%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ITP013+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 : n015.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 12:50:10 PM UTC 2026
% Result : Theorem 0.10s 0.57s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 12 unt; 2 def)
% Number of atoms : 160 ( 28 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 178 ( 60 ~; 52 |; 44 &)
% ( 13 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-3 aty)
% Number of variables : 78 ( 72 !; 6 ?)
% 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(f4,axiom,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [V0t_2E0] :
( ( ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_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,c_2Ebool_2ET_2E0)) )
& ( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
& ( ( p(s(tyop_2Emin_2Ebool,V0t_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_2ET_2E0))
=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [A_27a] :
( ! [V2t1_2E0,V3t2_2E0] : s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(A_27a,V2t1_2E0),s(A_27a,V3t2_2E0))) = s(A_27a,V3t2_2E0)
& ! [V0t1_2E0,V1t2_2E0] : s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(A_27a,V0t1_2E0),s(A_27a,V1t2_2E0))) = s(A_27a,V0t1_2E0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [A_27a,V0v_2E0,V1w_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0v_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1w_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0v_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1w_2E0))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [A_27a,A_27b] :
( ! [V2m_2E0,V3n_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,V2m_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,V2m_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,V2m_2E0)))))))))
& ! [V0m_2E0,V1n_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,V0m_2E0))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,conjecture,
! [A_27a,V0a_2E0,V1b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0))))
=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,V0a_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,V1b_2E0))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
~ ! [A_27a,V0a_2E0,V1b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0))))
=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,V0a_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,V1b_2E0))))) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f51,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(f52,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)],[f51]) ).
fof(f54,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)],[f52]) ).
fof(f56,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f134,plain,
! [V0t_2E0] :
( ( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_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)) )
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
& ( ( p(s(tyop_2Emin_2Ebool,V0t_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_2ET_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
& ( ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f135,plain,
! [V0t_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,V0t_2E0))
| ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
& p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| p(s(tyop_2Emin_2Ebool,V0t_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| ( ~ p(s(tyop_2Emin_2Ebool,V0t_2E0))
& p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| p(s(tyop_2Emin_2Ebool,V0t_2E0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| ( ~ p(s(tyop_2Emin_2Ebool,V0t_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_2ET_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_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,c_2Ebool_2ET_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
| ( ~ p(s(tyop_2Emin_2Ebool,V0t_2E0))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ) ) ),
inference(NNF_transformation,[status(thm)],[f134]) ).
fof(f136,plain,
( ! [V0t_2E0] :
( p(s(tyop_2Emin_2Ebool,V0t_2E0))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
& ! [V0t_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,V0t_2E0))
| ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
& p(s(tyop_2Emin_2Ebool,V0t_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,c_2Ebool_2ET_2E0))
| ( ! [V0t_2E0] : ~ p(s(tyop_2Emin_2Ebool,V0t_2E0))
& ! [V0t_2E0] : p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| ! [V0t_2E0] : p(s(tyop_2Emin_2Ebool,V0t_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,c_2Ebool_2EF_2E0)) ) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| ! [V0t_2E0] : ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
& ! [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))
| ~ 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,c_2Ebool_2ET_2E0)) ) ) ),
inference(miniscoping,[status(thm)],[f135]) ).
fof(f137,plain,
! [X0] :
( p(s(tyop_2Emin_2Ebool,X0))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f192,plain,
( ! [A_27a,V2t1_2E0,V3t2_2E0] : s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(A_27a,V2t1_2E0),s(A_27a,V3t2_2E0))) = s(A_27a,V3t2_2E0)
& ! [A_27a,V0t1_2E0,V1t2_2E0] : s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(A_27a,V0t1_2E0),s(A_27a,V1t2_2E0))) = s(A_27a,V0t1_2E0) ),
inference(miniscoping,[status(thm)],[f43]) ).
