%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM480+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 : n026.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 01:40:41 PM UTC 2026
% Result : Theorem 124.44s 16.11s
% Output : CNFRefutation 124.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 27
% Syntax : Number of formulae : 111 ( 18 unt; 16 def)
% Number of atoms : 359 ( 74 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 428 ( 180 ~; 189 |; 28 &)
% ( 18 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 15 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 89 ( 86 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f11,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 != sz00
=> ! [W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1) )
=> ( ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0)
| sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
=> W1 = W2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,W1)
& W0 != sz00 )
=> ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W1,W2)
& doDivides0(W0,W1) )
=> doDivides0(W0,W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,hypothesis,
( aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,hypothesis,
( doDivides0(xl,xm)
& xl != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
aNaturalNumber0(xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,conjecture,
sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtsldt0(sdtasdt0(xn,xm),xl),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f50,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f51,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f59,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f60,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,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(f62,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)],[f61]) ).
fof(f63,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f65,plain,
! [X0] :
( X0 = sdtasdt0(sz10,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f75,plain,
! [W0] :
( ! [W1,W2] :
( W1 = W2
| ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0)
& sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1) )
| W0 = sz00
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f76,plain,
! [X0,X1,X2] :
( X1 = X2
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f123,plain,
! [W0,W1] :
( ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f124,plain,
! [W0,W1] :
( ( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2) )
| doDivides0(W0,W1) )
& ( ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f123]) ).
fof(f125,plain,
! [W0,W1] :
( ( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2) )
| doDivides0(W0,W1) )
& ( ( W1 = sdtasdt0(W0,sK1_skl(W1,W0))
& aNaturalNumber0(sK1_skl(W1,W0)) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f124]) ).
fof(f128,plain,
! [X0,X1,X2] :
( X1 != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f129,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) )
| ~ doDivides0(W0,W1)
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f130,plain,
! [W0,W1] :
( ! [W2] :
( ( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2)
| W2 = sdtsldt0(W1,W0) )
& ( ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| W2 != sdtsldt0(W1,W0) ) )
| ~ doDivides0(W0,W1)
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f129]) ).
fof(f131,plain,
! [W0,W1] :
( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2)
| W2 = sdtsldt0(W1,W0) )
& ! [W2] :
( ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| W2 != sdtsldt0(W1,W0) ) )
| ~ doDivides0(W0,W1)
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(miniscoping,[status(thm)],[f130]) ).
fof(f132,plain,
! [X0,X1,X2] :
( aNaturalNumber0(X2)
| X2 != sdtsldt0(X1,X0)
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f135,plain,
! [W0,W1,W2] :
( doDivides0(W0,W2)
| ~ doDivides0(W1,W2)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f136,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f143,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f144,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f145,plain,
xl != sz00,
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f146,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f147,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f148,plain,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f149,plain,
sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtsldt0(sdtasdt0(xn,xm),xl),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f156,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f128]) ).
fof(f157,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f132]) ).
fof(f160,plain,
( sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl) ),
inference(paramodulation,[status(thm)],[f148,f62]) ).
fof(f163,definition,
( sQ0_spl
<=> aNaturalNumber0(xl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f165,plain,
( sQ0_spl
| ~ aNaturalNumber0(xl) ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,definition,
( sQ1_spl
<=> aNaturalNumber0(xn) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f168,plain,
( sQ1_spl
| ~ aNaturalNumber0(xn) ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f169,definition,
( sQ2_spl
<=> aNaturalNumber0(sdtsldt0(xm,xl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f171,plain,
( sQ2_spl
| ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,definition,
( sQ3_spl
<=> sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f173,plain,
( ~ sQ3_spl
| sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,plain,
( sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f160,f163,f166,f169,f172]) ).
fof(f187,plain,
( sQ2_spl
| ~ doDivides0(xl,xm)
| xl = sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(resolution,[status(thm)],[f171,f157]) ).
