%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL497+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 01:07:51 PM UTC 2026
% Result : Theorem 4.70s 1.10s
% Output : CNFRefutation 5.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 34
% Syntax : Number of formulae : 133 ( 23 unt; 19 def)
% Number of atoms : 339 ( 5 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 356 ( 150 ~; 155 |; 22 &)
% ( 27 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 30 ( 28 usr; 28 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 17 con; 0-2 aty)
% Number of variables : 180 ( 161 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
( implies_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
( cn2
<=> ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
( r4
<=> ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
( r5
<=> ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
r2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
r3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
r4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
r5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,conjecture,
cn2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
~ cn2,
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f47,plain,
( modus_ponens
<=> ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f48,plain,
( ( ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
| modus_ponens )
& ( ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) )
| ~ modus_ponens ) ),
inference(NNF_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
( ( ? [Y] :
( ~ is_a_theorem(Y)
& ? [X] :
( is_a_theorem(implies(X,Y))
& is_a_theorem(X) ) )
| modus_ponens )
& ( ! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) ) )
| ~ modus_ponens ) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,plain,
( ( ( ~ is_a_theorem(sK0_skl)
& is_a_theorem(implies(sK1_skl,sK0_skl))
& is_a_theorem(sK1_skl) )
| modus_ponens )
& ( ! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) ) )
| ~ modus_ponens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f73,plain,
( ( ? [X,Y,Z] : ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| implies_3 )
& ( ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| ~ implies_3 ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f74,plain,
( ( ~ is_a_theorem(implies(implies(sK10_skl,sK11_skl),implies(implies(sK11_skl,sK12_skl),implies(sK10_skl,sK12_skl))))
| implies_3 )
& ( ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| ~ implies_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl]),skolemize(X,sK10_skl),skolemize(Y,sK11_skl),skolemize(Z,sK12_skl)],[f73]) ).
fof(f75,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f76,plain,
( ~ is_a_theorem(implies(implies(sK10_skl,sK11_skl),implies(implies(sK11_skl,sK12_skl),implies(sK10_skl,sK12_skl))))
| implies_3 ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f129,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(P,implies(not(P),Q)))
| cn2 )
& ( ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q)))
| ~ cn2 ) ),
inference(NNF_transformation,[status(thm)],[f20]) ).
fof(f130,plain,
( ( ~ is_a_theorem(implies(sK41_skl,implies(not(sK41_skl),sK42_skl)))
| cn2 )
& ( ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q)))
| ~ cn2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41_skl,sK42_skl]),skolemize(P,sK41_skl),skolemize(Q,sK42_skl)],[f129]) ).
fof(f132,plain,
( ~ is_a_theorem(implies(sK41_skl,implies(not(sK41_skl),sK42_skl)))
| cn2 ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f141,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(Q,or(P,Q)))
| r2 )
& ( ! [P,Q] : is_a_theorem(implies(Q,or(P,Q)))
| ~ r2 ) ),
inference(NNF_transformation,[status(thm)],[f23]) ).
fof(f142,plain,
( ( ~ is_a_theorem(implies(sK46_skl,or(sK45_skl,sK46_skl)))
| r2 )
& ( ! [P,Q] : is_a_theorem(implies(Q,or(P,Q)))
| ~ r2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45_skl,sK46_skl]),skolemize(P,sK45_skl),skolemize(Q,sK46_skl)],[f141]) ).
fof(f143,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X1,X0)))
| ~ r2 ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f145,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(or(P,Q),or(Q,P)))
| r3 )
& ( ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P)))
| ~ r3 ) ),
inference(NNF_transformation,[status(thm)],[f24]) ).
fof(f146,plain,
( ( ~ is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl)))
| r3 )
& ( ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P)))
| ~ r3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl]),skolemize(P,sK47_skl),skolemize(Q,sK48_skl)],[f145]) ).
fof(f147,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f149,plain,
( ( ? [P,Q,R] : ~ is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))
| r4 )
& ( ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))
| ~ r4 ) ),
inference(NNF_transformation,[status(thm)],[f25]) ).
fof(f150,plain,
( ( ~ is_a_theorem(implies(or(sK49_skl,or(sK50_skl,sK51_skl)),or(sK50_skl,or(sK49_skl,sK51_skl))))
| r4 )
& ( ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))
| ~ r4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49_skl,sK50_skl,sK51_skl]),skolemize(P,sK49_skl),skolemize(Q,sK50_skl),skolemize(R,sK51_skl)],[f149]) ).
