%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO002^1 : 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 : n024.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 03:24:38 PM UTC 2025 % Result : Theorem 0.14s 0.38s % Output : Proof 0.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.14 % Problem : SYO002^1 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.14/0.36 % Computer : n024.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Thu Oct 9 00:53:53 EDT 2025 % 0.14/0.36 % CPUTime : % 0.14/0.38 % SZS status Theorem % 0.14/0.38 % Mode: mode213 % 0.14/0.38 % Inferences: 5 % 0.14/0.38 % SZS output start Proof % 0.14/0.38 thf(ty_eigen__2, type, eigen__2 : ($i>$i)). % 0.14/0.38 thf(ty_eigen__1, type, eigen__1 : $i). % 0.14/0.38 thf(ty_eigen__0, type, eigen__0 : $i). % 0.14/0.38 thf(ty_eigen__3, type, eigen__3 : ($i>$o)). % 0.14/0.38 thf(sP1,plain,sP1 <=> (eigen__3 @ (eigen__2 @ eigen__0)),introduced(definition,[new_symbols(definition,[sP1])])). % 0.14/0.38 thf(sP2,plain,sP2 <=> ((eigen__2 @ eigen__0) = (eigen__2 @ eigen__1)),introduced(definition,[new_symbols(definition,[sP2])])). % 0.14/0.38 thf(sP3,plain,sP3 <=> (eigen__0 = eigen__1),introduced(definition,[new_symbols(definition,[sP3])])). % 0.14/0.38 thf(sP4,plain,sP4 <=> (eigen__3 @ (eigen__2 @ eigen__1)),introduced(definition,[new_symbols(definition,[sP4])])). % 0.14/0.38 thf(def_leibeq,definition,(leibeq = (^[X1:$i]:(^[X2:$i]:(![X3:$i>$o]:((X3 @ X1) => (X3 @ X2))))))). % 0.14/0.38 thf(conj,conjecture,(![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i>$o]:((X4 @ X1) => (X4 @ X2))) => (![X4:$i>$o]:((X4 @ (X3 @ X1)) => (X4 @ (X3 @ X2))))))))). % 0.14/0.38 thf(h0,negated_conjecture,(~((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i>$o]:((X4 @ X1) => (X4 @ X2))) => (![X4:$i>$o]:((X4 @ (X3 @ X1)) => (X4 @ (X3 @ X2)))))))))),inference(assume_negation,[status(cth)],[conj])). % 0.14/0.38 thf(h1,assumption,(~((![X1:$i]:(![X2:$i>$i]:((![X3:$i>$o]:((X3 @ eigen__0) => (X3 @ X1))) => (![X3:$i>$o]:((X3 @ (X2 @ eigen__0)) => (X3 @ (X2 @ X1))))))))),introduced(assumption,[])). % 0.14/0.38 thf(h2,assumption,(~((![X1:$i>$i]:((![X2:$i>$o]:((X2 @ eigen__0) => (X2 @ eigen__1))) => (![X2:$i>$o]:((X2 @ (X1 @ eigen__0)) => (X2 @ (X1 @ eigen__1)))))))),introduced(assumption,[])). % 0.14/0.38 thf(h3,assumption,(~(((![X1:$i>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))) => (![X1:$i>$o]:((X1 @ (eigen__2 @ eigen__0)) => (X1 @ (eigen__2 @ eigen__1))))))),introduced(assumption,[])). % 0.14/0.38 thf(h4,assumption,(![X1:$i>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))),introduced(assumption,[])). % 0.14/0.38 thf(h5,assumption,(~((![X1:$i>$o]:((X1 @ (eigen__2 @ eigen__0)) => (X1 @ (eigen__2 @ eigen__1)))))),introduced(assumption,[])). % 0.14/0.38 thf(h6,assumption,(~((sP1 => sP4))),introduced(assumption,[])). % 0.14/0.38 thf(h7,assumption,sP1,introduced(assumption,[])). % 0.14/0.38 thf(h8,assumption,(~(sP4)),introduced(assumption,[])). % 0.14/0.38 thf(1,plain,(sP2 | ~(sP3)),inference(prop_rule,[status(thm)],[])). % 0.14/0.38 thf(2,plain,((~(sP1) | sP4) | ~(sP2)),inference(mating_rule,[status(thm)],[])). % 0.14/0.38 thf(3,plain,sP3,inference(normalize,[status(thm)],[h4]). % 0.14/0.38 thf(4,plain,$false,inference(prop_unsat,[status(thm),assumptions([h7,h8,h6,h4,h5,h3,h2,h1,h0])],[1,2,3,h7,h8])). % 0.14/0.38 thf(5,plain,$false,inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,4,h7,h8])). % 0.14/0.38 thf(6,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__3)],[h5,5,h6])). % 0.14/0.38 thf(7,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,6,h4,h5])). % 0.14/0.38 thf(8,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,7,h3])). % 0.14/0.38 thf(9,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,8,h2])). % 0.14/0.38 thf(10,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,9,h1])). % 0.14/0.38 thf(0,theorem,(![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i>$o]:((X4 @ X1) => (X4 @ X2))) => (![X4:$i>$o]:((X4 @ (X3 @ X1)) => (X4 @ (X3 @ X2)))))))),inference(contra,[status(thm),contra(discharge,[h0])],[10,h0])). % 0.14/0.38 % SZS output end Proof %------------------------------------------------------------------------------