%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SCT021-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n017.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 02:40:37 PM UTC 2026
% Result : Unsatisfiable 176.67s 24.32s
% Output : CNFRefutation 176.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 65 ( 25 unt; 0 def)
% Number of atoms : 168 ( 18 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 193 ( 90 ~; 103 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-4 aty)
% Number of variables : 96 ( 0 sgn 96 !; 0 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
fof(f659,axiom,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1(X0,X2)))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__UNIV_1) ).
fof(f766,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Relation_Otrans(X3,X2)
| ~ hBOOL(c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2)))
| ~ hBOOL(c_in(c_Pair(X4,X1,X2,X2),X3,tc_prod(X2,X2)))
| hBOOL(c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transD_0) ).
fof(f767,axiom,
! [X2,X0,X1] :
( ~ c_Relation_Oirrefl(X2,X1)
| ~ hBOOL(c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_0) ).
fof(f770,axiom,
! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).
fof(f771,axiom,
! [X0,X1] : hBOOL(c_in(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
fof(f772,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Relation_Ototal__on(X4,X3,X2)
| ~ hBOOL(c_in(X1,X4,X2))
| ~ hBOOL(c_in(X0,X4,X2))
| X1 = X0
| hBOOL(c_in(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2)))
| hBOOL(c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_0) ).
fof(f773,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Relation_Ototal__on(X4,X3,X2)
| ~ hBOOL(c_in(X1,X4,X2))
| ~ hBOOL(c_in(X0,X4,X2))
| X0 = X1
| hBOOL(c_in(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2)))
| hBOOL(c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2))) ),
inference(reorient_equations,[],[f772]) ).
fof(f774,axiom,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X1,X0))
| hBOOL(c_in(X0,X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
fof(f775,axiom,
! [X2,X0,X1] :
( ~ hBOOL(c_in(X1,X0,X2))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
fof(f776,negated_conjecture,
! [X0] : c_Relation_Otrans(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f777,negated_conjecture,
! [X0] : c_Relation_Oirrefl(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f778,negated_conjecture,
! [X0] : c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f779,negated_conjecture,
hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f780,negated_conjecture,
~ hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f781,negated_conjecture,
( ~ c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f782,negated_conjecture,
( ~ c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f784,negated_conjecture,
! [X2,X0,X1] :
( ~ c_Relation_Otrans(hAPP(X2,v_Pa(X2)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X2,v_Pa(X2)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X2,v_Pa(X2)),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X1
| ~ hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_8) ).
tcf(c_1326,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1(X0,X1))) ),
inference(cnf_transformation,[],[f659]) ).
tcf(c_1422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2)))
| ~ c_Relation_Otrans(X3,X2)
| ~ hBOOL(c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2)))
| ~ hBOOL(c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2))) ),
inference(cnf_transformation,[],[f766]) ).
tcf(c_1423,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_Relation_Oirrefl(X2,X1)
| ~ hBOOL(c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1))) ),
inference(cnf_transformation,[],[f767]) ).
tcf(c_1425,plain,
! [X0: $i,X1: $i] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1)),
inference(cnf_transformation,[],[f770]) ).
tcf(c_1426,plain,
! [X0: $i,X1: $i] : hBOOL(c_in(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)),
inference(cnf_transformation,[],[f771]) ).
tcf(c_1427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(c_in(c_Pair(X3,X0,X2,X2),X4,tc_prod(X2,X2)))
| hBOOL(c_in(c_Pair(X0,X3,X2,X2),X4,tc_prod(X2,X2)))
| ( X0 = X3 )
| ~ c_Relation_Ototal__on(X1,X4,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ hBOOL(c_in(X0,X1,X2)) ),
inference(cnf_transformation,[],[f773]) ).
tcf(c_1428,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(c_in(X1,X0,X2))
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[],[f774]) ).
tcf(c_1429,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(X1,X0))
| ~ hBOOL(c_in(X0,X1,X2)) ),
inference(cnf_transformation,[],[f775]) ).
tcf(c_1430,negated_conjecture,
! [X0: $i] : c_Relation_Otrans(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt),
inference(cnf_transformation,[],[f776]) ).
tcf(c_1431,negated_conjecture,
! [X0: $i] : c_Relation_Oirrefl(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt),
inference(cnf_transformation,[],[f777]) ).
tcf(c_1432,negated_conjecture,
! [X0: $i] : c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt),
inference(cnf_transformation,[],[f778]) ).
