TSTP Solution File: NUM923^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM923^1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n029.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 10:48:50 EDT 2023
% Result : Timeout 300.11s 295.14s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM923^1 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n029.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Aug 25 12:34:24 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.50 %----Proving TH0
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 % File : NUM923^1 : TPTP v8.1.2. Released v5.3.0.
% 0.21/0.50 % Domain : Number Theory
% 0.21/0.50 % Problem : Sum of two squares line 23, 100 axioms selected
% 0.21/0.50 % Version : Especial.
% 0.21/0.50 % English :
% 0.21/0.50
% 0.21/0.50 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.21/0.50 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.21/0.50 % Source : [Bla11]
% 0.21/0.50 % Names : s2s_100_thf_l23 [Bla11]
% 0.21/0.50
% 0.21/0.50 % Status : Theorem
% 0.21/0.50 % Rating : 1.00 v5.3.0
% 0.21/0.50 % Syntax : Number of formulae : 91 ( 46 unt; 16 typ; 0 def)
% 0.21/0.50 % Number of atoms : 113 ( 72 equ; 0 cnn)
% 0.21/0.50 % Maximal formula atoms : 3 ( 1 avg)
% 0.21/0.50 % Number of connectives : 665 ( 10 ~; 2 |; 2 &; 611 @)
% 0.21/0.50 % ( 17 <=>; 23 =>; 0 <=; 0 <~>)
% 0.21/0.50 % Maximal formula depth : 15 ( 6 avg)
% 0.21/0.50 % Number of types : 3 ( 2 usr)
% 0.21/0.50 % Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% 0.21/0.50 % Number of symbols : 15 ( 14 usr; 4 con; 0-3 aty)
% 0.21/0.50 % Number of variables : 235 ( 0 ^; 231 !; 4 ?; 235 :)
% 0.21/0.50 % SPC : TH0_THM_EQU_NAR
% 0.21/0.50
% 0.21/0.50 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.21/0.50 % 2011-08-09 19:02:52
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 %----Should-be-implicit typings (2)
% 0.21/0.50 thf(ty_ty_tc__Int__Oint,type,
% 0.21/0.50 int: $tType ).
% 0.21/0.50
% 0.21/0.50 thf(ty_ty_tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J,type,
% 0.21/0.50 product_prod_int_int: $tType ).
% 0.21/0.50
% 0.21/0.50 %----Explicit typings (14)
% 0.21/0.50 thf(sy_c_All,type,
% 0.21/0.50 all: ( product_prod_int_int > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Ex,type,
% 0.21/0.50 ex: ( product_prod_int_int > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Groups_Ominus__class_Ominus_000tc__Int__Oint,type,
% 0.21/0.50 minus_minus_int: int > int > int ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint,type,
% 0.21/0.50 plus_plus_int: int > int > int ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Groups_Otimes__class_Otimes_000tc__Int__Oint,type,
% 0.21/0.50 times_times_int: int > int > int ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Orderings_Oord__class_Oless__eq_000tc__Int__Oint,type,
% 0.21/0.50 ord_less_eq_int: int > int > $o ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Product__Type_OPair_000tc__Int__Oint_000tc__Int__Oint,type,
% 0.21/0.50 product_Pair_int_int: int > int > product_prod_int_int ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_Product__Type_Ocurry_000tc__Int__Oint_000tc__Int__Oint_000_Eo,type,
% 0.21/0.50 produc176579150_int_o: ( product_prod_int_int > $o ) > int > int > $o ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_TwoSquares__Mirabelle__fqdbopfjxb_Ois__sum2sq,type,
% 0.21/0.50 twoSqu1013291560sum2sq: int > $o ).
% 0.21/0.50
% 0.21/0.50 thf(sy_c_TwoSquares__Mirabelle__fqdbopfjxb_Osum2sq,type,
% 0.21/0.50 twoSqu1535104286sum2sq: product_prod_int_int > int ).
% 0.21/0.50
% 0.21/0.50 thf(sy_v_a,type,
% 0.21/0.50 a: int ).
% 0.21/0.50
% 0.21/0.50 thf(sy_v_b,type,
% 0.21/0.50 b: int ).
% 0.21/0.50
% 0.21/0.50 thf(sy_v_p,type,
% 0.21/0.50 p: int ).
% 0.21/0.50
% 0.21/0.50 thf(sy_v_q,type,
% 0.21/0.50 q: int ).
% 0.21/0.50
% 0.21/0.50 %----Relevant facts (74)
% 0.21/0.50 thf(fact_0_xzgcda__linear__aux1,axiom,
% 0.21/0.50 ! [A_42: int,R: int,B_39: int,M_1: int,C_29: int,D_12: int,N: int] :
% 0.21/0.50 ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A_42 @ ( times_times_int @ R @ B_39 ) ) @ M_1 ) @ ( times_times_int @ ( minus_minus_int @ C_29 @ ( times_times_int @ R @ D_12 ) ) @ N ) )
% 0.21/0.50 = ( minus_minus_int @ ( plus_plus_int @ ( times_times_int @ A_42 @ M_1 ) @ ( times_times_int @ C_29 @ N ) ) @ ( times_times_int @ R @ ( plus_plus_int @ ( times_times_int @ B_39 @ M_1 ) @ ( times_times_int @ D_12 @ N ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_1_mult__diff__mult,axiom,
% 0.21/0.50 ! [X_6: int,Y_6: int,A_45: int,B_42: int] :
% 0.21/0.50 ( ( minus_minus_int @ ( times_times_int @ X_6 @ Y_6 ) @ ( times_times_int @ A_45 @ B_42 ) )
% 0.21/0.50 = ( plus_plus_int @ ( times_times_int @ X_6 @ ( minus_minus_int @ Y_6 @ B_42 ) ) @ ( times_times_int @ ( minus_minus_int @ X_6 @ A_45 ) @ B_42 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_2_eq__add__iff2,axiom,
% 0.21/0.50 ! [A_44: int,E_4: int,C_31: int,B_41: int,D_11: int] :
% 0.21/0.50 ( ( ( plus_plus_int @ ( times_times_int @ A_44 @ E_4 ) @ C_31 )
