%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW492_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 : n002.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 11.33s 8.98s
% Output : Refutation 12.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 126
% Syntax : Number of formulae : 254 ( 59 unt; 0 typ; 0 def)
% Number of atoms : 798 ( 299 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 2880 ( 84 ~; 19 |; 40 &;2434 @)
% ( 23 <=>; 280 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 37 usr; 6 con; 0-5 aty)
% Number of variables : 557 ( 0 ^; 553 !; 4 ?; 557 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(comm_semiring_1_decl,type,
comm_semiring_1:
!>[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(order_decl,type,
order:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : $o ).
thf(comm_semiring_0_decl,type,
comm_semiring_0:
!>[TA: $tType] : $o ).
thf(fundam296178794t_poly_decl,type,
fundam296178794t_poly:
!>[TA: $tType] : ( ( TA @ poly ) > TA > ( TA @ poly ) ) ).
thf(fundam1280195782_psize_decl,type,
fundam1280195782_psize:
!>[TA: $tType] : ( ( TA @ poly ) > nat ) ).
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(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
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(order1_decl,type,
order1:
!>[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(p_decl,type,
p: a @ poly ).
thf(38,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_49_nat__case__0) ).
thf(257,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)],[38]) ).
thf(95,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ( TA @ poly @ zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ozero) ).
thf(457,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ( TA @ poly @ zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(21,axiom,
bool @ order,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
thf(204,plain,
bool @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
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_64_smult__0__left) ).
thf(365,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(35,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_37_leading__coeff__neq__0) ).
thf(249,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)],[35]) ).
thf(30,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_less__zeroE) ).
thf(234,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(122,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_66_poly__0) ).
thf(582,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)],[122]) ).
thf(26,axiom,
! [TA: $tType] :
( ( TA @ idom )
=> ! [A: TA,B: TA @ poly] :
( ( B
!= ( TA @ poly @ zero_zero ) )
=> ( B @ ( TA @ degree ) @ ( B @ ( A @ ( TA @ order1 ) ) @ ( nat @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_order__degree) ).
thf(217,plain,
! [TA: $tType] :
( ( TA @ idom )
=> ! [A: TA,B: TA @ poly] :
( ( B
!= ( TA @ poly @ zero_zero ) )
=> ( B @ ( TA @ degree ) @ ( B @ ( A @ ( TA @ order1 ) ) @ ( nat @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(41,axiom,
! [A: nat] :
( ( A @ suc )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_Suc__n__not__n) ).
thf(269,plain,
! [A: nat] :
( ( A @ suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(20,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(202,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(127,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_less__nat__zero__code) ).
thf(597,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(75,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_Suc__leD) ).
thf(384,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
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(65,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_16_zero__induct) ).
thf(344,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)],[65]) ).
thf(17,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_55_pCons__def) ).
thf(196,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)],[17]) ).
thf(119,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_le__0__eq) ).
thf(559,plain,
! [A: nat] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) ) )
& ( ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(45,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_31_coeff__pCons__0) ).
thf(284,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)],[45]) ).
thf(47,axiom,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ suc @ ( nat @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_Suc__less__eq) ).
thf(289,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ suc @ ( B @ suc @ ( nat @ ord_less ) ) ) )
& ( ( A @ suc @ ( B @ suc @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(92,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_le__antisym) ).
thf(448,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(54,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_44_monom__Suc) ).
thf(316,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)],[54]) ).
thf(100,axiom,
nat @ comm_semiring_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__0) ).
thf(475,plain,
nat @ comm_semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(14,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_45_monom__eq__iff) ).
thf(179,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)],[14]) ).
thf(104,axiom,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ ord_less_eq ) ) )
<=> ( ( B
= ( A @ suc ) )
| ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_le__Suc__eq) ).
thf(485,plain,
! [A: nat,B: nat] :
( ( ( ( B
= ( A @ suc ) )
| ( A @ ( B @ ( nat @ ord_less_eq ) ) ) )
=> ( A @ suc @ ( B @ ( nat @ ord_less_eq ) ) ) )
& ( ( A @ suc @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B
= ( A @ suc ) )
| ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(66,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_nat_Oinject) ).
thf(348,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)],[66]) ).
thf(102,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_52_offset__poly__0) ).
thf(480,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)],[102]) ).
thf(43,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly @ order ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Orderings_Oorder) ).
