%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW485_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 : n012.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 4.45s 1.91s
% Output : Refutation 4.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 47
% Syntax : Number of formulae : 96 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 290 ( 49 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 907 ( 10 ~; 3 |; 22 &; 743 @)
% ( 9 <=>; 120 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 6 con; 0-4 aty)
% Number of variables : 183 ( 0 ^; 179 !; 4 ?; 183 :)
% Comments :
%------------------------------------------------------------------------------
thf(complex_type,type,
complex: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(real_type,type,
real: $tType ).
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(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(ring_char_0_decl,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(comm_semiring_0_decl,type,
comm_semiring_0:
!>[TA: $tType] : $o ).
thf(dense_linorder_decl,type,
dense_linorder:
!>[TA: $tType] : $o ).
thf(real_normed_vector_decl,type,
real_normed_vector:
!>[TA: $tType] : $o ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : 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(poly_decl,type,
poly:
!>[TA: $tType] : ( ( TA @ poly1 ) > ( TA @ ( TA @ fun ) ) ) ).
thf(norm_norm_decl,type,
norm_norm:
!>[TA: $tType] : ( TA > real ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(cs_decl,type,
cs: complex @ poly1 ).
thf(r_decl,type,
r: real ).
thf(thesis_decl,type,
thesis: $o ).
thf(40,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_le__funI) ).
thf(170,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(6,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linordered_idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Olinordered__idom) ).
thf(56,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linordered_idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,axiom,
! [TA: $tType] :
( ( TA @ dense_linorder )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ! [D: TA] :
( ( D @ ( C @ ( TA @ ord_less ) ) )
=> ( ( B @ ( D @ ( TA @ ord_less ) ) )
=> ( A @ ( D @ ( TA @ ord_less_eq ) ) ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_dense__le__bounded) ).
thf(121,plain,
! [TA: $tType] :
( ( TA @ dense_linorder )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ! [D: TA] :
( ( D @ ( C @ ( TA @ ord_less ) ) )
=> ( ( B @ ( D @ ( TA @ ord_less ) ) )
=> ( A @ ( D @ ( TA @ ord_less_eq ) ) ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(8,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ ring_char_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Int_Oring__char__0) ).
thf(60,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ ring_char_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(30,axiom,
complex @ idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Oidom) ).
thf(156,plain,
complex @ idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(17,axiom,
! [TA: $tType] :
( ( ( TA @ idom )
& ( TA @ ring_char_0 ) )
=> ! [A: TA @ poly1,B: TA @ poly1] :
( ( ( B @ ( TA @ poly ) )
= ( A @ ( TA @ poly ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_poly__eq__iff) ).
thf(96,plain,
! [TA: $tType] :
( ( ( TA @ idom )
& ( TA @ ring_char_0 ) )
=> ! [A: TA @ poly1,B: TA @ poly1] :
( ( ( B = A )
=> ( ( B @ ( TA @ poly ) )
= ( A @ ( TA @ poly ) ) ) )
& ( ( ( B @ ( TA @ poly ) )
= ( A @ ( TA @ poly ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(42,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] : ( A @ ( TA @ norm_norm ) @ ( real @ zero_zero @ ( real @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_norm__ge__zero) ).
thf(173,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] : ( A @ ( TA @ norm_norm ) @ ( real @ zero_zero @ ( real @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(35,axiom,
real @ comm_semiring_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__semiring__0) ).
thf(161,plain,
real @ comm_semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(38,axiom,
real @ ord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Oord) ).
thf(167,plain,
real @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(36,axiom,
real @ ring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Oring__char__0) ).
thf(162,plain,
real @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(26,axiom,
complex @ ring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Oring__char__0) ).
thf(150,plain,
complex @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_le__funE) ).
thf(175,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ ord )
=> ( TA @ ( TB @ fun ) @ ord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
thf(87,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ ord )
=> ( TA @ ( TB @ fun ) @ ord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ( TA @ poly1 @ zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ozero) ).
thf(52,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ( TA @ poly1 @ zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(45,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_74_ext) ).
thf(184,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)],[45]) ).
thf(31,axiom,
complex @ real_normed_vector,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__normed__vector) ).
thf(157,plain,
complex @ real_normed_vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(28,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ( ( TA @ zero_zero @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_norm__zero) ).
thf(152,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ( ( TA @ zero_zero @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(12,axiom,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_ord__less__eq__trans) ).
thf(78,plain,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(11,axiom,
! [TA: $tType] :
( ( TA @ dense_linorder )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_dense__le) ).
thf(74,plain,
! [TA: $tType] :
( ( TA @ dense_linorder )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(15,axiom,
! [A: real,B: real] :
( ( B @ ( real @ zero_zero @ ( real @ ord_less ) ) )
=> ( ( A @ ( real @ zero_zero @ ( real @ ord_less ) ) )
=> ? [C: real] :
( ( A @ ( C @ ( real @ ord_less ) ) )
& ( B @ ( C @ ( real @ ord_less ) ) )
& ( C @ ( real @ zero_zero @ ( real @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_real__lbound__gt__zero) ).
