%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV254-1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n006.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 08:58:34 AM UTC 2026
% Result : Unsatisfiable 10.21s 3.80s
% Output : Refutation 10.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 124
% Syntax : Number of formulae : 249 ( 107 unt; 0 typ; 0 def)
% Number of atoms : 415 ( 166 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 2142 ( 168 ~; 166 |; 0 &;1808 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 6 con; 0-3 aty)
% Number of variables : 442 ( 0 ^; 442 !; 0 ?; 442 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(v_x_decl,type,
v_x: $i > $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(v_nat_decl,type,
v_nat: $i ).
thf(c_less_decl,type,
c_less: $i > $i > $i > $o ).
thf(c_0_decl,type,
c_0: $i ).
thf(c_1_decl,type,
c_1: $i ).
thf(c_times_decl,type,
c_times: $i > $i > $i > $i ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(c_plus_decl,type,
c_plus: $i > $i > $i > $i ).
thf(c_Binomial_Obinomial_decl,type,
c_Binomial_Obinomial: $i > $i > $i ).
thf(c_div_decl,type,
c_div: $i > $i > $i > $i ).
thf(c_minus_decl,type,
c_minus: $i > $i > $i > $i ).
thf(class_Nat_Opower_decl,type,
class_Nat_Opower: $i > $o ).
thf(class_Wellfounded__Recursion_Owellorder_decl,type,
class_Wellfounded__Recursion_Owellorder: $i > $o ).
thf(class_Parity_Oeven__odd_decl,type,
class_Parity_Oeven__odd: $i > $o ).
thf(c_Relation_Otrans_decl,type,
c_Relation_Otrans: $i > $i > $o ).
thf(c_Wellfounded__Relations_Oless__than_decl,type,
c_Wellfounded__Relations_Oless__than: $i ).
thf(class_OrderedGroup_Ocomm__monoid__mult_decl,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(class_Divides_Odiv_decl,type,
class_Divides_Odiv: $i > $o ).
thf(117,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_1) ).
thf(384,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(9,axiom,
tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0_1) ).
thf(138,plain,
tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(98,axiom,
! [B: $i,A: $i] :
( ( B = c_1 )
| ( ( c_0 @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_1) ).
thf(347,plain,
! [B: $i,A: $i] :
( ( B = c_1 )
| ( ( c_0 @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_0) ).
thf(249,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( B @ c_plus ) ) @ c_div ) ) )
= ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_div ) ) @ ( C @ c_plus ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self2_0) ).
thf(217,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( B @ c_plus ) ) @ c_div ) ) )
= ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_div ) ) @ ( C @ c_plus ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_1 @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( c_0 @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_1) ).
thf(247,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_1 @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( c_0 @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(31,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).
thf(185,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( C @ c_minus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_minus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__right_0) ).
thf(288,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( C @ c_minus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_minus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(1,negated_conjecture,
! [A: $i] : ( tc_nat @ ( A @ v_x @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(125,plain,
! [A: $i] : ( tc_nat @ ( A @ v_x @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(36,axiom,
c_0 != c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__0__neq__1_0) ).
thf(196,plain,
c_0 != c_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).
thf(189,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(89,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero_0) ).
thf(325,plain,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(16,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_1 @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_0) ).
thf(152,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_1 @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(86,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_div ) ) )
= B )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1__is__m_0) ).
thf(316,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_div ) ) )
= B )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(21,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0_0) ).
thf(164,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_1) ).
thf(179,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(54,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_minus ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).
thf(238,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_minus ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ c_div ) ) )
= ( tc_nat @ ( C @ ( B @ c_div ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult2_0) ).
thf(353,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ c_div ) ) )
= ( tc_nat @ ( C @ ( B @ c_div ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(14,axiom,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
thf(147,plain,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( C @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ c_plus ) ) )
= ( tc_nat @ ( A @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_minus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc2_0) ).
thf(293,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( C @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ c_plus ) ) )
= ( tc_nat @ ( A @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_minus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_0) ).
thf(132,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__leE_0) ).
thf(396,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(56,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_minus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_N_Odiff__0_0) ).
thf(243,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_minus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).
thf(233,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_2) ).
thf(380,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(38,axiom,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
thf(201,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ( B @ c_Suc @ ( A @ c_Suc @ c_Binomial_Obinomial ) )
= ( tc_nat @ ( B @ c_Suc @ ( A @ c_Binomial_Obinomial ) @ ( B @ ( A @ c_Binomial_Obinomial ) @ c_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__Suc_0) ).
