%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL490+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 : n011.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 0.12s 0.55s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 66 ( 30 unt; 0 def)
% Number of atoms : 149 ( 4 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 148 ( 65 ~; 54 |; 20 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 14 con; 0-2 aty)
% Number of variables : 120 ( 104 !; 16 ?)
% 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(f10,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,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(f25,axiom,
( r4
<=> ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
file('/export/starexec/sandbox/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/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(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(f39,axiom,
r4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
r5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,conjecture,
or_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
~ or_1,
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(f89,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,or(X,Y)))
| or_1 )
& ( ! [X,Y] : is_a_theorem(implies(X,or(X,Y)))
| ~ or_1 ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f90,plain,
( ( ~ is_a_theorem(implies(sK19_skl,or(sK19_skl,sK20_skl)))
| or_1 )
& ( ! [X,Y] : is_a_theorem(implies(X,or(X,Y)))
| ~ or_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl,sK20_skl]),skolemize(X,sK19_skl),skolemize(Y,sK20_skl)],[f89]) ).
fof(f92,plain,
( ~ is_a_theorem(implies(sK19_skl,or(sK19_skl,sK20_skl)))
| or_1 ),
inference(cnf_transformation,[status(thm)],[f90]) ).
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,
~ or_1,
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f181,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(backward_subsumption_resolution,[status(thm)],[f164,f167]) ).
fof(f184,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(f186,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X1,X0))),
inference(backward_subsumption_resolution,[status(thm)],[f143,f172]) ).
fof(f187,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(backward_subsumption_resolution,[status(thm)],[f147,f173]) ).
fof(f188,plain,
! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(backward_subsumption_resolution,[status(thm)],[f151,f174]) ).
fof(f189,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(backward_subsumption_resolution,[status(thm)],[f155,f175]) ).
fof(f193,plain,
~ is_a_theorem(implies(sK19_skl,or(sK19_skl,sK20_skl))),
inference(backward_subsumption_resolution,[status(thm)],[f92,f180]) ).
fof(f215,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,implies(sK19_skl,or(sK19_skl,sK20_skl))))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f184,f193]) ).
fof(f219,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,implies(X0,implies(sK19_skl,or(sK19_skl,sK20_skl)))))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f215,f184]) ).
fof(f284,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,or(not(X0),X2)))),
inference(paramodulation,[status(thm)],[f181,f188]) ).
fof(f285,plain,
! [X0,X1,X2] : is_a_theorem(implies(or(X0,implies(X1,X2)),or(not(X1),or(X0,X2)))),
inference(paramodulation,[status(thm)],[f181,f188]) ).
fof(f288,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,implies(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f181,f284]) ).
fof(f289,plain,
! [X0,X1,X2] : is_a_theorem(implies(or(X0,implies(X1,X2)),implies(X1,or(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f181,f285]) ).
fof(f293,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1)))),
inference(paramodulation,[status(thm)],[f181,f189]) ).
fof(f295,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f181,f293]) ).
fof(f315,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,or(sK19_skl,sK20_skl)))
| ~ is_a_theorem(implies(sK19_skl,X0)) ),
inference(resolution,[status(thm)],[f295,f219]) ).
fof(f340,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,implies(sK19_skl,X0)))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,or(sK19_skl,sK20_skl))) ),
inference(resolution,[status(thm)],[f315,f184]) ).
fof(f343,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,implies(sK19_skl,or(sK20_skl,sK19_skl))))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f340,f187]) ).
fof(f352,plain,
~ is_a_theorem(or(sK20_skl,implies(sK19_skl,sK19_skl))),
inference(resolution,[status(thm)],[f343,f289]) ).
fof(f357,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,or(sK20_skl,implies(sK19_skl,sK19_skl))))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f352,f184]) ).
fof(f358,plain,
~ is_a_theorem(implies(sK19_skl,or(sK20_skl,sK19_skl))),
inference(resolution,[status(thm)],[f357,f288]) ).
fof(f363,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f358,f186]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL490+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 00:35:40 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.55 % Refutation found
% 0.12/0.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.16/0.59 % Elapsed time: 0.230175 seconds
% 1.16/0.59 % CPU time: 1.511080 seconds
% 1.16/0.59 % Total memory used: 125.342 MB
% 1.16/0.59 % Net memory used: 122.617 MB
%------------------------------------------------------------------------------