%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SCT021-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 0.26s 0.65s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 28
% Syntax : Number of formulae : 95 ( 22 unt; 14 def)
% Number of atoms : 236 ( 10 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 265 ( 124 ~; 127 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 15 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-4 aty)
% Number of variables : 93 ( 93 !; 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,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/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,
! [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(f1765,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(f1768,definition,
( sQ1_spl
<=> 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) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f1770,plain,
( sQ1_spl
| ~ 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(component_clause,[status(thm)],[f1768]) ).
fof(f1771,definition,
( sQ2_spl
<=> c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f1773,plain,
( sQ2_spl
| ~ c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f1771]) ).
fof(f1774,definition,
( sQ3_spl
<=> c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1776,plain,
( sQ3_spl
| ~ c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f1774]) ).
fof(f1777,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f1721,f1765,f1768,f1771,f1774]) ).
fof(f1778,definition,
( sQ4_spl
<=> c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f1779,plain,
( ~ sQ4_spl
| c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f1778]) ).
fof(f1781,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f1722,f1778,f1768,f1771,f1774]) ).
fof(f1788,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1776,f1716]) ).
fof(f1789,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f1788]) ).
fof(f1790,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1773,f1717]) ).
fof(f1791,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f1790]) ).
fof(f1820,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1770,f1718]) ).
fof(f1821,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f1820]) ).
fof(f1882,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(f1903,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X0,c_Pair(X2,X2,X1,X1)))
| ~ c_Relation_Oirrefl(X0,X1) ),
inference(resolution,[status(thm)],[f1706,f1713]) ).
fof(f1905,plain,
! [X0,X1,X2,X3] :
( ~ c_Relation_Oirrefl(X3,X2)
| ~ c_Relation_Otrans(X3,X2)
| ~ 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(resolution,[status(thm)],[f1702,f1706]) ).
fof(f1939,plain,
! [X0] :
( ~ sQ4_spl
| ~ hBOOL(hAPP(v_F(v_P),c_Pair(X0,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolution,[status(thm)],[f1903,f1779]) ).
fof(f1942,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(f1946,definition,
( sQ11_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,[sQ11_spl])],[split_symbol_definition]) ).
fof(f1949,definition,
( sQ12_spl
<=> v_a = v_b ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f1950,plain,
( ~ sQ12_spl
| v_a = v_b ),
inference(component_clause,[status(thm)],[f1949]) ).
fof(f1952,definition,
! [X0] :
( sQ13_spl
<=> ( ~ 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)) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f1953,plain,
! [X0] :
( ~ sQ13_spl
| ~ 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)) ),
inference(component_clause,[status(thm)],[f1952]) ).
fof(f1955,plain,
( sQ13_spl
| sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f1942,f1946,f1949,f1952]) ).
fof(f1973,definition,
( sQ15_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,[sQ15_spl])],[split_symbol_definition]) ).
fof(f1975,plain,
( sQ15_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)],[f1973]) ).
fof(f1976,definition,
( sQ16_spl
<=> c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f1978,plain,
( sQ16_spl
| ~ c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f1976]) ).
fof(f1979,definition,
( sQ17_spl
<=> c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f1981,plain,
( sQ17_spl
| ~ c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f1979]) ).
fof(f1983,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1981,f1716]) ).
fof(f1984,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f1983]) ).
fof(f1985,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1978,f1717]) ).
fof(f1986,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f1985]) ).
fof(f1987,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1975,f1718]) ).
fof(f1988,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f1987]) ).
fof(f2062,plain,
( ~ sQ13_spl
| ~ 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)
| ~ hBOOL(c_in(v_a,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f1953,f1709]) ).
fof(f2064,definition,
( sQ19_spl
<=> hBOOL(c_in(v_a,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f2066,plain,
( sQ19_spl
| ~ hBOOL(c_in(v_a,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f2064]) ).
fof(f2067,definition,
( sQ20_spl
<=> 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) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f2069,plain,
( sQ20_spl
| ~ 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(component_clause,[status(thm)],[f2067]) ).
fof(f2070,plain,
( ~ sQ13_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2062,f2064,f2067,f1952]) ).
fof(f2071,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2069,f1718]) ).
fof(f2072,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f2071]) ).
fof(f2073,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2066,f1709]) ).
fof(f2074,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f2073]) ).
fof(f2394,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(X1,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(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)],[f1905,f1779]) ).
fof(f2398,definition,
! [X0,X1] :
( sQ22_spl
<=> ( ~ hBOOL(c_in(c_Pair(X1,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(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))) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f2399,plain,
! [X0,X1] :
( ~ sQ22_spl
| ~ hBOOL(c_in(c_Pair(X1,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(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(component_clause,[status(thm)],[f2398]) ).
fof(f2401,plain,
( ~ sQ4_spl
| ~ sQ0_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f2394,f2398,f1765,f1778]) ).
fof(f2457,plain,
( ~ sQ22_spl
| ~ 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)],[f2399,f1719]) ).
fof(f2483,plain,
( ~ sQ22_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 = v_a
| ~ 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)],[f2457,f1725]) ).
fof(f2487,plain,
( ~ sQ22_spl
| ~ sQ17_spl
| ~ sQ16_spl
| ~ sQ15_spl
| sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2483,f1946,f1949,f1973,f1976,f1979,f2398]) ).
fof(f2508,plain,
( ~ sQ12_spl
| 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)],[f1950,f1882]) ).
fof(f2512,plain,
( ~ sQ12_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2508,f1939]) ).
fof(f2513,plain,
( ~ sQ12_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f2512]) ).
fof(f2514,plain,
$false,
inference(sat_refutation,[status(thm)],[f1777,f1781,f1789,f1791,f1821,f1955,f1984,f1986,f1988,f2070,f2072,f2074,f2401,f2487,f2513]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT021-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n009.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 04:26:42 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.26/0.57 % Drodi V4.1.1
% 0.26/0.65 % Refutation found
% 0.26/0.65 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.26/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.26/0.72 % Elapsed time: 0.239094 seconds
% 0.26/0.72 % CPU time: 0.605272 seconds
% 0.26/0.72 % Total memory used: 94.659 MB
% 0.26/0.72 % Net memory used: 94.280 MB
%------------------------------------------------------------------------------