%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SCT020-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 0.29s 0.62s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 26
% Syntax : Number of formulae : 94 ( 21 unt; 12 def)
% Number of atoms : 244 ( 17 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 271 ( 121 ~; 138 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 13 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-4 aty)
% Number of variables : 112 ( 112 !; 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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f674,axiom,
! [T_a,V_x] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_x)),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f684,negated_conjecture,
! [V_xa] :
( ~ c_Relation_Otrans(hAPP(V_xa,hAPP(v_x,V_xa)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(V_xa,hAPP(v_x,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_xa,hAPP(v_x,V_xa)),tc_Arrow__Order__Mirabelle_Oalt)
| c_Relation_Otrans(v_F(V_xa),tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f685,negated_conjecture,
! [V_xa] :
( ~ c_Relation_Otrans(hAPP(V_xa,hAPP(v_x,V_xa)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(V_xa,hAPP(v_x,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_xa,hAPP(v_x,V_xa)),tc_Arrow__Order__Mirabelle_Oalt)
| c_Relation_Oirrefl(v_F(V_xa),tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f687,negated_conjecture,
! [V_a,V_b,V_P] :
( ~ 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_Pa(V_P)),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/sandbox/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(f1708,plain,
! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1)),
inference(cnf_transformation,[status(thm)],[f674]) ).
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,
! [X0] :
( ~ c_Relation_Otrans(hAPP(X0,hAPP(v_x,X0)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X0,hAPP(v_x,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,hAPP(v_x,X0)),tc_Arrow__Order__Mirabelle_Oalt)
| c_Relation_Otrans(v_F(X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(cnf_transformation,[status(thm)],[f684]) ).
fof(f1722,plain,
! [X0] :
( ~ c_Relation_Otrans(hAPP(X0,hAPP(v_x,X0)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X0,hAPP(v_x,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,hAPP(v_x,X0)),tc_Arrow__Order__Mirabelle_Oalt)
| c_Relation_Oirrefl(v_F(X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(cnf_transformation,[status(thm)],[f685]) ).
fof(f1724,plain,
! [V_P] :
( ~ 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_Pa(V_P)),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,X2] :
( ~ 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))) ),
inference(cnf_transformation,[status(thm)],[f1724]) ).
fof(f1780,plain,
( ~ c_Relation_Otrans(hAPP(v_P,hAPP(v_x,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,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f1721,f1717]) ).
fof(f1782,definition,
( sQ0_spl
<=> c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f1785,definition,
( sQ1_spl
<=> c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f1787,plain,
( sQ1_spl
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f1785]) ).
fof(f1788,definition,
( sQ2_spl
<=> c_Relation_Otrans(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f1790,plain,
( sQ2_spl
| ~ c_Relation_Otrans(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f1788]) ).
fof(f1791,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f1780,f1782,f1785,f1788]) ).
fof(f1792,definition,
( sQ3_spl
<=> c_Relation_Oirrefl(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1794,plain,
( sQ3_spl
| ~ c_Relation_Oirrefl(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f1792]) ).
fof(f1796,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1787,f1718]) ).
fof(f1797,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f1796]) ).
fof(f1801,plain,
! [X0,X1,X2] : hBOOL(c_in(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
inference(resolution,[status(thm)],[f1713,f1708]) ).
fof(f1802,plain,
! [X0,X1,X2,X3] :
( hBOOL(c_in(X0,X1,X3))
| ~ hBOOL(c_in(X0,X1,X2)) ),
inference(resolution,[status(thm)],[f1715,f1713]) ).
fof(f1828,plain,
! [X0] : ~ hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),X0)),
inference(resolution,[status(thm)],[f1802,f1720]) ).
fof(f1831,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(c_in(c_Pair(X2,X2,X1,X1),X0,X3))
| ~ c_Relation_Oirrefl(X0,X1) ),
inference(resolution,[status(thm)],[f1706,f1802]) ).
fof(f1876,plain,
! [X0,X1,X2] :
( ~ c_Relation_Otrans(hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(X0,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X1),X2)) ),
inference(resolution,[status(thm)],[f1831,f1722]) ).
fof(f1988,plain,
! [X0] :
( ~ 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)))
| 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))) ),
inference(resolution,[status(thm)],[f1702,f1719]) ).
fof(f1998,definition,
! [X0] :
( sQ7_spl
<=> ( ~ 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)))
| 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))) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f1999,plain,
! [X0] :
( ~ sQ7_spl
| ~ 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)))
| 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))) ),
inference(component_clause,[status(thm)],[f1998]) ).
fof(f2001,plain,
( ~ sQ0_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f1988,f1998,f1782]) ).
fof(f2002,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1790,f1716]) ).
fof(f2003,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f2002]) ).
fof(f2058,plain,
! [X0] :
( ~ sQ7_spl
| ~ 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_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| v_b = X0
| ~ hBOOL(c_in(c_Pair(v_b,X0,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,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(resolution,[status(thm)],[f1999,f1725]) ).
