0.03/0.11 % Problem : SLH0183^1 : TPTP v8.2.0. Released v8.2.0. 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s 0.11/0.32 Computer : n029.cluster.edu 0.11/0.32 Model : x86_64 x86_64 0.11/0.32 CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 RAMPerCPU : 8042.1875MB 0.11/0.32 OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 30 0.11/0.32 % DateTime : Mon Jul 3 04:02:42 EDT 2023 0.11/0.33 % CPUTime : 1.75/1.92 % SZS status Theorem 1.75/1.92 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1 1.75/1.92 % Inferences: 3 1.75/1.92 % SZS output start Proof 1.75/1.92 thf(ty_set_real, type, set_real : $tType). 1.75/1.92 thf(ty_nat, type, nat : $tType). 1.75/1.92 thf(ty_real, type, real : $tType). 1.75/1.92 thf(ty_a, type, a : real). 1.75/1.92 thf(ty_times_times_real, type, times_times_real : (real>real>real)). 1.75/1.92 thf(ty_minus_minus_real, type, minus_minus_real : (real>real>real)). 1.75/1.92 thf(ty_divide_divide_real, type, divide_divide_real : (real>real>real)). 1.75/1.92 thf(ty_plus_plus_real, type, plus_plus_real : (real>real>real)). 1.75/1.92 thf(ty_n, type, n : nat). 1.75/1.92 thf(ty_b, type, b : real). 1.75/1.92 thf(ty_eigen__0, type, eigen__0 : nat). 1.75/1.92 thf(ty_semiri5074537144036343181t_real, type, semiri5074537144036343181t_real : (nat>real)). 1.75/1.92 thf(ty_k, type, k : set_real). 1.75/1.92 thf(ty_set_or1222579329274155063t_real, type, set_or1222579329274155063t_real : (real>real>set_real)). 1.75/1.92 thf(ty_one_one_real, type, one_one_real : real). 1.75/1.92 thf(conj_0,conjecture,((ord_less_eq_set_real @ k) @ ((set_or1222579329274155063t_real @ a) @ b))). 1.75/1.92 thf(h0,negated_conjecture,(~(((ord_less_eq_set_real @ k) @ ((set_or1222579329274155063t_real @ a) @ b)))),inference(assume_negation,[status(cth)],[conj_0])). 1.75/1.92 thf(h1,assumption,(k = ((set_or1222579329274155063t_real @ ((plus_plus_real @ a) @ ((times_times_real @ ((minus_minus_real @ b) @ a)) @ ((divide_divide_real @ (semiri5074537144036343181t_real @ eigen__0)) @ (semiri5074537144036343181t_real @ n))))) @ ((plus_plus_real @ a) @ ((times_times_real @ ((minus_minus_real @ b) @ a)) @ ((divide_divide_real @ ((plus_plus_real @ one_one_real) @ (semiri5074537144036343181t_real @ eigen__0))) @ (semiri5074537144036343181t_real @ n)))))),introduced(assumption,[])). 1.75/1.92 tff(pax65, axiom, (p65=>![X4:set_real, X5:set_set_real]:(fmember_set_real @ X4 @ X5=>ford_less_eq_set_real @ X4 @ (fcomple3096694443085538997t_real @ X5))), file('', pax65)). 1.75/1.92 tff(pax2, axiom, (p2=>fmember_set_real @ fk @ (fregular_division @ fa @ fb @ fn)), file('', pax2)). 1.75/1.92 tff(pax4, axiom, (p4=>(fcomple3096694443085538997t_real @ (fregular_division @ fa @ fb @ fn))=(fset_or1222579329274155063t_real @ fa @ fb)), file('', pax4)). 1.75/1.92 tff(nax72, axiom, (p72<=ford_less_eq_set_real @ fk @ (fset_or1222579329274155063t_real @ fa @ fb)), file('', nax72)). 1.75/1.92 fof(ax9, axiom, ~(p72), file('', ax9)). 1.75/1.92 fof(ax16, axiom, p65, file('', ax16)). 1.75/1.92 fof(ax79, axiom, p2, file('', ax79)). 1.75/1.92 fof(ax77, axiom, p4, file('', ax77)). 1.75/1.92 tff(c_0_8, plain, ![X90:set_real, X91:set_set_real]:(~p65|(~fmember_set_real @ X90 @ X91|ford_less_eq_set_real @ X90 @ (fcomple3096694443085538997t_real @ X91))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax65])])])). 1.75/1.92 tff(c_0_9, plain, (~p2|fmember_set_real @ fk @ (fregular_division @ fa @ fb @ fn)), inference(fof_nnf,[status(thm)],[pax2])). 1.75/1.92 tff(c_0_10, plain, (~p4|(fcomple3096694443085538997t_real @ (fregular_division @ fa @ fb @ fn))=(fset_or1222579329274155063t_real @ fa @ fb)), inference(fof_nnf,[status(thm)],[pax4])). 