%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : GEG015^1 : TPTP v9.2.0. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n010.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 01:27:38 PM UTC 2025 % Result : Theorem 15.33s 15.87s % Output : Proof 15.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GEG015^1 : TPTP v9.2.0. Released v4.1.0. % 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.12/0.33 % Computer : n010.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Wed Oct 8 12:30:38 EDT 2025 % 0.12/0.33 % CPUTime : % 15.33/15.87 % SZS status Theorem % 15.33/15.87 % Mode: mode454 % 15.33/15.87 % Inferences: 21920 % 15.33/15.87 % SZS output start Proof % 15.33/15.87 thf(ty_reg, type, reg : $tType). % 15.33/15.87 thf(ty_a, type, a : ($i>$i>$o)). % 15.33/15.87 thf(ty_eigen__1, type, eigen__1 : $i). % 15.33/15.87 thf(ty_paris, type, paris : reg). % 15.33/15.87 thf(ty_eigen__0, type, eigen__0 : $i). % 15.33/15.87 thf(ty_france, type, france : reg). % 15.33/15.87 thf(ty_c, type, c : (reg>reg>$o)). % 15.33/15.87 thf(ty_eigen__31, type, eigen__31 : reg). % 15.33/15.87 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 15.33/15.87 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((((a @ eigen__0) @ X1) => (~((![X2:reg]:(![X3:reg]:((~((((![X4:reg]:(((c @ X4) @ X2) => ((c @ X4) @ X3))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2)))))) => (~((![X4:reg]:(((c @ X4) @ X2) => ((c @ X4) @ france)))))))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 15.33/15.87 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(((a @ X1) @ X2) => (~((![X3:reg]:(![X4:reg]:((~((((![X5:reg]:(((c @ X5) @ X3) => ((c @ X5) @ X4))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3)))))) => (~((![X5:reg]:(((c @ X5) @ X3) => ((c @ X5) @ france)))))))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ france)))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 15.33/15.87 thf(h1, assumption, (![X1:reg>$o]:(![X2:reg]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). % 15.33/15.87 thf(eigendef_eigen__31, definition, eigen__31 = (eps__1 @ (^[X1:reg]:(~((((c @ X1) @ france) => ((c @ X1) @ france)))))), introduced(definition,[new_symbols(definition,[eigen__31])])). % 15.33/15.87 thf(sP1,plain,sP1 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(((~(((![X3:reg]:(((c @ X3) @ paris) => ((c @ X3) @ france))) => (![X3:reg]:(((c @ X3) @ france) => ((c @ X3) @ paris)))))) => (~((![X3:reg]:((~((((c @ X3) @ paris) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ paris)))))))))))) => (((c @ X3) @ france) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ france)))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 15.33/15.87 thf(sP2,plain,sP2 <=> (![X1:reg]:(((c @ X1) @ france) => ((c @ X1) @ france))),introduced(definition,[new_symbols(definition,[sP2])])). % 15.33/15.87 thf(sP3,plain,sP3 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => (~((![X2:reg]:(![X3:reg]:((~((((![X4:reg]:(((c @ X4) @ X2) => ((c @ X4) @ X3))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2)))))) => (~((![X4:reg]:(((c @ X4) @ X2) => ((c @ X4) @ france)))))))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france)))))))))))),introduced(definition,[new_symbols(definition,[sP3])])). % 15.33/15.87 thf(sP4,plain,sP4 <=> ((![X1:reg]:(((c @ X1) @ france) => ((c @ X1) @ paris))) => (~((![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ france)))))),introduced(definition,[new_symbols(definition,[sP4])])). % 15.33/15.87 thf(sP5,plain,sP5 <=> (((a @ eigen__0) @ eigen__1) => (~(((~(((![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ france))) => (![X1:reg]:(((c @ X1) @ france) => ((c @ X1) @ paris)))))) => (~((![X1:reg]:((~((((c @ X1) @ paris) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))))) => (((c @ X1) @ france) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france)))))))))))))))))),introduced(definition,[new_symbols(definition,[sP5])])). % 15.33/15.87 thf(sP6,plain,sP6 <=> (![X1:reg]:(((c @ X1) @ france) => ((c @ X1) @ paris))),introduced(definition,[new_symbols(definition,[sP6])])). % 15.33/15.87 thf(sP7,plain,sP7 <=> ((c @ eigen__31) @ france),introduced(definition,[new_symbols(definition,[sP7])])). % 15.33/15.87 thf(sP8,plain,sP8 <=> ((~((sP4 => (~(sP2))))) => (~((![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ france)))))),introduced(definition,[new_symbols(definition,[sP8])])). % 15.33/15.87 thf(sP9,plain,sP9 <=> (((a @ eigen__0) @ eigen__1) => (~((![X1:reg]:(![X2:reg]:((~((((![X3:reg]:(((c @ X3) @ X1) => ((c @ X3) @ X2))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1)))))) => (~((![X3:reg]:(((c @ X3) @ X1) => ((c @ X3) @ france)))))))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france))))))))))),introduced(definition,[new_symbols(definition,[sP9])])). % 15.33/15.87 thf(sP10,plain,sP10 <=> (![X1:reg]:(![X2:reg]:((~((((![X3:reg]:(((c @ X3) @ X1) => ((c @ X3) @ X2))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1)))))) => (~((![X3:reg]:(((c @ X3) @ X1) => ((c @ X3) @ france)))))))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france)))))))),introduced(definition,[new_symbols(definition,[sP10])])). % 15.33/15.87 thf(sP11,plain,sP11 <=> (sP4 => (~(sP2))),introduced(definition,[new_symbols(definition,[sP11])])). % 15.33/15.87 thf(sP12,plain,sP12 <=> (sP7 => sP7),introduced(definition,[new_symbols(definition,[sP12])])). % 15.33/15.87 thf(sP13,plain,sP13 <=> ((~(((![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ france))) => sP6))) => (~((![X1:reg]:((~((((c @ X1) @ paris) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))))) => (((c @ X1) @ france) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france))))))))))))))),introduced(definition,[new_symbols(definition,[sP13])])). % 15.33/15.87 thf(sP14,plain,sP14 <=> (![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ france))),introduced(definition,[new_symbols(definition,[sP14])])). % 15.33/15.87 thf(sP15,plain,sP15 <=> (sP14 => sP6),introduced(definition,[new_symbols(definition,[sP15])])). % 15.33/15.87 thf(sP16,plain,sP16 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => (~(sP13)))),introduced(definition,[new_symbols(definition,[sP16])])). % 15.33/15.87 thf(sP17,plain,sP17 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(sP10))))),introduced(definition,[new_symbols(definition,[sP17])])). % 15.33/15.87 thf(sP18,plain,sP18 <=> (![X1:reg]:((~((((![X2:reg]:(((c @ X2) @ france) => ((c @ X2) @ X1))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ france)))))) => (~(sP2))))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ france))))))),introduced(definition,[new_symbols(definition,[sP18])])). % 15.33/15.87 thf(sP19,plain,sP19 <=> ((a @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP19])])). % 15.33/15.87 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))). % 15.33/15.87 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 15.33/15.87 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 15.33/15.87 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 15.33/15.87 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 15.33/15.87 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 15.33/15.87 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))). % 15.33/15.87 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 15.33/15.87 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))). % 15.33/15.87 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 15.33/15.87 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 15.33/15.87 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 15.33/15.87 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))). % 15.33/15.87 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 15.33/15.87 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 15.33/15.87 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 15.33/15.87 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 15.33/15.87 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 15.33/15.87 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 15.33/15.87 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 15.33/15.87 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 15.33/15.87 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 15.33/15.87 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))). % 15.33/15.87 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))). % 15.33/15.87 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))). % 15.33/15.87 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))). % 15.33/15.87 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))). % 15.33/15.87 