%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW490_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 17.10s 6.08s
% Output : Refutation 17.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 135
% Syntax : Number of formulae : 272 ( 60 unt; 0 typ; 0 def)
% Number of atoms : 851 ( 352 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 3098 ( 53 ~; 12 |; 41 &;2680 @)
% ( 20 <=>; 292 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 40 usr; 6 con; 0-5 aty)
% Number of variables : 627 ( 0 ^; 625 !; 2 ?; 627 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(cancel1352612707id_add_decl,type,
cancel1352612707id_add:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(idom_decl,type,
idom:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(ring_char_0_decl,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(monoid_add_decl,type,
monoid_add:
!>[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(comm_monoid_add_decl,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[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(fundam296178794t_poly_decl,type,
fundam296178794t_poly:
!>[TA: $tType] : ( ( TA @ poly ) > TA > ( TA @ poly ) ) ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( bool > TA > TA > TA ) ).
thf(suc_decl,type,
suc: nat > nat ).
thf(nat_case_decl,type,
nat_case:
!>[TA: $tType] : ( TA > ( TA @ ( nat @ fun ) ) > ( TA @ ( nat @ fun ) ) ) ).
thf(semiri532925092at_aux_decl,type,
semiri532925092at_aux:
!>[TA: $tType] : ( ( TA @ ( TA @ fun ) ) > nat > TA > TA ) ).
thf(abs_poly_decl,type,
abs_poly:
!>[TA: $tType] : ( ( TA @ ( nat @ fun ) ) > ( TA @ poly ) ) ).
thf(coeff_decl,type,
coeff:
!>[TA: $tType] : ( ( TA @ poly ) > ( TA @ ( nat @ fun ) ) ) ).
thf(degree_decl,type,
degree:
!>[TA: $tType] : ( ( TA @ poly ) > nat ) ).
thf(monom_decl,type,
monom:
!>[TA: $tType] : ( TA > nat > ( TA @ poly ) ) ).
thf(order_decl,type,
order:
!>[TA: $tType] : ( TA > ( TA @ poly ) > nat ) ).
thf(pCons_decl,type,
pCons:
!>[TA: $tType] : ( TA > ( TA @ poly ) > ( TA @ poly ) ) ).
thf(pcompose_decl,type,
pcompose:
!>[TA: $tType] : ( ( TA @ poly ) > ( TA @ poly ) > ( TA @ poly ) ) ).
thf(poly1_decl,type,
poly1:
!>[TA: $tType] : ( ( TA @ poly ) > ( TA @ ( TA @ fun ) ) ) ).
thf(poly_rec_decl,type,
poly_rec:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TB @ fun ) @ ( TA @ poly @ fun ) @ ( TA @ fun ) ) > ( TA @ poly ) > TB ) ).
thf(smult_decl,type,
smult:
!>[TA: $tType] : ( TA > ( TA @ poly ) > ( TA @ poly ) ) ).
thf(synthetic_div_decl,type,
synthetic_div:
!>[TA: $tType] : ( ( TA @ poly ) > TA > ( TA @ poly ) ) ).
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(fequal_decl,type,
fequal:
!>[TA: $tType] : ( TA > TA > bool ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(h_decl,type,
h: a ).
thf(97,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ( ( TA @ poly @ zero_zero @ ( TA @ degree ) )
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_degree__0) ).
thf(479,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ( ( TA @ poly @ zero_zero @ ( TA @ degree ) )
= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(109,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly] :
( ( A
!= ( TA @ poly @ zero_zero ) )
=> ( ( A @ ( TA @ degree ) @ ( A @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
!= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_leading__coeff__neq__0) ).
thf(518,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly] :
( ( A
!= ( TA @ poly @ zero_zero ) )
=> ( ( A @ ( TA @ degree ) @ ( A @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
!= ( TA @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(28,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_78_add__imp__eq) ).
thf(234,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)],[28]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ zero )
=> ! [A: TA,B: TA @ ( TA @ fun ) @ ( TB @ poly @ fun ) @ ( TB @ fun )] :
( ( ( A @ ( TB @ poly @ zero_zero @ ( TB @ zero_zero @ ( B @ ( TA @ ( TA @ fun ) @ ( TB @ poly @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TB @ poly @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A )
=> ( ( TB @ poly @ zero_zero @ ( B @ ( A @ ( TB @ ( TA @ poly_rec ) ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_poly__rec__0) ).
thf(333,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ zero )
=> ! [A: TA,B: TA @ ( TA @ fun ) @ ( TB @ poly @ fun ) @ ( TB @ fun )] :
( ( ( A @ ( TB @ poly @ zero_zero @ ( TB @ zero_zero @ ( B @ ( TA @ ( TA @ fun ) @ ( TB @ poly @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TB @ poly @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A )
=> ( ( TB @ poly @ zero_zero @ ( B @ ( A @ ( TB @ ( TA @ poly_rec ) ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(35,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: TA,B: nat,C: TA @ ( TA @ fun )] :
( ( A @ ( B @ suc @ ( C @ ( TA @ semiri532925092at_aux ) ) ) )
= ( A @ ( C @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ semiri532925092at_aux ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_of__nat__aux_Osimps_I2_J) ).
thf(249,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: TA,B: nat,C: TA @ ( TA @ fun )] :
( ( A @ ( B @ suc @ ( C @ ( TA @ semiri532925092at_aux ) ) ) )
= ( A @ ( C @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ semiri532925092at_aux ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(90,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA,B: TA @ poly] :
( ( B
!= ( TA @ poly @ zero_zero ) )
=> ( ( B @ ( A @ ( TA @ pCons ) ) @ ( TA @ degree ) )
= ( B @ ( TA @ degree ) @ suc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_degree__pCons__eq) ).
thf(449,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA,B: TA @ poly] :
( ( B
!= ( TA @ poly @ zero_zero ) )
=> ( ( B @ ( A @ ( TA @ pCons ) ) @ ( TA @ degree ) )
= ( B @ ( TA @ degree ) @ suc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(34,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(247,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ ab_semigroup_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(87,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA @ poly,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ smult ) ) )
= ( A @ ( B @ ( TA @ smult ) ) @ ( A @ ( C @ ( TA @ smult ) ) @ ( TA @ poly @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_smult__add__left) ).
