%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO277^5 : 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 : 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 03:25:16 PM UTC 2025 % Result : Theorem 0.13s 0.38s % Output : Proof 0.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SYO277^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % 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 : Thu Oct 9 01:29:23 EDT 2025 % 0.13/0.35 % CPUTime : % 0.13/0.38 % SZS status Theorem % 0.13/0.38 % Mode: mode213 % 0.13/0.38 % Inferences: 19 % 0.13/0.38 % SZS output start Proof % 0.13/0.38 thf(ty_eigen__2, type, eigen__2 : ($i>$i>$o)). % 0.13/0.38 thf(ty_eigen__1, type, eigen__1 : $i). % 0.13/0.38 thf(ty_eigen__0, type, eigen__0 : $i). % 0.13/0.38 thf(ty_eigen__4, type, eigen__4 : ($i>$o)). % 0.13/0.38 thf(sP1,plain,sP1 <=> (![X1:$i]:((eigen__2 @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP1])])). % 0.13/0.38 thf(sP2,plain,sP2 <=> ((eigen__2 @ eigen__0) @ eigen__0),introduced(definition,[new_symbols(definition,[sP2])])). % 0.13/0.38 thf(sP3,plain,sP3 <=> (eigen__4 @ eigen__1),introduced(definition,[new_symbols(definition,[sP3])])). % 0.13/0.38 thf(sP4,plain,sP4 <=> (eigen__0 = eigen__1),introduced(definition,[new_symbols(definition,[sP4])])). % 0.13/0.38 thf(sP5,plain,sP5 <=> ((eigen__2 @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP5])])). % 0.13/0.38 thf(sP6,plain,sP6 <=> (eigen__4 @ eigen__0),introduced(definition,[new_symbols(definition,[sP6])])). % 0.13/0.38 thf(sP7,plain,sP7 <=> (eigen__0 = eigen__0),introduced(definition,[new_symbols(definition,[sP7])])). % 0.13/0.38 thf(cTHM47D,conjecture,(![X1:$i]:(![X2:$i]:((![X3:$i>$o]:((X3 @ X1) => (X3 @ X2))) = (![X3:$i>$i>$o]:((![X4:$i]:((X3 @ X4) @ X4)) => ((X3 @ X1) @ X2))))))). % 0.13/0.38 thf(h0,negated_conjecture,(~((![X1:$i]:(![X2:$i]:((![X3:$i>$o]:((X3 @ X1) => (X3 @ X2))) = (![X3:$i>$i>$o]:((![X4:$i]:((X3 @ X4) @ X4)) => ((X3 @ X1) @ X2)))))))),inference(assume_negation,[status(cth)],[cTHM47D])). % 0.13/0.38 thf(h1,assumption,(~((![X1:$i]:((![X2:$i>$o]:((X2 @ eigen__0) => (X2 @ X1))) = (![X2:$i>$i>$o]:((![X3:$i]:((X2 @ X3) @ X3)) => ((X2 @ eigen__0) @ X1))))))),introduced(assumption,[])). % 0.13/0.38 thf(h2,assumption,(~(((![X1:$i>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))) = (![X1:$i>$i>$o]:((![X2:$i]:((X1 @ X2) @ X2)) => ((X1 @ eigen__0) @ eigen__1)))))),introduced(assumption,[])). % 0.13/0.38 thf(h3,assumption,(![X1:$i>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))),introduced(assumption,[])). % 0.13/0.38 thf(h4,assumption,(![X1:$i>$i>$o]:((![X2:$i]:((X1 @ X2) @ X2)) => ((X1 @ eigen__0) @ eigen__1))),introduced(assumption,[])). % 0.13/0.38 thf(h5,assumption,(~((![X1:$i>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))))),introduced(assumption,[])). % 0.13/0.38 thf(h6,assumption,(~((![X1:$i>$i>$o]:((![X2:$i]:((X1 @ X2) @ X2)) => ((X1 @ eigen__0) @ eigen__1))))),introduced(assumption,[])). % 0.13/0.38 thf(h7,assumption,(~((sP1 => sP5))),introduced(assumption,[])). % 0.13/0.38 thf(h8,assumption,sP1,introduced(assumption,[])). % 0.13/0.38 thf(h9,assumption,(~(sP5)),introduced(assumption,[])). % 0.13/0.38 thf(1,plain,sP7,inference(prop_rule,[status(thm)],[])). % 0.13/0.38 thf(2,plain,(((~(sP2) | sP5) | ~(sP7)) | ~(sP4)),inference(mating_rule,[status(thm)],[])). % 0.13/0.38 thf(3,plain,(~(sP1) | sP2),inference(all_rule,[status(thm)],[])). % 0.13/0.38 1: Could not find hyp name % 0.13/0.38 s = Pi:$i>$i>$o (\_:$i>$i>$o.imp (Pi:$i (\_:$i.