%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SCT024-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 02:07:13 PM UTC 2026
% Result : Unsatisfiable 0.24s 0.68s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT024-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.48 % Computer : n007.cluster.edu
% 0.19/0.48 % Model : x86_64 x86_64
% 0.19/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.48 % Memory : 8046.5625MB
% 0.19/0.48 % OS : Linux 6.8.0-71-generic
% 0.19/0.48 % CPULimit : 300
% 0.19/0.48 % WCLimit : 300
% 0.19/0.48 % DateTime : Mon Sep 21 04:24:20 UTC 2026
% 0.19/0.49 % CPUTime :
% 0.24/0.64 % Drodi V4.1.1
% 0.24/0.68 % Refutation found
% 0.24/0.68 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.24/0.68 % SZS output start CNFRefutation for theBenchmark
% 0.24/0.68 fof(f672,axiom,(
% 0.24/0.68 (![V_x,T_a,V_r]: (( ~ hBOOL(c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)))| ~ c_Relation_Oirrefl(V_r,T_a) ) ))),
% 0.24/0.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.68 fof(f677,axiom,(
% 0.24/0.68 (![V_x,V_S,T_a]: (( hBOOL(c_in(V_x,V_S,T_a))| ~ hBOOL(hAPP(V_S,V_x)) ) ))),
% 0.24/0.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.68 fof(f678,axiom,(
% 0.24/0.68 (![V_S,V_x,T_a]: (( hBOOL(hAPP(V_S,V_x))| ~ hBOOL(c_in(V_x,V_S,T_a)) ) ))),
% 0.24/0.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.68 fof(f679,negated_conjecture,(
% 0.24/0.68 (![V_x]: (c_Relation_Otrans(hAPP(v_P,V_x),tc_Arrow__Order__Mirabelle_Oalt) ))),
% 0.24/0.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.68 fof(f680,negated_conjecture,(
% 0.24/0.68 (![V_x]: (c_Relation_Oirrefl(hAPP(v_P,V_x),tc_Arrow__Order__Mirabelle_Oalt) ))),
% 0.24/0.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.68 fof(f681,negated_conjecture,(
% 0.24/0.68 (![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) ))),
% 0.24/0.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.68 fof(f682,negated_conjecture,(
% 0.24/0.68 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))) ),
% 0.24/0.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.68 fof(f683,negated_conjecture,(
% 0.24/0.68 ~ 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))) ),
% 0.24/0.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.68 fof(f687,negated_conjecture,(
% 0.24/0.68 (![V_a,V_b,V_P]: (( 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)))| ~ 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)))| 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_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_Otrans(hAPP(V_P,v_Pa(V_P)),tc_Arrow__Order__Mirabelle_Oalt) ) ))),
% 0.24/0.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.68 fof(f1705,plain,(
% 0.24/0.68 ![T_a,V_r]: ((![V_x]: ~hBOOL(c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))))|~c_Relation_Oirrefl(V_r,T_a))),
% 0.24/0.68 inference(miniscoping,[status(thm)],[f672])).
% 0.24/0.68 fof(f1706,plain,(
% 0.24/0.68 ![X0,X1,X2]: (~hBOOL(c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1)))|~c_Relation_Oirrefl(X2,X1))),
% 0.24/0.68 inference(cnf_transformation,[status(thm)],[f1705])).
% 0.24/0.68 fof(f1712,plain,(
% 0.24/0.68 ![V_x,V_S]: ((![T_a]: hBOOL(c_in(V_x,V_S,T_a)))|~hBOOL(hAPP(V_S,V_x)))),
% 0.24/0.68 inference(miniscoping,[status(thm)],[f677])).
% 0.24/0.68 fof(f1713,plain,(
% 0.24/0.68 ![X0,X1,X2]: (hBOOL(c_in(X0,X1,X2))|~hBOOL(hAPP(X1,X0)))),
% 0.24/0.68 inference(cnf_transformation,[status(thm)],[f1712])).