fof(f188,definition,
( sQ7_spl
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( sQ7_spl
| ~ aNaturalNumber0(xm) ),
inference(component_clause,[status(thm)],[f188]) ).
fof(f191,definition,
( sQ8_spl
<=> xl = sz00 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f192,plain,
( ~ sQ8_spl
| xl = sz00 ),
inference(component_clause,[status(thm)],[f191]) ).
fof(f194,definition,
( sQ9_spl
<=> doDivides0(xl,xm) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( sQ9_spl
| ~ doDivides0(xl,xm) ),
inference(component_clause,[status(thm)],[f194]) ).
fof(f197,plain,
( sQ2_spl
| ~ sQ9_spl
| sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f187,f163,f188,f191,f194,f169]) ).
fof(f198,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f165,f143]) ).
fof(f199,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f198]) ).
fof(f200,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f196,f146]) ).
fof(f201,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f200]) ).
fof(f202,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f192,f145]) ).
fof(f203,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f202]) ).
fof(f204,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f168,f147]) ).
fof(f205,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f204]) ).
fof(f206,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f190,f144]) ).
fof(f207,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f206]) ).
fof(f215,definition,
( sQ10_spl
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f217,plain,
( sQ10_spl
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,definition,
( sQ11_spl
<=> doDivides0(xl,sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( sQ11_spl
| ~ doDivides0(xl,sdtasdt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f225,definition,
( sQ13_spl
<=> aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xl)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f227,plain,
( sQ13_spl
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xl)) ),
inference(component_clause,[status(thm)],[f225]) ).
fof(f236,plain,
( sQ13_spl
| ~ doDivides0(xl,sdtasdt0(xn,xm))
| xl = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xl) ),
inference(resolution,[status(thm)],[f227,f157]) ).
fof(f237,plain,
( sQ13_spl
| ~ sQ11_spl
| sQ8_spl
| ~ sQ10_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f236,f163,f215,f191,f218,f225]) ).
fof(f286,plain,
( sQ10_spl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f217,f51]) ).
fof(f287,plain,
( sQ10_spl
| ~ sQ7_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f286,f166,f188,f215]) ).
fof(f1138,plain,
( ~ sQ3_spl
| sdtsldt0(sdtasdt0(xn,xm),xl) = sdtasdt0(xn,sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtasdt0(xn,sdtsldt0(xm,xl)))
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xl))
| xl = sz00
| ~ aNaturalNumber0(xl) ),
inference(resolution,[status(thm)],[f76,f173]) ).
fof(f1161,definition,
( sQ145_spl
<=> aNaturalNumber0(sdtasdt0(xn,sdtsldt0(xm,xl))) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f1163,plain,
( sQ145_spl
| ~ aNaturalNumber0(sdtasdt0(xn,sdtsldt0(xm,xl))) ),
inference(component_clause,[status(thm)],[f1161]) ).
fof(f1164,definition,
( sQ146_spl
<=> sdtsldt0(sdtasdt0(xn,xm),xl) = sdtasdt0(xn,sdtsldt0(xm,xl)) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f1165,plain,
( ~ sQ146_spl
| sdtsldt0(sdtasdt0(xn,xm),xl) = sdtasdt0(xn,sdtsldt0(xm,xl)) ),
inference(component_clause,[status(thm)],[f1164]) ).
fof(f1167,plain,
( ~ sQ3_spl
| sQ146_spl
| ~ sQ145_spl
| ~ sQ13_spl
| sQ8_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1138,f163,f191,f225,f1161,f1164,f172]) ).
fof(f2968,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f156,f51]) ).
fof(f3296,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f136,f2968]) ).
fof(f3320,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| doDivides0(X0,sdtasdt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3296]) ).
fof(f3321,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| doDivides0(X0,sdtasdt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3320,f51]) ).
fof(f6492,plain,
( sQ145_spl
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f1163,f51]) ).
