%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SCT157+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 02:07:58 PM UTC 2026
% Result : Theorem 0.07s 0.57s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 19 unt; 0 def)
% Number of atoms : 186 ( 59 equ)
% Maximal formula atoms : 36 ( 3 avg)
% Number of connectives : 208 ( 72 ~; 109 |; 8 &)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-5 aty)
% Number of variables : 52 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,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/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact__096a_A_126_061_Ab_H_A_G_Ab_A_061_Aa_H_096,axiom,
( v_b____ = v_a_H____
& v_a____ != v_b_H____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096a_A_126_061_Ab_H_A_G_Ab_A_061_Aa_H_096) ).
fof(fact__C4_C,axiom,
! [X17,X16,X5,X18,X19] :
( X19 != X18
=> ( X18 != X5
=> ( X19 != X5
=> ( 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)),X16,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)),X17,c_Arrow__Order__Mirabelle_OProf)
=> ( ! [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,X19,X18),hAPP(X16,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,X18,X5),hAPP(X17,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,X19,X18),hAPP(v_F,X16))
<=> 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,X18,X5),hAPP(v_F,X17)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C4_C) ).
fof(fact_A_I1_J,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_A_I1_J) ).
fof(fact_A_I5_J,axiom,
! [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,v_a____,v_b____),hAPP(v_P____,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,v_a_H____,v_b_H____),hAPP(v_P_H____,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_A_I5_J) ).
fof(fact_A_I3_J,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/sandbox2/benchmark/theBenchmark.p',fact_A_I3_J) ).
fof(fact_A_I2_J,axiom,
v_a_H____ != v_b_H____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_A_I2_J) ).
fof(fact_A_I4_J,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/sandbox2/benchmark/theBenchmark.p',fact_A_I4_J) ).
fof(c_0_8,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(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_9,plain,
( v_b____ = v_a_H____
& v_a____ != v_b_H____ ),
inference(fof_simplification,[status(thm)],[fact__096a_A_126_061_Ab_H_A_G_Ab_A_061_Aa_H_096]) ).
fof(c_0_10,plain,
! [X17,X16,X5,X18,X19] :
( X19 != X18
=> ( X18 != X5
=> ( X19 != X5
=> ( 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)),X16,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)),X17,c_Arrow__Order__Mirabelle_OProf)
=> ( ! [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,X19,X18),hAPP(X16,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,X18,X5),hAPP(X17,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,X19,X18),hAPP(v_F,X16))
<=> 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,X18,X5),hAPP(v_F,X17)) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact__C4_C]) ).
fof(c_0_11,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_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(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])]) ).
fof(c_0_12,plain,
( v_b____ = v_a_H____
& v_a____ != v_b_H____ ),
inference(fof_nnf,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
v_a____ != v_b____,
inference(fof_simplification,[status(thm)],[fact_A_I1_J]) ).
fof(c_0_14,plain,
! [X101,X102,X103,X104,X105] :
( ( X105 = X104
| X104 = X103
| X105 = X103
| ~ 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)),X102,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)),X101,c_Arrow__Order__Mirabelle_OProf)
| 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,X104,X103),hAPP(X101,esk2_5(X101,X102,X103,X104,X105)))
| 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,X105,X104),hAPP(X102,esk2_5(X101,X102,X103,X104,X105)))
| 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,X105,X104),hAPP(v_F,X102))
| ~ 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,X104,X103),hAPP(v_F,X101)) )
& ( X105 = X104
| X104 = X103
| X105 = X103
| ~ 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)),X102,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)),X101,c_Arrow__Order__Mirabelle_OProf)
| 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,X104,X103),hAPP(X101,esk2_5(X101,X102,X103,X104,X105)))
| 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,X105,X104),hAPP(X102,esk2_5(X101,X102,X103,X104,X105)))
| 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,X104,X103),hAPP(v_F,X101))
| ~ 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,X105,X104),hAPP(v_F,X102)) )
& ( X105 = X104
| X104 = X103
| X105 = X103
| ~ 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)),X102,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)),X101,c_Arrow__Order__Mirabelle_OProf)
| ~ 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,X104,X103),hAPP(X101,esk2_5(X101,X102,X103,X104,X105)))
| ~ 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,X105,X104),hAPP(X102,esk2_5(X101,X102,X103,X104,X105)))
| 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,X105,X104),hAPP(v_F,X102))
| ~ 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,X104,X103),hAPP(v_F,X101)) )
& ( X105 = X104
| X104 = X103
| X105 = X103
| ~ 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)),X102,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)),X101,c_Arrow__Order__Mirabelle_OProf)
| ~ 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,X104,X103),hAPP(X101,esk2_5(X101,X102,X103,X104,X105)))
| ~ 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,X105,X104),hAPP(X102,esk2_5(X101,X102,X103,X104,X105)))
| 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,X104,X103),hAPP(v_F,X101))
| ~ 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,X105,X104),hAPP(v_F,X102)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])]) ).