% 0.24/0.68 fof(f1714,plain,(
% 0.24/0.68 ![V_S,V_x]: (hBOOL(hAPP(V_S,V_x))|(![T_a]: ~hBOOL(c_in(V_x,V_S,T_a))))),
% 0.24/0.68 inference(miniscoping,[status(thm)],[f678])).
% 0.24/0.68 fof(f1715,plain,(
% 0.24/0.68 ![X0,X1,X2]: (hBOOL(hAPP(X0,X1))|~hBOOL(c_in(X1,X0,X2)))),
% 0.24/0.68 inference(cnf_transformation,[status(thm)],[f1714])).
% 0.24/0.68 fof(f1716,plain,(
% 0.24/0.68 ![X0]: (c_Relation_Otrans(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt))),
% 0.24/0.68 inference(cnf_transformation,[status(thm)],[f679])).
% 0.24/0.68 fof(f1717,plain,(
% 0.24/0.68 ![X0]: (c_Relation_Oirrefl(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt))),
% 0.24/0.68 inference(cnf_transformation,[status(thm)],[f680])).
% 0.24/0.68 fof(f1718,plain,(
% 0.24/0.68 ![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))),
% 0.24/0.68 inference(cnf_transformation,[status(thm)],[f681])).
% 0.24/0.68 fof(f1719,plain,(
% 0.24/0.68 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)))),
% 0.24/0.68 inference(cnf_transformation,[status(thm)],[f682])).
% 0.24/0.68 fof(f1720,plain,(
% 0.24/0.68 ~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)))),
% 0.24/0.68 inference(cnf_transformation,[status(thm)],[f683])).
% 0.24/0.68 fof(f1724,plain,(
% 0.24/0.68 ![V_P]: ((((![V_a,V_b]: ((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)))|~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))))|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_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_Otrans(hAPP(V_P,v_Pa(V_P)),tc_Arrow__Order__Mirabelle_Oalt))),
% 0.24/0.68 inference(miniscoping,[status(thm)],[f687])).
% 0.24/0.68 fof(f1725,plain,(
% 0.24/0.68 ![X0,X1,X2]: (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)))|~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)))|X0=X1|~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)|~c_Relation_Oirrefl(hAPP(X2,v_Pa(X2)),tc_Arrow__Order__Mirabelle_Oalt)|~c_Relation_Otrans(hAPP(X2,v_Pa(X2)),tc_Arrow__Order__Mirabelle_Oalt))),
% 0.24/0.68 inference(cnf_transformation,[status(thm)],[f1724])).
% 0.24/0.68 fof(f1885,plain,(
% 0.24/0.68 hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))),
% 0.24/0.68 inference(resolution,[status(thm)],[f1715,f1719])).
% 0.24/0.68 fof(f1926,plain,(
% 0.24/0.68 ![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)))),
% 0.24/0.68 inference(resolution,[status(thm)],[f1885,f1713])).
% 0.24/0.68 fof(f1932,plain,(
% 0.24/0.68 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)))|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_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_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)),
% 0.24/0.68 inference(resolution,[status(thm)],[f1725,f1926])).
% 0.24/0.68 fof(f1936,definition,(
% 0.24/0.68 sQ5_spl <=> (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))))),
% 0.24/0.68 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.24/0.68 fof(f1937,plain,(
% 0.24/0.68 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)))|~sQ5_spl),
% 0.24/0.68 inference(component_clause,[status(thm)],[f1936])).
% 0.24/0.68 fof(f1939,definition,(
% 0.24/0.68 sQ6_spl <=> (v_a=v_b)),
% 0.24/0.68 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.24/0.68 fof(f1940,plain,(
% 0.24/0.68 v_a=v_b|~sQ6_spl),
% 0.24/0.68 inference(component_clause,[status(thm)],[f1939])).
% 0.24/0.68 fof(f1942,definition,(
% 0.24/0.68 sQ7_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))),
% 0.24/0.68 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.24/0.68 fof(f1944,plain,(
% 0.24/0.68 ~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)|sQ7_spl),
% 0.24/0.72 inference(component_clause,[status(thm)],[f1942])).
