%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW488_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:10:40 AM UTC 2026
% Result : Theorem 10.71s 4.35s
% Output : Refutation 11.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 144
% Syntax : Number of formulae : 290 ( 62 unt; 0 typ; 0 def)
% Number of atoms : 801 ( 236 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 2887 ( 40 ~; 6 |; 39 &;2450 @)
% ( 28 <=>; 324 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 44 usr; 7 con; 0-5 aty)
% Number of variables : 581 ( 0 ^; 581 !; 0 ?; 581 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(comm_ring_1_decl,type,
comm_ring_1:
!>[TA: $tType] : $o ).
thf(cancel1352612707id_add_decl,type,
cancel1352612707id_add:
!>[TA: $tType] : $o ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(idom_decl,type,
idom:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(ring_1_decl,type,
ring_1:
!>[TA: $tType] : $o ).
thf(ring_char_0_decl,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(monoid_add_decl,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(zero_neq_one_decl,type,
zero_neq_one:
!>[TA: $tType] : $o ).
thf(comm_semiring_0_decl,type,
comm_semiring_0:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_decl,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_decl,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(linordered_semidom_decl,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_decl,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(ordere216010020id_add_decl,type,
ordere216010020id_add:
!>[TA: $tType] : $o ).
thf(ordere236663937imp_le_decl,type,
ordere236663937imp_le:
!>[TA: $tType] : $o ).
thf(ordere223160158up_add_decl,type,
ordere223160158up_add:
!>[TA: $tType] : $o ).
thf(semiri456707255roduct_decl,type,
semiri456707255roduct:
!>[TA: $tType] : $o ).
thf(fundam296178794t_poly_decl,type,
fundam296178794t_poly:
!>[TA: $tType] : ( ( TA @ poly1 ) > TA > ( TA @ poly1 ) ) ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(ring_1_Ints_decl,type,
ring_1_Ints:
!>[TA: $tType] : ( bool @ ( TA @ fun ) ) ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(coeff_decl,type,
coeff:
!>[TA: $tType] : ( ( TA @ poly1 ) > ( TA @ ( nat @ fun ) ) ) ).
thf(monom_decl,type,
monom:
!>[TA: $tType] : ( TA > nat > ( TA @ poly1 ) ) ).
thf(order_decl,type,
order:
!>[TA: $tType] : ( TA > ( TA @ poly1 ) > nat ) ).
thf(pcompose_decl,type,
pcompose:
!>[TA: $tType] : ( ( TA @ poly1 ) > ( TA @ poly1 ) > ( TA @ poly1 ) ) ).
thf(poly_decl,type,
poly:
!>[TA: $tType] : ( ( TA @ poly1 ) > ( TA @ ( TA @ fun ) ) ) ).
thf(poly_rec_decl,type,
poly_rec:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TB @ fun ) @ ( TA @ poly1 @ fun ) @ ( TA @ fun ) ) > ( TA @ poly1 ) > TB ) ).
thf(synthetic_div_decl,type,
synthetic_div:
!>[TA: $tType] : ( ( TA @ poly1 ) > TA > ( TA @ poly1 ) ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) > $o ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(h_decl,type,
h: a ).
thf(x_decl,type,
x: a ).
thf(108,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat] :
( ( ( A
!= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ poly1 @ one_one @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ zero_zero ) ) )
& ( ( A
= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ poly1 @ one_one @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ one_one ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_coeff__1) ).
thf(468,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat] :
( ( ( A
!= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ poly1 @ one_one @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ zero_zero ) ) )
& ( ( A
= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ poly1 @ one_one @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(103,axiom,
! [A: nat,B: nat] :
~ ( A @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_not__add__less2) ).
thf(449,plain,
! [A: nat,B: nat] :
~ ( A @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(79,axiom,
! [TA: $tType] :
( ( TA @ idom )
=> ( TA @ poly1 @ semiri456707255roduct ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(379,plain,
! [TA: $tType] :
( ( TA @ idom )
=> ( TA @ poly1 @ semiri456707255roduct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(30,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) )
<=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_add__is__0) ).
thf(202,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) )
=> ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) )
=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(99,axiom,
! [A: nat,B: nat] :
~ ( B @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_not__add__less1) ).
thf(440,plain,
! [A: nat,B: nat] :
~ ( B @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(123,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(511,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(81,axiom,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( C @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_add__strict__left__mono) ).
thf(385,plain,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( C @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(133,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ poly1 @ one_one @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_poly__1) ).
thf(550,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ poly1 @ one_one @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(130,axiom,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_plus__nat_Oadd__0) ).
thf(538,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(92,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_add__lessD1) ).