tcf(c_1433,negated_conjecture,
hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(cnf_transformation,[],[f779]) ).
tcf(c_1434,negated_conjecture,
~ hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(cnf_transformation,[],[f780]) ).
tcf(c_1435,negated_conjecture,
( c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(cnf_transformation,[],[f781]) ).
tcf(c_1436,negated_conjecture,
( c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(cnf_transformation,[],[f782]) ).
tcf(c_1438,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ( X0 = X1 )
| ~ c_Relation_Otrans(hAPP(X2,v_Pa(X2)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X2,v_Pa(X2)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X2,v_Pa(X2)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(cnf_transformation,[],[f784]) ).
tcf(c_3932,plain,
( c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1436,c_1430]) ).
tcf(c_3933,plain,
( c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1435,c_1430]) ).
tcf(c_3938,plain,
( c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3932,c_1431]) ).
tcf(c_3939,plain,
( c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3933,c_1431]) ).
tcf(c_3974,plain,
c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),
inference(backward_subsumption_resolution,[status(thm)],[c_3938,c_1432]) ).
tcf(c_3976,plain,
c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),
inference(backward_subsumption_resolution,[status(thm)],[c_3939,c_1432]) ).
tcf(c_22042,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ( X1 = X2 )
| ~ c_Relation_Otrans(hAPP(X0,v_Pa(X0)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X0,v_Pa(X0)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X0,v_Pa(X0)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(hAPP(hAPP(X0,v_i),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(superposition,[status(thm)],[c_1428,c_1438]) ).
tcf(c_22043,plain,
! [X0: $i,X1: $i] :
( hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ( X0 = X1 )
| ~ c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(superposition,[status(thm)],[c_1432,c_22042]) ).
tcf(c_22046,plain,
hBOOL(hAPP(v_F(v_P),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(superposition,[status(thm)],[c_1433,c_1429]) ).
tcf(c_22186,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X2))
| ~ hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1))) ),
inference(instantiation,[status(thm)],[c_1326]) ).
tcf(c_22187,plain,
! [X0: $i,X1: $i] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1))),
inference(instantiation,[status(thm)],[c_1425]) ).
tcf(c_22475,plain,
! [X0: $i] :
( hBOOL(c_in(c_Pair(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(superposition,[status(thm)],[c_1433,c_1422]) ).
tcf(c_22479,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( hBOOL(c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2)))
| hBOOL(c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2)))
| ( X0 = X4 )
| ~ hBOOL(hAPP(X1,X4))
| ~ c_Relation_Ototal__on(X1,X3,X2)
| ~ hBOOL(c_in(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_1428,c_1427]) ).
tcf(c_22576,plain,
! [X0: $i] :
( hBOOL(c_in(c_Pair(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(global_subsumption_just,[status(thm)],[c_22475,c_3976,c_22475]) ).
tcf(c_22579,plain,
! [X0: $i] :
( hBOOL(c_in(c_Pair(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(hAPP(v_F(v_P),c_Pair(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(superposition,[status(thm)],[c_1428,c_22576]) ).
tcf(c_22580,plain,
! [X0: $i] :
( hBOOL(c_in(c_Pair(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ( X0 = v_b )
| ~ c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(superposition,[status(thm)],[c_22043,c_22576]) ).
tcf(c_22622,plain,
( ~ c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(hAPP(v_F(v_P),c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(superposition,[status(thm)],[c_22579,c_1423]) ).
tcf(c_22633,plain,
( ( v_a = v_b )
| ~ c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(superposition,[status(thm)],[c_22580,c_1423]) ).
tcf(c_22733,plain,
~ hBOOL(hAPP(v_F(v_P),c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(global_subsumption_just,[status(thm)],[c_22622,c_3974,c_22622]) ).
tcf(c_23729,plain,
c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt),
inference(instantiation,[status(thm)],[c_1430]) ).
tcf(c_28262,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(c_in(c_Pair(X3,X2,X0,X0),X1,tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X2,X3,X0,X0),X1,tc_prod(X0,X0)))
| ( X2 = X3 )
| ~ hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X2))
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1,X0) ),
inference(superposition,[status(thm)],[c_1426,c_22479]) ).
tcf(c_28470,plain,
c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt),
inference(instantiation,[status(thm)],[c_1431]) ).
tcf(c_28924,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(c_in(c_Pair(X3,X2,X0,X0),X1,tc_prod(X0,X0)))
| hBOOL(c_in(c_Pair(X2,X3,X0,X0),X1,tc_prod(X0,X0)))
| ( X2 = X3 )
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_28262,c_22186,c_22187,c_28262]) ).
