%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL542+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 : n008.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 01:07:57 PM UTC 2026
% Result : Theorem 0.14s 10.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 16
% Syntax : Number of formulae : 58 ( 14 unt; 8 def)
% Number of atoms : 132 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 125 ( 51 ~; 52 |; 8 &)
% ( 12 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 13 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 42 ( 37 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,axiom,
( axiom_m2
<=> ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f75,axiom,
( op_strict_implies
=> ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f89,conjecture,
axiom_m2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f90,negated_conjecture,
~ axiom_m2,
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f121,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),X))
| and_1 )
& ( ! [X,Y] : is_a_theorem(implies(and(X,Y),X))
| ~ and_1 ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f122,plain,
( ( ~ is_a_theorem(implies(and(sK13_skl,sK14_skl),sK13_skl))
| and_1 )
& ( ! [X,Y] : is_a_theorem(implies(and(X,Y),X))
| ~ and_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(X,sK13_skl),skolemize(Y,sK14_skl)],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f219,plain,
and_1,
inference(cnf_transformation,[status(thm)],[f40]) ).
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(f296,plain,
( ( ? [X,Y] : ~ is_a_theorem(strict_implies(and(X,Y),X))
| axiom_m2 )
& ( ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X))
| ~ axiom_m2 ) ),
inference(NNF_transformation,[status(thm)],[f64]) ).
fof(f297,plain,
( ( ~ is_a_theorem(strict_implies(and(sK78_skl,sK79_skl),sK78_skl))
| axiom_m2 )
& ( ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X))
| ~ axiom_m2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78_skl,sK79_skl]),skolemize(X,sK78_skl),skolemize(Y,sK79_skl)],[f296]) ).
fof(f299,plain,
( ~ is_a_theorem(strict_implies(and(sK78_skl,sK79_skl),sK78_skl))
| axiom_m2 ),
inference(cnf_transformation,[status(thm)],[f297]) ).
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(f349,plain,
op_strict_implies,
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f352,plain,
~ axiom_m2,
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f431,definition,
( sQ21_spl
<=> and_1 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f433,plain,
( sQ21_spl
| ~ and_1 ),
inference(component_clause,[status(thm)],[f431]) ).
fof(f434,definition,
! [X0,X1] :
( sQ22_spl
<=> is_a_theorem(implies(and(X0,X1),X0)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f435,plain,
! [X0,X1] :
( ~ sQ22_spl
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f437,plain,
( sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f123,f431,f434]) ).
fof(f677,definition,
( sQ88_spl
<=> necessitation ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f679,plain,
( sQ88_spl
| ~ necessitation ),
inference(component_clause,[status(thm)],[f677]) ).
fof(f680,definition,
! [X0] :
( sQ89_spl
<=> ( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f681,plain,
! [X0] :
( ~ sQ89_spl
| is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f680]) ).
fof(f683,plain,
( sQ89_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f232,f677,f680]) ).
fof(f855,definition,
( sQ136_spl
<=> axiom_m2 ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f856,plain,
( ~ sQ136_spl
| axiom_m2 ),
inference(component_clause,[status(thm)],[f855]) ).
fof(f862,definition,
( sQ138_spl
<=> is_a_theorem(strict_implies(and(sK78_skl,sK79_skl),sK78_skl)) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f864,plain,
( sQ138_spl
| ~ is_a_theorem(strict_implies(and(sK78_skl,sK79_skl),sK78_skl)) ),
inference(component_clause,[status(thm)],[f862]) ).
fof(f865,plain,
( ~ sQ138_spl
| sQ136_spl ),
inference(split_clause,[status(thm)],[f299,f855,f862]) ).
fof(f968,definition,
( sQ167_spl
<=> op_strict_implies ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f970,plain,
( sQ167_spl
| ~ op_strict_implies ),
inference(component_clause,[status(thm)],[f968]) ).
fof(f971,definition,
! [X0,X1] :
( sQ168_spl
<=> strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f972,plain,
! [X0,X1] :
( ~ sQ168_spl
| strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
inference(component_clause,[status(thm)],[f971]) ).
fof(f974,plain,
( sQ168_spl
| ~ sQ167_spl ),
inference(split_clause,[status(thm)],[f337,f968,f971]) ).
fof(f986,plain,
( sQ88_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f679,f341]) ).
fof(f987,plain,
sQ88_spl,
inference(contradiction_clause,[status(thm)],[f986]) ).
fof(f990,plain,
( sQ167_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f970,f349]) ).
fof(f991,plain,
sQ167_spl,
inference(contradiction_clause,[status(thm)],[f990]) ).
fof(f1013,plain,
! [X0,X1] :
( ~ sQ168_spl
| ~ sQ89_spl
| is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f972,f681]) ).
fof(f1049,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f433,f219]) ).
fof(f1050,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f1049]) ).
fof(f1100,plain,
( ~ sQ168_spl
| ~ sQ89_spl
| sQ138_spl
| ~ is_a_theorem(implies(and(sK78_skl,sK79_skl),sK78_skl)) ),
inference(resolution,[status(thm)],[f864,f1013]) ).
fof(f1102,plain,
( ~ sQ168_spl
| ~ sQ89_spl
| sQ138_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1100,f435]) ).
fof(f1103,plain,
( ~ sQ168_spl
| ~ sQ89_spl
| sQ138_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f1102]) ).
fof(f1104,plain,
( ~ sQ136_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f856,f352]) ).
fof(f1105,plain,
~ sQ136_spl,
inference(contradiction_clause,[status(thm)],[f1104]) ).
fof(f1106,plain,
$false,
inference(sat_refutation,[status(thm)],[f437,f683,f865,f974,f987,f991,f1050,f1103,f1105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL542+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.38 % Computer : n008.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Mon Sep 21 00:38:35 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.14/10.40 % Drodi V4.1.1
% 0.14/10.42 % Refutation found
% 0.14/10.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/10.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/10.45 % Elapsed time: 0.055596 seconds
% 0.14/10.45 % CPU time: 0.181076 seconds
% 0.14/10.45 % Total memory used: 87.561 MB
% 0.14/10.45 % Net memory used: 87.452 MB
%------------------------------------------------------------------------------