thf(89,plain,
! [A: real,B: real] :
( ( B @ ( real @ zero_zero @ ( real @ ord_less ) ) )
=> ( ( A @ ( real @ zero_zero @ ( real @ ord_less ) ) )
=> ? [C: real] :
( ( A @ ( C @ ( real @ ord_less ) ) )
& ( B @ ( C @ ( real @ ord_less ) ) )
& ( C @ ( real @ zero_zero @ ( real @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(24,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
( ( real @ zero_zero @ ( A @ ( TA @ norm_norm ) @ ( real @ ord_less_eq ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_norm__le__zero__iff) ).
thf(133,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( real @ zero_zero @ ( A @ ( TA @ norm_norm ) @ ( real @ ord_less_eq ) ) ) )
& ( ( real @ zero_zero @ ( A @ ( TA @ norm_norm ) @ ( real @ ord_less_eq ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(34,axiom,
real @ idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oidom) ).
thf(160,plain,
real @ idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(48,axiom,
! [A: real] :
( ! [B: complex] :
( ( r @ ( B @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) )
=> ( A @ ( B @ ( cs @ ( complex @ poly ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) ) )
=> thesis ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(192,plain,
! [A: real] :
( ! [B: complex] :
( ( r @ ( B @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) )
=> ( A @ ( B @ ( cs @ ( complex @ poly ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) ) )
=> thesis ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(47,axiom,
complex @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ozero) ).
thf(191,plain,
complex @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(21,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA] :
( ( A @ ( TA @ poly1 @ zero_zero @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_poly__0) ).
thf(118,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA] :
( ( A @ ( TA @ poly1 @ zero_zero @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(5,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ poly1 @ comm_semiring_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Ocomm__semiring__0) ).
thf(54,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ poly1 @ comm_semiring_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
thesis,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ thesis,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(49,plain,
~ thesis,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(33,axiom,
real @ linordered_idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__idom) ).
thf(159,plain,
real @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(46,axiom,
? [A: real] :
( ! [B: complex] :
( ( r @ ( B @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) )
=> ( A @ ( B @ ( cs @ ( complex @ poly ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) ) )
& ( A @ ( real @ zero_zero @ ( real @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_pCons) ).
thf(187,plain,
? [A: real] :
( ! [B: complex] :
( ( r @ ( B @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) )
=> ( A @ ( B @ ( cs @ ( complex @ poly ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) ) )
& ( A @ ( real @ zero_zero @ ( real @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(41,axiom,
real @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ozero) ).
thf(172,plain,
real @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(18,axiom,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_ord__eq__le__trans) ).
thf(103,plain,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(25,axiom,
! [A: real,B: real] :
( ( A @ ( B @ ( real @ ord_less_eq ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( real @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_less__eq__real__def) ).
thf(140,plain,
! [A: real,B: real] :
( ( ( ( B = A )
| ( A @ ( B @ ( real @ ord_less ) ) ) )
=> ( A @ ( B @ ( real @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( real @ ord_less_eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( real @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(10,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_zero__reorient) ).
thf(66,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)],[10]) ).
thf(29,axiom,
real @ real_normed_vector,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___RealVector_Oreal__normed__vector) ).
thf(155,plain,
real @ real_normed_vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(3,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ ord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Orderings_Oord) ).
thf(50,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ ord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(44,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
( ( ( A @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_norm__eq__zero) ).
thf(177,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) ) )
& ( ( ( A @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(32,axiom,
complex @ comm_semiring_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ocomm__semiring__0) ).
thf(158,plain,
complex @ comm_semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(20,axiom,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_ord__le__eq__trans) ).
thf(114,plain,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(7,axiom,
! [TA: $tType] :
( ( TA @ idom )
=> ( TA @ poly1 @ idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Oidom) ).
thf(58,plain,
! [TA: $tType] :
( ( TA @ idom )
=> ( TA @ poly1 @ idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less ) ) )
<=> ( ~ ( B @ ( A @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
& ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_less__fun__def) ).
thf(82,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ( ( ~ ( B @ ( A @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
& ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less ) ) ) )
& ( ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less ) ) )
=> ( ~ ( B @ ( A @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
& ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(27,axiom,
real @ dense_linorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Odense__linorder) ).
thf(151,plain,
real @ dense_linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_le__funD) ).
thf(168,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(19,axiom,
! [TA: $tType] :
( ( ( TA @ idom )
& ( TA @ ring_char_0 ) )
=> ! [A: TA @ poly1] :
( ( ( A @ ( TA @ poly ) )
= ( TA @ poly1 @ zero_zero @ ( TA @ poly ) ) )
<=> ( A
= ( TA @ poly1 @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_poly__zero) ).
