%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SET924^1 : TPTP v9.2.0. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n029.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 02:26:34 PM UTC 2025 % Result : Theorem 1.07s 1.26s % Output : Proof 1.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET924^1 : TPTP v9.2.0. Released v8.1.0. % 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n029.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 14:38:53 EDT 2025 % 0.13/0.34 % CPUTime : % 1.07/1.26 % SZS status Theorem % 1.07/1.26 % Mode: mode506 % 1.07/1.26 % Inferences: 0 % 1.07/1.26 % SZS output start Proof % 1.07/1.26 thf(ty_mworld, type, mworld : $tType). % 1.07/1.26 thf(ty_singleton, type, singleton : ($i>$i)). % 1.07/1.26 thf(ty_mactual, type, mactual : mworld). % 1.07/1.26 thf(ty_qmltpeq, type, qmltpeq : ($i>$i>mworld>$o)). % 1.07/1.26 thf(ty_set_difference, type, set_difference : ($i>$i>$i)). % 1.07/1.26 thf(ty_in, type, in : ($i>$i>mworld>$o)). % 1.07/1.26 thf(sP1,plain,sP1 <=> (![X1:$i]:(![X2:$i]:((((qmltpeq @ ((set_difference @ (singleton @ X1)) @ X2)) @ (singleton @ X1)) @ mactual) = (~((((in @ X1) @ X2) @ mactual)))))),introduced(definition,[new_symbols(definition,[sP1])])). % 1.07/1.26 thf(def_mlocal,definition,(mlocal = (^[X1:mworld>$o]:(X1 @ mactual)))). % 1.07/1.26 thf(def_mnot,definition,(mnot = (^[X1:mworld>$o]:(^[X2:mworld]:(~((X1 @ X2))))))). % 1.07/1.26 thf(def_mand,definition,(mand = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 1.07/1.26 thf(def_mor,definition,(mor = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((~((X1 @ X3))) => (X2 @ X3))))))). % 1.07/1.26 thf(def_mimplies,definition,(mimplies = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) => (X2 @ X3))))))). % 1.07/1.26 thf(def_mequiv,definition,(mequiv = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) = (X2 @ X3))))))). % 1.07/1.26 thf(def_mbox,definition,(mbox = (^[X1:mworld>$o]:(^[X2:mworld]:(![X3:mworld]:(((mrel @ X2) @ X3) => (X1 @ X3))))))). % 1.07/1.26 thf(def_mdia,definition,(mdia = (^[X1:mworld>$o]:(^[X2:mworld]:(~((![X3:mworld]:(((mrel @ X2) @ X3) => (~((X1 @ X3))))))))))). % 1.07/1.26 thf(def_mforall_di,definition,(mforall_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(![X3:$i]:((X1 @ X3) @ X2)))))). % 1.07/1.26 thf(def_mexists_di,definition,(mexists_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(~((![X3:$i]:(~(((X1 @ X3) @ X2)))))))))). % 1.07/1.26 thf(t67_zfmisc_1,conjecture,sP1). % 1.07/1.26 thf(h0,negated_conjecture,(~(sP1)),inference(assume_negation,[status(cth)],[t67_zfmisc_1])). % 1.07/1.26 thf(l34_zfmisc_1,axiom,(mlocal @ (mforall_di @ (^[X1:$i]:(mforall_di @ (^[X2:$i]:((mequiv @ ((qmltpeq @ ((set_difference @ (singleton @ X1)) @ X2)) @ (singleton @ X1))) @ (mnot @ ((in @ X1) @ X2))))))))). % 1.07/1.26 thf(1,plain,sP1,inference(preprocess,[status(thm)],[l34_zfmisc_1]). % 1.07/1.26 thf(2,plain,$false,inference(tab_conflict,[status(thm),assumptions([h0])],[1,h0])). % 1.07/1.26 thf(0,theorem,sP1,inference(contra,[status(thm),contra(discharge,[h0])],[2,h0])). % 1.07/1.26 % SZS output end Proof %------------------------------------------------------------------------------