% 0.24/0.72 fof(f1945,definition,(
% 0.24/0.72 sQ8_spl <=> (c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt))),
% 0.24/0.72 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.24/0.72 fof(f1947,plain,(
% 0.24/0.72 ~c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)|sQ8_spl),
% 0.24/0.72 inference(component_clause,[status(thm)],[f1945])).
% 0.24/0.72 fof(f1948,definition,(
% 0.24/0.72 sQ9_spl <=> (c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt))),
% 0.24/0.72 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.24/0.72 fof(f1950,plain,(
% 0.24/0.72 ~c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)|sQ9_spl),
% 0.24/0.72 inference(component_clause,[status(thm)],[f1948])).
% 0.24/0.72 fof(f1951,plain,(
% 0.24/0.72 sQ5_spl|sQ6_spl|~sQ7_spl|~sQ8_spl|~sQ9_spl),
% 0.24/0.72 inference(split_clause,[status(thm)],[f1932,f1936,f1939,f1942,f1945,f1948])).
% 0.24/0.72 fof(f1962,plain,(
% 0.24/0.72 $false|sQ9_spl),
% 0.24/0.72 inference(forward_subsumption_resolution,[status(thm)],[f1950,f1716])).
% 0.24/0.72 fof(f1963,plain,(
% 0.24/0.72 sQ9_spl),
% 0.24/0.72 inference(contradiction_clause,[status(thm)],[f1962])).
% 0.24/0.72 fof(f1964,plain,(
% 0.24/0.72 $false|sQ8_spl),
% 0.24/0.72 inference(forward_subsumption_resolution,[status(thm)],[f1947,f1717])).
% 0.24/0.72 fof(f1965,plain,(
% 0.24/0.72 sQ8_spl),
% 0.24/0.72 inference(contradiction_clause,[status(thm)],[f1964])).
% 0.24/0.72 fof(f1966,plain,(
% 0.24/0.72 $false|sQ7_spl),
% 0.24/0.72 inference(forward_subsumption_resolution,[status(thm)],[f1944,f1718])).
% 0.24/0.72 fof(f1967,plain,(
% 0.24/0.72 sQ7_spl),
% 0.24/0.72 inference(contradiction_clause,[status(thm)],[f1966])).
% 0.24/0.72 fof(f1968,plain,(
% 0.24/0.72 $false|~sQ5_spl),
% 0.24/0.72 inference(forward_subsumption_resolution,[status(thm)],[f1937,f1720])).
% 0.24/0.72 fof(f1969,plain,(
% 0.24/0.72 ~sQ5_spl),
% 0.24/0.72 inference(contradiction_clause,[status(thm)],[f1968])).
% 0.24/0.72 fof(f1970,plain,(
% 0.24/0.72 ![X0]: (hBOOL(c_in(c_Pair(v_b,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),X0))|~sQ6_spl)),
% 0.24/0.72 inference(backward_demodulation,[status(thm)],[f1940,f1926])).
% 0.24/0.72 fof(f2069,plain,(
% 0.24/0.72 ~c_Relation_Oirrefl(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt)|~sQ6_spl),
% 0.24/0.72 inference(resolution,[status(thm)],[f1706,f1970])).
% 0.24/0.72 fof(f2071,plain,(
% 0.24/0.72 $false|~sQ6_spl),
% 0.24/0.72 inference(forward_subsumption_resolution,[status(thm)],[f2069,f1717])).
% 0.24/0.72 fof(f2072,plain,(
% 0.24/0.72 ~sQ6_spl),
% 0.24/0.72 inference(contradiction_clause,[status(thm)],[f2071])).
% 0.24/0.72 fof(f2073,plain,(
% 0.24/0.72 $false),
% 0.24/0.72 inference(sat_refutation,[status(thm)],[f1951,f1963,f1965,f1967,f1969,f2072])).
% 0.24/0.72 % SZS output end CNFRefutation for theBenchmark.p
% 0.24/0.73 % Elapsed time: 0.228604 seconds
% 0.24/0.73 % CPU time: 0.482628 seconds
% 0.24/0.73 % Total memory used: 85.291 MB
% 0.24/0.73 % Net memory used: 85.061 MB
%------------------------------------------------------------------------------