cnf(c_0_15,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_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(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
v_b____ = v_a_H____,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
v_a____ != v_b____,
inference(fof_nnf,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X100] :
( ( 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____,X100))
| ~ 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____,X100)) )
& ( 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____,X100))
| ~ 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____,X100)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_A_I5_J])])]) ).
cnf(c_0_19,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)),X3,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)),X5,c_Arrow__Order__Mirabelle_OProf)
| ~ 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,X1,X2),hAPP(v_F,X3))
| X1 = X2
| X2 = X4
| X1 = 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,X4),hAPP(X5,esk2_5(X5,X3,X4,X2,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,X1,X2),hAPP(X3,esk2_5(X5,X3,X4,X2,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,X4),hAPP(v_F,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,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_b____,v_b_H____),hAPP(v_F,v_P_H____)) ),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,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(split_conjunct,[status(thm)],[fact_A_I3_J]) ).
cnf(c_0_22,plain,
v_a____ != v_b____,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_23,plain,
v_a_H____ != v_b_H____,
inference(fof_simplification,[status(thm)],[fact_A_I2_J]) ).
cnf(c_0_24,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_P____,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)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,negated_conjecture,
( ~ 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)
| 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_b____,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_b____,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_b____,X1),hAPP(X2,esk2_5(X2,v_P____,X1,v_b____,v_a____)))
| 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____,esk2_5(X2,v_P____,X1,v_b____,v_a____)))
| v_a____ = X1
| v_b____ = X1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_26,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(split_conjunct,[status(thm)],[fact_A_I4_J]) ).
fof(c_0_27,plain,
v_a_H____ != v_b_H____,
inference(fof_nnf,[status(thm)],[c_0_23]) ).
cnf(c_0_28,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_P____,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_b____,v_b_H____),hAPP(v_P_H____,X1)) ),
inference(rw,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_29,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_b____,X1),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_b____,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_b____,X1),hAPP(v_P_H____,esk2_5(v_P_H____,v_P____,X1,v_b____,v_a____)))
| 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____,esk2_5(v_P_H____,v_P____,X1,v_b____,v_a____)))
| v_b____ = X1
| v_a____ = X1 ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
v_a_H____ != v_b_H____,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,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_b____,X1),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_b____,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_b____,X1),hAPP(v_P_H____,esk2_5(v_P_H____,v_P____,X1,v_b____,v_a____)))
| 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_b____,v_b_H____),hAPP(v_P_H____,esk2_5(v_P_H____,v_P____,X1,v_b____,v_a____)))
| v_a____ = X1
| v_b____ = X1 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,plain,
v_b_H____ != v_b____,
inference(rw,[status(thm)],[c_0_30,c_0_16]) ).
cnf(c_0_33,plain,
v_a____ != v_b_H____,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_34,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)),X3,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)),X5,c_Arrow__Order__Mirabelle_OProf)
| ~ 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,X4),hAPP(X5,esk2_5(X5,X3,X4,X2,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,X1,X2),hAPP(X3,esk2_5(X5,X3,X4,X2,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,X1,X2),hAPP(v_F,X3))
| X1 = X2
| X2 = X4
| X1 = 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,X4),hAPP(v_F,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_35,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_b____,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_b____,v_b_H____),hAPP(v_P_H____,esk2_5(v_P_H____,v_P____,v_b_H____,v_b____,v_a____))) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_31]),c_0_32]),c_0_33]) ).
cnf(c_0_36,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_P_H____,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)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_37,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_P____,esk2_5(v_P_H____,v_P____,v_b_H____,v_b____,v_a____)))
| 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_b____,v_b_H____),hAPP(v_F,v_P_H____)) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_26]),c_0_21])]),c_0_22]),c_0_33]),c_0_32]),c_0_20]) ).
cnf(c_0_38,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_b____,v_b_H____),hAPP(v_P_H____,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)) ),
inference(rw,[status(thm)],[c_0_36,c_0_16]) ).
