoms : 149 ( 64 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 124 ( 51 ~; 48 |; 16 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 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 : 63 ( 63 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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,axiom,
! [W0] :
( aInteger0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
aInteger0(xa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
sdtasdt0(smndt0(sz10),xa) = smndt0(xa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
sdtasdt0(smndt0(sz10),xa) != smndt0(xa),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f23,plain,
aInteger0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f24,plain,
! [W0] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f25,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f28,plain,
! [W0,W1] :
( aInteger0(sdtasdt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f29,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,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(f31,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)],[f30]) ).
fof(f34,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f35,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0] :
( X0 = sdtpldt0(sz00,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,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] :
( sdtpldt0(X0,smndt0(X0)) = sz00
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
! [X0] :
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f42,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f43,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f45,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f47,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(f48,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)],[f47]) ).
fof(f50,plain,
! [W0] :
( ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f51,plain,
! [X0] :
( sdtasdt0(X0,sz00) = sz00
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f53,plain,
aInteger0(xa),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f54,plain,
sdtasdt0(smndt0(sz10),xa) != smndt0(xa),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f60,plain,
! [X0] :
( ~ aInteger0(X0)
| smndt0(X0) = sdtpldt0(sz00,smndt0(X0)) ),
inference(resolution,[status(thm)],[f36,f25]) ).
fof(f64,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(smndt0(X0),sz10) = smndt0(X0) ),
inference(resolution,[status(thm)],[f45,f25]) ).
fof(f65,plain,
sdtasdt0(xa,sz10) = xa,
inference(resolution,[status(thm)],[f45,f53]) ).
fof(f77,plain,
sdtpldt0(xa,smndt0(xa)) = sz00,
inference(resolution,[status(thm)],[f38,f53]) ).
fof(f82,plain,
sz00 = sdtpldt0(smndt0(sz10),sz10),
inference(resolution,[status(thm)],[f39,f23]) ).
fof(f85,plain,
! [X0] :
( aInteger0(sdtasdt0(X0,xa))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f29,f53]) ).
fof(f86,plain,
! [X0] :
( aInteger0(sdtasdt0(X0,sz10))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f29,f23]) ).
fof(f88,plain,
! [X0] :
( ~ aInteger0(X0)
| aInteger0(sdtasdt0(smndt0(X0),xa)) ),
inference(resolution,[status(thm)],[f85,f25]) ).
fof(f103,plain,
! [X0] :
( ~ aInteger0(X0)
| aInteger0(sdtasdt0(smndt0(X0),sz10)) ),
inference(resolution,[status(thm)],[f86,f25]) ).
fof(f112,plain,
aInteger0(sdtasdt0(smndt0(sz10),xa)),
inference(resolution,[status(thm)],[f88,f23]) ).
fof(f120,plain,
! [X0,X1] :
( sdtpldt0(X0,sdtpldt0(xa,X1)) = sdtpldt0(sdtpldt0(X0,xa),X1)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f31,f53]) ).
fof(f157,plain,
sdtpldt0(sdtasdt0(smndt0(sz10),xa),sz00) = sdtasdt0(smndt0(sz10),xa),
inference(resolution,[status(thm)],[f112,f35]) ).
fof(f163,plain,
aInteger0(sdtasdt0(smndt0(xa),sz10)),
inference(resolution,[status(thm)],[f103,f53]) ).
fof(f164,plain,
aInteger0(sdtasdt0(smndt0(sz10),sz10)),
inference(resolution,[status(thm)],[f103,f23]) ).
fof(f222,plain,
smndt0(xa) = sdtpldt0(sz00,smndt0(xa)),
inference(resolution,[status(thm)],[f60,f53]) ).
fof(f232,plain,
sdtasdt0(smndt0(xa),sz10) = smndt0(xa),
inference(resolution,[status(thm)],[f64,f53]) ).
fof(f233,plain,
sdtasdt0(smndt0(sz10),sz10) = smndt0(sz10),
inference(resolution,[status(thm)],[f64,f23]) ).
fof(f234,plain,
aInteger0(smndt0(xa)),
inference(backward_demodulation,[status(thm)],[f232,f163]) ).
fof(f284,plain,
aInteger0(smndt0(sz10)),
inference(backward_demodulation,[status(thm)],[f233,f164]) ).
fof(f301,plain,
! [X0] :
( aInteger0(sdtasdt0(X0,smndt0(sz10)))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f284,f29]) ).
