%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SCT155+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 02:07:01 PM UTC 2026
% Result : Theorem 0.22s 0.62s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 27
% Syntax : Number of formulae : 132 ( 23 unt; 16 def)
% Number of atoms : 500 ( 142 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 578 ( 210 ~; 322 |; 13 &)
% ( 22 <=>; 9 =>; 0 <=; 2 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 17 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-6 aty)
% Number of variables : 187 ( 184 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
v_a_H____ != v_b_H____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
( v_b____ != v_a_H____
& v_a____ != v_b_H____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B_i] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,B_i))
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,B_i)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P____,c_Arrow__Order__Mirabelle_OProf),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P_H____,c_Arrow__Order__Mirabelle_OProf),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [V_A_2,V_x_2,T_a] :
( c_member(T_a,V_x_2,V_A_2)
<=> hBOOL(hAPP(V_A_2,V_x_2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [V_P_Ha_2,V_Pa_2,V_b_Ha_2,V_a_Ha_2,V_ba_2,V_aa_2] :
( V_aa_2 != V_ba_2
=> ( V_a_Ha_2 != V_b_Ha_2
=> ( V_aa_2 != V_b_Ha_2
=> ( V_ba_2 != V_a_Ha_2
=> ( c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_Pa_2,c_Arrow__Order__Mirabelle_OProf)
=> ( c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_P_Ha_2,c_Arrow__Order__Mirabelle_OProf)
=> ( ! [B_i] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_ba_2),hAPP(V_Pa_2,B_i))
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_a_Ha_2,V_b_Ha_2),hAPP(V_P_Ha_2,B_i)) )
=> ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_ba_2),hAPP(v_F,V_Pa_2))
=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_a_Ha_2,V_b_Ha_2),hAPP(v_F,V_P_Ha_2)) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f150,axiom,
! [V_x_2,V_A_2,V_y_2,T_a] :
( hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_x_2))
<=> ( hBOOL(hAPP(V_A_2,V_x_2))
| V_y_2 = V_x_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f164,axiom,
! [V_A_2,V_aa_2,T_a] :
( c_member(T_a,V_aa_2,V_A_2)
=> c_Set_Oinsert(T_a,V_aa_2,V_A_2) = V_A_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f529,conjecture,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_F,v_P____))
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_F,v_P_H____)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f530,negated_conjecture,
~ ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_F,v_P____))
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_F,v_P_H____)) ),
inference(negated_conjecture,[status(cth)],[f529]) ).
fof(f536,plain,
v_a____ != v_b____,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f537,plain,
v_a_H____ != v_b_H____,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f538,plain,
v_a____ != v_b_H____,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f539,plain,
v_b____ != v_a_H____,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f540,plain,
! [B_i] :
( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,B_i))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,B_i)) )
& ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,B_i))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,B_i)) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f541,plain,
( ! [B_i] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,B_i))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,B_i)) )
& ! [B_i] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,B_i))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,B_i)) ) ),
inference(miniscoping,[status(thm)],[f540]) ).
fof(f542,plain,
! [X0] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,X0))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,X0)) ),
inference(cnf_transformation,[status(thm)],[f541]) ).
fof(f543,plain,
! [X0] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,X0))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,X0)) ),
inference(cnf_transformation,[status(thm)],[f541]) ).
fof(f544,plain,
c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P____,c_Arrow__Order__Mirabelle_OProf),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f545,plain,
c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P_H____,c_Arrow__Order__Mirabelle_OProf),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f619,plain,
! [V_A_2,V_x_2,T_a] :
( ( ~ hBOOL(hAPP(V_A_2,V_x_2))
| c_member(T_a,V_x_2,V_A_2) )
& ( hBOOL(hAPP(V_A_2,V_x_2))
| ~ c_member(T_a,V_x_2,V_A_2) ) ),
inference(NNF_transformation,[status(thm)],[f23]) ).
fof(f620,plain,
( ! [V_A_2,V_x_2] :
( ~ hBOOL(hAPP(V_A_2,V_x_2))
| ! [T_a] : c_member(T_a,V_x_2,V_A_2) )
& ! [V_A_2,V_x_2] :
( hBOOL(hAPP(V_A_2,V_x_2))
| ! [T_a] : ~ c_member(T_a,V_x_2,V_A_2) ) ),
inference(miniscoping,[status(thm)],[f619]) ).