thf(417,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(61,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_add__less__imp__less__left) ).
thf(320,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(15,axiom,
nat @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(174,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(89,axiom,
! [TA: $tType] :
( ( TA @ cancel1352612707id_add )
=> ( TA @ poly1 @ cancel1352612707id_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ocancel__comm__monoid__add) ).
thf(404,plain,
! [TA: $tType] :
( ( TA @ cancel1352612707id_add )
=> ( TA @ poly1 @ cancel1352612707id_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(138,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_add__0) ).
thf(570,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(23,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(184,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(7,axiom,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( TA @ one_one )
= A )
<=> ( A
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_one__reorient) ).
thf(152,plain,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( A
= ( TA @ one_one ) )
=> ( ( TA @ one_one )
= A ) )
& ( ( ( TA @ one_one )
= A )
=> ( A
= ( TA @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(35,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly1,C: TA @ poly1] :
( ( A @ ( B @ ( C @ ( TA @ pcompose ) ) @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_poly__pcompose) ).
thf(228,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly1,C: TA @ poly1] :
( ( A @ ( B @ ( C @ ( TA @ pcompose ) ) @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(109,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(475,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(19,axiom,
nat @ ordere216010020id_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__comm__monoid__add) ).
thf(179,plain,
nat @ ordere216010020id_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(100,axiom,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( C @ ( D @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_add__strict__mono) ).
thf(443,plain,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( C @ ( D @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(38,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_add__less__mono) ).
thf(238,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(124,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(514,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(71,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(353,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(111,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ( TA @ poly1 @ ab_semigroup_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Oab__semigroup__add) ).
thf(480,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ( TA @ poly1 @ ab_semigroup_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ zero )
=> ! [A: TA,B: TA @ ( TA @ fun ) @ ( TB @ poly1 @ fun ) @ ( TB @ fun )] :
( ( ( A @ ( TB @ poly1 @ zero_zero @ ( TB @ zero_zero @ ( B @ ( TA @ ( TA @ fun ) @ ( TB @ poly1 @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TB @ poly1 @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A )
=> ( ( TB @ poly1 @ zero_zero @ ( B @ ( A @ ( TB @ ( TA @ poly_rec ) ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_poly__rec__0) ).
thf(492,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ zero )
=> ! [A: TA,B: TA @ ( TA @ fun ) @ ( TB @ poly1 @ fun ) @ ( TB @ fun )] :
( ( ( A @ ( TB @ poly1 @ zero_zero @ ( TB @ zero_zero @ ( B @ ( TA @ ( TA @ fun ) @ ( TB @ poly1 @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TB @ poly1 @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A )
=> ( ( TB @ poly1 @ zero_zero @ ( B @ ( A @ ( TB @ ( TA @ poly_rec ) ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(12,axiom,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ( TA @ ring_1_Ints @ ( TA @ one_one @ ( TA @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_Ints__1) ).
thf(164,plain,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ( TA @ ring_1_Ints @ ( TA @ one_one @ ( TA @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(49,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_add__0__right) ).
thf(280,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(34,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA,B: nat,C: nat] :
( ( ( C != B )
=> ( ( B @ ( C @ ( A @ ( TA @ monom ) ) @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ zero_zero ) ) )
& ( ( C = B )
=> ( ( B @ ( C @ ( A @ ( TA @ monom ) ) @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_coeff__monom) ).
thf(221,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA,B: nat,C: nat] :
( ( ( C != B )
=> ( ( B @ ( C @ ( A @ ( TA @ monom ) ) @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ zero_zero ) ) )
& ( ( C = B )
=> ( ( B @ ( C @ ( A @ ( TA @ monom ) ) @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(86,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
<=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_double__add__less__zero__iff__single__add__less__zero) ).
thf(396,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(45,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less ) ) )
=> ( ( ( C @ ( B @ ( nat @ plus_plus ) ) )
= ( A @ ( D @ ( nat @ plus_plus ) ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_less__add__eq__less) ).
thf(265,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less ) ) )
=> ( ( ( C @ ( B @ ( nat @ plus_plus ) ) )
= ( A @ ( D @ ( nat @ plus_plus ) ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(57,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ( TA @ one_one @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_zero__less__one) ).
thf(307,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ( TA @ one_one @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_ext) ).
thf(452,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(80,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( TA @ ring_1_Ints @ ( A @ ( TA @ member ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
<=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Ints__odd__less__0) ).
thf(381,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( TA @ ring_1_Ints @ ( A @ ( TA @ member ) ) )
=> ( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( A @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(74,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ( TA @ poly1 @ zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ozero) ).
