%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM525+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 : n010.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 01:40:51 PM UTC 2026
% Result : Theorem 123.16s 16.25s
% Output : CNFRefutation 123.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 16 unt; 2 def)
% Number of atoms : 75 ( 30 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 67 ( 30 ~; 23 |; 10 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 21 ( 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
( xq = sdtsldt0(xn,xp)
& xn = sdtasdt0(xp,xq)
& aNaturalNumber0(xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f65,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f66,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [W0,W1,W2] :
( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f68,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f168,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f170,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f183,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f196,plain,
aNaturalNumber0(xq),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f197,plain,
xn = sdtasdt0(xp,xq),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f199,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f224,plain,
sdtasdt0(xn,xn) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(backward_demodulation,[status(thm)],[f183,f199]) ).
fof(f252,plain,
! [X0] :
( sdtasdt0(X0,xn) = sdtasdt0(xn,X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f168,f66]) ).
fof(f271,plain,
! [X0] :
( sdtasdt0(sdtasdt0(X0,xq),xq) = sdtasdt0(X0,sdtasdt0(xq,xq))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f196,f68]) ).
fof(f274,plain,
! [X0,X1] :
( sdtasdt0(sdtasdt0(X0,xq),X1) = sdtasdt0(X0,sdtasdt0(xq,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f196,f68]) ).
fof(f517,definition,
( sQ0_spl
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f519,plain,
( sQ0_spl
| ~ aNaturalNumber0(xp) ),
inference(component_clause,[status(thm)],[f517]) ).
fof(f524,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f519,f170]) ).
fof(f525,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f524]) ).
fof(f592,plain,
sdtasdt0(xq,xn) = sdtasdt0(xn,xq),
inference(resolution,[status(thm)],[f252,f196]) ).
fof(f847,plain,
( sdtasdt0(xn,xq) = sdtasdt0(xp,sdtasdt0(xq,xq))
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f197,f271]) ).
fof(f852,definition,
( sQ36_spl
<=> sdtasdt0(xn,xq) = sdtasdt0(xp,sdtasdt0(xq,xq)) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f853,plain,
( ~ sQ36_spl
| sdtasdt0(xn,xq) = sdtasdt0(xp,sdtasdt0(xq,xq)) ),
inference(component_clause,[status(thm)],[f852]) ).
fof(f855,plain,
( sQ36_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f847,f517,f852]) ).
fof(f998,plain,
! [X0] :
( sdtasdt0(sdtasdt0(X0,xq),xn) = sdtasdt0(X0,sdtasdt0(xq,xn))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f274,f168]) ).
fof(f3335,plain,
( ~ sQ36_spl
| sdtasdt0(xn,xn) != sdtasdt0(xp,sdtasdt0(xn,xq)) ),
inference(backward_demodulation,[status(thm)],[f853,f224]) ).
fof(f3449,plain,
! [X0] :
( sdtasdt0(sdtasdt0(X0,xq),xn) = sdtasdt0(X0,sdtasdt0(xn,xq))
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f592,f998]) ).
fof(f3457,plain,
sdtasdt0(sdtasdt0(xp,xq),xn) = sdtasdt0(xp,sdtasdt0(xn,xq)),
inference(resolution,[status(thm)],[f3449,f170]) ).
fof(f3463,plain,
sdtasdt0(xn,xn) = sdtasdt0(xp,sdtasdt0(xn,xq)),
inference(forward_demodulation,[status(thm)],[f197,f3457]) ).
fof(f3464,plain,
( ~ sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3463,f3335]) ).
fof(f3465,plain,
~ sQ36_spl,
inference(contradiction_clause,[status(thm)],[f3464]) ).
fof(f3466,plain,
$false,
inference(sat_refutation,[status(thm)],[f525,f855,f3465]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM525+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.63 % Computer : n010.cluster.edu
% 0.19/0.63 % Model : x86_64 x86_64
% 0.19/0.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.63 % Memory : 8046.5625MB
% 0.19/0.63 % OS : Linux 6.8.0-71-generic
% 0.19/0.64 % CPULimit : 300
% 0.19/0.64 % WCLimit : 300
% 0.19/0.64 % DateTime : Mon Sep 21 02:37:55 UTC 2026
% 0.19/0.64 % CPUTime :
% 0.23/0.66 % Drodi V4.1.1
% 123.16/16.25 % Refutation found
% 123.16/16.25 % SZS status Theorem for theBenchmark: Theorem is valid
% 123.16/16.25 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 123.16/16.31 % Elapsed time: 15.656392 seconds
% 123.16/16.31 % CPU time: 123.709410 seconds
% 123.16/16.31 % Total memory used: 338.471 MB
% 123.16/16.31 % Net memory used: 312.413 MB
%------------------------------------------------------------------------------