%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL456+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 : n017.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 01:07:47 PM UTC 2026
% Result : Theorem 0.11s 0.48s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 24
% Syntax : Number of formulae : 88 ( 20 unt; 12 def)
% Number of atoms : 198 ( 25 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 195 ( 85 ~; 88 |; 4 &)
% ( 14 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 21 ( 19 usr; 19 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 84 ( 80 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( modus_tollens
<=> ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
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(f27,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
( op_and
=> ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
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_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
r3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ r3,
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f69,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| modus_tollens )
& ( ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| ~ modus_tollens ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f70,plain,
( ( ~ is_a_theorem(implies(implies(not(sK5_skl),not(sK4_skl)),implies(sK4_skl,sK5_skl)))
| modus_tollens )
& ( ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| ~ modus_tollens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(X,sK4_skl),skolemize(Y,sK5_skl)],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0)))
| ~ modus_tollens ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f153,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(f154,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)],[f153]) ).
fof(f156,plain,
( ~ is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl)))
| r3 ),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f165,plain,
( ! [X,Y] : or(X,Y) = not(and(not(X),not(Y)))
| ~ op_or ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f166,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[status(thm)],[f165]) ).
fof(f167,plain,
( ! [X,Y] : and(X,Y) = not(or(not(X),not(Y)))
| ~ op_and ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f168,plain,
! [X0,X1] :
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(cnf_transformation,[status(thm)],[f167]) ).
fof(f169,plain,
( ! [X,Y] : implies(X,Y) = not(and(X,not(Y)))
| ~ op_implies_and ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f170,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[status(thm)],[f169]) ).
fof(f171,plain,
( ! [X,Y] : implies(X,Y) = or(not(X),Y)
| ~ op_implies_or ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f172,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f175,plain,
op_or,
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f176,plain,
op_implies_and,
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f179,plain,
modus_tollens,
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f193,plain,
op_implies_or,
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f194,plain,
op_and,
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f196,plain,
~ r3,
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f231,definition,
( sQ9_spl
<=> modus_tollens ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( sQ9_spl
| ~ modus_tollens ),
inference(component_clause,[status(thm)],[f231]) ).
fof(f234,definition,
! [X0,X1] :
( sQ10_spl
<=> is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f235,plain,
! [X0,X1] :
( ~ sQ10_spl
| is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))) ),
inference(component_clause,[status(thm)],[f234]) ).
fof(f237,plain,
( sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f71,f231,f234]) ).
fof(f453,definition,
( sQ69_spl
<=> r3 ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( ~ sQ69_spl
| r3 ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f460,definition,
( sQ71_spl
<=> is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f462,plain,
( sQ71_spl
| ~ is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl))) ),
inference(component_clause,[status(thm)],[f460]) ).
fof(f463,plain,
( ~ sQ71_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f156,f453,f460]) ).
fof(f486,definition,
( sQ78_spl
<=> op_or ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f488,plain,
( sQ78_spl
| ~ op_or ),
inference(component_clause,[status(thm)],[f486]) ).
fof(f489,definition,
! [X0,X1] :
( sQ79_spl
<=> or(X0,X1) = not(and(not(X0),not(X1))) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f490,plain,
! [X0,X1] :
( ~ sQ79_spl
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(component_clause,[status(thm)],[f489]) ).
fof(f492,plain,
( sQ79_spl
| ~ sQ78_spl ),
inference(split_clause,[status(thm)],[f166,f486,f489]) ).
fof(f493,definition,
( sQ80_spl
<=> op_and ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f495,plain,
( sQ80_spl
| ~ op_and ),
inference(component_clause,[status(thm)],[f493]) ).
fof(f496,definition,
! [X0,X1] :
( sQ81_spl
<=> and(X0,X1) = not(or(not(X0),not(X1))) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f497,plain,
! [X0,X1] :
( ~ sQ81_spl
| and(X0,X1) = not(or(not(X0),not(X1))) ),
inference(component_clause,[status(thm)],[f496]) ).
fof(f499,plain,
( sQ81_spl
| ~ sQ80_spl ),
inference(split_clause,[status(thm)],[f168,f493,f496]) ).
fof(f500,definition,
( sQ82_spl
<=> op_implies_and ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f502,plain,
( sQ82_spl
| ~ op_implies_and ),
inference(component_clause,[status(thm)],[f500]) ).