thf(366,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ( TA @ poly1 @ zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(65,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ( TA @ poly1 @ comm_monoid_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ocomm__monoid__add) ).
thf(334,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ( TA @ poly1 @ comm_monoid_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(43,axiom,
! [TA: $tType] :
( ( TA @ cancel1352612707id_add )
=> ( TA @ poly1 @ cancel146912293up_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ocancel__ab__semigroup__add) ).
thf(260,plain,
! [TA: $tType] :
( ( TA @ cancel1352612707id_add )
=> ( TA @ poly1 @ cancel146912293up_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(84,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linordered_idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Olinordered__idom) ).
thf(392,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linordered_idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(53,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly1,C: TA @ poly1] :
( ( A @ ( B @ ( C @ ( TA @ poly1 @ plus_plus ) ) @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_poly__add) ).
thf(297,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly1,C: TA @ poly1] :
( ( A @ ( B @ ( C @ ( TA @ poly1 @ plus_plus ) ) @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(47,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linord219039673up_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Olinordered__ab__group__add) ).
thf(275,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linord219039673up_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(145,axiom,
! [TA: $tType] :
( ( TA @ idom )
=> ! [A: TA,B: TA @ poly1] :
( ( ( A @ ( B @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) )
<=> ( ( ( B @ ( A @ ( TA @ order ) ) )
!= ( nat @ zero_zero ) )
| ( B
= ( TA @ poly1 @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_order__root) ).
thf(598,plain,
! [TA: $tType] :
( ( TA @ idom )
=> ! [A: TA,B: TA @ poly1] :
( ( ( ( ( B @ ( A @ ( TA @ order ) ) )
!= ( nat @ zero_zero ) )
| ( B
= ( TA @ poly1 @ zero_zero ) ) )
=> ( ( A @ ( B @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) )
=> ( ( ( B @ ( A @ ( TA @ order ) ) )
!= ( nat @ zero_zero ) )
| ( B
= ( TA @ poly1 @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(8,axiom,
nat @ semiri456707255roduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(160,plain,
nat @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(113,axiom,
! [TA: $tType] :
( ( TA @ ring_char_0 )
=> ! [A: TA] :
( ( TA @ ring_1_Ints @ ( A @ ( TA @ member ) ) )
=> ( ( A @ ( A @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
!= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_Ints__odd__nonzero) ).
thf(484,plain,
! [TA: $tType] :
( ( TA @ ring_char_0 )
=> ! [A: TA] :
( ( TA @ ring_1_Ints @ ( A @ ( TA @ member ) ) )
=> ( ( A @ ( A @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
!= ( TA @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(42,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
<=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_add__gr__0) ).
thf(252,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(27,axiom,
nat @ cancel146912293up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(197,plain,
nat @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(97,axiom,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(435,plain,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(126,axiom,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ zero_zero )
!= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_zero__neq__one) ).
thf(522,plain,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ zero_zero )
!= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(63,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_double__zero__sym) ).
thf(324,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(60,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat] :
( ( A @ ( TA @ zero_zero @ ( TA @ monom ) ) )
= ( TA @ poly1 @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_monom__eq__0) ).
thf(317,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat] :
( ( A @ ( TA @ zero_zero @ ( TA @ monom ) ) )
= ( TA @ poly1 @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(72,axiom,
! [TA: $tType] :
( ( ( TA @ idom )
& ( TA @ ring_char_0 ) )
=> ! [A: TA @ poly1] :
( ( ( A @ ( TA @ poly ) )
= ( TA @ poly1 @ zero_zero @ ( TA @ poly ) ) )
<=> ( A
= ( TA @ poly1 @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_poly__zero) ).
thf(356,plain,
! [TA: $tType] :
( ( ( TA @ idom )
& ( TA @ ring_char_0 ) )
=> ! [A: TA @ poly1] :
( ( ( A
= ( TA @ poly1 @ zero_zero ) )
=> ( ( A @ ( TA @ poly ) )
= ( TA @ poly1 @ zero_zero @ ( TA @ poly ) ) ) )
& ( ( ( A @ ( TA @ poly ) )
= ( TA @ poly1 @ zero_zero @ ( TA @ poly ) ) )
=> ( A
= ( TA @ poly1 @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(119,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
<=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_add__less__cancel__right) ).
thf(499,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A @ ( C @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) )
& ( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(25,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clar_Rings_Ocomm__semiring__0__Groups_Ozero) ).
thf(193,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(115,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_add__left__imp__eq) ).
thf(489,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(31,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_gr0I) ).
thf(212,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(14,axiom,
nat @ comm_monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(173,plain,
nat @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(76,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( A @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_add__less__mono1) ).