fof(f621,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,X1))
| ~ c_member(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f620]) ).
fof(f622,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X2,X1))
| c_member(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f620]) ).
fof(f639,plain,
! [V_P_Ha_2,V_Pa_2,V_b_Ha_2,V_a_Ha_2,V_ba_2,V_aa_2] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_a_Ha_2,V_b_Ha_2),hAPP(v_F,V_P_Ha_2))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_ba_2),hAPP(v_F,V_Pa_2))
| ? [B_i] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_ba_2),hAPP(V_Pa_2,B_i))
<~> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_a_Ha_2,V_b_Ha_2),hAPP(V_P_Ha_2,B_i)) )
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_P_Ha_2,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_Pa_2,c_Arrow__Order__Mirabelle_OProf)
| V_ba_2 = V_a_Ha_2
| V_aa_2 = V_b_Ha_2
| V_a_Ha_2 = V_b_Ha_2
| V_aa_2 = V_ba_2 ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f640,plain,
! [V_P_Ha_2,V_Pa_2,V_b_Ha_2,V_a_Ha_2,V_ba_2,V_aa_2] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_a_Ha_2,V_b_Ha_2),hAPP(v_F,V_P_Ha_2))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_ba_2),hAPP(v_F,V_Pa_2))
| ? [B_i] :
( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_a_Ha_2,V_b_Ha_2),hAPP(V_P_Ha_2,B_i))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_ba_2),hAPP(V_Pa_2,B_i)) )
& ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_a_Ha_2,V_b_Ha_2),hAPP(V_P_Ha_2,B_i))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_ba_2),hAPP(V_Pa_2,B_i)) ) )
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_P_Ha_2,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_Pa_2,c_Arrow__Order__Mirabelle_OProf)
| V_ba_2 = V_a_Ha_2
| V_aa_2 = V_b_Ha_2
| V_a_Ha_2 = V_b_Ha_2
| V_aa_2 = V_ba_2 ),
inference(NNF_transformation,[status(thm)],[f639]) ).
fof(f641,plain,
! [V_ba_2,V_aa_2] :
( ! [V_b_Ha_2,V_a_Ha_2] :
( ! [V_Pa_2] :
( ! [V_P_Ha_2] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_a_Ha_2,V_b_Ha_2),hAPP(v_F,V_P_Ha_2))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_ba_2),hAPP(v_F,V_Pa_2))
| ? [B_i] :
( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_a_Ha_2,V_b_Ha_2),hAPP(V_P_Ha_2,B_i))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_ba_2),hAPP(V_Pa_2,B_i)) )
& ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_a_Ha_2,V_b_Ha_2),hAPP(V_P_Ha_2,B_i))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_ba_2),hAPP(V_Pa_2,B_i)) ) )
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_P_Ha_2,c_Arrow__Order__Mirabelle_OProf) )
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_Pa_2,c_Arrow__Order__Mirabelle_OProf) )
| V_ba_2 = V_a_Ha_2
| V_aa_2 = V_b_Ha_2
| V_a_Ha_2 = V_b_Ha_2 )
| V_aa_2 = V_ba_2 ),
inference(miniscoping,[status(thm)],[f640]) ).
fof(f642,plain,
! [V_ba_2,V_aa_2] :
( ! [V_b_Ha_2,V_a_Ha_2] :
( ! [V_Pa_2] :
( ! [V_P_Ha_2] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_a_Ha_2,V_b_Ha_2),hAPP(v_F,V_P_Ha_2))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_ba_2),hAPP(v_F,V_Pa_2))
| ( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_a_Ha_2,V_b_Ha_2),hAPP(V_P_Ha_2,sK8_skl(V_P_Ha_2,V_Pa_2,V_a_Ha_2,V_b_Ha_2,V_aa_2,V_ba_2)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_ba_2),hAPP(V_Pa_2,sK8_skl(V_P_Ha_2,V_Pa_2,V_a_Ha_2,V_b_Ha_2,V_aa_2,V_ba_2))) )
& ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_a_Ha_2,V_b_Ha_2),hAPP(V_P_Ha_2,sK8_skl(V_P_Ha_2,V_Pa_2,V_a_Ha_2,V_b_Ha_2,V_aa_2,V_ba_2)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_aa_2,V_ba_2),hAPP(V_Pa_2,sK8_skl(V_P_Ha_2,V_Pa_2,V_a_Ha_2,V_b_Ha_2,V_aa_2,V_ba_2))) ) )
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_P_Ha_2,c_Arrow__Order__Mirabelle_OProf) )
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_Pa_2,c_Arrow__Order__Mirabelle_OProf) )
| V_ba_2 = V_a_Ha_2
| V_aa_2 = V_b_Ha_2
| V_a_Ha_2 = V_b_Ha_2 )
| V_aa_2 = V_ba_2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(B_i,sK8_skl(V_P_Ha_2,V_Pa_2,V_a_Ha_2,V_b_Ha_2,V_aa_2,V_ba_2))],[f641]) ).