fof(f193,plain,
! [X0,X1,X2] : s(X0,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(X0,X1),s(X0,X2))) = s(X0,X1),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f195,plain,
! [X0,X1,X2] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X1),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X2))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X1),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X2))))),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f196,plain,
( ! [A_27b,V2m_2E0,V3n_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,V2m_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,V2m_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,V2m_2E0)))))))))
& ! [A_27a,V0m_2E0,V1n_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,V0m_2E0))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))))) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f198,plain,
! [X0,X1,X2] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X1))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X2))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X2),s(tyop_2Enum_2Enum,X1))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,X2))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X2),s(tyop_2Enum_2Enum,X1))))))))),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f199,plain,
? [A_27a,V0a_2E0,V1b_2E0] :
( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,V0a_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,V1b_2E0)))))
& p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f200,plain,
? [V0a_2E0,V1b_2E0] :
( ? [A_27a] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,V0a_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,V1b_2E0)))))
& p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) ),
inference(miniscoping,[status(thm)],[f199]) ).
fof(f201,plain,
( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK5_skl),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,sK3_skl),s(tyop_2Enum_2Enum,sK4_skl))))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK5_skl),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK5_skl),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,sK3_skl))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK5_skl),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,sK4_skl)))))
& p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,sK4_skl),s(tyop_2Enum_2Enum,sK3_skl)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(V0a_2E0,sK3_skl),skolemize(V1b_2E0,sK4_skl),skolemize(A_27a,sK5_skl)],[f200]) ).
fof(f202,plain,
p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,sK4_skl),s(tyop_2Enum_2Enum,sK3_skl)))),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f203,plain,
s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK5_skl),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,sK3_skl),s(tyop_2Enum_2Enum,sK4_skl))))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK5_skl),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK5_skl),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,sK3_skl))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK5_skl),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,sK4_skl))))),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f214,definition,
( sQ0_spl
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f215,plain,
( ~ sQ0_spl
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ),
inference(component_clause,[status(thm)],[f214]) ).
fof(f217,definition,
! [X0] :
( sQ1_spl
<=> p(s(tyop_2Emin_2Ebool,X0)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f218,plain,
! [X0] :
( ~ sQ1_spl
| p(s(tyop_2Emin_2Ebool,X0)) ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f220,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f137,f214,f217]) ).
fof(f257,plain,
! [X0,X1,X2] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X1))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X2))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X2),s(tyop_2Enum_2Enum,X1))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,X2))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X2),s(tyop_2Enum_2Enum,X1))))))))),
inference(forward_demodulation,[status(thm)],[f195,f198]) ).
fof(f278,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f56,f218]) ).
fof(f289,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f278]) ).
fof(f294,plain,
! [X0] :
( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,sK4_skl),s(tyop_2Enum_2Enum,sK3_skl)))
| ~ p(s(tyop_2Emin_2Ebool,X0)) ),
inference(resolution,[status(thm)],[f54,f202]) ).
fof(f308,plain,
( ~ sQ0_spl
| s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,sK4_skl),s(tyop_2Enum_2Enum,sK3_skl))) ),
inference(resolution,[status(thm)],[f215,f294]) ).
fof(f780,plain,
! [X0] :
( ~ sQ0_spl
| s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,sK3_skl))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,sK4_skl))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,sK3_skl),s(tyop_2Enum_2Enum,sK4_skl))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,sK4_skl),s(tyop_2Enum_2Enum,sK3_skl))))))))) ),
inference(paramodulation,[status(thm)],[f308,f257]) ).
fof(f819,plain,
( ~ sQ0_spl
| s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK5_skl),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,sK3_skl),s(tyop_2Enum_2Enum,sK4_skl))))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK5_skl),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,sK3_skl),s(tyop_2Enum_2Enum,sK4_skl))))) ),
inference(backward_demodulation,[status(thm)],[f820,f203]) ).
fof(f820,plain,
! [X0] :
( ~ sQ0_spl
| s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,sK3_skl))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,sK4_skl))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,sK3_skl),s(tyop_2Enum_2Enum,sK4_skl))))) ),
inference(forward_demodulation,[status(thm)],[f193,f780]) ).
fof(f885,plain,
( ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f819]) ).
fof(f886,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f885]) ).
fof(f887,plain,
$false,
inference(sat_refutation,[status(thm)],[f220,f289,f886]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP013+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 21:50:21 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.57 % Refutation found
% 0.10/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.85/0.60 % Elapsed time: 0.225584 seconds
% 0.85/0.60 % CPU time: 1.496330 seconds
% 0.85/0.60 % Total memory used: 156.918 MB
% 0.85/0.60 % Net memory used: 155.757 MB
%------------------------------------------------------------------------------