thf(371,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( A @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(120,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(503,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(69,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_add__left__cancel) ).
thf(343,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(41,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_nat__add__right__cancel) ).
thf(244,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C = A )
=> ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(122,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(508,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(131,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat,B: TA] :
( ( ( A @ ( B @ ( TA @ monom ) ) )
= ( TA @ poly1 @ zero_zero ) )
<=> ( B
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_monom__eq__0__iff) ).
thf(541,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat,B: TA] :
( ( ( B
= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ monom ) ) )
= ( TA @ poly1 @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ monom ) ) )
= ( TA @ poly1 @ zero_zero ) )
=> ( B
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(95,axiom,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ one_one )
!= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_one__neq__zero) ).
thf(430,plain,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ one_one )
!= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(13,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA,B: nat,C: TA] :
( ( ( B @ ( C @ ( TA @ monom ) ) )
= ( B @ ( A @ ( TA @ monom ) ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_monom__eq__iff) ).
thf(166,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA,B: nat,C: TA] :
( ( ( C = A )
=> ( ( B @ ( C @ ( TA @ monom ) ) )
= ( B @ ( A @ ( TA @ monom ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ monom ) ) )
= ( B @ ( A @ ( TA @ monom ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
nat @ comm_semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(148,plain,
nat @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
nat @ comm_semiring_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__0) ).
thf(161,plain,
nat @ comm_semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(139,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ( TA @ poly1 @ monoid_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Omonoid__add) ).
thf(573,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ( TA @ poly1 @ monoid_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(20,axiom,
nat @ monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
thf(180,plain,
nat @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(4,axiom,
nat @ one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(149,plain,
nat @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(142,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_neq0__conv) ).
thf(584,plain,
! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) )
& ( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(94,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_add__right__cancel) ).
thf(423,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( C = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(88,axiom,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ! [A: TA,B: TA] :
( ( TA @ ring_1_Ints @ ( B @ ( TA @ member ) ) )
=> ( ( TA @ ring_1_Ints @ ( A @ ( TA @ member ) ) )
=> ( TA @ ring_1_Ints @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ member ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_Ints__add) ).
thf(402,plain,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ! [A: TA,B: TA] :
( ( TA @ ring_1_Ints @ ( B @ ( TA @ member ) ) )
=> ( ( TA @ ring_1_Ints @ ( A @ ( TA @ member ) ) )
=> ( TA @ ring_1_Ints @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(141,axiom,
! [TA: $tType] :
( ( TA @ ring_char_0 )
=> ! [A: TA] :
( ( TA @ ring_1_Ints @ ( A @ ( TA @ member ) ) )
=> ( ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_Ints__double__eq__0__iff) ).
thf(577,plain,
! [TA: $tType] :
( ( TA @ ring_char_0 )
=> ! [A: TA] :
( ( TA @ ring_1_Ints @ ( A @ ( TA @ member ) ) )
=> ( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(51,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA] :
( ( A @ ( TA @ poly1 @ zero_zero @ ( TA @ synthetic_div ) ) )
= ( TA @ poly1 @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_synthetic__div__0) ).
thf(291,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA] :
( ( A @ ( TA @ poly1 @ zero_zero @ ( TA @ synthetic_div ) ) )
= ( TA @ poly1 @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(91,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member ) ) )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_mem__def) ).
thf(413,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member ) ) ) )
& ( ( A @ ( B @ ( TA @ member ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(101,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_trans__less__add1) ).
thf(445,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(21,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ monoid_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clar_Rings_Ocomm__semiring__0__Groups_Omonoid__add) ).
thf(181,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ monoid_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(70,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_nat__add__assoc) ).
thf(350,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(90,axiom,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA] :
( ( B
= ( A @ ( B @ ( TA @ plus_plus ) ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_add__0__iff) ).
thf(406,plain,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( B
= ( A @ ( B @ ( TA @ plus_plus ) ) ) ) )
& ( ( B
= ( A @ ( B @ ( TA @ plus_plus ) ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(33,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ( TA @ poly1 @ comm_semiring_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Ocomm__semiring__1) ).
thf(219,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ( TA @ poly1 @ comm_semiring_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(93,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
<=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_add__less__cancel__left) ).
thf(419,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(78,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ poly1 @ comm_semiring_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Ocomm__semiring__0) ).
thf(377,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ poly1 @ comm_semiring_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(137,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_nat__add__commute) ).
thf(567,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(55,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ ordere216010020id_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Oordered__comm__monoid__add) ).
