TSTP Solution File: ANA002-4 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : ANA002-4 : TPTP v8.1.2. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 10:08:43 EDT 2023
% Result : Unsatisfiable 21.38s 4.33s
% Output : Refutation 21.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 27
% Syntax : Number of formulae : 104 ( 11 unt; 10 typ; 0 def)
% Number of atoms : 265 ( 81 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 818 ( 152 ~; 139 |; 0 &; 527 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 77 ( 0 ^; 77 !; 0 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
thf(less_than_or_equal_type,type,
less_than_or_equal: $i > $i > $o ).
thf(f_type,type,
f: $i > $i ).
thf(l_type,type,
l: $i ).
thf(n0_type,type,
n0: $i ).
thf(g_type,type,
g: $i > $i ).
thf(q_type,type,
q: $i > $i > $i ).
thf(k_type,type,
k: $i > $i ).
thf(lower_bound_type,type,
lower_bound: $i ).
thf(upper_bound_type,type,
upper_bound: $i ).
thf(h_type,type,
h: $i > $i ).
thf(13,axiom,
less_than_or_equal @ ( f @ lower_bound ) @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_mapping) ).
thf(40,plain,
less_than_or_equal @ ( f @ lower_bound ) @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1,negated_conjecture,
( ~ ( less_than_or_equal @ ( f @ l ) @ n0 )
| ~ ( less_than_or_equal @ n0 @ ( f @ l ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_x_which_crosses) ).
thf(18,plain,
( ~ ( less_than_or_equal @ ( f @ l ) @ n0 )
| ~ ( less_than_or_equal @ n0 @ ( f @ l ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(19,plain,
( ~ ( less_than_or_equal @ ( f @ l ) @ n0 )
| ~ ( less_than_or_equal @ n0 @ ( f @ l ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(52,plain,
( ~ ( less_than_or_equal @ n0 @ ( f @ l ) )
| ( ( less_than_or_equal @ ( f @ lower_bound ) @ n0 )
!= ( less_than_or_equal @ ( f @ l ) @ n0 ) ) ),
inference(paramod_ordered,[status(thm)],[40,19]) ).
thf(59,plain,
( ~ ( less_than_or_equal @ n0 @ ( f @ l ) )
| ( ( f @ lower_bound )
!= ( f @ l ) )
| ( n0 != n0 ) ),
inference(simp,[status(thm)],[52]) ).
thf(69,plain,
( ~ ( less_than_or_equal @ n0 @ ( f @ l ) )
| ( ( f @ lower_bound )
!= ( f @ l ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(10,axiom,
less_than_or_equal @ n0 @ ( f @ upper_bound ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upper_mapping) ).
thf(36,plain,
less_than_or_equal @ n0 @ ( f @ upper_bound ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(55,plain,
( ~ ( less_than_or_equal @ ( f @ l ) @ n0 )
| ( ( less_than_or_equal @ n0 @ ( f @ upper_bound ) )
!= ( less_than_or_equal @ n0 @ ( f @ l ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,19]) ).
thf(63,plain,
( ~ ( less_than_or_equal @ ( f @ l ) @ n0 )
| ( n0 != n0 )
| ( ( f @ upper_bound )
!= ( f @ l ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(71,plain,
( ~ ( less_than_or_equal @ ( f @ l ) @ n0 )
| ( ( f @ upper_bound )
!= ( f @ l ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(329,plain,
( ( ( f @ upper_bound )
!= ( f @ l ) )
| ( ( less_than_or_equal @ ( f @ lower_bound ) @ n0 )
!= ( less_than_or_equal @ ( f @ l ) @ n0 ) ) ),
inference(paramod_ordered,[status(thm)],[40,71]) ).
thf(365,plain,
( ( upper_bound != l )
| ( ( f @ lower_bound )
!= ( f @ l ) )
| ( n0 != n0 ) ),
inference(simp,[status(thm)],[329]) ).