thf(440,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA @ poly,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ smult ) ) )
= ( A @ ( B @ ( TA @ smult ) ) @ ( A @ ( C @ ( TA @ smult ) ) @ ( TA @ poly @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(39,axiom,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_add__Suc__right) ).
thf(269,plain,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(74,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly] :
( ( ( A @ ( TA @ degree ) @ ( A @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ poly @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_leading__coeff__0__iff) ).
thf(384,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly] :
( ( ( A
= ( TA @ poly @ zero_zero ) )
=> ( ( A @ ( TA @ degree ) @ ( A @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( TA @ degree ) @ ( A @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ poly @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(118,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_91_double__eq__0__iff) ).
thf(550,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)],[118]) ).
thf(4,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fFalse @ ( TA @ if ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(142,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fFalse @ ( TA @ if ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(153,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(46,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly,C: TA @ poly] :
( ( A @ ( B @ ( C @ ( TA @ pcompose ) ) @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_poly__pcompose) ).
thf(288,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly,C: TA @ poly] :
( ( A @ ( B @ ( C @ ( TA @ pcompose ) ) @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(52,axiom,
! [TA: $tType,A: TA @ ( nat @ fun ),B: TA] :
( ( nat @ zero_zero @ ( A @ ( B @ ( TA @ nat_case ) ) @ ( TA @ ( nat @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_nat__case__0) ).
thf(301,plain,
! [TA: $tType,A: TA @ ( nat @ fun ),B: TA] :
( ( nat @ zero_zero @ ( A @ ( B @ ( TA @ nat_case ) ) @ ( TA @ ( nat @ aa ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(17,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_add__Suc) ).
thf(184,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(129,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ( TA @ poly @ comm_monoid_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ocomm__monoid__add) ).
thf(587,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ( TA @ poly @ comm_monoid_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(134,axiom,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_plus__nat_Oadd__0) ).
thf(606,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(44,axiom,
nat @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(284,plain,
nat @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(7,axiom,
nat @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(152,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
! [A: nat] :
( ( A @ suc )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_Suc__n__not__n) ).
thf(179,plain,
! [A: nat] :
( ( A @ suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(88,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_Suc__neq__Zero) ).
thf(443,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(56,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA,B: nat,C: TA] :
( ( B @ ( A @ ( TA @ monom ) ) @ ( B @ ( C @ ( TA @ monom ) ) @ ( TA @ poly @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ monom ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_add__monom) ).
thf(321,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA,B: nat,C: TA] :
( ( B @ ( A @ ( TA @ monom ) ) @ ( B @ ( C @ ( TA @ monom ) ) @ ( TA @ poly @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ monom ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(42,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fTrue @ ( TA @ if ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(280,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fTrue @ ( TA @ if ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(48,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly] :
~ ! [B: TA,C: TA @ poly] :
( A
!= ( C @ ( B @ ( TA @ pCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_pCons__cases) ).
thf(293,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly] :
~ ! [B: TA,C: TA @ poly] :
( A
!= ( C @ ( B @ ( TA @ pCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(32,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(243,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(83,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly] :
( ( A @ ( B @ ( TA @ synthetic_div ) ) @ ( A @ ( TA @ smult ) ) @ ( B @ ( TA @ poly @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ synthetic_div ) ) @ ( A @ ( B @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ pCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_synthetic__div__correct) ).
thf(428,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly] :
( ( A @ ( B @ ( TA @ synthetic_div ) ) @ ( A @ ( TA @ smult ) ) @ ( B @ ( TA @ poly @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ synthetic_div ) ) @ ( A @ ( B @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ pCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(54,axiom,
! [TA: $tType] :
( ( TA @ idom )
=> ! [A: TA @ poly,B: TA] :
( ( ( A @ ( B @ ( TA @ smult ) ) )
= ( TA @ poly @ zero_zero ) )
<=> ( ( A
= ( TA @ poly @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_smult__eq__0__iff) ).
thf(307,plain,
! [TA: $tType] :
( ( TA @ idom )
=> ! [A: TA @ poly,B: TA] :
( ( ( ( A
= ( TA @ poly @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( B @ ( TA @ smult ) ) )
= ( TA @ poly @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ smult ) ) )
= ( TA @ poly @ zero_zero ) )
=> ( ( A
= ( TA @ poly @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(91,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ( TA @ poly @ semiring_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Osemiring__1) ).
thf(452,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ( TA @ poly @ semiring_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(26,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_nat_Oinject) ).
thf(220,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ suc )
= ( A @ suc ) ) )
& ( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(114,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA] :
( ( A @ ( TA @ poly @ zero_zero @ ( B @ ( TA @ pCons ) ) @ ( TA @ fundam296178794t_poly ) ) )
= ( TA @ poly @ zero_zero @ ( B @ ( TA @ pCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_offset__poly__single) ).
thf(534,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA] :
( ( A @ ( TA @ poly @ zero_zero @ ( B @ ( TA @ pCons ) ) @ ( TA @ fundam296178794t_poly ) ) )
= ( TA @ poly @ zero_zero @ ( B @ ( TA @ pCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(65,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly @ linord219039673up_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Olinordered__ab__group__add) ).
thf(349,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly @ linord219039673up_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(120,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_74_add__0) ).
thf(561,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)],[120]) ).
thf(1,conjecture,
( ( h @ ( a @ poly @ zero_zero @ ( a @ fundam296178794t_poly ) ) @ ( a @ degree ) )
= ( a @ poly @ zero_zero @ ( a @ degree ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( h @ ( a @ poly @ zero_zero @ ( a @ fundam296178794t_poly ) ) @ ( a @ degree ) )
!= ( a @ poly @ zero_zero @ ( a @ degree ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(137,plain,
( ( h @ ( a @ poly @ zero_zero @ ( a @ fundam296178794t_poly ) ) @ ( a @ degree ) )
!= ( a @ poly @ zero_zero @ ( a @ degree ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
nat @ comm_semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(165,plain,
nat @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(99,axiom,
! [TA: $tType] :
( ( TA @ cancel1352612707id_add )
=> ( TA @ poly @ cancel1352612707id_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ocancel__comm__monoid__add) ).
