%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SCT135+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n003.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 : Fri Sep 25 02:40:48 PM UTC 2026
% Result : Theorem 0.70s 1.29s
% Output : CNFRefutation 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 58 ( 19 unt; 0 def)
% Number of atoms : 233 ( 76 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 264 ( 89 ~; 156 |; 4 &)
% ( 4 <=>; 8 =>; 0 <=; 3 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-6 aty)
% Number of variables : 76 ( 0 sgn 73 !; 3 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096a_A_126_061_Ab_096) ).
fof(f5,axiom,
v_a____ != v_b_H____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096a_A_126_061_Ab_H_096) ).
fof(f6,axiom,
v_b____ != v_a_H____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096b_A_126_061_Aa_H_096) ).
fof(f7,axiom,
v_a_H____ != v_b_H____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096a_H_A_126_061_Ab_H_096) ).
fof(f8,axiom,
! [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))
<=> 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)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_H_J_096) ).
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____,c_Arrow__Order__Mirabelle_OProf),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096P_A_058_AProf_096) ).
fof(f10,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__096P_H_A_058_AProf_096) ).
fof(f14,axiom,
! [X0,X1,X2,X3,X4,X5] :
( X5 != X4
=> ( X3 != X2
=> ( X5 != X2
=> ( X4 != 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)
=> ( 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)),X0,c_Arrow__Order__Mirabelle_OProf)
=> ( ! [X6] :
( 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,X5,X4),hAPP(X1,X6))
<=> 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,X3,X2),hAPP(X0,X6)) )
=> ( 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,X5,X4),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,X3,X2),hAPP(v_F,X0)) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C1_C) ).
fof(f521,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(f522,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)],[f521]) ).
fof(f523,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(ennf_transformation,[],[f522]) ).
fof(f525,plain,
! [X0,X1,X2,X3,X4,X5] :
( X4 = X5
| X2 = X3
| X2 = X5
| X3 = X4
| ~ 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)
| ~ 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)),X0,c_Arrow__Order__Mirabelle_OProf)
| ? [X6] :
( 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,X5,X4),hAPP(X1,X6))
<~> 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,X3,X2),hAPP(X0,X6)) )
| ~ 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,X5,X4),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,X3,X2),hAPP(v_F,X0)) ),
inference(ennf_transformation,[],[f14]) ).
fof(f526,plain,
! [X0,X1,X2,X3,X4,X5] :
( X4 = X5
| X2 = X3
| X2 = X5
| X3 = X4
| ~ 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)
| ~ 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)),X0,c_Arrow__Order__Mirabelle_OProf)
| ? [X6] :
( 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,X5,X4),hAPP(X1,X6))
<~> 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,X3,X2),hAPP(X0,X6)) )
| ~ 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,X5,X4),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,X3,X2),hAPP(v_F,X0)) ),
inference(flattening,[],[f525]) ).
fof(f534,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____)) )
& ( ~ 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(nnf_transformation,[],[f523]) ).
fof(f536,plain,
! [X0,X1,X2,X3,X4,X5] :
( X4 = X5
| X2 = X3
| X2 = X5
| X3 = X4
| ~ 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)
| ~ 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)),X0,c_Arrow__Order__Mirabelle_OProf)
| ? [X6] :
( ( 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,X5,X4),hAPP(X1,X6))
| 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,X3,X2),hAPP(X0,X6)) )
& ( ~ 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,X5,X4),hAPP(X1,X6))
| ~ 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,X3,X2),hAPP(X0,X6)) ) )
| ~ 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,X5,X4),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,X3,X2),hAPP(v_F,X0)) ),
inference(nnf_transformation,[],[f526]) ).
fof(f537,plain,
! [X0,X1,X2,X3,X4,X5] :
( X4 = X5
| X2 = X3
| X2 = X5
| X3 = X4
| ~ 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)
| ~ 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)),X0,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,X5,X4),hAPP(X1,sK1(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,X3,X2),hAPP(X0,sK1(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,X5,X4),hAPP(X1,sK1(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,X3,X2),hAPP(X0,sK1(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,X5,X4),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,X3,X2),hAPP(v_F,X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X6,sK1(X0,X1,X2,X3,X4,X5))],[f536]) ).
