%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : QUA004^1 : TPTP v9.2.0. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n013.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 02:16:17 PM UTC 2025 % Result : Theorem 32.64s 32.54s % Output : Proof 32.64s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : QUA004^1 : TPTP v9.2.0. Released v4.1.0. % 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.12/0.33 % Computer : n013.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 12:22:08 EDT 2025 % 0.12/0.34 % CPUTime : % 32.64/32.54 % SZS status Theorem % 32.64/32.54 % Mode: mode453 % 32.64/32.54 % Inferences: 521 % 32.64/32.54 % SZS output start Proof % 32.64/32.54 thf(ty_eigen__1, type, eigen__1 : $i). % 32.64/32.54 thf(ty_eigen__0, type, eigen__0 : $i). % 32.64/32.54 thf(ty_sup, type, sup : (($i>$o)>$i)). % 32.64/32.54 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 32.64/32.54 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~(((X1 = eigen__0) = ((~((X1 = eigen__0))) => (X1 = eigen__0))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 32.64/32.54 thf(sP1,plain,sP1 <=> (![X1:$i]:((sup @ (^[X2:$i]:(X2 = X1))) = X1)),introduced(definition,[new_symbols(definition,[sP1])])). % 32.64/32.54 thf(sP2,plain,sP2 <=> ((^[X1:$i]:(X1 = eigen__0)) = (^[X1:$i]:((~((X1 = eigen__0))) => (X1 = eigen__0)))),introduced(definition,[new_symbols(definition,[sP2])])). % 32.64/32.54 thf(sP3,plain,sP3 <=> ((sup @ (^[X1:$i]:(X1 = eigen__0))) = eigen__0),introduced(definition,[new_symbols(definition,[sP3])])). % 32.64/32.54 thf(sP4,plain,sP4 <=> ((~((eigen__1 = eigen__0))) => (eigen__1 = eigen__0)),introduced(definition,[new_symbols(definition,[sP4])])). % 32.64/32.54 thf(sP5,plain,sP5 <=> ((sup @ (^[X1:$i]:(X1 = eigen__0))) = (sup @ (^[X1:$i]:((~((X1 = eigen__0))) => (X1 = eigen__0))))),introduced(definition,[new_symbols(definition,[sP5])])). % 32.64/32.54 thf(sP6,plain,sP6 <=> ((eigen__1 = eigen__0) = sP4),introduced(definition,[new_symbols(definition,[sP6])])). % 32.64/32.54 thf(sP7,plain,sP7 <=> (eigen__1 = eigen__0),introduced(definition,[new_symbols(definition,[sP7])])). % 32.64/32.54 thf(sP8,plain,sP8 <=> ((sup @ (^[X1:$i]:((~((X1 = eigen__0))) => (X1 = eigen__0)))) = eigen__0),introduced(definition,[new_symbols(definition,[sP8])])). % 32.64/32.54 thf(sP9,plain,sP9 <=> (![X1:$i]:((X1 = eigen__0) = ((~((X1 = eigen__0))) => (X1 = eigen__0)))),introduced(definition,[new_symbols(definition,[sP9])])). % 32.64/32.54 thf(def_emptyset,definition,(emptyset = (^[X1:$i]:$false))). % 32.64/32.54 thf(def_union,definition,(union = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 32.64/32.54 thf(def_singleton,definition,(singleton = (^[X1:$i]:(^[X2:$i]:(X2 = X1))))). % 32.64/32.54 thf(def_supset,definition,(supset = (^[X1:($i>$o)>$o]:(^[X2:$i]:(~((![X3:$i>$o]:((X1 @ X3) => (~(((sup @ X3) = X2))))))))))). % 32.64/32.54 thf(def_unionset,definition,(unionset = (^[X1:($i>$o)>$o]:(^[X2:$i]:(~((![X3:$i>$o]:((X1 @ X3) => (~((X3 @ X2))))))))))). % 32.64/32.54 thf(def_addition,definition,(addition = (^[X1:$i]:(^[X2:$i]:(sup @ ((union @ (singleton @ X1)) @ (singleton @ X2))))))). % 32.64/32.54 thf(def_crossmult,definition,(crossmult = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(![X5:$i]:((~(((X1 @ X4) => (~((X2 @ X5)))))) => (~((X3 = ((multiplication @ X4) @ X5)))))))))))))). % 32.64/32.54 thf(addition_idemp,conjecture,(![X1:$i]:((sup @ (^[X2:$i]:((~((X2 = X1))) => (X2 = X1)))) = X1))). % 32.64/32.54 thf(h1,negated_conjecture,(~((![X1:$i]:((sup @ (^[X2:$i]:((~((X2 = X1))) => (X2 = X1)))) = X1)))),inference(assume_negation,[status(cth)],[addition_idemp])). % 32.64/32.54 thf(h2,assumption,(~(sP8)),introduced(assumption,[])). % 32.64/32.54 thf(1,plain,((~(sP4) | sP7) | sP7),inference(prop_rule,[status(thm)],[])). % 32.64/32.54 thf(2,plain,(sP4 | ~(sP7)),inference(prop_rule,[status(thm)],[])). % 32.64/32.54 thf(3,plain,((sP6 | ~(sP7)) | ~(sP4)),inference(prop_rule,[status(thm)],[])). % 32.64/32.54 thf(4,plain,((sP6 | sP7) | sP4),inference(prop_rule,[status(thm)],[])). % 32.64/32.54 thf(5,plain,(sP9 | ~(sP6)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 32.64/32.54 thf(6,plain,(sP2 | ~(sP9)),inference(prop_rule,[status(thm)],[])). % 32.64/32.54 thf(7,plain,(sP5 | ~(sP2)),inference(prop_rule,[status(thm)],[])). % 32.64/32.54 thf(8,plain,(((~(sP3) | sP8) | ~(sP5)) | ~(sP3)),inference(confrontation_rule,[status(thm)],[])). % 32.64/32.54 thf(9,plain,(~(sP1) | sP3),inference(all_rule,[status(thm)],[])). % 32.64/32.54 thf(sup_singleset,axiom,(![X1:$i]:((sup @ (singleton @ X1)) = X1))). % 32.64/32.54 thf(10,plain,sP1,inference(preprocess,[status(thm)],[sup_singleset]). % 32.64/32.54 thf(11,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,h2,10])). % 32.64/32.54 thf(12,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,11,h2])). % 32.64/32.54 thf(13,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[12,h0])). % 32.64/32.54 thf(0,theorem,(![X1:$i]:((sup @ (^[X2:$i]:((~((X2 = X1))) => (X2 = X1)))) = X1)),inference(contra,[status(thm),contra(discharge,[h1])],[12,h1])). % 32.64/32.54 % SZS output end Proof %------------------------------------------------------------------------------