%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM453+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 01:40:34 PM UTC 2026
% Result : Theorem 0.64s 0.93s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 60 ( 13 unt; 2 def)
% Number of atoms : 126 ( 54 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 118 ( 52 ~; 48 |; 11 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [W0] :
( aInteger0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [W0] :
( aInteger0(W0)
=> ( sz00 = sdtpldt0(smndt0(W0),W0)
& sdtpldt0(W0,smndt0(W0)) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& xp != sz00
& aInteger0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,conjecture,
( sdtpldt0(sz10,smndt0(xp)) != sz10
& sdtpldt0(sz10,xp) != sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
~ ( sdtpldt0(sz10,smndt0(xp)) != sz10
& sdtpldt0(sz10,xp) != sz10 ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f54,plain,
aInteger0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f55,plain,
! [W0] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f56,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f61,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(f62,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)],[f61]) ).
fof(f63,plain,
! [W0,W1] :
( sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f64,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f65,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f66,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f68,plain,
! [W0] :
( ( sz00 = sdtpldt0(smndt0(W0),W0)
& sdtpldt0(W0,smndt0(W0)) = sz00 )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f69,plain,
! [X0] :
( sdtpldt0(X0,smndt0(X0)) = sz00
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,plain,
! [X0] :
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f229,plain,
aInteger0(xp),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f230,plain,
xp != sz00,
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f234,plain,
( sdtpldt0(sz10,smndt0(xp)) = sz10
| sdtpldt0(sz10,xp) = sz10 ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f235,plain,
( sdtpldt0(sz10,smndt0(xp)) = sz10
| sdtpldt0(sz10,xp) = sz10 ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f247,definition,
( sQ0_spl
<=> sdtpldt0(sz10,xp) = sz10 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f248,plain,
( ~ sQ0_spl
| sdtpldt0(sz10,xp) = sz10 ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f249,plain,
( sQ0_spl
| sdtpldt0(sz10,xp) != sz10 ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,definition,
( sQ1_spl
<=> sdtpldt0(sz10,smndt0(xp)) = sz10 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f251,plain,
( ~ sQ1_spl
| sdtpldt0(sz10,smndt0(xp)) = sz10 ),
inference(component_clause,[status(thm)],[f250]) ).
fof(f253,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f235,f247,f250]) ).
fof(f289,plain,
aInteger0(smndt0(xp)),
inference(resolution,[status(thm)],[f56,f229]) ).
fof(f290,plain,
aInteger0(smndt0(sz10)),
inference(resolution,[status(thm)],[f56,f54]) ).
fof(f294,plain,
! [X0,X1] :
( sdtpldt0(xp,sdtpldt0(X0,X1)) = sdtpldt0(sdtpldt0(xp,X0),X1)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f62,f229]) ).
fof(f295,plain,
! [X0,X1] :
( sdtpldt0(sz10,sdtpldt0(X0,X1)) = sdtpldt0(sdtpldt0(sz10,X0),X1)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f62,f54]) ).
fof(f296,plain,
! [X0] :
( sdtpldt0(xp,X0) = sdtpldt0(X0,xp)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f64,f229]) ).
fof(f306,plain,
sdtpldt0(xp,sz00) = xp,
inference(resolution,[status(thm)],[f66,f229]) ).
fof(f307,plain,
sdtpldt0(sz10,sz00) = sz10,
inference(resolution,[status(thm)],[f66,f54]) ).
fof(f313,plain,
sdtpldt0(sz10,smndt0(sz10)) = sz00,
inference(resolution,[status(thm)],[f69,f54]) ).
fof(f315,plain,
sz00 = sdtpldt0(smndt0(xp),xp),
inference(resolution,[status(thm)],[f70,f229]) ).
fof(f482,plain,
! [X0] :
( sdtpldt0(xp,sdtpldt0(sz10,X0)) = sdtpldt0(sdtpldt0(xp,sz10),X0)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f294,f54]) ).
fof(f486,plain,
! [X0] :
( sdtpldt0(sz10,sdtpldt0(smndt0(xp),X0)) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),X0)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f295,f289]) ).
fof(f644,plain,
sdtpldt0(xp,sz10) = sdtpldt0(sz10,xp),
inference(resolution,[status(thm)],[f296,f54]) ).
fof(f648,plain,
! [X0] :
( ~ sQ0_spl
| sdtpldt0(xp,sdtpldt0(sz10,X0)) = sdtpldt0(sz10,X0)
| ~ aInteger0(X0) ),
inference(backward_demodulation,[status(thm)],[f650,f482]) ).
fof(f650,plain,
( ~ sQ0_spl
| sdtpldt0(xp,sz10) = sz10 ),
inference(forward_demodulation,[status(thm)],[f248,f644]) ).
fof(f652,plain,
( ~ sQ0_spl
| sdtpldt0(xp,sdtpldt0(sz10,smndt0(sz10))) = sdtpldt0(sz10,smndt0(sz10)) ),
inference(resolution,[status(thm)],[f648,f290]) ).
fof(f658,plain,
( ~ sQ0_spl
| sdtpldt0(xp,sz00) = sdtpldt0(sz10,smndt0(sz10)) ),
inference(forward_demodulation,[status(thm)],[f313,f652]) ).
fof(f659,plain,
( ~ sQ0_spl
| xp = sdtpldt0(sz10,smndt0(sz10)) ),
inference(forward_demodulation,[status(thm)],[f306,f658]) ).
fof(f660,plain,
( ~ sQ0_spl
| xp = sz00 ),
inference(forward_demodulation,[status(thm)],[f313,f659]) ).
fof(f661,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f660,f230]) ).
fof(f662,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f661]) ).
fof(f664,plain,
! [X0] :
( ~ sQ1_spl
| sdtpldt0(sz10,sdtpldt0(smndt0(xp),X0)) = sdtpldt0(sz10,X0)
| ~ aInteger0(X0) ),
inference(forward_demodulation,[status(thm)],[f251,f486]) ).
fof(f669,plain,
( sQ0_spl
| sdtpldt0(xp,sz10) != sz10 ),
inference(forward_demodulation,[status(thm)],[f644,f249]) ).
fof(f681,plain,
( ~ sQ1_spl
| sdtpldt0(sz10,sdtpldt0(smndt0(xp),xp)) = sdtpldt0(sz10,xp) ),
inference(resolution,[status(thm)],[f664,f229]) ).
fof(f687,plain,
( ~ sQ1_spl
| sdtpldt0(sz10,sz00) = sdtpldt0(sz10,xp) ),
inference(forward_demodulation,[status(thm)],[f315,f681]) ).
fof(f688,plain,
( ~ sQ1_spl
| sz10 = sdtpldt0(sz10,xp) ),
inference(forward_demodulation,[status(thm)],[f307,f687]) ).
fof(f689,plain,
( ~ sQ1_spl
| sz10 = sdtpldt0(xp,sz10) ),
inference(forward_demodulation,[status(thm)],[f644,f688]) ).
fof(f690,plain,
( ~ sQ1_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f689,f669]) ).
fof(f691,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f690]) ).
fof(f692,plain,
$false,
inference(sat_refutation,[status(thm)],[f253,f662,f691]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM453+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n016.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Mon Sep 21 02:36:08 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.43 % Drodi V4.1.1
% 0.64/0.93 % Refutation found
% 0.64/0.93 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.64/0.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.64/0.97 % Elapsed time: 0.537831 seconds
% 0.64/0.97 % CPU time: 3.737784 seconds
% 0.64/0.97 % Total memory used: 136.704 MB
% 0.64/0.97 % Net memory used: 133.653 MB
%------------------------------------------------------------------------------