%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM926+1 : TPTP v8.2.0. Released v5.3.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n024.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 : Mon Jun 24 12:27:10 EDT 2024 % Result : Theorem 0.56s 0.70s % Output : CNFRefutation 0.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.14 % Problem : NUM926+1 : TPTP v8.2.0. Released v5.3.0. % 0.10/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.14/0.36 % Computer : n024.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Sat Jun 22 20:35:39 EDT 2024 % 0.14/0.36 % CPUTime : % 0.50/0.59 start to proof:theBenchmark % 0.56/0.68 %------------------------------------------- % 0.56/0.68 % File :CSE---1.7 % 0.56/0.68 % Problem :theBenchmark % 0.56/0.68 % Transform :cnf % 0.56/0.68 % Format :tptp:raw % 0.56/0.68 % Command :java -jar mcs_scs.jar %d %s % 0.56/0.68 % 0.56/0.68 % Result :Theorem 0.020000s % 0.56/0.68 % Output :CNFRefutation 0.020000s % 0.56/0.68 %------------------------------------------- % 0.56/0.68 %------------------------------------------------------------------------------ % 0.56/0.68 % File : NUM926+1 : TPTP v8.2.0. Released v5.3.0. % 0.56/0.68 % Domain : Number Theory % 0.56/0.68 % Problem : Sum of two squares line 258, 100 axioms selected % 0.56/0.68 % Version : Especial. % 0.56/0.68 % English : % 0.56/0.68 % 0.56/0.68 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 0.56/0.68 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 0.56/0.68 % Source : [Bla11] % 0.56/0.68 % Names : s2s_100_fofmg_l258 [Bla11] % 0.56/0.68 % 0.56/0.68 % Status : Theorem % 0.56/0.68 % Rating : 0.22 v8.2.0, 0.19 v8.1.0, 0.14 v7.5.0, 0.16 v7.4.0, 0.23 v7.3.0, 0.17 v7.1.0, 0.22 v7.0.0, 0.20 v6.4.0, 0.27 v6.3.0, 0.29 v6.2.0, 0.36 v6.1.0, 0.27 v6.0.0, 0.30 v5.5.0, 0.41 v5.4.0, 0.46 v5.3.0 % 0.56/0.68 % Syntax : Number of formulae : 124 ( 76 unt; 0 def) % 0.56/0.68 % Number of atoms : 183 ( 87 equ) % 0.56/0.68 % Maximal formula atoms : 7 ( 1 avg) % 0.56/0.68 % Number of connectives : 67 ( 8 ~; 3 |; 3 &) % 0.56/0.68 % ( 36 <=>; 17 =>; 0 <=; 0 <~>) % 0.56/0.68 % Maximal formula depth : 8 ( 3 avg) % 0.56/0.68 % Maximal term depth : 10 ( 2 avg) % 0.56/0.68 % Number of predicates : 7 ( 6 usr; 0 prp; 1-2 aty) % 0.56/0.68 % Number of functors : 16 ( 16 usr; 6 con; 0-2 aty) % 0.56/0.68 % Number of variables : 244 ( 238 !; 6 ?) % 0.56/0.68 % SPC : FOF_THM_RFO_SEQ % 0.56/0.68 % 0.56/0.68 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 0.56/0.68 % 2011-08-09 15:34:05 % 0.56/0.68 % : Encoded with monomorphized guards. % 0.56/0.68 %------------------------------------------------------------------------------ % 0.56/0.68 %----Relevant facts (123) % 0.56/0.68 fof(fact_0_tpos,axiom, % 0.56/0.68 ord_less_eq_int(one_one_int,t) ). % 0.56/0.68 % 0.56/0.68 fof(fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom, % 0.56/0.68 ( t = one_one_int % 0.56/0.68 => ? [X,Y] : plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ) ). % 0.56/0.68 % 0.56/0.68 fof(fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom, % 0.56/0.68 ( ord_less_int(one_one_int,t) % 0.56/0.68 => ? [X,Y] : plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ) ). % 0.56/0.68 % 0.56/0.68 fof(fact_3_t__l__p,axiom, % 0.56/0.68 ord_less_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) ). % 0.56/0.68 % 0.56/0.68 fof(fact_4_p,axiom, % 0.56/0.68 zprime(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) ). % 0.56/0.68 % 0.56/0.68 fof(fact_5_t,axiom, % 0.56/0.68 plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) ). % 0.56/0.68 % 0.56/0.68 fof(fact_6_qf1pt,axiom, % 0.56/0.68 twoSqu526106917sum2sq(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t)) ). % 0.56/0.68 % 0.56/0.68 fof(fact_7_zadd__power2,axiom, % 0.56/0.68 ! [A_8,B_4] : power_power_int(plus_plus_int(A_8,B_4),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(A_8,number_number_of_nat(bit0(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),A_8),B_4)),power_power_int(B_4,number_number_of_nat(bit0(bit1(pls))))) ). % 0.56/0.68 % 0.56/0.68 fof(fact_8_zadd__power3,axiom, % 0.56/0.68 ! [A_8,B_4] : power_power_int(plus_plus_int(A_8,B_4),number_number_of_nat(bit1(bit1(pls)))) = plus_plus_int(plus_plus_int(plus_plus_int(power_power_int(A_8,number_number_of_nat(bit1(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),power_power_int(A_8,number_number_of_nat(bit0(bit1(pls))))),B_4)),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),A_8),power_power_int(B_4,number_number_of_nat(bit0(bit1(pls)))))),power_power_int(B_4,number_number_of_nat(bit1(bit1(pls))))) ). % 0.56/0.68 % 0.56/0.68 fof(fact_9_power2__sum,axiom, % 0.56/0.68 ! [X_2,Y_2] : power_power_nat(plus_plus_nat(X_2,Y_2),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(plus_plus_nat(power_power_nat(X_2,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(Y_2,number_number_of_nat(bit0(bit1(pls))))),times_times_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls))),X_2),Y_2)) ). % 