TSTP Solution File: NUM926+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM926+1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n005.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 Aug 31 10:25:49 EDT 2023
% Result : Theorem 0.68s 0.80s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM926+1 : TPTP v8.1.2. Released v5.3.0.
% 0.10/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 09:27:53 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 0.68/0.78 %-------------------------------------------
% 0.68/0.78 % File :CSE---1.6
% 0.68/0.78 % Problem :theBenchmark
% 0.68/0.78 % Transform :cnf
% 0.68/0.78 % Format :tptp:raw
% 0.68/0.78 % Command :java -jar mcs_scs.jar %d %s
% 0.68/0.78
% 0.68/0.78 % Result :Theorem 0.140000s
% 0.68/0.78 % Output :CNFRefutation 0.140000s
% 0.68/0.78 %-------------------------------------------
% 0.68/0.78 %------------------------------------------------------------------------------
% 0.68/0.78 % File : NUM926+1 : TPTP v8.1.2. Released v5.3.0.
% 0.68/0.78 % Domain : Number Theory
% 0.68/0.78 % Problem : Sum of two squares line 258, 100 axioms selected
% 0.68/0.78 % Version : Especial.
% 0.68/0.78 % English :
% 0.68/0.78
% 0.68/0.78 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.68/0.78 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.68/0.78 % Source : [Bla11]
% 0.68/0.78 % Names : s2s_100_fofmg_l258 [Bla11]
% 0.68/0.78
% 0.68/0.78 % Status : Theorem
% 0.68/0.78 % Rating : 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
% 0.68/0.78 % Syntax : Number of formulae : 124 ( 76 unt; 0 def)
% 0.68/0.78 % Number of atoms : 183 ( 87 equ)
% 0.68/0.78 % Maximal formula atoms : 7 ( 1 avg)
% 0.68/0.78 % Number of connectives : 67 ( 8 ~; 3 |; 3 &)
% 0.68/0.78 % ( 36 <=>; 17 =>; 0 <=; 0 <~>)
% 0.68/0.78 % Maximal formula depth : 8 ( 3 avg)
% 0.68/0.78 % Maximal term depth : 10 ( 2 avg)
% 0.68/0.78 % Number of predicates : 7 ( 6 usr; 0 prp; 1-2 aty)
% 0.68/0.78 % Number of functors : 16 ( 16 usr; 6 con; 0-2 aty)
% 0.68/0.78 % Number of variables : 244 ( 238 !; 6 ?)
% 0.68/0.78 % SPC : FOF_THM_RFO_SEQ
% 0.68/0.78
% 0.68/0.78 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.68/0.78 % 2011-08-09 15:34:05
% 0.68/0.78 % : Encoded with monomorphized guards.
% 0.68/0.78 %------------------------------------------------------------------------------
% 0.68/0.78 %----Relevant facts (123)
% 0.68/0.78 fof(fact_0_tpos,axiom,
% 0.68/0.78 ord_less_eq_int(one_one_int,t) ).
% 0.68/0.78
% 0.68/0.78 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,
% 0.68/0.78 ( t = one_one_int
% 0.68/0.78 => ? [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) ) ).
% 0.68/0.78
% 0.68/0.78 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,
% 0.68/0.78 ( ord_less_int(one_one_int,t)
% 0.68/0.78 => ? [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) ) ).
% 0.68/0.78
% 0.68/0.78 fof(fact_3_t__l__p,axiom,
% 0.68/0.78 ord_less_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) ).
% 0.68/0.78
% 0.68/0.78 fof(fact_4_p,axiom,
% 0.68/0.78 zprime(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) ).
% 0.68/0.78
% 0.68/0.78 fof(fact_5_t,axiom,
% 0.68/0.78 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) ).
% 0.68/0.78
% 0.68/0.78 fof(fact_6_qf1pt,axiom,
% 0.68/0.78 twoSqu526106917sum2sq(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t)) ).
% 0.68/0.78
% 0.68/0.78 fof(fact_7_zadd__power2,axiom,
% 0.68/0.78 ! [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))))) ).
% 0.68/0.78
% 0.68/0.78 fof(fact_8_zadd__power3,axiom,
% 0.68/0.78 ! [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))))) ).
% 0.68/0.78
% 0.68/0.78 fof(fact_9_power2__sum,axiom,
% 0.68/0.78 ! [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)) ).
% 0.68/0.78
% 0.68/0.78 fof(fact_10_power2__sum,axiom,
% 0.68/0.78 ! [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)) ).
% 0.68/0.78
% 0.68/0.78 fof(fact_11_power2__eq__square__number__of,axiom,
% 0.68/0.78 ! [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)) ).
% 0.68/0.78
% 0.68/0.78 fof(fact_12_power2__eq__square__number__of,axiom,
% 0.68/0.78 ! [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)) ).
% 0.68/0.78
% 0.68/0.78 fof(fact_13_cube__square,axiom,
% 0.68/0.78 ! [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)))) ).
% 0.68/0.78
% 0.68/0.78 fof(fact_14_one__power2,axiom,
% 0.68/0.78 power_power_nat(one_one_nat,number_number_of_nat(bit0(bit1(pls)))) = one_one_nat ).
% 0.68/0.78
% 0.68/0.78 fof(fact_15_one__power2,axiom,
% 0.68/0.78 power_power_int(one_one_int,number_number_of_nat(bit0(bit1(pls)))) = one_one_int ).
% 0.68/0.78
% 0.68/0.78 fof(fact_16_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 0.68/0.78 ! [X_7] : times_times_int(X_7,X_7) = power_power_int(X_7,number_number_of_nat(bit0(bit1(pls)))) ).
% 0.68/0.78
% 0.68/0.78 fof(fact_17_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 0.68/0.78 ! [X_7] : times_times_nat(X_7,X_7) = power_power_nat(X_7,number_number_of_nat(bit0(bit1(pls)))) ).