fof(f643,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X3),hAPP(v_F,X5))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_F,X4))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X3),hAPP(X5,sK8_skl(X5,X4,X2,X3,X0,X1)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(X4,sK8_skl(X5,X4,X2,X3,X0,X1)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4,c_Arrow__Order__Mirabelle_OProf)
| X1 = X2
| X0 = X3
| X2 = X3
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f642]) ).
fof(f644,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X3),hAPP(v_F,X5))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_F,X4))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X3),hAPP(X5,sK8_skl(X5,X4,X2,X3,X0,X1)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(X4,sK8_skl(X5,X4,X2,X3,X0,X1)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4,c_Arrow__Order__Mirabelle_OProf)
| X1 = X2
| X0 = X3
| X2 = X3
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f642]) ).
fof(f1104,plain,
! [V_x_2,V_A_2,V_y_2,T_a] :
( ( ( ~ hBOOL(hAPP(V_A_2,V_x_2))
& V_y_2 != V_x_2 )
| hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_x_2)) )
& ( hBOOL(hAPP(V_A_2,V_x_2))
| V_y_2 = V_x_2
| ~ hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_x_2)) ) ),
inference(NNF_transformation,[status(thm)],[f150]) ).
fof(f1105,plain,
( ! [V_x_2,V_A_2,V_y_2] :
( ( ~ hBOOL(hAPP(V_A_2,V_x_2))
& V_y_2 != V_x_2 )
| ! [T_a] : hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_x_2)) )
& ! [V_x_2,V_A_2,V_y_2] :
( hBOOL(hAPP(V_A_2,V_x_2))
| V_y_2 = V_x_2
| ! [T_a] : ~ hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_x_2)) ) ),
inference(miniscoping,[status(thm)],[f1104]) ).
fof(f1107,plain,
! [X0,X1,X2,X3] :
( X1 != X3
| hBOOL(hAPP(c_Set_Oinsert(X0,X1,X2),X3)) ),
inference(cnf_transformation,[status(thm)],[f1105]) ).
fof(f1146,plain,
! [V_A_2,V_aa_2,T_a] :
( c_Set_Oinsert(T_a,V_aa_2,V_A_2) = V_A_2
| ~ c_member(T_a,V_aa_2,V_A_2) ),
inference(pre_NNF_transformation,[status(thm)],[f164]) ).
fof(f1147,plain,
! [X0,X1,X2] :
( c_Set_Oinsert(X0,X1,X2) = X2
| ~ c_member(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f1146]) ).
fof(f2121,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_F,v_P____))
<~> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_F,v_P_H____)) ),
inference(pre_NNF_transformation,[status(thm)],[f530]) ).
fof(f2122,plain,
( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_F,v_P_H____))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_F,v_P____)) )
& ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_F,v_P_H____))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_F,v_P____)) ) ),
inference(NNF_transformation,[status(thm)],[f2121]) ).
fof(f2123,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_F,v_P_H____))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_F,v_P____)) ),
inference(cnf_transformation,[status(thm)],[f2122]) ).
fof(f2124,plain,
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_F,v_P_H____))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_F,v_P____)) ),
inference(cnf_transformation,[status(thm)],[f2122]) ).
fof(f2157,definition,
( sQ0_spl
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_F,v_P____)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f2159,plain,
( sQ0_spl
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_F,v_P____)) ),
inference(component_clause,[status(thm)],[f2157]) ).
fof(f2160,definition,
( sQ1_spl
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_F,v_P_H____)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f2162,plain,
( sQ1_spl
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_F,v_P_H____)) ),
inference(component_clause,[status(thm)],[f2160]) ).
fof(f2163,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f2123,f2157,f2160]) ).