thf(484,plain,
! [TA: $tType] :
( ( TA @ cancel1352612707id_add )
=> ( TA @ poly @ cancel1352612707id_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(36,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_66_add__left__cancel) ).
thf(252,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)],[36]) ).
thf(69,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: TA,B: TA @ ( TA @ fun )] :
( ( A @ ( nat @ zero_zero @ ( B @ ( TA @ semiri532925092at_aux ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_of__nat__aux_Osimps_I1_J) ).
thf(361,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: TA,B: TA @ ( TA @ fun )] :
( ( A @ ( nat @ zero_zero @ ( B @ ( TA @ semiri532925092at_aux ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(93,axiom,
! [TA: $tType] :
( ( TA @ idom )
=> ! [A: TA,B: TA @ poly] :
( ( ( A @ ( B @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) )
<=> ( ( ( B @ ( A @ ( TA @ order ) ) )
!= ( nat @ zero_zero ) )
| ( B
= ( TA @ poly @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_order__root) ).
thf(461,plain,
! [TA: $tType] :
( ( TA @ idom )
=> ! [A: TA,B: TA @ poly] :
( ( ( ( ( B @ ( A @ ( TA @ order ) ) )
!= ( nat @ zero_zero ) )
| ( B
= ( TA @ poly @ zero_zero ) ) )
=> ( ( A @ ( B @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) )
=> ( ( ( B @ ( A @ ( TA @ order ) ) )
!= ( nat @ zero_zero ) )
| ( B
= ( TA @ poly @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(57,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ poly @ comm_semiring_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Ocomm__semiring__0) ).
thf(324,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ poly @ comm_semiring_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(45,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_79_add__left__imp__eq) ).
thf(285,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)],[45]) ).
thf(126,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA] :
( ( TA @ poly @ zero_zero @ ( A @ ( TA @ smult ) ) )
= ( TA @ poly @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_smult__0__right) ).
thf(578,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA] :
( ( TA @ poly @ zero_zero @ ( A @ ( TA @ smult ) ) )
= ( TA @ poly @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(55,axiom,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ suc @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_zero__induct) ).
thf(317,plain,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ suc @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(10,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: TA,C: TA @ poly,D: TA] :
( ( ( C @ ( D @ ( TA @ pCons ) ) )
= ( A @ ( B @ ( TA @ pCons ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_pCons__eq__iff) ).
thf(156,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: TA,C: TA @ poly,D: TA] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ pCons ) ) )
= ( A @ ( B @ ( TA @ pCons ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ pCons ) ) )
= ( A @ ( B @ ( TA @ pCons ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: TA @ poly] :
( ( 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_20_expand__poly__eq) ).
thf(169,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: TA @ poly] :
( ( ! [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)],[13]) ).
thf(59,axiom,
! [TA: $tType] :
( ( TA @ cancel1352612707id_add )
=> ( TA @ poly @ cancel146912293up_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ocancel__ab__semigroup__add) ).
thf(328,plain,
! [TA: $tType] :
( ( TA @ cancel1352612707id_add )
=> ( TA @ poly @ cancel146912293up_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(101,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly,C: TA] :
( ( ( B @ ( A @ ( TA @ pCons ) ) @ ( B @ ( C @ ( TA @ smult ) ) @ ( TA @ poly @ plus_plus ) ) )
= ( TA @ poly @ zero_zero ) )
=> ( B
= ( TA @ poly @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_offset__poly__eq__0__lemma) ).
thf(488,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly,C: TA] :
( ( ( B @ ( A @ ( TA @ pCons ) ) @ ( B @ ( C @ ( TA @ smult ) ) @ ( TA @ poly @ plus_plus ) ) )
= ( TA @ poly @ zero_zero ) )
=> ( B
= ( TA @ poly @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(96,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ pCons ) ) @ ( TA @ fundam296178794t_poly ) ) )
= ( A @ ( B @ ( TA @ fundam296178794t_poly ) ) @ ( C @ ( TA @ pCons ) ) @ ( A @ ( B @ ( TA @ fundam296178794t_poly ) ) @ ( A @ ( TA @ smult ) ) @ ( TA @ poly @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_offset__poly__pCons) ).
thf(476,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ pCons ) ) @ ( TA @ fundam296178794t_poly ) ) )
= ( A @ ( B @ ( TA @ fundam296178794t_poly ) ) @ ( C @ ( TA @ pCons ) ) @ ( A @ ( B @ ( TA @ fundam296178794t_poly ) ) @ ( A @ ( TA @ smult ) ) @ ( TA @ poly @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(112,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_nat_Osimps_I3_J) ).
thf(526,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(117,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_add__0__left) ).
thf(547,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(20,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(193,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ monoid_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(115,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat,B: TA] :
( ( ( A @ ( B @ ( TA @ monom ) ) )
= ( TA @ poly @ zero_zero ) )
<=> ( B
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_monom__eq__0__iff) ).
thf(537,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat,B: TA] :
( ( ( B
= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ monom ) ) )
= ( TA @ poly @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ monom ) ) )
= ( TA @ poly @ zero_zero ) )
=> ( B
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(76,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly] :
( ( ( A @ ( B @ ( TA @ synthetic_div ) ) )
= ( TA @ poly @ zero_zero ) )
<=> ( ( B @ ( TA @ degree ) )
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_synthetic__div__eq__0__iff) ).
thf(393,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly] :
( ( ( ( B @ ( TA @ degree ) )
= ( nat @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ synthetic_div ) ) )
= ( TA @ poly @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ synthetic_div ) ) )
= ( TA @ poly @ zero_zero ) )
=> ( ( B @ ( TA @ degree ) )
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(108,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA] :
( ( A @ ( TA @ poly @ zero_zero @ ( TA @ synthetic_div ) ) )
= ( TA @ poly @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_synthetic__div__0) ).
