%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SWV435^4 : TPTP v9.2.0. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n015.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Oct 9 03:07:22 PM UTC 2025 % Result : Theorem 1.06s 1.27s % Output : Proof 1.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SWV435^4 : TPTP v9.2.0. Released v3.6.0. % 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.12/0.34 % Computer : n015.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Wed Oct 8 14:07:38 EDT 2025 % 0.12/0.34 % CPUTime : % 1.06/1.27 % SZS status Theorem % 1.06/1.27 % Mode: mode506 % 1.06/1.27 % Inferences: 10 % 1.06/1.27 % SZS output start Proof % 1.06/1.27 thf(ty_a, type, a : ($i>$o)). % 1.06/1.27 thf(ty_eigen__1, type, eigen__1 : $i). % 1.06/1.27 thf(ty_eigen__0, type, eigen__0 : $i). % 1.06/1.27 thf(ty_rel, type, rel : ($i>$i>$o)). % 1.06/1.27 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 1.06/1.27 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((((rel @ eigen__0) @ X1) => (a @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 1.06/1.27 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(((rel @ X1) @ X2) => (a @ X2))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 1.06/1.27 thf(sP1,plain,sP1 <=> (![X1:$i]:(((rel @ eigen__0) @ X1) => (a @ X1))),introduced(definition,[new_symbols(definition,[sP1])])). % 1.06/1.27 thf(sP2,plain,sP2 <=> (![X1:$o]:(((a @ eigen__1) = X1) => (~(X1)))),introduced(definition,[new_symbols(definition,[sP2])])). % 1.06/1.27 thf(sP3,plain,sP3 <=> (((rel @ eigen__0) @ eigen__1) => (a @ eigen__1)),introduced(definition,[new_symbols(definition,[sP3])])). % 1.06/1.27 thf(sP4,plain,sP4 <=> (![X1:$i]:((a @ X1) = (~($false)))),introduced(definition,[new_symbols(definition,[sP4])])). % 1.06/1.27 thf(sP5,plain,sP5 <=> ((a @ eigen__1) = (~($false))),introduced(definition,[new_symbols(definition,[sP5])])). % 1.06/1.27 thf(sP6,plain,sP6 <=> (![X1:$o>$o]:((X1 @ (a @ eigen__1)) => (![X2:$o]:(((a @ eigen__1) = X2) => (X1 @ X2))))),introduced(definition,[new_symbols(definition,[sP6])])). % 1.06/1.27 thf(sP7,plain,sP7 <=> ((~((a @ eigen__1))) => sP2),introduced(definition,[new_symbols(definition,[sP7])])). % 1.06/1.27 thf(sP8,plain,sP8 <=> (![X1:$i]:(![X2:$i]:(((rel @ X1) @ X2) => (a @ X2)))),introduced(definition,[new_symbols(definition,[sP8])])). % 1.06/1.27 thf(sP9,plain,sP9 <=> (a @ eigen__1),introduced(definition,[new_symbols(definition,[sP9])])). % 1.06/1.27 thf(sP10,plain,sP10 <=> (a = (^[X1:$i]:(~($false)))),introduced(definition,[new_symbols(definition,[sP10])])). % 1.06/1.27 thf(sP11,plain,sP11 <=> (![X1:$o]:(![X2:$o>$o]:((X2 @ X1) => (![X3:$o]:((X1 = X3) => (X2 @ X3)))))),introduced(definition,[new_symbols(definition,[sP11])])). % 1.06/1.27 thf(def_mfalse,definition,(mfalse = (^[X1:$i]:$false))). % 1.06/1.27 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 1.06/1.27 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 1.06/1.27 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 1.06/1.27 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 1.06/1.27 thf(def_mimpl,definition,(mimpl = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 1.06/1.27 thf(def_miff,definition,(miff = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimpl @ X1) @ X2)) @ ((mimpl @ X2) @ X1)))))). % 1.06/1.27 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 1.06/1.27 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(((X1 @ X3) @ X4) => (~((X2 @ X4)))))))))))). % 1.06/1.27 thf(def_mall,definition,(mall = (^[X1:individuals>$i>$o]:(^[X2:$i]:(![X3:individuals]:((X1 @ X3) @ X2)))))). % 1.06/1.27 thf(def_mexists,definition,(mexists = (^[X1:individuals>$i>$o]:(^[X2:$i]:(~((![X3:individuals]:(~(((X1 @ X3) @ X2)))))))))). % 1.06/1.27 thf(def_mvalid,definition,(mvalid = (!!))). % 1.06/1.27 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 1.06/1.27 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 1.06/1.27 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 1.06/1.27 thf(def_icl_atom,definition,(icl_atom = (mbox @ rel))). % 1.06/1.27 thf(def_icl_princ,definition,(icl_princ = (^[X1:$i>$o]:X1))). % 1.06/1.27 thf(def_icl_and,definition,(icl_and = mand)). % 1.06/1.27 thf(def_icl_or,definition,(icl_or = mor)). % 1.06/1.27 thf(def_icl_impl,definition,(icl_impl = (^[X1:$i>$o]:(^[X2:$i>$o]:((mbox @ rel) @ ((mimpl @ X1) @ X2)))))). % 1.06/1.27 thf(def_icl_true,definition,(icl_true = mtrue)). % 1.06/1.27 thf(def_icl_false,definition,(icl_false = mfalse)). % 1.06/1.27 thf(def_icl_says,definition,(icl_says = (^[X1:$i>$o]:(^[X2:$i>$o]:((mbox @ rel) @ ((mor @ X1) @ X2)))))). % 1.06/1.27 thf(def_iclval,definition,(iclval = mvalid)). % 1.06/1.27 thf(untrust,conjecture,(![X1:$i]:(![X2:$i]:(((rel @ X1) @ X2) => (~((~((a @ X2))))))))). % 1.06/1.27 thf(h1,negated_conjecture,(~(sP8)),inference(assume_negation,[status(cth)],[untrust])). % 1.06/1.27 thf(1,plain,(~(sP4) | sP5),inference(all_rule,[status(thm)],[])). % 1.06/1.27 thf(2,plain,(~(sP2) | ~(sP5)),inference(all_rule,[status(thm)],[])). % 1.06/1.27 thf(3,plain,((~(sP7) | sP9) | sP2),inference(prop_rule,[status(thm)],[])). % 1.06/1.27 thf(4,plain,(~(sP6) | sP7),inference(all_rule,[status(thm)],[])). % 1.06/1.27 thf(5,plain,(~(sP11) | sP6),inference(all_rule,[status(thm)],[])). % 1.06/1.27 thf(6,plain,sP11,inference(eq_ind,[status(thm)],[])). % 1.06/1.27 thf(7,plain,(~(sP10) | sP4),inference(prop_rule,[status(thm)],[])). % 1.06/1.27 thf(8,plain,(sP3 | ~(sP9)),inference(prop_rule,[status(thm)],[])). % 1.06/1.27 thf(9,plain,(sP1 | ~(sP3)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 1.06/1.27 thf(10,plain,(sP8 | ~(sP1)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 1.06/1.27 thf(ax1,axiom,((icl_princ @ a) = icl_true)). % 1.06/1.27 thf(11,plain,sP10,inference(preprocess,[status(thm)],[ax1]). % 1.06/1.27 thf(12,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h1])). % 1.06/1.27 thf(13,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[12,h0])). % 1.06/1.27 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((rel @ X1) @ X2) => (~((~((a @ X2)))))))),inference(contra,[status(thm),contra(discharge,[h1])],[12,h1])). % 1.06/1.27 % SZS output end Proof %------------------------------------------------------------------------------