thf(280,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly @ order ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(113,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_32_poly__rec_Osimps) ).
thf(527,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)],[113]) ).
thf(53,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_nat_Osimps_I2_J) ).
thf(312,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(117,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_84_synthetic__div__unique__lemma) ).
thf(546,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)],[117]) ).
thf(19,axiom,
bool @ preorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
thf(201,plain,
bool @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(74,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_63_smult__0__right) ).
thf(381,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)],[74]) ).
thf(27,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA @ poly,B: TA] : ( A @ ( TA @ degree ) @ ( A @ ( B @ ( TA @ smult ) ) @ ( TA @ degree ) @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_degree__smult__le) ).
thf(220,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA @ poly,B: TA] : ( A @ ( TA @ degree ) @ ( A @ ( B @ ( TA @ smult ) ) @ ( TA @ degree ) @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(110,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_17_nat__induct) ).
thf(512,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)],[110]) ).
thf(90,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly] :
( ( ( A
!= ( TA @ poly @ zero_zero ) )
=> ( ( A @ ( TA @ fundam1280195782_psize ) )
= ( A @ ( TA @ degree ) @ suc ) ) )
& ( ( A
= ( TA @ poly @ zero_zero ) )
=> ( ( A @ ( TA @ fundam1280195782_psize ) )
= ( nat @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_psize__def) ).
thf(439,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly] :
( ( ( A
!= ( TA @ poly @ zero_zero ) )
=> ( ( A @ ( TA @ fundam1280195782_psize ) )
= ( A @ ( TA @ degree ) @ suc ) ) )
& ( ( A
= ( TA @ poly @ zero_zero ) )
=> ( ( A @ ( TA @ fundam1280195782_psize ) )
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(59,axiom,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_le0) ).
thf(334,plain,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(51,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_29_expand__poly__eq) ).
thf(302,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)],[51]) ).
thf(39,axiom,
! [A: nat,B: nat] :
( ~ ( A @ ( B @ ( nat @ ord_less_eq ) ) )
<=> ( B @ ( A @ suc @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_not__less__eq__eq) ).
thf(260,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ suc @ ( nat @ ord_less_eq ) ) )
=> ~ ( A @ ( B @ ( nat @ ord_less_eq ) ) ) )
& ( ~ ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( B @ ( A @ suc @ ( nat @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(84,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_22_poly__rec__0) ).
thf(424,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)],[84]) ).
thf(36,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(252,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ poly @ comm_semiring_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(68,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
| ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_nat__le__linear) ).
thf(361,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
| ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(88,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ? [B: nat] :
( A
= ( B @ suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_not0__implies__Suc) ).
thf(435,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ? [B: nat] :
( A
= ( B @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(79,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_51_offset__poly__eq__0__iff) ).
thf(403,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)],[79]) ).
thf(126,axiom,
! [A: nat] :
( A
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_n__not__Suc__n) ).
thf(593,plain,
! [A: nat] :
( A
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(99,axiom,
! [A: nat,B: nat] :
( ( B = A )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_eq__imp__le) ).
thf(471,plain,
! [A: nat,B: nat] :
( ( B = A )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(29,axiom,
! [TA: $tType] :
( ( TA @ idom )
=> ! [A: TA,B: TA @ poly] :
( ( ( A @ ( B @ ( TA @ poly1 ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) )
<=> ( ( ( B @ ( A @ ( TA @ order1 ) ) )
!= ( nat @ zero_zero ) )
| ( B
= ( TA @ poly @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_order__root) ).
thf(225,plain,
! [TA: $tType] :
( ( TA @ idom )
=> ! [A: TA,B: TA @ poly] :
( ( ( ( ( B @ ( A @ ( TA @ order1 ) ) )
!= ( 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 @ order1 ) ) )
!= ( nat @ zero_zero ) )
| ( B
= ( TA @ poly @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(63,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_41_offset__poly__single) ).
thf(339,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)],[63]) ).
thf(16,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(193,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)],[16]) ).
thf(101,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ~ ! [B: nat] :
( A
!= ( B @ suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_nat_Oexhaust) ).
thf(476,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ~ ! [B: nat] :
( A
!= ( B @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(24,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_82_poly__pcompose) ).
thf(212,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)],[24]) ).
thf(33,axiom,
! [A: nat] : ( A @ ( A @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_le__refl) ).