thf(379,plain,
( ( upper_bound != l )
| ( ( f @ lower_bound )
!= ( f @ l ) ) ),
inference(simp,[status(thm)],[365]) ).
thf(16,axiom,
! [A: $i] :
( ( less_than_or_equal @ ( g @ A ) @ upper_bound )
| ( less_than_or_equal @ l @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',crossover2_and_g_function1) ).
thf(44,plain,
! [A: $i] :
( ( less_than_or_equal @ ( g @ A ) @ upper_bound )
| ( less_than_or_equal @ l @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(45,plain,
! [A: $i] :
( ( less_than_or_equal @ ( g @ A ) @ upper_bound )
| ( less_than_or_equal @ l @ A ) ),
inference(cnf,[status(esa)],[44]) ).
thf(3,axiom,
! [A: $i] :
( ~ ( less_than_or_equal @ ( g @ A ) @ A )
| ( less_than_or_equal @ l @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',crossover4_and_g_function3) ).
thf(22,plain,
! [A: $i] :
( ~ ( less_than_or_equal @ ( g @ A ) @ A )
| ( less_than_or_equal @ l @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(23,plain,
! [A: $i] :
( ~ ( less_than_or_equal @ ( g @ A ) @ A )
| ( less_than_or_equal @ l @ A ) ),
inference(cnf,[status(esa)],[22]) ).
thf(173,plain,
! [B: $i,A: $i] :
( ( less_than_or_equal @ l @ A )
| ( less_than_or_equal @ l @ B )
| ( ( less_than_or_equal @ ( g @ A ) @ upper_bound )
!= ( less_than_or_equal @ ( g @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[45,23]) ).
thf(174,plain,
( ( less_than_or_equal @ l @ upper_bound )
| ( less_than_or_equal @ l @ upper_bound ) ),
inference(pattern_uni,[status(thm)],[173:[bind(A,$thf( upper_bound )),bind(B,$thf( upper_bound ))]]) ).
thf(193,plain,
less_than_or_equal @ l @ upper_bound,
inference(simp,[status(thm)],[174]) ).
thf(318,plain,
( ( ( f @ upper_bound )
!= ( f @ l ) )
| ( ( less_than_or_equal @ ( f @ l ) @ n0 )
!= ( less_than_or_equal @ l @ upper_bound ) ) ),
inference(paramod_ordered,[status(thm)],[193,71]) ).
thf(344,plain,
( ( upper_bound != l )
| ( ( f @ l )
!= l )
| ( upper_bound != n0 ) ),
inference(simp,[status(thm)],[318]) ).
thf(317,plain,
( ~ ( less_than_or_equal @ ( f @ l ) @ n0 )
| ( upper_bound != l ) ),
inference(simp,[status(thm)],[71]) ).
thf(14,axiom,
! [A: $i] :
( ( less_than_or_equal @ A @ l )
| ~ ( less_than_or_equal @ A @ upper_bound )
| ~ ( less_than_or_equal @ ( f @ A ) @ n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',crossover1) ).
thf(41,plain,
! [A: $i] :
( ( less_than_or_equal @ A @ l )
| ~ ( less_than_or_equal @ A @ upper_bound )
| ~ ( less_than_or_equal @ ( f @ A ) @ n0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(114,plain,
( ( ( f @ lower_bound )
!= ( f @ l ) )
| ( ( less_than_or_equal @ n0 @ ( f @ upper_bound ) )
!= ( less_than_or_equal @ n0 @ ( f @ l ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,69]) ).
thf(129,plain,
( ( lower_bound != l )
| ( n0 != n0 )
| ( ( f @ upper_bound )
!= ( f @ l ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(134,plain,
( ( lower_bound != l )
| ( ( f @ upper_bound )
!= ( f @ l ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(7,axiom,
! [A: $i] :
( ( less_than_or_equal @ ( f @ ( g @ A ) ) @ n0 )
| ( less_than_or_equal @ l @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',crossover3_and_g_function2) ).