fof(f538,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____,v_b____),hAPP(v_P____,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_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(nnf_transformation,[],[f8]) ).
fof(f543,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(cnf_transformation,[],[f534]) ).
fof(f544,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(cnf_transformation,[],[f534]) ).
fof(f546,plain,
! [X2,X3,X0,X1,X4,X5] :
( X4 = X5
| X2 = X3
| X2 = X5
| X3 = X4
| ~ 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)
| ~ 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)),X0,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,X5,X4),hAPP(X1,sK1(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,X3,X2),hAPP(X0,sK1(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,X5,X4),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,X3,X2),hAPP(v_F,X0)) ),
inference(cnf_transformation,[],[f537]) ).
fof(f547,plain,
! [X2,X3,X0,X1,X4,X5] :
( X4 = X5
| X2 = X3
| X2 = X5
| X3 = X4
| ~ 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)
| ~ 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)),X0,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,X5,X4),hAPP(X1,sK1(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,X3,X2),hAPP(X0,sK1(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,X5,X4),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,X3,X2),hAPP(v_F,X0)) ),
inference(cnf_transformation,[],[f537]) ).
fof(f548,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____,v_b____),hAPP(v_P____,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)) ),
inference(cnf_transformation,[],[f538]) ).
fof(f549,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,[],[f538]) ).
fof(f550,plain,
v_a____ != v_b_H____,
inference(cnf_transformation,[],[f5]) ).
fof(f551,plain,
v_a____ != v_b____,
inference(cnf_transformation,[],[f4]) ).
fof(f561,plain,
v_b____ != v_a_H____,
inference(cnf_transformation,[],[f6]) ).
fof(f562,plain,
v_b_H____ != v_a_H____,
inference(cnf_transformation,[],[f7]) ).
fof(f568,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,[],[f9]) ).
fof(f569,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,[],[f10]) ).
tcf(c_49,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(cnf_transformation,[],[f544]) ).
tcf(c_50,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(cnf_transformation,[],[f543]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $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,X0,X1),hAPP(v_F,X2))
| ( X4 = X5 )
| ( X1 = X5 )
| ( X0 = X4 )
| ( 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)),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)),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,X5,X4),hAPP(v_F,X3))
| ~ 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,X5,X4),hAPP(X3,sK1(X2,X3,X1,X0,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,X0,X1),hAPP(X2,sK1(X2,X3,X1,X0,X4,X5))) ),
inference(cnf_transformation,[],[f547]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $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,X4,X5),hAPP(v_F,X3))
| 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,X5),hAPP(X3,sK1(X3,X2,X5,X4,X1,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,X0,X1),hAPP(X2,sK1(X3,X2,X5,X4,X1,X0)))
| ( X4 = X5 )
| ( X1 = X4 )
| ( X0 = X5 )
| ( 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)),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)),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,X0,X1),hAPP(v_F,X2)) ),
inference(cnf_transformation,[],[f546]) ).
tcf(c_54,plain,
! [X0: $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____,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)) ),
inference(cnf_transformation,[],[f549]) ).
tcf(c_55,plain,
! [X0: $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____,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,[],[f548]) ).
tcf(c_56,plain,
v_b_H____ != v_a____,
inference(cnf_transformation,[],[f550]) ).
tcf(c_57,plain,
v_a____ != v_b____,
inference(cnf_transformation,[],[f551]) ).
tcf(c_58,plain,
v_a_H____ != v_b____,
inference(cnf_transformation,[],[f561]) ).
tcf(c_59,plain,
v_a_H____ != v_b_H____,
inference(cnf_transformation,[],[f562]) ).
tcf(c_64,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,[],[f568]) ).