% 0.21/0.50 = ( plus_plus_int @ ( times_times_int @ B_41 @ E_4 ) @ D_11 ) )
% 0.21/0.50 <=> ( C_31
% 0.21/0.50 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B_41 @ A_44 ) @ E_4 ) @ D_11 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_3_eq__add__iff1,axiom,
% 0.21/0.50 ! [A_43: int,E_3: int,C_30: int,B_40: int,D_10: int] :
% 0.21/0.50 ( ( ( plus_plus_int @ ( times_times_int @ A_43 @ E_3 ) @ C_30 )
% 0.21/0.50 = ( plus_plus_int @ ( times_times_int @ B_40 @ E_3 ) @ D_10 ) )
% 0.21/0.50 <=> ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A_43 @ B_40 ) @ E_3 ) @ C_30 )
% 0.21/0.50 = D_10 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_4_is__sum2sq__def,axiom,
% 0.21/0.50 ! [X_5: int] :
% 0.21/0.50 ( ( twoSqu1013291560sum2sq @ X_5 )
% 0.21/0.50 <=> ? [A_14: int,B_14: int] :
% 0.21/0.50 ( ( twoSqu1535104286sum2sq @ ( product_Pair_int_int @ A_14 @ B_14 ) )
% 0.21/0.50 = X_5 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_5_Int2_Oaux1,axiom,
% 0.21/0.50 ! [A_42: int,B_39: int,C_29: int] :
% 0.21/0.50 ( ( ( minus_minus_int @ A_42 @ B_39 )
% 0.21/0.50 = C_29 )
% 0.21/0.50 => ( A_42
% 0.21/0.50 = ( plus_plus_int @ C_29 @ B_39 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_6_zdiff__zmult__distrib2,axiom,
% 0.21/0.50 ! [W: int,Z1: int,Z2: int] :
% 0.21/0.50 ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z2 ) )
% 0.21/0.50 = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z2 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_7_zdiff__zmult__distrib,axiom,
% 0.21/0.50 ! [Z1: int,Z2: int,W: int] :
% 0.21/0.50 ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z2 ) @ W )
% 0.21/0.50 = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z2 @ W ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_8_zadd__zmult__distrib2,axiom,
% 0.21/0.50 ! [W: int,Z1: int,Z2: int] :
% 0.21/0.50 ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z2 ) )
% 0.21/0.50 = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z2 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_9_zadd__zmult__distrib,axiom,
% 0.21/0.50 ! [Z1: int,Z2: int,W: int] :
% 0.21/0.50 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z2 ) @ W )
% 0.21/0.50 = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z2 @ W ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_10_diff__add__cancel,axiom,
% 0.21/0.50 ! [A_41: int,B_38: int] :
% 0.21/0.50 ( ( plus_plus_int @ ( minus_minus_int @ A_41 @ B_38 ) @ B_38 )
% 0.21/0.50 = A_41 ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_11_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.21/0.50 ! [A_40: int,B_37: int,C_28: int] :
% 0.21/0.50 ( ( times_times_int @ ( times_times_int @ A_40 @ B_37 ) @ C_28 )
% 0.21/0.50 = ( times_times_int @ A_40 @ ( times_times_int @ B_37 @ C_28 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_12_add__right__imp__eq,axiom,
% 0.21/0.50 ! [B_36: int,A_39: int,C_27: int] :
% 0.21/0.50 ( ( ( plus_plus_int @ B_36 @ A_39 )
% 0.21/0.50 = ( plus_plus_int @ C_27 @ A_39 ) )
% 0.21/0.50 => ( B_36 = C_27 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_13_add__imp__eq,axiom,
% 0.21/0.50 ! [A_38: int,B_35: int,C_26: int] :
% 0.21/0.50 ( ( ( plus_plus_int @ A_38 @ B_35 )
% 0.21/0.50 = ( plus_plus_int @ A_38 @ C_26 ) )
% 0.21/0.50 => ( B_35 = C_26 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_14_add__left__imp__eq,axiom,
% 0.21/0.50 ! [A_37: int,B_34: int,C_25: int] :
% 0.21/0.50 ( ( ( plus_plus_int @ A_37 @ B_34 )
% 0.21/0.50 = ( plus_plus_int @ A_37 @ C_25 ) )
% 0.21/0.50 => ( B_34 = C_25 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_15_add__right__cancel,axiom,
% 0.21/0.50 ! [B_33: int,A_36: int,C_24: int] :
% 0.21/0.50 ( ( ( plus_plus_int @ B_33 @ A_36 )
% 0.21/0.50 = ( plus_plus_int @ C_24 @ A_36 ) )
% 0.21/0.50 <=> ( B_33 = C_24 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_16_add__left__cancel,axiom,
% 0.21/0.50 ! [A_35: int,B_32: int,C_23: int] :
% 0.21/0.50 ( ( ( plus_plus_int @ A_35 @ B_32 )
% 0.21/0.50 = ( plus_plus_int @ A_35 @ C_23 ) )
% 0.21/0.50 <=> ( B_32 = C_23 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_17_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.21/0.50 ! [A_34: int,B_31: int,C_22: int] :
% 0.21/0.50 ( ( plus_plus_int @ ( plus_plus_int @ A_34 @ B_31 ) @ C_22 )
% 0.21/0.50 = ( plus_plus_int @ A_34 @ ( plus_plus_int @ B_31 @ C_22 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_18_diff__eq__diff__eq,axiom,
% 0.21/0.50 ! [A_33: int,B_30: int,C_21: int,D_9: int] :
% 0.21/0.50 ( ( ( minus_minus_int @ A_33 @ B_30 )
% 0.21/0.50 = ( minus_minus_int @ C_21 @ D_9 ) )
% 0.21/0.50 => ( ( A_33 = B_30 )
% 0.21/0.50 <=> ( C_21 = D_9 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_19_zmult__assoc,axiom,
% 0.21/0.50 ! [Z1: int,Z2: int,Z3: int] :
% 0.21/0.50 ( ( times_times_int @ ( times_times_int @ Z1 @ Z2 ) @ Z3 )
% 0.21/0.50 = ( times_times_int @ Z1 @ ( times_times_int @ Z2 @ Z3 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_20_zmult__commute,axiom,
% 0.21/0.50 ! [Z: int,W: int] :
% 0.21/0.50 ( ( times_times_int @ Z @ W )