thf(303,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ ordere216010020id_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(82,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA @ poly1] :
( ( A @ ( TA @ poly1 @ zero_zero @ ( TA @ pcompose ) ) )
= ( TA @ poly1 @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_pcompose__0) ).
thf(387,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA @ poly1] :
( ( A @ ( TA @ poly1 @ zero_zero @ ( TA @ pcompose ) ) )
= ( TA @ poly1 @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(39,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_add__less__imp__less__right) ).
thf(240,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(28,axiom,
nat @ cancel1352612707id_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__comm__monoid__add) ).
thf(198,plain,
nat @ cancel1352612707id_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(106,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(462,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(105,axiom,
! [TA: $tType] :
( ( ( TA @ idom )
& ( TA @ ring_char_0 ) )
=> ! [A: TA @ poly1,B: TA @ poly1] :
( ( ( B @ ( TA @ poly ) )
= ( A @ ( TA @ poly ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_poly__eq__iff) ).
thf(455,plain,
! [TA: $tType] :
( ( ( TA @ idom )
& ( TA @ ring_char_0 ) )
=> ! [A: TA @ poly1,B: TA @ poly1] :
( ( ( B = A )
=> ( ( B @ ( TA @ poly ) )
= ( A @ ( TA @ poly ) ) ) )
& ( ( ( B @ ( TA @ poly ) )
= ( A @ ( TA @ poly ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(85,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_zero__less__two) ).
thf(394,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(98,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ( TA @ poly1 @ one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Oone) ).
thf(438,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ( TA @ poly1 @ one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(132,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ ring_char_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Int_Oring__char__0) ).
thf(548,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ ring_char_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(114,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: TA,C: TA] :
( ( C @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_pos__add__strict) ).
thf(487,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: TA,C: TA] :
( ( C @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(134,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_add__0__left) ).
thf(553,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(10,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(162,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(129,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly1,B: TA @ poly1] :
( ( B = A )
<=> ! [C: nat] :
( ( C @ ( B @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( C @ ( A @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_expand__poly__eq) ).
thf(531,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly1,B: TA @ poly1] :
( ( ! [C: nat] :
( ( C @ ( B @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( C @ ( A @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ! [C: nat] :
( ( C @ ( B @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( C @ ( A @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(127,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_add__right__imp__eq) ).
thf(525,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(5,axiom,
nat @ ab_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(150,plain,
nat @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(29,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_linorder__neqE__linordered__idom) ).
thf(199,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(17,axiom,
nat @ ordere236663937imp_le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(177,plain,
nat @ ordere236663937imp_le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(64,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat] :
( ( A @ ( TA @ poly1 @ zero_zero @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_coeff__0) ).
thf(331,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat] :
( ( A @ ( TA @ poly1 @ zero_zero @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(67,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(338,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(66,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ ordere223160158up_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(336,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ ordere223160158up_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(16,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ comm_monoid_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clar_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add) ).
thf(175,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ comm_monoid_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(144,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_Nat_Oadd__0__right) ).
thf(595,plain,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(112,axiom,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_add__pos__pos) ).
thf(482,plain,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(117,axiom,
a @ comm_semiring_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
thf(495,plain,
a @ comm_semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(75,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA] :
( ( A @ ( TA @ poly1 @ zero_zero @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_poly__0) ).
thf(368,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA] :
( ( A @ ( TA @ poly1 @ zero_zero @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(107,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_nat__add__left__commute) ).
thf(465,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(36,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= B )
=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_add__eq__self__zero) ).
thf(231,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= B )
=> ( A
= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(73,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_less__nat__zero__code) ).
thf(363,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(135,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_nat__add__left__cancel) ).
thf(556,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B = A )
=> ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(125,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_gr__implies__not0) ).
thf(517,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(83,axiom,
! [TA: $tType] :
( ( TA @ comm_ring_1 )
=> ( TA @ poly1 @ ring_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Oring__1) ).
thf(390,plain,
! [TA: $tType] :
( ( TA @ comm_ring_1 )
=> ( TA @ poly1 @ ring_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(24,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly1,B: TA @ poly1] :
( ( ( B @ ( TA @ coeff ) )
= ( A @ ( TA @ coeff ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_coeff__inject) ).
thf(186,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly1,B: TA @ poly1] :
( ( ( B = A )
=> ( ( B @ ( TA @ coeff ) )
= ( A @ ( TA @ coeff ) ) ) )
& ( ( ( B @ ( TA @ coeff ) )
= ( A @ ( TA @ coeff ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(37,axiom,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_add__imp__eq) ).
thf(235,plain,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(96,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ ordere236663937imp_le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(433,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ ordere236663937imp_le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(110,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linordered_semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Olinordered__semidom) ).