tcf(c_65,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,[],[f569]) ).
tcf(c_956,plain,
! [X0: $i,X1: $i,X2: $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,X1,X2),hAPP(v_F,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____,sK1(X0,v_P____,X2,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,X1,X2),hAPP(X0,sK1(X0,v_P____,X2,X1,v_b____,v_a____)))
| ( v_a____ = v_b____ )
| ( X2 = v_a____ )
| ( X1 = v_b____ )
| ( X1 = X2 )
| ~ 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)),X0,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_a____,v_b____),hAPP(v_F,v_P____)) ),
inference(superposition,[status(thm)],[c_53,c_55]) ).
tcf(c_957,plain,
! [X0: $i,X1: $i,X2: $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,X1,X2),hAPP(v_F,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____,sK1(X0,v_P_H____,X2,X1,v_b_H____,v_a_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,X1,X2),hAPP(X0,sK1(X0,v_P_H____,X2,X1,v_b_H____,v_a_H____)))
| ( v_a_H____ = v_b_H____ )
| ( X2 = v_a_H____ )
| ( X1 = v_b_H____ )
| ( X1 = X2 )
| ~ 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)),X0,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_a_H____,v_b_H____),hAPP(v_F,v_P_H____)) ),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_960,plain,
! [X0: $i,X1: $i,X2: $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,X1,X2),hAPP(v_F,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____,sK1(X0,v_P_H____,X2,X1,v_b_H____,v_a_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,X1,X2),hAPP(X0,sK1(X0,v_P_H____,X2,X1,v_b_H____,v_a_H____)))
| ( X2 = v_a_H____ )
| ( X1 = v_b_H____ )
| ( X1 = X2 )
| ~ 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)),X0,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_a_H____,v_b_H____),hAPP(v_F,v_P_H____)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_957,c_59,c_65]) ).
tcf(c_969,plain,
! [X0: $i,X1: $i,X2: $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,X1,X2),hAPP(v_F,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____,sK1(X0,v_P____,X2,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,X1,X2),hAPP(X0,sK1(X0,v_P____,X2,X1,v_b____,v_a____)))
| ( X2 = v_a____ )
| ( X1 = v_b____ )
| ( X1 = X2 )
| ~ 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)),X0,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_a____,v_b____),hAPP(v_F,v_P____)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_956,c_57,c_64]) ).
tcf(c_1015,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____,v_b____),hAPP(v_P____,sK1(v_P____,v_P_H____,v_b____,v_a____,v_b_H____,v_a_H____)))
| ( v_a____ = v_b____ )
| ( v_b_H____ = v_a____ )
| ( v_a_H____ = 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)
| ~ 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(equality_factoring,[status(thm)],[c_960]) ).
tcf(c_1017,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____,v_b____),hAPP(v_P____,sK1(v_P____,v_P_H____,v_b____,v_a____,v_b_H____,v_a_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____)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1015,c_57,c_56,c_58,c_64]) ).
tcf(c_1034,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____,v_b____),hAPP(v_P____,sK1(v_P____,v_P_H____,v_b____,v_a____,v_b_H____,v_a_H____))) ),
inference(global_subsumption_just,[status(thm)],[c_1017,c_50,c_1017]) ).
tcf(c_1040,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_P_H____,sK1(v_P____,v_P_H____,v_b____,v_a____,v_b_H____,v_a_H____))) ),
inference(superposition,[status(thm)],[c_1034,c_55]) ).
tcf(c_1069,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_H____,v_b_H____),hAPP(v_P_H____,sK1(v_P_H____,v_P____,v_b_H____,v_a_H____,v_b____,v_a____)))
| ( v_b_H____ = v_a____ )
| ( v_a_H____ = 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)
| ~ 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(equality_factoring,[status(thm)],[c_969]) ).
tcf(c_1071,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_H____,v_b_H____),hAPP(v_P_H____,sK1(v_P_H____,v_P____,v_b_H____,v_a_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_a____,v_b____),hAPP(v_F,v_P____)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1069,c_56,c_58,c_59,c_65]) ).