thf(220,plain,
! [B: $i,A: $i] :
( ( B @ c_Suc @ ( A @ c_Suc @ c_Binomial_Obinomial ) )
= ( tc_nat @ ( B @ c_Suc @ ( A @ c_Binomial_Obinomial ) @ ( B @ ( A @ c_Binomial_Obinomial ) @ c_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(105,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).
thf(366,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_1) ).
thf(334,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(80,axiom,
( ( tc_nat @ ( c_1 @ ( c_1 @ c_times ) ) )
= ( c_0 @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_2) ).
thf(302,plain,
( ( tc_nat @ ( c_1 @ ( c_1 @ c_times ) ) )
= ( c_0 @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_0) ).
thf(160,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_1) ).
thf(275,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) )
= ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__Suc__right_0) ).
thf(229,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) )
= ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).
thf(285,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(48,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_minus ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__0__eq__0_0) ).
thf(224,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_minus ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_1) ).
thf(388,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(101,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_0) ).
thf(356,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(23,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
thf(169,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(11,axiom,
! [A: $i] :
( ( c_0 @ ( A @ c_Binomial_Obinomial ) )
= c_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__0_0) ).
thf(141,plain,
! [A: $i] :
( ( c_0 @ ( A @ c_Binomial_Obinomial ) )
= c_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_div ) ) )
= c_0 )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__less_0) ).
thf(193,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_div ) ) )
= c_0 )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq_0) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( C @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ c_Suc @ c_minus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( B @ c_Suc @ c_minus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq2_0) ).
thf(328,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( C @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ c_Suc @ c_minus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( B @ c_Suc @ c_minus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_minus ) ) )
= c_0 )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_H_0) ).
thf(256,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_minus ) ) )
= c_0 )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(121,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_div ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__le__dividend_0) ).
thf(393,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_div ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(25,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(173,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_0) ).
thf(129,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(108,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__leE_1) ).
thf(371,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).
thf(134,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_times ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( B @ c_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__Suc_0) ).
thf(266,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_times ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( B @ c_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(84,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__is__0_0) ).
thf(311,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(3,axiom,
tc_nat @ ( c_1 @ ( c_0 @ c_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_1) ).
thf(128,plain,
tc_nat @ ( c_1 @ ( c_0 @ c_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(96,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_div ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__1_0) ).
thf(343,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_div ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(65,axiom,
( ( c_0 @ c_Suc )
= ( tc_nat @ ( c_1 @ ( c_1 @ c_times ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_2) ).
thf(264,plain,
( ( c_0 @ c_Suc )
= ( tc_nat @ ( c_1 @ ( c_1 @ c_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ c_div ) ) )
= B )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self__is__m_0) ).
thf(279,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ c_div ) ) )
= B )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( C @ c_plus ) ) )
= ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ c_minus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc_0) ).
thf(296,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( C @ c_plus ) ) )
= ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ c_minus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_0) ).
thf(375,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__less_0) ).
thf(191,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(76,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_plus ) ) )
= ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__Suc_0) ).
thf(291,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_plus ) ) )
= ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ c_Suc @ ( C @ c_minus ) ) )
= ( tc_nat @ ( B @ c_Suc @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_minus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq1_0) ).
thf(259,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ c_Suc @ ( C @ c_minus ) ) )
= ( tc_nat @ ( B @ c_Suc @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_minus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(115,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(382,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ ( c_0 @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( c_1 @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_1 @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_2) ).
thf(236,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ ( c_0 @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( c_1 @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_1 @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(29,axiom,
( c_1
= ( c_0 @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OOne__nat__def_0) ).
thf(181,plain,
( c_1
= ( c_0 @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(99,axiom,
! [A: $i] :
( ( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_minus ) ) @ c_Suc )
= A )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__pred_0) ).
thf(350,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_minus ) ) @ c_Suc )
= A )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(32,axiom,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_1) ).
thf(187,plain,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(112,axiom,
tc_nat @ class_Parity_Oeven__odd,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_47) ).
thf(377,plain,
tc_nat @ class_Parity_Oeven__odd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_minus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ ( A @ c_minus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__left_0) ).
thf(362,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_minus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ ( A @ c_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(57,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_div ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__0_0) ).
thf(245,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_div ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(68,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_minus ) ) )
= ( tc_nat @ ( B @ ( A @ c_minus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__Suc_0) ).
thf(271,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_minus ) ) )
= ( tc_nat @ ( B @ ( A @ c_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_1) ).
thf(208,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(97,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_times ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( A @ c_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__Suc__right_0) ).