fof(f6493,plain,
( sQ145_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f6492,f166,f169,f1161]) ).
fof(f8221,definition,
( sQ802_spl
<=> xn = sdtasdt0(sz10,xn) ),
introduced(definition,[new_symbols(definition,[sQ802_spl])],[split_symbol_definition]) ).
fof(f8222,plain,
( ~ sQ802_spl
| xn = sdtasdt0(sz10,xn) ),
inference(component_clause,[status(thm)],[f8221]) ).
fof(f8223,plain,
( sQ802_spl
| xn != sdtasdt0(sz10,xn) ),
inference(component_clause,[status(thm)],[f8221]) ).
fof(f9817,definition,
( sQ982_spl
<=> sdtasdt0(xm,sdtasdt0(sz10,xn)) = sdtasdt0(xn,xm) ),
introduced(definition,[new_symbols(definition,[sQ982_spl])],[split_symbol_definition]) ).
fof(f9818,plain,
( ~ sQ982_spl
| sdtasdt0(xm,sdtasdt0(sz10,xn)) = sdtasdt0(xn,xm) ),
inference(component_clause,[status(thm)],[f9817]) ).
fof(f9819,plain,
( sQ982_spl
| sdtasdt0(xm,sdtasdt0(sz10,xn)) != sdtasdt0(xn,xm) ),
inference(component_clause,[status(thm)],[f9817]) ).
fof(f12401,plain,
( sQ802_spl
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f8223,f65]) ).
fof(f12402,plain,
( sQ802_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f12401,f166,f8221]) ).
fof(f15055,plain,
( ~ sQ146_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1165,f149]) ).
fof(f15056,plain,
~ sQ146_spl,
inference(contradiction_clause,[status(thm)],[f15055]) ).
fof(f17042,plain,
( ~ sQ982_spl
| ~ sQ802_spl
| sdtasdt0(xm,xn) = sdtasdt0(xn,xm) ),
inference(forward_demodulation,[status(thm)],[f8222,f9818]) ).
fof(f18993,plain,
( sQ11_spl
| ~ sQ982_spl
| ~ sQ802_spl
| ~ doDivides0(xl,sdtasdt0(xm,xn)) ),
inference(backward_demodulation,[status(thm)],[f17042,f220]) ).
fof(f19141,plain,
( sQ982_spl
| ~ sQ802_spl
| sdtasdt0(xm,xn) != sdtasdt0(xn,xm) ),
inference(forward_demodulation,[status(thm)],[f8222,f9819]) ).
fof(f19213,plain,
( sQ982_spl
| ~ sQ802_spl
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f19141,f60]) ).
fof(f19215,plain,
( sQ982_spl
| ~ sQ802_spl
| ~ sQ1_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f19213,f188,f166,f8221,f9817]) ).
fof(f19883,plain,
( sQ11_spl
| ~ sQ982_spl
| ~ sQ802_spl
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(resolution,[status(thm)],[f18993,f3321]) ).
fof(f19886,plain,
( sQ11_spl
| ~ sQ982_spl
| ~ sQ802_spl
| ~ sQ1_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f19883,f163,f188,f194,f166,f8221,f9817,f218]) ).
fof(f19895,plain,
$false,
inference(sat_refutation,[status(thm)],[f175,f197,f199,f201,f203,f205,f207,f237,f287,f1167,f6493,f12402,f15056,f19215,f19886]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM480+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 02:36:36 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 124.44/16.11 % Refutation found
% 124.44/16.11 % SZS status Theorem for theBenchmark: Theorem is valid
% 124.44/16.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 124.44/16.18 % Elapsed time: 15.784223 seconds
% 124.44/16.18 % CPU time: 124.893752 seconds
% 124.44/16.18 % Total memory used: 454.158 MB
% 124.44/16.18 % Net memory used: 418.527 MB
%------------------------------------------------------------------------------