thf(244,plain,
! [A: nat] : ( A @ ( A @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(40,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly] :
( ( A @ ( B @ ( TA @ fundam296178794t_poly ) ) @ ( TA @ degree ) )
= ( B @ ( TA @ degree ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_degree__offset__poly) ).
thf(266,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly] :
( ( A @ ( B @ ( TA @ fundam296178794t_poly ) ) @ ( TA @ degree ) )
= ( B @ ( TA @ degree ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(22,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(205,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal ) ) @ pp )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(108,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(508,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ( TA @ poly @ comm_semiring_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(78,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_Suc__inject) ).
thf(398,plain,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(114,axiom,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ suc @ ( nat @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_Suc__le__mono) ).
thf(530,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ suc @ ( B @ suc @ ( nat @ ord_less_eq ) ) ) )
& ( ( A @ suc @ ( B @ suc @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(1,conjecture,
~ ( ( ( p
!= ( a @ poly @ zero_zero ) )
=> ( ( p @ ( a @ degree ) @ suc )
= ( nat @ zero_zero ) ) )
<=> ( p
!= ( a @ poly @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ~ ( ( ( p
!= ( a @ poly @ zero_zero ) )
=> ( ( p @ ( a @ degree ) @ suc )
= ( nat @ zero_zero ) ) )
<=> ( p
!= ( a @ poly @ zero_zero ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(128,plain,
~ ~ ( ( ( p
!= ( a @ poly @ zero_zero ) )
=> ( ( p
!= ( a @ poly @ zero_zero ) )
=> ( ( p @ ( a @ degree ) @ suc )
= ( nat @ zero_zero ) ) ) )
& ( ( ( p
!= ( a @ poly @ zero_zero ) )
=> ( ( p @ ( a @ degree ) @ suc )
= ( nat @ zero_zero ) ) )
=> ( p
!= ( a @ poly @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(31,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_28_coeff__pCons__Suc) ).
thf(237,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)],[31]) ).
thf(81,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_33_poly__rec__pCons) ).
thf(412,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)],[81]) ).
thf(86,axiom,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_less__eq__nat_Osimps_I1_J) ).
thf(430,plain,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(10,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] : ( A @ ( A @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_order__refl) ).
thf(166,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] : ( A @ ( A @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,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_40_pCons__cases) ).
thf(148,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)],[6]) ).
thf(121,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_26_pCons__eq__0__iff) ).
thf(573,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)],[121]) ).
thf(49,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_36_of__nat__aux_Osimps_I1_J) ).
thf(296,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)],[49]) ).
thf(72,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat,B: TA @ poly] :
( ( ( A @ ( B @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
!= ( TA @ zero_zero ) )
=> ( B @ ( TA @ degree ) @ ( A @ ( nat @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_le__degree) ).
thf(375,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat,B: TA @ poly] :
( ( ( A @ ( B @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
!= ( TA @ zero_zero ) )
=> ( B @ ( TA @ degree ) @ ( A @ ( nat @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(93,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_Suc__not__Zero) ).
thf(451,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(120,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_9_synthetic__div__eq__0__iff) ).
thf(567,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)],[120]) ).
thf(56,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_39_poly__ext) ).
thf(323,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)],[56]) ).
thf(103,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly @ preorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Orderings_Opreorder) ).
thf(483,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly @ preorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(32,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_38_pCons__induct) ).
thf(240,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)],[32]) ).
thf(58,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ ord_less_eq ) ) )
=> ? [C: nat] :
( A
= ( C @ suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_Suc__le__D) ).
thf(330,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ ord_less_eq ) ) )
=> ? [C: nat] :
( A
= ( C @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(97,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ suc @ ( B @ suc @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_Suc__mono) ).
thf(462,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ suc @ ( B @ suc @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(94,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(455,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly @ ring_char_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(77,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_Zero__not__Suc) ).
thf(394,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(50,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_34_degree__pCons__0) ).
thf(299,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)],[50]) ).
thf(107,axiom,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ~ ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( B
= ( A @ suc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_le__SucE) ).
thf(505,plain,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ~ ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( B
= ( A @ suc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(89,axiom,
nat @ order,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
thf(438,plain,
nat @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
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_57_synthetic__div__pCons) ).
thf(209,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(111,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_zero__reorient) ).
