%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYN999^1 : 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 : 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 03:19:01 PM UTC 2025 % Result : Theorem 0.13s 0.36s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SYN999^1 : TPTP v9.2.0. Released v3.7.0. % 0.06/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n023.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 : Wed Oct 8 15:21:23 EDT 2025 % 0.13/0.34 % CPUTime : % 0.13/0.36 % SZS status Theorem % 0.13/0.36 % Mode: mode213 % 0.13/0.36 % Inferences: 4 % 0.13/0.36 % SZS output start Proof % 0.13/0.36 thf(ty_eigen__2, type, eigen__2 : ($i>$o)). % 0.13/0.36 thf(ty_eigen__1, type, eigen__1 : $i). % 0.13/0.36 thf(ty_eigen__0, type, eigen__0 : $i). % 0.13/0.36 thf(sP1,plain,sP1 <=> (eigen__2 @ eigen__1),introduced(definition,[new_symbols(definition,[sP1])])). % 0.13/0.36 thf(sP2,plain,sP2 <=> ((eigen__0 = eigen__1) => (eigen__1 = eigen__0)),introduced(definition,[new_symbols(definition,[sP2])])). % 0.13/0.36 thf(sP3,plain,sP3 <=> (![X1:$i]:(![X2:$i]:((X1 = X2) => (X2 = X1)))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.13/0.36 thf(sP4,plain,sP4 <=> (![X1:$i]:((eigen__0 = X1) => (X1 = eigen__0))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.13/0.36 thf(sP5,plain,sP5 <=> (eigen__0 = eigen__1),introduced(definition,[new_symbols(definition,[sP5])])). % 0.13/0.36 thf(sP6,plain,sP6 <=> (eigen__2 @ eigen__0),introduced(definition,[new_symbols(definition,[sP6])])). % 0.13/0.36 thf(sP7,plain,sP7 <=> (eigen__1 = eigen__0),introduced(definition,[new_symbols(definition,[sP7])])). % 0.13/0.36 thf(def_leibeq,definition,(leibeq = (^[X1:$i]:(^[X2:$i]:(![X3:$i>$o]:((X3 @ X1) => (X3 @ X2))))))). % 0.13/0.36 thf(conj,conjecture,(![X1:$i]:(![X2:$i]:((![X3:$i>$o]:((X3 @ X1) => (X3 @ X2))) => (![X3:$i>$o]:((X3 @ X2) => (X3 @ X1))))))). % 0.13/0.36 thf(h0,negated_conjecture,(~((![X1:$i]:(![X2:$i]:((![X3:$i>$o]:((X3 @ X1) => (X3 @ X2))) => (![X3:$i>$o]:((X3 @ X2) => (X3 @ X1)))))))),inference(assume_negation,[status(cth)],[conj])). % 0.13/0.36 thf(h1,assumption,(~((![X1:$i]:((![X2:$i>$o]:((X2 @ eigen__0) => (X2 @ X1))) => (![X2:$i>$o]:((X2 @ X1) => (X2 @ eigen__0))))))),introduced(assumption,[])). % 0.13/0.36 thf(h2,assumption,(~(((![X1:$i>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))) => (![X1:$i>$o]:((X1 @ eigen__1) => (X1 @ eigen__0)))))),introduced(assumption,[])). % 0.13/0.36 thf(h3,assumption,(![X1:$i>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))),introduced(assumption,[])). % 0.13/0.36 thf(h4,assumption,(~((![X1:$i>$o]:((X1 @ eigen__1) => (X1 @ eigen__0))))),introduced(assumption,[])). % 0.13/0.36 thf(h5,assumption,(~((sP1 => sP6))),introduced(assumption,[])). % 0.13/0.36 thf(h6,assumption,sP1,introduced(assumption,[])). % 0.13/0.36 thf(h7,assumption,(~(sP6)),introduced(assumption,[])). % 0.13/0.36 thf(1,plain,((~(sP1) | sP6) | ~(sP7)),inference(mating_rule,[status(thm)],[])). % 0.13/0.36 thf(2,plain,((~(sP2) | ~(sP5)) | sP7),inference(prop_rule,[status(thm)],[])). % 0.13/0.36 thf(3,plain,(~(sP4) | sP2),inference(all_rule,[status(thm)],[])). % 0.13/0.36 thf(4,plain,(~(sP3) | sP4),inference(all_rule,[status(thm)],[])). % 0.13/0.36 thf(5,plain,sP3,inference(eq_sym,[status(thm)],[])). % 0.13/0.36 thf(6,plain,sP5,inference(normalize,[status(thm)],[h3]). % 0.13/0.36 thf(7,plain,$false,inference(prop_unsat,[status(thm),assumptions([h6,h7,h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,h6,h7])). % 0.13/0.36 thf(8,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,7,h6,h7])). % 0.13/0.36 thf(9,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,8,h5])). % 0.13/0.36 thf(10,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,9,h3,h4])). % 0.13/0.36 thf(11,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,10,h2])). % 0.13/0.36 thf(12,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,11,h1])). % 0.13/0.36 thf(0,theorem,(![X1:$i]:(![X2:$i]:((![X3:$i>$o]:((X3 @ X1) => (X3 @ X2))) => (![X3:$i>$o]:((X3 @ X2) => (X3 @ X1)))))),inference(contra,[status(thm),contra(discharge,[h0])],[12,h0])). % 0.13/0.36 % SZS output end Proof %------------------------------------------------------------------------------