0.03/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s 0.13/0.35 Computer : n020.cluster.edu 0.13/0.35 Model : x86_64 x86_64 0.13/0.35 CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 RAMPerCPU : 8042.1875MB 0.13/0.35 OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 1440 0.13/0.35 % DateTime : Mon Jul 3 07:45:46 EDT 2023 0.13/0.35 % CPUTime : 1.12/1.59 % SZS status Theorem 1.12/1.59 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1 1.12/1.59 % Inferences: 0 1.12/1.59 % SZS output start Proof 1.12/1.59 thf(ty_finite1489363574real_n, type, finite1489363574real_n : $tType). 1.12/1.59 thf(ty_n, type, n : $tType). 1.12/1.59 thf(ty_int, type, int : $tType). 1.12/1.59 thf(ty_real, type, real : $tType). 1.12/1.59 thf(ty_minus_minus_real, type, minus_minus_real : (real>real>real)). 1.12/1.59 thf(ty_eigen__0, type, eigen__0 : int). 1.12/1.59 thf(ty_y, type, y : finite1489363574real_n). 1.12/1.59 thf(ty_i, type, i : n). 1.12/1.59 thf(ty_finite772340589real_n, type, finite772340589real_n : (finite1489363574real_n>n>real)). 1.12/1.59 thf(ty_x, type, x : finite1489363574real_n). 1.12/1.59 thf(ty_ring_1_of_int_real, type, ring_1_of_int_real : (int>real)). 1.12/1.59 thf(conj_0,conjecture,((ring_1_of_int_real @ (abs_abs_int @ m)) = (abs_abs_real @ ((finite772340589real_n @ ((minus_1037315151real_n @ x) @ y)) @ i)))). 1.12/1.59 thf(h0,negated_conjecture,(~(((ring_1_of_int_real @ (abs_abs_int @ m)) = (abs_abs_real @ ((finite772340589real_n @ ((minus_1037315151real_n @ x) @ y)) @ i))))),inference(assume_negation,[status(cth)],[conj_0])). 1.12/1.59 thf(h1,assumption,((ring_1_of_int_real @ eigen__0) = ((minus_minus_real @ ((finite772340589real_n @ x) @ i)) @ ((finite772340589real_n @ y) @ i))),introduced(assumption,[])). 1.12/1.59 tff(pax78, axiom, (p78=>![X5:int]:(fring_1_of_int_real @ (fabs_abs_int @ X5))=(fabs_abs_real @ (fring_1_of_int_real @ X5))), file('', pax78)). 1.12/1.59 tff(pax16, axiom, (p16=>(fring_1_of_int_real @ f__0)=(fminus_minus_real @ (ffinite772340589real_n @ fx @ fi) @ (ffinite772340589real_n @ fy @ fi))), file('', pax16)). 1.12/1.59 tff(nax59, axiom, (p59<=(fring_1_of_int_real @ (fabs_abs_int @ fm))=(fabs_abs_real @ (ffinite772340589real_n @ (fminus_1037315151real_n @ fx @ fy) @ fi))), file('', nax59)). 1.12/1.59 fof(ax3, axiom, p78, file('', ax3)). 1.12/1.59 fof(ax22, axiom, ~(p59), file('', ax22)). 1.12/1.59 tff(pax39, axiom, (p39=>![X51:finite1489363574real_n, X52:finite1489363574real_n, X53:n]:(ffinite772340589real_n @ (fminus_1037315151real_n @ X51 @ X52) @ X53)=(fminus_minus_real @ (ffinite772340589real_n @ X51 @ X53) @ (ffinite772340589real_n @ X52 @ X53))), file('', pax39)). 1.12/1.59 tff(pax32, axiom, (p32=>(fring_1_of_int_real @ fm)=(fminus_minus_real @ (ffinite772340589real_n @ fx @ fi) @ (ffinite772340589real_n @ fy @ fi))), file('', pax32)). 1.12/1.59 fof(ax65, axiom, p16, file('', ax65)). 1.12/1.59 fof(ax42, axiom, p39, file('', ax42)). 1.12/1.59 fof(ax49, axiom, p32, file('', ax49)). 1.12/1.59 tff(c_0_10, plain, ![X86:int]:(~p78|(fring_1_of_int_real @ (fabs_abs_int @ X86))=(fabs_abs_real @ (fring_1_of_int_real @ X86))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax78])])])). 1.12/1.59 tff(c_0_11, plain, (~p16|(fring_1_of_int_real @ f__0)=(fminus_minus_real @ (ffinite772340589real_n @ fx @ fi) @ (ffinite772340589real_n @ fy @ fi))), inference(fof_nnf,[status(thm)],[pax16])). 1.12/1.59 tff(c_0_12, plain, ((fring_1_of_int_real @ (fabs_abs_int @ fm))!=(fabs_abs_real @ (ffinite772340589real_n @ (fminus_1037315151real_n @ fx @ fy) @ fi))|p59), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax59])])). 1.12/1.59 thf(c_0_13, plain, ![X5:int]:((fring_1_of_int_real @ (fabs_abs_int @ X5))=(fabs_abs_real @ (fring_1_of_int_real @ X5))|~p78), inference(split_conjunct,[status(thm)],[c_0_10])). 1.12/1.59 thf(c_0_14, plain, (p78), inference(split_conjunct,[status(thm)],[ax3])). 1.12/1.59 fof(c_0_15, plain, ~p59, inference(fof_simplification,[status(thm)],[ax22])). 