thf(478,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linordered_semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(6,axiom,
nat @ linordered_semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(151,plain,
nat @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(54,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_not__less0) ).
thf(300,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(102,axiom,
! [TA: $tType] :
( ( TA @ idom )
=> ( TA @ poly1 @ idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Oidom) ).
thf(447,plain,
! [TA: $tType] :
( ( TA @ idom )
=> ( TA @ poly1 @ idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(59,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ~ ( TA @ zero_zero @ ( TA @ one_one @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_not__one__less__zero) ).
thf(315,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ~ ( TA @ zero_zero @ ( TA @ one_one @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(44,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA @ poly1] :
( ( TA @ poly1 @ zero_zero @ ( A @ ( TA @ poly1 @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_add__poly__code_I2_J) ).
thf(262,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA @ poly1] :
( ( TA @ poly1 @ zero_zero @ ( A @ ( TA @ poly1 @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(1,conjecture,
( ( x @ ( h @ ( a @ poly1 @ zero_zero @ ( a @ fundam296178794t_poly ) ) @ ( a @ poly ) @ ( a @ ( a @ aa ) ) ) )
= ( x @ ( h @ ( a @ plus_plus ) ) @ ( a @ poly1 @ zero_zero @ ( a @ poly ) @ ( a @ ( a @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( x @ ( h @ ( a @ poly1 @ zero_zero @ ( a @ fundam296178794t_poly ) ) @ ( a @ poly ) @ ( a @ ( a @ aa ) ) ) )
!= ( x @ ( h @ ( a @ plus_plus ) ) @ ( a @ poly1 @ zero_zero @ ( a @ poly ) @ ( a @ ( a @ aa ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(146,plain,
( ( x @ ( h @ ( a @ poly1 @ zero_zero @ ( a @ fundam296178794t_poly ) ) @ ( a @ poly ) @ ( a @ ( a @ aa ) ) ) )
!= ( x @ ( h @ ( a @ plus_plus ) ) @ ( a @ poly1 @ zero_zero @ ( a @ poly ) @ ( a @ ( a @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,axiom,
nat @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(183,plain,
nat @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(77,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
<=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_even__less__0__iff) ).
thf(373,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(136,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA @ poly1] :
( ( A @ ( TA @ poly1 @ zero_zero @ ( TA @ poly1 @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_add__poly__code_I1_J) ).
thf(564,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA @ poly1] :
( ( A @ ( TA @ poly1 @ zero_zero @ ( TA @ poly1 @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(56,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA] : ( TA @ one_one @ ( A @ ( TA @ plus_plus ) ) @ ( A @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_less__add__one) ).
thf(305,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA] : ( TA @ one_one @ ( A @ ( TA @ plus_plus ) ) @ ( A @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(40,axiom,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_add__strict__right__mono) ).
thf(242,plain,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(52,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA,B: nat,C: TA] :
( ( B @ ( A @ ( TA @ monom ) ) @ ( B @ ( C @ ( TA @ monom ) ) @ ( TA @ poly1 @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ monom ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_add__monom) ).
thf(294,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA,B: nat,C: TA] :
( ( B @ ( A @ ( TA @ monom ) ) @ ( B @ ( C @ ( TA @ monom ) ) @ ( TA @ poly1 @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ monom ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(68,axiom,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ( TA @ ring_1_Ints @ ( TA @ zero_zero @ ( TA @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_Ints__0) ).
thf(341,plain,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ( TA @ ring_1_Ints @ ( TA @ zero_zero @ ( TA @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(26,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ ab_semigroup_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clar_Rings_Ocomm__semiring__0__Groups_Oab__semigroup__add) ).
thf(195,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ ab_semigroup_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(87,axiom,
! [TA: $tType] :
( ( TA @ cancel1352612707id_add )
=> ( TA @ poly1 @ cancel_semigroup_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ocancel__semigroup__add) ).
thf(400,plain,
! [TA: $tType] :
( ( TA @ cancel1352612707id_add )
=> ( TA @ poly1 @ cancel_semigroup_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(50,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_zero__reorient) ).
thf(283,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= A ) )
& ( ( ( TA @ zero_zero )
= A )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(121,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_trans__less__add2) ).
thf(506,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(46,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_double__eq__0__iff) ).
thf(268,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(140,axiom,
! [TA: $tType] :
( ( TA @ comm_ring_1 )
=> ( TA @ poly1 @ comm_ring_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Ocomm__ring__1) ).
