%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : AGT030^1 : 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 : n023.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 36.47s 36.72s % Output : Proof 36.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : AGT030^1 : TPTP v9.2.0. Released v5.2.0. % 0.08/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.15/0.36 % Computer : n023.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Wed Oct 8 12:29:38 EDT 2025 % 0.15/0.36 % CPUTime : % 36.47/36.72 % SZS status Theorem % 36.47/36.72 % Mode: mode438:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=3.:SINE_DEPTH=0 % 36.47/36.72 % Inferences: 1057 % 36.47/36.72 % SZS output start Proof % 36.47/36.72 thf(ty_mu, type, mu : $tType). % 36.47/36.72 thf(ty_r4, type, r4 : ($i>$i>$o)). % 36.47/36.72 thf(ty_eigen__0, type, eigen__0 : $i). % 36.47/36.72 thf(ty_john, type, john : mu). % 36.47/36.72 thf(ty_good_in_maths, type, good_in_maths : (mu>$i>$o)). % 36.47/36.72 thf(ty_r1, type, r1 : ($i>$i>$o)). % 36.47/36.72 thf(ty_maths_teacher, type, maths_teacher : (mu>$i>$o)). % 36.47/36.72 thf(sP1,plain,sP1 <=> ((![X1:$i]:(((r1 @ eigen__0) @ X1) => ((good_in_maths @ john) @ X1))) => (~((![X1:$i]:(((r1 @ eigen__0) @ X1) => (~(((good_in_maths @ john) @ X1)))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 36.47/36.72 thf(sP2,plain,sP2 <=> (![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((r4 @ X1) @ X3) => (X2 @ X3))) => (![X3:$i]:(((r1 @ X1) @ X3) => (X2 @ X3)))))),introduced(definition,[new_symbols(definition,[sP2])])). % 36.47/36.72 thf(sP3,plain,sP3 <=> (![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((r1 @ X1) @ X3) => (X2 @ X3))) => (~((![X3:$i]:(((r1 @ X1) @ X3) => (~((X2 @ X3)))))))))),introduced(definition,[new_symbols(definition,[sP3])])). % 36.47/36.72 thf(sP4,plain,sP4 <=> ((![X1:$i]:(((r4 @ eigen__0) @ X1) => ((good_in_maths @ john) @ X1))) => (![X1:$i]:(((r1 @ eigen__0) @ X1) => ((good_in_maths @ john) @ X1)))),introduced(definition,[new_symbols(definition,[sP4])])). % 36.47/36.72 thf(sP5,plain,sP5 <=> (![X1:mu]:(((maths_teacher @ X1) @ eigen__0) => (![X2:$i]:(((r4 @ eigen__0) @ X2) => ((good_in_maths @ X1) @ X2))))),introduced(definition,[new_symbols(definition,[sP5])])). % 36.47/36.72 thf(sP6,plain,sP6 <=> (![X1:$i]:(((r1 @ eigen__0) @ X1) => (~(((good_in_maths @ john) @ X1))))),introduced(definition,[new_symbols(definition,[sP6])])). % 36.47/36.72 thf(sP7,plain,sP7 <=> ((maths_teacher @ john) @ eigen__0),introduced(definition,[new_symbols(definition,[sP7])])). % 36.47/36.72 thf(sP8,plain,sP8 <=> (![X1:$i]:(![X2:mu]:(((maths_teacher @ X2) @ X1) => (![X3:$i]:(((r4 @ X1) @ X3) => ((good_in_maths @ X2) @ X3)))))),introduced(definition,[new_symbols(definition,[sP8])])). % 36.47/36.72 thf(sP9,plain,sP9 <=> (![X1:$i>$o]:((![X2:$i]:(((r4 @ eigen__0) @ X2) => (X1 @ X2))) => (![X2:$i]:(((r1 @ eigen__0) @ X2) => (X1 @ X2))))),introduced(definition,[new_symbols(definition,[sP9])])). % 36.47/36.72 thf(sP10,plain,sP10 <=> (![X1:$i>$o]:((![X2:$i]:(((r1 @ eigen__0) @ X2) => (X1 @ X2))) => (~((![X2:$i]:(((r1 @ eigen__0) @ X2) => (~((X1 @ X2))))))))),introduced(definition,[new_symbols(definition,[sP10])])). % 36.47/36.72 thf(sP11,plain,sP11 <=> (![X1:mu]:(![X2:$i]:(((r1 @ eigen__0) @ X2) => (~(((good_in_maths @ X1) @ X2)))))),introduced(definition,[new_symbols(definition,[sP11])])). % 36.47/36.72 thf(sP12,plain,sP12 <=> (![X1:$i]:(((r4 @ eigen__0) @ X1) => ((good_in_maths @ john) @ X1))),introduced(definition,[new_symbols(definition,[sP12])])). % 36.47/36.72 thf(sP13,plain,sP13 <=> (sP7 => sP12),introduced(definition,[new_symbols(definition,[sP13])])). % 36.47/36.72 thf(sP14,plain,sP14 <=> (![X1:$i]:(((r1 @ eigen__0) @ X1) => ((good_in_maths @ john) @ X1))),introduced(definition,[new_symbols(definition,[sP14])])). % 36.47/36.72 thf(sP15,plain,sP15 <=> ((!!) @ (maths_teacher @ john)),introduced(definition,[new_symbols(definition,[sP15])])). % 36.47/36.72 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 36.47/36.72 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 36.47/36.72 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 36.47/36.72 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 36.47/36.72 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 36.47/36.72 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 36.47/36.72 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 36.47/36.72 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 36.47/36.72 thf(def_mvalid,definition,(mvalid = (!!))). % 36.47/36.72 thf(conj,conjecture,(![X1:$i]:(~((![X2:mu]:(~((~((![X3:$i]:(((r1 @ X1) @ X3) => (~(((good_in_maths @ X2) @ X3)))))))))))))). % 36.47/36.72 thf(h0,negated_conjecture,(~((![X1:$i]:(~((![X2:mu]:(![X3:$i]:(((r1 @ X1) @ X3) => (~(((good_in_maths @ X2) @ X3))))))))))),inference(assume_negation,[status(cth)],[conj])). % 36.47/36.72 thf(h1,assumption,sP11,introduced(assumption,[])). % 36.47/36.72 thf(1,plain,(~(sP9) | sP4),inference(all_rule,[status(thm)],[])). % 36.47/36.72 thf(2,plain,((~(sP4) | ~(sP12)) | sP14),inference(prop_rule,[status(thm)],[])). % 36.47/36.72 thf(3,plain,(~(sP2) | sP9),inference(all_rule,[status(thm)],[])). % 36.47/36.72 thf(4,plain,(~(sP3) | sP10),inference(all_rule,[status(thm)],[])). % 36.47/36.72 thf(5,plain,(~(sP10) | sP1),inference(all_rule,[status(thm)],[])). % 36.47/36.72 thf(6,plain,((~(sP1) | ~(sP14)) | ~(sP6)),inference(prop_rule,[status(thm)],[])). % 36.47/36.72 thf(7,plain,((~(sP13) | ~(sP7)) | sP12),inference(prop_rule,[status(thm)],[])). % 36.47/36.72 thf(8,plain,(~(sP5) | sP13),inference(all_rule,[status(thm)],[])). % 36.47/36.72 thf(9,plain,(~(sP8) | sP5),inference(all_rule,[status(thm)],[])). % 36.47/36.72 thf(10,plain,(~(sP15) | sP7),inference(all_rule,[status(thm)],[])). % 36.47/36.72 thf(11,plain,(~(sP11) | sP6),inference(all_rule,[status(thm)],[])). % 36.47/36.72 thf(axiom_r1,axiom,(mvalid @ (mforall_ind @ (^[X1:mu]:((mimplies @ (maths_teacher @ X1)) @ ((mbox @ r4) @ (good_in_maths @ X1))))))). % 36.47/36.72 thf(12,plain,sP8,inference(preprocess,[status(thm)],[axiom_r1]). % 36.47/36.72 thf(axiom_a6,axiom,(mvalid @ (maths_teacher @ john))). % 36.47/36.72 thf(13,plain,sP15,inference(preprocess,[status(thm)],[axiom_a6]). % 36.47/36.72 thf(axiom_D_for_r1,axiom,(mvalid @ (mforall_prop @ (^[X1:$i>$o]:((mimplies @ ((mbox @ r1) @ X1)) @ (mnot @ ((mbox @ r1) @ (mnot @ X1)))))))). % 36.47/36.72 thf(14,plain,sP3,inference(preprocess,[status(thm)],[axiom_D_for_r1]). % 36.47/36.72 thf(axiom_I_for_r4_r1,axiom,(mvalid @ (mforall_prop @ (^[X1:$i>$o]:((mimplies @ ((mbox @ r4) @ X1)) @ ((mbox @ r1) @ X1)))))). % 36.47/36.72 thf(15,plain,sP2,inference(preprocess,[status(thm)],[axiom_I_for_r4_r1]). % 36.47/36.72 thf(16,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,h1])). % 36.47/36.72 thf(17,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,16,h1])). % 36.47/36.72 thf(0,theorem,(![X1:$i]:(~((![X2:mu]:(~((~((![X3:$i]:(((r1 @ X1) @ X3) => (~(((good_in_maths @ X2) @ X3))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[17,h0])). % 36.47/36.72 % SZS output end Proof %------------------------------------------------------------------------------