thf(515,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA] :
( ( A @ ( TA @ poly @ zero_zero @ ( TA @ synthetic_div ) ) )
= ( TA @ poly @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(123,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA @ poly,B: TA @ poly,C: TA] :
( ( A @ ( B @ ( TA @ poly @ plus_plus ) ) @ ( C @ ( TA @ smult ) ) )
= ( A @ ( C @ ( TA @ smult ) ) @ ( B @ ( C @ ( TA @ smult ) ) @ ( TA @ poly @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_smult__add__right) ).
thf(569,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA @ poly,B: TA @ poly,C: TA] :
( ( A @ ( B @ ( TA @ poly @ plus_plus ) ) @ ( C @ ( TA @ smult ) ) )
= ( A @ ( C @ ( TA @ smult ) ) @ ( B @ ( C @ ( TA @ smult ) ) @ ( TA @ poly @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(104,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly,C: TA @ poly] :
( ( A @ ( B @ ( C @ ( TA @ poly @ plus_plus ) ) @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_poly__add) ).
thf(503,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly,C: TA @ poly] :
( ( A @ ( B @ ( C @ ( TA @ poly @ plus_plus ) ) @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(33,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_77_add__right__imp__eq) ).
thf(244,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)],[33]) ).
thf(113,axiom,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ suc @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_nat__induct) ).
thf(530,plain,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ suc @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(63,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat] :
( ( A @ ( TA @ poly @ zero_zero @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_coeff__0) ).
thf(343,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat] :
( ( A @ ( TA @ poly @ zero_zero @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(29,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_81_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(237,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)],[29]) ).
thf(82,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ monom ) ) @ ( TA @ degree ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_degree__monom__eq) ).
thf(425,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ monom ) ) @ ( TA @ degree ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(107,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ( TA @ poly @ monoid_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Omonoid__add) ).
thf(513,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ( TA @ poly @ monoid_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(12,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(166,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)],[12]) ).
thf(6,axiom,
! [A: nat] :
( A
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_n__not__Suc__n) ).
thf(148,plain,
! [A: nat] :
( A
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(49,axiom,
! [TA: $tType,A: nat,B: TA @ ( nat @ fun ),C: TA] :
( ( A @ suc @ ( B @ ( C @ ( TA @ nat_case ) ) @ ( TA @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( TA @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_nat__case__Suc) ).
thf(296,plain,
! [TA: $tType,A: nat,B: TA @ ( nat @ fun ),C: TA] :
( ( A @ suc @ ( B @ ( C @ ( TA @ nat_case ) ) @ ( TA @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( TA @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(128,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA @ poly] :
( ( A @ ( TA @ poly @ zero_zero @ ( TA @ poly @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_add__poly__code_I1_J) ).
thf(584,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA @ poly] :
( ( A @ ( TA @ poly @ zero_zero @ ( TA @ poly @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(14,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat,B: TA @ poly,C: TA] :
( ( A @ suc @ ( B @ ( C @ ( TA @ pCons ) ) @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_coeff__pCons__Suc) ).
thf(176,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat,B: TA @ poly,C: TA] :
( ( A @ suc @ ( B @ ( C @ ( TA @ pCons ) ) @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(78,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_zero__reorient) ).
thf(402,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)],[78]) ).
thf(47,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(291,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(37,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: TA] :
( ( A @ ( B @ ( TA @ pCons ) ) )
= ( A @ ( TA @ coeff ) @ ( B @ ( TA @ nat_case ) ) @ ( TA @ abs_poly ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_pCons__def) ).
thf(259,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: TA] :
( ( A @ ( B @ ( TA @ pCons ) ) )
= ( A @ ( TA @ coeff ) @ ( B @ ( TA @ nat_case ) ) @ ( TA @ abs_poly ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(75,axiom,
! [TA: $tType] :
( ( TA @ idom )
=> ( TA @ poly @ idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Oidom) ).
thf(391,plain,
! [TA: $tType] :
( ( TA @ idom )
=> ( TA @ poly @ idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(124,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: TA,C: TB,D: TB @ ( TB @ fun ) @ ( TA @ poly @ fun ) @ ( TA @ fun )] :
( ( ( C @ ( TA @ poly @ zero_zero @ ( TA @ zero_zero @ ( D @ ( TB @ ( TB @ fun ) @ ( TA @ poly @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TA @ poly @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) )
= C )
=> ( ( A @ ( B @ ( TA @ pCons ) ) @ ( D @ ( C @ ( TA @ ( TB @ poly_rec ) ) ) ) )
= ( A @ ( D @ ( C @ ( TA @ ( TB @ poly_rec ) ) ) ) @ ( A @ ( B @ ( D @ ( TB @ ( TB @ fun ) @ ( TA @ poly @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TA @ poly @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_poly__rec__pCons) ).
thf(572,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: TA,C: TB,D: TB @ ( TB @ fun ) @ ( TA @ poly @ fun ) @ ( TA @ fun )] :
( ( ( C @ ( TA @ poly @ zero_zero @ ( TA @ zero_zero @ ( D @ ( TB @ ( TB @ fun ) @ ( TA @ poly @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TA @ poly @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) )
= C )
=> ( ( A @ ( B @ ( TA @ pCons ) ) @ ( D @ ( C @ ( TA @ ( TB @ poly_rec ) ) ) ) )
= ( A @ ( D @ ( C @ ( TA @ ( TB @ poly_rec ) ) ) ) @ ( A @ ( B @ ( D @ ( TB @ ( TB @ fun ) @ ( TA @ poly @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TA @ poly @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(18,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly] :
( ( A @ ( TA @ coeff ) @ ( TA @ abs_poly ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_coeff__inverse) ).
thf(187,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly] :
( ( A @ ( TA @ coeff ) @ ( TA @ abs_poly ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(80,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly,C: TA] :
( ( ( B @ ( C @ ( TA @ smult ) ) )
= ( B @ ( A @ ( TA @ pCons ) ) ) )
=> ( B
= ( TA @ poly @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_synthetic__div__unique__lemma) ).
