%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWW305+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 03:08:56 PM UTC 2026
% Result : Theorem 113.32s 15.55s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW305+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.37 % DateTime : Mon Sep 21 09:51:38 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.78/1.03 % Drodi V4.1.1
% 113.32/15.55 % Refutation found
% 113.32/15.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 113.32/15.55 % SZS output start CNFRefutation for theBenchmark
% 113.32/15.55 fof(f18,axiom,(
% 113.32/15.55 (! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )),
% 113.32/15.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 113.32/15.55 fof(f89,axiom,(
% 113.32/15.55 (! [V_A_2,V_f_2,T_b,T_c] :( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))<=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) )),
% 113.32/15.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 113.32/15.55 fof(f93,axiom,(
% 113.32/15.55 (! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 )),
% 113.32/15.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 113.32/15.55 fof(f95,axiom,(
% 113.32/15.55 (! [V_B_2,V_a_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)) )),
% 113.32/15.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 113.32/15.55 fof(f765,axiom,(
% 113.32/15.55 (! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2 )),
% 113.32/15.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 113.32/15.55 fof(f789,axiom,(
% 113.32/15.55 (! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )),
% 113.32/15.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 113.32/15.55 fof(f5206,axiom,(
% 113.32/15.55 (! [V_R_2,V_Qa_2,V_Pa_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_Pa_2),V_Qa_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Qa_2,V_R_2)) )),
% 113.32/15.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 113.32/15.55 fof(f5207,axiom,(
% 113.32/15.55 (! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Qa_2) )),
% 113.32/15.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 113.32/15.55 fof(f5224,hypothesis,(
% 113.32/15.55 c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ),
% 113.32/15.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 113.32/15.55 fof(f5225,conjecture,(
% 113.32/15.55 c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY)),v_Q)),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pn),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_HOL_Obool))))),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),v_Q)),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pn),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_HOL_Obool))))) ),
% 113.32/15.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 113.32/15.55 fof(f5226,negated_conjecture,(
% 113.32/15.55 ~(c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY)),v_Q)),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pn),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_HOL_Obool))))),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),v_Q)),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pn),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_HOL_Obool))))) )),
% 113.32/15.55 inference(negated_conjecture,[status(cth)],[f5225])).
% 113.32/15.55 fof(f5270,plain,(
% 113.32/15.55 ![X0,X1,X2,X3]: (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),X3))=hAPP(hAPP(c_Set_Oinsert(X0),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),X3)))),
% 113.32/15.55 inference(cnf_transformation,[status(thm)],[f18])).
% 113.32/15.55 fof(f5500,plain,(
% 113.32/15.55 ![V_A_2,V_f_2,T_b,T_c]: ((~hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)=c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))&(hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)=c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))|~V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),
% 113.32/15.55 inference(NNF_transformation,[status(thm)],[f89])).
% 113.32/15.55 fof(f5501,plain,(
% 113.32/15.55 (![V_A_2,T_c]: ((![V_f_2,T_b]: ~hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)=c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))&(![V_A_2,T_c]: ((![V_f_2,T_b]: hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)=c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))|~V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),
% 113.32/15.55 inference(miniscoping,[status(thm)],[f5500])).
% 113.32/15.55 fof(f5503,plain,(
% 113.32/15.55 ![X0,X1,X2,X3]: (hAPP(c_Set_Oimage(X0,X1,X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~X3=c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),
% 113.32/15.55 inference(cnf_transformation,[status(thm)],[f5501])).
% 113.32/15.55 fof(f5514,plain,(
% 113.32/15.55 ![X0,X1]: (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))=X1)),
% 113.32/15.55 inference(cnf_transformation,[status(thm)],[f93])).
% 113.32/15.55 fof(f5516,plain,(
% 113.32/15.55 ![X0,X1,X2,X3,X4]: (hAPP(c_Set_Oimage(X0,X1,X2),hAPP(hAPP(c_Set_Oinsert(X0),X3),X4))=hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X0,X1,X2),X4)))),
% 113.32/15.55 inference(cnf_transformation,[status(thm)],[f95])).