fof(f503,definition,
! [X0,X1] :
( sQ83_spl
<=> implies(X0,X1) = not(and(X0,not(X1))) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f504,plain,
! [X0,X1] :
( ~ sQ83_spl
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(component_clause,[status(thm)],[f503]) ).
fof(f506,plain,
( sQ83_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f170,f500,f503]) ).
fof(f507,definition,
( sQ84_spl
<=> op_implies_or ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f509,plain,
( sQ84_spl
| ~ op_implies_or ),
inference(component_clause,[status(thm)],[f507]) ).
fof(f510,definition,
! [X0,X1] :
( sQ85_spl
<=> implies(X0,X1) = or(not(X0),X1) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f511,plain,
! [X0,X1] :
( ~ sQ85_spl
| implies(X0,X1) = or(not(X0),X1) ),
inference(component_clause,[status(thm)],[f510]) ).
fof(f513,plain,
( sQ85_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f172,f507,f510]) ).
fof(f523,plain,
( sQ84_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f509,f193]) ).
fof(f524,plain,
sQ84_spl,
inference(contradiction_clause,[status(thm)],[f523]) ).
fof(f525,plain,
( sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f502,f176]) ).
fof(f526,plain,
sQ82_spl,
inference(contradiction_clause,[status(thm)],[f525]) ).
fof(f527,plain,
( sQ80_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f495,f194]) ).
fof(f528,plain,
sQ80_spl,
inference(contradiction_clause,[status(thm)],[f527]) ).
fof(f529,plain,
( sQ78_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f488,f175]) ).
fof(f530,plain,
sQ78_spl,
inference(contradiction_clause,[status(thm)],[f529]) ).
fof(f559,plain,
! [X0,X1] :
( ~ sQ81_spl
| ~ sQ85_spl
| and(X0,X1) = not(implies(X0,not(X1))) ),
inference(forward_demodulation,[status(thm)],[f511,f497]) ).
fof(f561,plain,
! [X0,X1] :
( ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))) ),
inference(backward_demodulation,[status(thm)],[f564,f235]) ).
fof(f564,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| or(X0,X1) = implies(not(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f504,f490]) ).
fof(f610,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f233,f179]) ).
fof(f611,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f610]) ).
fof(f630,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| ~ sQ79_spl
| or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f504,f564]) ).
fof(f631,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ81_spl
| ~ sQ85_spl
| and(not(X0),X1) = not(or(X0,not(X1))) ),
inference(paramodulation,[status(thm)],[f564,f559]) ).
fof(f695,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ10_spl
| is_a_theorem(implies(or(X0,not(not(X1))),or(X1,X0))) ),
inference(paramodulation,[status(thm)],[f564,f561]) ).
fof(f726,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ81_spl
| ~ sQ85_spl
| implies(or(X0,not(X1)),X2) = or(and(not(X0),X1),X2) ),
inference(paramodulation,[status(thm)],[f631,f511]) ).
fof(f730,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ10_spl
| ~ sQ81_spl
| ~ sQ85_spl
| is_a_theorem(or(and(not(X0),not(X1)),or(X1,X0))) ),
inference(backward_demodulation,[status(thm)],[f726,f695]) ).
fof(f734,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ10_spl
| ~ sQ81_spl
| ~ sQ85_spl
| is_a_theorem(implies(implies(not(X0),X1),or(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f630,f730]) ).
fof(f735,plain,
( sQ71_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ10_spl
| ~ sQ81_spl
| ~ sQ85_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f462,f736]) ).
fof(f736,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ10_spl
| ~ sQ81_spl
| ~ sQ85_spl
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f564,f734]) ).
fof(f737,plain,
( sQ71_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ10_spl
| ~ sQ81_spl
| ~ sQ85_spl ),
inference(contradiction_clause,[status(thm)],[f735]) ).
fof(f738,plain,
( ~ sQ69_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f454,f196]) ).
fof(f739,plain,
~ sQ69_spl,
inference(contradiction_clause,[status(thm)],[f738]) ).
fof(f740,plain,
$false,
inference(sat_refutation,[status(thm)],[f237,f463,f492,f499,f506,f513,f524,f526,f528,f530,f611,f737,f739]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL456+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n017.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 00:28:27 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.48 % Refutation found
% 0.11/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.50 % Elapsed time: 0.129108 seconds
% 0.11/0.50 % CPU time: 0.722714 seconds
% 0.11/0.50 % Total memory used: 98.493 MB
% 0.11/0.50 % Net memory used: 97.912 MB
%------------------------------------------------------------------------------