% 0.68/0.78
% 0.68/0.78 fof(fact_18_power2__eq__square,axiom,
% 0.68/0.78 ! [A_7] : power_power_int(A_7,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(A_7,A_7) ).
% 0.68/0.78
% 0.68/0.78 fof(fact_19_power2__eq__square,axiom,
% 0.68/0.78 ! [A_7] : power_power_nat(A_7,number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(A_7,A_7) ).
% 0.68/0.78
% 0.68/0.78 fof(fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 0.68/0.78 ! [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)) ).
% 0.68/0.78
% 0.68/0.78 fof(fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 0.68/0.79 ! [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)) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_22_add__special_I2_J,axiom,
% 0.68/0.79 ! [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)) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_23_add__special_I3_J,axiom,
% 0.68/0.79 ! [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))) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_24_one__add__one__is__two,axiom,
% 0.68/0.79 plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))) ).
% 0.68/0.79
% 0.68/0.79 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,
% 0.68/0.79 ~ ! [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) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_26_zle__refl,axiom,
% 0.68/0.79 ! [W] : ord_less_eq_int(W,W) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_27_zle__linear,axiom,
% 0.68/0.79 ! [Z,W] :
% 0.68/0.79 ( ord_less_eq_int(Z,W)
% 0.68/0.79 | ord_less_eq_int(W,Z) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_28_zless__le,axiom,
% 0.68/0.79 ! [Z_1,W_1] :
% 0.68/0.79 ( ord_less_int(Z_1,W_1)
% 0.68/0.79 <=> ( ord_less_eq_int(Z_1,W_1)
% 0.68/0.79 & Z_1 != W_1 ) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_29_zless__linear,axiom,
% 0.68/0.79 ! [X_1,Y_1] :
% 0.68/0.79 ( ord_less_int(X_1,Y_1)
% 0.68/0.79 | X_1 = Y_1
% 0.68/0.79 | ord_less_int(Y_1,X_1) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_30_zle__trans,axiom,
% 0.68/0.79 ! [K_1,I,J] :
% 0.68/0.79 ( ord_less_eq_int(I,J)
% 0.68/0.79 => ( ord_less_eq_int(J,K_1)
% 0.68/0.79 => ord_less_eq_int(I,K_1) ) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_31_zle__antisym,axiom,
% 0.68/0.79 ! [Z,W] :
% 0.68/0.79 ( ord_less_eq_int(Z,W)
% 0.68/0.79 => ( ord_less_eq_int(W,Z)
% 0.68/0.79 => Z = W ) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 0.68/0.79 ! [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)) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 0.68/0.79 ! [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)) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_34_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 0.68/0.79 ! [X_4] : power_power_int(X_4,one_one_nat) = X_4 ).
% 0.68/0.79
% 0.68/0.79 fof(fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 0.68/0.79 ! [X_4] : power_power_nat(X_4,one_one_nat) = X_4 ).
% 0.68/0.79
% 0.68/0.79 fof(fact_36_zpower__zpower,axiom,
% 0.68/0.79 ! [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)) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_37_le__number__of__eq__not__less,axiom,
% 0.68/0.79 ! [V_2,W_1] :
% 0.68/0.79 ( ord_less_eq_nat(number_number_of_nat(V_2),number_number_of_nat(W_1))
% 0.68/0.79 <=> ~ ord_less_nat(number_number_of_nat(W_1),number_number_of_nat(V_2)) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_38_le__number__of__eq__not__less,axiom,
% 0.68/0.79 ! [V_2,W_1] :
% 0.68/0.79 ( ord_less_eq_int(number_number_of_int(V_2),number_number_of_int(W_1))
% 0.68/0.79 <=> ~ ord_less_int(number_number_of_int(W_1),number_number_of_int(V_2)) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_39_less__number__of,axiom,
% 0.68/0.79 ! [X_2,Y_2] :
% 0.68/0.79 ( ord_less_int(number_number_of_int(X_2),number_number_of_int(Y_2))
% 0.68/0.79 <=> ord_less_int(X_2,Y_2) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_40_le__number__of,axiom,
% 0.68/0.79 ! [X_2,Y_2] :
% 0.68/0.79 ( ord_less_eq_int(number_number_of_int(X_2),number_number_of_int(Y_2))
% 0.68/0.79 <=> ord_less_eq_int(X_2,Y_2) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_41_zadd__zless__mono,axiom,
% 0.68/0.79 ! [Z_2,Z,W_2,W] :
% 0.68/0.79 ( ord_less_int(W_2,W)
% 0.68/0.79 => ( ord_less_eq_int(Z_2,Z)
% 0.68/0.79 => ord_less_int(plus_plus_int(W_2,Z_2),plus_plus_int(W,Z)) ) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 0.68/0.79 ! [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)) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 0.68/0.79 ! [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)) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_44_zpower__zadd__distrib,axiom,
% 0.68/0.79 ! [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)) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_45_nat__mult__2,axiom,
% 0.68/0.79 ! [Z] : times_times_nat(number_number_of_nat(bit0(bit1(pls))),Z) = plus_plus_nat(Z,Z) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_46_nat__mult__2__right,axiom,
% 0.68/0.79 ! [Z] : times_times_nat(Z,number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(Z,Z) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_47_nat__1__add__1,axiom,
% 0.68/0.79 plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_48_less__int__code_I16_J,axiom,
% 0.68/0.79 ! [K1,K2] :
% 0.68/0.79 ( ord_less_int(bit1(K1),bit1(K2))
% 0.68/0.79 <=> ord_less_int(K1,K2) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_49_rel__simps_I17_J,axiom,
% 0.68/0.79 ! [K,L] :
% 0.68/0.79 ( ord_less_int(bit1(K),bit1(L))
% 0.68/0.79 <=> ord_less_int(K,L) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_50_less__eq__int__code_I16_J,axiom,
% 0.68/0.79 ! [K1,K2] :
% 0.68/0.79 ( ord_less_eq_int(bit1(K1),bit1(K2))