cnf(c_0_39,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)),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)),X3,c_Arrow__Order__Mirabelle_OProf)
| ~ 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,X1,X2),hAPP(v_F,X3))
| X4 = X1
| X1 = X2
| X4 = 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,X1,X2),hAPP(X3,esk2_5(X3,X5,X2,X1,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,X4,X1),hAPP(X5,esk2_5(X3,X5,X2,X1,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,X4,X1),hAPP(v_F,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_40,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_b____,v_b_H____),hAPP(v_F,v_P_H____)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_35]) ).
cnf(c_0_41,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_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(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_42,negated_conjecture,
( ~ 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)
| 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,X1,v_b____),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,X1,v_b____),hAPP(X2,esk2_5(v_P_H____,X2,v_b_H____,v_b____,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_b____,v_b_H____),hAPP(v_P_H____,esk2_5(v_P_H____,X2,v_b_H____,v_b____,X1)))
| v_b____ = X1
| v_b_H____ = X1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_26])]),c_0_32]) ).
cnf(c_0_43,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_b____,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(rw,[status(thm)],[c_0_41,c_0_16]) ).
cnf(c_0_44,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)),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)),X3,c_Arrow__Order__Mirabelle_OProf)
| ~ 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,X1,X2),hAPP(X3,esk2_5(X3,X5,X2,X1,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,X4,X1),hAPP(X5,esk2_5(X3,X5,X2,X1,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,X1,X2),hAPP(v_F,X3))
| X4 = X1
| X1 = X2
| X4 = 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,X4,X1),hAPP(v_F,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_45,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,X1,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,X1,v_b____),hAPP(v_P____,esk2_5(v_P_H____,v_P____,v_b_H____,v_b____,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_b____,v_b_H____),hAPP(v_P_H____,esk2_5(v_P_H____,v_P____,v_b_H____,v_b____,X1)))
| v_b_H____ = X1
| v_b____ = X1 ),
inference(spm,[status(thm)],[c_0_42,c_0_21]) ).
cnf(c_0_46,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____)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_40])]) ).
cnf(c_0_47,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)),X2,c_Arrow__Order__Mirabelle_OProf)
| ~ 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_b____,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_b____,X1),hAPP(X2,esk2_5(X2,v_P____,X1,v_b____,v_a____)))
| ~ 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_b____,v_b_H____),hAPP(v_P_H____,esk2_5(X2,v_P____,X1,v_b____,v_a____)))
| 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____))
| v_b____ = X1
| X1 = v_a____ ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_38]),c_0_21])]),c_0_22]) ).
cnf(c_0_48,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_b____,v_b_H____),hAPP(v_P_H____,esk2_5(v_P_H____,v_P____,v_b_H____,v_b____,v_a____))),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_45]),c_0_22]),c_0_33]),c_0_46]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_48]),c_0_40]),c_0_26])]),c_0_33]),c_0_32]),c_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SCT157+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.52 % Computer : n012.cluster.edu
% 0.05/0.52 % Model : x86_64 x86_64
% 0.05/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.52 % Memory : 8046.5625MB
% 0.05/0.52 % OS : Linux 6.8.0-71-generic
% 0.05/0.52 % CPULimit : 300
% 0.05/0.52 % WCLimit : 300
% 0.05/0.52 % DateTime : Mon Sep 21 04:35:00 UTC 2026
% 0.05/0.52 % CPUTime :
% 0.05/0.52 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.54 Running first-order theorem proving
% 0.07/0.54 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.57 % Version: 3.5.1
% 0.07/0.57 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.07/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.57 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.07/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.07/0.57 % Starting sh5l with 300s (1) cores
% 0.07/0.57 % new_bool_3 with pid 1564954 completed with status 0
% 0.07/0.57 % Result found by new_bool_3
% 0.07/0.57 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.07/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.57 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.07/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/0.57 % Search class: FGHSF-FFLS33-MFFFFFNN
% 0.07/0.57 % partial match(2): FGHSF-FSLS33-SFFFFFNN
% 0.07/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.57 % SubtermCWHack with pid 1564957 completed with status 0
% 0.07/0.57 % Result found by SubtermCWHack
% 0.07/0.57 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.07/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.57 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.07/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/0.57 % Search class: FGHSF-FFLS33-MFFFFFNN
% 0.07/0.57 % partial match(2): FGHSF-FSLS33-SFFFFFNN
% 0.07/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.57 % Preprocessing time : 0.002 s
% 0.07/0.57
% 0.07/0.57 % Proof found!