fof(f404,plain,
! [X0] :
( sdtasdt0(X0,xa) = sdtasdt0(xa,X0)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f43,f53]) ).
fof(f497,plain,
aInteger0(sdtasdt0(xa,smndt0(sz10))),
inference(resolution,[status(thm)],[f301,f53]) ).
fof(f570,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,sz10)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,sz10))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f48,f23]) ).
fof(f628,plain,
sdtasdt0(smndt0(sz10),xa) = sdtasdt0(xa,smndt0(sz10)),
inference(resolution,[status(thm)],[f404,f284]) ).
fof(f756,plain,
sdtasdt0(xa,sz00) = sz00,
inference(resolution,[status(thm)],[f51,f53]) ).
fof(f1313,plain,
sdtasdt0(xa,smndt0(sz10)) != smndt0(xa),
inference(backward_demodulation,[status(thm)],[f628,f54]) ).
fof(f1837,plain,
sdtpldt0(sdtasdt0(xa,smndt0(sz10)),sz00) = sdtasdt0(smndt0(sz10),xa),
inference(forward_demodulation,[status(thm)],[f628,f157]) ).
fof(f1838,plain,
sdtpldt0(sdtasdt0(xa,smndt0(sz10)),sz00) = sdtasdt0(xa,smndt0(sz10)),
inference(forward_demodulation,[status(thm)],[f628,f1837]) ).
fof(f2220,plain,
! [X0] :
( sdtpldt0(X0,sdtpldt0(xa,smndt0(xa))) = sdtpldt0(sdtpldt0(X0,xa),smndt0(xa))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f120,f234]) ).
fof(f2225,plain,
! [X0] :
( sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,xa),smndt0(xa))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f77,f2220]) ).
fof(f2232,plain,
sdtpldt0(sdtasdt0(xa,smndt0(sz10)),sz00) = sdtpldt0(sdtpldt0(sdtasdt0(xa,smndt0(sz10)),xa),smndt0(xa)),
inference(resolution,[status(thm)],[f2225,f497]) ).
fof(f2243,plain,
sdtasdt0(xa,smndt0(sz10)) = sdtpldt0(sdtpldt0(sdtasdt0(xa,smndt0(sz10)),xa),smndt0(xa)),
inference(forward_demodulation,[status(thm)],[f1838,f2232]) ).
fof(f3980,plain,
! [X0] :
( sdtasdt0(X0,sdtpldt0(smndt0(sz10),sz10)) = sdtpldt0(sdtasdt0(X0,smndt0(sz10)),sdtasdt0(X0,sz10))
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f570,f284]) ).
fof(f3987,plain,
! [X0] :
( sdtasdt0(X0,sz00) = sdtpldt0(sdtasdt0(X0,smndt0(sz10)),sdtasdt0(X0,sz10))
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f82,f3980]) ).
fof(f3999,plain,
sdtasdt0(xa,sz00) = sdtpldt0(sdtasdt0(xa,smndt0(sz10)),sdtasdt0(xa,sz10)),
inference(resolution,[status(thm)],[f3987,f53]) ).
fof(f4011,plain,
sz00 = sdtpldt0(sdtasdt0(xa,smndt0(sz10)),sdtasdt0(xa,sz10)),
inference(forward_demodulation,[status(thm)],[f756,f3999]) ).
fof(f4012,plain,
sz00 = sdtpldt0(sdtasdt0(xa,smndt0(sz10)),xa),
inference(forward_demodulation,[status(thm)],[f65,f4011]) ).
fof(f4769,plain,
sdtasdt0(xa,smndt0(sz10)) = sdtpldt0(sz00,smndt0(xa)),
inference(forward_demodulation,[status(thm)],[f4012,f2243]) ).
fof(f4770,plain,
sdtasdt0(xa,smndt0(sz10)) = smndt0(xa),
inference(forward_demodulation,[status(thm)],[f222,f4769]) ).
fof(f4771,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4770,f1313]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM422+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 02:27:57 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 25.30/3.97 % Refutation found
% 25.30/3.97 % SZS status Theorem for theBenchmark: Theorem is valid
% 25.30/3.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 27.83/4.04 % Elapsed time: 3.655952 seconds
% 27.83/4.04 % CPU time: 28.438514 seconds
% 27.83/4.04 % Total memory used: 240.697 MB
% 27.83/4.04 % Net memory used: 214.681 MB
%------------------------------------------------------------------------------