% 0.68/0.79 <=> ord_less_eq_int(K1,K2) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_51_rel__simps_I34_J,axiom,
% 0.68/0.79 ! [K,L] :
% 0.68/0.79 ( ord_less_eq_int(bit1(K),bit1(L))
% 0.68/0.79 <=> ord_less_eq_int(K,L) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_52_rel__simps_I2_J,axiom,
% 0.68/0.79 ~ ord_less_int(pls,pls) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_53_less__int__code_I13_J,axiom,
% 0.68/0.79 ! [K1,K2] :
% 0.68/0.79 ( ord_less_int(bit0(K1),bit0(K2))
% 0.68/0.79 <=> ord_less_int(K1,K2) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_54_rel__simps_I14_J,axiom,
% 0.68/0.79 ! [K,L] :
% 0.68/0.79 ( ord_less_int(bit0(K),bit0(L))
% 0.68/0.79 <=> ord_less_int(K,L) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_55_rel__simps_I19_J,axiom,
% 0.68/0.79 ord_less_eq_int(pls,pls) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_56_less__eq__int__code_I13_J,axiom,
% 0.68/0.79 ! [K1,K2] :
% 0.68/0.79 ( ord_less_eq_int(bit0(K1),bit0(K2))
% 0.68/0.79 <=> ord_less_eq_int(K1,K2) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_57_rel__simps_I31_J,axiom,
% 0.68/0.79 ! [K,L] :
% 0.68/0.79 ( ord_less_eq_int(bit0(K),bit0(L))
% 0.68/0.79 <=> ord_less_eq_int(K,L) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_58_less__number__of__int__code,axiom,
% 0.68/0.79 ! [K,L] :
% 0.68/0.79 ( ord_less_int(number_number_of_int(K),number_number_of_int(L))
% 0.68/0.79 <=> ord_less_int(K,L) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_59_less__eq__number__of__int__code,axiom,
% 0.68/0.79 ! [K,L] :
% 0.68/0.79 ( ord_less_eq_int(number_number_of_int(K),number_number_of_int(L))
% 0.68/0.79 <=> ord_less_eq_int(K,L) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_60_zadd__strict__right__mono,axiom,
% 0.68/0.79 ! [K_1,I,J] :
% 0.68/0.79 ( ord_less_int(I,J)
% 0.68/0.79 => ord_less_int(plus_plus_int(I,K_1),plus_plus_int(J,K_1)) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_61_zadd__left__mono,axiom,
% 0.68/0.79 ! [K_1,I,J] :
% 0.68/0.79 ( ord_less_eq_int(I,J)
% 0.68/0.79 => ord_less_eq_int(plus_plus_int(K_1,I),plus_plus_int(K_1,J)) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_62_add__nat__number__of,axiom,
% 0.68/0.79 ! [V_1,V] :
% 0.68/0.79 ( ( ord_less_int(V,pls)
% 0.68/0.79 => plus_plus_nat(number_number_of_nat(V),number_number_of_nat(V_1)) = number_number_of_nat(V_1) )
% 0.68/0.79 & ( ~ ord_less_int(V,pls)
% 0.68/0.79 => ( ( ord_less_int(V_1,pls)
% 0.68/0.79 => plus_plus_nat(number_number_of_nat(V),number_number_of_nat(V_1)) = number_number_of_nat(V) )
% 0.68/0.79 & ( ~ ord_less_int(V_1,pls)
% 0.68/0.79 => plus_plus_nat(number_number_of_nat(V),number_number_of_nat(V_1)) = number_number_of_nat(plus_plus_int(V,V_1)) ) ) ) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_63_nat__numeral__1__eq__1,axiom,
% 0.68/0.79 number_number_of_nat(bit1(pls)) = one_one_nat ).
% 0.68/0.79
% 0.68/0.79 fof(fact_64_Numeral1__eq1__nat,axiom,
% 0.68/0.79 one_one_nat = number_number_of_nat(bit1(pls)) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_65_rel__simps_I29_J,axiom,
% 0.68/0.79 ! [K] :
% 0.68/0.79 ( ord_less_eq_int(bit1(K),pls)
% 0.68/0.79 <=> ord_less_int(K,pls) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_66_rel__simps_I5_J,axiom,
% 0.68/0.79 ! [K] :
% 0.68/0.79 ( ord_less_int(pls,bit1(K))
% 0.68/0.79 <=> ord_less_eq_int(pls,K) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_67_less__eq__int__code_I15_J,axiom,
% 0.68/0.79 ! [K1,K2] :
% 0.68/0.79 ( ord_less_eq_int(bit1(K1),bit0(K2))
% 0.68/0.79 <=> ord_less_int(K1,K2) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_68_rel__simps_I33_J,axiom,
% 0.68/0.79 ! [K,L] :
% 0.68/0.79 ( ord_less_eq_int(bit1(K),bit0(L))
% 0.68/0.79 <=> ord_less_int(K,L) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_69_less__int__code_I14_J,axiom,
% 0.68/0.79 ! [K1,K2] :
% 0.68/0.79 ( ord_less_int(bit0(K1),bit1(K2))
% 0.68/0.79 <=> ord_less_eq_int(K1,K2) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_70_rel__simps_I15_J,axiom,
% 0.68/0.79 ! [K,L] :
% 0.68/0.79 ( ord_less_int(bit0(K),bit1(L))
% 0.68/0.79 <=> ord_less_eq_int(K,L) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_71_zless__imp__add1__zle,axiom,
% 0.68/0.79 ! [W,Z] :
% 0.68/0.79 ( ord_less_int(W,Z)
% 0.68/0.79 => ord_less_eq_int(plus_plus_int(W,one_one_int),Z) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_72_add1__zle__eq,axiom,
% 0.68/0.79 ! [W_1,Z_1] :
% 0.68/0.79 ( ord_less_eq_int(plus_plus_int(W_1,one_one_int),Z_1)
% 0.68/0.79 <=> ord_less_int(W_1,Z_1) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_73_zle__add1__eq__le,axiom,
% 0.68/0.79 ! [W_1,Z_1] :
% 0.68/0.79 ( ord_less_int(W_1,plus_plus_int(Z_1,one_one_int))
% 0.68/0.79 <=> ord_less_eq_int(W_1,Z_1) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_74_zprime__2,axiom,
% 0.68/0.79 zprime(number_number_of_int(bit0(bit1(pls)))) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_75_is__mult__sum2sq,axiom,
% 0.68/0.79 ! [Y_1,X_1] :
% 0.68/0.79 ( twoSqu526106917sum2sq(X_1)
% 0.68/0.79 => ( twoSqu526106917sum2sq(Y_1)
% 0.68/0.79 => twoSqu526106917sum2sq(times_times_int(X_1,Y_1)) ) ) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 0.68/0.79 ! [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)) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 0.68/0.79 ! [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)) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 0.68/0.79 ! [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)) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 0.68/0.79 ! [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)) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 0.68/0.79 ! [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))) ).
