%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL531+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 : n002.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 01:07:56 PM UTC 2026
% Result : Theorem 0.11s 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 25
% Syntax : Number of formulae : 91 ( 20 unt; 13 def)
% Number of atoms : 230 ( 5 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 232 ( 93 ~; 96 |; 20 &)
% ( 20 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 22 ( 20 usr; 20 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 77 ( 67 !; 10 ?)
% 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(f5,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
( axiom_m4
<=> ! [X] : is_a_theorem(strict_implies(X,and(X,X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f75,axiom,
( op_strict_implies
=> ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f88,conjecture,
axiom_m4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f89,negated_conjecture,
~ axiom_m4,
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f90,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(f91,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)],[f90]) ).
fof(f92,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)],[f91]) ).
fof(f93,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)],[f92]) ).
fof(f94,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f112,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| implies_2 )
& ( ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| ~ implies_2 ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f113,plain,
( ( ~ is_a_theorem(implies(implies(sK8_skl,implies(sK8_skl,sK9_skl)),implies(sK8_skl,sK9_skl)))
| implies_2 )
& ( ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| ~ implies_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(X,sK8_skl),skolemize(Y,sK9_skl)],[f112]) ).
fof(f114,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f128,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,and(X,Y))))
| and_3 )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y))))
| ~ and_3 ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f129,plain,
( ( ~ is_a_theorem(implies(sK17_skl,implies(sK18_skl,and(sK17_skl,sK18_skl))))
| and_3 )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y))))
| ~ and_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(X,sK17_skl),skolemize(Y,sK18_skl)],[f128]) ).
fof(f130,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f213,plain,
modus_ponens,
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f216,plain,
implies_2,
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f220,plain,
and_3,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f228,plain,
( necessitation
<=> ! [X] :
( is_a_theorem(necessarily(X))
| ~ is_a_theorem(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f229,plain,
( ( ? [X] :
( ~ is_a_theorem(necessarily(X))
& is_a_theorem(X) )
| necessitation )
& ( ! [X] :
( is_a_theorem(necessarily(X))
| ~ is_a_theorem(X) )
| ~ necessitation ) ),
inference(NNF_transformation,[status(thm)],[f228]) ).
fof(f230,plain,
( ( ( ~ is_a_theorem(necessarily(sK55_skl))
& is_a_theorem(sK55_skl) )
| necessitation )
& ( ! [X] :
( is_a_theorem(necessarily(X))
| ~ is_a_theorem(X) )
| ~ necessitation ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl]),skolemize(X,sK55_skl)],[f229]) ).
fof(f231,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0)
| ~ necessitation ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f303,plain,
( ( ? [X] : ~ is_a_theorem(strict_implies(X,and(X,X)))
| axiom_m4 )
& ( ! [X] : is_a_theorem(strict_implies(X,and(X,X)))
| ~ axiom_m4 ) ),
inference(NNF_transformation,[status(thm)],[f66]) ).
fof(f304,plain,
( ( ~ is_a_theorem(strict_implies(sK83_skl,and(sK83_skl,sK83_skl)))
| axiom_m4 )
& ( ! [X] : is_a_theorem(strict_implies(X,and(X,X)))
| ~ axiom_m4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83_skl]),skolemize(X,sK83_skl)],[f303]) ).
fof(f306,plain,
( ~ is_a_theorem(strict_implies(sK83_skl,and(sK83_skl,sK83_skl)))
| axiom_m4 ),
inference(cnf_transformation,[status(thm)],[f304]) ).
fof(f335,plain,
( ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y))
| ~ op_strict_implies ),
inference(pre_NNF_transformation,[status(thm)],[f75]) ).
fof(f336,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[status(thm)],[f335]) ).
fof(f340,plain,
necessitation,
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f347,plain,
op_strict_implies,
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f350,plain,
~ axiom_m4,
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f351,definition,
( sQ0_spl
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f353,plain,
( sQ0_spl
| ~ modus_ponens ),
inference(component_clause,[status(thm)],[f351]) ).
fof(f354,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(f355,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f354]) ).
fof(f357,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f94,f351,f354]) ).
fof(f407,definition,
( sQ15_spl
<=> implies_2 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f409,plain,
( sQ15_spl
| ~ implies_2 ),
inference(component_clause,[status(thm)],[f407]) ).
fof(f410,definition,
! [X0,X1] :
( sQ16_spl
<=> is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f411,plain,
! [X0,X1] :
( ~ sQ16_spl
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(component_clause,[status(thm)],[f410]) ).
fof(f413,plain,
( sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f114,f407,f410]) ).
fof(f451,definition,
( sQ27_spl
<=> and_3 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f453,plain,
( sQ27_spl
| ~ and_3 ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f454,definition,
! [X0,X1] :
( sQ28_spl
<=> is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f455,plain,
! [X0,X1] :
( ~ sQ28_spl
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(component_clause,[status(thm)],[f454]) ).
fof(f457,plain,
( sQ28_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f130,f451,f454]) ).