thf(107,plain,
! [TA: $tType] :
( ( ( TA @ idom )
& ( TA @ ring_char_0 ) )
=> ! [A: TA @ poly1] :
( ( ( A
= ( TA @ poly1 @ zero_zero ) )
=> ( ( A @ ( TA @ poly ) )
= ( TA @ poly1 @ zero_zero @ ( TA @ poly ) ) ) )
& ( ( ( A @ ( TA @ poly ) )
= ( TA @ poly1 @ zero_zero @ ( TA @ poly ) ) )
=> ( A
= ( TA @ poly1 @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(23,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
( ( A @ ( TA @ norm_norm ) @ ( real @ zero_zero @ ( real @ ord_less ) ) )
<=> ( A
!= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_zero__less__norm__iff) ).
thf(126,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
( ( ( A
!= ( TA @ zero_zero ) )
=> ( A @ ( TA @ norm_norm ) @ ( real @ zero_zero @ ( real @ ord_less ) ) ) )
& ( ( A @ ( TA @ norm_norm ) @ ( real @ zero_zero @ ( real @ ord_less ) ) )
=> ( A
!= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(16,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
~ ( real @ zero_zero @ ( A @ ( TA @ norm_norm ) @ ( real @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_norm__not__less__zero) ).
thf(94,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
~ ( real @ zero_zero @ ( A @ ( TA @ norm_norm ) @ ( real @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
<=> ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_le__fun__def) ).
thf(163,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ( ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(9,axiom,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_ord__eq__less__trans) ).
thf(62,plain,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(200,plain,
$false,
inference(e,[status(thm)],[170,56,121,60,156,96,173,161,167,162,150,175,87,52,184,157,152,78,74,89,133,160,192,191,118,54,49,159,187,172,103,140,66,155,50,177,158,114,58,82,151,168,107,126,94,163,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWW485_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.04 % 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
% 0.08/0.33 % Computer : n012.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Sat Sep 26 16:08:05 UTC 2026
% 0.08/0.33 % CPUTime :
% 0.08/0.33 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
% 0.52/0.64 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.01/0.81 % [INFO] Parsing done (164ms).
% 1.01/0.81 % [INFO] Running in sequential loop mode.
% 1.49/1.02 % [INFO] eprover registered as external prover.
% 1.49/1.03 % [INFO] Scanning for conjecture ...
% 1.49/1.10 % [INFO] Found a conjecture (or negated_conjecture) and 140 axioms. Running axiom selection ...
% 1.68/1.16 % [INFO] Axiom selection finished. Selected 46 axioms (removed 94 axioms).
% 1.91/1.23 % [INFO] Problem is typed first-order (TPTP TFF).
% 1.91/1.23 % [INFO] Type checking passed.
% 1.91/1.24 % [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 ...
% 4.45/1.90 % External prover 'e' found a proof!
% 4.45/1.90 % [INFO] Killing All external provers ...
% 4.45/1.90 % Time passed: 1488ms (effective reasoning time: 1085ms)
% 4.45/1.90 % 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)>
% 4.45/1.90 % Axioms used in derivation (46): fact_67_zero__reorient, fact_68_real__lbound__gt__zero, arity_Polynomial_Opoly___Rings_Olinordered__idom, arity_RealDef_Oreal___Rings_Oidom, arity_RealDef_Oreal___Int_Oring__char__0, arity_RealDef_Oreal___Rings_Ocomm__semiring__0, fact_30_ord__eq__less__trans, fact_66_less__fun__def, fact_3_norm__ge__zero, conj_0, fact_58_le__funI, arity_Complex_Ocomplex___Rings_Ocomm__semiring__0, arity_fun___Orderings_Oord, arity_RealDef_Oreal___Groups_Ozero, fact_63_dense__le__bounded, fact_13_poly__0, fact_35_poly__zero, fact_2_poly__eq__iff, fact_12_ord__le__eq__trans, fact_5_le__fun__def, arity_Complex_Ocomplex___Rings_Oidom, arity_Complex_Ocomplex___Int_Oring__char__0, fact_64_dense__le, fact_0_pCons, fact_65_less__eq__real__def, arity_Polynomial_Opoly___Rings_Oidom, fact_74_ext, arity_RealDef_Oreal___Orderings_Oord, fact_9_le__funD, arity_Polynomial_Opoly___Groups_Ozero, fact_36_norm__not__less__zero, arity_Polynomial_Opoly___Orderings_Oord, arity_Polynomial_Opoly___Int_Oring__char__0, arity_RealDef_Oreal___Orderings_Odense__linorder, fact_14_norm__eq__zero, fact_15_norm__zero, arity_RealDef_Oreal___Rings_Olinordered__idom, fact_11_ord__eq__le__trans, arity_RealDef_Oreal___RealVector_Oreal__normed__vector, fact_4_norm__le__zero__iff, fact_31_ord__less__eq__trans, arity_Polynomial_Opoly___Rings_Ocomm__semiring__0, arity_Complex_Ocomplex___Groups_Ozero, arity_Complex_Ocomplex___RealVector_Oreal__normed__vector, fact_55_le__funE, fact_16_zero__less__norm__iff
% 4.45/1.90 % No. of inferences in proof: 96
% 4.45/1.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1488 ms resp. 1085 ms w/o parsing
% 4.45/1.95 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.45/1.95 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------