%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SCT022-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Thu Sep 24 02:06:48 PM UTC 2026
% Result : Unsatisfiable 0.28s 0.58s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 60 ( 21 unt; 0 def)
% Number of atoms : 158 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 190 ( 92 ~; 98 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-4 aty)
% Number of variables : 86 ( 86 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f670,axiom,
! [V_x,V_z,T_a,V_r,V_y] :
( ~ c_Relation_Otrans(V_r,T_a)
| ~ hBOOL(c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_y,V_z,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| hBOOL(c_in(c_Pair(V_x,V_z,T_a,T_a),V_r,tc_prod(T_a,T_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f672,axiom,
! [V_x,T_a,V_r] :
( ~ c_Relation_Oirrefl(V_r,T_a)
| ~ hBOOL(c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f675,axiom,
! [V_x,T_a] : hBOOL(c_in(V_x,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f676,axiom,
! [V_xa,V_x,T_a,V_r,V_A] :
( ~ c_Relation_Ototal__on(V_A,V_r,T_a)
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ hBOOL(c_in(V_xa,V_A,T_a))
| V_x = V_xa
| hBOOL(c_in(c_Pair(V_x,V_xa,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| hBOOL(c_in(c_Pair(V_xa,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f677,axiom,
! [V_x,V_S,T_a] :
( ~ hBOOL(hAPP(V_S,V_x))
| hBOOL(c_in(V_x,V_S,T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f678,axiom,
! [V_S,V_x,T_a] :
( ~ hBOOL(c_in(V_x,V_S,T_a))
| hBOOL(hAPP(V_S,V_x)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f679,negated_conjecture,
! [V_x] : c_Relation_Otrans(hAPP(v_P,V_x),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f680,negated_conjecture,
! [V_x] : c_Relation_Oirrefl(hAPP(v_P,V_x),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f681,negated_conjecture,
! [V_x] : 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),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f682,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f683,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f684,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f685,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f687,negated_conjecture,
! [V_a,V_b] :
( ~ c_Relation_Otrans(hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_xa),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_xa),tc_Arrow__Order__Mirabelle_Oalt)
| V_a = V_b
| ~ 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)))
| 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f1701,plain,
! [T_a,V_r] :
( ~ c_Relation_Otrans(V_r,T_a)
| ! [V_x,V_y] :
( ~ hBOOL(c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ! [V_z] :
( ~ hBOOL(c_in(c_Pair(V_y,V_z,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| hBOOL(c_in(c_Pair(V_x,V_z,T_a,T_a),V_r,tc_prod(T_a,T_a))) ) ) ),
inference(miniscoping,[status(thm)],[f670]) ).
fof(f1702,plain,
! [X0,X1,X2,X3,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))) ),
inference(cnf_transformation,[status(thm)],[f1701]) ).
fof(f1705,plain,
! [T_a,V_r] :
( ~ c_Relation_Oirrefl(V_r,T_a)
| ! [V_x] : ~ hBOOL(c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))) ),
inference(miniscoping,[status(thm)],[f672]) ).
fof(f1706,plain,
! [X0,X1,X2] :
( ~ c_Relation_Oirrefl(X2,X1)
| ~ hBOOL(c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1))) ),
inference(cnf_transformation,[status(thm)],[f1705]) ).
fof(f1709,plain,
! [X0,X1] : hBOOL(c_in(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)),
inference(cnf_transformation,[status(thm)],[f675]) ).
fof(f1710,plain,
! [T_a,V_r,V_A] :
( ~ c_Relation_Ototal__on(V_A,V_r,T_a)
| ! [V_x] :
( ~ hBOOL(c_in(V_x,V_A,T_a))
| ! [V_xa] :
( ~ hBOOL(c_in(V_xa,V_A,T_a))
| V_x = V_xa
| hBOOL(c_in(c_Pair(V_x,V_xa,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| hBOOL(c_in(c_Pair(V_xa,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))) ) ) ),
inference(miniscoping,[status(thm)],[f676]) ).
fof(f1711,plain,
! [X0,X1,X2,X3,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))) ),
inference(cnf_transformation,[status(thm)],[f1710]) ).
fof(f1712,plain,
! [V_x,V_S] :
( ~ hBOOL(hAPP(V_S,V_x))
| ! [T_a] : hBOOL(c_in(V_x,V_S,T_a)) ),
inference(miniscoping,[status(thm)],[f677]) ).
fof(f1713,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X1,X0))
| hBOOL(c_in(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f1712]) ).
fof(f1714,plain,
! [V_S,V_x] :
( ! [T_a] : ~ hBOOL(c_in(V_x,V_S,T_a))
| hBOOL(hAPP(V_S,V_x)) ),
inference(miniscoping,[status(thm)],[f678]) ).
fof(f1715,plain,
! [X0,X1,X2] :
( ~ hBOOL(c_in(X1,X0,X2))
| hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f1714]) ).
fof(f1716,plain,
! [X0] : c_Relation_Otrans(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt),
inference(cnf_transformation,[status(thm)],[f679]) ).
fof(f1717,plain,
! [X0] : c_Relation_Oirrefl(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt),
inference(cnf_transformation,[status(thm)],[f680]) ).