fof(f531,definition,
! [X0] :
( sQ49_spl
<=> is_a_theorem(implies(X0,and(X0,X0))) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f532,plain,
! [X0] :
( ~ sQ49_spl
| is_a_theorem(implies(X0,and(X0,X0))) ),
inference(component_clause,[status(thm)],[f531]) ).
fof(f675,definition,
( sQ88_spl
<=> necessitation ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f677,plain,
( sQ88_spl
| ~ necessitation ),
inference(component_clause,[status(thm)],[f675]) ).
fof(f678,definition,
! [X0] :
( sQ89_spl
<=> ( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f679,plain,
! [X0] :
( ~ sQ89_spl
| is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f678]) ).
fof(f681,plain,
( sQ89_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f231,f675,f678]) ).
fof(f875,definition,
( sQ142_spl
<=> axiom_m4 ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f876,plain,
( ~ sQ142_spl
| axiom_m4 ),
inference(component_clause,[status(thm)],[f875]) ).
fof(f882,definition,
( sQ144_spl
<=> is_a_theorem(strict_implies(sK83_skl,and(sK83_skl,sK83_skl))) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f884,plain,
( sQ144_spl
| ~ is_a_theorem(strict_implies(sK83_skl,and(sK83_skl,sK83_skl))) ),
inference(component_clause,[status(thm)],[f882]) ).
fof(f885,plain,
( ~ sQ144_spl
| sQ142_spl ),
inference(split_clause,[status(thm)],[f306,f875,f882]) ).
fof(f966,definition,
( sQ167_spl
<=> op_strict_implies ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f968,plain,
( sQ167_spl
| ~ op_strict_implies ),
inference(component_clause,[status(thm)],[f966]) ).
fof(f969,definition,
! [X0,X1] :
( sQ168_spl
<=> strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f970,plain,
! [X0,X1] :
( ~ sQ168_spl
| strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
inference(component_clause,[status(thm)],[f969]) ).
fof(f972,plain,
( sQ168_spl
| ~ sQ167_spl ),
inference(split_clause,[status(thm)],[f336,f966,f969]) ).
fof(f982,plain,
( sQ167_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f968,f347]) ).
fof(f983,plain,
sQ167_spl,
inference(contradiction_clause,[status(thm)],[f982]) ).
fof(f1035,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f353,f213]) ).
fof(f1036,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f1035]) ).
fof(f1037,plain,
( sQ88_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f677,f340]) ).
fof(f1038,plain,
sQ88_spl,
inference(contradiction_clause,[status(thm)],[f1037]) ).
fof(f1113,plain,
( sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f453,f220]) ).
fof(f1114,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f1113]) ).
fof(f1117,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f409,f216]) ).
fof(f1118,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f1117]) ).
fof(f1147,plain,
! [X0,X1] :
( ~ sQ168_spl
| ~ sQ89_spl
| is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f970,f679]) ).
fof(f1181,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ16_spl
| is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) ),
inference(resolution,[status(thm)],[f411,f355]) ).
fof(f1369,plain,
( sQ144_spl
| ~ sQ168_spl
| ~ sQ89_spl
| ~ is_a_theorem(implies(sK83_skl,and(sK83_skl,sK83_skl))) ),
inference(resolution,[status(thm)],[f1147,f884]) ).
fof(f1606,plain,
! [X0] :
( ~ sQ28_spl
| ~ sQ1_spl
| ~ sQ16_spl
| is_a_theorem(implies(X0,and(X0,X0))) ),
inference(resolution,[status(thm)],[f1181,f455]) ).
fof(f1611,plain,
( ~ sQ28_spl
| ~ sQ1_spl
| ~ sQ16_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f1606,f531,f410,f354,f454]) ).
fof(f1616,plain,
( sQ144_spl
| ~ sQ168_spl
| ~ sQ89_spl
| ~ sQ49_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1369,f532]) ).
fof(f1617,plain,
( sQ144_spl
| ~ sQ168_spl
| ~ sQ89_spl
| ~ sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f1616]) ).
fof(f1618,plain,
( ~ sQ142_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f876,f350]) ).
fof(f1619,plain,
~ sQ142_spl,
inference(contradiction_clause,[status(thm)],[f1618]) ).
fof(f1620,plain,
$false,
inference(sat_refutation,[status(thm)],[f357,f413,f457,f681,f885,f972,f983,f1036,f1038,f1114,f1118,f1611,f1617,f1619]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL531+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.35 % Computer : n002.cluster.edu
% 0.06/0.35 % Model : x86_64 x86_64
% 0.06/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.35 % Memory : 8046.5625MB
% 0.06/0.35 % OS : Linux 6.8.0-71-generic
% 0.06/0.35 % CPULimit : 300
% 0.06/0.35 % WCLimit : 300
% 0.06/0.35 % DateTime : Mon Sep 21 00:39:48 UTC 2026
% 0.06/0.35 % CPUTime :
% 0.06/0.37 % Drodi V4.1.1
% 0.11/0.41 % Refutation found
% 0.11/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.46 % Elapsed time: 0.099737 seconds
% 0.11/0.46 % CPU time: 0.279110 seconds
% 0.11/0.46 % Total memory used: 41.121 MB
% 0.11/0.46 % Net memory used: 40.924 MB
%------------------------------------------------------------------------------