thf(516,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)],[111]) ).
thf(64,axiom,
! [TA: $tType] :
( ( TA @ idom )
=> ( TA @ poly @ idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Oidom) ).
thf(342,plain,
! [TA: $tType] :
( ( TA @ idom )
=> ( TA @ poly @ idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(5,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly] :
( ( A @ ( TA @ coeff ) @ ( TA @ abs_poly ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_coeff__inverse) ).
thf(145,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly] :
( ( A @ ( TA @ coeff ) @ ( TA @ abs_poly ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(48,axiom,
nat @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(295,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(44,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( nat @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_le__trans) ).
thf(282,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( nat @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
thf(199,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(123,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_47_monom__eq__0) ).
thf(585,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)],[123]) ).
thf(106,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_35_degree__pCons__eq) ).
thf(502,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)],[106]) ).
thf(62,axiom,
a @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
thf(338,plain,
a @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(60,axiom,
nat @ preorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).
thf(336,plain,
nat @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(8,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_24_pCons__eq__iff) ).
thf(154,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)],[8]) ).
thf(76,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_neq0__conv) ).
thf(386,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)],[76]) ).
thf(91,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat,B: TA] : ( A @ ( A @ ( B @ ( TA @ monom ) ) @ ( TA @ degree ) @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_degree__monom__le) ).
thf(446,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat,B: TA] : ( A @ ( A @ ( B @ ( TA @ monom ) ) @ ( TA @ degree ) @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(69,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: TA] : ( A @ ( TA @ degree ) @ suc @ ( A @ ( B @ ( TA @ pCons ) ) @ ( TA @ degree ) @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_degree__pCons__le) ).
thf(363,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly,B: TA] : ( A @ ( TA @ degree ) @ suc @ ( A @ ( B @ ( TA @ pCons ) ) @ ( TA @ degree ) @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(112,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_25_pCons__0__0) ).
thf(524,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)],[112]) ).
thf(105,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_23_leading__coeff__0__iff) ).
thf(495,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)],[105]) ).
thf(71,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_48_coeff__monom) ).
thf(368,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)],[71]) ).
thf(124,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_Suc__neq__Zero) ).
thf(588,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(55,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_nat_Osimps_I3_J) ).
thf(319,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(15,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_77_poly__eq__iff) ).
thf(186,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)],[15]) ).
thf(12,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_30_coeff__inject) ).
thf(171,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)],[12]) ).
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(73,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_27_coeff__0) ).
thf(378,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)],[73]) ).
thf(34,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat,B: TA @ poly] :
( ( A @ ( B @ ( TA @ degree ) @ ( nat @ ord_less_eq ) ) )
=> ( ( ( A @ ( B @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ degree ) @ ( nat @ ord_less ) ) )
| ( B
= ( TA @ poly @ zero_zero ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_eq__zero__or__degree__less) ).
thf(246,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: nat,B: TA @ poly] :
( ( A @ ( B @ ( TA @ degree ) @ ( nat @ ord_less_eq ) ) )
=> ( ( ( A @ ( B @ ( TA @ coeff ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ degree ) @ ( nat @ ord_less ) ) )
| ( B
= ( TA @ poly @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(109,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: nat,B: nat,C: TA @ ( nat @ fun )] :
( ! [D: nat] : ( D @ suc @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( D @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( B @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_lift__Suc__mono__le) ).
thf(510,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: nat,B: nat,C: TA @ ( nat @ fun )] :
( ! [D: nat] : ( D @ suc @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( D @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( B @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(118,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_65_smult__eq__0__iff) ).
thf(549,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)],[118]) ).
thf(115,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_20_degree__pCons__eq__if) ).
thf(536,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)],[115]) ).
thf(46,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ suc @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_le__SucI) ).
thf(287,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ suc @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(7,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(151,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(87,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_50_nat__case__Suc) ).
thf(432,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)],[87]) ).
thf(80,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly @ linordered_idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Olinordered__idom) ).
thf(410,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly @ linordered_idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(11,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_42_coeff__pCons) ).
thf(168,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)],[11]) ).
thf(83,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(422,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ( TA @ poly @ semiring_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(42,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_56_degree__smult__eq) ).
thf(273,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)],[42]) ).
thf(57,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_Zero__neq__Suc) ).