% 0.21/0.50 = ( times_times_int @ W @ Z ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_21_zadd__assoc,axiom,
% 0.21/0.50 ! [Z1: int,Z2: int,Z3: int] :
% 0.21/0.50 ( ( plus_plus_int @ ( plus_plus_int @ Z1 @ Z2 ) @ Z3 )
% 0.21/0.50 = ( plus_plus_int @ Z1 @ ( plus_plus_int @ Z2 @ Z3 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_22_zadd__left__commute,axiom,
% 0.21/0.50 ! [X_5: int,Y_5: int,Z: int] :
% 0.21/0.50 ( ( plus_plus_int @ X_5 @ ( plus_plus_int @ Y_5 @ Z ) )
% 0.21/0.50 = ( plus_plus_int @ Y_5 @ ( plus_plus_int @ X_5 @ Z ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_23_zadd__commute,axiom,
% 0.21/0.50 ! [Z: int,W: int] :
% 0.21/0.50 ( ( plus_plus_int @ Z @ W )
% 0.21/0.50 = ( plus_plus_int @ W @ Z ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_24_combine__common__factor,axiom,
% 0.21/0.50 ! [A_32: int,E_2: int,B_29: int,C_20: int] :
% 0.21/0.50 ( ( plus_plus_int @ ( times_times_int @ A_32 @ E_2 ) @ ( plus_plus_int @ ( times_times_int @ B_29 @ E_2 ) @ C_20 ) )
% 0.21/0.50 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A_32 @ B_29 ) @ E_2 ) @ C_20 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_25_comm__semiring__class_Odistrib,axiom,
% 0.21/0.50 ! [A_31: int,B_28: int,C_19: int] :
% 0.21/0.50 ( ( times_times_int @ ( plus_plus_int @ A_31 @ B_28 ) @ C_19 )
% 0.21/0.50 = ( plus_plus_int @ ( times_times_int @ A_31 @ C_19 ) @ ( times_times_int @ B_28 @ C_19 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_26_add__diff__add,axiom,
% 0.21/0.50 ! [A_30: int,C_18: int,B_27: int,D_8: int] :
% 0.21/0.50 ( ( minus_minus_int @ ( plus_plus_int @ A_30 @ C_18 ) @ ( plus_plus_int @ B_27 @ D_8 ) )
% 0.21/0.50 = ( plus_plus_int @ ( minus_minus_int @ A_30 @ B_27 ) @ ( minus_minus_int @ C_18 @ D_8 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_27_add__diff__cancel,axiom,
% 0.21/0.50 ! [A_29: int,B_26: int] :
% 0.21/0.50 ( ( minus_minus_int @ ( plus_plus_int @ A_29 @ B_26 ) @ B_26 )
% 0.21/0.50 = A_29 ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_28_crossproduct__eq,axiom,
% 0.21/0.50 ! [W_1: int,Y_4: int,X_4: int,Z_2: int] :
% 0.21/0.50 ( ( ( plus_plus_int @ ( times_times_int @ W_1 @ Y_4 ) @ ( times_times_int @ X_4 @ Z_2 ) )
% 0.21/0.50 = ( plus_plus_int @ ( times_times_int @ W_1 @ Z_2 ) @ ( times_times_int @ X_4 @ Y_4 ) ) )
% 0.21/0.50 <=> ( ( W_1 = X_4 )
% 0.21/0.50 | ( Y_4 = Z_2 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_29_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 0.21/0.50 ! [A_28: int,M: int,B_25: int] :
% 0.21/0.50 ( ( plus_plus_int @ ( times_times_int @ A_28 @ M ) @ ( times_times_int @ B_25 @ M ) )
% 0.21/0.50 = ( times_times_int @ ( plus_plus_int @ A_28 @ B_25 ) @ M ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_30_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 0.21/0.50 ! [A_27: int,B_24: int,C_17: int] :
% 0.21/0.50 ( ( times_times_int @ ( plus_plus_int @ A_27 @ B_24 ) @ C_17 )
% 0.21/0.50 = ( plus_plus_int @ ( times_times_int @ A_27 @ C_17 ) @ ( times_times_int @ B_24 @ C_17 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_31_crossproduct__noteq,axiom,
% 0.21/0.50 ! [C_16: int,D_7: int,A_26: int,B_23: int] :
% 0.21/0.50 ( ( ( A_26 != B_23 )
% 0.21/0.50 & ( C_16 != D_7 ) )
% 0.21/0.50 <=> ( ( plus_plus_int @ ( times_times_int @ A_26 @ C_16 ) @ ( times_times_int @ B_23 @ D_7 ) )
% 0.21/0.50 != ( plus_plus_int @ ( times_times_int @ A_26 @ D_7 ) @ ( times_times_int @ B_23 @ C_16 ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 0.21/0.50 ! [X_3: int,Y_3: int,Z_1: int] :
% 0.21/0.50 ( ( times_times_int @ X_3 @ ( plus_plus_int @ Y_3 @ Z_1 ) )
% 0.21/0.50 = ( plus_plus_int @ ( times_times_int @ X_3 @ Y_3 ) @ ( times_times_int @ X_3 @ Z_1 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_33_Pair__inject,axiom,
% 0.21/0.50 ! [A_25: int,B_22: int,A_24: int,B_21: int] :
% 0.21/0.50 ( ( ( product_Pair_int_int @ A_25 @ B_22 )
% 0.21/0.50 = ( product_Pair_int_int @ A_24 @ B_21 ) )
% 0.21/0.50 => ~ ( ( A_25 = A_24 )
% 0.21/0.50 => ( B_22 != B_21 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_34_Pair__eq,axiom,
% 0.21/0.50 ! [A_23: int,B_20: int,A_22: int,B_19: int] :
% 0.21/0.50 ( ( ( product_Pair_int_int @ A_23 @ B_20 )
% 0.21/0.50 = ( product_Pair_int_int @ A_22 @ B_19 ) )
% 0.21/0.50 <=> ( ( A_23 = A_22 )
% 0.21/0.50 & ( B_20 = B_19 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 0.21/0.50 ! [A_21: int,B_18: int] :
% 0.21/0.50 ( ( times_times_int @ A_21 @ B_18 )
% 0.21/0.50 = ( times_times_int @ B_18 @ A_21 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_36_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 0.21/0.50 ! [Lx_6: int,Rx_6: int,Ry_4: int] :
% 0.21/0.50 ( ( times_times_int @ Lx_6 @ ( times_times_int @ Rx_6 @ Ry_4 ) )
% 0.21/0.50 = ( times_times_int @ Rx_6 @ ( times_times_int @ Lx_6 @ Ry_4 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_37_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 0.21/0.50 ! [Lx_5: int,Rx_5: int,Ry_3: int] :
% 0.21/0.50 ( ( times_times_int @ Lx_5 @ ( times_times_int @ Rx_5 @ Ry_3 ) )
