%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SWV435^3 : 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 : n014.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 0.13s 0.37s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWV435^3 : TPTP v9.2.0. Released v3.6.0. % 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n014.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Oct 8 14:05:23 EDT 2025 % 0.13/0.34 % CPUTime : % 0.13/0.37 % SZS status Theorem % 0.13/0.37 % Mode: mode213 % 0.13/0.37 % Inferences: 14 % 0.13/0.37 % SZS output start Proof % 0.13/0.37 thf(ty_a, type, a : ($i>$o)). % 0.13/0.37 thf(ty_eigen__1, type, eigen__1 : $i). % 0.13/0.37 thf(ty_eigen__0, type, eigen__0 : $i). % 0.13/0.37 thf(ty_rel, type, rel : ($i>$i>$o)). % 0.13/0.37 thf(sP1,plain,sP1 <=> (![X1:$i]:((a @ X1) = (~($false)))),introduced(definition,[new_symbols(definition,[sP1])])). % 0.13/0.37 thf(sP2,plain,sP2 <=> ((a @ eigen__1) = (~($false))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.13/0.37 thf(sP3,plain,sP3 <=> $false,introduced(definition,[new_symbols(definition,[sP3])])). % 0.13/0.37 thf(sP4,plain,sP4 <=> (a = (^[X1:$i]:(~(sP3)))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.13/0.37 thf(sP5,plain,sP5 <=> (a @ eigen__1),introduced(definition,[new_symbols(definition,[sP5])])). % 0.13/0.37 thf(def_mfalse,definition,(mfalse = (^[X1:$i]:sP3))). % 0.13/0.37 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~(sP3))))). % 0.13/0.37 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 0.13/0.37 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 0.13/0.37 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 0.13/0.37 thf(def_mimpl,definition,(mimpl = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 0.13/0.37 thf(def_miff,definition,(miff = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimpl @ X1) @ X2)) @ ((mimpl @ X2) @ X1)))))). % 0.13/0.37 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 0.13/0.37 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(((X1 @ X3) @ X4) => (~((X2 @ X4)))))))))))). % 0.13/0.37 thf(def_mall,definition,(mall = (^[X1:individuals>$i>$o]:(^[X2:$i]:(![X3:individuals]:((X1 @ X3) @ X2)))))). % 0.13/0.37 thf(def_mexists,definition,(mexists = (^[X1:individuals>$i>$o]:(^[X2:$i]:(~((![X3:individuals]:(~(((X1 @ X3) @ X2)))))))))). % 0.13/0.37 thf(def_mvalid,definition,(mvalid = (!!))). % 0.13/0.37 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 0.13/0.37 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 0.13/0.37 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 0.13/0.37 thf(def_icl_atom,definition,(icl_atom = (mbox @ rel))). % 0.13/0.37 thf(def_icl_princ,definition,(icl_princ = (^[X1:$i>$o]:X1))). % 0.13/0.37 thf(def_icl_and,definition,(icl_and = mand)). % 0.13/0.37 thf(def_icl_or,definition,(icl_or = mor)). % 0.13/0.37 thf(def_icl_impl,definition,(icl_impl = (^[X1:$i>$o]:(^[X2:$i>$o]:((mbox @ rel) @ ((mimpl @ X1) @ X2)))))). % 0.13/0.37 thf(def_icl_true,definition,(icl_true = mtrue)). % 0.13/0.37 thf(def_icl_false,definition,(icl_false = mfalse)). % 0.13/0.37 thf(def_icl_says,definition,(icl_says = (^[X1:$i>$o]:(^[X2:$i>$o]:((mbox @ rel) @ ((mor @ X1) @ X2)))))). % 0.13/0.37 thf(def_iclval,definition,(iclval = mvalid)). % 0.13/0.37 thf(untrust,conjecture,(![X1:$i]:(![X2:$i]:(((rel @ X1) @ X2) => (~((~((a @ X2))))))))). % 0.13/0.37 thf(h0,negated_conjecture,(~((![X1:$i]:(![X2:$i]:(((rel @ X1) @ X2) => (a @ X2)))))),inference(assume_negation,[status(cth)],[untrust])). % 0.13/0.37 thf(h1,assumption,(~((![X1:$i]:(((rel @ eigen__0) @ X1) => (a @ X1))))),introduced(assumption,[])). % 0.13/0.37 thf(h2,assumption,(~((((rel @ eigen__0) @ eigen__1) => sP5))),introduced(assumption,[])). % 0.13/0.37 thf(h3,assumption,((rel @ eigen__0) @ eigen__1),introduced(assumption,[])). % 0.13/0.37 thf(h4,assumption,(~(sP5)),introduced(assumption,[])). % 0.13/0.37 thf(1,plain,((~(sP2) | sP5) | sP3),inference(prop_rule,[status(thm)],[])). % 0.13/0.37 thf(2,plain,(~(sP1) | sP2),inference(all_rule,[status(thm)],[])). % 0.13/0.37 thf(3,plain,~(sP3),inference(prop_rule,[status(thm)],[])). % 0.13/0.37 thf(4,plain,(~(sP4) | sP1),inference(prop_rule,[status(thm)],[])). % 0.13/0.37 thf(ax1,axiom,((icl_princ @ a) = icl_true)). % 0.13/0.37 thf(5,plain,sP4,inference(preprocess,[status(thm)],[ax1]). % 0.13/0.37 thf(6,plain,$false,inference(prop_unsat,[status(thm),assumptions([h3,h4,h2,h1,h0])],[1,2,3,4,5,h4])). % 0.13/0.37 thf(7,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,6,h3,h4])). % 0.13/0.37 thf(8,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,7,h2])). % 0.13/0.37 thf(9,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,8,h1])). % 0.13/0.37 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((rel @ X1) @ X2) => (~((~((a @ X2)))))))),inference(contra,[status(thm),contra(discharge,[h0])],[9,h0])). % 0.13/0.37 % SZS output end Proof %------------------------------------------------------------------------------