%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO008^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n002.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 03:24:39 PM UTC 2025 % Result : Theorem 0.19s 0.36s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYO008^1 : TPTP v9.2.0. Released v3.7.0. % 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n002.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 : Thu Oct 9 01:12:38 EDT 2025 % 0.13/0.34 % CPUTime : % 0.19/0.36 % SZS status Theorem % 0.19/0.36 % Mode: mode213 % 0.19/0.36 % Inferences: 8 % 0.19/0.36 % SZS output start Proof % 0.19/0.36 thf(ty_eigen__2, type, eigen__2 : (($i>$i)>$o)). % 0.19/0.36 thf(ty_eigen__1, type, eigen__1 : ($i>$i)). % 0.19/0.36 thf(ty_eigen__0, type, eigen__0 : ($i>$i)). % 0.19/0.36 thf(sP1,plain,sP1 <=> (eigen__2 @ eigen__0),introduced(definition,[new_symbols(definition,[sP1])])). % 0.19/0.36 thf(sP2,plain,sP2 <=> (![X1:$i]:((eigen__0 @ X1) = (eigen__1 @ X1))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.19/0.36 thf(sP3,plain,sP3 <=> (eigen__2 @ eigen__1),introduced(definition,[new_symbols(definition,[sP3])])). % 0.19/0.36 thf(sP4,plain,sP4 <=> (eigen__0 = eigen__1),introduced(definition,[new_symbols(definition,[sP4])])). % 0.19/0.36 thf(def_leibeq1,definition,(leibeq1 = (^[X1:$i]:(^[X2:$i]:(![X3:$i>$o]:((X3 @ X1) => (X3 @ X2))))))). % 0.19/0.36 thf(def_leibeq2,definition,(leibeq2 = (^[X1:$i>$i]:(^[X2:$i>$i]:(![X3:($i>$i)>$o]:((X3 @ X1) => (X3 @ X2))))))). % 0.19/0.36 thf(conj,conjecture,(![X1:$i>$i]:(![X2:$i>$i]:((![X3:$i]:(![X4:$i>$o]:((X4 @ (X1 @ X3)) => (X4 @ (X2 @ X3))))) => (![X3:($i>$i)>$o]:((X3 @ X1) => (X3 @ X2))))))). % 0.19/0.36 thf(h0,negated_conjecture,(~((![X1:$i>$i]:(![X2:$i>$i]:((![X3:$i]:(![X4:$i>$o]:((X4 @ (X1 @ X3)) => (X4 @ (X2 @ X3))))) => (![X3:($i>$i)>$o]:((X3 @ X1) => (X3 @ X2)))))))),inference(assume_negation,[status(cth)],[conj])). % 0.19/0.36 thf(h1,assumption,(~((![X1:$i>$i]:((![X2:$i]:(![X3:$i>$o]:((X3 @ (eigen__0 @ X2)) => (X3 @ (X1 @ X2))))) => (![X2:($i>$i)>$o]:((X2 @ eigen__0) => (X2 @ X1))))))),introduced(assumption,[])). % 0.19/0.36 thf(h2,assumption,(~(((![X1:$i]:(![X2:$i>$o]:((X2 @ (eigen__0 @ X1)) => (X2 @ (eigen__1 @ X1))))) => (![X1:($i>$i)>$o]:((X1 @ eigen__0) => (X1 @ eigen__1)))))),introduced(assumption,[])). % 0.19/0.36 thf(h3,assumption,(![X1:$i]:(![X2:$i>$o]:((X2 @ (eigen__0 @ X1)) => (X2 @ (eigen__1 @ X1))))),introduced(assumption,[])). % 0.19/0.36 thf(h4,assumption,(~((![X1:($i>$i)>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))))),introduced(assumption,[])). % 0.19/0.36 thf(h5,assumption,(~((sP1 => sP3))),introduced(assumption,[])). % 0.19/0.36 thf(h6,assumption,sP1,introduced(assumption,[])). % 0.19/0.36 thf(h7,assumption,(~(sP3)),introduced(assumption,[])). % 0.19/0.36 thf(1,plain,(sP4 | ~(sP2)),inference(prop_rule,[status(thm)],[])). % 0.19/0.36 thf(2,plain,((~(sP1) | sP3) | ~(sP4)),inference(mating_rule,[status(thm)],[])). % 0.19/0.36 thf(3,plain,sP2,inference(normalize,[status(thm)],[h3]). % 0.19/0.36 thf(4,plain,$false,inference(prop_unsat,[status(thm),assumptions([h6,h7,h5,h3,h4,h2,h1,h0])],[1,2,3,h6,h7])). % 0.19/0.36 thf(5,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,4,h6,h7])). % 0.19/0.36 thf(6,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,5,h5])). % 0.19/0.36 thf(7,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,6,h3,h4])). % 0.19/0.36 thf(8,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,7,h2])). % 0.19/0.36 thf(9,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,8,h1])). % 0.19/0.36 thf(0,theorem,(![X1:$i>$i]:(![X2:$i>$i]:((![X3:$i]:(![X4:$i>$o]:((X4 @ (X1 @ X3)) => (X4 @ (X2 @ X3))))) => (![X3:($i>$i)>$o]:((X3 @ X1) => (X3 @ X2)))))),inference(contra,[status(thm),contra(discharge,[h0])],[9,h0])). % 0.19/0.36 % SZS output end Proof %------------------------------------------------------------------------------