%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ITP010+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 12:50:06 PM UTC 2026
% Result : Theorem 0.15s 0.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 11 ( 3 unt; 1 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 26 ( 14 ~; 6 |; 2 &)
% ( 3 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 2 prp; 0-1 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 16 ( 8 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f40,conjecture,
! [A_27a,A_27b,V0s_2E0,V1t_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))
<=> ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
~ ! [A_27a,A_27b,V0s_2E0,V1t_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))
<=> ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f216,plain,
? [A_27a,A_27b,V0s_2E0,V1t_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))
<~> ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f217,plain,
? [A_27a,A_27b,V0s_2E0,V1t_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))
| p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))) ) ),
inference(NNF_transformation,[status(thm)],[f216]) ).
fof(f218,plain,
( ( p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK3_skl,tyop_2Emin_2Ebool),sK5_skl),s(tyop_2Emin_2Efun(sK4_skl,tyop_2Emin_2Ebool),sK6_skl))))
| p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK3_skl,tyop_2Emin_2Ebool),sK5_skl),s(tyop_2Emin_2Efun(sK4_skl,tyop_2Emin_2Ebool),sK6_skl)))) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK3_skl,tyop_2Emin_2Ebool),sK5_skl),s(tyop_2Emin_2Efun(sK4_skl,tyop_2Emin_2Ebool),sK6_skl))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK3_skl,tyop_2Emin_2Ebool),sK5_skl),s(tyop_2Emin_2Efun(sK4_skl,tyop_2Emin_2Ebool),sK6_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_2E0,sK5_skl),skolemize(V1t_2E0,sK6_skl)],[f217]) ).
fof(f219,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK3_skl,tyop_2Emin_2Ebool),sK5_skl),s(tyop_2Emin_2Efun(sK4_skl,tyop_2Emin_2Ebool),sK6_skl))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK3_skl,tyop_2Emin_2Ebool),sK5_skl),s(tyop_2Emin_2Efun(sK4_skl,tyop_2Emin_2Ebool),sK6_skl)))) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f220,plain,
( p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK3_skl,tyop_2Emin_2Ebool),sK5_skl),s(tyop_2Emin_2Efun(sK4_skl,tyop_2Emin_2Ebool),sK6_skl))))
| p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK3_skl,tyop_2Emin_2Ebool),sK5_skl),s(tyop_2Emin_2Efun(sK4_skl,tyop_2Emin_2Ebool),sK6_skl)))) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f338,definition,
( sQ11_spl
<=> p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sK3_skl,tyop_2Emin_2Ebool),sK5_skl),s(tyop_2Emin_2Efun(sK4_skl,tyop_2Emin_2Ebool),sK6_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f341,plain,
~ sQ11_spl,
inference(split_clause,[status(thm)],[f219,f338]) ).
fof(f342,plain,
sQ11_spl,
inference(split_clause,[status(thm)],[f220,f338]) ).
fof(f361,plain,
$false,
inference(sat_refutation,[status(thm)],[f341,f342]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP010+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/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 : Sun Sep 20 21:40:11 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 0.15/0.41 % Refutation found
% 0.15/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.43 % Elapsed time: 0.057964 seconds
% 0.15/0.43 % CPU time: 0.149863 seconds
% 0.15/0.43 % Total memory used: 108.669 MB
% 0.15/0.43 % Net memory used: 108.484 MB
%------------------------------------------------------------------------------