%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : LCL579^2 : TPTP v9.3.1. Released v5.1.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n026.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 01:02:04 PM UTC 2026 % Result : Theorem 0.12s 0.38s % Output : Proof 0.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL579^2 : TPTP v9.3.1. Released v5.1.0. % 0.00/0.03 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.09/0.35 % Computer : n026.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Sun Sep 6 00:16:41 UTC 2026 % 0.12/0.36 % CPUTime : % 0.12/0.38 % SZS status Theorem % 0.12/0.38 % Mode: mode213 % 0.12/0.38 % Inferences: 4 % 0.12/0.38 % SZS output start Proof % 0.12/0.38 thf(ty_cY, type, cY : $i). % 0.12/0.38 thf(ty_eigen__0, type, eigen__0 : ($i>$o)). % 0.12/0.38 thf(ty_cX, type, cX : $i). % 0.12/0.38 thf(sP1,plain,sP1 <=> (eigen__0 @ cX),introduced(definition,[new_symbols(definition,[sP1])])). % 0.12/0.38 thf(sP2,plain,sP2 <=> ((cY = cX) => (cX = cY)),introduced(definition,[new_symbols(definition,[sP2])])). % 0.12/0.38 thf(sP3,plain,sP3 <=> (![X1:$i]:(![X2:$i]:((X1 = X2) => (X2 = X1)))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.12/0.38 thf(sP4,plain,sP4 <=> (![X1:$i]:((cY = X1) => (X1 = cY))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.12/0.38 thf(sP5,plain,sP5 <=> (cY = cX),introduced(definition,[new_symbols(definition,[sP5])])). % 0.12/0.38 thf(sP6,plain,sP6 <=> (eigen__0 @ cY),introduced(definition,[new_symbols(definition,[sP6])])). % 0.12/0.38 thf(sP7,plain,sP7 <=> (cX = cY),introduced(definition,[new_symbols(definition,[sP7])])). % 0.12/0.38 thf(cTHM76A,conjecture,((![X1:$i>$o]:((X1 @ cY) => (X1 @ cX))) => (![X1:$i>$o]:((X1 @ cX) => (X1 @ cY))))). % 0.12/0.38 thf(h0,negated_conjecture,(~(((![X1:$i>$o]:((X1 @ cY) => (X1 @ cX))) => (![X1:$i>$o]:((X1 @ cX) => (X1 @ cY)))))),inference(assume_negation,[status(cth)],[cTHM76A])). % 0.12/0.38 thf(h1,assumption,(![X1:$i>$o]:((X1 @ cY) => (X1 @ cX))),introduced(assumption,[])). % 0.12/0.38 thf(h2,assumption,(~((![X1:$i>$o]:((X1 @ cX) => (X1 @ cY))))),introduced(assumption,[])). % 0.12/0.38 thf(h3,assumption,(~((sP1 => sP6))),introduced(assumption,[])). % 0.12/0.38 thf(h4,assumption,sP1,introduced(assumption,[])). % 0.12/0.38 thf(h5,assumption,(~(sP6)),introduced(assumption,[])). % 0.12/0.38 thf(1,plain,((~(sP1) | sP6) | ~(sP7)),inference(mating_rule,[status(thm)],[])). % 0.12/0.38 thf(2,plain,((~(sP2) | ~(sP5)) | sP7),inference(prop_rule,[status(thm)],[])). % 0.12/0.38 thf(3,plain,(~(sP4) | sP2),inference(all_rule,[status(thm)],[])). % 0.12/0.38 thf(4,plain,(~(sP3) | sP4),inference(all_rule,[status(thm)],[])). % 0.12/0.38 thf(5,plain,sP3,inference(eq_sym,[status(thm)],[])). % 0.12/0.38 thf(6,plain,sP5,inference(normalize,[status(thm)],[h1]). % 0.12/0.38 thf(7,plain,$false,inference(prop_unsat,[status(thm),assumptions([h4,h5,h3,h1,h2,h0])],[1,2,3,4,5,6,h4,h5])). % 0.12/0.38 thf(8,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h1,h2,h0]),tab_negimp(discharge,[h4,h5])],[h3,7,h4,h5])). % 0.12/0.38 thf(9,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,8,h3])). % 0.12/0.38 thf(10,plain,$false,inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,9,h1,h2])). % 0.12/0.38 thf(0,theorem,((![X1:$i>$o]:((X1 @ cY) => (X1 @ cX))) => (![X1:$i>$o]:((X1 @ cX) => (X1 @ cY)))),inference(contra,[status(thm),contra(discharge,[h0])],[10,h0])). % 0.12/0.38 % SZS output end Proof %------------------------------------------------------------------------------