%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SCT131+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 : n006.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 38.15s 17.12s
% Output : CNFRefutation 38.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 61 ( 40 unt; 8 def)
% Number of atoms : 177 ( 39 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 84 ( 39 ~; 34 |; 2 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 9 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-5 aty)
% Number of variables : 108 ( 0 sgn 107 !; 1 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_u) ).
fof(f6,axiom,
! [X0] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_b_H____)),hAPP(v_Q____,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bi_O_Ab_A_060_092_060_094bsub_062Q_Ai_092_060_094esub_062_Ab_H_096) ).
fof(f32,axiom,
hBOOL(hAPP(hAPP(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_Q____),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096Q_A_058_AProf_096) ).
fof(f47,axiom,
! [X0] :
( c_Arrow__Order__Mirabelle_Ounanimity(X0)
<=> ! [X1] :
( hBOOL(hAPP(hAPP(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))
=> ! [X2,X3] :
( ! [X4] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X1,X4)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X0,X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unanimity__def) ).
fof(f322,axiom,
! [X0,X1,X2,X3,X4] :
( hAPP(X4,X3) = X2
=> c_Fun_Ofun__upd(X1,X0,X4,X3,X2) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem) ).
fof(f323,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( X5 != X4
=> hAPP(c_Fun_Ofun__upd(X3,X2,X1,X4,X0),X5) = hAPP(X1,X5) )
& ( X5 = X4
=> hAPP(c_Fun_Ofun__upd(X3,X2,X1,X4,X0),X5) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__def) ).
fof(f535,conjecture,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_b_H____)),hAPP(v_F,v_Q____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f536,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_b_H____)),hAPP(v_F,v_Q____))),
inference(negated_conjecture,[status(cth)],[f535]) ).
fof(f540,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_b_H____)),hAPP(v_F,v_Q____))),
inference(flattening,[],[f536]) ).
fof(f544,plain,
! [X0] :
( c_Arrow__Order__Mirabelle_Ounanimity(X0)
=> ! [X1] :
( hBOOL(hAPP(hAPP(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))
=> ! [X2,X3] :
( ! [X4] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X1,X4)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X0,X1))) ) ) ),
inference(unused_predicate_definition_removal,[],[f47]) ).
fof(f577,plain,
! [X0] :
( ~ c_Arrow__Order__Mirabelle_Ounanimity(X0)
| ! [X1] :
( ~ hBOOL(hAPP(hAPP(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))
| ! [X2,X3] :
( ? [X4] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X1,X4)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X0,X1))) ) ) ),
inference(ennf_transformation,[],[f544]) ).
fof(f885,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(X4,X3) != X2
| c_Fun_Ofun__upd(X1,X0,X4,X3,X2) = X4 ),
inference(ennf_transformation,[],[f322]) ).
fof(f886,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( X4 = X5
| hAPP(c_Fun_Ofun__upd(X3,X2,X1,X4,X0),X5) = hAPP(X1,X5) )
& ( X4 != X5
| hAPP(c_Fun_Ofun__upd(X3,X2,X1,X4,X0),X5) = X0 ) ),
inference(ennf_transformation,[],[f323]) ).
fof(f1057,plain,
! [X0] :
( ~ c_Arrow__Order__Mirabelle_Ounanimity(X0)
| ! [X1] :
( ~ hBOOL(hAPP(hAPP(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))
| ! [X2,X3] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X1,sK7(X1,X2,X3))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X0,X1))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X4,sK7(X1,X2,X3))],[f577]) ).
fof(f1242,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(cnf_transformation,[],[f2]) ).
fof(f1246,plain,
! [X0] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_b_H____)),hAPP(v_Q____,X0))),
inference(cnf_transformation,[],[f6]) ).
fof(f1293,plain,
hBOOL(hAPP(hAPP(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_Q____),c_Arrow__Order__Mirabelle_OProf)),
inference(cnf_transformation,[],[f32]) ).
fof(f1344,plain,
! [X2,X3,X0,X1] :
( ~ c_Arrow__Order__Mirabelle_Ounanimity(X0)
| ~ hBOOL(hAPP(hAPP(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))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X1,sK7(X1,X2,X3))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X0,X1))) ),
inference(cnf_transformation,[],[f1057]) ).
fof(f1742,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(X4,X3) != X2
| c_Fun_Ofun__upd(X1,X0,X4,X3,X2) = X4 ),
inference(cnf_transformation,[],[f885]) ).