% 0.68/0.79
% 0.68/0.79 fof(fact_81_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 0.68/0.80 ! [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))) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_82_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 0.68/0.80 ! [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) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_83_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 0.68/0.80 ! [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) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 0.68/0.80 ! [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)) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_85_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 0.68/0.80 ! [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)) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_86_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 0.68/0.80 ! [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) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_87_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 0.68/0.80 ! [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) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_88_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 0.68/0.80 ! [Lx,Rx,Ry] : times_times_int(Lx,times_times_int(Rx,Ry)) = times_times_int(Rx,times_times_int(Lx,Ry)) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_89_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 0.68/0.80 ! [Lx,Rx,Ry] : times_times_nat(Lx,times_times_nat(Rx,Ry)) = times_times_nat(Rx,times_times_nat(Lx,Ry)) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 0.68/0.80 ! [A_6,B_3] : times_times_int(A_6,B_3) = times_times_int(B_3,A_6) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 0.68/0.80 ! [A_6,B_3] : times_times_nat(A_6,B_3) = times_times_nat(B_3,A_6) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 0.68/0.80 ! [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)) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 0.68/0.80 ! [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)) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 0.68/0.80 ! [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) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 0.68/0.80 ! [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) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 0.68/0.80 ! [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)) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 0.68/0.80 ! [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)) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 0.68/0.80 ! [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) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 0.68/0.80 ! [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) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 0.68/0.80 ! [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)) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 0.68/0.80 ! [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)) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 0.68/0.80 ! [A,C] : plus_plus_int(A,C) = plus_plus_int(C,A) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 0.68/0.80 ! [A,C] : plus_plus_nat(A,C) = plus_plus_nat(C,A) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_104_eq__number__of,axiom,
% 0.68/0.80 ! [X_2,Y_2] :
% 0.68/0.80 ( number_number_of_int(X_2) = number_number_of_int(Y_2)
% 0.68/0.80 <=> X_2 = Y_2 ) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_105_number__of__reorient,axiom,
% 0.68/0.80 ! [W_1,X_2] :
% 0.68/0.80 ( number_number_of_nat(W_1) = X_2
% 0.68/0.80 <=> X_2 = number_number_of_nat(W_1) ) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_106_number__of__reorient,axiom,
% 0.68/0.80 ! [W_1,X_2] :
% 0.68/0.80 ( number_number_of_int(W_1) = X_2
% 0.68/0.80 <=> X_2 = number_number_of_int(W_1) ) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_107_rel__simps_I51_J,axiom,
% 0.68/0.80 ! [K,L] :
% 0.68/0.80 ( bit1(K) = bit1(L)
% 0.68/0.80 <=> K = L ) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_108_rel__simps_I48_J,axiom,
% 0.68/0.80 ! [K,L] :
% 0.68/0.80 ( bit0(K) = bit0(L)
% 0.68/0.80 <=> K = L ) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_109_zmult__assoc,axiom,
% 0.68/0.80 ! [Z1,Z2,Z3] : times_times_int(times_times_int(Z1,Z2),Z3) = times_times_int(Z1,times_times_int(Z2,Z3)) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_110_zmult__commute,axiom,
% 0.68/0.80 ! [Z,W] : times_times_int(Z,W) = times_times_int(W,Z) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_111_number__of__is__id,axiom,
% 0.68/0.80 ! [K_1] : number_number_of_int(K_1) = K_1 ).
% 0.68/0.80
% 0.68/0.80 fof(fact_112_zadd__assoc,axiom,
% 0.68/0.80 ! [Z1,Z2,Z3] : plus_plus_int(plus_plus_int(Z1,Z2),Z3) = plus_plus_int(Z1,plus_plus_int(Z2,Z3)) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_113_zadd__left__commute,axiom,
% 0.68/0.80 ! [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)) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_114_zadd__commute,axiom,
% 0.68/0.80 ! [Z,W] : plus_plus_int(Z,W) = plus_plus_int(W,Z) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_115_rel__simps_I12_J,axiom,
% 0.68/0.80 ! [K] :
% 0.68/0.80 ( ord_less_int(bit1(K),pls)
% 0.68/0.80 <=> ord_less_int(K,pls) ) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_116_less__int__code_I15_J,axiom,
% 0.68/0.80 ! [K1,K2] :
% 0.68/0.80 ( ord_less_int(bit1(K1),bit0(K2))
% 0.68/0.80 <=> ord_less_int(K1,K2) ) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_117_rel__simps_I16_J,axiom,
% 0.68/0.80 ! [K,L] :
% 0.68/0.80 ( ord_less_int(bit1(K),bit0(L))
% 0.68/0.80 <=> ord_less_int(K,L) ) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_118_rel__simps_I10_J,axiom,
% 0.68/0.80 ! [K] :
% 0.68/0.80 ( ord_less_int(bit0(K),pls)
% 0.68/0.80 <=> ord_less_int(K,pls) ) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_119_rel__simps_I4_J,axiom,
% 0.68/0.80 ! [K] :
% 0.68/0.80 ( ord_less_int(pls,bit0(K))
% 0.68/0.80 <=> ord_less_int(pls,K) ) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_120_rel__simps_I22_J,axiom,
% 0.68/0.80 ! [K] :
% 0.68/0.80 ( ord_less_eq_int(pls,bit1(K))
% 0.68/0.80 <=> ord_less_eq_int(pls,K) ) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_121_less__eq__int__code_I14_J,axiom,
% 0.68/0.80 ! [K1,K2] :
% 0.68/0.80 ( ord_less_eq_int(bit0(K1),bit1(K2))
% 0.68/0.80 <=> ord_less_eq_int(K1,K2) ) ).