thf(419,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly,C: TA] :
( ( ( B @ ( C @ ( TA @ smult ) ) )
= ( B @ ( A @ ( TA @ pCons ) ) ) )
=> ( B
= ( TA @ poly @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(73,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly] :
( ( ( A @ ( B @ ( TA @ fundam296178794t_poly ) ) )
= ( TA @ poly @ zero_zero ) )
<=> ( B
= ( TA @ poly @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_offset__poly__eq__0__iff) ).
thf(377,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly] :
( ( ( B
= ( TA @ poly @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ fundam296178794t_poly ) ) )
= ( TA @ poly @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ fundam296178794t_poly ) ) )
= ( TA @ poly @ zero_zero ) )
=> ( B
= ( TA @ poly @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(27,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal ) ) @ pp )
| ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(230,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal ) ) @ pp )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(122,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ( TA @ poly @ comm_semiring_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Ocomm__semiring__1) ).
thf(567,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ( TA @ poly @ comm_semiring_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(85,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: nat,B: TA @ poly,C: TA @ poly] :
( ( A @ ( B @ ( C @ ( TA @ poly @ 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_69_coeff__add) ).
thf(434,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: nat,B: TA @ poly,C: TA @ poly] :
( ( A @ ( B @ ( C @ ( TA @ poly @ 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)],[85]) ).
thf(136,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_67_double__zero__sym) ).
thf(616,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)],[136]) ).
thf(71,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly,C: TA,D: TA @ poly] :
( ( ( B @ ( C @ ( TA @ smult ) ) @ ( D @ ( TA @ poly @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ pCons ) ) ) )
=> ( ( B
= ( C @ ( D @ ( TA @ synthetic_div ) ) ) )
& ( A
= ( C @ ( D @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_synthetic__div__unique) ).
thf(367,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly,C: TA,D: TA @ poly] :
( ( ( B @ ( C @ ( TA @ smult ) ) @ ( D @ ( TA @ poly @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ pCons ) ) ) )
=> ( ( B
= ( C @ ( D @ ( TA @ synthetic_div ) ) ) )
& ( A
= ( C @ ( D @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(135,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA,B: TA @ poly] :
( ( ( B
!= ( TA @ poly @ zero_zero ) )
=> ( ( B @ ( A @ ( TA @ pCons ) ) @ ( TA @ degree ) )
= ( B @ ( TA @ degree ) @ suc ) ) )
& ( ( B
= ( TA @ poly @ zero_zero ) )
=> ( ( B @ ( A @ ( TA @ pCons ) ) @ ( TA @ degree ) )
= ( nat @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_degree__pCons__eq__if) ).
thf(609,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA,B: TA @ poly] :
( ( ( B
!= ( TA @ poly @ zero_zero ) )
=> ( ( B @ ( A @ ( TA @ pCons ) ) @ ( TA @ degree ) )
= ( B @ ( TA @ degree ) @ suc ) ) )
& ( ( B
= ( TA @ poly @ zero_zero ) )
=> ( ( B @ ( A @ ( TA @ pCons ) ) @ ( TA @ degree ) )
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(25,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_14_monom__eq__iff) ).
thf(213,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)],[25]) ).
thf(30,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clar_Rings_Ocomm__semiring__0__Groups_Ozero) ).
thf(240,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(60,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA] :
( ( A @ ( TA @ poly @ zero_zero @ ( TA @ fundam296178794t_poly ) ) )
= ( TA @ poly @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_offset__poly__0) ).
thf(330,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA] :
( ( A @ ( TA @ poly @ zero_zero @ ( TA @ fundam296178794t_poly ) ) )
= ( TA @ poly @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(110,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ~ ! [B: nat] :
( A
!= ( B @ suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_nat_Oexhaust) ).
thf(521,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ~ ! [B: nat] :
( A
!= ( B @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(77,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA @ poly] :
( ( TA @ poly @ zero_zero @ ( A @ ( TA @ poly @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_add__poly__code_I2_J) ).
thf(399,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA @ poly] :
( ( TA @ poly @ zero_zero @ ( A @ ( TA @ poly @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(50,axiom,
nat @ cancel146912293up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(299,plain,
nat @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(84,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_92_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(431,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)],[84]) ).
thf(95,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_93_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(473,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)],[95]) ).
thf(130,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_18_coeff__monom) ).
thf(589,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)],[130]) ).
thf(67,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA @ poly,B: TA,C: TA @ poly,D: TA] :
( ( A @ ( B @ ( TA @ pCons ) ) @ ( C @ ( D @ ( TA @ pCons ) ) @ ( TA @ poly @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ poly @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ pCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_add__pCons) ).
thf(355,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA @ poly,B: TA,C: TA @ poly,D: TA] :
( ( A @ ( B @ ( TA @ pCons ) ) @ ( C @ ( D @ ( TA @ pCons ) ) @ ( TA @ poly @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ poly @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ pCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(5,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(145,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(111,axiom,
a @ comm_semiring_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
thf(525,plain,
a @ comm_semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(119,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: bool @ ( TA @ poly @ fun )] :
( ( TA @ poly @ zero_zero @ ( B @ ( bool @ ( TA @ poly @ aa ) ) ) @ pp )
=> ( ! [C: TA,D: TA @ poly] :
( ( D @ ( B @ ( bool @ ( TA @ poly @ aa ) ) ) @ pp )
=> ( D @ ( C @ ( TA @ pCons ) ) @ ( B @ ( bool @ ( TA @ poly @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ poly @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_pCons__induct) ).
thf(557,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: bool @ ( TA @ poly @ fun )] :
( ( TA @ poly @ zero_zero @ ( B @ ( bool @ ( TA @ poly @ aa ) ) ) @ pp )
=> ( ! [C: TA,D: TA @ poly] :
( ( D @ ( B @ ( bool @ ( TA @ poly @ aa ) ) ) @ pp )
=> ( D @ ( C @ ( TA @ pCons ) ) @ ( B @ ( bool @ ( TA @ poly @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ poly @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: TA,C: TB @ ( TB @ fun ) @ ( TA @ poly @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ pCons ) ) @ ( C @ ( D @ ( TA @ ( TB @ poly_rec ) ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ ( TB @ poly_rec ) ) ) ) @ ( D @ ( TA @ poly @ zero_zero @ ( A @ ( TA @ poly @ fequal ) ) @ ( TB @ if ) ) ) @ ( A @ ( B @ ( C @ ( TB @ ( TB @ fun ) @ ( TA @ poly @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TA @ poly @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_poly__rec_Osimps) ).
