%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG427-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/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 06:46:59 AM UTC 2026
% Result : Unsatisfiable 23.47s 6.13s
% Output : Refutation 22.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 60
% Syntax : Number of formulae : 121 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 235 ( 148 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 928 ( 124 ~; 114 |; 0 &; 690 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 7 con; 0-3 aty)
% Number of variables : 208 ( 0 ^; 208 !; 0 ?; 208 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_thesis_____decl,type,
v_thesis____: $o ).
thf(class_HOL_Ozero_decl,type,
class_HOL_Ozero: $i > $o ).
thf(c_Polynomial_Omonom_decl,type,
c_Polynomial_Omonom: $i > $i > $i > $i ).
thf(c_HOL_Ozero__class_Ozero_decl,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(tc_Polynomial_Opoly_decl,type,
tc_Polynomial_Opoly: $i > $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(c_Polynomial_OpCons_decl,type,
c_Polynomial_OpCons: $i > $i > $i > $i ).
thf(c_Polynomial_Ocoeff_decl,type,
c_Polynomial_Ocoeff: $i > $i > $i > $i ).
thf(c_Polynomial_Odegree_decl,type,
c_Polynomial_Odegree: $i > $i > $i ).
thf(class_Ring__and__Field_Ocomm__semiring__0_decl,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
thf(c_Polynomial_Osynthetic__div_decl,type,
c_Polynomial_Osynthetic__div: $i > $i > $i > $i ).
thf(c_Polynomial_Opoly_decl,type,
c_Polynomial_Opoly: $i > $i > $i > $i ).
thf(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly_decl,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: $i > $i > $i > $i ).
thf(c_Complex_Ocnj_decl,type,
c_Complex_Ocnj: $i > $i ).
thf(tc_Complex_Ocomplex_decl,type,
tc_Complex_Ocomplex: $i ).
thf(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1_decl,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1: $i > $i ).
thf(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2_decl,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2: $i > $i ).
thf(v_p_decl,type,
v_p: $i ).
thf(class_RealVector_Oreal__normed__algebra__1_decl,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
thf(class_RealVector_Oreal__normed__div__algebra_decl,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
thf(c_Complex_Oii_decl,type,
c_Complex_Oii: $i ).
thf(v_q_decl,type,
v_q: $i ).
thf(class_RealVector_Oreal__field_decl,type,
class_RealVector_Oreal__field: $i > $o ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ c_Polynomial_Odegree ) )
= ( A @ ( B @ c_Polynomial_Odegree ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__offset__poly_0) ).
thf(142,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ c_Polynomial_Odegree ) )
= ( A @ ( B @ c_Polynomial_Odegree ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) @ c_Suc ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__pCons__eq_0) ).
thf(174,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) @ c_Suc ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(35,axiom,
! [A: $i] :
( ( ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Odegree ) @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_leading__coeff__0__iff_1) ).
thf(160,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Odegree ) @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(42,axiom,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
thf(181,plain,
tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(45,axiom,
! [A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_OpCons ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__0__0_0) ).
thf(187,plain,
! [A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_OpCons ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__monom_1) ).
thf(80,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Omonom ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monom__eq__0_0) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Omonom ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(69,plain,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ c_Suc @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ ( D @ ( C @ c_Polynomial_Ocoeff ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__pCons__Suc_0) ).
thf(88,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ c_Suc @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ ( D @ ( C @ c_Polynomial_Ocoeff ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(18,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(115,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(57,axiom,
( c_Complex_Oii
!= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__i__not__zero_0) ).
thf(217,plain,
( c_Complex_Oii
!= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(44,axiom,
! [A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__0_0) ).
thf(184,plain,
! [A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Ocoeff ) ) )
= B )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__pCons__0_0) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Ocoeff ) ) )
= B )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(56,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__div__algebra,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
thf(216,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__div__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__0_0) ).
thf(106,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osynthetic__div ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__0_0) ).
thf(121,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osynthetic__div ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(61,plain,
~ v_thesis____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(25,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__0) ).
thf(133,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(52,axiom,
! [A: $i] :
( ( A
= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ c_Complex_Ocnj )
!= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj__zero__iff_0) ).
thf(206,plain,
! [A: $i] :
( ( A
= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ c_Complex_Ocnj )
!= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_1) ).