tcf(c_1088,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_H____,v_b_H____),hAPP(v_P_H____,sK1(v_P_H____,v_P____,v_b_H____,v_a_H____,v_b____,v_a____))) ),
inference(global_subsumption_just,[status(thm)],[c_1071,c_50,c_1071]) ).
tcf(c_1094,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_P____,sK1(v_P_H____,v_P____,v_b_H____,v_a_H____,v_b____,v_a____))) ),
inference(superposition,[status(thm)],[c_1088,c_54]) ).
tcf(c_1213,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____))
| ( v_a____ = v_b____ )
| ( v_b_H____ = v_a____ )
| ( v_a_H____ = 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____,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_H____,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_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____,sK1(v_P____,v_P_H____,v_b____,v_a____,v_b_H____,v_a_H____))) ),
inference(superposition,[status(thm)],[c_1034,c_52]) ).
tcf(c_1214,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____))
| ( v_a____ = v_b____ )
| ( v_b_H____ = v_a____ )
| ( v_a_H____ = 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____,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_H____,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_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____,sK1(v_P_H____,v_P____,v_b_H____,v_a_H____,v_b____,v_a____))) ),
inference(superposition,[status(thm)],[c_1088,c_52]) ).
tcf(c_1215,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____,v_b____),hAPP(v_P____,sK1(v_P_H____,v_P____,v_b_H____,v_a_H____,v_b____,v_a____))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1214,c_57,c_56,c_58,c_59,c_64,c_65]) ).
tcf(c_1219,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____))
| ~ 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____,sK1(v_P____,v_P_H____,v_b____,v_a____,v_b_H____,v_a_H____))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1213,c_57,c_56,c_58,c_59,c_64,c_65]) ).
tcf(c_1243,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1215,c_1219,c_1094,c_1040,c_49,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT135+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 08:52:35 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 0.70/1.29 % SZS status Started for theBenchmark.p
% 0.70/1.29 % SZS status Theorem for theBenchmark.p
% 0.70/1.29
% 0.70/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.70/1.29
% 0.70/1.29 % ------ iProver source info
% 0.70/1.29
% 0.70/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.70/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.70/1.29 % git: non_committed_changes: false
% 0.70/1.29
% 0.70/1.29 % ------ Parsing...
% 0.70/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.70/1.29
% 0.70/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.70/1.29
% 0.70/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.70/1.29
% 0.70/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.70/1.29 % ------ Proving...
% 0.70/1.29 % ------ Problem Properties
% 0.70/1.29
% 0.70/1.29 %
% 0.70/1.29 % clauses 15
% 0.70/1.29 % conjectures 2
% 0.70/1.29 % EPR 4
% 0.70/1.29 % Horn 12
% 0.70/1.29 % unary 6
% 0.70/1.29 % binary 7
% 0.70/1.29 % lits 40
% 0.70/1.29 % lits eq 18
% 0.70/1.29 % fd_pure 0
% 0.70/1.29 % fd_pseudo 0
% 0.70/1.29 % fd_cond 0
% 0.70/1.29 % fd_pseudo_cond 5
% 0.70/1.29 % AC symbols 0
% 0.70/1.29
% 0.70/1.29 % ------ Schedule dynamic 5 is on
% 0.70/1.29
% 0.70/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.70/1.29
% 0.70/1.29
% 0.70/1.29 % ------
% 0.70/1.29 % Current options:
% 0.70/1.29 % ------
% 0.70/1.29
% 0.70/1.29
% 0.70/1.29 %
% 0.70/1.29
% 0.70/1.29 % ------ Proving...
% 0.70/1.29 %
% 0.70/1.29
% 0.70/1.29 % SZS status Theorem for theBenchmark.p
% 0.70/1.29
% 0.70/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.70/1.30
% 0.70/1.30
%------------------------------------------------------------------------------