fof(f2164,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f2124,f2157,f2160]) ).
fof(f2216,plain,
! [X0,X1,X2] : hBOOL(hAPP(c_Set_Oinsert(X0,X1,X2),X1)),
inference(destructive_equality_resolution,[status(thm)],[f1107]) ).
fof(f2278,plain,
! [X0,X1,X2,X3] : c_member(X0,X1,c_Set_Oinsert(X2,X1,X3)),
inference(resolution,[status(thm)],[f622,f2216]) ).
fof(f2281,plain,
! [X0,X1,X2,X3] :
( ~ c_member(X3,X1,X2)
| c_member(X0,X1,X2) ),
inference(resolution,[status(thm)],[f622,f621]) ).
fof(f2282,plain,
! [X0] :
( sQ0_spl
| ~ c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_F,v_P____)) ),
inference(resolution,[status(thm)],[f2281,f2159]) ).
fof(f2298,plain,
c_Set_Oinsert(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P_H____,c_Arrow__Order__Mirabelle_OProf) = c_Arrow__Order__Mirabelle_OProf,
inference(resolution,[status(thm)],[f1147,f545]) ).
fof(f2299,plain,
c_Set_Oinsert(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P____,c_Arrow__Order__Mirabelle_OProf) = c_Arrow__Order__Mirabelle_OProf,
inference(resolution,[status(thm)],[f1147,f544]) ).
fof(f2301,plain,
! [X0] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,X0))
| c_Set_Oinsert(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,X0)) = hAPP(v_P____,X0) ),
inference(resolution,[status(thm)],[f1147,f543]) ).
fof(f2312,plain,
! [X0,X1,X2,X3] :
( ~ c_member(X3,X1,X2)
| c_Set_Oinsert(X0,X1,X2) = X2 ),
inference(resolution,[status(thm)],[f1147,f2281]) ).
fof(f2313,plain,
! [X0] : c_member(X0,v_P_H____,c_Arrow__Order__Mirabelle_OProf),
inference(paramodulation,[status(thm)],[f2298,f2278]) ).
fof(f2315,plain,
! [X0] : c_member(X0,v_P____,c_Arrow__Order__Mirabelle_OProf),
inference(paramodulation,[status(thm)],[f2299,f2278]) ).
fof(f2318,plain,
! [X0,X1] :
( ~ c_member(X1,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,X0))
| c_Set_Oinsert(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,X0)) = hAPP(v_P____,X0) ),
inference(resolution,[status(thm)],[f2301,f2281]) ).
fof(f2346,plain,
! [X0,X1,X2] :
( sQ0_spl
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_F,X2))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sK8_skl(v_P____,X2,v_a____,v_b____,X0,X1)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(X2,sK8_skl(v_P____,X2,v_a____,v_b____,X0,X1)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P____,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2,c_Arrow__Order__Mirabelle_OProf)
| X1 = v_a____
| X0 = v_b____
| v_a____ = v_b____
| X0 = X1 ),
inference(resolution,[status(thm)],[f643,f2282]) ).
fof(f2348,definition,
! [X0,X1,X2] :
( sQ2_spl
<=> ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_F,X2))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sK8_skl(v_P____,X2,v_a____,v_b____,X0,X1)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(X2,sK8_skl(v_P____,X2,v_a____,v_b____,X0,X1)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2,c_Arrow__Order__Mirabelle_OProf)
| X1 = v_a____
| X0 = v_b____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f2349,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_F,X2))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sK8_skl(v_P____,X2,v_a____,v_b____,X0,X1)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(X2,sK8_skl(v_P____,X2,v_a____,v_b____,X0,X1)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2,c_Arrow__Order__Mirabelle_OProf)
| X1 = v_a____
| X0 = v_b____
| X0 = X1 ),
inference(component_clause,[status(thm)],[f2348]) ).
fof(f2351,definition,
( sQ3_spl
<=> v_a____ = v_b____ ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f2352,plain,
( ~ sQ3_spl
| v_a____ = v_b____ ),
inference(component_clause,[status(thm)],[f2351]) ).
fof(f2354,definition,
( sQ4_spl
<=> c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P____,c_Arrow__Order__Mirabelle_OProf) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f2356,plain,
( sQ4_spl
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P____,c_Arrow__Order__Mirabelle_OProf) ),
inference(component_clause,[status(thm)],[f2354]) ).
