%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SEV288^5 : 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 : n021.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 02:56:36 PM UTC 2025 % Result : Theorem 0.14s 0.38s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SEV288^5 : TPTP v9.2.0. Released v4.0.0. % 0.13/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.14/0.35 % Computer : n021.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 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Wed Oct 8 19:33:38 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: 4 % 0.14/0.38 % SZS output start Proof % 0.14/0.38 thf(ty_a, type, a : $tType). % 0.14/0.38 thf(ty_eigen__2, type, eigen__2 : (a>$o)). % 0.14/0.38 thf(ty_eigen__1, type, eigen__1 : a). % 0.14/0.38 thf(ty_eigen__0, type, eigen__0 : a). % 0.14/0.38 thf(sP1,plain,sP1 <=> (eigen__2 @ eigen__1),introduced(definition,[new_symbols(definition,[sP1])])). % 0.14/0.38 thf(sP2,plain,sP2 <=> (eigen__2 @ eigen__0),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(cE1_eq__pme,conjecture,((^[X1:a]:(^[X2:a]:(![X3:a>$o]:((X3 @ X1) => (X3 @ X2))))) = (=))). % 0.14/0.38 thf(h0,negated_conjecture,(~(((^[X1:a]:(^[X2:a]:(![X3:a>$o]:((X3 @ X1) => (X3 @ X2))))) = (=)))),inference(assume_negation,[status(cth)],[cE1_eq__pme])). % 0.14/0.38 thf(h1,assumption,(~((![X1:a]:((^[X2:a]:(![X3:a>$o]:((X3 @ X1) => (X3 @ X2)))) = ((=) @ X1))))),introduced(assumption,[])). % 0.14/0.38 thf(h2,assumption,(~(((^[X1:a]:(![X2:a>$o]:((X2 @ eigen__0) => (X2 @ X1)))) = ((=) @ eigen__0)))),introduced(assumption,[])). % 0.14/0.38 thf(h3,assumption,(~((![X1:a]:((![X2:a>$o]:((X2 @ eigen__0) => (X2 @ X1))) = (eigen__0 = X1))))),introduced(assumption,[])). % 0.14/0.38 thf(h4,assumption,(~(((![X1:a>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))) = sP3))),introduced(assumption,[])). % 0.14/0.38 thf(h5,assumption,(![X1:a>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))),introduced(assumption,[])). % 0.14/0.38 thf(h6,assumption,sP3,introduced(assumption,[])). % 0.14/0.38 thf(h7,assumption,(~((![X1:a>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))))),introduced(assumption,[])). % 0.14/0.38 thf(h8,assumption,(~(sP3)),introduced(assumption,[])). % 0.14/0.38 2: Could not find hyp name % 0.14/0.38 s = eq:a __0 __1 % 0.14/0.38 hyp: % 0.14/0.38 h5: Pi:a>$o (\_:a>$o.imp (^0 __0) (^0 __1)) % 0.14/0.38 h6: imp (eq:a __0 __1) False % 0.14/0.38 h4: imp (eq:$o (Pi:a>$o (\_:a>$o.imp (^0 __0) (^0 __1))) (eq:a __0 __1)) False % 0.14/0.38 h3: imp (Pi:a (\_:a.eq:$o (Pi:a>$o (\_:a>$o.imp (^0 __0) (^0 ^1))) (eq:a __0 ^0))) False % 0.14/0.38 h2: imp (eq:a>$o (\_:a.Pi:a>$o (\_:a>$o.imp (^0 __0) (^0 ^1))) (eq:a __0)) False % 0.14/0.38 h1: imp (Pi:a (\_:a.eq:a>$o (\_:a.Pi:a>$o (\_:a>$o.imp (^0 ^2) (^0 ^1))) (eq:a ^0))) False % 0.14/0.38 h0: imp (eq:a>a>$o (\_:a.\_:a.Pi:a>$o (\_:a>$o.imp (^0 ^2) (^0 ^1))) eq:a) False % 0.21/0.46 % SZS status Theorem % 0.21/0.46 % Mode: mode506 % 0.21/0.46 % Inferences: 23530 % 0.21/0.46 % SZS output start Proof % 0.21/0.46 thf(ty_a, type, a : $tType). % 0.21/0.46 thf(ty_eigen__2, type, eigen__2 : (a>$o)). % 0.21/0.46 thf(ty_eigen__1, type, eigen__1 : a). % 0.21/0.46 thf(ty_eigen__0, type, eigen__0 : a). % 0.21/0.46 thf(h0, assumption, (![X1:a>$o]:(![X2:a]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 0.21/0.46 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:a]:(~(((![X2:a>$o]:((X2 @ eigen__0) => (X2 @ X1))) = (eigen__0 = X1)))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 0.21/0.46 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:a]:(~(((^[X2:a]:(![X3:a>$o]:((X3 @ X1) => (X3 @ X2)))) = ((=) @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 