thf(345,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_times ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( A @ c_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(17,axiom,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( A @ c_div ) ) )
= c_1 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__self_0) ).
thf(155,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( A @ c_div ) ) )
= c_1 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ ( B @ c_plus ) ) @ c_div ) ) )
= ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_div ) ) @ ( C @ c_plus ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1_0) ).
thf(240,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ ( B @ c_plus ) ) @ c_div ) ) )
= ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_div ) ) @ ( C @ c_plus ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ c_plus ) ) )
= B )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse2_0) ).
thf(251,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ c_plus ) ) )
= B )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_0 )
| ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= ( tc_nat @ ( B @ ( C @ c_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_0) ).
thf(299,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_0 )
| ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= ( tc_nat @ ( B @ ( C @ c_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ( A = c_1 )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= ( c_0 @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_0) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( A = c_1 )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= ( c_0 @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_1) ).
thf(167,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(122,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_24) ).
thf(394,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(82,axiom,
! [B: $i,A: $i] :
( ( A = c_1 )
| ( ( c_0 @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_0) ).
thf(306,plain,
! [B: $i,A: $i] :
( ( A = c_1 )
| ( ( c_0 @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).
thf(162,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(110,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__le__self_0) ).
thf(374,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_2) ).
thf(145,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(73,axiom,
! [B: $i,A: $i] :
( ( B = c_1 )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= ( c_0 @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_1) ).
thf(282,plain,
! [B: $i,A: $i] :
( ( B = c_1 )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= ( c_0 @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ c_Suc @ ( c_0 @ c_Binomial_Obinomial ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__0__Suc_0) ).
thf(150,plain,
! [A: $i] :
( ( A @ c_Suc @ ( c_0 @ c_Binomial_Obinomial ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ ( A @ c_Binomial_Obinomial ) )
= c_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__n_0) ).
thf(199,plain,
! [A: $i] :
( ( A @ ( A @ c_Binomial_Obinomial ) )
= c_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_0) ).
thf(177,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_0 )
| ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= ( tc_nat @ ( C @ ( A @ c_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_0) ).
thf(331,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_0 )
| ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= ( tc_nat @ ( C @ ( A @ c_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(107,axiom,
tc_nat @ class_Nat_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_12) ).
thf(370,plain,
tc_nat @ class_Nat_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(94,axiom,
! [A: $i] :
( c_0
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc_0) ).
thf(338,plain,
! [A: $i] :
( c_0
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
thf(359,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(93,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_minus ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__less_0) ).
thf(336,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_minus ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_minus ) ) @ c_minus ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_minus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__diff__diff_0) ).
thf(314,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_minus ) ) @ c_minus ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_div ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( c_1 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__less__dividend_0) ).
thf(143,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_div ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( c_1 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ ( A @ c_Suc @ c_Binomial_Obinomial ) )
= ( A @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__n_0) ).
thf(175,plain,
! [A: $i] :
( ( A @ ( A @ c_Suc @ c_Binomial_Obinomial ) )
= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_times ) ) @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_2) ).
thf(386,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_times ) ) @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(51,axiom,
( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_2) ).
thf(231,plain,
( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_2) ).
thf(203,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(87,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_div ) ) )
= ( tc_nat @ ( C @ ( B @ c_div ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult1_0) ).
thf(319,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_div ) ) )
= ( tc_nat @ ( C @ ( B @ c_div ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_times ) ) )
= ( tc_nat @ ( B @ ( c_0 @ c_times ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_1) ).
thf(304,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_times ) ) )
= ( tc_nat @ ( B @ ( c_0 @ c_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_1) ).
thf(158,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(120,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( B @ c_minus ) ) )
= A )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__cancel_0) ).
thf(390,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( B @ c_minus ) ) )
= A )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_1) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(10,axiom,
! [A: $i] :
( ( c_0 @ c_Suc @ ( A @ c_Binomial_Obinomial ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__1_0) ).
thf(139,plain,
! [A: $i] :
( ( c_0 @ c_Suc @ ( A @ c_Binomial_Obinomial ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).
thf(378,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(41,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
thf(207,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(116,axiom,
tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Otrans ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__less__than_0) ).
thf(383,plain,
tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Otrans ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(64,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_plus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(262,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(30,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_0) ).
thf(183,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(69,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_plus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).
thf(273,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(109,axiom,
tc_nat @ class_Wellfounded__Recursion_Owellorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_8) ).
thf(373,plain,
tc_nat @ class_Wellfounded__Recursion_Owellorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_0) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_1 @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( c_0 @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_0) ).
thf(341,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_1 @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( c_0 @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(67,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_minus ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).