0.56/0.68 % 0.56/0.68 fof(fact_10_power2__sum,axiom, % 0.56/0.68 ! [X_2,Y_2] : power_power_int(plus_plus_int(X_2,Y_2),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(X_2,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y_2,number_number_of_nat(bit0(bit1(pls))))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),X_2),Y_2)) ). % 0.56/0.68 % 0.56/0.68 fof(fact_11_power2__eq__square__number__of,axiom, % 0.56/0.68 ! [W_4] : power_power_int(number_number_of_int(W_4),number_number_of_nat(bit0(bit1(pls)))) = times_times_int(number_number_of_int(W_4),number_number_of_int(W_4)) ). % 0.56/0.68 % 0.56/0.68 fof(fact_12_power2__eq__square__number__of,axiom, % 0.56/0.68 ! [W_4] : power_power_nat(number_number_of_nat(W_4),number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(number_number_of_nat(W_4),number_number_of_nat(W_4)) ). % 0.56/0.68 % 0.56/0.68 fof(fact_13_cube__square,axiom, % 0.56/0.68 ! [A_8] : times_times_int(A_8,power_power_int(A_8,number_number_of_nat(bit0(bit1(pls))))) = power_power_int(A_8,number_number_of_nat(bit1(bit1(pls)))) ). % 0.56/0.68 % 0.56/0.68 fof(fact_14_one__power2,axiom, % 0.56/0.68 power_power_nat(one_one_nat,number_number_of_nat(bit0(bit1(pls)))) = one_one_nat ). % 0.56/0.68 % 0.56/0.68 fof(fact_15_one__power2,axiom, % 0.56/0.68 power_power_int(one_one_int,number_number_of_nat(bit0(bit1(pls)))) = one_one_int ). % 0.56/0.68 % 0.56/0.68 fof(fact_16_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom, % 0.56/0.69 ! [X_7] : times_times_int(X_7,X_7) = power_power_int(X_7,number_number_of_nat(bit0(bit1(pls)))) ). % 0.56/0.69 % 0.56/0.69 fof(fact_17_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom, % 0.56/0.69 ! [X_7] : times_times_nat(X_7,X_7) = power_power_nat(X_7,number_number_of_nat(bit0(bit1(pls)))) ). % 0.56/0.69 % 0.56/0.69 fof(fact_18_power2__eq__square,axiom, % 0.56/0.69 ! [A_7] : power_power_int(A_7,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(A_7,A_7) ). % 0.56/0.69 % 0.56/0.69 fof(fact_19_power2__eq__square,axiom, % 0.56/0.69 ! [A_7] : power_power_nat(A_7,number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(A_7,A_7) ). % 0.56/0.69 % 0.56/0.69 fof(fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom, % 0.56/0.69 ! [X_6,N] : power_power_int(X_6,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N)) = times_times_int(power_power_int(X_6,N),power_power_int(X_6,N)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom, % 0.56/0.69 ! [X_6,N] : power_power_nat(X_6,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N)) = times_times_nat(power_power_nat(X_6,N),power_power_nat(X_6,N)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_22_add__special_I2_J,axiom, % 0.56/0.69 ! [W_3] : plus_plus_int(one_one_int,number_number_of_int(W_3)) = number_number_of_int(plus_plus_int(bit1(pls),W_3)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_23_add__special_I3_J,axiom, % 0.56/0.69 ! [V_3] : plus_plus_int(number_number_of_int(V_3),one_one_int) = number_number_of_int(plus_plus_int(V_3,bit1(pls))) ). % 0.56/0.69 % 0.56/0.69 fof(fact_24_one__add__one__is__two,axiom, % 0.56/0.69 plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))) ). % 0.56/0.69 % 0.56/0.69 fof(fact_25__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_,axiom, % 0.56/0.69 ~ ! [T] : plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) != times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),T) ). % 0.56/0.69 % 0.56/0.69 fof(fact_26_zle__refl,axiom, % 0.56/0.69 ! [W] : ord_less_eq_int(W,W) ). % 0.56/0.69 % 0.56/0.69 fof(fact_27_zle__linear,axiom, % 0.56/0.69 ! [Z,W] : % 0.56/0.69 ( ord_less_eq_int(Z,W) % 0.56/0.69 | ord_less_eq_int(W,Z) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_28_zless__le,axiom, % 0.56/0.69 ! [Z_1,W_1] : % 0.56/0.69 ( ord_less_int(Z_1,W_1) % 0.56/0.69 <=> ( ord_less_eq_int(Z_1,W_1) % 0.56/0.69 & Z_1 != W_1 ) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_29_zless__linear,axiom, % 0.56/0.69 ! [X_1,Y_1] : % 0.56/0.69 ( ord_less_int(X_1,Y_1) % 0.56/0.69 | X_1 = Y_1 % 0.56/0.69 | ord_less_int(Y_1,X_1) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_30_zle__trans,axiom, % 0.56/0.69 ! [K_1,I,J] : % 0.56/0.69 ( ord_less_eq_int(I,J) % 0.56/0.69 => ( ord_less_eq_int(J,K_1) % 0.56/0.69 => ord_less_eq_int(I,K_1) ) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_31_zle__antisym,axiom, % 0.56/0.69 ! [Z,W] : % 0.56/0.69 ( ord_less_eq_int(Z,W) % 0.56/0.69 => ( ord_less_eq_int(W,Z) % 0.56/0.69 => Z = W ) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom, % 0.56/0.69 ! [X_5,P_1,Q_1] : power_power_int(power_power_int(X_5,P_1),Q_1) = power_power_int(X_5,times_times_nat(P_1,Q_1)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom, % 0.56/0.69 ! [X_5,P_1,Q_1] : power_power_nat(power_power_nat(X_5,P_1),Q_1) = power_power_nat(X_5,times_times_nat(P_1,Q_1)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_34_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom, % 0.56/0.69 ! [X_4] : power_power_int(X_4,one_one_nat) = X_4 ). % 0.56/0.69 % 0.56/0.69 fof(fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom, % 0.56/0.69 ! [X_4] : power_power_nat(X_4,one_one_nat) = X_4 ). % 0.56/0.69 % 0.56/0.69 fof(fact_36_zpower__zpower,axiom, % 0.56/0.69 ! [X_1,Y_1,Z] : power_power_int(power_power_int(X_1,Y_1),Z) = power_power_int(X_1,times_times_nat(Y_1,Z)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_37_le__number__of__eq__not__less,axiom, % 0.56/0.69 ! [V_2,W_1] : % 0.56/0.69 ( ord_less_eq_nat(number_number_of_nat(V_2),number_number_of_nat(W_1)) % 0.56/0.69 <=> ~ ord_less_nat(number_number_of_nat(W_1),number_number_of_nat(V_2)) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_38_le__number__of__eq__not__less,axiom, % 0.56/0.69 ! [V_2,W_1] : % 0.56/0.69 ( ord_less_eq_int(number_number_of_int(V_2),number_number_of_int(W_1)) % 0.56/0.69 <=> ~ ord_less_int(number_number_of_int(W_1),number_number_of_int(V_2)) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_39_less__number__of,axiom, % 0.56/0.69 ! [X_2,Y_2] : % 0.56/0.69 ( ord_less_int(number_number_of_int(X_2),number_number_of_int(Y_2)) % 0.56/0.69 <=> ord_less_int(X_2,Y_2) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_40_le__number__of,axiom, % 0.56/0.69 ! [X_2,Y_2] : % 0.56/0.69 ( ord_less_eq_int(number_number_of_int(X_2),number_number_of_int(Y_2)) % 0.56/0.69 <=> ord_less_eq_int(X_2,Y_2) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_41_zadd__zless__mono,axiom, % 0.56/0.69 ! [Z_2,Z,W_2,W] : % 0.56/0.69 ( ord_less_int(W_2,W) % 0.56/0.69 => ( ord_less_eq_int(Z_2,Z) % 0.56/0.69 => ord_less_int(plus_plus_int(W_2,Z_2),plus_plus_int(W,Z)) ) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom, % 0.56/0.69 ! [X_3,P,Q] : times_times_int(power_power_int(X_3,P),power_power_int(X_3,Q)) = power_power_int(X_3,plus_plus_nat(P,Q)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom, % 0.56/0.69 ! [X_3,P,Q] : times_times_nat(power_power_nat(X_3,P),power_power_nat(X_3,Q)) = power_power_nat(X_3,plus_plus_nat(P,Q)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_44_zpower__zadd__distrib,axiom, % 0.56/0.69 ! [X_1,Y_1,Z] : power_power_int(X_1,plus_plus_nat(Y_1,Z)) = times_times_int(power_power_int(X_1,Y_1),power_power_int(X_1,Z)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_45_nat__mult__2,axiom, % 0.56/0.69 ! [Z] : times_times_nat(number_number_of_nat(bit0(bit1(pls))),Z) = plus_plus_nat(Z,Z) ). % 0.56/0.69 % 0.56/0.69 fof(fact_46_nat__mult__2__right,axiom, % 0.56/0.69 ! [Z] : times_times_nat(Z,number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(Z,Z) ). % 0.56/0.69 % 0.56/0.69 fof(fact_47_nat__1__add__1,axiom, % 0.56/0.69 plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))) ). % 0.56/0.69 % 0.56/0.69 fof(fact_48_less__int__code_I16_J,axiom, % 0.56/0.69 ! [K1,K2] : % 0.56/0.69 ( ord_less_int(bit1(K1),bit1(K2)) % 0.56/0.69 <=> ord_less_int(K1,K2) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_49_rel__simps_I17_J,axiom, % 0.56/0.69 ! [K,L] : % 0.56/0.69 ( ord_less_int(bit1(K),bit1(L)) % 0.56/0.69 <=> ord_less_int(K,L) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_50_less__eq__int__code_I16_J,axiom, % 0.56/0.69 ! [K1,K2] : % 0.56/0.69 ( ord_less_eq_int(bit1(K1),bit1(K2)) % 0.56/0.69 <=> ord_less_eq_int(K1,K2) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_51_rel__simps_I34_J,axiom, % 0.56/0.69 ! [K,L] : % 0.56/0.69 ( ord_less_eq_int(bit1(K),bit1(L)) % 0.56/0.69 <=> ord_less_eq_int(K,L) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_52_rel__simps_I2_J,axiom, % 0.56/0.69 ~ ord_less_int(pls,pls) ). % 0.56/0.69 % 0.56/0.69 fof(fact_53_less__int__code_I13_J,axiom, % 0.56/0.69 ! [K1,K2] : % 0.56/0.69 ( ord_less_int(bit0(K1),bit0(K2)) % 0.56/0.69 <=> ord_less_int(K1,K2) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_54_rel__simps_I14_J,axiom, % 0.56/0.69 ! [K,L] : % 0.56/0.69 ( ord_less_int(bit0(K),bit0(L)) % 0.56/0.69 <=> ord_less_int(K,L) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_55_rel__simps_I19_J,axiom, % 0.56/0.69 ord_less_eq_int(pls,pls) ). % 0.56/0.69 % 0.56/0.69 fof(fact_56_less__eq__int__code_I13_J,axiom, % 0.56/0.69 ! [K1,K2] : % 0.56/0.69 ( ord_less_eq_int(bit0(K1),bit0(K2)) % 0.56/0.69 <=> ord_less_eq_int(K1,K2) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_57_rel__simps_I31_J,axiom, % 0.56/0.69 ! [K,L] : % 0.56/0.69 ( ord_less_eq_int(bit0(K),bit0(L)) % 0.56/0.69 <=> ord_less_eq_int(K,L) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_58_less__number__of__int__code,axiom, % 0.56/0.69 ! [K,L] : % 0.56/0.69 ( ord_less_int(number_number_of_int(K),number_number_of_int(L)) % 0.56/0.69 <=> ord_less_int(K,L) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_59_less__eq__number__of__int__code,axiom, % 