% 0.21/0.50 = ( times_times_int @ ( times_times_int @ Lx_5 @ Rx_5 ) @ Ry_3 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_38_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 0.21/0.50 ! [Lx_4: int,Ly_4: int,Rx_4: int] :
% 0.21/0.50 ( ( times_times_int @ ( times_times_int @ Lx_4 @ Ly_4 ) @ Rx_4 )
% 0.21/0.50 = ( times_times_int @ Lx_4 @ ( times_times_int @ Ly_4 @ Rx_4 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_39_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 0.21/0.50 ! [Lx_3: int,Ly_3: int,Rx_3: int] :
% 0.21/0.50 ( ( times_times_int @ ( times_times_int @ Lx_3 @ Ly_3 ) @ Rx_3 )
% 0.21/0.50 = ( times_times_int @ ( times_times_int @ Lx_3 @ Rx_3 ) @ Ly_3 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_40_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 0.21/0.50 ! [Lx_2: int,Ly_2: int,Rx_2: int,Ry_2: int] :
% 0.21/0.50 ( ( times_times_int @ ( times_times_int @ Lx_2 @ Ly_2 ) @ ( times_times_int @ Rx_2 @ Ry_2 ) )
% 0.21/0.50 = ( times_times_int @ Lx_2 @ ( times_times_int @ Ly_2 @ ( times_times_int @ Rx_2 @ Ry_2 ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 0.21/0.50 ! [Lx_1: int,Ly_1: int,Rx_1: int,Ry_1: int] :
% 0.21/0.50 ( ( times_times_int @ ( times_times_int @ Lx_1 @ Ly_1 ) @ ( times_times_int @ Rx_1 @ Ry_1 ) )
% 0.21/0.50 = ( times_times_int @ Rx_1 @ ( times_times_int @ ( times_times_int @ Lx_1 @ Ly_1 ) @ Ry_1 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 0.21/0.50 ! [Lx: int,Ly: int,Rx: int,Ry: int] :
% 0.21/0.50 ( ( times_times_int @ ( times_times_int @ Lx @ Ly ) @ ( times_times_int @ Rx @ Ry ) )
% 0.21/0.50 = ( times_times_int @ ( times_times_int @ Lx @ Rx ) @ ( times_times_int @ Ly @ Ry ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 0.21/0.50 ! [A_20: int,C_15: int] :
% 0.21/0.50 ( ( plus_plus_int @ A_20 @ C_15 )
% 0.21/0.50 = ( plus_plus_int @ C_15 @ A_20 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 0.21/0.50 ! [A_19: int,C_14: int,D_6: int] :
% 0.21/0.50 ( ( plus_plus_int @ A_19 @ ( plus_plus_int @ C_14 @ D_6 ) )
% 0.21/0.50 = ( plus_plus_int @ C_14 @ ( plus_plus_int @ A_19 @ D_6 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 0.21/0.50 ! [A_18: int,C_13: int,D_5: int] :
% 0.21/0.50 ( ( plus_plus_int @ A_18 @ ( plus_plus_int @ C_13 @ D_5 ) )
% 0.21/0.50 = ( plus_plus_int @ ( plus_plus_int @ A_18 @ C_13 ) @ D_5 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 0.21/0.50 ! [A_17: int,B_17: int,C_12: int] :
% 0.21/0.50 ( ( plus_plus_int @ ( plus_plus_int @ A_17 @ B_17 ) @ C_12 )
% 0.21/0.50 = ( plus_plus_int @ A_17 @ ( plus_plus_int @ B_17 @ C_12 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_47_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 0.21/0.50 ! [A_16: int,B_16: int,C_11: int] :
% 0.21/0.50 ( ( plus_plus_int @ ( plus_plus_int @ A_16 @ B_16 ) @ C_11 )
% 0.21/0.50 = ( plus_plus_int @ ( plus_plus_int @ A_16 @ C_11 ) @ B_16 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_48_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 0.21/0.50 ! [A_15: int,B_15: int,C_10: int,D_4: int] :
% 0.21/0.50 ( ( plus_plus_int @ ( plus_plus_int @ A_15 @ B_15 ) @ ( plus_plus_int @ C_10 @ D_4 ) )
% 0.21/0.50 = ( plus_plus_int @ ( plus_plus_int @ A_15 @ C_10 ) @ ( plus_plus_int @ B_15 @ D_4 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_49_split__paired__All,axiom,
% 0.21/0.50 ! [P_2: product_prod_int_int > $o] :
% 0.21/0.50 ( ( all @ P_2 )
% 0.21/0.50 <=> ! [A_14: int,B_14: int] : ( P_2 @ ( product_Pair_int_int @ A_14 @ B_14 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_50_split__paired__Ex,axiom,
% 0.21/0.50 ! [P_1: product_prod_int_int > $o] :
% 0.21/0.50 ( ( ex @ P_1 )
% 0.21/0.50 <=> ? [A_14: int,B_14: int] : ( P_1 @ ( product_Pair_int_int @ A_14 @ B_14 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_51_prod_Oexhaust,axiom,
% 0.21/0.50 ! [Y_2: product_prod_int_int] :
% 0.21/0.50 ~ ! [A_14: int,B_14: int] :
% 0.21/0.50 ( Y_2
% 0.21/0.50 != ( product_Pair_int_int @ A_14 @ B_14 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_52_PairE,axiom,
% 0.21/0.50 ! [P: product_prod_int_int] :
% 0.21/0.50 ~ ! [X_2: int,Y_1: int] :
% 0.21/0.50 ( P
% 0.21/0.50 != ( product_Pair_int_int @ X_2 @ Y_1 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_53_curryI,axiom,
% 0.21/0.50 ! [F_3: product_prod_int_int > $o,A_13: int,B_13: int] :
% 0.21/0.50 ( ( F_3 @ ( product_Pair_int_int @ A_13 @ B_13 ) )
% 0.21/0.50 => ( produc176579150_int_o @ F_3 @ A_13 @ B_13 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_54_curryD,axiom,
% 0.21/0.50 ! [F_2: product_prod_int_int > $o,A_12: int,B_12: int] :
% 0.21/0.50 ( ( produc176579150_int_o @ F_2 @ A_12 @ B_12 )
% 0.21/0.50 => ( F_2 @ ( product_Pair_int_int @ A_12 @ B_12 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_55_curryE,axiom,
% 0.21/0.50 ! [F_1: product_prod_int_int > $o,A_11: int,B_11: int] :
% 0.21/0.50 ( ( produc176579150_int_o @ F_1 @ A_11 @ B_11 )
% 0.21/0.50 => ( F_1 @ ( product_Pair_int_int @ A_11 @ B_11 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_56_curry__conv,axiom,
% 0.21/0.50 ! [F: product_prod_int_int > $o,A_10: int,B_10: int] :
% 0.21/0.50 ( ( produc176579150_int_o @ F @ A_10 @ B_10 )