fof(f2357,plain,
( sQ0_spl
| ~ sQ4_spl
| sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f2346,f2348,f2351,f2354,f2157]) ).
fof(f2375,plain,
! [X0,X1,X2] :
( sQ1_spl
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_F,X2))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sK8_skl(v_P_H____,X2,v_a_H____,v_b_H____,X0,X1)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(X2,sK8_skl(v_P_H____,X2,v_a_H____,v_b_H____,X0,X1)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P_H____,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2,c_Arrow__Order__Mirabelle_OProf)
| X1 = v_a_H____
| X0 = v_b_H____
| v_a_H____ = v_b_H____
| X0 = X1 ),
inference(resolution,[status(thm)],[f2162,f644]) ).
fof(f2376,plain,
! [X0,X1,X2] :
( sQ1_spl
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_F,X2))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sK8_skl(v_P_H____,X2,v_a_H____,v_b_H____,X0,X1)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(X2,sK8_skl(v_P_H____,X2,v_a_H____,v_b_H____,X0,X1)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P_H____,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2,c_Arrow__Order__Mirabelle_OProf)
| X1 = v_a_H____
| X0 = v_b_H____
| v_a_H____ = v_b_H____
| X0 = X1 ),
inference(resolution,[status(thm)],[f2162,f643]) ).
fof(f2378,definition,
! [X0,X1,X2] :
( sQ5_spl
<=> ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_F,X2))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sK8_skl(v_P_H____,X2,v_a_H____,v_b_H____,X0,X1)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(X2,sK8_skl(v_P_H____,X2,v_a_H____,v_b_H____,X0,X1)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2,c_Arrow__Order__Mirabelle_OProf)
| X1 = v_a_H____
| X0 = v_b_H____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f2379,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_F,X2))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sK8_skl(v_P_H____,X2,v_a_H____,v_b_H____,X0,X1)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(X2,sK8_skl(v_P_H____,X2,v_a_H____,v_b_H____,X0,X1)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2,c_Arrow__Order__Mirabelle_OProf)
| X1 = v_a_H____
| X0 = v_b_H____
| X0 = X1 ),
inference(component_clause,[status(thm)],[f2378]) ).
fof(f2381,definition,
( sQ6_spl
<=> v_a_H____ = v_b_H____ ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f2382,plain,
( ~ sQ6_spl
| v_a_H____ = v_b_H____ ),
inference(component_clause,[status(thm)],[f2381]) ).
fof(f2384,definition,
( sQ7_spl
<=> c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P_H____,c_Arrow__Order__Mirabelle_OProf) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f2386,plain,
( sQ7_spl
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P_H____,c_Arrow__Order__Mirabelle_OProf) ),
inference(component_clause,[status(thm)],[f2384]) ).
fof(f2387,plain,
( sQ1_spl
| ~ sQ7_spl
| sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f2375,f2378,f2381,f2384,f2160]) ).
fof(f2388,definition,
! [X0,X1,X2] :
( sQ8_spl
<=> ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_F,X2))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sK8_skl(v_P_H____,X2,v_a_H____,v_b_H____,X0,X1)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(X2,sK8_skl(v_P_H____,X2,v_a_H____,v_b_H____,X0,X1)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2,c_Arrow__Order__Mirabelle_OProf)
| X1 = v_a_H____
| X0 = v_b_H____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f2389,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_F,X2))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sK8_skl(v_P_H____,X2,v_a_H____,v_b_H____,X0,X1)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(X2,sK8_skl(v_P_H____,X2,v_a_H____,v_b_H____,X0,X1)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2,c_Arrow__Order__Mirabelle_OProf)
| X1 = v_a_H____
| X0 = v_b_H____
| X0 = X1 ),
inference(component_clause,[status(thm)],[f2388]) ).
fof(f2391,plain,
( sQ1_spl
| ~ sQ7_spl
| sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f2376,f2388,f2381,f2384,f2160]) ).
fof(f2392,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2386,f2313]) ).
fof(f2393,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f2392]) ).
fof(f2394,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2382,f537]) ).
fof(f2395,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f2394]) ).
fof(f2396,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2356,f2315]) ).
fof(f2397,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f2396]) ).
