0.03/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.10 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s 0.09/0.30 Computer : n005.cluster.edu 0.09/0.30 Model : x86_64 x86_64 0.09/0.30 CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.30 RAMPerCPU : 8042.1875MB 0.09/0.30 OS : Linux 3.10.0-693.el7.x86_64 0.09/0.30 % CPULimit : 1440 0.09/0.30 % DateTime : Mon Jul 3 07:27:45 EDT 2023 0.09/0.30 % CPUTime : 10.90/11.19 % SZS status Theorem 10.90/11.19 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1 10.90/11.19 % Inferences: 4 10.90/11.19 % SZS output start Proof 10.90/11.19 thf(ty_a, type, a : $tType). 10.90/11.19 thf(ty_product_prod_a_a, type, product_prod_a_a : $tType). 10.90/11.19 thf(ty_set_Product_prod_a_a, type, set_Product_prod_a_a : $tType). 10.90/11.19 thf(ty_real, type, real : $tType). 10.90/11.19 thf(ty_zero_zero_real, type, zero_zero_real : real). 10.90/11.19 thf(ty_real_V1035702895aleR_a, type, real_V1035702895aleR_a : (real>a>a)). 10.90/11.19 thf(ty_relation, type, relation : set_Product_prod_a_a). 10.90/11.19 thf(ty_member449909584od_a_a, type, member449909584od_a_a : (product_prod_a_a>set_Product_prod_a_a>$o)). 10.90/11.19 thf(ty_v, type, v : real). 10.90/11.19 thf(ty_plus_plus_a, type, plus_plus_a : (a>a>a)). 10.90/11.19 thf(ty_u, type, u : real). 10.90/11.19 thf(ty_y, type, y : a). 10.90/11.19 thf(ty_one_one_real, type, one_one_real : real). 10.90/11.19 thf(ty_x, type, x : a). 10.90/11.19 thf(ty_product_Pair_a_a, type, product_Pair_a_a : (a>a>product_prod_a_a)). 10.90/11.19 thf(sP1,plain,sP1 <=> (u = zero_zero_real),introduced(definition,[new_symbols(definition,[sP1])])). 10.90/11.19 thf(sP2,plain,sP2 <=> ((member449909584od_a_a @ ((product_Pair_a_a @ ((plus_plus_a @ ((real_V1035702895aleR_a @ u) @ x)) @ ((real_V1035702895aleR_a @ v) @ y))) @ y)) @ relation),introduced(definition,[new_symbols(definition,[sP2])])). 10.90/11.19 thf(conj_0,conjecture,sP2). 10.90/11.19 thf(h0,negated_conjecture,(~(sP2)),inference(assume_negation,[status(cth)],[conj_0])). 10.90/11.19 thf(h1,assumption,(~(sP1)),introduced(assumption,[])). 10.90/11.19 thf(h2,assumption,sP2,introduced(assumption,[])). 10.90/11.19 thf(h3,assumption,((~(sP1)) => (u = one_one_real)),introduced(assumption,[])). 10.90/11.19 thf(h4,assumption,sP1,introduced(assumption,[])). 10.90/11.19 thf(h5,assumption,(u = one_one_real),introduced(assumption,[])). 10.90/11.19 thf(1,plain,$false,inference(tab_conflict,[status(thm),assumptions([h4,h3,h1,h0])],[h4,h1])). 10.90/11.19 tff(pax53, axiom, (p53=>(fu)=(fone_one_real)), file('', pax53)). 10.90/11.19 tff(pax19, axiom, (p19=>![X45:a, X46:a, X39:a]:((fplus_plus_a @ X45 @ X46)=(fplus_plus_a @ X45 @ X39)=>(X46)=(X39))), file('', pax19)). 10.90/11.19 tff(pax9, axiom, (p9=>![X52:a]:(fplus_plus_a @ X52 @ fzero_zero_a)=(X52)), file('', pax9)). 10.90/11.19 tff(pax20, axiom, (p20=>![X43:real, X44:real, X39:a]:(freal_V1035702895aleR_a @ (fplus_plus_real @ X43 @ X44) @ X39)=(fplus_plus_a @ (freal_V1035702895aleR_a @ X43 @ X39) @ (freal_V1035702895aleR_a @ X44 @ X39))), file('', pax20)). 