%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ITP010+5 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 12:50:07 PM UTC 2026
% Result : Theorem 22.67s 19.58s
% Output : CNFRefutation 22.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 11 ( 3 unt; 1 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 46 ( 14 ~; 6 |; 14 &)
% ( 3 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 16 ( 8 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8598,conjecture,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1t] :
( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8599,negated_conjecture,
~ ! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1t] :
( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f8598]) ).
fof(f53185,plain,
? [A_27a] :
( ? [A_27b] :
( ? [V0s] :
( ? [V1t] :
( ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<~> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) )
& mem(V1t,arr(A_27b,bool)) )
& mem(V0s,arr(A_27a,bool)) )
& ne(A_27b) )
& ne(A_27a) ),
inference(pre_NNF_transformation,[status(thm)],[f8599]) ).
fof(f53186,plain,
? [A_27a] :
( ? [A_27b] :
( ? [V0s] :
( ? [V1t] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
| p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) )
& mem(V1t,arr(A_27b,bool)) )
& mem(V0s,arr(A_27a,bool)) )
& ne(A_27b) )
& ne(A_27a) ),
inference(NNF_transformation,[status(thm)],[f53185]) ).
fof(f53187,plain,
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK14171_skl,sK14172_skl),sK14173_skl),sK14174_skl))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK14171_skl,sK14172_skl),sK14173_skl),sK14174_skl)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK14171_skl,sK14172_skl),sK14173_skl),sK14174_skl))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK14171_skl,sK14172_skl),sK14173_skl),sK14174_skl)) )
& mem(sK14174_skl,arr(sK14172_skl,bool))
& mem(sK14173_skl,arr(sK14171_skl,bool))
& ne(sK14172_skl)
& ne(sK14171_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14171_skl,sK14172_skl,sK14173_skl,sK14174_skl]),skolemize(A_27a,sK14171_skl),skolemize(A_27b,sK14172_skl),skolemize(V0s,sK14173_skl),skolemize(V1t,sK14174_skl)],[f53186]) ).
fof(f53192,plain,
( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK14171_skl,sK14172_skl),sK14173_skl),sK14174_skl))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK14171_skl,sK14172_skl),sK14173_skl),sK14174_skl)) ),
inference(cnf_transformation,[status(thm)],[f53187]) ).
fof(f53193,plain,
( p(ap(ap(c_2Ecardinal_2Ecardleq(sK14171_skl,sK14172_skl),sK14173_skl),sK14174_skl))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK14171_skl,sK14172_skl),sK14173_skl),sK14174_skl)) ),
inference(cnf_transformation,[status(thm)],[f53187]) ).
fof(f60537,definition,
( sQ807_spl
<=> p(ap(ap(c_2Ecardinal_2Ecardleq(sK14171_skl,sK14172_skl),sK14173_skl),sK14174_skl)) ),
introduced(definition,[new_symbols(definition,[sQ807_spl])],[split_symbol_definition]) ).
fof(f60540,plain,
~ sQ807_spl,
inference(split_clause,[status(thm)],[f53192,f60537]) ).
fof(f60541,plain,
sQ807_spl,
inference(split_clause,[status(thm)],[f53193,f60537]) ).
fof(f60542,plain,
$false,
inference(sat_refutation,[status(thm)],[f60540,f60541]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP010+5 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.46 % Computer : n004.cluster.edu
% 0.16/0.46 % Model : x86_64 x86_64
% 0.16/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.46 % Memory : 8046.5625MB
% 0.16/0.46 % OS : Linux 6.8.0-71-generic
% 0.16/0.46 % CPULimit : 300
% 0.16/0.46 % WCLimit : 300
% 0.16/0.46 % DateTime : Sun Sep 20 21:44:50 UTC 2026
% 0.16/0.47 % CPUTime :
% 18.59/18.95 % Drodi V4.1.1
% 22.67/19.58 % Refutation found
% 22.67/19.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 22.67/19.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 21.59/19.87 % Elapsed time: 19.368782 seconds
% 21.59/19.87 % CPU time: 23.194244 seconds
% 21.59/19.87 % Total memory used: 2.719 GB
% 21.59/19.87 % Net memory used: 2.703 GB
%------------------------------------------------------------------------------