thf(268,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_minus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(2,negated_conjecture,
! [A: $i] :
( ( A @ v_x )
= v_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(126,plain,
! [A: $i] :
( ( A @ v_x )
= v_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_times ) ) @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_2) ).
thf(136,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_times ) ) @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(123,axiom,
tc_nat @ class_Divides_Odiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_44) ).
thf(395,plain,
tc_nat @ class_Divides_Odiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(5,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
thf(131,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(71,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_times ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__0__right_0) ).
thf(277,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_times ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(106,axiom,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_1) ).
thf(369,plain,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(61,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_div ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__DIV_0) ).
thf(254,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_div ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( A @ c_plus ) ) )
= B )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse_0) ).
thf(322,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( A @ c_plus ) ) )
= B )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(83,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_times ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__0_0) ).
thf(309,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_times ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_times ) ) )
= ( tc_nat @ ( c_0 @ ( B @ c_times ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_1) ).
thf(222,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_times ) ) )
= ( tc_nat @ ( c_0 @ ( B @ c_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(104,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_0) ).
thf(364,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(398,plain,
$false,
inference(e,[status(thm)],[384,138,347,249,217,247,185,288,125,196,189,325,152,316,164,179,238,353,147,293,132,396,243,233,380,201,220,366,334,302,160,275,229,285,224,388,356,169,141,193,212,328,256,393,173,129,371,134,266,205,311,128,343,264,279,296,375,191,291,259,382,236,181,350,187,377,362,245,271,208,345,155,240,251,299,226,167,394,306,162,374,145,282,150,199,177,331,370,338,359,336,314,143,175,386,231,203,319,304,158,390,171,139,378,207,383,262,183,273,373,210,341,268,126,136,395,131,277,369,254,322,309,222,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV254-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.40 % Computer : n006.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sat Sep 26 13:23:27 UTC 2026
% 0.11/0.41 % CPUTime :
% 0.11/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.87/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.68/1.50 % [INFO] Parsing done (504ms).
% 2.68/1.52 % [INFO] Running in sequential loop mode.
% 3.47/1.91 % [INFO] eprover registered as external prover.
% 3.47/1.91 % [INFO] Scanning for conjecture ...
% 4.59/2.22 % [INFO] Found a conjecture (or negated_conjecture) and 2787 axioms. Running axiom selection ...
% 5.50/2.45 % [INFO] Axiom selection finished. Selected 122 axioms (removed 2665 axioms).
% 5.97/2.56 % [INFO] Problem is propositional (TPTP CNF).
% 5.97/2.57 % [INFO] Type checking passed.
% 5.97/2.57 % [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 ...
% 9.86/3.79 % External prover 'e' found a proof!
% 9.86/3.80 % [INFO] Killing All external provers ...
