%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : LCL623^1 : TPTP v9.3.1. Bugfixed v7.3.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n015.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 01:02:08 PM UTC 2026 % Result : Theorem 1.04s 1.30s % Output : Proof 1.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL623^1 : TPTP v9.3.1. Bugfixed v7.3.0. % 0.00/0.03 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.11/0.36 % Computer : n015.cluster.edu % 0.11/0.36 % Model : x86_64 x86_64 % 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.36 % Memory : 8046.5625MB % 0.11/0.36 % OS : Linux 6.8.0-71-generic % 0.11/0.36 % CPULimit : 300 % 0.11/0.36 % WCLimit : 300 % 0.11/0.36 % DateTime : Sat Sep 5 21:11:13 UTC 2026 % 0.11/0.37 % CPUTime : % 1.04/1.30 % SZS status Theorem % 1.04/1.30 % Mode: mode506 % 1.04/1.30 % Inferences: 0 % 1.04/1.30 % SZS output start Proof % 1.04/1.30 thf(ty_r, type, r : ($i>$i>$o)). % 1.04/1.30 thf(sP1,plain,sP1 <=> (![X1:$i>$o]:(![X2:$i]:((![X3:$i]:(((r @ X2) @ X3) => ((![X4:$i]:(((r @ X3) @ X4) => (X1 @ X4))) => (X1 @ X3)))) => (![X3:$i]:(((r @ X2) @ X3) => (X1 @ X3)))))),introduced(definition,[new_symbols(definition,[sP1])])). % 1.04/1.30 thf(def_mfalse,definition,(mfalse = (^[X1:$i]:$false))). % 1.04/1.30 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 1.04/1.30 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 1.04/1.30 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 1.04/1.30 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 1.04/1.30 thf(def_mimpl,definition,(mimpl = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 1.04/1.30 thf(def_miff,definition,(miff = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimpl @ X1) @ X2)) @ ((mimpl @ X2) @ X1)))))). % 1.04/1.30 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 1.04/1.30 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(((X1 @ X3) @ X4) => (~((X2 @ X4)))))))))))). % 1.04/1.30 thf(def_mall,definition,(mall = (^[X1:individuals>$i>$o]:(^[X2:$i]:(![X3:individuals]:((X1 @ X3) @ X2)))))). % 1.04/1.30 thf(def_mexists,definition,(mexists = (^[X1:individuals>$i>$o]:(^[X2:$i]:(~((![X3:individuals]:(~(((X1 @ X3) @ X2)))))))))). % 1.04/1.30 thf(def_mvalid,definition,(mvalid = (!!))). % 1.04/1.30 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 1.04/1.30 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 1.04/1.30 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 1.04/1.30 thf(loeb,conjecture,(![X1:$i>$o]:(![X2:$i]:((~((~((![X3:$i]:(((r @ X2) @ X3) => ((~((~((![X4:$i]:(((r @ X3) @ X4) => (X1 @ X4))))))) => (X1 @ X3)))))))) => (![X3:$i]:(((r @ X2) @ X3) => (X1 @ X3))))))). % 1.04/1.30 thf(h0,negated_conjecture,(~(sP1)),inference(assume_negation,[status(cth)],[loeb])). % 1.04/1.30 thf(gl,axiom,(![X1:$i>$o]:(mvalid @ ((mimpl @ ((mbox @ r) @ ((mimpl @ ((mbox @ r) @ X1)) @ X1))) @ ((mbox @ r) @ X1))))). % 1.04/1.30 thf(1,plain,sP1,inference(preprocess,[status(thm)],[gl]). % 1.04/1.30 thf(2,plain,$false,inference(tab_conflict,[status(thm),assumptions([h0])],[1,h0])). % 1.04/1.30 thf(0,theorem,(![X1:$i>$o]:(![X2:$i]:((~((~((![X3:$i]:(((r @ X2) @ X3) => ((~((~((![X4:$i]:(((r @ X3) @ X4) => (X1 @ X4))))))) => (X1 @ X3)))))))) => (![X3:$i]:(((r @ X2) @ X3) => (X1 @ X3)))))),inference(contra,[status(thm),contra(discharge,[h0])],[2,h0])). % 1.04/1.30 % SZS output end Proof %------------------------------------------------------------------------------