% 0.21/0.50 <=> ( F @ ( product_Pair_int_int @ A_10 @ B_10 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_57_le__add__iff1,axiom,
% 0.21/0.50 ! [A_9: int,E_1: int,C_9: int,B_9: int,D_3: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A_9 @ E_1 ) @ C_9 ) @ ( plus_plus_int @ ( times_times_int @ B_9 @ E_1 ) @ D_3 ) )
% 0.21/0.50 <=> ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A_9 @ B_9 ) @ E_1 ) @ C_9 ) @ D_3 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_58_le__add__iff2,axiom,
% 0.21/0.50 ! [A_8: int,E: int,C_8: int,B_8: int,D_2: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A_8 @ E ) @ C_8 ) @ ( plus_plus_int @ ( times_times_int @ B_8 @ E ) @ D_2 ) )
% 0.21/0.50 <=> ( ord_less_eq_int @ C_8 @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B_8 @ A_8 ) @ E ) @ D_2 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_59_zadd__left__mono,axiom,
% 0.21/0.50 ! [K: int,I: int,J: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ I @ J )
% 0.21/0.50 => ( ord_less_eq_int @ ( plus_plus_int @ K @ I ) @ ( plus_plus_int @ K @ J ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_60_diff__eq__diff__less__eq,axiom,
% 0.21/0.50 ! [A_7: int,B_7: int,C_7: int,D_1: int] :
% 0.21/0.50 ( ( ( minus_minus_int @ A_7 @ B_7 )
% 0.21/0.50 = ( minus_minus_int @ C_7 @ D_1 ) )
% 0.21/0.50 => ( ( ord_less_eq_int @ A_7 @ B_7 )
% 0.21/0.50 <=> ( ord_less_eq_int @ C_7 @ D_1 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_61_add__le__imp__le__left,axiom,
% 0.21/0.50 ! [C_6: int,A_6: int,B_6: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ ( plus_plus_int @ C_6 @ A_6 ) @ ( plus_plus_int @ C_6 @ B_6 ) )
% 0.21/0.50 => ( ord_less_eq_int @ A_6 @ B_6 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_62_add__le__imp__le__right,axiom,
% 0.21/0.50 ! [A_5: int,C_5: int,B_5: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ ( plus_plus_int @ A_5 @ C_5 ) @ ( plus_plus_int @ B_5 @ C_5 ) )
% 0.21/0.50 => ( ord_less_eq_int @ A_5 @ B_5 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_63_add__mono,axiom,
% 0.21/0.50 ! [C_4: int,D: int,A_4: int,B_4: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ A_4 @ B_4 )
% 0.21/0.50 => ( ( ord_less_eq_int @ C_4 @ D )
% 0.21/0.50 => ( ord_less_eq_int @ ( plus_plus_int @ A_4 @ C_4 ) @ ( plus_plus_int @ B_4 @ D ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_64_add__left__mono,axiom,
% 0.21/0.50 ! [C_3: int,A_3: int,B_3: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ A_3 @ B_3 )
% 0.21/0.50 => ( ord_less_eq_int @ ( plus_plus_int @ C_3 @ A_3 ) @ ( plus_plus_int @ C_3 @ B_3 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_65_add__right__mono,axiom,
% 0.21/0.50 ! [C_2: int,A_2: int,B_2: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ A_2 @ B_2 )
% 0.21/0.50 => ( ord_less_eq_int @ ( plus_plus_int @ A_2 @ C_2 ) @ ( plus_plus_int @ B_2 @ C_2 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_66_add__le__cancel__left,axiom,
% 0.21/0.50 ! [C_1: int,A_1: int,B_1: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ ( plus_plus_int @ C_1 @ A_1 ) @ ( plus_plus_int @ C_1 @ B_1 ) )
% 0.21/0.50 <=> ( ord_less_eq_int @ A_1 @ B_1 ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_67_add__le__cancel__right,axiom,
% 0.21/0.50 ! [A: int,C: int,B: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.21/0.50 <=> ( ord_less_eq_int @ A @ B ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_68_order__refl,axiom,
% 0.21/0.50 ! [X_1: int] : ( ord_less_eq_int @ X_1 @ X_1 ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_69_linorder__le__cases,axiom,
% 0.21/0.50 ! [X: int,Y: int] :
% 0.21/0.50 ( ~ ( ord_less_eq_int @ X @ Y )
% 0.21/0.50 => ( ord_less_eq_int @ Y @ X ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_70_zle__refl,axiom,
% 0.21/0.50 ! [W: int] : ( ord_less_eq_int @ W @ W ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_71_zle__linear,axiom,
% 0.21/0.50 ! [Z: int,W: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ Z @ W )
% 0.21/0.50 | ( ord_less_eq_int @ W @ Z ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_72_zle__trans,axiom,
% 0.21/0.50 ! [K: int,I: int,J: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ I @ J )
% 0.21/0.50 => ( ( ord_less_eq_int @ J @ K )
% 0.21/0.50 => ( ord_less_eq_int @ I @ K ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(fact_73_zle__antisym,axiom,
% 0.21/0.50 ! [Z: int,W: int] :
% 0.21/0.50 ( ( ord_less_eq_int @ Z @ W )
% 0.21/0.50 => ( ( ord_less_eq_int @ W @ Z )
% 0.21/0.50 => ( Z = W ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----Conjectures (1)
% 0.21/0.50 thf(conj_0,conjecture,
% 0.21/0.50 ( ( times_times_int @ ( twoSqu1535104286sum2sq @ ( product_Pair_int_int @ a @ b ) ) @ ( twoSqu1535104286sum2sq @ ( product_Pair_int_int @ p @ q ) ) )
% 0.21/0.52 = ( twoSqu1535104286sum2sq @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ a @ p ) @ ( times_times_int @ b @ q ) ) @ ( minus_minus_int @ ( times_times_int @ a @ q ) @ ( times_times_int @ b @ p ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.rNsYRdnOKi/cvc5---1.0.5_18634.p...