thf(470,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: TA,C: TB @ ( TB @ fun ) @ ( TA @ poly @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ pCons ) ) @ ( C @ ( D @ ( TA @ ( TB @ poly_rec ) ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ ( TB @ poly_rec ) ) ) ) @ ( D @ ( TA @ poly @ zero_zero @ ( A @ ( TA @ poly @ fequal ) ) @ ( TB @ if ) ) ) @ ( A @ ( B @ ( C @ ( TB @ ( TB @ fun ) @ ( TA @ poly @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TA @ poly @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(116,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_add__0__right) ).
thf(544,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(62,axiom,
! [TA: $tType] :
( ( TA @ idom )
=> ! [A: TA @ poly,B: TA] :
( ( ( B
!= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ smult ) ) @ ( TA @ degree ) )
= ( A @ ( TA @ degree ) ) ) )
& ( ( B
= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ smult ) ) @ ( TA @ degree ) )
= ( nat @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_degree__smult__eq) ).
thf(336,plain,
! [TA: $tType] :
( ( TA @ idom )
=> ! [A: TA @ poly,B: TA] :
( ( ( B
!= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ smult ) ) @ ( TA @ degree ) )
= ( A @ ( TA @ degree ) ) ) )
& ( ( B
= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ smult ) ) @ ( TA @ degree ) )
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(9,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(154,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ comm_monoid_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(132,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( nat @ zero_zero @ ( A @ ( TA @ monom ) ) )
= ( TA @ poly @ zero_zero @ ( A @ ( TA @ pCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_monom__0) ).
thf(600,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( nat @ zero_zero @ ( A @ ( TA @ monom ) ) )
= ( TA @ poly @ zero_zero @ ( A @ ( TA @ pCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(98,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly @ ring_char_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Int_Oring__char__0) ).
thf(482,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly @ ring_char_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(127,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA] :
( ( A @ ( TA @ poly @ zero_zero @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_poly__0) ).
thf(581,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA] :
( ( A @ ( TA @ poly @ zero_zero @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(53,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ? [B: nat] :
( A
= ( B @ suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_not0__implies__Suc) ).
thf(304,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ? [B: nat] :
( A
= ( B @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(66,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_Zero__neq__Suc) ).
thf(351,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(3,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(139,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(106,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat] :
( ( A @ ( TA @ zero_zero @ ( TA @ monom ) ) )
= ( TA @ poly @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_monom__eq__0) ).
thf(510,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat] :
( ( A @ ( TA @ zero_zero @ ( TA @ monom ) ) )
= ( TA @ poly @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(23,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ pCons ) ) @ ( TA @ synthetic_div ) ) )
= ( A @ ( B @ ( TA @ synthetic_div ) ) @ ( A @ ( B @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ pCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_synthetic__div__pCons) ).
thf(207,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ pCons ) ) @ ( TA @ synthetic_div ) ) )
= ( A @ ( B @ ( TA @ synthetic_div ) ) @ ( A @ ( B @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ pCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(40,axiom,
nat @ comm_monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(272,plain,
nat @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(64,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( TA @ poly @ zero_zero @ ( A @ ( TA @ pCons ) ) @ ( TA @ degree ) )
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_degree__pCons__0) ).
thf(346,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( TA @ poly @ zero_zero @ ( A @ ( TA @ pCons ) ) @ ( TA @ degree ) )
= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(51,axiom,
nat @ cancel1352612707id_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__comm__monoid__add) ).
thf(300,plain,
nat @ cancel1352612707id_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(89,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly @ linordered_idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Olinordered__idom) ).
thf(447,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly @ linordered_idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(79,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: TA] :
( ( ( A @ ( B @ ( TA @ pCons ) ) )
= ( TA @ poly @ zero_zero ) )
<=> ( ( A
= ( TA @ poly @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_pCons__eq__0__iff) ).
thf(410,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: TA] :
( ( ( ( A
= ( TA @ poly @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( B @ ( TA @ pCons ) ) )
= ( TA @ poly @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ pCons ) ) )
= ( TA @ poly @ zero_zero ) )
=> ( ( A
= ( TA @ poly @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(38,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_65_add__right__cancel) ).
thf(262,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)],[38]) ).
thf(19,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: TA] :
( ( A @ ( B @ ( TA @ pCons ) ) @ ( TA @ coeff ) )
= ( A @ ( TA @ coeff ) @ ( B @ ( TA @ nat_case ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_coeff__pCons) ).
thf(190,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: TA] :
( ( A @ ( B @ ( TA @ pCons ) ) @ ( TA @ coeff ) )
= ( A @ ( TA @ coeff ) @ ( B @ ( TA @ nat_case ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(16,axiom,
nat @ ab_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(183,plain,
nat @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(81,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA,C: TA @ poly] :
( ( A @ ( B @ ( C @ ( TA @ fundam296178794t_poly ) ) @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_poly__offset__poly) ).
thf(422,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA,C: TA @ poly] :
( ( A @ ( B @ ( C @ ( TA @ fundam296178794t_poly ) ) @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(41,axiom,
! [TA: $tType] :
( ( ( TA @ idom )
& ( TA @ ring_char_0 ) )
=> ! [A: TA @ poly,B: TA @ poly] :
( ( ( B @ ( TA @ poly1 ) )
= ( A @ ( TA @ poly1 ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_poly__eq__iff) ).
thf(273,plain,
! [TA: $tType] :
( ( ( TA @ idom )
& ( TA @ ring_char_0 ) )
=> ! [A: TA @ poly,B: TA @ poly] :
( ( ( B = A )
=> ( ( B @ ( TA @ poly1 ) )
= ( A @ ( TA @ poly1 ) ) ) )
& ( ( ( B @ ( TA @ poly1 ) )
= ( A @ ( TA @ poly1 ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(72,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_Zero__not__Suc) ).