fof(f2400,plain,
! [X0,X1,X2] :
( sQ0_spl
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_F,X2))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sK8_skl(v_P____,X2,v_a____,v_b____,X0,X1)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(X2,sK8_skl(v_P____,X2,v_a____,v_b____,X0,X1)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P____,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2,c_Arrow__Order__Mirabelle_OProf)
| X1 = v_a____
| X0 = v_b____
| v_a____ = v_b____
| X0 = X1 ),
inference(resolution,[status(thm)],[f2282,f644]) ).
fof(f2403,definition,
! [X0,X1,X2] :
( sQ9_spl
<=> ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_F,X2))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sK8_skl(v_P____,X2,v_a____,v_b____,X0,X1)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(X2,sK8_skl(v_P____,X2,v_a____,v_b____,X0,X1)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2,c_Arrow__Order__Mirabelle_OProf)
| X1 = v_a____
| X0 = v_b____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f2404,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_F,X2))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sK8_skl(v_P____,X2,v_a____,v_b____,X0,X1)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(X2,sK8_skl(v_P____,X2,v_a____,v_b____,X0,X1)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2,c_Arrow__Order__Mirabelle_OProf)
| X1 = v_a____
| X0 = v_b____
| X0 = X1 ),
inference(component_clause,[status(thm)],[f2403]) ).
fof(f2406,plain,
( sQ0_spl
| ~ sQ4_spl
| sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f2400,f2403,f2351,f2354,f2157]) ).
fof(f2408,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2352,f536]) ).
fof(f2409,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f2408]) ).
fof(f2415,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sK8_skl(v_P____,X2,v_a____,v_b____,X0,X1)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_F,X2))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(X2,sK8_skl(v_P____,X2,v_a____,v_b____,X0,X1)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2,c_Arrow__Order__Mirabelle_OProf)
| X1 = v_a____
| X0 = v_b____
| X0 = X1 ),
inference(resolution,[status(thm)],[f2404,f543]) ).
fof(f2423,definition,
( sQ10_spl
<=> v_a_H____ = v_b____ ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f2424,plain,
( ~ sQ10_spl
| v_a_H____ = v_b____ ),
inference(component_clause,[status(thm)],[f2423]) ).
fof(f2426,definition,
( sQ11_spl
<=> v_b_H____ = v_a____ ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f2427,plain,
( ~ sQ11_spl
| v_b_H____ = v_a____ ),
inference(component_clause,[status(thm)],[f2426]) ).
fof(f2440,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sK8_skl(v_P_H____,X2,v_a_H____,v_b_H____,X0,X1)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_F,X2))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(X2,sK8_skl(v_P_H____,X2,v_a_H____,v_b_H____,X0,X1)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2,c_Arrow__Order__Mirabelle_OProf)
| X1 = v_a_H____
| X0 = v_b_H____
| X0 = X1 ),
inference(resolution,[status(thm)],[f2379,f542]) ).
fof(f2443,plain,
! [X0,X1,X2,X3] :
( ~ sQ2_spl
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X3),hAPP(v_F,X1))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X3),hAPP(X1,sK8_skl(v_P____,X1,v_a____,v_b____,X2,X3)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| X3 = v_a____
| X2 = v_b____
| X2 = X3
| c_Set_Oinsert(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sK8_skl(v_P____,X1,v_a____,v_b____,X2,X3))) = hAPP(v_P____,sK8_skl(v_P____,X1,v_a____,v_b____,X2,X3)) ),
inference(resolution,[status(thm)],[f2312,f2349]) ).
fof(f2444,plain,
! [X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,X1))
| c_Set_Oinsert(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,X1)) = hAPP(v_P____,X1) ),
inference(resolution,[status(thm)],[f2312,f543]) ).
fof(f2445,plain,
! [X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,X1))
| c_Set_Oinsert(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,X1)) = hAPP(v_P_H____,X1) ),
inference(resolution,[status(thm)],[f2312,f542]) ).
fof(f2472,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| c_Set_Oinsert(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sK8_skl(v_P_H____,X2,v_a_H____,v_b_H____,X0,X1))) = hAPP(v_P____,sK8_skl(v_P_H____,X2,v_a_H____,v_b_H____,X0,X1))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(v_F,X2))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),hAPP(X2,sK8_skl(v_P_H____,X2,v_a_H____,v_b_H____,X0,X1)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2,c_Arrow__Order__Mirabelle_OProf)
| X1 = v_a_H____
| X0 = v_b_H____
| X0 = X1 ),
inference(resolution,[status(thm)],[f2389,f2318]) ).