% 0.21/0.52 (declare-sort $$unsorted 0)
% 0.21/0.52 (declare-sort tptp.int 0)
% 0.21/0.52 (declare-sort tptp.product_prod_int_int 0)
% 0.21/0.52 (declare-fun tptp.all ((-> tptp.product_prod_int_int Bool)) Bool)
% 0.21/0.52 (declare-fun tptp.ex ((-> tptp.product_prod_int_int Bool)) Bool)
% 0.21/0.52 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 0.21/0.52 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 0.21/0.52 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 0.21/0.52 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 0.21/0.52 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 0.21/0.52 (declare-fun tptp.produc176579150_int_o ((-> tptp.product_prod_int_int Bool) tptp.int tptp.int) Bool)
% 0.21/0.52 (declare-fun tptp.twoSqu1013291560sum2sq (tptp.int) Bool)
% 0.21/0.52 (declare-fun tptp.twoSqu1535104286sum2sq (tptp.product_prod_int_int) tptp.int)
% 0.21/0.52 (declare-fun tptp.a () tptp.int)
% 0.21/0.52 (declare-fun tptp.b () tptp.int)
% 0.21/0.52 (declare-fun tptp.p () tptp.int)
% 0.21/0.52 (declare-fun tptp.q () tptp.int)
% 0.21/0.52 (assert (forall ((A_42 tptp.int) (R tptp.int) (B_39 tptp.int) (M_1 tptp.int) (C_29 tptp.int) (D_12 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.times_times_int R))) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A_42) (@ _let_1 B_39))) M_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int C_29) (@ _let_1 D_12))) N)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_42) M_1)) (@ (@ tptp.times_times_int C_29) N))) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_39) M_1)) (@ (@ tptp.times_times_int D_12) N))))))))
% 0.21/0.52 (assert (forall ((X_6 tptp.int) (Y_6 tptp.int) (A_45 tptp.int) (B_42 tptp.int)) (let ((_let_1 (@ tptp.times_times_int X_6))) (= (@ (@ tptp.minus_minus_int (@ _let_1 Y_6)) (@ (@ tptp.times_times_int A_45) B_42)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_int Y_6) B_42))) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X_6) A_45)) B_42))))))
% 0.21/0.52 (assert (forall ((A_44 tptp.int) (E_4 tptp.int) (C_31 tptp.int) (B_41 tptp.int) (D_11 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_44) E_4)) C_31) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_41) E_4)) D_11)) (= C_31 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B_41) A_44)) E_4)) D_11)))))
% 0.21/0.52 (assert (forall ((A_43 tptp.int) (E_3 tptp.int) (C_30 tptp.int) (B_40 tptp.int) (D_10 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_43) E_3)) C_30) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_40) E_3)) D_10)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A_43) B_40)) E_3)) C_30) D_10))))
% 0.21/0.52 (assert (forall ((X_5 tptp.int)) (= (@ tptp.twoSqu1013291560sum2sq X_5) (exists ((A_14 tptp.int) (B_14 tptp.int)) (= (@ tptp.twoSqu1535104286sum2sq (@ (@ tptp.product_Pair_int_int A_14) B_14)) X_5)))))
% 0.21/0.52 (assert (forall ((A_42 tptp.int) (B_39 tptp.int) (C_29 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A_42) B_39) C_29) (= A_42 (@ (@ tptp.plus_plus_int C_29) B_39)))))
% 0.21/0.52 (assert (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.minus_minus_int Z1) Z2)) (@ (@ tptp.minus_minus_int (@ _let_1 Z1)) (@ _let_1 Z2))))))
% 0.21/0.52 (assert (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z1) Z2)) W) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z2) W)))))
% 0.21/0.52 (assert (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z1) Z2)) (@ (@ tptp.plus_plus_int (@ _let_1 Z1)) (@ _let_1 Z2))))))
% 0.21/0.52 (assert (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z1) Z2)) W) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z2) W)))))
% 0.21/0.52 (assert (forall ((A_41 tptp.int) (B_38 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A_41) B_38)) B_38) A_41)))
% 0.21/0.52 (assert (forall ((A_40 tptp.int) (B_37 tptp.int) (C_28 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A_40))) (= (@ (@ tptp.times_times_int (@ _let_1 B_37)) C_28) (@ _let_1 (@ (@ tptp.times_times_int B_37) C_28))))))
% 0.21/0.52 (assert (forall ((B_36 tptp.int) (A_39 tptp.int) (C_27 tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B_36) A_39) (@ (@ tptp.plus_plus_int C_27) A_39)) (= B_36 C_27))))
% 0.21/0.52 (assert (forall ((A_38 tptp.int) (B_35 tptp.int) (C_26 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_38))) (=> (= (@ _let_1 B_35) (@ _let_1 C_26)) (= B_35 C_26)))))
% 0.21/0.52 (assert (forall ((A_37 tptp.int) (B_34 tptp.int) (C_25 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_37))) (=> (= (@ _let_1 B_34) (@ _let_1 C_25)) (= B_34 C_25)))))
% 0.21/0.52 (assert (forall ((B_33 tptp.int) (A_36 tptp.int) (C_24 tptp.int)) (= (= (@ (@ tptp.plus_plus_int B_33) A_36) (@ (@ tptp.plus_plus_int C_24) A_36)) (= B_33 C_24))))
% 0.21/0.52 (assert (forall ((A_35 tptp.int) (B_32 tptp.int) (C_23 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_35))) (= (= (@ _let_1 B_32) (@ _let_1 C_23)) (= B_32 C_23)))))
% 0.21/0.52 (assert (forall ((A_34 tptp.int) (B_31 tptp.int) (C_22 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_34))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_31)) C_22) (@ _let_1 (@ (@ tptp.plus_plus_int B_31) C_22))))))
% 0.21/0.52 (assert (forall ((A_33 tptp.int) (B_30 tptp.int) (C_21 tptp.int) (D_9 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A_33) B_30) (@ (@ tptp.minus_minus_int C_21) D_9)) (= (= A_33 B_30) (= C_21 D_9)))))
% 0.21/0.52 (assert (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z1))) (= (@ (@ tptp.times_times_int (@ _let_1 Z2)) Z3) (@ _let_1 (@ (@ tptp.times_times_int Z2) Z3))))))
