%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : AGT028^2 : TPTP v9.2.0. Released v5.2.0. % 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 01:08:58 PM UTC 2025 % Result : Theorem 1.08s 1.32s % Output : Proof 1.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : AGT028^2 : TPTP v9.2.0. Released v5.2.0. % 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.12/0.33 % Computer : n015.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Wed Oct 8 12:27:53 EDT 2025 % 0.12/0.33 % CPUTime : % 1.08/1.32 % SZS status Theorem % 1.08/1.32 % Mode: mode506 % 1.08/1.32 % Inferences: 38778 % 1.08/1.32 % SZS output start Proof % 1.08/1.32 thf(ty_mu, type, mu : $tType). % 1.08/1.32 thf(ty_r4, type, r4 : ($i>$i>$o)). % 1.08/1.32 thf(ty_eigen__0, type, eigen__0 : $i). % 1.08/1.32 thf(ty_john, type, john : mu). % 1.08/1.32 thf(ty_good_in_maths, type, good_in_maths : (mu>$i>$o)). % 1.08/1.32 thf(ty_maths_teacher, type, maths_teacher : (mu>$i>$o)). % 1.08/1.32 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 1.08/1.32 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((~((![X2:mu]:(~((![X3:$i]:(((r4 @ X1) @ X3) => ((good_in_maths @ X2) @ X3)))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 1.08/1.32 thf(sP1,plain,sP1 <=> (![X1:$i]:(![X2:mu]:(((maths_teacher @ X2) @ X1) => (![X3:$i]:(((r4 @ X1) @ X3) => ((good_in_maths @ X2) @ X3)))))),introduced(definition,[new_symbols(definition,[sP1])])). % 1.08/1.32 thf(sP2,plain,sP2 <=> (![X1:mu]:(((maths_teacher @ X1) @ eigen__0) => (![X2:$i]:(((r4 @ eigen__0) @ X2) => ((good_in_maths @ X1) @ X2))))),introduced(definition,[new_symbols(definition,[sP2])])). % 1.08/1.32 thf(sP3,plain,sP3 <=> (![X1:$i]:(((r4 @ eigen__0) @ X1) => ((good_in_maths @ john) @ X1))),introduced(definition,[new_symbols(definition,[sP3])])). % 1.08/1.32 thf(sP4,plain,sP4 <=> (((maths_teacher @ john) @ eigen__0) => sP3),introduced(definition,[new_symbols(definition,[sP4])])). % 1.08/1.32 thf(sP5,plain,sP5 <=> ((!!) @ (maths_teacher @ john)),introduced(definition,[new_symbols(definition,[sP5])])). % 1.08/1.32 thf(sP6,plain,sP6 <=> (![X1:mu]:(~((![X2:$i]:(((r4 @ eigen__0) @ X2) => ((good_in_maths @ X1) @ X2)))))),introduced(definition,[new_symbols(definition,[sP6])])). % 1.08/1.32 thf(sP7,plain,sP7 <=> (![X1:$i]:(~((![X2:mu]:(~((![X3:$i]:(((r4 @ X1) @ X3) => ((good_in_maths @ X2) @ X3))))))))),introduced(definition,[new_symbols(definition,[sP7])])). % 1.08/1.32 thf(sP8,plain,sP8 <=> ((maths_teacher @ john) @ eigen__0),introduced(definition,[new_symbols(definition,[sP8])])). % 1.08/1.32 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))). % 1.08/1.32 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 1.08/1.32 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 1.08/1.32 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 1.08/1.32 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 1.08/1.32 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 1.08/1.32 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))). % 1.08/1.32 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 1.08/1.32 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))). % 1.08/1.32 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 1.08/1.32 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 1.08/1.32 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 1.08/1.32 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))). % 1.08/1.32 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 1.08/1.32 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 1.08/1.32 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 1.08/1.32 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 1.08/1.32 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 1.08/1.32 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 1.08/1.32 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 1.08/1.32 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 1.08/1.32 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 1.08/1.32 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))). % 1.08/1.32 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))). % 1.08/1.32 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))). % 1.08/1.32 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))). % 1.08/1.32 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))). % 1.08/1.32 thf(def_mvalid,definition,(mvalid = (!!))). % 1.08/1.32 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 1.08/1.32 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 1.08/1.32 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 1.08/1.32 thf(conj,conjecture,sP7). % 1.08/1.32 thf(h1,negated_conjecture,(~(sP7)),inference(assume_negation,[status(cth)],[conj])). % 1.08/1.32 thf(1,plain,(~(sP2) | sP4),inference(all_rule,[status(thm)],[])). % 1.08/1.32 thf(2,plain,((~(sP4) | ~(sP8)) | sP3),inference(prop_rule,[status(thm)],[])). % 1.08/1.32 thf(3,plain,(~(sP5) | sP8),inference(all_rule,[status(thm)],[])). % 1.08/1.32 thf(4,plain,(~(sP1) | sP2),inference(all_rule,[status(thm)],[])). % 1.08/1.32 thf(5,plain,(~(sP6) | ~(sP3)),inference(all_rule,[status(thm)],[])). % 1.08/1.32 thf(6,plain,(sP7 | sP6),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 1.08/1.32 thf(axiom_a6,axiom,(mvalid @ (maths_teacher @ john))). % 1.08/1.32 thf(7,plain,sP5,inference(preprocess,[status(thm)],[axiom_a6]). % 1.08/1.32 thf(axiom_r1,axiom,(mvalid @ (mforall_ind @ (^[X1:mu]:((mimplies @ (maths_teacher @ X1)) @ ((mbox @ r4) @ (good_in_maths @ X1))))))). % 1.08/1.32 thf(8,plain,sP1,inference(preprocess,[status(thm)],[axiom_r1]). % 1.08/1.32 thf(9,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,h1])). % 1.08/1.32 thf(10,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[9,h0])). % 1.08/1.32 thf(0,theorem,sP7,inference(contra,[status(thm),contra(discharge,[h1])],[9,h1])). % 1.08/1.32 % SZS output end Proof %------------------------------------------------------------------------------