fof(f1744,plain,
! [X2,X3,X0,X1,X4,X5] :
( X4 != X5
| hAPP(c_Fun_Ofun__upd(X3,X2,X1,X4,X0),X5) = X0 ),
inference(cnf_transformation,[],[f886]) ).
fof(f2031,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_b_H____)),hAPP(v_F,v_Q____))),
inference(cnf_transformation,[],[f540]) ).
fof(f2115,plain,
! [X3,X0,X1,X4] : c_Fun_Ofun__upd(X1,X0,X4,X3,hAPP(X4,X3)) = X4,
inference(equality_resolution,[],[f1742]) ).
fof(f2116,plain,
! [X2,X3,X0,X1,X5] : hAPP(c_Fun_Ofun__upd(X3,X2,X1,X5,X0),X5) = X0,
inference(equality_resolution,[],[f1744]) ).
tcf(c_50,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(cnf_transformation,[],[f1242]) ).
tcf(c_54,plain,
! [X0: $i] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_b_H____)),hAPP(v_Q____,X0))),
inference(cnf_transformation,[],[f1246]) ).
tcf(c_90,plain,
hBOOL(hAPP(hAPP(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_Q____),c_Arrow__Order__Mirabelle_OProf)),
inference(cnf_transformation,[],[f1293]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)),hAPP(X3,X2)))
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X3)
| ~ hBOOL(hAPP(hAPP(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))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)),hAPP(X2,sK7(X2,X0,X1)))) ),
inference(cnf_transformation,[],[f1344]) ).
tcf(c_526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Fun_Ofun__upd(X0,X1,X2,X3,hAPP(X2,X3)) = X2,
inference(cnf_transformation,[],[f2115]) ).
tcf(c_527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hAPP(c_Fun_Ofun__upd(X0,X1,X2,X3,X4),X3) = X4,
inference(cnf_transformation,[],[f2116]) ).
tcf(c_810,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_b_H____)),hAPP(v_F,v_Q____))),
inference(cnf_transformation,[],[f2031]) ).
tcf(c_8806,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X0,X3)))
| ~ hBOOL(hAPP(hAPP(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))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,sK7(X3,X1,X2))))
| ( X0 != v_F ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_138]) ).
tcf(c_8807,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)),hAPP(v_F,X2)))
| ~ hBOOL(hAPP(hAPP(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))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)),hAPP(X2,sK7(X2,X0,X1)))) ),
inference(unflattening,[status(thm)],[c_8806]) ).
tcf(c_20407,definition,
iPr_def_10 = tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_20408,definition,
iPr_def_11 = c_member(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_20409,definition,
iPr_def_12 = c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_20410,definition,
iPr_def_13 = hAPP(iPr_def_12,v_b____),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_20411,definition,
iPr_def_14 = hAPP(iPr_def_13,v_b_H____),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_20412,definition,
iPr_def_15 = hAPP(iPr_def_11,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_20413,definition,
iPr_def_16 = hAPP(v_F,v_Q____),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_20414,definition,
iPr_def_17 = hAPP(iPr_def_15,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_20415,negated_conjecture,
~ hBOOL(iPr_def_17),
inference(demodulation,[status(thm)],[c_810,c_20413,c_20409,c_20410,c_20411,c_20407,c_20408,c_20412,c_20414]) ).
tcf(c_30969,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(iPr_def_11,hAPP(hAPP(iPr_def_12,X0),X1)),hAPP(v_F,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(iPr_def_10,tc_HOL_Obool))),X2),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(iPr_def_11,hAPP(hAPP(iPr_def_12,X0),X1)),hAPP(X2,sK7(X2,X0,X1)))) ),
inference(light_normalisation,[status(thm)],[c_8807,c_20407,c_20408,c_20409]) ).
tcf(c_30993,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(iPr_def_11,hAPP(hAPP(iPr_def_12,v_b____),X0)),hAPP(v_F,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(iPr_def_10,tc_HOL_Obool))),X1),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(iPr_def_11,hAPP(iPr_def_13,X0)),hAPP(X1,sK7(X1,v_b____,X0)))) ),
inference(superposition,[status(thm)],[c_20410,c_30969]) ).
tcf(c_30994,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(iPr_def_11,hAPP(iPr_def_13,X0)),hAPP(v_F,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(iPr_def_10,tc_HOL_Obool))),X1),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(iPr_def_11,hAPP(iPr_def_13,X0)),hAPP(X1,sK7(X1,v_b____,X0)))) ),
inference(light_normalisation,[status(thm)],[c_30993,c_20410]) ).