% 0.21/0.52 (assert (forall ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int Z) W) (@ (@ tptp.times_times_int W) Z))))
% 0.21/0.52 (assert (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int Z1))) (= (@ (@ tptp.plus_plus_int (@ _let_1 Z2)) Z3) (@ _let_1 (@ (@ tptp.plus_plus_int Z2) Z3))))))
% 0.21/0.52 (assert (forall ((X_5 tptp.int) (Y_5 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X_5))) (let ((_let_2 (@ tptp.plus_plus_int Y_5))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.21/0.52 (assert (forall ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.plus_plus_int Z) W) (@ (@ tptp.plus_plus_int W) Z))))
% 0.21/0.52 (assert (forall ((A_32 tptp.int) (E_2 tptp.int) (B_29 tptp.int) (C_20 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_32) E_2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_29) E_2)) C_20)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_32) B_29)) E_2)) C_20))))
% 0.21/0.52 (assert (forall ((A_31 tptp.int) (B_28 tptp.int) (C_19 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_31) B_28)) C_19) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_31) C_19)) (@ (@ tptp.times_times_int B_28) C_19)))))
% 0.21/0.52 (assert (forall ((A_30 tptp.int) (C_18 tptp.int) (B_27 tptp.int) (D_8 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A_30) C_18)) (@ (@ tptp.plus_plus_int B_27) D_8)) (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A_30) B_27)) (@ (@ tptp.minus_minus_int C_18) D_8)))))
% 0.21/0.52 (assert (forall ((A_29 tptp.int) (B_26 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A_29) B_26)) B_26) A_29)))
% 0.21/0.52 (assert (forall ((W_1 tptp.int) (Y_4 tptp.int) (X_4 tptp.int) (Z_2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int X_4))) (let ((_let_2 (@ tptp.times_times_int W_1))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y_4)) (@ _let_1 Z_2)) (@ (@ tptp.plus_plus_int (@ _let_2 Z_2)) (@ _let_1 Y_4))) (or (= W_1 X_4) (= Y_4 Z_2)))))))
% 0.21/0.52 (assert (forall ((A_28 tptp.int) (M tptp.int) (B_25 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_28) M)) (@ (@ tptp.times_times_int B_25) M)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_28) B_25)) M))))
% 0.21/0.52 (assert (forall ((A_27 tptp.int) (B_24 tptp.int) (C_17 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_27) B_24)) C_17) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_27) C_17)) (@ (@ tptp.times_times_int B_24) C_17)))))
% 0.21/0.52 (assert (forall ((C_16 tptp.int) (D_7 tptp.int) (A_26 tptp.int) (B_23 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B_23))) (let ((_let_2 (@ tptp.times_times_int A_26))) (= (and (not (= A_26 B_23)) (not (= C_16 D_7))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C_16)) (@ _let_1 D_7)) (@ (@ tptp.plus_plus_int (@ _let_2 D_7)) (@ _let_1 C_16)))))))))
% 0.21/0.52 (assert (forall ((X_3 tptp.int) (Y_3 tptp.int) (Z_1 tptp.int)) (let ((_let_1 (@ tptp.times_times_int X_3))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Y_3) Z_1)) (@ (@ tptp.plus_plus_int (@ _let_1 Y_3)) (@ _let_1 Z_1))))))
% 0.21/0.52 (assert (forall ((A_25 tptp.int) (B_22 tptp.int) (A_24 tptp.int) (B_21 tptp.int)) (=> (= (@ (@ tptp.product_Pair_int_int A_25) B_22) (@ (@ tptp.product_Pair_int_int A_24) B_21)) (not (=> (= A_25 A_24) (not (= B_22 B_21)))))))
% 0.21/0.52 (assert (forall ((A_23 tptp.int) (B_20 tptp.int) (A_22 tptp.int) (B_19 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int A_23) B_20) (@ (@ tptp.product_Pair_int_int A_22) B_19)) (and (= A_23 A_22) (= B_20 B_19)))))
% 0.21/0.52 (assert (forall ((A_21 tptp.int) (B_18 tptp.int)) (= (@ (@ tptp.times_times_int A_21) B_18) (@ (@ tptp.times_times_int B_18) A_21))))
% 0.21/0.52 (assert (forall ((Lx_6 tptp.int) (Rx_6 tptp.int) (Ry_4 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx_6))) (let ((_let_2 (@ tptp.times_times_int Rx_6))) (= (@ _let_1 (@ _let_2 Ry_4)) (@ _let_2 (@ _let_1 Ry_4)))))))
% 0.21/0.52 (assert (forall ((Lx_5 tptp.int) (Rx_5 tptp.int) (Ry_3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx_5))) (= (@ _let_1 (@ (@ tptp.times_times_int Rx_5) Ry_3)) (@ (@ tptp.times_times_int (@ _let_1 Rx_5)) Ry_3)))))
% 0.21/0.52 (assert (forall ((Lx_4 tptp.int) (Ly_4 tptp.int) (Rx_4 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx_4))) (= (@ (@ tptp.times_times_int (@ _let_1 Ly_4)) Rx_4) (@ _let_1 (@ (@ tptp.times_times_int Ly_4) Rx_4))))))
% 0.21/0.52 (assert (forall ((Lx_3 tptp.int) (Ly_3 tptp.int) (Rx_3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx_3))) (= (@ (@ tptp.times_times_int (@ _let_1 Ly_3)) Rx_3) (@ (@ tptp.times_times_int (@ _let_1 Rx_3)) Ly_3)))))
% 0.21/0.52 (assert (forall ((Lx_2 tptp.int) (Ly_2 tptp.int) (Rx_2 tptp.int) (Ry_2 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int Rx_2) Ry_2))) (let ((_let_2 (@ tptp.times_times_int Lx_2))) (= (@ (@ tptp.times_times_int (@ _let_2 Ly_2)) _let_1) (@ _let_2 (@ (@ tptp.times_times_int Ly_2) _let_1)))))))
% 0.21/0.52 (assert (forall ((Lx_1 tptp.int) (Ly_1 tptp.int) (Rx_1 tptp.int) (Ry_1 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.times_times_int Lx_1) Ly_1)))) (let ((_let_2 (@ tptp.times_times_int Rx_1))) (= (@ _let_1 (@ _let_2 Ry_1)) (@ _let_2 (@ _let_1 Ry_1)))))))
% 0.21/0.52 (assert (forall ((Lx tptp.int) (Ly tptp.int) (Rx tptp.int) (Ry tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx))) (= (@ (@ tptp.times_times_int (@ _let_1 Ly)) (@ (@ tptp.times_times_int Rx) Ry)) (@ (@ tptp.times_times_int (@ _let_1 Rx)) (@ (@ tptp.times_times_int Ly) Ry))))))
% 0.21/0.52 (assert (forall ((A_20 tptp.int) (C_15 tptp.int)) (= (@ (@ tptp.plus_plus_int A_20) C_15) (@ (@ tptp.plus_plus_int C_15) A_20))))