^1 ^0 ^0)) (^0 __0 __1)) % 0.13/0.38 hyp: % 0.13/0.38 h8: Pi:$i (\_:$i.__2 ^0 ^0) % 0.13/0.38 h9: imp (__2 __0 __1) False % 0.13/0.38 h7: imp (imp (Pi:$i (\_:$i.__2 ^0 ^0)) (__2 __0 __1)) False % 0.13/0.38 h3: Pi:$i>$o (\_:$i>$o.imp (^0 __0) (^0 __1)) % 0.13/0.38 h4: imp (Pi:$i>$i>$o (\_:$i>$i>$o.imp (Pi:$i (\_:$i.^1 ^0 ^0)) (^0 __0 __1))) False % 0.13/0.38 h2: imp (eq:$o (Pi:$i>$o (\_:$i>$o.imp (^0 __0) (^0 __1))) (Pi:$i>$i>$o (\_:$i>$i>$o.imp (Pi:$i (\_:$i.^1 ^0 ^0)) (^0 __0 __1)))) False % 0.13/0.38 h1: imp (Pi:$i (\_:$i.eq:$o (Pi:$i>$o (\_:$i>$o.imp (^0 __0) (^0 ^1))) (Pi:$i>$i>$o (\_:$i>$i>$o.imp (Pi:$i (\_:$i.^1 ^0 ^0)) (^0 __0 ^1))))) False % 0.13/0.38 h0: imp (Pi:$i (\_:$i.Pi:$i (\_:$i.eq:$o (Pi:$i>$o (\_:$i>$o.imp (^0 ^2) (^0 ^1))) (Pi:$i>$i>$o (\_:$i>$i>$o.imp (Pi:$i (\_:$i.^1 ^0 ^0)) (^0 ^2 ^1)))))) False % 0.43/0.72 % SZS status Theorem % 0.43/0.72 % Mode: mode506 % 0.43/0.72 % Inferences: 88827 % 0.43/0.72 % SZS output start Proof % 0.43/0.72 thf(ty_eigen__2, type, eigen__2 : ($i>$o)). % 0.43/0.72 thf(ty_eigen__25, type, eigen__25 : $i). % 0.43/0.72 thf(ty_eigen__1, type, eigen__1 : $i). % 0.43/0.72 thf(ty_eigen__0, type, eigen__0 : $i). % 0.43/0.72 thf(ty_eigen__3, type, eigen__3 : ($i>$i>$o)). % 0.43/0.72 thf(h0, assumption, (![X1:($i>$i>$o)>$o]:(![X2:$i>$i>$o]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 0.43/0.72 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i>$i>$o]:(~(((![X2:$i]:((X1 @ X2) @ X2)) => ((X1 @ eigen__0) @ eigen__1)))))), introduced(definition,[new_symbols(definition,[eigen__3])])). % 0.43/0.72 thf(h1, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). % 0.43/0.72 thf(eigendef_eigen__1, definition, eigen__1 = (eps__1 @ (^[X1:$i]:(~(((![X2:$i>$o]:((X2 @ eigen__0) => (X2 @ X1))) = (![X2:$i>$i>$o]:((![X3:$i]:((X2 @ X3) @ X3)) => ((X2 @ eigen__0) @ X1)))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 0.43/0.72 thf(eigendef_eigen__0, definition, eigen__0 = (eps__1 @ (^[X1:$i]:(~((![X2:$i]:((![X3:$i>$o]:((X3 @ X1) => (X3 @ X2))) = (![X3:$i>$i>$o]:((![X4:$i]:((X3 @ X4) @ X4)) => ((X3 @ X1) @ X2))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 0.43/0.72 thf(h2, assumption, (![X1:($i>$o)>$o]:(![X2:$i>$o]:((X1 @ X2) => (X1 @ (eps__2 @ X1))))),introduced(assumption,[])). % 0.43/0.72 thf(eigendef_eigen__2, definition, eigen__2 = (eps__2 @ (^[X1:$i>$o]:(~(((X1 @ eigen__0) => (X1 @ eigen__1)))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 0.43/0.72 thf(eigendef_eigen__25, definition, eigen__25 = (eps__1 @ (^[X1:$i]:(~((X1 = X1))))), introduced(definition,[new_symbols(definition,[eigen__25])])). % 0.43/0.72 thf(sP1,plain,sP1 <=> (![X1:$i]:((![X2:$i>$o]:((X2 @ eigen__0) => (X2 @ X1))) = (![X2:$i>$i>$o]:((![X3:$i]:((X2 @ X3) @ X3)) => ((X2 @ eigen__0) @ X1))))),introduced(definition,[new_symbols(definition,[sP1])])). % 0.43/0.72 thf(sP2,plain,sP2 <=> (((eigen__3 @ eigen__0) @ eigen__0) => ((eigen__3 @ eigen__0) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP2])])). % 0.43/0.72 thf(sP3,plain,sP3 <=> (![X1:$i]:(X1 = X1)),introduced(definition,[new_symbols(definition,[sP3])])). % 0.43/0.72 thf(sP4,plain,sP4 <=> (![X1:$i>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.43/0.72 thf(sP5,plain,sP5 <=> ((eigen__3 @ eigen__0) @ eigen__0),introduced(definition,[new_symbols(definition,[sP5])])). % 0.43/0.72 thf(sP6,plain,sP6 <=> ((eigen__3 @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP6])])). % 0.43/0.72 thf(sP7,plain,sP7 <=> (![X1:$i]:((eigen__3 @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP7])])). % 0.43/0.72 thf(sP8,plain,sP8 <=> (eigen__2 @ eigen__0),introduced(definition,[new_symbols(definition,[sP8])])). % 0.43/0.72 thf(sP9,plain,sP9 <=> (![X1:$i>$i>$o]:((![X2:$i]:((X1 @ X2) @ X2)) => ((X1 @ eigen__0) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP9])])). % 0.43/0.72 thf(sP10,plain,sP10 <=> (sP7 => sP6),introduced(definition,[new_symbols(definition,[sP10])])). % 0.43/0.72 thf(sP11,plain,sP11 <=> (eigen__0 = eigen__1),introduced(definition,[new_symbols(definition,[sP11])])). % 0.43/0.72 thf(sP12,plain,sP12 <=> (sP4 = sP9),introduced(definition,[new_symbols(definition,[sP12])])). % 0.43/0.72 thf(sP13,plain,sP13 <=> (![X1:$i]:(![X2:$i]:((![X3:$i>$o]:((X3 @ X1) => (X3 @ X2))) = (![X3:$i>$i>$o]:((![X4:$i]:((X3 @ X4) @ X4)) => ((X3 @ X1) @ X2)))))),introduced(definition,[new_symbols(definition,[sP13])])). % 0.43/0.72 thf(sP14,plain,sP14 <=> (sP8 => (eigen__2 @ eigen__1)),introduced(definition,[new_symbols(definition,[sP14])])). % 0.43/0.72 thf(sP15,plain,sP15 <=> (eigen__25 = eigen__25),introduced(definition,[new_symbols(definition,[sP15])])). % 0.43/0.72 thf(sP16,plain,sP16 <=> (eigen__2 @ eigen__1),introduced(definition,[new_symbols(definition,[sP16])])). % 0.43/0.72 thf(sP17,plain,sP17 <=> (sP3 => sP11),introduced(definition,[new_symbols(definition,[sP17])])). % 0.43/0.72 thf(cTHM47D,conjecture,sP13). % 0.43/0.72 thf(h3,negated_conjecture,(~(sP13)),inference(assume_negation,[status(cth)],[cTHM47D])). % 0.43/0.72 thf(1,plain,sP15,inference(prop_rule,[status(thm)],[])). % 0.43/0.72 thf(2,plain,(sP3 | ~(sP15)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__25])). % 0.43/0.72 thf(3,plain,((~(sP17) | ~(sP3)) | sP11),inference(prop_rule,[status(thm)],[])). % 0.43/0.72 thf(4,plain,(~(sP9) | sP17),inference(all_rule,[status(thm)],[])). % 0.43/0.72 thf(5,plain,(~(sP7) | sP5),inference(all_rule,[status(thm)],[])). % 0.43/0.72 thf(6,plain,((~(sP2) | ~(sP5)) | sP6),inference(prop_rule,[status(thm)],[])). % 0.43/0.72 thf(7,plain,(~(sP4) | sP2),inference(all_rule,[status(thm)],[])). % 0.43/0.72 thf(8,plain,(sP10 | ~(sP6)),inference(prop_rule,[status(thm)],[])). % 0.43/0.72 thf(9,plain,(sP10 | sP7),inference(prop_rule,[status(thm)],[])). % 0.43/0.72 thf(10,plain,(sP9 | ~(sP10)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])). % 0.43/0.72 thf(11,plain,((~(sP8) | sP16) | ~(sP11)),inference(mating_rule,[status(thm)],[])). % 0.43/0.72 thf(12,plain,(sP14 | ~(sP16)),inference(prop_rule,[status(thm)],[])). % 0.43/0.72 thf(13,plain,(sP14 | sP8),inference(prop_rule,[status(thm)],[])). % 0.43/0.72 thf(14,plain,(sP4 | ~(sP14)),inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__2])). % 0.43/0.72 thf(15,plain,((sP12 | ~(sP4)) | ~(sP9)),inference(prop_rule,[status(thm)],[])). % 0.43/0.72 thf(16,plain,((sP12 | sP4) | sP9),inference(prop_rule,[status(thm)],[])). % 0.43/0.72 thf(17,plain,(sP1 | ~(sP12)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1])). % 0.43/0.72 thf(18,plain,(sP13 | ~(sP1)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0])). % 0.43/0.72 thf(19,plain,$false,inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,h3])). % 0.43/0.72 thf(20,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[19,h2])). % 0.43/0.72 thf(21,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[20,h1])). % 0.43/0.72 thf(22,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[21,h0])). % 0.43/0.72 thf(0,theorem,sP13,inference(contra,[status(thm),contra(discharge,[h3])],[19,h3])). % 0.43/0.72 % SZS output end Proof %------------------------------------------------------------------------------