%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SEV121^5 : 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 : n009.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 02:56:18 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 % 0.11/0.12 % Problem : SEV121^5 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n009.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 19:16:23 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: 15 % 0.13/0.36 % SZS output start Proof % 0.13/0.36 thf(ty_eigen__2, type, eigen__2 : ($i>$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 : $i). % 0.13/0.36 thf(sP1,plain,sP1 <=> (![X1:$i]:((eigen__2 @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP1])])). % 0.13/0.36 thf(sP2,plain,sP2 <=> ((eigen__2 @ eigen__0) @ eigen__0),introduced(definition,[new_symbols(definition,[sP2])])). % 0.13/0.36 thf(sP3,plain,sP3 <=> (eigen__0 = eigen__1),introduced(definition,[new_symbols(definition,[sP3])])). % 0.13/0.36 thf(sP4,plain,sP4 <=> ((eigen__2 @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP4])])). % 0.13/0.36 thf(sP5,plain,sP5 <=> (eigen__0 = eigen__0),introduced(definition,[new_symbols(definition,[sP5])])). % 0.13/0.36 thf(cTHM47C_pme,conjecture,((=) = (^[X1:$i]:(^[X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:((X3 @ X4) @ X4)) => ((X3 @ X1) @ X2))))))). % 0.13/0.36 thf(h0,negated_conjecture,(~(((=) = (^[X1:$i]:(^[X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:((X3 @ X4) @ X4)) => ((X3 @ X1) @ X2)))))))),inference(assume_negation,[status(cth)],[cTHM47C_pme])). % 0.13/0.36 thf(h1,assumption,(~((![X1:$i]:(((=) @ X1) = (^[X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:((X3 @ X4) @ X4)) => ((X3 @ X1) @ X2)))))))),introduced(assumption,[])). % 0.13/0.36 thf(h2,assumption,(~((((=) @ eigen__0) = (^[X1:$i]:(![X2:$i>$i>$o]:((![X3:$i]:((X2 @ X3) @ X3)) => ((X2 @ eigen__0) @ X1))))))),introduced(assumption,[])). % 0.13/0.36 thf(h3,assumption,(~((![X1:$i]:((eigen__0 = X1) = (![X2:$i>$i>$o]:((![X3:$i]:((X2 @ X3) @ X3)) => ((X2 @ eigen__0) @ X1))))))),introduced(assumption,[])). % 0.13/0.36 thf(h4,assumption,(~((sP3 = (![X1:$i>$i>$o]:((![X2:$i]:((X1 @ X2) @ X2)) => ((X1 @ eigen__0) @ eigen__1)))))),introduced(assumption,[])). % 0.13/0.36 thf(h5,assumption,sP3,introduced(assumption,[])). % 0.13/0.36 thf(h6,assumption,(![X1:$i>$i>$o]:((![X2:$i]:((X1 @ X2) @ X2)) => ((X1 @ eigen__0) @ eigen__1))),introduced(assumption,[])). % 0.13/0.36 thf(h7,assumption,(~(sP3)),introduced(assumption,[])). % 0.13/0.36 thf(h8,assumption,(~((![X1:$i>$i>$o]:((![X2:$i]:((X1 @ X2) @ X2)) => ((X1 @ eigen__0) @ eigen__1))))),introduced(assumption,[])). % 0.13/0.36 thf(h9,assumption,(~((sP1 => sP4))),introduced(assumption,[])). % 0.13/0.36 thf(h10,assumption,sP1,introduced(assumption,[])). % 0.13/0.36 thf(h11,assumption,(~(sP4)),introduced(assumption,[])). % 0.13/0.36 thf(1,plain,sP5,inference(prop_rule,[status(thm)],[])). % 0.13/0.36 thf(2,plain,(((~(sP2) | sP4) | ~(sP5)) | ~(sP3)),inference(mating_rule,[status(thm)],[])). % 0.13/0.36 thf(3,plain,(~(sP1) | sP2),inference(all_rule,[status(thm)],[])). % 0.13/0.36 thf(4,plain,$false,inference(prop_unsat,[status(thm),assumptions([h10,h11,h9,h5,h6,h4,h3,h2,h1,h0])],[1,2,3,h5,h10,h11])). % 0.13/0.36 thf(5,plain,$false,inference(tab_negimp,[status(thm),assumptions([h9,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,4,h10,h11])). % 0.13/0.36 thf(6,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h6,5,h9])). % 0.13/0.36 thf(7,plain,sP3,inference(normalize,[status(thm)],[h8]). % 0.13/0.36 thf(8,plain,$false,inference(tab_conflict,[status(thm),assumptions([h7,h8,h4,h3,h2,h1,h0])],[7,h7])). % 0.13/0.36 thf(9,plain,$false,inference(tab_be,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_be(discharge,[h5,h6]),tab_be(discharge,[h7,h8])],[h4,6,8,h5,h6,h7,h8])). % 0.13/0.36 thf(10,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,9,h4])). % 0.13/0.36 thf(11,plain,$false,inference(tab_fe,[status(thm),assumptions([h2,h1,h0]),tab_fe(discharge,[h3])],[h2,10,h3])). % 0.13/0.36 thf(12,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,11,h2])). % 0.13/0.36 thf(13,plain,$false,inference(tab_fe,[status(thm),assumptions([h0]),tab_fe(discharge,[h1])],[h0,12,h1])). % 0.13/0.36 thf(0,theorem,((=) = (^[X1:$i]:(^[X2:$i]:(![X3:$i>$i>$o]:((![X4:$i]:((X3 @ X4) @ X4)) => ((X3 @ X1) @ X2)))))),inference(contra,[status(thm),contra(discharge,[h0])],[13,h0])). % 0.13/0.36 % SZS output end Proof %------------------------------------------------------------------------------