thf(def_mvalid,definition,(mvalid = (!!))). % 15.33/15.87 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 15.33/15.87 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 15.33/15.87 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 15.33/15.87 thf(def_dc,definition,(dc = (^[X1:reg]:(^[X2:reg]:(~(((c @ X1) @ X2))))))). % 15.33/15.87 thf(def_p,definition,(p = (^[X1:reg]:(^[X2:reg]:(![X3:reg]:(((c @ X3) @ X1) => ((c @ X3) @ X2))))))). % 15.33/15.87 thf(def_eq,definition,(eq = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => (~(((p @ X2) @ X1)))))))))). % 15.33/15.87 thf(def_o,definition,(o = (^[X1:reg]:(^[X2:reg]:(~((![X3:reg]:(((p @ X3) @ X1) => (~(((p @ X3) @ X2))))))))))). % 15.33/15.87 thf(def_po,definition,(po = (^[X1:reg]:(^[X2:reg]:(~(((~((((o @ X1) @ X2) => ((p @ X1) @ X2)))) => ((p @ X2) @ X1)))))))). % 15.33/15.87 thf(def_ec,definition,(ec = (^[X1:reg]:(^[X2:reg]:(~((((c @ X1) @ X2) => ((o @ X1) @ X2)))))))). % 15.33/15.87 thf(def_pp,definition,(pp = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => ((p @ X2) @ X1)))))))). % 15.33/15.87 thf(def_tpp,definition,(tpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))). % 15.33/15.87 thf(def_ntpp,definition,(ntpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (~((![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))))). % 15.33/15.87 thf(con,conjecture,(![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~((![X3:reg]:(![X4:reg]:((~(((~((~(((![X5:reg]:(((c @ X5) @ X3) => ((c @ X5) @ X4))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3)))))))))) => (~((![X5:reg]:(((c @ X5) @ X3) => ((c @ X5) @ france)))))))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ france)))))))))))))). % 15.33/15.87 thf(h2,negated_conjecture,(~(sP17)),inference(assume_negation,[status(cth)],[con])). % 15.33/15.87 thf(1,plain,(sP12 | ~(sP7)),inference(prop_rule,[status(thm)],[])). % 15.33/15.87 thf(2,plain,(sP12 | sP7),inference(prop_rule,[status(thm)],[])). % 15.33/15.87 thf(3,plain,(sP4 | sP6),inference(prop_rule,[status(thm)],[])). % 15.33/15.87 thf(4,plain,(sP2 | ~(sP12)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__31])). % 15.33/15.87 thf(5,plain,(~(sP18) | sP8),inference(all_rule,[status(thm)],[])). % 15.33/15.87 thf(6,plain,((~(sP8) | sP11) | ~(sP14)),inference(prop_rule,[status(thm)],[])). % 15.33/15.87 thf(7,plain,((~(sP11) | ~(sP4)) | ~(sP2)),inference(prop_rule,[status(thm)],[])). % 15.33/15.87 thf(8,plain,(~(sP10) | sP18),inference(all_rule,[status(thm)],[])). % 15.33/15.87 thf(9,plain,(sP15 | ~(sP6)),inference(prop_rule,[status(thm)],[])). % 15.33/15.87 thf(10,plain,(sP15 | sP14),inference(prop_rule,[status(thm)],[])). % 15.33/15.87 thf(11,plain,(sP13 | ~(sP15)),inference(prop_rule,[status(thm)],[])). % 15.33/15.87 thf(12,plain,(~(sP1) | sP16),inference(all_rule,[status(thm)],[])). % 15.33/15.87 thf(13,plain,(~(sP16) | sP5),inference(all_rule,[status(thm)],[])). % 15.33/15.87 thf(14,plain,((~(sP5) | ~(sP19)) | ~(sP13)),inference(prop_rule,[status(thm)],[])). % 15.33/15.87 thf(15,plain,(sP9 | sP10),inference(prop_rule,[status(thm)],[])). % 15.33/15.87 thf(16,plain,(sP9 | sP19),inference(prop_rule,[status(thm)],[])). % 15.33/15.87 thf(17,plain,(sP3 | ~(sP9)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 15.33/15.87 thf(18,plain,(sP17 | ~(sP3)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 15.33/15.87 thf(ax3,axiom,(mvalid @ ((mbox @ a) @ (^[X1:$i]:((ntpp @ paris) @ france))))). % 15.33/15.87 thf(19,plain,sP1,inference(preprocess,[status(thm)],[ax3]). % 15.33/15.87 thf(20,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,h2])). % 15.33/15.87 thf(21,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[20,h1])). % 15.33/15.87 thf(22,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[21,h0])). % 15.33/15.87 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~((![X3:reg]:(![X4:reg]:((~(((~((~(((![X5:reg]:(((c @ X5) @ X3) => ((c @ X5) @ X4))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3)))))))))) => (~((![X5:reg]:(((c @ X5) @ X3) => ((c @ X5) @ france)))))))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ france))))))))))))),inference(contra,[status(thm),contra(discharge,[h2])],[20,h2])). % 15.33/15.87 % SZS output end Proof %------------------------------------------------------------------------------