0.21/0.46 thf(h1, assumption, (![X1:(a>$o)>$o]:(![X2:a>$o]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). % 0.21/0.46 thf(eigendef_eigen__2, definition, eigen__2 = (eps__1 @ (^[X1:a>$o]:(~(((X1 @ eigen__0) => (X1 @ eigen__1)))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 0.21/0.46 thf(sP1,plain,sP1 <=> (eigen__0 = eigen__0),introduced(definition,[new_symbols(definition,[sP1])])). % 0.21/0.46 thf(sP2,plain,sP2 <=> (sP1 => (eigen__0 = eigen__1)),introduced(definition,[new_symbols(definition,[sP2])])). % 0.21/0.46 thf(sP3,plain,sP3 <=> (eigen__2 @ eigen__0),introduced(definition,[new_symbols(definition,[sP3])])). % 0.21/0.46 thf(sP4,plain,sP4 <=> (eigen__2 @ eigen__1),introduced(definition,[new_symbols(definition,[sP4])])). % 0.21/0.46 thf(sP5,plain,sP5 <=> ((![X1:a>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))) = (eigen__0 = eigen__1)),introduced(definition,[new_symbols(definition,[sP5])])). % 0.21/0.46 thf(sP6,plain,sP6 <=> ((^[X1:a]:(![X2:a>$o]:((X2 @ eigen__0) => (X2 @ X1)))) = ((=) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP6])])). % 0.21/0.46 thf(sP7,plain,sP7 <=> (sP3 => sP4),introduced(definition,[new_symbols(definition,[sP7])])). % 0.21/0.46 thf(sP8,plain,sP8 <=> (![X1:a]:((![X2:a>$o]:((X2 @ eigen__0) => (X2 @ X1))) = (eigen__0 = X1))),introduced(definition,[new_symbols(definition,[sP8])])). % 0.21/0.46 thf(sP9,plain,sP9 <=> (![X1:a>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))),introduced(definition,[new_symbols(definition,[sP9])])). % 0.21/0.46 thf(sP10,plain,sP10 <=> ((^[X1:a]:(^[X2:a]:(![X3:a>$o]:((X3 @ X1) => (X3 @ X2))))) = (=)),introduced(definition,[new_symbols(definition,[sP10])])). % 0.21/0.46 thf(sP11,plain,sP11 <=> (![X1:a]:((^[X2:a]:(![X3:a>$o]:((X3 @ X1) => (X3 @ X2)))) = ((=) @ X1))),introduced(definition,[new_symbols(definition,[sP11])])). % 0.21/0.46 thf(sP12,plain,sP12 <=> (eigen__0 = eigen__1),introduced(definition,[new_symbols(definition,[sP12])])). % 0.21/0.46 thf(cE1_eq__pme,conjecture,sP10). % 0.21/0.46 thf(h2,negated_conjecture,(~(sP10)),inference(assume_negation,[status(cth)],[cE1_eq__pme])). % 0.21/0.46 thf(1,plain,sP1,inference(prop_rule,[status(thm)],[])). % 0.21/0.46 thf(2,plain,((~(sP3) | sP4) | ~(sP12)),inference(mating_rule,[status(thm)],[])). % 0.21/0.46 thf(3,plain,((~(sP2) | ~(sP1)) | sP12),inference(prop_rule,[status(thm)],[])). % 0.21/0.46 thf(4,plain,(~(sP9) | sP2),inference(all_rule,[status(thm)],[])). % 0.21/0.46 thf(5,plain,(sP7 | ~(sP4)),inference(prop_rule,[status(thm)],[])). % 0.21/0.46 thf(6,plain,(sP7 | sP3),inference(prop_rule,[status(thm)],[])). % 0.21/0.46 thf(7,plain,(sP9 | ~(sP7)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2])). % 0.21/0.46 thf(8,plain,((sP5 | ~(sP9)) | ~(sP12)),inference(prop_rule,[status(thm)],[])). % 0.21/0.46 thf(9,plain,((sP5 | sP9) | sP12),inference(prop_rule,[status(thm)],[])). % 0.21/0.46 thf(10,plain,(sP8 | ~(sP5)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 0.21/0.46 thf(11,plain,(sP6 | ~(sP8)),inference(prop_rule,[status(thm)],[])). % 0.21/0.46 thf(12,plain,(sP11 | ~(sP6)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 0.21/0.46 thf(13,plain,(sP10 | ~(sP11)),inference(prop_rule,[status(thm)],[])). % 0.21/0.46 thf(14,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,h2])). % 0.21/0.46 thf(15,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[14,h1])). % 0.21/0.46 thf(16,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[15,h0])). % 0.21/0.46 thf(0,theorem,sP10,inference(contra,[status(thm),contra(discharge,[h2])],[14,h2])). % 0.21/0.46 % SZS output end Proof %------------------------------------------------------------------------------