thf(30,plain,
! [A: $i] :
( ( less_than_or_equal @ ( f @ ( g @ A ) ) @ n0 )
| ( less_than_or_equal @ l @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(31,plain,
! [A: $i] :
( ( less_than_or_equal @ ( f @ ( g @ A ) ) @ n0 )
| ( less_than_or_equal @ l @ A ) ),
inference(cnf,[status(esa)],[30]) ).
thf(207,plain,
( ( lower_bound != l )
| ( upper_bound != l ) ),
inference(simp,[status(thm)],[134]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( less_than_or_equal @ ( q @ A @ B ) @ A )
| ( less_than_or_equal @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',interpolation2) ).
thf(24,plain,
! [B: $i,A: $i] :
( ~ ( less_than_or_equal @ ( q @ A @ B ) @ A )
| ( less_than_or_equal @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(128,plain,
( ( ( f @ lower_bound )
!= ( f @ l ) )
| ( n0 != n0 )
| ( ( f @ upper_bound )
!= ( f @ l ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(133,plain,
( ( ( f @ lower_bound )
!= ( f @ l ) )
| ( ( f @ upper_bound )
!= ( f @ l ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(1034,plain,
( ( ( f @ lower_bound )
!= ( f @ l ) )
| ( ( f @ upper_bound )
!= ( f @ lower_bound ) )
| ( ( f @ l )
!= ( f @ l ) ) ),
inference(eqfactor_ordered,[status(thm)],[133]) ).
thf(1046,plain,
( ( lower_bound != l )
| ( upper_bound != lower_bound ) ),
inference(simp,[status(thm)],[1034]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ~ ( less_than_or_equal @ A @ ( q @ B @ A ) )
| ( less_than_or_equal @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',interpolation1) ).
thf(37,plain,
! [B: $i,A: $i] :
( ~ ( less_than_or_equal @ A @ ( q @ B @ A ) )
| ( less_than_or_equal @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ~ ( less_than_or_equal @ ( q @ A @ B ) @ A )
| ( less_than_or_equal @ B @ A ) ),
inference(cnf,[status(esa)],[24]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( less_than_or_equal @ A @ B )
| ( less_than_or_equal @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_less) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( less_than_or_equal @ A @ B )
| ( less_than_or_equal @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,axiom,
! [A: $i] :
( ( less_than_or_equal @ n0 @ ( f @ A ) )
| ~ ( less_than_or_equal @ ( k @ A ) @ A )
| ~ ( less_than_or_equal @ lower_bound @ A )
| ~ ( less_than_or_equal @ A @ upper_bound ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity3) ).
thf(46,plain,
! [A: $i] :
( ( less_than_or_equal @ n0 @ ( f @ A ) )
| ~ ( less_than_or_equal @ ( k @ A ) @ A )
| ~ ( less_than_or_equal @ lower_bound @ A )
| ~ ( less_than_or_equal @ A @ upper_bound ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( less_than_or_equal @ ( f @ A ) @ n0 )
| ~ ( less_than_or_equal @ B @ A )
| ~ ( less_than_or_equal @ ( f @ B ) @ n0 )
| ( less_than_or_equal @ B @ ( h @ A ) )
| ~ ( less_than_or_equal @ lower_bound @ A )
| ~ ( less_than_or_equal @ A @ upper_bound ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity2) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( less_than_or_equal @ ( f @ A ) @ n0 )
| ~ ( less_than_or_equal @ B @ A )
| ~ ( less_than_or_equal @ ( f @ B ) @ n0 )
| ( less_than_or_equal @ B @ ( h @ A ) )
| ~ ( less_than_or_equal @ lower_bound @ A )
| ~ ( less_than_or_equal @ A @ upper_bound ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( less_than_or_equal @ ( f @ A ) @ n0 )
| ~ ( less_than_or_equal @ B @ A )
| ~ ( less_than_or_equal @ ( f @ B ) @ n0 )
| ( less_than_or_equal @ B @ ( h @ A ) )
| ~ ( less_than_or_equal @ lower_bound @ A )
| ~ ( less_than_or_equal @ A @ upper_bound ) ),
inference(cnf,[status(esa)],[28]) ).
