%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL546+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 : 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 01:07:58 PM UTC 2026
% Result : Theorem 1.08s 0.84s
% Output : CNFRefutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 59 ( 23 unt; 0 def)
% Number of atoms : 148 ( 4 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 151 ( 62 ~; 56 |; 22 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 76 ( 65 !; 11 ?)
% 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(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
implies_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(f55,axiom,
( axiom_M
<=> ! [X] : is_a_theorem(implies(necessarily(X),X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,axiom,
( axiom_B
<=> ! [X] : is_a_theorem(implies(X,necessarily(possibly(X)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,axiom,
( axiom_m6
<=> ! [X] : is_a_theorem(strict_implies(X,possibly(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(f80,axiom,
axiom_M,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f82,axiom,
axiom_B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f89,conjecture,
axiom_m6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f90,negated_conjecture,
~ axiom_m6,
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f91,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(f92,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)],[f91]) ).
fof(f93,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)],[f92]) ).
fof(f94,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)],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f117,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(f118,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)],[f117]) ).
fof(f119,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)],[f118]) ).
fof(f214,plain,
modus_ponens,
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f218,plain,
implies_3,
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f229,plain,
( necessitation
<=> ! [X] :
( is_a_theorem(necessarily(X))
| ~ is_a_theorem(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f230,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)],[f229]) ).
fof(f231,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)],[f230]) ).
fof(f232,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0)
| ~ necessitation ),
inference(cnf_transformation,[status(thm)],[f231]) ).
fof(f260,plain,
( ( ? [X] : ~ is_a_theorem(implies(necessarily(X),X))
| axiom_M )
& ( ! [X] : is_a_theorem(implies(necessarily(X),X))
| ~ axiom_M ) ),
inference(NNF_transformation,[status(thm)],[f55]) ).
fof(f261,plain,
( ( ~ is_a_theorem(implies(necessarily(sK64_skl),sK64_skl))
| axiom_M )
& ( ! [X] : is_a_theorem(implies(necessarily(X),X))
| ~ axiom_M ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64_skl]),skolemize(X,sK64_skl)],[f260]) ).
fof(f262,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[status(thm)],[f261]) ).
fof(f268,plain,
( ( ? [X] : ~ is_a_theorem(implies(X,necessarily(possibly(X))))
| axiom_B )
& ( ! [X] : is_a_theorem(implies(X,necessarily(possibly(X))))
| ~ axiom_B ) ),
inference(NNF_transformation,[status(thm)],[f57]) ).
fof(f269,plain,
( ( ~ is_a_theorem(implies(sK66_skl,necessarily(possibly(sK66_skl))))
| axiom_B )
& ( ! [X] : is_a_theorem(implies(X,necessarily(possibly(X))))
| ~ axiom_B ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66_skl]),skolemize(X,sK66_skl)],[f268]) ).
fof(f270,plain,
! [X0] :
( is_a_theorem(implies(X0,necessarily(possibly(X0))))
| ~ axiom_B ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f312,plain,
( ( ? [X] : ~ is_a_theorem(strict_implies(X,possibly(X)))
| axiom_m6 )
& ( ! [X] : is_a_theorem(strict_implies(X,possibly(X)))
| ~ axiom_m6 ) ),
inference(NNF_transformation,[status(thm)],[f68]) ).
fof(f313,plain,
( ( ~ is_a_theorem(strict_implies(sK87_skl,possibly(sK87_skl)))
| axiom_m6 )
& ( ! [X] : is_a_theorem(strict_implies(X,possibly(X)))
| ~ axiom_m6 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87_skl]),skolemize(X,sK87_skl)],[f312]) ).
fof(f315,plain,
( ~ is_a_theorem(strict_implies(sK87_skl,possibly(sK87_skl)))
| axiom_m6 ),
inference(cnf_transformation,[status(thm)],[f313]) ).
fof(f336,plain,
( ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y))
| ~ op_strict_implies ),
inference(pre_NNF_transformation,[status(thm)],[f75]) ).
fof(f337,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[status(thm)],[f336]) ).
fof(f341,plain,
necessitation,
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f343,plain,
axiom_M,
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f345,plain,
axiom_B,
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f349,plain,
op_strict_implies,
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f352,plain,
~ axiom_m6,
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f353,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f95,f214]) ).
fof(f361,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(forward_subsumption_resolution,[status(thm)],[f119,f218]) ).
fof(f362,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f361,f353]) ).
fof(f398,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f232,f341]) ).
fof(f402,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),X0)),
inference(forward_subsumption_resolution,[status(thm)],[f262,f343]) ).
fof(f406,plain,
! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0)))),
inference(forward_subsumption_resolution,[status(thm)],[f270,f345]) ).
fof(f408,plain,
~ is_a_theorem(strict_implies(sK87_skl,possibly(sK87_skl))),
inference(forward_subsumption_resolution,[status(thm)],[f315,f352]) ).
fof(f418,plain,
! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(forward_subsumption_resolution,[status(thm)],[f337,f349]) ).
fof(f422,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f418,f398]) ).
fof(f455,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f362,f353]) ).
fof(f811,plain,
~ is_a_theorem(implies(sK87_skl,possibly(sK87_skl))),
inference(resolution,[status(thm)],[f422,f408]) ).
fof(f987,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,possibly(sK87_skl)))
| ~ is_a_theorem(implies(sK87_skl,X0)) ),
inference(resolution,[status(thm)],[f455,f811]) ).
fof(f1002,plain,
~ is_a_theorem(implies(sK87_skl,necessarily(possibly(sK87_skl)))),
inference(resolution,[status(thm)],[f987,f402]) ).
fof(f1011,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1002,f406]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL546+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n016.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 21 00:42:22 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 1.08/0.84 % Refutation found
% 1.08/0.84 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.08/0.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.43/0.89 % Elapsed time: 0.491734 seconds
% 0.43/0.89 % CPU time: 3.584053 seconds
% 0.43/0.89 % Total memory used: 151.818 MB
% 0.43/0.89 % Net memory used: 148.182 MB
%------------------------------------------------------------------------------