1.75/1.92 tff(c_0_11, plain, (~ford_less_eq_set_real @ fk @ (fset_or1222579329274155063t_real @ fa @ fb)|p72), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax72])])). 1.75/1.92 fof(c_0_12, plain, ~p72, inference(fof_simplification,[status(thm)],[ax9])). 1.75/1.92 thf(c_0_13, plain, ![X5:set_set_real, X1:set_real]:(ford_less_eq_set_real @ X1 @ (fcomple3096694443085538997t_real @ X5)|~p65|~fmember_set_real @ X1 @ X5), inference(split_conjunct,[status(thm)],[c_0_8])). 1.75/1.92 thf(c_0_14, plain, (p65), inference(split_conjunct,[status(thm)],[ax16])). 1.75/1.92 thf(c_0_15, plain, (fmember_set_real @ fk @ (fregular_division @ fa @ fb @ fn)|~p2), inference(split_conjunct,[status(thm)],[c_0_9])). 1.75/1.92 thf(c_0_16, plain, (p2), inference(split_conjunct,[status(thm)],[ax79])). 1.75/1.92 thf(c_0_17, plain, ((fcomple3096694443085538997t_real @ (fregular_division @ fa @ fb @ fn))=(fset_or1222579329274155063t_real @ fa @ fb)|~p4), inference(split_conjunct,[status(thm)],[c_0_10])). 1.75/1.92 thf(c_0_18, plain, (p4), inference(split_conjunct,[status(thm)],[ax77])). 1.75/1.92 thf(c_0_19, plain, (p72|~ford_less_eq_set_real @ fk @ (fset_or1222579329274155063t_real @ fa @ fb)), inference(split_conjunct,[status(thm)],[c_0_11])). 1.75/1.92 thf(c_0_20, plain, (~p72), inference(split_conjunct,[status(thm)],[c_0_12])). 1.75/1.92 thf(c_0_21, plain, ![X5:set_set_real, X1:set_real]:(ford_less_eq_set_real @ X1 @ (fcomple3096694443085538997t_real @ X5)|~fmember_set_real @ X1 @ X5), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13, c_0_14])])). 1.75/1.92 thf(c_0_22, plain, fmember_set_real @ fk @ (fregular_division @ fa @ fb @ fn), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15, c_0_16])])). 1.75/1.92 thf(c_0_23, plain, (fcomple3096694443085538997t_real @ (fregular_division @ fa @ fb @ fn))=(fset_or1222579329274155063t_real @ fa @ fb), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17, c_0_18])])). 1.75/1.92 thf(c_0_24, plain, ~ford_less_eq_set_real @ fk @ (fset_or1222579329274155063t_real @ fa @ fb), inference(sr,[status(thm)],[c_0_19, c_0_20])). 1.75/1.92 thf(c_0_25, plain, ($false), inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_22]), c_0_23]), c_0_24]), ['proof']). 1.75/1.92 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h1,h0])],[])). 1.75/1.92 thf(fact_1261__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062k_O_AK_A_061_A_123a_A_L_A_Ib_A_N_Aa_J_A_K_A_Ireal_Ak_A_P_Areal_An_J_O_Oa_A_L_A_Ib_A_N_Aa_J_A_K_A_I_I1_A_L_Areal_Ak_J_A_P_Areal_An_J_125_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,(~((![X1:nat]:(~((k = ((set_or1222579329274155063t_real @ ((plus_plus_real @ a) @ ((times_times_real @ ((minus_minus_real @ b) @ a)) @ ((divide_divide_real @ (semiri5074537144036343181t_real @ X1)) @ (semiri5074537144036343181t_real @ n))))) @ ((plus_plus_real @ a) @ ((times_times_real @ ((minus_minus_real @ b) @ a)) @ ((divide_divide_real @ ((plus_plus_real @ one_one_real) @ (semiri5074537144036343181t_real @ X1))) @ (semiri5074537144036343181t_real @ n)))))))))))). 1.75/1.92 thf(2,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_1261__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062k_O_AK_A_061_A_123a_A_L_A_Ib_A_N_Aa_J_A_K_A_Ireal_Ak_A_P_Areal_An_J_O_Oa_A_L_A_Ib_A_N_Aa_J_A_K_A_I_I1_A_L_Areal_Ak_J_A_P_Areal_An_J_125_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,1,h1])). 1.75/1.92 thf(0,theorem,((ord_less_eq_set_real @ k) @ ((set_or1222579329274155063t_real @ a) @ b)),inference(contra,[status(thm),contra(discharge,[h0])],[2,h0])). 1.75/1.92 % SZS output end Proof 1.75/1.92 EOF