thf(373,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(133,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA @ poly] :
( ( A @ ( TA @ poly @ zero_zero @ ( TA @ pcompose ) ) )
= ( TA @ poly @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_pcompose__0) ).
thf(603,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA @ poly] :
( ( A @ ( TA @ poly @ zero_zero @ ( TA @ pcompose ) ) )
= ( TA @ poly @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(121,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: TA] :
( ( nat @ zero_zero @ ( A @ ( B @ ( TA @ pCons ) ) @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_coeff__pCons__0) ).
thf(564,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: TA] :
( ( nat @ zero_zero @ ( A @ ( B @ ( TA @ pCons ) ) @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(24,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: TA @ poly] :
( ! [C: nat] :
( ( C @ ( B @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( C @ ( A @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_poly__ext) ).
thf(210,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: TA @ poly] :
( ! [C: nat] :
( ( C @ ( B @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( C @ ( A @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(58,axiom,
! [TA: $tType] :
( ( TA @ cancel1352612707id_add )
=> ( TA @ poly @ cancel_semigroup_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ocancel__semigroup__add) ).
thf(326,plain,
! [TA: $tType] :
( ( TA @ cancel1352612707id_add )
=> ( TA @ poly @ cancel_semigroup_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(31,axiom,
nat @ comm_semiring_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__0) ).
thf(242,plain,
nat @ comm_semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(105,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Suc__not__Zero) ).
thf(506,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(68,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_76_add_Ocomm__neutral) ).
thf(358,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)],[68]) ).
thf(21,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_Suc__inject) ).
thf(195,plain,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(86,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ( ( TA @ poly @ zero_zero @ ( TA @ zero_zero @ ( TA @ pCons ) ) )
= ( TA @ poly @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_pCons__0__0) ).
thf(437,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ( ( TA @ poly @ zero_zero @ ( TA @ zero_zero @ ( TA @ pCons ) ) )
= ( TA @ poly @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(43,axiom,
nat @ monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
thf(283,plain,
nat @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(125,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat,B: TA] :
( ( A @ suc @ ( B @ ( TA @ monom ) ) )
= ( A @ ( B @ ( TA @ monom ) ) @ ( TA @ zero_zero @ ( TA @ pCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_monom__Suc) ).
thf(575,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat,B: TA] :
( ( A @ suc @ ( B @ ( TA @ monom ) ) )
= ( A @ ( B @ ( TA @ monom ) ) @ ( TA @ zero_zero @ ( TA @ pCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(131,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_nat_Osimps_I2_J) ).
thf(596,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(22,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: TA @ poly] :
( ( ( B @ ( TA @ coeff ) )
= ( A @ ( TA @ coeff ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_coeff__inject) ).
thf(200,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: TA @ poly] :
( ( ( B = A )
=> ( ( B @ ( TA @ coeff ) )
= ( A @ ( TA @ coeff ) ) ) )
& ( ( ( B @ ( TA @ coeff ) )
= ( A @ ( TA @ coeff ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(103,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ( TA @ poly @ ab_semigroup_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Oab__semigroup__add) ).
thf(501,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ( TA @ poly @ ab_semigroup_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(100,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ( TA @ poly @ zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ozero) ).
thf(486,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ( TA @ poly @ zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(102,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_94_add__is__0) ).
thf(491,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)],[102]) ).
thf(92,axiom,
! [TA: $tType] :
( ( ( TA @ idom )
& ( TA @ ring_char_0 ) )
=> ! [A: TA @ poly] :
( ( ( A @ ( TA @ poly1 ) )
= ( TA @ poly @ zero_zero @ ( TA @ poly1 ) ) )
<=> ( A
= ( TA @ poly @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_poly__zero) ).
thf(454,plain,
! [TA: $tType] :
( ( ( TA @ idom )
& ( TA @ ring_char_0 ) )
=> ! [A: TA @ poly] :
( ( ( A
= ( TA @ poly @ zero_zero ) )
=> ( ( A @ ( TA @ poly1 ) )
= ( TA @ poly @ zero_zero @ ( TA @ poly1 ) ) ) )
& ( ( ( A @ ( TA @ poly1 ) )
= ( TA @ poly @ zero_zero @ ( TA @ poly1 ) ) )
=> ( A
= ( TA @ poly @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(70,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA @ poly] :
( ( A @ ( TA @ zero_zero @ ( TA @ smult ) ) )
= ( TA @ poly @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_smult__0__left) ).
thf(364,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA @ poly] :
( ( A @ ( TA @ zero_zero @ ( TA @ smult ) ) )
= ( TA @ poly @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(632,plain,
$false,
inference(e,[status(thm)],[479,518,234,333,249,449,247,440,269,384,550,142,153,288,301,184,587,606,284,152,179,443,321,280,293,243,428,307,452,220,534,349,561,137,165,484,252,361,461,324,285,578,317,156,169,328,488,476,526,547,193,537,393,515,569,503,244,530,343,237,425,513,166,148,296,584,176,402,291,259,391,572,187,419,377,230,567,434,616,367,609,213,240,330,521,399,299,431,473,589,355,145,525,557,470,544,336,154,600,482,581,304,351,139,510,207,272,346,300,447,410,262,190,183,422,273,373,603,564,210,326,242,506,358,195,437,283,575,596,200,501,486,491,454,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW490_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % 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
% 0.14/0.40 % Computer : n008.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 16:09:55 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.86/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.88/1.31 % [INFO] Parsing done (314ms).
% 1.88/1.32 % [INFO] Running in sequential loop mode.
% 2.74/1.73 % [INFO] eprover registered as external prover.
% 2.74/1.74 % [INFO] Scanning for conjecture ...
% 3.14/1.90 % [INFO] Found a conjecture (or negated_conjecture) and 134 axioms. Running axiom selection ...
% 3.14/2.03 % [INFO] Axiom selection finished. Selected 134 axioms (removed 0 axioms).