thf(201,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(58,axiom,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ ( A @ ( v_q @ c_Polynomial_Opoly ) ) )
= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) )
| ( v_p
!= ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( v_p
!= ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( v_q
!= ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_Complex_Ocomplex @ ( A @ ( v_p @ c_Polynomial_Opoly ) ) )
!= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_calculation_3) ).
thf(220,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ ( A @ ( v_q @ c_Polynomial_Opoly ) ) )
= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) )
| ( v_p
!= ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( v_p
!= ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( v_q
!= ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_Complex_Ocomplex @ ( A @ ( v_p @ c_Polynomial_Opoly ) ) )
!= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(97,plain,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(59,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__field,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).
thf(224,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Osynthetic__div ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Osynthetic__div ) ) @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__pCons_0) ).
thf(109,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Osynthetic__div ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Osynthetic__div ) ) @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(47,axiom,
( ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ c_Complex_Ocnj )
= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cnj_Ozero_0) ).
thf(193,plain,
( ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ c_Complex_Ocnj )
= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_0) ).
thf(212,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(21,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__iff_0) ).
thf(124,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(60,axiom,
! [A: $i] :
( ( A
= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) )
| v_thesis____
| ( v_p
!= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_Polynomial_OpCons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_that_0) ).
thf(225,plain,
! [A: $i] :
( ( A
= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) )
| v_thesis____
| ( v_p
!= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_Polynomial_OpCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(26,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).
thf(134,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Polynomial_Osynthetic__div ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_Polynomial_Odegree ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__eq__0__iff_1) ).
thf(128,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Polynomial_Osynthetic__div ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_Polynomial_Odegree ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Complex_Ocnj )
!= ( B @ c_Complex_Ocnj ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj__cancel__iff_0) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Complex_Ocnj )
!= ( B @ c_Complex_Ocnj ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__pCons__0_0) ).
thf(148,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(118,plain,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(51,axiom,
( ( tc_Complex_Ocomplex @ ( v_p @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
thf(204,plain,
( ( tc_Complex_Ocomplex @ ( v_p @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) )
!= ( A @ ( C @ ( D @ c_Polynomial_Omonom ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monom__eq__iff_0) ).
thf(103,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) )
!= ( A @ ( C @ ( D @ c_Polynomial_Omonom ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Ocoeff ) ) )
= B )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__monom_0) ).
thf(91,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Ocoeff ) ) )
= B )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(66,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(49,axiom,
( v_p
!= ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(198,plain,
( v_p
!= ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__single_0) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monom__eq__0__iff_0) ).
thf(112,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_Omonom ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monom__0_0) ).
thf(145,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_Omonom ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(22,axiom,
tc_nat @ class_HOL_Ozero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ozero) ).
thf(127,plain,
tc_nat @ class_HOL_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(40,axiom,
tc_Complex_Ocomplex @ class_HOL_Ozero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).
thf(177,plain,
tc_Complex_Ocomplex @ class_HOL_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ c_Complex_Ocnj @ c_Complex_Ocnj )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj__cnj_0) ).
thf(182,plain,
! [A: $i] :
( ( A @ c_Complex_Ocnj @ c_Complex_Ocnj )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__eq__0__iff_0) ).
thf(154,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Polynomial_Omonom ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monom__Suc_0) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Polynomial_Omonom ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(38,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( B @ c_Polynomial_Ocoeff ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_leading__coeff__0__iff_0) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( B @ c_Polynomial_Ocoeff ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Osynthetic__div ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__eq__0__iff_0) ).
thf(139,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Osynthetic__div ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__0_0) ).
thf(151,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(46,axiom,
( v_p
!= ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pe_0) ).
thf(190,plain,
( v_p
!= ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(27,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = E )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__iff_1) ).
thf(136,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = E )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(48,axiom,
! [A: $i] :
( ( A
= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1 @ c_Polynomial_OpCons ) ) ) )
| ( ( tc_Complex_Ocomplex @ ( A @ v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2 @ ( A @ c_Polynomial_Opoly ) ) )
= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fundamental__theorem__of__algebra__alt_1) ).
thf(195,plain,
! [A: $i] :
( ( A
= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1 @ c_Polynomial_OpCons ) ) ) )
| ( ( tc_Complex_Ocomplex @ ( A @ v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2 @ ( A @ c_Polynomial_Opoly ) ) )
= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(11,axiom,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(94,plain,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(24,axiom,
! [A: $i] :
( ~ ( A @ class_HOL_Ozero )
| ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__HOL_Ozero) ).