0.56/0.69 ! [K,L] : % 0.56/0.69 ( ord_less_eq_int(number_number_of_int(K),number_number_of_int(L)) % 0.56/0.69 <=> ord_less_eq_int(K,L) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_60_zadd__strict__right__mono,axiom, % 0.56/0.69 ! [K_1,I,J] : % 0.56/0.69 ( ord_less_int(I,J) % 0.56/0.69 => ord_less_int(plus_plus_int(I,K_1),plus_plus_int(J,K_1)) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_61_zadd__left__mono,axiom, % 0.56/0.69 ! [K_1,I,J] : % 0.56/0.69 ( ord_less_eq_int(I,J) % 0.56/0.69 => ord_less_eq_int(plus_plus_int(K_1,I),plus_plus_int(K_1,J)) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_62_add__nat__number__of,axiom, % 0.56/0.69 ! [V_1,V] : % 0.56/0.69 ( ( ord_less_int(V,pls) % 0.56/0.69 => plus_plus_nat(number_number_of_nat(V),number_number_of_nat(V_1)) = number_number_of_nat(V_1) ) % 0.56/0.69 & ( ~ ord_less_int(V,pls) % 0.56/0.69 => ( ( ord_less_int(V_1,pls) % 0.56/0.69 => plus_plus_nat(number_number_of_nat(V),number_number_of_nat(V_1)) = number_number_of_nat(V) ) % 0.56/0.69 & ( ~ ord_less_int(V_1,pls) % 0.56/0.69 => plus_plus_nat(number_number_of_nat(V),number_number_of_nat(V_1)) = number_number_of_nat(plus_plus_int(V,V_1)) ) ) ) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_63_nat__numeral__1__eq__1,axiom, % 0.56/0.69 number_number_of_nat(bit1(pls)) = one_one_nat ). % 0.56/0.69 % 0.56/0.69 fof(fact_64_Numeral1__eq1__nat,axiom, % 0.56/0.69 one_one_nat = number_number_of_nat(bit1(pls)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_65_rel__simps_I29_J,axiom, % 0.56/0.69 ! [K] : % 0.56/0.69 ( ord_less_eq_int(bit1(K),pls) % 0.56/0.69 <=> ord_less_int(K,pls) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_66_rel__simps_I5_J,axiom, % 0.56/0.69 ! [K] : % 0.56/0.69 ( ord_less_int(pls,bit1(K)) % 0.56/0.69 <=> ord_less_eq_int(pls,K) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_67_less__eq__int__code_I15_J,axiom, % 0.56/0.69 ! [K1,K2] : % 0.56/0.69 ( ord_less_eq_int(bit1(K1),bit0(K2)) % 0.56/0.69 <=> ord_less_int(K1,K2) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_68_rel__simps_I33_J,axiom, % 0.56/0.69 ! [K,L] : % 0.56/0.69 ( ord_less_eq_int(bit1(K),bit0(L)) % 0.56/0.69 <=> ord_less_int(K,L) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_69_less__int__code_I14_J,axiom, % 0.56/0.69 ! [K1,K2] : % 0.56/0.69 ( ord_less_int(bit0(K1),bit1(K2)) % 0.56/0.69 <=> ord_less_eq_int(K1,K2) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_70_rel__simps_I15_J,axiom, % 0.56/0.69 ! [K,L] : % 0.56/0.69 ( ord_less_int(bit0(K),bit1(L)) % 0.56/0.69 <=> ord_less_eq_int(K,L) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_71_zless__imp__add1__zle,axiom, % 0.56/0.69 ! [W,Z] : % 0.56/0.69 ( ord_less_int(W,Z) % 0.56/0.69 => ord_less_eq_int(plus_plus_int(W,one_one_int),Z) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_72_add1__zle__eq,axiom, % 0.56/0.69 ! [W_1,Z_1] : % 0.56/0.69 ( ord_less_eq_int(plus_plus_int(W_1,one_one_int),Z_1) % 0.56/0.69 <=> ord_less_int(W_1,Z_1) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_73_zle__add1__eq__le,axiom, % 0.56/0.69 ! [W_1,Z_1] : % 0.56/0.69 ( ord_less_int(W_1,plus_plus_int(Z_1,one_one_int)) % 0.56/0.69 <=> ord_less_eq_int(W_1,Z_1) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_74_zprime__2,axiom, % 0.56/0.69 zprime(number_number_of_int(bit0(bit1(pls)))) ). % 0.56/0.69 % 0.56/0.69 fof(fact_75_is__mult__sum2sq,axiom, % 0.56/0.69 ! [Y_1,X_1] : % 0.56/0.69 ( twoSqu526106917sum2sq(X_1) % 0.56/0.69 => ( twoSqu526106917sum2sq(Y_1) % 0.56/0.69 => twoSqu526106917sum2sq(times_times_int(X_1,Y_1)) ) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom, % 0.56/0.69 ! [Lx_6,Ly_4,Rx_6,Ry_4] : times_times_int(times_times_int(Lx_6,Ly_4),times_times_int(Rx_6,Ry_4)) = times_times_int(times_times_int(Lx_6,Rx_6),times_times_int(Ly_4,Ry_4)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom, % 0.56/0.69 ! [Lx_6,Ly_4,Rx_6,Ry_4] : times_times_nat(times_times_nat(Lx_6,Ly_4),times_times_nat(Rx_6,Ry_4)) = times_times_nat(times_times_nat(Lx_6,Rx_6),times_times_nat(Ly_4,Ry_4)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom, % 0.56/0.69 ! [Lx_5,Ly_3,Rx_5,Ry_3] : times_times_int(times_times_int(Lx_5,Ly_3),times_times_int(Rx_5,Ry_3)) = times_times_int(Rx_5,times_times_int(times_times_int(Lx_5,Ly_3),Ry_3)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom, % 0.56/0.69 ! [Lx_5,Ly_3,Rx_5,Ry_3] : times_times_nat(times_times_nat(Lx_5,Ly_3),times_times_nat(Rx_5,Ry_3)) = times_times_nat(Rx_5,times_times_nat(times_times_nat(Lx_5,Ly_3),Ry_3)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom, % 0.56/0.69 ! [Lx_4,Ly_2,Rx_4,Ry_2] : times_times_int(times_times_int(Lx_4,Ly_2),times_times_int(Rx_4,Ry_2)) = times_times_int(Lx_4,times_times_int(Ly_2,times_times_int(Rx_4,Ry_2))) ). % 0.56/0.69 % 0.56/0.69 fof(fact_81_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom, % 