% 0.68/0.80
% 0.68/0.80 fof(fact_122_rel__simps_I32_J,axiom,
% 0.68/0.80 ! [K,L] :
% 0.68/0.80 ( ord_less_eq_int(bit0(K),bit1(L))
% 0.68/0.80 <=> ord_less_eq_int(K,L) ) ).
% 0.68/0.80
% 0.68/0.80 %----Conjectures (1)
% 0.68/0.80 fof(conj_0,conjecture,
% 0.68/0.80 ? [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) ).
% 0.68/0.80
% 0.68/0.80 %------------------------------------------------------------------------------
% 0.68/0.80 %-------------------------------------------
% 0.68/0.80 % Proof found
% 0.68/0.80 % SZS status Theorem for theBenchmark
% 0.68/0.80 % SZS output start Proof
% 0.68/0.80 %ClaNum:174(EqnAxiom:28)
% 0.68/0.80 %VarNum:420(SingletonVarNum:195)
% 0.68/0.80 %MaxLitNum:3
% 0.68/0.80 %MaxfuncDepth:6
% 0.68/0.80 %SharedTerms:51
% 0.68/0.80 %goalClause: 103
% 0.68/0.80 %singleGoalClaCount:1
% 0.68/0.80 [31]P1(a12,a13)
% 0.68/0.80 [102]~P3(a1,a1)
% 0.68/0.80 [30]E(f4(f2(a1)),a11)
% 0.68/0.80 [36]P2(f3(f2(a1)))
% 0.68/0.80 [37]E(f3(f2(a1)),f15(a12,a12))
% 0.68/0.80 [38]E(f4(f3(f2(a1))),f16(a11,a11))
% 0.68/0.80 [47]E(f14(a12,f4(f3(f2(a1)))),a12)
% 0.68/0.80 [48]E(f17(a11,f4(f3(f2(a1)))),a11)
% 0.68/0.80 [93]P2(f15(f19(f3(f3(f2(a1))),a5),a12))
% 0.68/0.80 [94]P3(a13,f15(f19(f3(f3(f2(a1))),a5),a12))
% 0.68/0.80 [95]E(f19(f15(f19(f3(f3(f2(a1))),a5),a12),a13),f15(f14(a18,f4(f3(f2(a1)))),a12))
% 0.68/0.80 [96]E(f19(f15(f19(f3(f3(f2(a1))),a5),a12),a6),f15(f14(a18,f4(f3(f2(a1)))),a12))
% 0.68/0.80 [97]P5(f19(f15(f19(f3(f3(f2(a1))),a5),a12),a13))
% 0.68/0.80 [35]P1(x351,x351)
% 0.68/0.80 [33]E(f14(x331,a11),x331)
% 0.68/0.80 [34]E(f17(x341,a11),x341)
% 0.68/0.80 [45]E(f15(x451,f2(a1)),f15(x451,a12))
% 0.68/0.80 [46]E(f15(f2(a1),x461),f15(a12,x461))
% 0.68/0.80 [49]E(f19(x491,x491),f14(x491,f4(f3(f2(a1)))))
% 0.68/0.80 [50]E(f20(x501,x501),f17(x501,f4(f3(f2(a1)))))
% 0.68/0.80 [52]E(f14(x521,f4(f3(f2(a1)))),f19(x521,x521))
% 0.68/0.80 [53]E(f17(x531,f4(f3(f2(a1)))),f20(x531,x531))
% 0.68/0.80 [54]E(f20(x541,f4(f3(f2(a1)))),f16(x541,x541))
% 0.68/0.80 [55]E(f20(f4(f3(f2(a1))),x551),f16(x551,x551))
% 0.68/0.80 [86]E(f19(x861,f14(x861,f4(f3(f2(a1))))),f14(x861,f4(f2(f2(a1)))))
% 0.68/0.80 [40]E(f15(x401,x402),f15(x402,x401))
% 0.68/0.80 [42]E(f19(x421,x422),f19(x422,x421))
% 0.68/0.80 [43]E(f16(x431,x432),f16(x432,x431))
% 0.68/0.80 [44]E(f20(x441,x442),f20(x442,x441))
% 0.68/0.80 [91]E(f14(x911,f20(f4(f3(f2(a1))),x912)),f19(f14(x911,x912),f14(x911,x912)))
% 0.68/0.80 [92]E(f17(x921,f20(f4(f3(f2(a1))),x922)),f20(f17(x921,x922),f17(x921,x922)))
% 0.68/0.80 [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)))))
% 0.68/0.80 [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)))))
% 0.68/0.80 [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)))))
% 0.68/0.80 [103]~E(f15(f14(x1031,f4(f3(f2(a1)))),f14(x1032,f4(f3(f2(a1))))),f15(f19(f3(f3(f2(a1))),a5),a12))
% 0.68/0.80 [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)))))
% 0.68/0.80 [58]E(f15(x581,f15(x582,x583)),f15(x582,f15(x581,x583)))
% 0.68/0.80 [59]E(f19(x591,f19(x592,x593)),f19(x592,f19(x591,x593)))
% 0.68/0.80 [60]E(f16(x601,f16(x602,x603)),f16(x602,f16(x601,x603)))
% 0.68/0.80 [61]E(f20(x611,f20(x612,x613)),f20(x612,f20(x611,x613)))
% 0.68/0.80 [67]E(f14(f14(x671,x672),x673),f14(x671,f20(x672,x673)))
% 0.68/0.80 [69]E(f15(f15(x691,x692),x693),f15(x691,f15(x692,x693)))