10.90/11.19 tff(pax13, axiom, (p13=>(fplus_plus_real @ fu @ fv)=(fone_one_real)), file('', pax13)). 10.90/11.19 fof(ax26, axiom, p53, file('', ax26)). 10.90/11.19 tff(pax18, axiom, (p18=>![X45:a]:(freal_V1035702895aleR_a @ fone_one_real @ X45)=(X45)), file('', pax18)). 10.90/11.19 fof(ax48, axiom, p19, file('', ax48)). 10.90/11.19 fof(ax58, axiom, p9, file('', ax58)). 10.90/11.19 fof(ax47, axiom, p20, file('', ax47)). 10.90/11.19 fof(ax54, axiom, p13, file('', ax54)). 10.90/11.19 fof(ax49, axiom, p18, file('', ax49)). 10.90/11.19 tff(nax30, axiom, (p30<=fmember449909584od_a_a @ (fproduct_Pair_a_a @ (fplus_plus_a @ (freal_V1035702895aleR_a @ fu @ fx) @ (freal_V1035702895aleR_a @ fv @ fy)) @ fy) @ frelation), file('', nax30)). 10.90/11.19 fof(ax37, axiom, ~(p30), file('', ax37)). 10.90/11.19 tff(pax44, axiom, (p44=>fmember449909584od_a_a @ (fproduct_Pair_a_a @ fx @ fy) @ frelation), file('', pax44)). 10.90/11.19 fof(ax23, axiom, p44, file('', ax23)). 10.90/11.19 tff(c_0_16, plain, (~p53|(fu)=(fone_one_real)), inference(fof_nnf,[status(thm)],[pax53])). 10.90/11.19 tff(c_0_17, plain, ![X222:a, X223:a, X224:a]:(~p19|((fplus_plus_a @ X222 @ X223)!=(fplus_plus_a @ X222 @ X224)|(X223)=(X224))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax19])])])). 10.90/11.19 tff(c_0_18, plain, ![X262:a]:(~p9|(fplus_plus_a @ X262 @ fzero_zero_a)=(X262)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax9])])])). 10.90/11.19 tff(c_0_19, plain, ![X216:real, X217:real, X218:a]:(~p20|(freal_V1035702895aleR_a @ (fplus_plus_real @ X216 @ X217) @ X218)=(fplus_plus_a @ (freal_V1035702895aleR_a @ X216 @ X218) @ (freal_V1035702895aleR_a @ X217 @ X218))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax20])])])). 10.90/11.19 tff(c_0_20, plain, (~p13|(fplus_plus_real @ fu @ fv)=(fone_one_real)), inference(fof_nnf,[status(thm)],[pax13])). 10.90/11.19 thf(c_0_21, plain, ((fu)=(fone_one_real)|~p53), inference(split_conjunct,[status(thm)],[c_0_16])). 10.90/11.19 thf(c_0_22, plain, (p53), inference(split_conjunct,[status(thm)],[ax26])). 10.90/11.19 tff(c_0_23, plain, ![X228:a]:(~p18|(freal_V1035702895aleR_a @ fone_one_real @ X228)=(X228)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax18])])])). 10.90/11.19 thf(c_0_24, plain, ![X3:a, X2:a, X1:a]:((X2)=(X3)|~p19|(fplus_plus_a @ X1 @ X2)!=(fplus_plus_a @ X1 @ X3)), inference(split_conjunct,[status(thm)],[c_0_17])). 10.90/11.19 thf(c_0_25, plain, (p19), inference(split_conjunct,[status(thm)],[ax48])). 10.90/11.19 thf(c_0_26, plain, ![X1:a]:((fplus_plus_a @ X1 @ fzero_zero_a)=(X1)|~p9), inference(split_conjunct,[status(thm)],[c_0_18])). 10.90/11.19 thf(c_0_27, plain, (p9), inference(split_conjunct,[status(thm)],[ax58])). 10.90/11.19 thf(c_0_28, plain, ![X1:a, X7:real, X6:real]:((freal_V1035702895aleR_a @ (fplus_plus_real @ X6 @ X7) @ X1)=(fplus_plus_a @ (freal_V1035702895aleR_a @ X6 @ X1) @ (freal_V1035702895aleR_a @ X7 @ X1))|~p20), inference(split_conjunct,[status(thm)],[c_0_19])). 