0.56/0.69 ! [Lx_4,Ly_2,Rx_4,Ry_2] : times_times_nat(times_times_nat(Lx_4,Ly_2),times_times_nat(Rx_4,Ry_2)) = times_times_nat(Lx_4,times_times_nat(Ly_2,times_times_nat(Rx_4,Ry_2))) ). % 0.56/0.69 % 0.56/0.69 fof(fact_82_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom, % 0.56/0.69 ! [Lx_3,Ly_1,Rx_3] : times_times_int(times_times_int(Lx_3,Ly_1),Rx_3) = times_times_int(times_times_int(Lx_3,Rx_3),Ly_1) ). % 0.56/0.69 % 0.56/0.69 fof(fact_83_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom, % 0.56/0.69 ! [Lx_3,Ly_1,Rx_3] : times_times_nat(times_times_nat(Lx_3,Ly_1),Rx_3) = times_times_nat(times_times_nat(Lx_3,Rx_3),Ly_1) ). % 0.56/0.69 % 0.56/0.69 fof(fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom, % 0.56/0.69 ! [Lx_2,Ly,Rx_2] : times_times_int(times_times_int(Lx_2,Ly),Rx_2) = times_times_int(Lx_2,times_times_int(Ly,Rx_2)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_85_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom, % 0.56/0.69 ! [Lx_2,Ly,Rx_2] : times_times_nat(times_times_nat(Lx_2,Ly),Rx_2) = times_times_nat(Lx_2,times_times_nat(Ly,Rx_2)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_86_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom, % 0.56/0.69 ! [Lx_1,Rx_1,Ry_1] : times_times_int(Lx_1,times_times_int(Rx_1,Ry_1)) = times_times_int(times_times_int(Lx_1,Rx_1),Ry_1) ). % 0.56/0.69 % 0.56/0.69 fof(fact_87_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom, % 0.56/0.69 ! [Lx_1,Rx_1,Ry_1] : times_times_nat(Lx_1,times_times_nat(Rx_1,Ry_1)) = times_times_nat(times_times_nat(Lx_1,Rx_1),Ry_1) ). % 0.56/0.69 % 0.56/0.69 fof(fact_88_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom, % 0.56/0.69 ! [Lx,Rx,Ry] : times_times_int(Lx,times_times_int(Rx,Ry)) = times_times_int(Rx,times_times_int(Lx,Ry)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_89_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom, % 0.56/0.69 ! [Lx,Rx,Ry] : times_times_nat(Lx,times_times_nat(Rx,Ry)) = times_times_nat(Rx,times_times_nat(Lx,Ry)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom, % 0.56/0.69 ! [A_6,B_3] : times_times_int(A_6,B_3) = times_times_int(B_3,A_6) ). % 0.56/0.69 % 0.56/0.69 fof(fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom, % 0.56/0.69 ! [A_6,B_3] : times_times_nat(A_6,B_3) = times_times_nat(B_3,A_6) ). % 0.56/0.69 % 0.56/0.69 fof(fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 0.56/0.69 ! [A_5,B_2,C_5,D_2] : plus_plus_int(plus_plus_int(A_5,B_2),plus_plus_int(C_5,D_2)) = plus_plus_int(plus_plus_int(A_5,C_5),plus_plus_int(B_2,D_2)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 0.56/0.69 ! [A_5,B_2,C_5,D_2] : plus_plus_nat(plus_plus_nat(A_5,B_2),plus_plus_nat(C_5,D_2)) = plus_plus_nat(plus_plus_nat(A_5,C_5),plus_plus_nat(B_2,D_2)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 0.56/0.69 ! [A_4,B_1,C_4] : plus_plus_int(plus_plus_int(A_4,B_1),C_4) = plus_plus_int(plus_plus_int(A_4,C_4),B_1) ). % 0.56/0.69 % 0.56/0.69 fof(fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 0.56/0.69 ! [A_4,B_1,C_4] : plus_plus_nat(plus_plus_nat(A_4,B_1),C_4) = plus_plus_nat(plus_plus_nat(A_4,C_4),B_1) ). % 0.56/0.69 % 0.56/0.69 fof(fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 0.56/0.69 ! [A_3,B,C_3] : plus_plus_int(plus_plus_int(A_3,B),C_3) = plus_plus_int(A_3,plus_plus_int(B,C_3)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 0.56/0.69 ! [A_3,B,C_3] : plus_plus_nat(plus_plus_nat(A_3,B),C_3) = plus_plus_nat(A_3,plus_plus_nat(B,C_3)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 0.56/0.69 ! [A_2,C_2,D_1] : plus_plus_int(A_2,plus_plus_int(C_2,D_1)) = plus_plus_int(plus_plus_int(A_2,C_2),D_1) ). % 0.56/0.69 % 0.56/0.69 fof(fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 0.56/0.69 ! [A_2,C_2,D_1] : plus_plus_nat(A_2,plus_plus_nat(C_2,D_1)) = plus_plus_nat(plus_plus_nat(A_2,C_2),D_1) ). % 0.56/0.69 % 0.56/0.69 fof(fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 0.56/0.69 ! [A_1,C_1,D] : plus_plus_int(A_1,plus_plus_int(C_1,D)) = plus_plus_int(C_1,plus_plus_int(A_1,D)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 0.56/0.69 ! [A_1,C_1,D] : plus_plus_nat(A_1,plus_plus_nat(C_1,D)) = plus_plus_nat(C_1,plus_plus_nat(A_1,D)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 0.56/0.69 ! [A,C] : plus_plus_int(A,C) = plus_plus_int(C,A) ). % 0.56/0.69 % 0.56/0.69 fof(fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 0.56/0.69 ! [A,C] : plus_plus_nat(A,C) = plus_plus_nat(C,A) ). % 0.56/0.69 % 0.56/0.69 fof(fact_104_eq__number__of,axiom, % 0.56/0.69 ! [X_2,Y_2] : % 0.56/0.69 ( number_number_of_int(X_2) = number_number_of_int(Y_2) % 0.56/0.69 <=> X_2 = Y_2 ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_105_number__of__reorient,axiom, % 0.56/0.69 ! [W_1,X_2] : % 0.56/0.69 ( number_number_of_nat(W_1) = X_2 % 0.56/0.69 <=> X_2 = number_number_of_nat(W_1) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_106_number__of__reorient,axiom, % 0.56/0.69 ! [W_1,X_2] : % 0.56/0.69 ( number_number_of_int(W_1) = X_2 % 0.56/0.69 <=> X_2 = number_number_of_int(W_1) ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_107_rel__simps_I51_J,axiom, % 0.56/0.69 ! [K,L] : % 0.56/0.69 ( bit1(K) = bit1(L) % 0.56/0.69 <=> K = L ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_108_rel__simps_I48_J,axiom, % 0.56/0.69 ! [K,L] : % 0.56/0.69 ( bit0(K) = bit0(L) % 0.56/0.69 <=> K = L ) ). % 0.56/0.69 % 0.56/0.69 fof(fact_109_zmult__assoc,axiom, % 0.56/0.69 ! [Z1,Z2,Z3] : times_times_int(times_times_int(Z1,Z2),Z3) = times_times_int(Z1,times_times_int(Z2,Z3)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_110_zmult__commute,axiom, % 0.56/0.69 ! [Z,W] : times_times_int(Z,W) = times_times_int(W,Z) ). % 0.56/0.69 % 0.56/0.69 fof(fact_111_number__of__is__id,axiom, % 0.56/0.69 ! [K_1] : number_number_of_int(K_1) = K_1 ). % 0.56/0.69 % 0.56/0.69 fof(fact_112_zadd__assoc,axiom, % 0.56/0.69 ! [Z1,Z2,Z3] : plus_plus_int(plus_plus_int(Z1,Z2),Z3) = plus_plus_int(Z1,plus_plus_int(Z2,Z3)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_113_zadd__left__commute,axiom, % 0.56/0.69 ! [X_1,Y_1,Z] : plus_plus_int(X_1,plus_plus_int(Y_1,Z)) = plus_plus_int(Y_1,plus_plus_int(X_1,Z)) ). % 0.56/0.69 % 0.56/0.69 fof(fact_114_zadd__commute,axiom, % 0.56/0.69 ! [Z,W] : plus_plus_int(Z,W) = plus_plus_int(W,Z) ). % 0.56/0.70 % 0.56/0.70 fof(fact_115_rel__simps_I12_J,axiom, % 0.56/0.70 ! [K] : % 0.56/0.70 ( ord_less_int(bit1(K),pls) % 0.56/0.70 <=> ord_less_int(K,pls) ) ). % 0.56/0.70 % 0.56/0.70 fof(fact_116_less__int__code_I15_J,axiom, % 0.56/0.70 ! [K1,K2] : % 0.56/0.70 ( ord_less_int(bit1(K1),bit0(K2)) % 0.56/0.70 <=> ord_less_int(K1,K2) ) ). % 0.56/0.70 % 0.56/0.70 fof(fact_117_rel__simps_I16_J,axiom, % 0.56/0.70 ! [K,L] : % 0.56/0.70 ( ord_less_int(bit1(K),bit0(L)) % 0.56/0.70 <=> ord_less_int(K,L) ) ). % 0.56/0.70 % 0.56/0.70 fof(fact_118_rel__simps_I10_J,axiom, % 0.56/0.70 ! [K] : % 0.56/0.70 ( ord_less_int(bit0(K),pls) % 0.56/0.70 <=> ord_less_int(K,pls) ) ). % 0.56/0.70 % 0.56/0.70 fof(fact_119_rel__simps_I4_J,axiom, % 0.56/0.70 ! [K] : % 0.56/0.70 ( ord_less_int(pls,bit0(K)) % 0.56/0.70 <=> ord_less_int(pls,K) ) ). % 0.56/0.70 % 0.56/0.70 fof(fact_120_rel__simps_I22_J,axiom, % 0.56/0.70 ! [K] : % 0.56/0.70 ( ord_less_eq_int(pls,bit1(K)) % 0.56/0.70 <=> ord_less_eq_int(pls,K) ) ). % 0.56/0.70 % 0.56/0.70 fof(fact_121_less__eq__int__code_I14_J,axiom, % 0.56/0.70 ! [K1,K2] : % 0.56/0.70 ( ord_less_eq_int(bit0(K1),bit1(K2)) % 0.56/0.70 <=> ord_less_eq_int(K1,K2) ) ). % 0.56/0.70 % 0.56/0.70 fof(fact_122_rel__simps_I32_J,axiom, % 0.56/0.70 ! [K,L] : % 0.56/0.70 ( ord_less_eq_int(bit0(K),bit1(L)) % 0.56/0.70 <=> ord_less_eq_int(K,L) ) ). % 0.56/0.70 % 0.56/0.70 %----Conjectures (1) % 0.56/0.70 fof(conj_0,conjecture, % 0.56/0.70 ? [X,Y] : plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ). % 0.56/0.70 % 0.56/0.70 %------------------------------------------------------------------------------ % 0.56/0.70 %------------------------------------------- % 0.56/0.70 % Proof found % 0.56/0.70 % SZS status Theorem for theBenchmark % 0.56/0.70 % SZS output start Proof % 0.56/0.70 %ClaNum:174(EqnAxiom:28) % 0.56/0.70 %VarNum:420(SingletonVarNum:195) % 0.56/0.70 %MaxLitNum:3 % 0.56/0.70 %MaxfuncDepth:6 % 0.56/0.70 %SharedTerms:51 % 0.56/0.70 %goalClause: 103 % 0.56/0.70 %singleGoalClaCount:1 % 0.56/0.70 [31]P1(a12,a13) % 0.56/0.70 [102]~P3(a1,a1) % 0.56/0.70 [30]E(f4(f2(a1)),a11) % 0.56/0.70 [36]P2(f3(f2(a1))) % 0.56/0.70 [37]E(f3(f2(a1)),f15(a12,a12)) % 0.56/0.70 [38]E(f4(f3(f2(a1))),f16(a11,a11)) % 0.56/0.70 [47]E(f14(a12,f4(f3(f2(a1)))),a12) % 0.56/0.70 [48]E(f17(a11,f4(f3(f2(a1)))),a11) % 0.56/0.70 [93]P2(f15(f19(f3(f3(f2(a1))),a5),a12)) % 0.56/0.70 [94]P3(a13,f15(f19(f3(f3(f2(a1))),a5),a12)) % 0.56/0.70 [95]E(f19(f15(f19(f3(f3(f2(a1))),a5),a12),a13),f15(f14(a18,f4(f3(f2(a1)))),a12)) % 0.56/0.70 [96]E(f19(f15(f19(f3(f3(f2(a1))),a5),a12),a6),f15(f14(a18,f4(f3(f2(a1)))),a12)) % 0.56/0.70 [97]P5(f19(f15(f19(f3(f3(f2(a1))),a5),a12),a13)) % 0.56/0.70 [35]P1(x351,x351) % 0.56/0.70 [33]E(f14(x331,a11),x331) % 0.56/0.70 [34]E(f17(x341,a11),x341) % 0.56/0.70 [45]E(f15(x451,f2(a1)),f15(x451,a12)) % 0.56/0.70 [46]E(f15(f2(a1),x461),f15(a12,x461)) % 0.56/0.70 [49]E(f19(x491,x491),f14(x491,f4(f3(f2(a1))))) % 0.56/0.70 [50]E(f20(x501,x501),f17(x501,f4(f3(f2(a1))))) % 0.56/0.70 [52]E(f14(x521,f4(f3(f2(a1)))),f19(x521,x521)) % 0.56/0.70 [53]E(f17(x531,f4(f3(f2(a1)))),f20(x531,x531)) % 0.56/0.70 [54]E(f20(x541,f4(f3(f2(a1)))),f16(x541,x541)) % 0.56/0.70 [55]E(f20(f4(f3(f2(a1))),x551),f16(x551,x551)) % 0.56/0.70 [86]E(f19(x861,f14(x861,f4(f3(f2(a1))))),f14(x861,f4(f2(f2(a1))))) % 0.56/0.70 [40]E(f15(x401,x402),f15(x402,x401)) % 0.56/0.70 [42]E(f19(x421,x422),f19(x422,x421)) % 0.56/0.70 [43]E(f16(x431,x432),f16(x432,x431)) % 