fof(f2481,plain,
! [X0,X1,X2] :
( ~ c_member(X2,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,X1))
| c_Set_Oinsert(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,X1)) = hAPP(v_P____,X1) ),
inference(resolution,[status(thm)],[f2444,f2281]) ).
fof(f2482,definition,
! [X0] :
( sQ15_spl
<=> c_Set_Oinsert(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sK8_skl(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____))) = hAPP(v_P____,sK8_skl(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f2483,plain,
! [X0] :
( ~ sQ15_spl
| c_Set_Oinsert(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sK8_skl(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____))) = hAPP(v_P____,sK8_skl(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____)) ),
inference(component_clause,[status(thm)],[f2482]) ).
fof(f2494,plain,
! [X0,X1,X2] :
( ~ c_member(X2,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,X1))
| c_Set_Oinsert(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,X1)) = hAPP(v_P_H____,X1) ),
inference(resolution,[status(thm)],[f2445,f2281]) ).
fof(f2588,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_F,v_P____))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sK8_skl(v_P_H____,v_P____,v_a_H____,v_b_H____,v_a____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P____,c_Arrow__Order__Mirabelle_OProf)
| v_b____ = v_a_H____
| v_a____ = v_b_H____
| v_a____ = v_b____
| c_Set_Oinsert(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sK8_skl(v_P_H____,v_P____,v_a_H____,v_b_H____,v_a____,v_b____))) = hAPP(v_P____,sK8_skl(v_P_H____,v_P____,v_a_H____,v_b_H____,v_a____,v_b____))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_F,v_P____))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P____,c_Arrow__Order__Mirabelle_OProf)
| v_b____ = v_a_H____
| v_a____ = v_b_H____
| v_a____ = v_b____ ),
inference(resolution,[status(thm)],[f2472,f2440]) ).
fof(f2593,definition,
( sQ23_spl
<=> c_Set_Oinsert(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sK8_skl(v_P_H____,v_P____,v_a_H____,v_b_H____,v_a____,v_b____))) = hAPP(v_P____,sK8_skl(v_P_H____,v_P____,v_a_H____,v_b_H____,v_a____,v_b____)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f2594,plain,
( ~ sQ23_spl
| c_Set_Oinsert(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sK8_skl(v_P_H____,v_P____,v_a_H____,v_b_H____,v_a____,v_b____))) = hAPP(v_P____,sK8_skl(v_P_H____,v_P____,v_a_H____,v_b_H____,v_a____,v_b____)) ),
inference(component_clause,[status(thm)],[f2593]) ).
fof(f2596,definition,
( sQ24_spl
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sK8_skl(v_P_H____,v_P____,v_a_H____,v_b_H____,v_a____,v_b____))) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f2598,plain,
( sQ24_spl
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sK8_skl(v_P_H____,v_P____,v_a_H____,v_b_H____,v_a____,v_b____))) ),
inference(component_clause,[status(thm)],[f2596]) ).
fof(f2599,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ24_spl
| sQ23_spl
| ~ sQ0_spl
| ~ sQ4_spl
| sQ10_spl
| sQ11_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f2588,f2351,f2426,f2423,f2354,f2157,f2593,f2596,f2388,f2378]) ).
fof(f2615,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2424,f539]) ).
fof(f2616,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f2615]) ).
fof(f2617,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2427,f538]) ).
fof(f2618,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f2617]) ).
fof(f2642,definition,
( sQ30_spl
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sK8_skl(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____))) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f2644,plain,
( sQ30_spl
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sK8_skl(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____))) ),
inference(component_clause,[status(thm)],[f2642]) ).
fof(f2678,plain,
! [X0] :
( ~ sQ15_spl
| c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sK8_skl(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____))) ),
inference(paramodulation,[status(thm)],[f2483,f2278]) ).
fof(f2681,plain,
! [X0,X1] :
( ~ sQ2_spl
| c_Set_Oinsert(X1,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sK8_skl(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____))) = hAPP(v_P____,sK8_skl(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_F,v_P_H____))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P_H____,c_Arrow__Order__Mirabelle_OProf)
| v_b_H____ = v_a____
| v_a_H____ = v_b____
| v_a_H____ = v_b_H____
| c_Set_Oinsert(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sK8_skl(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____))) = hAPP(v_P____,sK8_skl(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____)) ),
inference(resolution,[status(thm)],[f2443,f2481]) ).