% 9.86/3.80 % Time passed: 3244ms (effective reasoning time: 2266ms)
% 10.21/3.80 % Axioms used in derivation (122): cls_Nat_Oadd__is__0_1, cls_Nat_Omult__cancel1_0, cls_Nat_Onot__gr0_0, cls_Divides_Odiv__mult__self1_0, cls_Nat_Onot__less0_0, cls_Nat_Oone__eq__mult__iff_0, cls_NatArith_Oadd__diff__assoc2_0, cls_Nat_Onat__add__left__cancel__less_1, cls_Nat_Onat__add__right__cancel_0, cls_Nat_Omult__le__cancel1_1, cls_Nat_Oop_A_K_Omult__Suc_0, cls_Binomial_Obinomial__Suc__n_0, cls_Nat_Oless__one_1, cls_Nat_Odiff__is__0__eq_0, cls_Nat_OSuc__Suc__eq_0, cls_Nat_Oop_A_K_Omult__0_0, cls_Nat_Odiff__0__eq__0_0, cls_Divides_Odiv__less_0, cls_Divides_Odiv__1_0, cls_Nat_Oless__irrefl_0, cls_Nat_Odiff__le__self_0, cls_Nat_Oadd__is__0_0, cls_Nat_Ozero__less__diff_1, clsarity_nat_47, cls_Nat_Omult__less__cancel2_1, cls_NatArith_Odiff__diff__right_0, cls_Divides_Odiv__mult__self__is__m_0, cls_Nat_Omult__0__right_0, cls_Nat_Onat__add__left__cancel__le_0, cls_Divides_Odiv__less__dividend_0, cls_Nat_Oadd__leE_1, cls_Nat_Omult__less__cancel1_1, cls_Nat_Omult__eq__1__iff_0, cls_Nat_Oadd__gr__0_2, cls_Nat_Onat__add__left__cancel__less_0, cls_Nat_Oless__one_0, cls_Nat_Odiff__Suc__Suc_0, cls_Nat_Omult__eq__1__iff_2, cls_Nat_Omult__le__cancel1_0, cls_Nat_Ole__add__diff__inverse2_0, clsarity_nat_44, cls_Nat_Omult__less__cancel2_0, cls_Nat_Omult__le__cancel2_2, cls_Nat_Omult__cancel1_1, cls_Nat_Onat__0__less__mult__iff_0, cls_Divides_Odiv__mult__mult2_0, cls_Nat_Ole__0__eq_0, cls_Divides_Odiv__mult__self1__is__m_0, cls_NatArith_Odiff__less_0, cls_Divides_ODIVISION__BY__ZERO__DIV_0, cls_Nat_Ozero__less__diff_0, cls_Nat_Oone__le__mult__iff_1, cls_Nat_OSuc__le__mono_0, cls_Nat_OSuc__less__eq_1, cls_Nat_Omult__cancel2_0, cls_Nat_Omult__less__cancel1_0, cls_Nat_Onat__add__left__cancel__le_1, cls_Nat_Ozero__less__Suc_0, cls_Nat_Odiff__self__eq__0_0, cls_Nat_OSuc__diff__diff_0, cls_Nat_Omult__cancel2_1, cls_Nat_Onat__0__less__mult__iff_1, cls_Binomial_Obinomial__n__n_0, cls_NatArith_Odiff__Suc__diff__eq2_0, cls_Nat_OSuc__le__mono_1, cls_Binomial_Obinomial__Suc__Suc_0, cls_Nat_Oadd__leE_0, cls_Wellfounded__Relations_Otrans__less__than_0, cls_Nat_Oadd__gr__0_0, cls_Nat_Odiff__is__0__eq_H_0, cls_Nat_Oop_A_N_Odiff__0_0, cls_Nat_Oless__Suc0_0, cls_Nat_Onot__add__less1_0, cls_NatArith_Odiff__diff__cancel_0, cls_Nat_Oadd__is__0_2, clsarity_nat_12, cls_Nat_OOne__nat__def_0, cls_Nat_Omult__le__cancel2_1, cls_Nat_Oone__eq__mult__iff_2, cls_Nat_Odiff__Suc__less_0, cls_Nat_Oadd__0__right_0, cls_Nat_Ole__add__diff__inverse_0, cls_Binomial_Obinomial__n__0_0, cls_Nat_Oadd__Suc__right_0, cls_Nat_Onot__gr0_1, cls_Nat_Onot__add__less2_0, cls_NatArith_Odiff__Suc__diff__eq1_0, cls_Nat_Oone__le__mult__iff_0, cls_Nat_Odiff__diff__left_0, cls_NatArith_Oadd__diff__assoc_0, cls_Binomial_Obinomial__1_0, cls_Divides_Odiv__mult__self2_0, cls_Divides_Odiv__0_0, cls_Divides_Odiv__mult__mult1_0, cls_Nat_OSuc__not__Zero_0, cls_Nat_Omult__less__cancel1_2, cls_Nat_Oless__Suc0_1, cls_Nat_Onat__add__left__cancel_0, cls_Nat_Onat__0__less__mult__iff_2, clsarity_nat_8, cls_Nat_Oone__le__mult__iff_2, clsarity_nat_24, cls_Nat_Ole0_0, cls_Nat_OSuc__less__eq_0, cls_IntDef_Oint__0__neq__1_0, cls_Nat_Oop_A_L_Oadd__0_0, cls_Nat_Oadd__gr__0_1, cls_Nat_Ole__0__eq_1, cls_Nat_Omult__le__cancel1_2, cls_Divides_Odiv__le__dividend_0, cls_Nat_Oop_A_L_Oadd__Suc_0, cls_Nat_Omult__le__cancel2_0, cls_Nat_OZero__not__Suc_0, cls_Nat_OlessI_0, cls_Nat_Omult__less__cancel2_2, cls_Nat_OSuc__pred_0, cls_Divides_Odiv__self_0, cls_Nat_Omult__eq__1__iff_1, cls_Nat_Omult__Suc__right_0, cls_Nat_Omult__is__0_0, cls_Nat_Oone__eq__mult__iff_1, cls_Binomial_Obinomial__0__Suc_0
% 10.21/3.80 % No. of inferences in proof: 249
% 10.21/3.80 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3244 ms resp. 2266 ms w/o parsing
% 10.56/3.99 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.56/3.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------