% 0.68/0.80 [71]E(f19(f19(x711,x712),x713),f19(x711,f19(x712,x713)))
% 0.68/0.80 [72]E(f16(f16(x721,x722),x723),f16(x721,f16(x722,x723)))
% 0.68/0.80 [73]E(f17(f17(x731,x732),x733),f17(x731,f20(x732,x733)))
% 0.68/0.80 [74]E(f20(f20(x741,x742),x743),f20(x741,f20(x742,x743)))
% 0.68/0.80 [75]E(f15(f15(x751,x752),x753),f15(f15(x751,x753),x752))
% 0.68/0.80 [76]E(f19(f19(x761,x762),x763),f19(f19(x761,x763),x762))
% 0.68/0.80 [77]E(f16(f16(x771,x772),x773),f16(f16(x771,x773),x772))
% 0.68/0.80 [78]E(f20(f20(x781,x782),x783),f20(f20(x781,x783),x782))
% 0.68/0.80 [80]E(f19(f14(x801,x802),f14(x801,x803)),f14(x801,f16(x802,x803)))
% 0.68/0.80 [81]E(f20(f17(x811,x812),f17(x811,x813)),f17(x811,f16(x812,x813)))
% 0.68/0.80 [82]E(f15(f15(x821,x822),f15(x823,x824)),f15(f15(x821,x823),f15(x822,x824)))
% 0.68/0.80 [83]E(f19(f19(x831,x832),f19(x833,x834)),f19(f19(x831,x833),f19(x832,x834)))
% 0.68/0.80 [84]E(f16(f16(x841,x842),f16(x843,x844)),f16(f16(x841,x843),f16(x842,x844)))
% 0.68/0.80 [85]E(f20(f20(x851,x852),f20(x853,x854)),f20(f20(x851,x853),f20(x852,x854)))
% 0.68/0.80 [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))
% 0.68/0.80 [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))
% 0.68/0.80 [111]~P1(a1,x1111)+P1(a1,f2(x1111))
% 0.68/0.80 [112]~P1(a1,x1121)+P3(a1,f2(x1121))
% 0.68/0.80 [113]~P3(a1,x1131)+P3(a1,f3(x1131))
% 0.68/0.80 [114]~P3(x1141,a1)+P1(f2(x1141),a1)
% 0.68/0.80 [115]~P3(x1151,a1)+P3(f2(x1151),a1)
% 0.68/0.80 [116]~P3(x1161,a1)+P3(f3(x1161),a1)
% 0.68/0.80 [118]P3(x1181,a1)+~P1(f2(x1181),a1)
% 0.68/0.80 [119]P3(x1191,a1)+~P3(f2(x1191),a1)
% 0.68/0.80 [120]P3(x1201,a1)+~P3(f3(x1201),a1)
% 0.68/0.80 [121]P1(a1,x1211)+~P1(a1,f2(x1211))
% 0.68/0.80 [122]P1(a1,x1221)+~P3(a1,f2(x1221))
% 0.68/0.80 [123]P3(a1,x1231)+~P3(a1,f3(x1231))
% 0.68/0.80 [106]~P3(x1061,x1062)+~E(x1061,x1062)
% 0.68/0.80 [107]P1(x1072,x1071)+P1(x1071,x1072)
% 0.68/0.80 [108]P3(x1082,x1081)+P1(x1081,x1082)
% 0.68/0.80 [110]~P3(x1101,x1102)+P1(x1101,x1102)
% 0.68/0.80 [125]~P3(x1252,x1251)+~P1(x1251,x1252)
% 0.68/0.80 [104]E(x1041,x1042)+~E(f2(x1041),f2(x1042))
% 0.68/0.80 [105]E(x1051,x1052)+~E(f3(x1051),f3(x1052))
% 0.68/0.80 [128]~P1(x1281,x1282)+P1(f2(x1281),f2(x1282))
% 0.68/0.80 [130]~P3(x1301,x1302)+P1(f2(x1301),f3(x1302))
% 0.68/0.80 [132]~P1(x1321,x1322)+P1(f3(x1321),f2(x1322))
% 0.68/0.80 [134]~P1(x1341,x1342)+P1(f3(x1341),f3(x1342))
% 0.68/0.80 [136]~P3(x1361,x1362)+P3(f2(x1361),f2(x1362))
% 0.68/0.80 [138]~P3(x1381,x1382)+P3(f2(x1381),f3(x1382))
% 0.68/0.80 [140]~P1(x1401,x1402)+P3(f3(x1401),f2(x1402))
% 0.68/0.80 [142]~P3(x1421,x1422)+P3(f3(x1421),f3(x1422))
% 0.68/0.80 [144]P4(f4(x1441),f4(x1442))+P6(f4(x1442),f4(x1441))
% 0.68/0.80 [146]P1(x1461,x1462)+~P1(f2(x1461),f2(x1462))
% 0.68/0.80 [148]P1(x1481,x1482)+~P1(f3(x1481),f2(x1482))
% 0.68/0.80 [150]P1(x1501,x1502)+~P1(f3(x1501),f3(x1502))
% 0.68/0.80 [152]P1(x1521,x1522)+~P3(f3(x1521),f2(x1522))
% 0.68/0.80 [154]P3(x1541,x1542)+~P1(f2(x1541),f3(x1542))
% 0.68/0.80 [156]P3(x1561,x1562)+~P3(f2(x1561),f2(x1562))
% 0.68/0.80 [158]P3(x1581,x1582)+~P3(f2(x1581),f3(x1582))
% 0.68/0.80 [160]P3(x1601,x1602)+~P3(f3(x1601),f3(x1602))
% 0.68/0.80 [162]~P1(x1621,x1622)+P3(x1621,f15(x1622,a12))
% 0.68/0.80 [164]~P3(x1641,x1642)+P1(f15(x1641,a12),x1642)
% 0.68/0.80 [166]P1(x1661,x1662)+~P3(x1661,f15(x1662,a12))