thf(326,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(67,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_10_synthetic__div__0) ).
thf(358,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)],[67]) ).
thf(82,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_81_poly__zero) ).
thf(415,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)],[82]) ).
thf(98,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_46_monom__eq__0__iff) ).
thf(464,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)],[98]) ).
thf(85,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_43_monom__0) ).
thf(427,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)],[85]) ).
thf(96,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_21_pcompose__0) ).
thf(459,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)],[96]) ).
thf(9,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(163,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fTrue @ ( TA @ if ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(178,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(37,axiom,
! [A: nat] :
~ ( A @ ( A @ suc @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Suc__n__not__le__n) ).
thf(254,plain,
! [A: nat] :
~ ( A @ ( A @ suc @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(61,axiom,
nat @ comm_semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(337,plain,
nat @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(52,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_54_degree__monom__eq) ).
thf(309,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)],[52]) ).
thf(116,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_19_of__nat__aux_Osimps_I2_J) ).
thf(543,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)],[116]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ order )
=> ( TA @ ( TB @ fun ) @ order ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
thf(215,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ order )
=> ( TA @ ( TB @ fun ) @ order ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(28,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ( ( TA @ poly @ zero_zero @ ( TA @ degree ) )
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_degree__0) ).
thf(222,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ( ( TA @ poly @ zero_zero @ ( TA @ degree ) )
= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(125,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(592,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(627,plain,
$false,
inference(e,[status(thm)],[257,457,204,365,249,234,582,217,269,202,597,384,142,344,196,559,284,289,448,316,475,179,485,348,480,280,527,312,546,201,381,220,512,439,334,302,260,424,252,361,435,403,593,471,225,339,193,476,212,244,266,205,508,398,530,128,237,412,430,166,148,573,296,375,451,567,323,483,240,330,462,455,394,299,505,438,209,516,342,145,295,282,199,585,502,338,336,154,386,446,363,524,495,368,588,319,186,171,139,378,246,510,549,536,287,151,432,410,168,422,273,326,358,415,464,427,459,163,178,254,337,309,543,215,222,592]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW492_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
% 0.13/5.61 % Computer : n002.cluster.edu
% 0.13/5.61 % Model : x86_64 x86_64
% 0.13/5.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.61 % Memory : 8046.5625MB
% 0.13/5.61 % OS : Linux 6.8.0-71-generic
% 0.13/5.61 % CPULimit : 300
% 0.13/5.61 % WCLimit : 300
% 0.13/5.61 % DateTime : Sat Sep 26 16:11:57 UTC 2026
% 0.13/5.61 % CPUTime :
% 0.13/5.61 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
% 0.84/6.19 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.51/6.45 % [INFO] Parsing done (261ms).
% 1.51/6.46 % [INFO] Running in sequential loop mode.
% 2.24/6.74 % [INFO] eprover registered as external prover.
% 2.24/6.75 % [INFO] Scanning for conjecture ...
% 2.54/6.83 % [INFO] Found a conjecture (or negated_conjecture) and 125 axioms. Running axiom selection ...
% 2.54/6.89 % [INFO] Axiom selection finished. Selected 125 axioms (removed 0 axioms).
% 2.81/7.02 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.29/7.03 % [INFO] Type checking passed.
% 3.29/7.03 % [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 ...
% 3.63/7.18 % [INFO] [Domain constraints] Detected constraint on bool
% 3.63/7.19 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 11.33/8.98 % External prover 'e' found a proof!
% 11.33/8.98 % [INFO] Killing All external provers ...