1.12/1.59 tff(c_0_16, plain, ![X188:finite1489363574real_n, X189:finite1489363574real_n, X190:n]:(~p39|(ffinite772340589real_n @ (fminus_1037315151real_n @ X188 @ X189) @ X190)=(fminus_minus_real @ (ffinite772340589real_n @ X188 @ X190) @ (ffinite772340589real_n @ X189 @ X190))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax39])])])). 1.12/1.59 tff(c_0_17, plain, (~p32|(fring_1_of_int_real @ fm)=(fminus_minus_real @ (ffinite772340589real_n @ fx @ fi) @ (ffinite772340589real_n @ fy @ fi))), inference(fof_nnf,[status(thm)],[pax32])). 1.12/1.59 thf(c_0_18, plain, ((fring_1_of_int_real @ f__0)=(fminus_minus_real @ (ffinite772340589real_n @ fx @ fi) @ (ffinite772340589real_n @ fy @ fi))|~p16), inference(split_conjunct,[status(thm)],[c_0_11])). 1.12/1.59 thf(c_0_19, plain, (p16), inference(split_conjunct,[status(thm)],[ax65])). 1.12/1.59 thf(c_0_20, plain, (p59|(fring_1_of_int_real @ (fabs_abs_int @ fm))!=(fabs_abs_real @ (ffinite772340589real_n @ (fminus_1037315151real_n @ fx @ fy) @ fi))), inference(split_conjunct,[status(thm)],[c_0_12])). 1.12/1.59 thf(c_0_21, plain, ![X5:int]:(fring_1_of_int_real @ (fabs_abs_int @ X5))=(fabs_abs_real @ (fring_1_of_int_real @ X5)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13, c_0_14])])). 1.12/1.59 thf(c_0_22, plain, (~p59), inference(split_conjunct,[status(thm)],[c_0_15])). 1.12/1.59 thf(c_0_23, plain, ![X10:n, X2:finite1489363574real_n, X1:finite1489363574real_n]:((ffinite772340589real_n @ (fminus_1037315151real_n @ X1 @ X2) @ X10)=(fminus_minus_real @ (ffinite772340589real_n @ X1 @ X10) @ (ffinite772340589real_n @ X2 @ X10))|~p39), inference(split_conjunct,[status(thm)],[c_0_16])). 1.12/1.59 thf(c_0_24, plain, (p39), inference(split_conjunct,[status(thm)],[ax42])). 1.12/1.59 thf(c_0_25, plain, ((fring_1_of_int_real @ fm)=(fminus_minus_real @ (ffinite772340589real_n @ fx @ fi) @ (ffinite772340589real_n @ fy @ fi))|~p32), inference(split_conjunct,[status(thm)],[c_0_17])). 1.12/1.59 thf(c_0_26, plain, (fminus_minus_real @ (ffinite772340589real_n @ fx @ fi) @ (ffinite772340589real_n @ fy @ fi))=(fring_1_of_int_real @ f__0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18, c_0_19])])). 1.12/1.59 thf(c_0_27, plain, (p32), inference(split_conjunct,[status(thm)],[ax49])). 1.12/1.59 thf(c_0_28, plain, (fabs_abs_real @ (ffinite772340589real_n @ (fminus_1037315151real_n @ fx @ fy) @ fi))!=(fabs_abs_real @ (fring_1_of_int_real @ fm)), inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_21]), c_0_22])). 1.12/1.59 thf(c_0_29, plain, ![X10:n, X2:finite1489363574real_n, X1:finite1489363574real_n]:(ffinite772340589real_n @ (fminus_1037315151real_n @ X1 @ X2) @ X10)=(fminus_minus_real @ (ffinite772340589real_n @ X1 @ X10) @ (ffinite772340589real_n @ X2 @ X10)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23, c_0_24])])). 1.12/1.59 thf(c_0_30, plain, (fring_1_of_int_real @ f__0)=(fring_1_of_int_real @ fm), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25, c_0_26]), c_0_27])])). 1.12/1.59 thf(c_0_31, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28, c_0_29]), c_0_26]), c_0_30])]), ['proof']). 1.12/1.59 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h1,h0])],[])). 1.12/1.59 thf(fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_Areal__of__int_Am_A_061_Ax_A_E_Ai_A_N_Ay_A_E_Ai_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,(~((![X1:int]:(~(((ring_1_of_int_real @ X1) = ((minus_minus_real @ ((finite772340589real_n @ x) @ i)) @ ((finite772340589real_n @ y) @ i))))))))). 1.12/1.59 thf(2,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_Areal__of__int_Am_A_061_Ax_A_E_Ai_A_N_Ay_A_E_Ai_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,1,h1])). 1.12/1.59 thf(0,theorem,((ring_1_of_int_real @ (abs_abs_int @ m)) = (abs_abs_real @ ((finite772340589real_n @ ((minus_1037315151real_n @ x) @ y)) @ i))),inference(contra,[status(thm),contra(discharge,[h0])],[2,h0])). 1.12/1.59 % SZS output end Proof 1.12/1.59 EOF