thf(131,plain,
! [A: $i] :
( ~ ( A @ class_HOL_Ozero )
| ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__0_0) ).
thf(163,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(41,axiom,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ ( A @ v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2 @ ( A @ c_Polynomial_Opoly ) ) )
= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1 )
!= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fundamental__theorem__of__algebra__alt_0) ).
thf(178,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ ( A @ v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2 @ ( A @ c_Polynomial_Opoly ) ) )
= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1 )
!= ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(55,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
thf(215,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Odegree ) )
= C )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__monom__eq_0) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Odegree ) )
= C )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1298,plain,
$false,
inference(e,[status(thm)],[142,174,160,181,187,80,63,75,69,88,115,217,184,157,216,106,121,61,133,206,201,220,97,224,109,193,212,124,225,134,128,166,148,118,204,103,91,66,198,209,112,145,127,177,182,154,72,171,139,151,190,136,195,94,131,163,178,83,215,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG427-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40 % Computer : n002.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 22:03:06 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.90/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.96/1.55 % [INFO] Parsing done (560ms).
% 2.96/1.57 % [INFO] Running in sequential loop mode.
% 4.19/2.12 % [INFO] eprover registered as external prover.
% 4.19/2.13 % [INFO] Scanning for conjecture ...
% 5.17/2.40 % [INFO] Found a conjecture (or negated_conjecture) and 837 axioms. Running axiom selection ...
% 6.10/2.61 % [INFO] Axiom selection finished. Selected 59 axioms (removed 778 axioms).
% 6.57/2.72 % [INFO] Problem is propositional (TPTP CNF).
% 6.57/2.73 % [INFO] Type checking passed.
% 6.57/2.74 % [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 ...
% 23.47/6.12 % External prover 'e' found a proof!
% 23.47/6.12 % [INFO] Killing All external provers ...
% 23.47/6.12 % Time passed: 5571ms (effective reasoning time: 4543ms)
% 23.47/6.12 % Axioms used in derivation (59): cls_Suc__n__not__n_0, cls_coeff__monom_1, cls_pe_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1, cls_synthetic__div__eq__0__iff_1, cls_poly__0_0, cls_leading__coeff__0__iff_1, cls_nat_Oinject_0, cls_offset__poly__0_0, clsarity_nat__Ring__and__Field_Ocomm__semiring__0, cls_offset__poly__eq__0__iff_0, cls_pCons__0__0_0, cls_Suc__inject_0, cls_degree__pCons__eq_0, cls_degree__pCons__0_0, cls_CHAINED_0, cls_fundamental__theorem__of__algebra__alt_0, clsarity_nat__HOL_Ozero, cls_synthetic__div__eq__0__iff_0, cls_complex__cnj__cancel__iff_0, cls_monom__eq__iff_0, cls_fundamental__theorem__of__algebra__alt_1, cls_monom__Suc_0, clsarity_Polynomial__Opoly__HOL_Ozero, cls_coeff__0_0, cls_calculation_3, cls_degree__0_0, cls_cnj_Ozero_0, cls_leading__coeff__0__iff_0, cls_CHAINED_0_01, cls_pCons__eq__0__iff_1, cls_Suc__neq__Zero_0, cls_pCons__eq__iff_0, cls_monom__0_0, cls_complex__i__not__zero_0, cls_coeff__monom_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra, cls_monom__eq__0__iff_0, cls_nat_Osimps_I2_J_0, cls_Zero__neq__Suc_0, cls_monom__eq__0_0, cls_complex__cnj__zero__iff_0, cls_synthetic__div__pCons_0, cls_pCons__eq__0__iff_0, cls_pCons__eq__iff_1, cls_coeff__pCons__Suc_0, cls_degree__offset__poly_0, cls_nat_Osimps_I3_J_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0, cls_degree__monom__eq_0, cls_complex__cnj__cnj_0, cls_synthetic__div__0_0, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0, cls_n__not__Suc__n_0, clsarity_Complex__Ocomplex__RealVector_Oreal__field, cls_that_0, cls_coeff__pCons__0_0, cls_offset__poly__single_0, clsarity_Complex__Ocomplex__HOL_Ozero
% 23.47/6.12 % No. of inferences in proof: 121
% 23.47/6.13 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 5571 ms resp. 4543 ms w/o parsing
% 22.84/6.23 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 22.84/6.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------