% 11.33/8.98 % Time passed: 3233ms (effective reasoning time: 2511ms)
% 11.33/8.98 % 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)>
% 11.33/8.98 % Axioms used in derivation (125): arity_fun___Orderings_Oorder, arity_Nat_Onat___Rings_Ocomm__semiring__0, fact_29_expand__poly__eq, fact_82_poly__pcompose, arity_HOL_Obool___Orderings_Oorder, fact_48_coeff__monom, fact_71_not__less__eq__eq, fact_83_coeff__inverse, tfree_0, fact_20_degree__pCons__eq__if, fact_50_nat__case__Suc, arity_HOL_Obool___Orderings_Opreorder, fact_61_le__0__eq, arity_Nat_Onat___Rings_Osemiring__1, fact_58_degree__pCons__le, fact_95_neq0__conv, fact_75_degree__smult__le, fact_97_Suc__less__eq, fact_19_of__nat__aux_Osimps_I2_J, fact_62_Suc__le__mono, fact_47_monom__eq__0, fact_11_zero__reorient, fact_81_poly__zero, fact_10_synthetic__div__0, fact_80_le__antisym, fact_7_Zero__neq__Suc, arity_Nat_Onat___Orderings_Opreorder, fact_34_degree__pCons__0, fact_77_poly__eq__iff, fact_96_Suc__mono, fact_67_Suc__leD, fact_54_degree__monom__eq, fact_37_leading__coeff__neq__0, fact_3_Zero__not__Suc, fact_9_synthetic__div__eq__0__iff, fact_64_smult__0__left, fact_40_pCons__cases, fact_24_pCons__eq__iff, fact_28_coeff__pCons__Suc, fact_68_le__SucE, fact_49_nat__case__0, fact_25_pCons__0__0, arity_Polynomial_Opoly___Rings_Oidom, fact_17_nat__induct, fact_44_monom__Suc, fact_86_le__degree, arity_Polynomial_Opoly___Groups_Ozero, fact_43_monom__0, fact_35_degree__pCons__eq, fact_6_nat_Osimps_I3_J, fact_14_n__not__Suc__n, help_If_1_1_T, arity_Polynomial_Opoly___Int_Oring__char__0, fact_8_Suc__neq__Zero, fact_5_Suc__not__Zero, fact_56_degree__smult__eq, arity_Polynomial_Opoly___Rings_Ocomm__semiring__1, fact_55_pCons__def, arity_Polynomial_Opoly___Orderings_Oorder, arity_fun___Orderings_Opreorder, fact_63_smult__0__right, fact_73_ext, fact_84_synthetic__div__unique__lemma, arity_Polynomial_Opoly___Rings_Olinordered__idom, fact_59_le0, fact_72_Suc__n__not__le__n, fact_18_not0__implies__Suc, fact_22_poly__rec__0, fact_4_nat_Osimps_I2_J, fact_27_coeff__0, fact_32_poly__rec_Osimps, fact_92_eq__zero__or__degree__less, fact_88_order__root, fact_39_poly__ext, fact_1_psize__def, help_fequal_1_1_T, fact_0_degree__0, fact_78_eq__imp__le, arity_Nat_Onat___Rings_Ocomm__semiring__1, fact_15_nat_Oexhaust, arity_Nat_Onat___Groups_Ozero, fact_13_Suc__n__not__n, help_If_3_1_T, help_If_2_1_T, fact_36_of__nat__aux_Osimps_I1_J, arity_Polynomial_Opoly___Rings_Osemiring__1, fact_87_lift__Suc__mono__le, fact_30_coeff__inject, fact_53_degree__offset__poly, help_fequal_2_1_T, fact_89_Suc__le__D, fact_60_less__eq__nat_Osimps_I1_J, fact_41_offset__poly__single, fact_31_coeff__pCons__0, fact_94_less__nat__zero__code, fact_52_offset__poly__0, fact_2_nat_Oinject, fact_69_le__SucI, arity_Polynomial_Opoly___Orderings_Opreorder, arity_Nat_Onat___Orderings_Oorder, fact_79_le__trans, fact_33_poly__rec__pCons, fact_45_monom__eq__iff, help_pp_1_1_U, fact_21_pcompose__0, fact_90_order__degree, fact_93_less__zeroE, fact_91_order__refl, fact_16_zero__induct, fact_76_nat__le__linear, help_pp_2_1_U, fact_57_synthetic__div__pCons, fact_74_le__refl, fact_23_leading__coeff__0__iff, arity_Polynomial_Opoly___Rings_Ocomm__semiring__0, fact_66_poly__0, fact_12_Suc__inject, fact_26_pCons__eq__0__iff, fact_38_pCons__induct, fact_65_smult__eq__0__iff, fact_70_le__Suc__eq, fact_46_monom__eq__0__iff, fact_42_coeff__pCons, fact_85_degree__monom__le, fact_51_offset__poly__eq__0__iff
% 11.33/8.98 % No. of inferences in proof: 254
% 11.33/8.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3233 ms resp. 2511 ms w/o parsing
% 12.12/9.05 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.12/9.05 % [INFO] Killing All external provers ...
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