10.90/11.19 thf(c_0_29, plain, (p20), inference(split_conjunct,[status(thm)],[ax47])). 10.90/11.19 thf(c_0_30, plain, ((fplus_plus_real @ fu @ fv)=(fone_one_real)|~p13), inference(split_conjunct,[status(thm)],[c_0_20])). 10.90/11.19 thf(c_0_31, plain, (fone_one_real)=(fu), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21, c_0_22])])). 10.90/11.19 thf(c_0_32, plain, (p13), inference(split_conjunct,[status(thm)],[ax54])). 10.90/11.19 thf(c_0_33, plain, ![X1:a]:((freal_V1035702895aleR_a @ fone_one_real @ X1)=(X1)|~p18), inference(split_conjunct,[status(thm)],[c_0_23])). 10.90/11.19 thf(c_0_34, plain, (p18), inference(split_conjunct,[status(thm)],[ax49])). 10.90/11.19 tff(c_0_35, plain, (~fmember449909584od_a_a @ (fproduct_Pair_a_a @ (fplus_plus_a @ (freal_V1035702895aleR_a @ fu @ fx) @ (freal_V1035702895aleR_a @ fv @ fy)) @ fy) @ frelation|p30), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax30])])). 10.90/11.19 fof(c_0_36, plain, ~p30, inference(fof_simplification,[status(thm)],[ax37])). 10.90/11.19 thf(c_0_37, plain, ![X1:a, X2:a, X3:a]:((X1)=(X2)|(fplus_plus_a @ X3 @ X1)!=(fplus_plus_a @ X3 @ X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24, c_0_25])])). 10.90/11.19 thf(c_0_38, plain, ![X1:a]:(fplus_plus_a @ X1 @ fzero_zero_a)=(X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26, c_0_27])])). 10.90/11.19 thf(c_0_39, plain, ![X1:a, X7:real, X6:real]:(freal_V1035702895aleR_a @ (fplus_plus_real @ X6 @ X7) @ X1)=(fplus_plus_a @ (freal_V1035702895aleR_a @ X6 @ X1) @ (freal_V1035702895aleR_a @ X7 @ X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28, c_0_29])])). 10.90/11.19 thf(c_0_40, plain, (fplus_plus_real @ fu @ fv)=(fu), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30, c_0_31]), c_0_32])])). 10.90/11.19 thf(c_0_41, plain, ![X1:a]:(freal_V1035702895aleR_a @ fu @ X1)=(X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33, c_0_31]), c_0_34])])). 10.90/11.19 tff(c_0_42, plain, (~p44|fmember449909584od_a_a @ (fproduct_Pair_a_a @ fx @ fy) @ frelation), inference(fof_nnf,[status(thm)],[pax44])). 10.90/11.19 thf(c_0_43, plain, (p30|~fmember449909584od_a_a @ (fproduct_Pair_a_a @ (fplus_plus_a @ (freal_V1035702895aleR_a @ fu @ fx) @ (freal_V1035702895aleR_a @ fv @ fy)) @ fy) @ frelation), inference(split_conjunct,[status(thm)],[c_0_35])). 10.90/11.19 thf(c_0_44, plain, (~p30), inference(split_conjunct,[status(thm)],[c_0_36])). 10.90/11.19 thf(c_0_45, plain, ![X1:a, X2:a]:((X1)=(fzero_zero_a)|(fplus_plus_a @ X2 @ X1)!=(X2)), inference(spm,[status(thm)],[c_0_37, c_0_38])). 10.90/11.19 thf(c_0_46, plain, ![X1:a]:(fplus_plus_a @ X1 @ (freal_V1035702895aleR_a @ fv @ X1))=(X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_40]), c_0_41]), c_0_41])). 10.90/11.19 thf(c_0_47, plain, (fmember449909584od_a_a @ (fproduct_Pair_a_a @ fx @ fy) @ frelation|~p44), inference(split_conjunct,[status(thm)],[c_0_42])). 