thf(575,plain,
! [TA: $tType] :
( ( TA @ comm_ring_1 )
=> ( TA @ poly1 @ comm_ring_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(128,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: nat,B: TA @ poly1,C: TA @ poly1] :
( ( A @ ( B @ ( C @ ( TA @ poly1 @ plus_plus ) ) @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) @ ( A @ ( C @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_coeff__add) ).
thf(528,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: nat,B: TA @ poly1,C: TA @ poly1] :
( ( A @ ( B @ ( C @ ( TA @ poly1 @ plus_plus ) ) @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) @ ( A @ ( C @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(11,axiom,
nat @ ordere223160158up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(163,plain,
nat @ ordere223160158up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(18,axiom,
nat @ zero_neq_one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(178,plain,
nat @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(48,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_add_Ocomm__neutral) ).
thf(277,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(62,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ( TA @ poly1 @ zero_neq_one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Ozero__neq__one) ).
thf(322,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ( TA @ poly1 @ zero_neq_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(58,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_nat__add__left__cancel__less) ).
thf(309,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(32,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_zero__less__double__add__iff__zero__less__single__add) ).
thf(215,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(143,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA] :
( ( A @ ( TA @ poly1 @ zero_zero @ ( TA @ fundam296178794t_poly ) ) )
= ( TA @ poly1 @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_offset__poly__0) ).
thf(592,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA] :
( ( A @ ( TA @ poly1 @ zero_zero @ ( TA @ fundam296178794t_poly ) ) )
= ( TA @ poly1 @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(118,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_less__zeroE) ).
thf(496,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(609,plain,
$false,
inference(e,[status(thm)],[468,449,379,202,440,511,385,550,538,417,320,174,404,570,184,152,228,475,179,443,238,514,353,480,492,164,280,221,396,265,307,452,381,366,334,260,392,297,275,598,160,484,252,197,435,522,324,317,356,499,193,489,212,173,371,503,343,244,508,541,430,166,148,161,573,180,149,584,423,402,577,291,413,445,181,350,406,219,419,377,567,303,387,240,198,462,455,394,438,548,487,553,162,531,525,150,199,177,331,338,336,175,595,482,495,368,465,231,363,556,517,390,186,235,433,478,151,300,447,315,262,146,183,373,564,305,242,294,341,195,400,283,506,268,575,528,163,178,277,322,309,215,592,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW488_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.39 % Computer : n008.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat Sep 26 16:09:39 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.87/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.47/1.29 % [INFO] Parsing done (315ms).
% 1.89/1.30 % [INFO] Running in sequential loop mode.
% 2.32/1.69 % [INFO] eprover registered as external prover.
% 2.53/1.70 % [INFO] Scanning for conjecture ...
% 2.70/1.87 % [INFO] Found a conjecture (or negated_conjecture) and 143 axioms. Running axiom selection ...
% 2.89/1.99 % [INFO] Axiom selection finished. Selected 143 axioms (removed 0 axioms).
% 3.60/2.20 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.60/2.22 % [INFO] Type checking passed.
% 3.60/2.22 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 10.71/4.35 % External prover 'e' found a proof!
% 10.71/4.35 % [INFO] Killing All external provers ...
% 10.71/4.35 % Time passed: 3820ms (effective reasoning time: 3040ms)