% 0.21/0.52 (assert (forall ((A_19 tptp.int) (C_14 tptp.int) (D_6 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_19))) (let ((_let_2 (@ tptp.plus_plus_int C_14))) (= (@ _let_1 (@ _let_2 D_6)) (@ _let_2 (@ _let_1 D_6)))))))
% 0.21/0.52 (assert (forall ((A_18 tptp.int) (C_13 tptp.int) (D_5 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_18))) (= (@ _let_1 (@ (@ tptp.plus_plus_int C_13) D_5)) (@ (@ tptp.plus_plus_int (@ _let_1 C_13)) D_5)))))
% 0.21/0.52 (assert (forall ((A_17 tptp.int) (B_17 tptp.int) (C_12 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_17))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_17)) C_12) (@ _let_1 (@ (@ tptp.plus_plus_int B_17) C_12))))))
% 0.21/0.52 (assert (forall ((A_16 tptp.int) (B_16 tptp.int) (C_11 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_16))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_16)) C_11) (@ (@ tptp.plus_plus_int (@ _let_1 C_11)) B_16)))))
% 0.21/0.52 (assert (forall ((A_15 tptp.int) (B_15 tptp.int) (C_10 tptp.int) (D_4 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_15))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_15)) (@ (@ tptp.plus_plus_int C_10) D_4)) (@ (@ tptp.plus_plus_int (@ _let_1 C_10)) (@ (@ tptp.plus_plus_int B_15) D_4))))))
% 0.21/0.52 (assert (forall ((P_2 (-> tptp.product_prod_int_int Bool))) (= (@ tptp.all P_2) (forall ((A_14 tptp.int) (B_14 tptp.int)) (@ P_2 (@ (@ tptp.product_Pair_int_int A_14) B_14))))))
% 0.21/0.52 (assert (forall ((P_1 (-> tptp.product_prod_int_int Bool))) (= (@ tptp.ex P_1) (exists ((A_14 tptp.int) (B_14 tptp.int)) (@ P_1 (@ (@ tptp.product_Pair_int_int A_14) B_14))))))
% 0.21/0.52 (assert (forall ((Y_2 tptp.product_prod_int_int)) (not (forall ((A_14 tptp.int) (B_14 tptp.int)) (not (= Y_2 (@ (@ tptp.product_Pair_int_int A_14) B_14)))))))
% 0.21/0.52 (assert (forall ((P tptp.product_prod_int_int)) (not (forall ((X_2 tptp.int) (Y_1 tptp.int)) (not (= P (@ (@ tptp.product_Pair_int_int X_2) Y_1)))))))
% 0.21/0.52 (assert (forall ((F_3 (-> tptp.product_prod_int_int Bool)) (A_13 tptp.int) (B_13 tptp.int)) (=> (@ F_3 (@ (@ tptp.product_Pair_int_int A_13) B_13)) (@ (@ (@ tptp.produc176579150_int_o F_3) A_13) B_13))))
% 0.21/0.52 (assert (forall ((F_2 (-> tptp.product_prod_int_int Bool)) (A_12 tptp.int) (B_12 tptp.int)) (=> (@ (@ (@ tptp.produc176579150_int_o F_2) A_12) B_12) (@ F_2 (@ (@ tptp.product_Pair_int_int A_12) B_12)))))
% 0.21/0.52 (assert (forall ((F_1 (-> tptp.product_prod_int_int Bool)) (A_11 tptp.int) (B_11 tptp.int)) (=> (@ (@ (@ tptp.produc176579150_int_o F_1) A_11) B_11) (@ F_1 (@ (@ tptp.product_Pair_int_int A_11) B_11)))))
% 0.21/0.52 (assert (forall ((F (-> tptp.product_prod_int_int Bool)) (A_10 tptp.int) (B_10 tptp.int)) (= (@ (@ (@ tptp.produc176579150_int_o F) A_10) B_10) (@ F (@ (@ tptp.product_Pair_int_int A_10) B_10)))))
% 0.21/0.52 (assert (forall ((A_9 tptp.int) (E_1 tptp.int) (C_9 tptp.int) (B_9 tptp.int) (D_3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_9) E_1)) C_9)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_9) E_1)) D_3)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A_9) B_9)) E_1)) C_9)) D_3))))
% 0.21/0.52 (assert (forall ((A_8 tptp.int) (E tptp.int) (C_8 tptp.int) (B_8 tptp.int) (D_2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_8) E)) C_8)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_8) E)) D_2)) (@ (@ tptp.ord_less_eq_int C_8) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B_8) A_8)) E)) D_2)))))
% 0.21/0.52 (assert (forall ((K tptp.int) (I tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_eq_int (@ _let_1 I)) (@ _let_1 J))))))
% 0.21/0.52 (assert (forall ((A_7 tptp.int) (B_7 tptp.int) (C_7 tptp.int) (D_1 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A_7) B_7) (@ (@ tptp.minus_minus_int C_7) D_1)) (= (@ (@ tptp.ord_less_eq_int A_7) B_7) (@ (@ tptp.ord_less_eq_int C_7) D_1)))))
% 0.21/0.52 (assert (forall ((C_6 tptp.int) (A_6 tptp.int) (B_6 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_6))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A_6)) (@ _let_1 B_6)) (@ (@ tptp.ord_less_eq_int A_6) B_6)))))
% 0.21/0.52 (assert (forall ((A_5 tptp.int) (C_5 tptp.int) (B_5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A_5) C_5)) (@ (@ tptp.plus_plus_int B_5) C_5)) (@ (@ tptp.ord_less_eq_int A_5) B_5))))
% 0.21/0.52 (assert (forall ((C_4 tptp.int) (D tptp.int) (A_4 tptp.int) (B_4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_4) B_4) (=> (@ (@ tptp.ord_less_eq_int C_4) D) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A_4) C_4)) (@ (@ tptp.plus_plus_int B_4) D))))))
% 0.21/0.52 (assert (forall ((C_3 tptp.int) (A_3 tptp.int) (B_3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_3))) (=> (@ (@ tptp.ord_less_eq_int A_3) B_3) (@ (@ tptp.ord_less_eq_int (@ _let_1 A_3)) (@ _let_1 B_3))))))
% 0.21/0.52 (assert (forall ((C_2 tptp.int) (A_2 tptp.int) (B_2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_2) B_2) (@ (@ tptp.ord_less_eq_int (cvc5 interrupted by timeout.
% 300.11/295.14 /export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 18819 CPU time limit exceeded (core dumped) ( read result; case "$result" in
% 300.11/295.14 unsat)
% 300.11/295.14 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 300.11/295.14 ;;
% 300.11/295.14 sat)
% 300.11/295.14 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 300.11/295.14 ;;
% 300.11/295.14 esac; exit 1 )
% 300.11/295.15 Cputime limit exceeded (core dumped) (core dumped)
% 300.11/295.15 % cvc5---1.0.5 exiting
% 300.11/295.15 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------