% 3.94/2.25 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.94/2.28 % [INFO] Type checking passed.
% 3.94/2.28 % [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 ...
% 4.79/2.55 % [INFO] [Domain constraints] Detected constraint on bool
% 4.79/2.55 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 17.10/6.07 % External prover 'e' found a proof!
% 17.10/6.07 % [INFO] Killing All external provers ...
% 17.10/6.07 % Time passed: 5524ms (effective reasoning time: 4740ms)
% 17.10/6.07 % 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)>
% 17.10/6.07 % Axioms used in derivation (134): fact_37_degree__smult__eq, fact_71_smult__add__left, help_fequal_1_1_T, tfree_0, fact_45_monom__Suc, fact_17_coeff__0, fact_69_coeff__add, fact_39_synthetic__div__0, arity_Nat_Onat___Rings_Osemiring__1, fact_49_Zero__not__Suc, fact_2_zero__reorient, fact_35_pCons__cases, fact_78_add__imp__eq, fact_56_Suc__not__Zero, fact_43_synthetic__div__unique__lemma, fact_90_synthetic__div__correct, fact_6_leading__coeff__neq__0, fact_0_offset__poly__0, fact_88_offset__poly__eq__0__lemma, arity_Polynomial_Opoly___Groups_Olinordered__ab__group__add, fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_89_offset__poly__pCons, fact_31_synthetic__div__pCons, arity_Polynomial_Opoly___Groups_Omonoid__add, fact_97_plus__nat_Oadd__0, fact_86_poly__offset__poly, fact_29_pCons__induct, fact_79_add__left__imp__eq, fact_40_smult__0__left, fact_52_Suc__inject, arity_Nat_Onat___Groups_Ocomm__monoid__add, fact_83_add__poly__code_I1_J, fact_10_poly__0, arity_Nat_Onat___Groups_Ocancel__comm__monoid__add, fact_84_add__poly__code_I2_J, arity_Polynomial_Opoly___Groups_Ocancel__semigroup__add, arity_Polynomial_Opoly___Rings_Oidom, fact_53_Suc__neq__Zero, fact_41_smult__eq__0__iff, fact_34_poly__ext, fact_5_poly__rec__0, arity_Polynomial_Opoly___Groups_Ozero, clar_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add, help_If_1_1_T, arity_Polynomial_Opoly___Int_Oring__char__0, fact_46_nat_Oinject, arity_Polynomial_Opoly___Groups_Ocancel__ab__semigroup__add, fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, arity_Polynomial_Opoly___Rings_Ocomm__semiring__1, clar_Rings_Ocomm__semiring__0__Groups_Oab__semigroup__add, fact_21_poly__eq__iff, fact_23_coeff__pCons__0, clar_Rings_Ocomm__semiring__0__Groups_Omonoid__add, fact_94_add__is__0, fact_73_ext, fact_54_Zero__neq__Suc, fact_27_degree__pCons__0, fact_77_add__right__imp__eq, arity_Polynomial_Opoly___Rings_Olinordered__idom, fact_61_not0__implies__Suc, arity_Polynomial_Opoly___Groups_Ocomm__monoid__add, fact_33_degree__pCons__eq__if, clar_Rings_Ocomm__semiring__0__Groups_Ozero, fact_80_add__monom, fact_19_monom__0, arity_Nat_Onat___Rings_Ocomm__semiring__1, fact_9_degree__0, fact_62_of__nat__aux_Osimps_I2_J, arity_Nat_Onat___Groups_Ozero, fact_13_pCons__eq__iff, fact_15_pCons__eq__0__iff, fact_22_coeff__inject, fact_3_leading__coeff__0__iff, fact_26_poly__zero, help_If_3_1_T, fact_81_ab__semigroup__add__class_Oadd__ac_I1_J, help_If_2_1_T, fact_24_poly__pcompose, fact_4_offset__poly__single, fact_66_add__left__cancel, fact_64_synthetic__div__unique, fact_47_nat__case__Suc, arity_Nat_Onat___Rings_Ocomm__semiring__0, fact_96_add__Suc, fact_70_poly__add, fact_82_smult__add__right, fact_16_pCons__0__0, arity_Polynomial_Opoly___Groups_Ocancel__comm__monoid__add, arity_Polynomial_Opoly___Rings_Osemiring__1, fact_63_pCons__def, fact_59_zero__induct, fact_58_nat_Oexhaust, fact_44_degree__pCons__eq, fact_76_add_Ocomm__neutral, fact_11_degree__monom__eq, help_fequal_2_1_T, fact_38_smult__0__right, fact_7_monom__eq__0, fact_75_add__0__right, fact_25_poly__rec_Osimps, fact_72_add__0__left, fact_20_expand__poly__eq, fact_85_coeff__inverse, fact_12_pcompose__0, fact_91_double__eq__0__iff, fact_32_synthetic__div__eq__0__iff, fact_65_add__right__cancel, fact_36_coeff__pCons, fact_57_nat_Osimps_I2_J, fact_95_add__Suc__right, help_pp_1_1_U, fact_30_order__root, fact_8_monom__eq__0__iff, fact_74_add__0, fact_1_offset__poly__eq__0__iff, fact_60_nat__induct, fact_18_coeff__monom, arity_Polynomial_Opoly___Groups_Oab__semigroup__add, arity_Nat_Onat___Groups_Oab__semigroup__add, arity_Nat_Onat___Groups_Omonoid__add, fact_55_nat_Osimps_I3_J, fact_48_nat__case__0, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_67_double__zero__sym, fact_87_of__nat__aux_Osimps_I1_J, help_pp_2_1_U, fact_51_Suc__n__not__n, fact_68_add__pCons, arity_Polynomial_Opoly___Rings_Ocomm__semiring__0, fact_50_n__not__Suc__n, fact_28_poly__rec__pCons, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_42_coeff__pCons__Suc, fact_14_monom__eq__iff
% 17.10/6.07 % No. of inferences in proof: 272
% 17.10/6.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5524 ms resp. 4740 ms w/o parsing
% 17.88/6.20 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 17.88/6.20 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------