% 0.07/0.57 % SZS status Theorem
% 0.07/0.57 % SZS output start CNFRefutation
% See solution above
% 0.07/0.57 % Parsed axioms : 529
% 0.07/0.57 % Removed by relevancy pruning/SinE : 509
% 0.07/0.57 % Initial clauses : 43
% 0.07/0.57 % Removed in clause preprocessing : 10
% 0.07/0.57 % Initial clauses in saturation : 33
% 0.07/0.57 % Processed clauses : 65
% 0.07/0.57 % ...of these trivial : 4
% 0.07/0.57 % ...subsumed : 6
% 0.07/0.57 % ...remaining for further processing : 55
% 0.07/0.57 % Other redundant clauses eliminated : 0
% 0.07/0.57 % Clauses deleted for lack of memory : 0
% 0.07/0.57 % Backward-subsumed : 0
% 0.07/0.57 % Backward-rewritten : 24
% 0.07/0.57 % Generated clauses : 84
% 0.07/0.57 % ...of the previous two non-redundant : 53
% 0.07/0.57 % ...aggressively subsumed : 0
% 0.07/0.57 % Contextual simplify-reflections : 2
% 0.07/0.57 % Paramodulations : 79
% 0.07/0.57 % Factorizations : 2
% 0.07/0.57 % NegExts : 0
% 0.07/0.57 % Equation resolutions : 3
% 0.07/0.57 % Disequality decompositions : 0
% 0.07/0.57 % Total rewrite steps : 104
% 0.07/0.57 % ...of those cached : 99
% 0.07/0.57 % Propositional unsat checks : 0
% 0.07/0.57 % Propositional check models : 0
% 0.07/0.57 % Propositional check unsatisfiable : 0
% 0.07/0.57 % Propositional clauses : 0
% 0.07/0.57 % Propositional clauses after purity: 0
% 0.07/0.57 % Propositional unsat core size : 0
% 0.07/0.57 % Propositional preprocessing time : 0.000
% 0.07/0.57 % Propositional encoding time : 0.000
% 0.07/0.57 % Propositional solver time : 0.000
% 0.07/0.57 % Success case prop preproc time : 0.000
% 0.07/0.57 % Success case prop encoding time : 0.000
% 0.07/0.57 % Success case prop solver time : 0.000
% 0.07/0.57 % Current number of processed clauses : 31
% 0.07/0.57 % Positive orientable unit clauses : 5
% 0.07/0.57 % Positive unorientable unit clauses: 0
% 0.07/0.57 % Negative unit clauses : 4
% 0.07/0.57 % Non-unit-clauses : 22
% 0.07/0.57 % Current number of unprocessed clauses: 21
% 0.07/0.57 % ...number of literals in the above : 186
% 0.07/0.57 % Current number of archived formulas : 0
% 0.07/0.57 % Current number of archived clauses : 24
% 0.07/0.57 % Clause-clause subsumption calls (NU) : 1445
% 0.07/0.57 % Rec. Clause-clause subsumption calls : 58
% 0.07/0.57 % Non-unit clause-clause subsumptions : 8
% 0.07/0.57 % Unit Clause-clause subsumption calls : 46
% 0.07/0.57 % Rewrite failures with RHS unbound : 0
% 0.07/0.57 % BW rewrite match attempts : 132
% 0.07/0.57 % BW rewrite match successes : 1
% 0.07/0.57 % Condensation attempts : 0
% 0.07/0.57 % Condensation successes : 0
% 0.07/0.57 % Termbank termtop insertions : 20720
% 0.07/0.57 % Search garbage collected termcells : 5015
% 0.07/0.57
% 0.07/0.57 % -------------------------------------------------
% 0.07/0.57 % User time : 0.008 s
% 0.07/0.57 % System time : 0.003 s
% 0.07/0.57 % Total time : 0.012 s
% 0.07/0.57 % Maximum resident set size: 4604 pages
% 0.07/0.57
% 0.07/0.57 % -------------------------------------------------
% 0.07/0.57 % User time : 0.017 s
% 0.07/0.57 % System time : 0.007 s
% 0.07/0.57 % Total time : 0.024 s
% 0.07/0.57 % Maximum resident set size: 5376 pages
% 0.07/0.57 % E exiting
%------------------------------------------------------------------------------