%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ITP020+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 : n010.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 12:50:18 PM UTC 2026
% Result : Theorem 9.37s 1.87s
% Output : CNFRefutation 9.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 45 ( 12 unt; 5 def)
% Number of atoms : 119 ( 11 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 121 ( 47 ~; 46 |; 16 &)
% ( 10 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 70 ( 61 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [V0_2E0,V1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
<=> p(s(tyop_2Emin_2Ebool,V1_2E0)) )
=> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [V0t_2E0] :
( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
( ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& ! [V0t_2E0] :
( ~ ~ p(s(tyop_2Emin_2Ebool,V0t_2E0))
<=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [A_27a,A_27b,V0s_2E0,V1t_2E0] :
( ? [V2f_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))
<=> ? [V3g_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
? [V0f_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f59,conjecture,
? [V0f_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,negated_conjecture,
~ ? [V0f_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))),
inference(negated_conjecture,[status(cth)],[f59]) ).
fof(f64,plain,
! [V0_2E0,V1_2E0] :
( s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0)
| ( p(s(tyop_2Emin_2Ebool,V0_2E0))
<~> p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f65,plain,
! [V0_2E0,V1_2E0] :
( s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0)
| ( ( ~ p(s(tyop_2Emin_2Ebool,V1_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,V1_2E0))
| p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ) ),
inference(NNF_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1)
| p(s(tyop_2Emin_2Ebool,X1))
| p(s(tyop_2Emin_2Ebool,X0)) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f68,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f70,plain,
! [X0] :
( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f168,plain,
( ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
& ! [V0t_2E0] :
( ( ~ p(s(tyop_2Emin_2Ebool,V0t_2E0))
| p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ) ),
inference(NNF_transformation,[status(thm)],[f33]) ).
fof(f169,plain,
( ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
& ! [V0t_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,V0t_2E0))
| p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
& ! [V0t_2E0] :
( p(s(tyop_2Emin_2Ebool,V0t_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ),
inference(miniscoping,[status(thm)],[f168]) ).
fof(f173,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ),
inference(cnf_transformation,[status(thm)],[f169]) ).
fof(f263,plain,
! [A_27a,A_27b,V0s_2E0,V1t_2E0] :
( ( ! [V3g_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))
| ? [V2f_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))) )
& ( ? [V3g_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))
| ! [V2f_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),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)],[f47]) ).
fof(f264,plain,
( ! [A_27a,A_27b,V0s_2E0,V1t_2E0] :
( ! [V3g_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))
| ? [V2f_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))) )
& ! [A_27a,A_27b,V0s_2E0,V1t_2E0] :
( ? [V3g_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))
| ! [V2f_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))) ) ),
inference(miniscoping,[status(thm)],[f263]) ).
fof(f265,plain,
( ! [A_27a,A_27b,V0s_2E0,V1t_2E0] :
( ! [V3g_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))
| p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),sK26_skl(V1t_2E0,V0s_2E0,A_27b,A_27a)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))) )
& ! [A_27a,A_27b,V0s_2E0,V1t_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),sK25_skl(V1t_2E0,V0s_2E0,A_27b,A_27a)),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))
| ! [V2f_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25_skl,sK26_skl]),skolemize(V3g_2E0,sK25_skl(V1t_2E0,V0s_2E0,A_27b,A_27a)),skolemize(V2f_2E0,sK26_skl(V1t_2E0,V0s_2E0,A_27b,A_27a))],[f264]) ).
fof(f267,plain,
! [X0,X1,X2,X3,X4] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X1,X0),X4),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3))))
| p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(X0,X1),sK26_skl(X2,X3,X1,X0)),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2)))) ),
inference(cnf_transformation,[status(thm)],[f265]) ).
fof(f351,plain,
p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sK27_skl),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27_skl]),skolemize(V0f_2E0,sK27_skl)],[f58]) ).
fof(f352,plain,
p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sK27_skl),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))),
inference(cnf_transformation,[status(thm)],[f351]) ).
fof(f353,plain,
! [V0f_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))),
inference(pre_NNF_transformation,[status(thm)],[f60]) ).
fof(f354,plain,
! [X0] : ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))),
inference(cnf_transformation,[status(thm)],[f353]) ).
fof(f467,definition,
( sQ0_spl
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f478,definition,
( sQ3_spl
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f498,plain,
( ~ sQ0_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f173,f478,f467]) ).
fof(f569,definition,
! [X0] :
( sQ15_spl
<=> ( p(s(tyop_2Emin_2Ebool,X0))
| p(s(tyop_2Emin_2Ebool,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f570,plain,
! [X0] :
( ~ sQ15_spl
| p(s(tyop_2Emin_2Ebool,X0))
| p(s(tyop_2Emin_2Ebool,X0)) ),
inference(component_clause,[status(thm)],[f569]) ).
fof(f623,plain,
! [X0] :
( ~ sQ15_spl
| p(s(tyop_2Emin_2Ebool,X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f570]) ).
fof(f626,plain,
( ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f354,f623]) ).
fof(f627,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f626]) ).
fof(f924,plain,
! [X0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| p(s(tyop_2Emin_2Ebool,X0))
| p(s(tyop_2Emin_2Ebool,X0)) ),
inference(paramodulation,[status(thm)],[f66,f68]) ).
fof(f926,plain,
( sQ3_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f924,f569,f478]) ).
fof(f993,plain,
! [X0] :
( s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ),
inference(paramodulation,[status(thm)],[f70,f354]) ).
fof(f1096,definition,
! [X0] :
( sQ52_spl
<=> s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f1097,plain,
! [X0] :
( ~ sQ52_spl
| s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
inference(component_clause,[status(thm)],[f1096]) ).
fof(f1099,plain,
( sQ52_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f993,f478,f1096]) ).
fof(f3036,plain,
! [X0] :
( ~ sQ52_spl
| ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ),
inference(paramodulation,[status(thm)],[f1097,f267]) ).
fof(f3039,definition,
! [X0] :
( sQ233_spl
<=> ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f3040,plain,
! [X0] :
( ~ sQ233_spl
| ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) ),
inference(component_clause,[status(thm)],[f3039]) ).
fof(f3042,plain,
( ~ sQ52_spl
| sQ233_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f3036,f467,f3039,f1096]) ).
fof(f3048,plain,
( ~ sQ233_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f352,f3040]) ).
fof(f3049,plain,
~ sQ233_spl,
inference(contradiction_clause,[status(thm)],[f3048]) ).
fof(f3050,plain,
$false,
inference(sat_refutation,[status(thm)],[f498,f627,f926,f1099,f3042,f3049]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP020+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.57 % Computer : n010.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Sun Sep 20 21:52:25 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.59 % Drodi V4.1.1
% 9.37/1.87 % Refutation found
% 9.37/1.87 % SZS status Theorem for theBenchmark: Theorem is valid
% 9.37/1.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.46/1.91 % Elapsed time: 1.322930 seconds
% 1.46/1.91 % CPU time: 10.139695 seconds
% 1.46/1.91 % Total memory used: 266.184 MB
% 1.46/1.91 % Net memory used: 256.825 MB
%------------------------------------------------------------------------------