%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL488+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 01:07:50 PM UTC 2026
% Result : Theorem 0.10s 0.42s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 65 ( 32 unt; 0 def)
% Number of atoms : 135 ( 20 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 117 ( 47 ~; 44 |; 16 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 102 ( 92 !; 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/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
( and_2
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
( op_and
=> ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
r2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
r3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,conjecture,
and_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
~ and_2,
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(f81,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),Y))
| and_2 )
& ( ! [X,Y] : is_a_theorem(implies(and(X,Y),Y))
| ~ and_2 ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f82,plain,
( ( ~ is_a_theorem(implies(and(sK15_skl,sK16_skl),sK16_skl))
| and_2 )
& ( ! [X,Y] : is_a_theorem(implies(and(X,Y),Y))
| ~ and_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl]),skolemize(X,sK15_skl),skolemize(Y,sK16_skl)],[f81]) ).
fof(f84,plain,
( ~ is_a_theorem(implies(and(sK15_skl,sK16_skl),sK16_skl))
| and_2 ),
inference(cnf_transformation,[status(thm)],[f82]) ).
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(f157,plain,
( ! [X,Y] : or(X,Y) = not(and(not(X),not(Y)))
| ~ op_or ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f158,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f159,plain,
( ! [X,Y] : and(X,Y) = not(or(not(X),not(Y)))
| ~ op_and ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f160,plain,
! [X0,X1] :
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f161,plain,
( ! [X,Y] : implies(X,Y) = not(and(X,not(Y)))
| ~ op_implies_and ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f162,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[status(thm)],[f161]) ).
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(f168,plain,
op_and,
inference(cnf_transformation,[status(thm)],[f33]) ).
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(f177,plain,
op_or,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f178,plain,
op_implies_and,
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f180,plain,
~ and_2,
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f182,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f51,f170]) ).
fof(f185,plain,
~ is_a_theorem(implies(and(sK15_skl,sK16_skl),sK16_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f84,f180]) ).
fof(f188,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X1,X0))),
inference(forward_subsumption_resolution,[status(thm)],[f143,f172]) ).
fof(f189,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(forward_subsumption_resolution,[status(thm)],[f164,f167]) ).
fof(f190,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(paramodulation,[status(thm)],[f189,f188]) ).
fof(f196,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[status(thm)],[f147,f173]) ).
fof(f197,plain,
! [X0,X1] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f196,f182]) ).
fof(f229,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(forward_subsumption_resolution,[status(thm)],[f158,f177]) ).
fof(f233,plain,
! [X0,X1] :
( and(X0,X1) = not(implies(X0,not(X1)))
| ~ op_and ),
inference(forward_demodulation,[status(thm)],[f189,f160]) ).
fof(f234,plain,
! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1))),
inference(forward_subsumption_resolution,[status(thm)],[f233,f168]) ).
fof(f238,plain,
! [X0,X1,X2] : or(implies(X0,not(X1)),X2) = not(and(and(X0,X1),not(X2))),
inference(paramodulation,[status(thm)],[f234,f229]) ).
fof(f240,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(backward_demodulation,[status(thm)],[f241,f229]) ).
fof(f241,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[status(thm)],[f162,f178]) ).
fof(f257,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X1,not(X0)))),
inference(paramodulation,[status(thm)],[f240,f190]) ).
fof(f284,plain,
! [X0,X1] : is_a_theorem(or(implies(X0,not(X1)),X1)),
inference(resolution,[status(thm)],[f197,f257]) ).
fof(f588,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)),
inference(backward_demodulation,[status(thm)],[f589,f284]) ).
fof(f589,plain,
! [X0,X1,X2] : or(implies(X0,not(X1)),X2) = implies(and(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f241,f238]) ).
fof(f761,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f185,f588]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL488+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 00:35:27 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.10/0.42 % Refutation found
% 0.10/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.46 % Elapsed time: 0.068650 seconds
% 0.10/0.46 % CPU time: 0.223010 seconds
% 0.10/0.46 % Total memory used: 50.627 MB
% 0.10/0.46 % Net memory used: 50.494 MB
%------------------------------------------------------------------------------