% 113.32/15.55 fof(f7447,plain,(
% 113.32/15.55 ![X0,X1]: (hAPP(c_Set_OCollect(X0),X1)=X1)),
% 113.32/15.55 inference(cnf_transformation,[status(thm)],[f765])).
% 113.32/15.55 fof(f7500,plain,(
% 113.32/15.55 ![X0,X1]: (hAPP(c_Set_OCollect(X0),hAPP(c_fequal,X1))=hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))))),
% 113.32/15.55 inference(cnf_transformation,[status(thm)],[f789])).
% 113.32/15.55 fof(f20031,plain,(
% 113.32/15.55 ![X0,X1,X2,X3,X4,X5]: (hAPP(hAPP(hAPP(c_COMBB(X0,X1,X2),X3),X4),X5)=hAPP(X3,hAPP(X4,X5)))),
% 113.32/15.55 inference(cnf_transformation,[status(thm)],[f5206])).
% 113.32/15.55 fof(f20032,plain,(
% 113.32/15.55 ![X0,X1,X2,X3,X4,X5]: (hAPP(hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4),X5)=hAPP(hAPP(X3,X5),X4))),
% 113.32/15.55 inference(cnf_transformation,[status(thm)],[f5207])).
% 113.32/15.55 fof(f20057,plain,(
% 113.32/15.55 c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))),
% 113.32/15.55 inference(cnf_transformation,[status(thm)],[f5224])).
% 113.32/15.55 fof(f20058,plain,(
% 113.32/15.55 ~c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY)),v_Q)),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pn),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_HOL_Obool))))),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),v_Q)),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pn),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_HOL_Obool)))))),
% 113.32/15.55 inference(cnf_transformation,[status(thm)],[f5226])).
% 113.32/15.55 fof(f20383,plain,(
% 113.32/15.55 ![X0,X1,X2]: (hAPP(c_Set_Oimage(X0,X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
% 113.32/15.55 inference(destructive_equality_resolution,[status(thm)],[f5503])).
% 113.32/15.55 fof(f20636,plain,(
% 113.32/15.55 ![X0,X1]: (hAPP(c_fequal,X0)=hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
% 113.32/15.55 inference(forward_demodulation,[status(thm)],[f7447,f7500])).
% 113.32/15.55 fof(f24231,plain,(
% 113.32/15.55 c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)))),
% 113.32/15.55 inference(forward_demodulation,[status(thm)],[f20636,f20057])).
% 113.32/15.55 fof(f24232,plain,(
% 113.32/15.55 ~c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY)),v_Q)),hAPP(c_fequal,v_pn))),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),v_Q)),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pn),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_HOL_Obool)))))),
% 113.32/15.55 inference(forward_demodulation,[status(thm)],[f20636,f20058])).
% 113.32/15.55 fof(f24233,plain,(
% 113.32/15.55 ~c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY)),v_Q)),hAPP(c_fequal,v_pn))),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),v_Q)),hAPP(c_fequal,v_pn)))),
% 113.32/15.55 inference(forward_demodulation,[status(thm)],[f20636,f24232])).
% 113.32/15.55 fof(f25400,plain,(
% 113.32/15.55 ![X0,X1,X2]: (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))))=hAPP(hAPP(c_Set_Oinsert(X0),X2),X1))),
% 113.32/15.55 inference(paramodulation,[status(thm)],[f5514,f5270])).
% 113.32/15.55 fof(f25419,plain,(
% 113.32/15.55 ![X0,X1,X2]: (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),hAPP(c_fequal,X2))=hAPP(hAPP(c_Set_Oinsert(X0),X2),X1))),
% 113.32/15.55 inference(forward_demodulation,[status(thm)],[f20636,f25400])).