tcf(c_28965,plain,
( hBOOL(c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ( v_a = v_b )
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(superposition,[status(thm)],[c_28924,c_1434]) ).
tcf(c_29151,plain,
( hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ( v_a = v_b )
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(superposition,[status(thm)],[c_28965,c_1429]) ).
tcf(c_29154,plain,
( hBOOL(c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ( v_a = v_b )
| ~ c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(superposition,[status(thm)],[c_28965,c_1438]) ).
tcf(c_29177,plain,
( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt)
| ( v_a = v_b ) ),
inference(global_subsumption_just,[status(thm)],[c_29154,c_3974,c_22633,c_23729,c_28470,c_29151]) ).
tcf(c_29178,plain,
( ( v_a = v_b )
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(renaming,[status(thm)],[c_29177]) ).
tcf(c_29179,plain,
v_a = v_b,
inference(superposition,[status(thm)],[c_1432,c_29178]) ).
tcf(c_29246,plain,
~ hBOOL(hAPP(v_F(v_P),c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(superposition,[status(thm)],[c_29179,c_22733]) ).
tcf(c_29251,plain,
hBOOL(hAPP(v_F(v_P),c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(superposition,[status(thm)],[c_29179,c_22046]) ).
tcf(c_29255,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_29246,c_29251]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT021-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.62 % Computer : n017.cluster.edu
% 0.14/0.62 % Model : x86_64 x86_64
% 0.14/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.62 % Memory : 8046.5625MB
% 0.14/0.62 % OS : Linux 6.8.0-71-generic
% 0.14/0.62 % CPULimit : 300
% 0.14/0.62 % WCLimit : 300
% 0.14/0.62 % DateTime : Thu Sep 24 08:29:18 UTC 2026
% 0.14/0.62 % CPUTime :
% 0.14/0.62 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.20/0.68 Running first-order theorem proving
% 0.20/0.68 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.69
% 0.20/0.69 % ======== iProver multi-core TPTP/SMT =========
% 0.20/0.69
% 0.20/0.69 % Detected problem language: tptp
% 0.20/0.71 % Proving...
% 176.67/24.32 % SZS status Started for theBenchmark.p
% 176.67/24.32 % SZS status Unsatisfiable for theBenchmark.p
% 176.67/24.32
% 176.67/24.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 176.67/24.32
% 176.67/24.32 % ------ iProver source info
% 176.67/24.32
% 176.67/24.32 % git: date: 2026-07-19 20:42:38 +0200
% 176.67/24.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 176.67/24.32 % git: non_committed_changes: false
% 176.67/24.32
% 176.67/24.32 % ------ Parsing...% successful
% 176.67/24.32
% 176.67/24.32
% 176.67/24.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 176.67/24.32
% 176.67/24.32 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 176.67/24.32
% 176.67/24.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 176.67/24.32
% 176.67/24.32 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 176.67/24.32 % ------ Proving...
% 176.67/24.32 % ------ Problem Properties
% 176.67/24.32
% 176.67/24.32 %
% 176.67/24.32 % clauses 600
% 176.67/24.32 % conjectures 6
% 176.67/24.32 % EPR 21
% 176.67/24.32 % Horn 531
% 176.67/24.32 % unary 179
% 176.67/24.32 % binary 262
% 176.67/24.32 % lits 1218
% 176.67/24.32 % lits eq 292
% 176.67/24.32 % fd_pure 0
% 176.67/24.32 % fd_pseudo 0
% 176.67/24.32 % fd_cond 0
% 176.67/24.32 % fd_pseudo_cond 47
% 176.67/24.32 % AC symbols 0
% 176.67/24.32
% 176.67/24.32 % ------ Input Options Time Limit: Unbounded
% 176.67/24.32
% 176.67/24.32
% 176.67/24.32 % ------
% 176.67/24.32 % Current options:
% 176.67/24.32 % ------
% 176.67/24.32
% 176.67/24.32
% 176.67/24.32 %
% 176.67/24.32
% 176.67/24.32 % ------ Proving...
% 176.67/24.32 %
% 176.67/24.32
% 176.67/24.32 % SZS status Unsatisfiable for theBenchmark.p
% 176.67/24.32
% 176.67/24.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 176.67/24.32
% 176.67/24.32
%------------------------------------------------------------------------------