fof(f2685,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| sQ11_spl
| sQ10_spl
| sQ6_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f2681,f2482,f2381,f2423,f2426,f2384,f2160,f2348]) ).
fof(f2690,plain,
! [X0] :
( ~ sQ15_spl
| c_Set_Oinsert(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sK8_skl(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____))) = hAPP(v_P_H____,sK8_skl(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____)) ),
inference(resolution,[status(thm)],[f2678,f2494]) ).
fof(f2719,plain,
! [X0] :
( ~ sQ23_spl
| c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sK8_skl(v_P_H____,v_P____,v_a_H____,v_b_H____,v_a____,v_b____))) ),
inference(paramodulation,[status(thm)],[f2594,f2278]) ).
fof(f2749,plain,
! [X0] :
( ~ sQ15_spl
| c_member(X0,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sK8_skl(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____))) ),
inference(paramodulation,[status(thm)],[f2690,f2278]) ).
fof(f2751,plain,
( ~ sQ9_spl
| ~ sQ15_spl
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_F,v_P_H____))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sK8_skl(v_P____,v_P_H____,v_a____,v_b____,v_a_H____,v_b_H____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P_H____,c_Arrow__Order__Mirabelle_OProf)
| v_b_H____ = v_a____
| v_a_H____ = v_b____
| v_a_H____ = v_b_H____ ),
inference(resolution,[status(thm)],[f2749,f2415]) ).
fof(f2754,plain,
( ~ sQ9_spl
| ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ30_spl
| ~ sQ7_spl
| sQ11_spl
| sQ10_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f2751,f2381,f2423,f2426,f2384,f2642,f2160,f2482,f2403]) ).
fof(f2755,plain,
( sQ30_spl
| ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2644,f2749]) ).
fof(f2756,plain,
( sQ30_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f2755]) ).
fof(f2850,plain,
( ~ sQ23_spl
| ~ sQ5_spl
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_F,v_P____))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sK8_skl(v_P_H____,v_P____,v_a_H____,v_b_H____,v_a____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P____,c_Arrow__Order__Mirabelle_OProf)
| v_b____ = v_a_H____
| v_a____ = v_b_H____
| v_a____ = v_b____ ),
inference(resolution,[status(thm)],[f2440,f2719]) ).
fof(f2853,plain,
( ~ sQ23_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ24_spl
| ~ sQ4_spl
| sQ10_spl
| sQ11_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f2850,f2351,f2426,f2423,f2354,f2596,f2157,f2378,f2593]) ).
fof(f2861,plain,
( sQ24_spl
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a_H____,v_b_H____),hAPP(v_P_H____,sK8_skl(v_P_H____,v_P____,v_a_H____,v_b_H____,v_a____,v_b____))) ),
inference(resolution,[status(thm)],[f2598,f543]) ).
fof(f2865,plain,
( ~ sQ8_spl
| sQ24_spl
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_F,v_P____))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a____,v_b____),hAPP(v_P____,sK8_skl(v_P_H____,v_P____,v_a_H____,v_b_H____,v_a____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P____,c_Arrow__Order__Mirabelle_OProf)
| v_b____ = v_a_H____
| v_a____ = v_b_H____
| v_a____ = v_b____ ),
inference(resolution,[status(thm)],[f2861,f2389]) ).
fof(f2868,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| sQ24_spl
| ~ sQ4_spl
| sQ10_spl
| sQ11_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f2865,f2351,f2426,f2423,f2354,f2596,f2157,f2388]) ).
fof(f2869,plain,
$false,
inference(sat_refutation,[status(thm)],[f2163,f2164,f2357,f2387,f2391,f2393,f2395,f2397,f2406,f2409,f2599,f2616,f2618,f2685,f2754,f2756,f2853,f2868]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT155+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.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 : Mon Sep 21 04:32:36 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.42 % Drodi V4.1.1
% 0.22/0.62 % Refutation found
% 0.22/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.19/0.65 % Elapsed time: 0.276390 seconds
% 1.19/0.65 % CPU time: 1.580668 seconds
% 1.19/0.65 % Total memory used: 175.531 MB
% 1.19/0.65 % Net memory used: 174.299 MB
%------------------------------------------------------------------------------