fof(f151,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f153,plain,
( ( ? [P,Q,R] : ~ is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))
| r5 )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))
| ~ r5 ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f154,plain,
( ( ~ is_a_theorem(implies(implies(sK53_skl,sK54_skl),implies(or(sK52_skl,sK53_skl),or(sK52_skl,sK54_skl))))
| r5 )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))
| ~ r5 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl,sK53_skl,sK54_skl]),skolemize(P,sK52_skl),skolemize(Q,sK53_skl),skolemize(R,sK54_skl)],[f153]) ).
fof(f155,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1))))
| ~ r5 ),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f163,plain,
( ! [X,Y] : implies(X,Y) = or(not(X),Y)
| ~ op_implies_or ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f164,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f167,plain,
op_implies_or,
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f170,plain,
modus_ponens,
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f172,plain,
r2,
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f173,plain,
r3,
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f174,plain,
r4,
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f175,plain,
r5,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f180,plain,
~ cn2,
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f181,definition,
( sQ0_spl
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f183,plain,
( sQ0_spl
| ~ modus_ponens ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,definition,
! [X0,X1] :
( sQ1_spl
<=> ( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f185,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f187,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f51,f181,f184]) ).
fof(f248,definition,
( sQ18_spl
<=> implies_3 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f251,definition,
! [X0,X1,X2] :
( sQ19_spl
<=> is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f252,plain,
! [X0,X1,X2] :
( ~ sQ19_spl
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f254,plain,
( sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f75,f248,f251]) ).
fof(f255,definition,
( sQ20_spl
<=> is_a_theorem(implies(implies(sK10_skl,sK11_skl),implies(implies(sK11_skl,sK12_skl),implies(sK10_skl,sK12_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f257,plain,
( sQ20_spl
| ~ is_a_theorem(implies(implies(sK10_skl,sK11_skl),implies(implies(sK11_skl,sK12_skl),implies(sK10_skl,sK12_skl)))) ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f258,plain,
( ~ sQ20_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f76,f248,f255]) ).
fof(f295,definition,
! [X0,X1] :
( sQ31_spl
<=> is_a_theorem(implies(X0,or(X0,X1))) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f296,plain,
! [X0,X1] :
( ~ sQ31_spl
| is_a_theorem(implies(X0,or(X0,X1))) ),
inference(component_clause,[status(thm)],[f295]) ).
fof(f306,definition,
! [X0,X1] :
( sQ34_spl
<=> is_a_theorem(implies(X0,or(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f307,plain,
! [X0,X1] :
( ~ sQ34_spl
| is_a_theorem(implies(X0,or(X1,X0))) ),
inference(component_clause,[status(thm)],[f306]) ).
fof(f396,definition,
( sQ58_spl
<=> cn2 ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f397,plain,
( ~ sQ58_spl
| cn2 ),
inference(component_clause,[status(thm)],[f396]) ).
fof(f399,definition,
! [X0,X1] :
( sQ59_spl
<=> is_a_theorem(implies(X0,implies(not(X0),X1))) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f400,plain,
! [X0,X1] :
( ~ sQ59_spl
| is_a_theorem(implies(X0,implies(not(X0),X1))) ),
inference(component_clause,[status(thm)],[f399]) ).
fof(f403,definition,
( sQ60_spl
<=> is_a_theorem(implies(sK41_skl,implies(not(sK41_skl),sK42_skl))) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f405,plain,
( sQ60_spl
| ~ is_a_theorem(implies(sK41_skl,implies(not(sK41_skl),sK42_skl))) ),
inference(component_clause,[status(thm)],[f403]) ).
fof(f406,plain,
( ~ sQ60_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f132,f396,f403]) ).
fof(f429,definition,
( sQ67_spl
<=> r2 ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f431,plain,
( sQ67_spl
| ~ r2 ),
inference(component_clause,[status(thm)],[f429]) ).
fof(f432,plain,
( sQ34_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f143,f429,f306]) ).
fof(f437,definition,
( sQ69_spl
<=> r3 ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f439,plain,
( sQ69_spl
| ~ r3 ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f440,definition,
! [X0,X1] :
( sQ70_spl
<=> is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f441,plain,
! [X0,X1] :
( ~ sQ70_spl
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,plain,
( sQ70_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f147,f437,f440]) ).