thf(106,plain,
( ~ ( less_than_or_equal @ n0 @ ( f @ l ) )
| ( lower_bound != l ) ),
inference(simp,[status(thm)],[69]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( less_than_or_equal @ A @ B )
| ( less_than_or_equal @ B @ A ) ),
inference(cnf,[status(esa)],[20]) ).
thf(170,plain,
! [C: $i,B: $i,A: $i] :
( ( less_than_or_equal @ A @ B )
| ( less_than_or_equal @ l @ C )
| ( ( less_than_or_equal @ B @ A )
!= ( less_than_or_equal @ ( g @ C ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[21,23]) ).
thf(171,plain,
! [A: $i] :
( ( less_than_or_equal @ A @ ( g @ A ) )
| ( less_than_or_equal @ l @ A ) ),
inference(pattern_uni,[status(thm)],[170:[bind(A,$thf( A )),bind(B,$thf( g @ A )),bind(C,$thf( A ))]]) ).
thf(218,plain,
! [A: $i] :
( ( less_than_or_equal @ A @ ( g @ A ) )
| ( ( less_than_or_equal @ l @ A )
!= ( less_than_or_equal @ A @ ( g @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[171]) ).
thf(229,plain,
! [A: $i] :
( ( less_than_or_equal @ A @ ( g @ A ) )
| ( l != A )
| ( ( g @ A )
!= A ) ),
inference(simp,[status(thm)],[218]) ).
thf(238,plain,
( ( less_than_or_equal @ l @ ( g @ l ) )
| ( ( g @ l )
!= l ) ),
inference(simp,[status(thm)],[229]) ).
thf(12,axiom,
less_than_or_equal @ lower_bound @ upper_bound,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_interval) ).
thf(39,plain,
less_than_or_equal @ lower_bound @ upper_bound,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(111,plain,
( ( ( f @ lower_bound )
!= ( f @ l ) )
| ( ( less_than_or_equal @ lower_bound @ upper_bound )
!= ( less_than_or_equal @ n0 @ ( f @ l ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,69]) ).
thf(132,plain,
( ( lower_bound != l )
| ( lower_bound != n0 )
| ( ( f @ l )
!= upper_bound ) ),
inference(simp,[status(thm)],[111]) ).
thf(178,plain,
! [A: $i] :
( ( less_than_or_equal @ l @ A )
| ( ( less_than_or_equal @ ( g @ A ) @ A )
!= ( less_than_or_equal @ ( f @ lower_bound ) @ n0 ) ) ),
inference(paramod_ordered,[status(thm)],[40,23]) ).
thf(185,plain,
! [A: $i] :
( ( less_than_or_equal @ l @ A )
| ( ( g @ A )
!= ( f @ lower_bound ) )
| ( A != n0 ) ),
inference(simp,[status(thm)],[178]) ).
thf(192,plain,
( ( less_than_or_equal @ l @ n0 )
| ( ( g @ n0 )
!= ( f @ lower_bound ) ) ),
inference(simp,[status(thm)],[185]) ).
thf(140,plain,
! [A: $i] :
( ( less_than_or_equal @ l @ A )
| ( ( less_than_or_equal @ ( f @ ( g @ A ) ) @ n0 )
!= ( less_than_or_equal @ l @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[31]) ).
thf(147,plain,
! [A: $i] :
( ( less_than_or_equal @ l @ A )
| ( ( f @ ( g @ A ) )
!= l )
| ( n0 != A ) ),
inference(simp,[status(thm)],[140]) ).