tcf(c_31396,plain,
! [X0: $i,X1: $i] : c_Fun_Ofun__upd(X0,X1,v_F,v_Q____,iPr_def_16) = v_F,
inference(superposition,[status(thm)],[c_20413,c_526]) ).
tcf(c_31400,plain,
! [X0: $i,X1: $i] : c_Fun_Ofun__upd(X0,X1,iPr_def_12,v_b____,iPr_def_13) = iPr_def_12,
inference(superposition,[status(thm)],[c_20410,c_526]) ).
tcf(c_31401,plain,
! [X0: $i,X1: $i] : c_Fun_Ofun__upd(X0,X1,iPr_def_13,v_b_H____,iPr_def_14) = iPr_def_13,
inference(superposition,[status(thm)],[c_20411,c_526]) ).
tcf(c_31402,plain,
! [X0: $i,X1: $i] : c_Fun_Ofun__upd(X0,X1,iPr_def_11,iPr_def_14,iPr_def_15) = iPr_def_11,
inference(superposition,[status(thm)],[c_20412,c_526]) ).
tcf(c_31403,plain,
! [X0: $i,X1: $i] : c_Fun_Ofun__upd(X0,X1,iPr_def_15,iPr_def_16,iPr_def_17) = iPr_def_15,
inference(superposition,[status(thm)],[c_20414,c_526]) ).
tcf(c_31412,plain,
hAPP(v_F,v_Q____) = iPr_def_16,
inference(superposition,[status(thm)],[c_31396,c_527]) ).
tcf(c_31413,plain,
hAPP(iPr_def_12,v_b____) = iPr_def_13,
inference(superposition,[status(thm)],[c_31400,c_527]) ).
tcf(c_31414,plain,
hAPP(iPr_def_13,v_b_H____) = iPr_def_14,
inference(superposition,[status(thm)],[c_31401,c_527]) ).
tcf(c_31415,plain,
hAPP(iPr_def_11,iPr_def_14) = iPr_def_15,
inference(superposition,[status(thm)],[c_31402,c_527]) ).
tcf(c_31416,plain,
hAPP(iPr_def_15,iPr_def_16) = iPr_def_17,
inference(superposition,[status(thm)],[c_31403,c_527]) ).
tcf(c_31522,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(iPr_def_11,hAPP(iPr_def_13,v_b_H____)),hAPP(v_F,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(iPr_def_10,tc_HOL_Obool))),X0),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(iPr_def_11,iPr_def_14),hAPP(X0,sK7(X0,v_b____,v_b_H____)))) ),
inference(superposition,[status(thm)],[c_31414,c_30994]) ).
tcf(c_31526,plain,
! [X0: $i] :
( hBOOL(hAPP(iPr_def_15,hAPP(v_F,X0)))
| ~ hBOOL(hAPP(iPr_def_15,hAPP(X0,sK7(X0,v_b____,v_b_H____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(iPr_def_10,tc_HOL_Obool))),X0),c_Arrow__Order__Mirabelle_OProf)) ),
inference(light_normalisation,[status(thm)],[c_31522,c_31414,c_31415]) ).
tcf(c_32709,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(iPr_def_10,tc_HOL_Obool))),v_Q____),c_Arrow__Order__Mirabelle_OProf)),
inference(light_normalisation,[status(thm)],[c_90,c_20407]) ).
tcf(c_38398,plain,
! [X0: $i] : hBOOL(hAPP(iPr_def_15,hAPP(v_Q____,X0))),
inference(light_normalisation,[status(thm)],[c_54,c_20407,c_20408,c_20409,c_31413,c_31414,c_31415]) ).
tcf(c_43333,plain,
( hBOOL(hAPP(iPr_def_15,hAPP(v_F,v_Q____)))
| ~ hBOOL(hAPP(iPr_def_15,hAPP(v_Q____,sK7(v_Q____,v_b____,v_b_H____)))) ),
inference(superposition,[status(thm)],[c_32709,c_31526]) ).
tcf(c_43341,plain,
( hBOOL(iPr_def_17)
| ~ hBOOL(hAPP(iPr_def_15,hAPP(v_Q____,sK7(v_Q____,v_b____,v_b_H____)))) ),
inference(light_normalisation,[status(thm)],[c_43333,c_31412,c_31416]) ).