fof(f448,definition,
( sQ72_spl
<=> r4 ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f450,plain,
( sQ72_spl
| ~ r4 ),
inference(component_clause,[status(thm)],[f448]) ).
fof(f451,definition,
! [X0,X1,X2] :
( sQ73_spl
<=> is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f452,plain,
! [X0,X1,X2] :
( ~ sQ73_spl
| is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f454,plain,
( sQ73_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f151,f448,f451]) ).
fof(f459,definition,
( sQ75_spl
<=> r5 ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f461,plain,
( sQ75_spl
| ~ r5 ),
inference(component_clause,[status(thm)],[f459]) ).
fof(f462,definition,
! [X0,X1,X2] :
( sQ76_spl
<=> is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f463,plain,
! [X0,X1,X2] :
( ~ sQ76_spl
| is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))) ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f465,plain,
( sQ76_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f155,f459,f462]) ).
fof(f491,definition,
( sQ84_spl
<=> op_implies_or ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f493,plain,
( sQ84_spl
| ~ op_implies_or ),
inference(component_clause,[status(thm)],[f491]) ).
fof(f494,definition,
! [X0,X1] :
( sQ85_spl
<=> implies(X0,X1) = or(not(X0),X1) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f495,plain,
! [X0,X1] :
( ~ sQ85_spl
| implies(X0,X1) = or(not(X0),X1) ),
inference(component_clause,[status(thm)],[f494]) ).
fof(f497,plain,
( sQ85_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f164,f491,f494]) ).
fof(f507,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f183,f170]) ).
fof(f508,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f507]) ).
fof(f511,plain,
( sQ84_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f493,f167]) ).
fof(f512,plain,
sQ84_spl,
inference(contradiction_clause,[status(thm)],[f511]) ).
fof(f519,plain,
( sQ75_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f461,f175]) ).
fof(f520,plain,
sQ75_spl,
inference(contradiction_clause,[status(thm)],[f519]) ).
fof(f528,plain,
( sQ67_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f431,f172]) ).
fof(f529,plain,
sQ67_spl,
inference(contradiction_clause,[status(thm)],[f528]) ).
fof(f539,plain,
! [X0,X1,X2] :
( ~ sQ85_spl
| ~ sQ73_spl
| is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,or(not(X0),X2)))) ),
inference(paramodulation,[status(thm)],[f495,f452]) ).
fof(f544,plain,
( sQ72_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f450,f174]) ).
fof(f545,plain,
sQ72_spl,
inference(contradiction_clause,[status(thm)],[f544]) ).
fof(f546,plain,
! [X0,X1,X2] :
( ~ sQ85_spl
| ~ sQ73_spl
| is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,implies(X0,X2)))) ),
inference(forward_demodulation,[status(thm)],[f495,f539]) ).
fof(f552,plain,
( sQ69_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f439,f173]) ).
fof(f553,plain,
sQ69_spl,
inference(contradiction_clause,[status(thm)],[f552]) ).
fof(f564,plain,
( sQ60_spl
| ~ sQ59_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f405,f400]) ).
fof(f565,plain,
( sQ60_spl
| ~ sQ59_spl ),
inference(contradiction_clause,[status(thm)],[f564]) ).
fof(f663,plain,
! [X0] :
( ~ sQ1_spl
| sQ20_spl
| ~ is_a_theorem(implies(X0,implies(implies(sK10_skl,sK11_skl),implies(implies(sK11_skl,sK12_skl),implies(sK10_skl,sK12_skl)))))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f257,f185]) ).
fof(f679,plain,
! [X0,X1,X2] :
( ~ sQ85_spl
| ~ sQ76_spl
| is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1)))) ),
inference(paramodulation,[status(thm)],[f495,f463]) ).
fof(f681,plain,
! [X0,X1,X2] :
( ~ sQ85_spl
| ~ sQ76_spl
| is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))) ),
inference(forward_demodulation,[status(thm)],[f495,f679]) ).
fof(f697,plain,
! [X0,X1,X2] :
( ~ sQ85_spl
| ~ sQ73_spl
| is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,or(not(X0),X2)))) ),
inference(paramodulation,[status(thm)],[f495,f452]) ).