fof(f1718,plain,
! [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),
inference(cnf_transformation,[status(thm)],[f681]) ).
fof(f1719,plain,
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,[status(thm)],[f682]) ).
fof(f1720,plain,
~ 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,[status(thm)],[f683]) ).
fof(f1721,plain,
( ~ 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) ),
inference(cnf_transformation,[status(thm)],[f684]) ).
fof(f1722,plain,
( ~ 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) ),
inference(cnf_transformation,[status(thm)],[f685]) ).
fof(f1724,plain,
( ~ c_Relation_Otrans(hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_xa),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_xa),tc_Arrow__Order__Mirabelle_Oalt)
| ! [V_a,V_b] :
( V_a = V_b
| ~ 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)))
| 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(miniscoping,[status(thm)],[f687]) ).
fof(f1725,plain,
! [X0,X1] :
( ~ c_Relation_Otrans(hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_xa),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_xa),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(v_P,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(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(cnf_transformation,[status(thm)],[f1724]) ).
fof(f1768,plain,
( ~ 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_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(forward_subsumption_resolution,[status(thm)],[f1721,f1718]) ).
fof(f1769,plain,
( ~ c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f1768,f1717]) ).
fof(f1770,plain,
c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),
inference(forward_subsumption_resolution,[status(thm)],[f1769,f1716]) ).
fof(f1771,plain,
( ~ 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_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(forward_subsumption_resolution,[status(thm)],[f1722,f1718]) ).
fof(f1772,plain,
( ~ c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f1771,f1717]) ).
fof(f1773,plain,
c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),
inference(forward_subsumption_resolution,[status(thm)],[f1772,f1716]) ).
fof(f1775,plain,
hBOOL(hAPP(v_F(v_P),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(resolution,[status(thm)],[f1715,f1719]) ).
fof(f1782,plain,
! [X0,X1] :
( ~ c_Relation_Otrans(hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_xa),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(v_P,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(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1725,f1718]) ).
fof(f1783,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X1
| 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))) ),
inference(resolution,[status(thm)],[f1782,f1713]) ).
fof(f1784,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = X1
| 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))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1783,f1717]) ).
fof(f1810,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X0 = X1
| 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))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1784,f1716]) ).
fof(f1853,plain,
! [X0] :
( ~ c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(X0,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)))
| hBOOL(c_in(c_Pair(X0,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(resolution,[status(thm)],[f1702,f1719]) ).
fof(f1865,plain,
! [X0] :
( ~ hBOOL(c_in(c_Pair(X0,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)))
| hBOOL(c_in(c_Pair(X0,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(forward_subsumption_resolution,[status(thm)],[f1853,f1770]) ).
fof(f1887,plain,
! [X0] :
( ~ c_Relation_Ototal__on(X0,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ hBOOL(c_in(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt))
| v_a = v_b
| 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))) ),
inference(resolution,[status(thm)],[f1711,f1720]) ).
fof(f1902,plain,
( ~ c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ 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))) ),
inference(resolution,[status(thm)],[f1865,f1706]) ).
fof(f1906,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))),
inference(forward_subsumption_resolution,[status(thm)],[f1902,f1773]) ).
fof(f1907,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_b = v_a ),
inference(resolution,[status(thm)],[f1906,f1810]) ).
fof(f1909,plain,
~ hBOOL(hAPP(v_F(v_P),c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(resolution,[status(thm)],[f1906,f1713]) ).
fof(f1996,plain,
! [X0] :
( hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Ototal__on(X0,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ hBOOL(c_in(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt))
| v_a = v_b ),
inference(resolution,[status(thm)],[f1887,f1715]) ).
fof(f2001,plain,
! [X0] :
( ~ c_Relation_Ototal__on(X0,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ hBOOL(c_in(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt))
| v_a = v_b ),
inference(forward_subsumption_resolution,[status(thm)],[f1996,f1907]) ).
fof(f2080,plain,
( ~ hBOOL(c_in(v_a,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt))
| ~ hBOOL(c_in(v_b,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt))
| v_a = v_b ),
inference(resolution,[status(thm)],[f2001,f1718]) ).
fof(f2081,plain,
( ~ hBOOL(c_in(v_a,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt))
| v_a = v_b ),
inference(forward_subsumption_resolution,[status(thm)],[f2080,f1709]) ).
fof(f2088,plain,
~ hBOOL(hAPP(v_F(v_P),c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(backward_demodulation,[status(thm)],[f2095,f1909]) ).
fof(f2092,plain,
hBOOL(hAPP(v_F(v_P),c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(backward_demodulation,[status(thm)],[f2095,f1775]) ).
fof(f2095,plain,
v_a = v_b,
inference(forward_subsumption_resolution,[status(thm)],[f2081,f1709]) ).
fof(f2098,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2092,f2088]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SCT022-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n003.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Mon Sep 21 04:28:15 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.28/0.53 % Drodi V4.1.1
% 0.28/0.58 % Refutation found
% 0.28/0.58 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.28/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.28/0.64 % Elapsed time: 0.187117 seconds
% 0.28/0.64 % CPU time: 0.421447 seconds
% 0.28/0.64 % Total memory used: 73.139 MB
% 0.28/0.64 % Net memory used: 72.943 MB
%------------------------------------------------------------------------------