thf(149,plain,
( ( less_than_or_equal @ l @ n0 )
| ( ( f @ ( g @ n0 ) )
!= l ) ),
inference(simp,[status(thm)],[147]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( less_than_or_equal @ A @ B )
| ~ ( less_than_or_equal @ A @ C )
| ~ ( less_than_or_equal @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( less_than_or_equal @ A @ B )
| ~ ( less_than_or_equal @ A @ C )
| ~ ( less_than_or_equal @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [A: $i] :
( ( less_than_or_equal @ ( f @ A ) @ n0 )
| ~ ( less_than_or_equal @ A @ ( h @ A ) )
| ~ ( less_than_or_equal @ lower_bound @ A )
| ~ ( less_than_or_equal @ A @ upper_bound ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity1) ).
thf(34,plain,
! [A: $i] :
( ( less_than_or_equal @ ( f @ A ) @ n0 )
| ~ ( less_than_or_equal @ A @ ( h @ A ) )
| ~ ( less_than_or_equal @ lower_bound @ A )
| ~ ( less_than_or_equal @ A @ upper_bound ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(194,plain,
( ( ( f @ lower_bound )
!= ( f @ l ) )
| ( ( less_than_or_equal @ n0 @ ( f @ l ) )
!= ( less_than_or_equal @ l @ upper_bound ) ) ),
inference(paramod_ordered,[status(thm)],[193,69]) ).
thf(204,plain,
( ( lower_bound != l )
| ( n0 != l )
| ( ( f @ l )
!= upper_bound ) ),
inference(simp,[status(thm)],[194]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( less_than_or_equal @ n0 @ ( f @ A ) )
| ~ ( less_than_or_equal @ A @ B )
| ~ ( less_than_or_equal @ n0 @ ( f @ B ) )
| ( less_than_or_equal @ ( k @ A ) @ B )
| ~ ( less_than_or_equal @ lower_bound @ A )
| ~ ( less_than_or_equal @ A @ upper_bound ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity4) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( less_than_or_equal @ n0 @ ( f @ A ) )
| ~ ( less_than_or_equal @ A @ B )
| ~ ( less_than_or_equal @ n0 @ ( f @ B ) )
| ( less_than_or_equal @ ( k @ A ) @ B )
| ~ ( less_than_or_equal @ lower_bound @ A )
| ~ ( less_than_or_equal @ A @ upper_bound ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( less_than_or_equal @ n0 @ ( f @ A ) )
| ~ ( less_than_or_equal @ A @ B )
| ~ ( less_than_or_equal @ n0 @ ( f @ B ) )
| ( less_than_or_equal @ ( k @ A ) @ B )
| ~ ( less_than_or_equal @ lower_bound @ A )
| ~ ( less_than_or_equal @ A @ upper_bound ) ),
inference(cnf,[status(esa)],[26]) ).
thf(248,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( less_than_or_equal @ B @ A )
| ( less_than_or_equal @ D @ C )
| ( ( less_than_or_equal @ A @ B )
!= ( less_than_or_equal @ ( q @ C @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[21,25]) ).
thf(249,plain,
! [B: $i,A: $i] :
( ( less_than_or_equal @ A @ ( q @ A @ B ) )
| ( less_than_or_equal @ B @ A ) ),
inference(pattern_uni,[status(thm)],[248:[bind(A,$thf( q @ B @ F )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( F ))]]) ).
thf(274,plain,
! [B: $i,A: $i] :
( ( less_than_or_equal @ A @ ( q @ A @ B ) )
| ( less_than_or_equal @ B @ A ) ),
inference(simp,[status(thm)],[249]) ).
thf(1044,plain,
( ( lower_bound != l )
| ( ( f @ upper_bound )
!= ( f @ lower_bound ) ) ),
inference(simp,[status(thm)],[1034]) ).
thf(15,axiom,
! [A: $i] : ( less_than_or_equal @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_less) ).