% 10.71/4.35 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 10.71/4.35 % Axioms used in derivation (143): fact_42_plus__nat_Oadd__0, arity_Nat_Onat___Rings_Olinordered__semidom, arity_Polynomial_Opoly___Rings_Ocomm__ring__1, fact_35_poly__pcompose, fact_32_monom__eq__0__iff, fact_88_less__add__one, tfree_0, arity_Polynomial_Opoly___Groups_Oordered__cancel__ab__semigroup__add, fact_15_add__right__imp__eq, fact_57_coeff__1, fact_95_zero__less__two, fact_93_coeff__inject, fact_17_add__left__imp__eq, fact_2_poly__add, fact_45_Ints__odd__nonzero, fact_14_zero__reorient, fact_8_add__0__left, fact_46_nat__add__right__cancel, fact_48_poly__1, arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, arity_Polynomial_Opoly___Groups_Oordered__comm__monoid__add, fact_37_Ints__double__eq__0__iff, fact_11_add__0__right, fact_74_mem__def, fact_50_nat__add__left__commute, fact_0_offset__poly__0, fact_31_poly__rec__0, arity_Polynomial_Opoly___Groups_Olinordered__ab__group__add, fact_25_poly__eq__iff, arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, fact_18_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_36_add__monom, arity_Polynomial_Opoly___Groups_Omonoid__add, arity_Polynomial_Opoly___Groups_Oone, fact_82_add__lessD1, fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, arity_Nat_Onat___Groups_Ocomm__monoid__add, fact_86_trans__less__add2, fact_3_double__zero__sym, fact_27_add_Ocomm__neutral, arity_Nat_Onat___Groups_Ocancel__comm__monoid__add, fact_39_Ints__0, arity_Polynomial_Opoly___Groups_Ocancel__semigroup__add, arity_Polynomial_Opoly___Rings_Oring__1, arity_Polynomial_Opoly___Rings_Oidom, fact_79_add__strict__mono, arity_Polynomial_Opoly___Rings_Ozero__neq__one, arity_Polynomial_Opoly___Groups_Ozero, fact_64_add__gr__0, clar_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add, arity_Polynomial_Opoly___Int_Oring__char__0, arity_Polynomial_Opoly___Rings_Olinordered__semidom, fact_34_synthetic__div__0, fact_47_nat__add__left__cancel, fact_7_poly__zero, arity_Polynomial_Opoly___Groups_Oordered__ab__semigroup__add__imp__le, fact_49_nat__add__assoc, fact_81_add__less__imp__less__left, fact_68_coeff__add, arity_Polynomial_Opoly___Groups_Ocancel__ab__semigroup__add, fact_51_nat__add__commute, arity_Polynomial_Opoly___Rings_Ocomm__semiring__1, clar_Rings_Ocomm__semiring__0__Groups_Oab__semigroup__add, fact_73_ext, fact_96_even__less__0__iff, clar_Rings_Ocomm__semiring__0__Groups_Omonoid__add, fact_61_nat__add__left__cancel__less, arity_Polynomial_Opoly___Rings_Olinordered__idom, fact_13_add__poly__code_I1_J, fact_80_add__less__imp__less__right, clar_Rings_Ocomm__semiring__0__Groups_Ozero, arity_Polynomial_Opoly___Groups_Ocomm__monoid__add, fact_62_add__less__cancel__right, arity_Nat_Onat___Rings_Ocomm__semiring__1, fact_55_one__neq__zero, fact_60_neq0__conv, arity_Nat_Onat___Groups_Ozero, arity_Polynomial_Opoly___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, arity_Nat_Onat___Groups_Oordered__comm__monoid__add, fact_54_zero__neq__one, fact_90_not__add__less1, fact_12_add__poly__code_I2_J, fact_30_pcompose__0, fact_70_not__one__less__zero, fact_28_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_76_gr0I, fact_22_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, arity_Nat_Onat___Rings_Ocomm__semiring__0, fact_40_Ints__add, fact_38_monom__eq__iff, fact_94_linorder__neqE__linordered__idom, arity_Polynomial_Opoly___Groups_Ocancel__comm__monoid__add, fact_85_add__less__mono1, fact_71_not__less0, fact_43_Nat_Oadd__0__right, fact_16_add__imp__eq, fact_44_add__eq__self__zero, fact_20_ab__semigroup__add__class_Oadd__ac_I1_J, fact_5_add__left__cancel, arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_33_monom__eq__0, fact_67_coeff__0, fact_84_add__less__mono, fact_75_gr__implies__not0, fact_56_Ints__odd__less__0, arity_Nat_Onat___Groups_Oone, fact_29_order__root, fact_72_zero__less__one, fact_53_Ints__1, fact_6_add__right__cancel, fact_83_less__add__eq__less, fact_69_coeff__monom, fact_92_expand__poly__eq, fact_9_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_24_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_97_add__pos__pos, fact_10_add__0, help_pp_1_1_U, fact_23_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_58_less__zeroE, fact_52_one__reorient, fact_87_trans__less__add1, fact_77_add__strict__right__mono, arity_Polynomial_Opoly___Groups_Oab__semigroup__add, arity_Nat_Onat___Groups_Omonoid__add, fact_91_pos__add__strict, arity_Nat_Onat___Groups_Oab__semigroup__add, fact_41_add__is__0, fact_66_double__add__less__zero__iff__single__add__less__zero, fact_65_zero__less__double__add__iff__zero__less__single__add, help_pp_2_1_U, fact_63_add__less__cancel__left, fact_4_double__eq__0__iff, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_59_less__nat__zero__code, arity_Nat_Onat___Rings_Ozero__neq__one, arity_Polynomial_Opoly___Rings_Ocomm__semiring__0, fact_89_not__add__less2, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_26_add__0__iff, fact_1_poly__0, fact_78_add__strict__left__mono
% 10.71/4.35 % No. of inferences in proof: 290
% 10.71/4.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3820 ms resp. 3040 ms w/o parsing
% 11.24/4.50 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.24/4.50 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------