% 113.32/15.55 fof(f25539,plain,(
% 113.32/15.55 ![X0,X1,X2,X3]: (hAPP(c_Set_Oimage(X0,X1,X2),hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))))=hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
% 113.32/15.55 inference(paramodulation,[status(thm)],[f20383,f5516])).
% 113.32/15.55 fof(f25567,plain,(
% 113.32/15.55 ![X0,X1,X2,X3]: (hAPP(c_Set_Oimage(X0,X1,X2),hAPP(c_fequal,X3))=hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
% 113.32/15.55 inference(forward_demodulation,[status(thm)],[f20636,f25539])).
% 113.32/15.55 fof(f25613,plain,(
% 113.32/15.55 ~c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY)),v_Q)),hAPP(c_fequal,v_pn))),hAPP(c_fequal,hAPP(hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),v_Q),v_pn)))),
% 113.32/15.55 inference(backward_demodulation,[status(thm)],[f25617,f24233])).
% 113.32/15.55 fof(f25617,plain,(
% 113.32/15.55 ![X0,X1,X2,X3]: (hAPP(c_Set_Oimage(X0,X1,X2),hAPP(c_fequal,X3))=hAPP(c_fequal,hAPP(X2,X3)))),
% 113.32/15.55 inference(forward_demodulation,[status(thm)],[f20636,f25567])).
% 113.32/15.55 fof(f25937,plain,(
% 113.32/15.55 ~c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_fequal,hAPP(hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY)),v_Q),v_pn))),hAPP(c_fequal,hAPP(hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),v_Q),v_pn)))),
% 113.32/15.55 inference(forward_demodulation,[status(thm)],[f25617,f25613])).
% 113.32/15.55 fof(f25938,plain,(
% 113.32/15.55 ~c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY)),v_Q),v_pn)),v_G),hAPP(c_fequal,hAPP(hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),v_Q),v_pn)))),
% 113.32/15.55 inference(forward_demodulation,[status(thm)],[f25419,f25937])).
% 113.32/15.55 fof(f25939,plain,(
% 113.32/15.55 ~c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY),v_pn),v_Q)),v_G),hAPP(c_fequal,hAPP(hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),v_Q),v_pn)))),
% 113.32/15.55 inference(forward_demodulation,[status(thm)],[f20032,f25938])).
% 113.32/15.55 fof(f25940,plain,(
% 113.32/15.55 ~c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(c_fequal,hAPP(hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),v_Q),v_pn)))),
% 113.32/15.55 inference(forward_demodulation,[status(thm)],[f20031,f25939])).
% 113.32/15.55 fof(f25941,plain,(
% 113.32/15.55 ~c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(c_fequal,hAPP(hAPP(hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody)),v_pn),v_Q)))),
% 113.32/15.55 inference(forward_demodulation,[status(thm)],[f20032,f25940])).
% 113.32/15.55 fof(f25942,plain,(
% 113.32/15.55 ~c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody),v_pn)),v_Q)))),
% 113.32/15.55 inference(forward_demodulation,[status(thm)],[f20031,f25941])).
% 113.32/15.55 fof(f25943,plain,(
% 113.32/15.55 ~c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)))),
% 113.32/15.64 inference(forward_demodulation,[status(thm)],[f20031,f25942])).
% 113.32/15.64 fof(f25944,plain,(
% 113.32/15.64 $false),
% 113.32/15.64 inference(forward_subsumption_resolution,[status(thm)],[f25943,f24231])).
% 113.32/15.64 % SZS output end CNFRefutation for theBenchmark.p
% 23.26/15.86 % Elapsed time: 15.466770 seconds
% 23.26/15.86 % CPU time: 117.111893 seconds
% 23.26/15.86 % Total memory used: 1.376 GB
% 23.26/15.86 % Net memory used: 1.340 GB
%------------------------------------------------------------------------------