%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ITP010+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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 12:50:07 PM UTC 2026
% Result : Theorem 0.14s 0.47s
% Output : CNFRefutation 0.14s
% 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(f41,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(f42,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)],[f41]) ).
fof(f192,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)],[f42]) ).
fof(f193,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)],[f192]) ).
fof(f194,plain,
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK3_skl,sK4_skl),sK5_skl),sK6_skl))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK3_skl,sK4_skl),sK5_skl),sK6_skl)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK3_skl,sK4_skl),sK5_skl),sK6_skl))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK3_skl,sK4_skl),sK5_skl),sK6_skl)) )
& mem(sK6_skl,arr(sK4_skl,bool))
& mem(sK5_skl,arr(sK3_skl,bool))
& ne(sK4_skl)
& ne(sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(A_27a,sK3_skl),skolemize(A_27b,sK4_skl),skolemize(V0s,sK5_skl),skolemize(V1t,sK6_skl)],[f193]) ).
fof(f199,plain,
( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK3_skl,sK4_skl),sK5_skl),sK6_skl))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK3_skl,sK4_skl),sK5_skl),sK6_skl)) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f200,plain,
( p(ap(ap(c_2Ecardinal_2Ecardleq(sK3_skl,sK4_skl),sK5_skl),sK6_skl))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK3_skl,sK4_skl),sK5_skl),sK6_skl)) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f282,definition,
( sQ5_spl
<=> p(ap(ap(c_2Ecardinal_2Ecardleq(sK3_skl,sK4_skl),sK5_skl),sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f285,plain,
~ sQ5_spl,
inference(split_clause,[status(thm)],[f199,f282]) ).
fof(f286,plain,
sQ5_spl,
inference(split_clause,[status(thm)],[f200,f282]) ).
fof(f287,plain,
$false,
inference(sat_refutation,[status(thm)],[f285,f286]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ITP010+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.42 % Computer : n017.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sun Sep 20 21:39:56 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.44 % Drodi V4.1.1
% 0.14/0.47 % Refutation found
% 0.14/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.49 % Elapsed time: 0.061014 seconds
% 0.14/0.49 % CPU time: 0.153823 seconds
% 0.14/0.49 % Total memory used: 52.706 MB
% 0.14/0.49 % Net memory used: 52.621 MB
%------------------------------------------------------------------------------