thf(43,plain,
! [A: $i] : ( less_than_or_equal @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(51,plain,
! [A: $i] :
( ~ ( less_than_or_equal @ ( f @ l ) @ n0 )
| ( ( less_than_or_equal @ A @ A )
!= ( less_than_or_equal @ n0 @ ( f @ l ) ) ) ),
inference(paramod_ordered,[status(thm)],[43,19]) ).
thf(64,plain,
! [A: $i] :
( ~ ( less_than_or_equal @ ( f @ l ) @ n0 )
| ( A != n0 )
| ( A
!= ( f @ l ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(67,plain,
( ~ ( less_than_or_equal @ ( f @ l ) @ n0 )
| ( ( f @ l )
!= n0 ) ),
inference(simp,[status(thm)],[64]) ).
thf(73,plain,
! [A: $i] :
( ( ( f @ l )
!= n0 )
| ( ( less_than_or_equal @ A @ A )
!= ( less_than_or_equal @ ( f @ l ) @ n0 ) ) ),
inference(paramod_ordered,[status(thm)],[43,67]) ).
thf(77,plain,
! [A: $i] :
( ( ( f @ l )
!= n0 )
| ( A
!= ( f @ l ) )
| ( A != n0 ) ),
inference(simp,[status(thm)],[73]) ).
thf(80,plain,
( ( f @ l )
!= n0 ),
inference(simp,[status(thm)],[77]) ).
thf(385,plain,
! [B: $i,A: $i] :
( ( less_than_or_equal @ B @ A )
| ( upper_bound != l )
| ( ( less_than_or_equal @ A @ B )
!= ( less_than_or_equal @ ( f @ l ) @ n0 ) ) ),
inference(paramod_ordered,[status(thm)],[21,317]) ).
thf(386,plain,
( ( less_than_or_equal @ n0 @ ( f @ l ) )
| ( upper_bound != l ) ),
inference(pattern_uni,[status(thm)],[385:[bind(A,$thf( f @ l )),bind(B,$thf( n0 ))]]) ).
thf(7240,plain,
$false,
inference(e,[status(thm)],[69,379,344,317,193,41,134,71,18,31,207,24,1046,37,25,20,46,29,106,238,132,133,28,192,21,45,149,32,34,22,44,204,27,274,39,1044,80,386,43,40,26,171,23,36,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : ANA002-4 : TPTP v8.1.2. Released v1.1.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n003.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 17:59:31 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.97/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.30/1.03 % [INFO] Parsing done (139ms).
% 1.30/1.04 % [INFO] Running in sequential loop mode.
% 1.68/1.31 % [INFO] eprover registered as external prover.
% 1.68/1.31 % [INFO] cvc4 registered as external prover.
% 1.68/1.32 % [INFO] Scanning for conjecture ...
% 1.90/1.38 % [INFO] Found a conjecture and 16 axioms. Running axiom selection ...
% 2.06/1.42 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.06/1.44 % [INFO] Problem is propositional (TPTP CNF).
% 2.06/1.45 % [INFO] Type checking passed.
% 2.06/1.45 % [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 ...
% 21.38/4.33 % External prover 'e' found a proof!
% 21.38/4.33 % [INFO] Killing All external provers ...
% 21.38/4.33 % Time passed: 3814ms (effective reasoning time: 3288ms)
% 21.38/4.33 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 21.38/4.33 % Axioms used in derivation (16): continuity1, continuity2, interpolation1, upper_mapping, continuity3, crossover3_and_g_function2, crossover2_and_g_function1, interpolation2, totality_of_less, continuity4, lower_mapping, crossover1, reflexivity_of_less, transitivity_of_less, the_interval, crossover4_and_g_function3
% 21.38/4.33 % No. of inferences in proof: 94
% 21.38/4.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3814 ms resp. 3288 ms w/o parsing
% 21.38/4.36 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 21.38/4.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------