10.90/11.19 thf(c_0_48, plain, (p44), inference(split_conjunct,[status(thm)],[ax23])). 10.90/11.19 thf(c_0_49, plain, ~fmember449909584od_a_a @ (fproduct_Pair_a_a @ (fplus_plus_a @ fx @ (freal_V1035702895aleR_a @ fv @ fy)) @ fy) @ frelation, inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_43, c_0_41]), c_0_44])). 10.90/11.19 thf(c_0_50, plain, ![X1:a]:(freal_V1035702895aleR_a @ fv @ X1)=(fzero_zero_a), inference(spm,[status(thm)],[c_0_45, c_0_46])). 10.90/11.19 thf(c_0_51, plain, fmember449909584od_a_a @ (fproduct_Pair_a_a @ fx @ fy) @ frelation, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47, c_0_48])])). 10.90/11.19 thf(c_0_52, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49, c_0_50]), c_0_38]), c_0_51])]), ['proof']). 10.90/11.19 thf(2,plain,$false,inference(eprover,[status(thm),assumptions([h5,h3,h1,h0])],[])). 10.90/11.19 thf(3,plain,$false,inference(tab_imp,[status(thm),assumptions([h3,h1,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h5])],[h3,1,2,h4,h5])). 10.90/11.19 thf(4,plain,$false,inference(tab_conflict,[status(thm),assumptions([h2,h1,h0])],[h2,h0])). 10.90/11.19 thf(fact_6__092_060open_062u_A_092_060noteq_062_A0_A_092_060and_062_Au_A_092_060noteq_062_A1_A_092_060longrightarrow_062_Au_A_K_092_060_094sub_062R_Ax_A_L_Av_A_K_092_060_094sub_062R_Ay_A_092_060succeq_062_Ay_092_060close_062,axiom,((~(((~(sP1)) => (u = one_one_real)))) => sP2)). 10.90/11.19 thf(5,plain,$false,inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h2])],[fact_6__092_060open_062u_A_092_060noteq_062_A0_A_092_060and_062_Au_A_092_060noteq_062_A1_A_092_060longrightarrow_062_Au_A_K_092_060_094sub_062R_Ax_A_L_Av_A_K_092_060_094sub_062R_Ay_A_092_060succeq_062_Ay_092_060close_062,3,4,h3,h2])). 10.90/11.19 thf(6,plain,$false,inference(tab_conflict,[status(thm),assumptions([h4,h3,h2,h0])],[h2,h0])). 10.90/11.19 thf(7,plain,$false,inference(tab_conflict,[status(thm),assumptions([h5,h3,h2,h0])],[h2,h0])). 10.90/11.19 thf(8,plain,$false,inference(tab_imp,[status(thm),assumptions([h3,h2,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h5])],[h3,6,7,h4,h5])). 10.90/11.19 thf(9,plain,$false,inference(tab_conflict,[status(thm),assumptions([h2,h2,h0])],[h2,h0])). 10.90/11.19 thf(10,plain,$false,inference(tab_imp,[status(thm),assumptions([h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h2])],[fact_6__092_060open_062u_A_092_060noteq_062_A0_A_092_060and_062_Au_A_092_060noteq_062_A1_A_092_060longrightarrow_062_Au_A_K_092_060_094sub_062R_Ax_A_L_Av_A_K_092_060_094sub_062R_Ay_A_092_060succeq_062_Ay_092_060close_062,8,9,h3,h2])). 10.90/11.19 thf(fact_7_u__0,axiom,(sP1 => sP2)). 10.90/11.19 thf(11,plain,$false,inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_7_u__0,5,10,h1,h2])). 10.90/11.19 thf(0,theorem,sP2,inference(contra,[status(thm),contra(discharge,[h0])],[11,h0])). 10.90/11.19 % SZS output end Proof 10.90/11.19 EOF