tcf(c_43342,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_43341,c_20415,c_38398]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT131+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.19/10.46 % Computer : n006.cluster.edu
% 0.19/10.46 % Model : x86_64 x86_64
% 0.19/10.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/10.46 % Memory : 8046.5625MB
% 0.19/10.46 % OS : Linux 6.8.0-71-generic
% 0.19/10.46 % CPULimit : 300
% 0.19/10.46 % WCLimit : 300
% 0.19/10.46 % DateTime : Thu Sep 24 08:49:54 UTC 2026
% 0.19/10.47 % CPUTime :
% 0.19/10.47 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.24/10.53 Running first-order theorem proving
% 0.24/10.53 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
% 0.24/10.55
% 0.24/10.55 % ======== iProver multi-core TPTP/SMT =========
% 0.24/10.55
% 0.24/10.55 % Detected problem language: tptp
% 0.24/10.57 % Proving...
% 38.15/17.12 % SZS status Started for theBenchmark.p
% 38.15/17.12 ERROR - "ProverProcess:heur/421498:1.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 38.15/17.12 Fatal error: exception Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 38.15/17.12 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 8 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 2 --comb_sup_mult 0 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 512 --inst_dismatching true --inst_eager_unprocessed_to_passive false --inst_eq_res_simp true --inst_learning_factor 8 --inst_learning_loop_flag true --inst_learning_start 128 --inst_lit_activity_flag false --inst_lit_sel "[+sign;+prop]" --inst_lit_sel_side none --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[+num_symb;-age;-age];[+num_symb;+conj_non_prolific_symb]]" --inst_passive_queues_freq "[512;10]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew model --inst_solver_calls_frac 0.006221608720445637 --inst_solver_per_active 32768 --inst_sos_flag true --inst_sos_phase false --inst_sos_sth_lit_sel "[+non_prol_conj_symb;+sign;-depth;-prop]" --inst_start_prop_sim_after_learn 9 --inst_subs_given true --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[ACNormalisation]" --sup_immed_fw_main "[]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_bw "[]" --sup_input_fw "[ACNormalisation]" --sup_input_triv "[Unflattening]" --sup_iter_deepening 2 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]" --sup_passive_queues_freq "[8;4;4]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 2 --sup_score sim_d_gen --sup_share_max_num_cl 500 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering invfreq --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 0.33" --time_out_real 1.00 /export/starexec/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_zpr10wmg/t_ggmqsx 2>> /export/starexec/sandbox2/tmp/iprover_out_zpr10wmg/t_ggmqsx_error
% 38.15/17.12 % SZS status Theorem for theBenchmark.p
% 38.15/17.12
% 38.15/17.12 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 38.15/17.12
% 38.15/17.12 % ------ iProver source info
% 38.15/17.12
% 38.15/17.12 % git: date: 2026-07-19 20:42:38 +0200
% 38.15/17.12 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 38.15/17.12 % git: non_committed_changes: false
% 38.15/17.12
% 38.15/17.12 % ------ Parsing...
% 38.15/17.12 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 38.15/17.12
% 38.15/17.12 % ------ Preprocessing... sup_sim: 12 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e %
% 38.15/17.12
% 38.15/17.12 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 38.15/17.12
% 38.15/17.12 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 38.15/17.12 % ------ Proving...
% 38.15/17.12 % ------ Problem Properties
% 38.15/17.12
% 38.15/17.12 %
% 38.15/17.12 % clauses 630
% 38.15/17.12 % conjectures 1
% 38.15/17.12 % EPR 36
% 38.15/17.12 % Horn 489
% 38.15/17.12 % unary 138
% 38.15/17.12 % binary 268
% 38.15/17.12 % lits 1426
% 38.15/17.12 % lits eq 293
% 38.15/17.12 % fd_pure 0
% 38.15/17.12 % fd_pseudo 0
% 38.15/17.12 % fd_cond 0
% 38.15/17.12 % fd_pseudo_cond 74
% 38.15/17.12 % AC symbols 0
% 38.15/17.12
% 38.15/17.12 % ------ Schedule dynamic 5 is on
% 38.15/17.12
% 38.15/17.12 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 38.15/17.12
% 38.15/17.12
% 38.15/17.12 % ------
% 38.15/17.12 % Current options:
% 38.15/17.12 % ------
% 38.15/17.12
% 38.15/17.12
% 38.15/17.12 %
% 38.15/17.12
% 38.15/17.12 % ------ Proving...
% 38.15/17.12 %
% 38.15/17.12
% 38.15/17.12 % SZS status Theorem for theBenchmark.p
% 38.15/17.12
% 38.15/17.12 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 38.15/17.12
%------------------------------------------------------------------------------