% 0.68/0.80 [167]P3(x1671,x1672)+~P1(f15(x1671,a12),x1672)
% 0.68/0.80 [169]~P4(f4(x1691),f4(x1692))+~P6(f4(x1692),f4(x1691))
% 0.68/0.80 [143]~P3(x1431,a1)+E(f16(f4(x1431),f4(x1432)),f4(x1432))
% 0.68/0.80 [170]~P1(x1702,x1703)+P1(f15(x1701,x1702),f15(x1701,x1703))
% 0.68/0.80 [171]~P3(x1711,x1713)+P3(f15(x1711,x1712),f15(x1713,x1712))
% 0.68/0.80 [109]P3(x1092,x1091)+P3(x1091,x1092)+E(x1091,x1092)
% 0.68/0.80 [117]P3(x1171,x1172)+~P1(x1171,x1172)+E(x1171,x1172)
% 0.68/0.80 [126]~P1(x1262,x1261)+~P1(x1261,x1262)+E(x1261,x1262)
% 0.68/0.80 [124]~P5(x1242)+~P5(x1241)+P5(f19(x1241,x1242))
% 0.68/0.80 [165]P3(x1651,a1)+~P3(x1652,a1)+E(f16(f4(x1651),f4(x1652)),f4(x1651))
% 0.68/0.80 [168]P3(x1681,a1)+P3(x1682,a1)+E(f16(f4(x1681),f4(x1682)),f4(f15(x1681,x1682)))
% 0.68/0.80 [161]~P1(x1611,x1613)+P1(x1611,x1612)+~P1(x1613,x1612)
% 0.68/0.80 [172]~P1(x1722,x1724)+~P3(x1721,x1723)+P3(f15(x1721,x1722),f15(x1723,x1724))
% 0.68/0.80 %EqnAxiom
% 0.68/0.80 [1]E(x11,x11)
% 0.68/0.80 [2]E(x22,x21)+~E(x21,x22)
% 0.68/0.80 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.68/0.80 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 0.68/0.80 [5]~E(x51,x52)+E(f4(x51),f4(x52))
% 0.68/0.80 [6]~E(x61,x62)+E(f15(x61,x63),f15(x62,x63))
% 0.68/0.80 [7]~E(x71,x72)+E(f15(x73,x71),f15(x73,x72))
% 0.68/0.80 [8]~E(x81,x82)+E(f3(x81),f3(x82))
% 0.68/0.80 [9]~E(x91,x92)+E(f14(x91,x93),f14(x92,x93))
% 0.68/0.80 [10]~E(x101,x102)+E(f14(x103,x101),f14(x103,x102))
% 0.68/0.80 [11]~E(x111,x112)+E(f17(x111,x113),f17(x112,x113))
% 0.68/0.80 [12]~E(x121,x122)+E(f17(x123,x121),f17(x123,x122))
% 0.68/0.80 [13]~E(x131,x132)+E(f19(x131,x133),f19(x132,x133))
% 0.68/0.80 [14]~E(x141,x142)+E(f19(x143,x141),f19(x143,x142))
% 0.68/0.80 [15]~E(x151,x152)+E(f20(x151,x153),f20(x152,x153))
% 0.68/0.80 [16]~E(x161,x162)+E(f20(x163,x161),f20(x163,x162))
% 0.68/0.80 [17]~E(x171,x172)+E(f16(x171,x173),f16(x172,x173))
% 0.68/0.80 [18]~E(x181,x182)+E(f16(x183,x181),f16(x183,x182))
% 0.68/0.80 [19]P1(x192,x193)+~E(x191,x192)+~P1(x191,x193)
% 0.68/0.80 [20]P1(x203,x202)+~E(x201,x202)+~P1(x203,x201)
% 0.68/0.80 [21]P3(x212,x213)+~E(x211,x212)+~P3(x211,x213)
% 0.68/0.80 [22]P3(x223,x222)+~E(x221,x222)+~P3(x223,x221)
% 0.68/0.80 [23]P4(x232,x233)+~E(x231,x232)+~P4(x231,x233)
% 0.68/0.80 [24]P4(x243,x242)+~E(x241,x242)+~P4(x243,x241)
% 0.68/0.80 [25]~P2(x251)+P2(x252)+~E(x251,x252)
% 0.68/0.80 [26]P6(x262,x263)+~E(x261,x262)+~P6(x261,x263)
% 0.68/0.80 [27]P6(x273,x272)+~E(x271,x272)+~P6(x273,x271)
% 0.68/0.80 [28]~P5(x281)+P5(x282)+~E(x281,x282)
% 0.68/0.80
% 0.68/0.80 %-------------------------------------------
% 0.68/0.80 cnf(175,plain,
% 0.68/0.80 (E(a11,f4(f2(a1)))),
% 0.68/0.80 inference(scs_inference,[],[30,2])).
% 0.68/0.80 cnf(176,plain,
% 0.68/0.80 (~P3(x1761,x1761)),
% 0.68/0.80 inference(scs_inference,[],[35,30,2,125])).
% 0.68/0.80 cnf(181,plain,
% 0.68/0.80 (~E(f15(f14(x1811,f4(f3(f2(a1)))),f14(x1812,f4(f3(f2(a1))))),f15(f19(f3(f3(f2(a1))),a5),a12))),
% 0.68/0.80 inference(rename_variables,[],[103])).
% 0.68/0.80 cnf(182,plain,
% 0.68/0.80 (~E(a13,a12)),
% 0.68/0.80 inference(scs_inference,[],[103,181,35,30,2,125,106,174,173])).
% 0.68/0.80 cnf(183,plain,
% 0.68/0.80 (~E(f15(f14(x1831,f4(f3(f2(a1)))),f14(x1832,f4(f3(f2(a1))))),f15(f19(f3(f3(f2(a1))),a5),a12))),
% 0.68/0.80 inference(rename_variables,[],[103])).