0.56/0.70 [44]E(f20(x441,x442),f20(x442,x441)) % 0.56/0.70 [91]E(f14(x911,f20(f4(f3(f2(a1))),x912)),f19(f14(x911,x912),f14(x911,x912))) % 0.56/0.70 [92]E(f17(x921,f20(f4(f3(f2(a1))),x922)),f20(f17(x921,x922),f17(x921,x922))) % 0.56/0.70 [98]E(f15(f15(f14(x981,f4(f3(f2(a1)))),f14(x982,f4(f3(f2(a1))))),f19(f19(f3(f2(a1)),x981),x982)),f14(f15(x981,x982),f4(f3(f2(a1))))) % 0.56/0.70 [99]E(f15(f15(f14(x991,f4(f3(f2(a1)))),f19(f19(f3(f2(a1)),x991),x992)),f14(x992,f4(f3(f2(a1))))),f14(f15(x991,x992),f4(f3(f2(a1))))) % 0.56/0.70 [101]E(f15(f15(f15(f14(x1011,f4(f2(f2(a1)))),f19(f19(f2(f2(a1)),f14(x1011,f4(f3(f2(a1))))),x1012)),f19(f19(f2(f2(a1)),x1011),f14(x1012,f4(f3(f2(a1)))))),f14(x1012,f4(f2(f2(a1))))),f14(f15(x1011,x1012),f4(f2(f2(a1))))) % 0.56/0.70 [103]~E(f15(f14(x1031,f4(f3(f2(a1)))),f14(x1032,f4(f3(f2(a1))))),f15(f19(f3(f3(f2(a1))),a5),a12)) % 0.56/0.70 [100]E(f16(f16(f17(x1001,f4(f3(f2(a1)))),f17(x1002,f4(f3(f2(a1))))),f20(f20(f4(f3(f2(a1))),x1001),x1002)),f17(f16(x1001,x1002),f4(f3(f2(a1))))) % 0.56/0.70 [58]E(f15(x581,f15(x582,x583)),f15(x582,f15(x581,x583))) % 0.56/0.70 [59]E(f19(x591,f19(x592,x593)),f19(x592,f19(x591,x593))) % 0.56/0.70 [60]E(f16(x601,f16(x602,x603)),f16(x602,f16(x601,x603))) % 0.56/0.70 [61]E(f20(x611,f20(x612,x613)),f20(x612,f20(x611,x613))) % 0.56/0.70 [67]E(f14(f14(x671,x672),x673),f14(x671,f20(x672,x673))) % 0.56/0.70 [69]E(f15(f15(x691,x692),x693),f15(x691,f15(x692,x693))) % 0.56/0.70 [71]E(f19(f19(x711,x712),x713),f19(x711,f19(x712,x713))) % 0.56/0.70 [72]E(f16(f16(x721,x722),x723),f16(x721,f16(x722,x723))) % 0.56/0.70 [73]E(f17(f17(x731,x732),x733),f17(x731,f20(x732,x733))) % 0.56/0.70 [74]E(f20(f20(x741,x742),x743),f20(x741,f20(x742,x743))) % 0.56/0.70 [75]E(f15(f15(x751,x752),x753),f15(f15(x751,x753),x752)) % 0.56/0.70 [76]E(f19(f19(x761,x762),x763),f19(f19(x761,x763),x762)) % 0.56/0.70 [77]E(f16(f16(x771,x772),x773),f16(f16(x771,x773),x772)) % 0.56/0.70 [78]E(f20(f20(x781,x782),x783),f20(f20(x781,x783),x782)) % 0.56/0.70 [80]E(f19(f14(x801,x802),f14(x801,x803)),f14(x801,f16(x802,x803))) % 0.56/0.70 [81]E(f20(f17(x811,x812),f17(x811,x813)),f17(x811,f16(x812,x813))) % 0.56/0.70 [82]E(f15(f15(x821,x822),f15(x823,x824)),f15(f15(x821,x823),f15(x822,x824))) % 0.56/0.70 [83]E(f19(f19(x831,x832),f19(x833,x834)),f19(f19(x831,x833),f19(x832,x834))) % 0.56/0.70 [84]E(f16(f16(x841,x842),f16(x843,x844)),f16(f16(x841,x843),f16(x842,x844))) % 0.56/0.70 [85]E(f20(f20(x851,x852),f20(x853,x854)),f20(f20(x851,x853),f20(x852,x854))) % 0.56/0.70 [173]~E(a13,a12)+E(f15(f14(a7,f4(f3(f2(a1)))),f14(a8,f4(f3(f2(a1))))),f15(f19(f3(f3(f2(a1))),a5),a12)) % 0.56/0.70 [174]~P3(a12,a13)+E(f15(f14(a9,f4(f3(f2(a1)))),f14(a10,f4(f3(f2(a1))))),f15(f19(f3(f3(f2(a1))),a5),a12)) % 0.56/0.70 [111]~P1(a1,x1111)+P1(a1,f2(x1111)) % 0.56/0.70 [112]~P1(a1,x1121)+P3(a1,f2(x1121)) % 0.56/0.70 [113]~P3(a1,x1131)+P3(a1,f3(x1131)) % 0.56/0.70 [114]~P3(x1141,a1)+P1(f2(x1141),a1) % 0.56/0.70 [115]~P3(x1151,a1)+P3(f2(x1151),a1) % 0.56/0.70 [116]~P3(x1161,a1)+P3(f3(x1161),a1) % 0.56/0.70 [118]P3(x1181,a1)+~P1(f2(x1181),a1) % 0.56/0.70 [119]P3(x1191,a1)+~P3(f2(x1191),a1) % 0.56/0.70 [120]P3(x1201,a1)+~P3(f3(x1201),a1) % 0.56/0.70 [121]P1(a1,x1211)+~P1(a1,f2(x1211)) % 0.56/0.70 [122]P1(a1,x1221)+~P3(a1,f2(x1221)) % 0.56/0.70 [123]P3(a1,x1231)+~P3(a1,f3(x1231)) % 0.56/0.70 [106]~P3(x1061,x1062)+~E(x1061,x1062) % 0.56/0.70 [107]P1(x1072,x1071)+P1(x1071,x1072) % 0.56/0.70 [108]P3(x1082,x1081)+P1(x1081,x1082) % 0.56/0.70 [110]~P3(x1101,x1102)+P1(x1101,x1102) % 0.56/0.70 [125]~P3(x1252,x1251)+~P1(x1251,x1252) % 0.56/0.70 [104]E(x1041,x1042)+~E(f2(x1041),f2(x1042)) % 0.56/0.70 [105]E(x1051,x1052)+~E(f3(x1051),f3(x1052)) % 0.56/0.70 [128]~P1(x1281,x1282)+P1(f2(x1281),f2(x1282)) % 0.56/0.70 [130]~P3(x1301,x1302)+P1(f2(x1301),f3(x1302)) % 0.56/0.70 [132]~P1(x1321,x1322)+P1(f3(x1321),f2(x1322)) % 0.56/0.70 [134]~P1(x1341,x1342)+P1(f3(x1341),f3(x1342)) % 0.56/0.70 [136]~P3(x1361,x1362)+P3(f2(x1361),f2(x1362)) % 0.56/0.70 [138]~P3(x1381,x1382)+P3(f2(x1381),f3(x1382)) % 0.56/0.70 [140]~P1(x1401,x1402)+P3(f3(x1401),f2(x1402)) % 0.56/0.70 [142]~P3(x1421,x1422)+P3(f3(x1421),f3(x1422)) % 0.56/0.70 [144]P4(f4(x1441),f4(x1442))+P6(f4(x1442),f4(x1441)) % 0.56/0.70 [146]P1(x1461,x1462)+~P1(f2(x1461),f2(x1462)) % 0.56/0.70 [148]P1(x1481,x1482)+~P1(f3(x1481),f2(x1482)) % 0.56/0.70 [150]P1(x1501,x1502)+~P1(f3(x1501),f3(x1502)) % 0.56/0.70 [152]P1(x1521,x1522)+~P3(f3(x1521),f2(x1522)) % 0.56/0.70 [154]P3(x1541,x1542)+~P1(f2(x1541),f3(x1542)) % 0.56/0.70 [156]P3(x1561,x1562)+~P3(f2(x1561),f2(x1562)) % 0.56/0.70 [158]P3(x1581,x1582)+~P3(f2(x1581),f3(x1582)) % 0.56/0.70 [160]P3(x1601,x1602)+~P3(f3(x1601),f3(x1602)) % 0.56/0.70 [162]~P1(x1621,x1622)+P3(x1621,f15(x1622,a12)) % 0.56/0.70 [164]~P3(x1641,x1642)+P1(f15(x1641,a12),x1642) % 0.56/0.70 [166]P1(x1661,x1662)+~P3(x1661,f15(x1662,a12)) % 0.56/0.70 [167]P3(x1671,x1672)+~P1(f15(x1671,a12),x1672) % 0.56/0.70 [169]~P4(f4(x1691),f4(x1692))+~P6(f4(x1692),f4(x1691)) % 0.56/0.70 [143]~P3(x1431,a1)+E(f16(f4(x1431),f4(x1432)),f4(x1432)) % 0.56/0.70 [170]~P1(x1702,x1703)+P1(f15(x1701,x1702),f15(x1701,x1703)) % 0.56/0.70 [171]~P3(x1711,x1713)+P3(f15(x1711,x1712),f15(x1713,x1712)) % 0.56/0.70 [109]P3(x1092,x1091)+P3(x1091,x1092)+E(x1091,x1092) % 0.56/0.70 [117]P3(x1171,x1172)+~P1(x1171,x1172)+E(x1171,x1172) % 0.56/0.70 [126]~P1(x1262,x1261)+~P1(x1261,x1262)+E(x1261,x1262) % 0.56/0.70 [124]~P5(x1242)+~P5(x1241)+P5(f19(x1241,x1242)) % 0.56/0.70 [165]P3(x1651,a1)+~P3(x1652,a1)+E(f16(f4(x1651),f4(x1652)),f4(x1651)) % 0.56/0.70 [168]P3(x1681,a1)+P3(x1682,a1)+E(f16(f4(x1681),f4(x1682)),f4(f15(x1681,x1682))) % 0.56/0.70 [161]~P1(x1611,x1613)+P1(x1611,x1612)+~P1(x1613,x1612) % 0.56/0.70 [172]~P1(x1722,x1724)+~P3(x1721,x1723)+P3(f15(x1721,x1722),f15(x1723,x1724)) % 0.56/0.70 %EqnAxiom % 0.56/0.70 [1]E(x11,x11) % 0.56/0.70 [2]E(x22,x21)+~E(x21,x22) % 0.56/0.70 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.56/0.70 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 0.56/0.70 [5]~E(x51,x52)+E(f4(x51),f4(x52)) % 0.56/0.70 [6]~E(x61,x62)+E(f15(x61,x63),f15(x62,x63)) % 0.56/0.70 [7]~E(x71,x72)+E(f15(x73,x71),f15(x73,x72)) % 0.56/0.70 [8]~E(x81,x82)+E(f3(x81),f3(x82)) % 0.56/0.70 [9]~E(x91,x92)+E(f14(x91,x93),f14(x92,x93)) % 0.56/0.70 [10]~E(x101,x102)+E(f14(x103,x101),f14(x103,x102)) % 0.56/0.70 [11]~E(x111,x112)+E(f17(x111,x113),f17(x112,x113)) % 0.56/0.70 [12]~E(x121,x122)+E(f17(x123,x121),f17(x123,x122)) % 0.56/0.70 [13]~E(x131,x132)+E(f19(x131,x133),f19(x132,x133)) % 0.56/0.70 [14]~E(x141,x142)+E(f19(x143,x141),f19(x143,x142)) % 0.56/0.70 [15]~E(x151,x152)+E(f20(x151,x153),f20(x152,x153)) % 0.56/0.70 [16]~E(x161,x162)+E(f20(x163,x161),f20(x163,x162)) % 0.56/0.70 [17]~E(x171,x172)+E(f16(x171,x173),f16(x172,x173)) % 0.56/0.70 [18]~E(x181,x182)+E(f16(x183,x181),f16(x183,x182)) % 0.56/0.70 [19]P1(x192,x193)+~E(x191,x192)+~P1(x191,x193) % 0.56/0.70 [20]P1(x203,x202)+~E(x201,x202)+~P1(x203,x201) % 0.56/0.70 [21]P3(x212,x213)+~E(x211,x212)+~P3(x211,x213) % 0.56/0.70 [22]P3(x223,x222)+~E(x221,x222)+~P3(x223,x221) % 0.56/0.70 [23]P4(x232,x233)+~E(x231,x232)+~P4(x231,x233) % 0.56/0.70 [24]P4(x243,x242)+~E(x241,x242)+~P4(x243,x241) % 0.56/0.70 [25]~P2(x251)+P2(x252)+~E(x251,x252) % 0.56/0.70 [26]P6(x262,x263)+~E(x261,x262)+~P6(x261,x263) % 0.56/0.70 [27]P6(x273,x272)+~E(x271,x272)+~P6(x273,x271) % 0.56/0.70 [28]~P5(x281)+P5(x282)+~E(x281,x282) % 0.56/0.70 % 0.56/0.70 %------------------------------------------- % 0.56/0.70 cnf(177,plain, % 0.56/0.70 (~P3(x1771,x1771)), % 0.56/0.70 inference(equality_inference,[],[106])). % 0.56/0.70 cnf(178,plain, % 0.56/0.70 (~E(a13,a12)), % 0.56/0.70 inference(scs_inference,[],[103,173])). % 0.56/0.70 cnf(179,plain, % 0.56/0.70 (~E(f15(f14(x1791,f4(f3(f2(a1)))),f14(x1792,f4(f3(f2(a1))))),f15(f19(f3(f3(f2(a1))),a5),a12))), % 0.56/0.70 inference(rename_variables,[],[103])). % 0.56/0.70 cnf(180,plain, % 0.56/0.70 (~P3(f15(x1801,x1802),f15(x1802,x1801))), % 0.56/0.70 inference(scs_inference,[],[103,40,173,106])). % 0.56/0.70 cnf(183,plain, % 0.56/0.70 (~E(f15(f14(x1831,f4(f3(f2(a1)))),f14(x1832,f4(f3(f2(a1))))),f15(f19(f3(f3(f2(a1))),a5),a12))), % 0.56/0.70 inference(rename_variables,[],[103])). % 0.56/0.70 cnf(184,plain, % 0.56/0.70 (E(x1841,f14(x1841,a11))), % 0.56/0.70 inference(scs_inference,[],[103,179,40,33,173,106,174,2])). % 0.56/0.70 cnf(188,plain, % 0.56/0.70 (~P3(x1881,x1881)), % 0.56/0.70 inference(rename_variables,[],[177])). % 0.56/0.70 cnf(190,plain, % 0.56/0.70 (P1(a13,f19(f3(f3(f2(a1))),a5))), % 0.56/0.70 inference(scs_inference,[],[103,179,177,40,33,31,94,173,106,174,2,125,162,166])). % 0.56/0.70 cnf(193,plain, % 0.56/0.70 (P1(x1931,x1931)), % 0.56/0.70 inference(rename_variables,[],[35])). % 0.56/0.70 cnf(195,plain, % 0.56/0.70 (E(a12,a13)), % 0.56/0.70 inference(scs_inference,[],[103,179,177,35,40,33,31,94,173,106,174,2,125,162,166,167,109])). % 0.56/0.70 cnf(198,plain, % 0.56/0.70 (E(f15(x1981,x1982),f15(x1982,x1981))), % 0.56/0.70 inference(rename_variables,[],[40])). % 0.56/0.70 cnf(200,plain, % 0.56/0.70 (P1(x2001,x2001)), % 0.56/0.70 inference(rename_variables,[],[35])). % 0.56/0.70 cnf(204,plain, % 0.56/0.70 (~P3(x2041,x2041)), % 0.56/0.70 inference(rename_variables,[],[177])). % 0.56/0.70 cnf(211,plain, % 0.56/0.70 (P1(x2111,f15(x2111,a12))), % 0.56/0.70 inference(scs_inference,[],[103,179,183,177,188,204,35,193,200,40,198,42,33,31,94,93,97,173,106,174,2,125,162,166,167,109,3,19,20,21,22,25,28,107])). % 0.56/0.70 cnf(231,plain, % 0.56/0.70 ($false), % 0.56/0.70 inference(scs_inference,[],[178,180,195,184,211,190,125,162,167,110,106,2]), % 0.56/0.70 ['proof']). % 0.56/0.70 % SZS output end Proof % 0.56/0.70 % Total time :0.020000s %------------------------------------------------------------------------------