%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO233^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n017.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 03:25:11 PM UTC 2025 % Result : Theorem 0.14s 0.37s % Output : Proof 0.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SYO233^5 : TPTP v9.2.0. Released v4.0.0. % 0.08/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.14/0.35 % Computer : n017.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Thu Oct 9 00:58:23 EDT 2025 % 0.14/0.35 % CPUTime : % 0.14/0.37 % SZS status Theorem % 0.14/0.37 % Mode: mode213 % 0.14/0.37 % Inferences: 2 % 0.14/0.37 % SZS output start Proof % 0.14/0.37 thf(ty_eigen__0, type, eigen__0 : $i). % 0.14/0.37 thf(ty_cM, type, cM : ($i>$i)). % 0.14/0.37 thf(ty_cN, type, cN : ($i>$i)). % 0.14/0.37 thf(sP1,plain,sP1 <=> (![X1:$i]:((cM @ X1) = (cN @ X1))),introduced(definition,[new_symbols(definition,[sP1])])). % 0.14/0.37 thf(sP2,plain,sP2 <=> ((cM @ eigen__0) = (cN @ eigen__0)),introduced(definition,[new_symbols(definition,[sP2])])). % 0.14/0.37 thf(cLEIBNIZ,conjecture,((![X1:$i]:(![X2:$i>$o]:((X2 @ (cM @ X1)) => (X2 @ (cN @ X1))))) => (cM = cN))). % 0.14/0.37 thf(h0,negated_conjecture,(~(((![X1:$i]:(![X2:$i>$o]:((X2 @ (cM @ X1)) => (X2 @ (cN @ X1))))) => (cM = cN)))),inference(assume_negation,[status(cth)],[cLEIBNIZ])). % 0.14/0.37 thf(h1,assumption,(![X1:$i]:(![X2:$i>$o]:((X2 @ (cM @ X1)) => (X2 @ (cN @ X1))))),introduced(assumption,[])). % 0.14/0.37 thf(h2,assumption,(~((cM = cN))),introduced(assumption,[])). % 0.14/0.37 thf(h3,assumption,(~(sP1)),introduced(assumption,[])). % 0.14/0.37 thf(h4,assumption,(~(sP2)),introduced(assumption,[])). % 0.14/0.37 thf(1,plain,(~(sP1) | sP2),inference(all_rule,[status(thm)],[])). % 0.14/0.37 thf(2,plain,sP1,inference(normalize,[status(thm)],[h1]). % 0.14/0.37 thf(3,plain,$false,inference(prop_unsat,[status(thm),assumptions([h4,h3,h1,h2,h0])],[1,2,h4])). % 0.14/0.37 thf(4,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h1,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__0)],[h3,3,h4])). % 0.14/0.37 thf(5,plain,$false,inference(tab_fe,[status(thm),assumptions([h1,h2,h0]),tab_fe(discharge,[h3])],[h2,4,h3])). % 0.14/0.37 thf(6,plain,$false,inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,5,h1,h2])). % 0.14/0.37 thf(0,theorem,((![X1:$i]:(![X2:$i>$o]:((X2 @ (cM @ X1)) => (X2 @ (cN @ X1))))) => (cM = cN)),inference(contra,[status(thm),contra(discharge,[h0])],[6,h0])). % 0.14/0.37 % SZS output end Proof %------------------------------------------------------------------------------