fof(f2060,definition,
! [X0] :
( sQ8_spl
<=> ( v_b = X0
| ~ hBOOL(c_in(c_Pair(v_b,X0,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,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))) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f2061,plain,
! [X0] :
( ~ sQ8_spl
| v_b = X0
| ~ hBOOL(c_in(c_Pair(v_b,X0,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,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(component_clause,[status(thm)],[f2060]) ).
fof(f2063,definition,
( sQ9_spl
<=> 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) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f2065,plain,
( sQ9_spl
| ~ 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(component_clause,[status(thm)],[f2063]) ).
fof(f2066,definition,
( sQ10_spl
<=> c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f2068,plain,
( sQ10_spl
| ~ c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f2066]) ).
fof(f2069,definition,
( sQ11_spl
<=> c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f2071,plain,
( sQ11_spl
| ~ c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f2069]) ).
fof(f2072,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f2058,f2060,f2063,f2066,f2069,f1998]) ).
fof(f2073,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2071,f1716]) ).
fof(f2074,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f2073]) ).
fof(f2075,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2068,f1717]) ).
fof(f2076,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f2075]) ).
fof(f2107,plain,
! [X0,X1,X2] :
( ~ hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt))
| ~ hBOOL(c_in(X0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X0
| hBOOL(c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X2),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),hAPP(v_P,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolution,[status(thm)],[f1711,f1718]) ).
fof(f2114,plain,
! [X0,X1,X2] :
( ~ hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X0
| hBOOL(c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X2),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),hAPP(v_P,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(forward_subsumption_resolution,[status(thm)],[f2107,f1801]) ).
fof(f2201,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2065,f1718]) ).
fof(f2202,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f2201]) ).
fof(f2315,plain,
! [X0,X1] :
( ~ sQ8_spl
| ~ hBOOL(c_in(c_Pair(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),X1))
| v_b = X0
| 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))) ),
inference(resolution,[status(thm)],[f2061,f1802]) ).
fof(f2317,plain,
! [X0,X1,X2] :
( X1 = X0
| hBOOL(c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X2),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),hAPP(v_P,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(forward_subsumption_resolution,[status(thm)],[f2114,f1801]) ).
fof(f2319,plain,
( 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)],[f2317,f1828]) ).
fof(f2327,definition,
( sQ14_spl
<=> 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))) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f2328,plain,
( ~ sQ14_spl
| 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(component_clause,[status(thm)],[f2327]) ).
fof(f2330,definition,
( sQ15_spl
<=> v_a = v_b ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f2331,plain,
( ~ sQ15_spl
| v_a = v_b ),
inference(component_clause,[status(thm)],[f2330]) ).
fof(f2333,plain,
( sQ15_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f2319,f2327,f2330]) ).
fof(f2337,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| v_b = v_a
| hBOOL(c_in(c_Pair(v_a,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)],[f2328,f2315]) ).
fof(f2341,definition,
( sQ16_spl
<=> hBOOL(c_in(c_Pair(v_a,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))) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f2342,plain,
( ~ sQ16_spl
| hBOOL(c_in(c_Pair(v_a,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(component_clause,[status(thm)],[f2341]) ).
fof(f2344,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| sQ15_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f2337,f2341,f2330,f2327,f2060]) ).
fof(f2384,plain,
( ~ sQ15_spl
| hBOOL(c_in(c_Pair(v_b,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(backward_demodulation,[status(thm)],[f2331,f1719]) ).
fof(f2423,plain,
( ~ sQ15_spl
| ~ c_Relation_Otrans(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,hAPP(v_x,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,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f2384,f1876]) ).
fof(f2428,plain,
( ~ sQ15_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f2423,f1785,f1792,f1788,f2330]) ).
fof(f2439,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1794,f1717]) ).
fof(f2440,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f2439]) ).
fof(f2514,plain,
( ~ sQ16_spl
| ~ c_Relation_Otrans(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,hAPP(v_x,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,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f2342,f1876]) ).
fof(f2520,plain,
( ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f2514,f1785,f1792,f1788,f2341]) ).
fof(f2531,plain,
$false,
inference(sat_refutation,[status(thm)],[f1791,f1797,f2001,f2003,f2072,f2074,f2076,f2202,f2333,f2344,f2428,f2440,f2520]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT020-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.39 % Computer : n019.cluster.edu
% 0.15/0.39 % Model : x86_64 x86_64
% 0.15/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.39 % Memory : 8046.5625MB
% 0.15/0.39 % OS : Linux 6.8.0-71-generic
% 0.15/0.39 % CPULimit : 300
% 0.15/0.39 % WCLimit : 300
% 0.15/0.39 % DateTime : Mon Sep 21 04:26:49 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.19/0.51 % Drodi V4.1.1
% 0.29/0.62 % Refutation found
% 0.29/0.62 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.29/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.29/0.67 % Elapsed time: 0.257128 seconds
% 0.29/0.67 % CPU time: 0.901221 seconds
% 0.29/0.67 % Total memory used: 153.445 MB
% 0.29/0.67 % Net memory used: 152.943 MB
%------------------------------------------------------------------------------