% 0.68/0.80 cnf(184,plain,
% 0.68/0.80 (P3(x1841,f15(x1841,a12))),
% 0.68/0.80 inference(scs_inference,[],[103,181,35,30,2,125,106,174,173,167])).
% 0.68/0.80 cnf(185,plain,
% 0.68/0.80 (P1(x1851,x1851)),
% 0.68/0.80 inference(rename_variables,[],[35])).
% 0.68/0.80 cnf(191,plain,
% 0.68/0.80 (P5(f15(f14(a18,f4(f3(f2(a1)))),a12))),
% 0.68/0.80 inference(scs_inference,[],[103,181,35,30,94,97,95,2,125,106,174,173,167,166,162,28])).
% 0.68/0.80 cnf(197,plain,
% 0.68/0.80 (P1(x1971,x1971)),
% 0.68/0.80 inference(rename_variables,[],[35])).
% 0.68/0.80 cnf(199,plain,
% 0.68/0.80 (P1(x1991,x1991)),
% 0.68/0.80 inference(rename_variables,[],[35])).
% 0.68/0.80 cnf(212,plain,
% 0.68/0.80 (~P3(a1,f3(a1))),
% 0.68/0.80 inference(scs_inference,[],[103,181,35,185,197,31,102,30,36,37,94,97,95,33,40,2,125,106,174,173,167,166,162,28,25,22,21,20,19,3,117,110,108,107,164,123])).
% 0.68/0.80 cnf(214,plain,
% 0.68/0.80 (~P3(f3(a1),a1)),
% 0.68/0.80 inference(scs_inference,[],[103,181,35,185,197,31,102,30,36,37,94,97,95,33,40,2,125,106,174,173,167,166,162,28,25,22,21,20,19,3,117,110,108,107,164,123,120])).
% 0.68/0.80 cnf(221,plain,
% 0.68/0.80 (P1(x2211,x2211)),
% 0.68/0.80 inference(rename_variables,[],[35])).
% 0.68/0.80 cnf(224,plain,
% 0.68/0.80 (P1(x2241,x2241)),
% 0.68/0.80 inference(rename_variables,[],[35])).
% 0.68/0.80 cnf(253,plain,
% 0.68/0.80 (~P3(f3(f15(f19(f3(f3(f2(a1))),a5),a12)),f2(f19(f3(f3(f2(a1))),a5)))),
% 0.68/0.80 inference(scs_inference,[],[103,181,35,185,197,199,221,31,102,30,36,37,94,97,95,33,40,2,125,106,174,173,167,166,162,28,25,22,21,20,19,3,117,110,108,107,164,123,120,119,118,112,111,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,171,170,160,158,156,154,152])).
% 0.68/0.80 cnf(259,plain,
% 0.68/0.80 (~P1(f2(f15(f19(f3(f3(f2(a1))),a5),a12)),f2(f19(f3(f3(f2(a1))),a5)))),
% 0.68/0.80 inference(scs_inference,[],[103,181,35,185,197,199,221,31,102,30,36,37,94,97,95,33,40,2,125,106,174,173,167,166,162,28,25,22,21,20,19,3,117,110,108,107,164,123,120,119,118,112,111,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,171,170,160,158,156,154,152,150,148,146])).
% 0.68/0.80 cnf(263,plain,
% 0.68/0.80 (P3(f3(x2631),f2(x2631))),
% 0.68/0.80 inference(scs_inference,[],[103,181,35,185,197,199,221,224,31,102,30,36,37,94,97,95,33,40,2,125,106,174,173,167,166,162,28,25,22,21,20,19,3,117,110,108,107,164,123,120,119,118,112,111,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,171,170,160,158,156,154,152,150,148,146,142,140])).
% 0.68/0.80 cnf(271,plain,
% 0.68/0.80 (P1(f3(x2711),f2(x2711))),
% 0.68/0.80 inference(scs_inference,[],[103,181,35,185,197,199,221,224,31,102,30,36,37,94,97,95,33,40,2,125,106,174,173,167,166,162,28,25,22,21,20,19,3,117,110,108,107,164,123,120,119,118,112,111,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,171,170,160,158,156,154,152,150,148,146,142,140,138,136,134,132])).
% 0.68/0.80 cnf(285,plain,
% 0.68/0.80 (P3(a13,a12)),
% 0.68/0.80 inference(scs_inference,[],[103,181,183,35,185,197,199,221,224,31,102,30,36,37,94,97,95,33,40,2,125,106,174,173,167,166,162,28,25,22,21,20,19,3,117,110,108,107,164,123,120,119,118,112,111,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,171,170,160,158,156,154,152,150,148,146,142,140,138,136,134,132,130,128,105,104,161,126,109])).
% 0.68/0.80 cnf(307,plain,
% 0.68/0.80 (~E(f3(x3071),f2(x3071))),
% 0.68/0.80 inference(scs_inference,[],[94,263,259,184,113,125,110,107,106])).
% 0.68/0.80 cnf(327,plain,
% 0.68/0.80 (E(f17(x3271,a11),x3271)),
% 0.68/0.80 inference(rename_variables,[],[34])).
% 0.68/0.80 cnf(336,plain,
% 0.68/0.80 (P3(f15(f3(x3361),x3362),f15(f2(x3361),x3362))),
% 0.68/0.80 inference(scs_inference,[],[103,175,93,34,327,40,35,31,94,176,263,259,253,184,191,212,214,182,113,125,110,107,106,126,168,108,167,166,164,162,136,25,22,21,3,109,124,172])).
% 0.68/0.80 cnf(359,plain,
% 0.68/0.80 ($false),
% 0.68/0.80 inference(scs_inference,[],[38,31,307,336,285,271,110,126,106,125]),
% 0.68/0.80 ['proof']).
% 0.68/0.80 % SZS output end Proof
% 0.68/0.80 % Total time :0.140000s
%------------------------------------------------------------------------------