fof(f701,plain,
! [X0,X1,X2] :
( ~ sQ85_spl
| ~ sQ73_spl
| is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,implies(X0,X2)))) ),
inference(forward_demodulation,[status(thm)],[f495,f697]) ).
fof(f706,plain,
! [X0,X1,X2] :
( ~ sQ85_spl
| ~ sQ73_spl
| is_a_theorem(implies(implies(X0,implies(X1,X2)),or(not(X1),implies(X0,X2)))) ),
inference(paramodulation,[status(thm)],[f495,f546]) ).
fof(f710,plain,
! [X0,X1,X2] :
( ~ sQ85_spl
| ~ sQ73_spl
| is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2)))) ),
inference(forward_demodulation,[status(thm)],[f495,f706]) ).
fof(f827,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ34_spl
| is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,or(X1,X0)),X2)) ),
inference(resolution,[status(thm)],[f307,f185]) ).
fof(f846,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ70_spl
| is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(or(X0,X1),or(X1,X0)),X2)) ),
inference(resolution,[status(thm)],[f441,f185]) ).
fof(f3874,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ31_spl
| is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,or(X0,X1)),X2)) ),
inference(resolution,[status(thm)],[f296,f185]) ).
fof(f4436,plain,
! [X0,X1] :
( ~ sQ85_spl
| ~ sQ73_spl
| ~ sQ1_spl
| ~ sQ31_spl
| is_a_theorem(or(X0,implies(X0,X1))) ),
inference(resolution,[status(thm)],[f3874,f701]) ).
fof(f4532,plain,
! [X0,X1] :
( ~ sQ85_spl
| ~ sQ73_spl
| ~ sQ1_spl
| ~ sQ31_spl
| is_a_theorem(implies(X0,implies(not(X0),X1))) ),
inference(paramodulation,[status(thm)],[f495,f4436]) ).
fof(f4536,plain,
( ~ sQ85_spl
| ~ sQ73_spl
| ~ sQ1_spl
| ~ sQ31_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f4532,f399,f295,f184,f451,f494]) ).
fof(f4537,plain,
( ~ sQ58_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f397,f180]) ).
fof(f4538,plain,
~ sQ58_spl,
inference(contradiction_clause,[status(thm)],[f4537]) ).
fof(f5356,plain,
( ~ sQ1_spl
| sQ20_spl
| ~ sQ85_spl
| ~ sQ73_spl
| ~ is_a_theorem(implies(implies(sK11_skl,sK12_skl),implies(implies(sK10_skl,sK11_skl),implies(sK10_skl,sK12_skl)))) ),
inference(resolution,[status(thm)],[f710,f663]) ).
fof(f5372,plain,
( ~ sQ1_spl
| sQ20_spl
| ~ sQ85_spl
| ~ sQ73_spl
| ~ sQ76_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5356,f681]) ).
fof(f5373,plain,
( ~ sQ1_spl
| sQ20_spl
| ~ sQ85_spl
| ~ sQ73_spl
| ~ sQ76_spl ),
inference(contradiction_clause,[status(thm)],[f5372]) ).
fof(f5471,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ34_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(or(X0,X1),X2),implies(X1,X2))) ),
inference(resolution,[status(thm)],[f252,f827]) ).
fof(f8380,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ70_spl
| ~ sQ34_spl
| ~ sQ19_spl
| is_a_theorem(implies(X0,or(X0,X1))) ),
inference(resolution,[status(thm)],[f5471,f846]) ).
fof(f8410,plain,
( ~ sQ1_spl
| ~ sQ70_spl
| ~ sQ34_spl
| ~ sQ19_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f8380,f295,f251,f306,f440,f184]) ).
fof(f8411,plain,
$false,
inference(sat_refutation,[status(thm)],[f187,f254,f258,f406,f432,f443,f454,f465,f497,f508,f512,f520,f529,f545,f553,f565,f4536,f4538,f5373,f8410]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL497+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.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 00:41:59 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 4.70/1.10 % Refutation found
% 4.70/1.10 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.70/1.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.25/1.15 % Elapsed time: 0.770248 seconds
% 5.25/1.15 % CPU time: 5.792474 seconds
% 5.25/1.15 % Total memory used: 227.244 MB
% 5.25/1.15 % Net memory used: 221.177 MB
%------------------------------------------------------------------------------