%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ANA004-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:09:31 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.17s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 104 ( 59 unt; 0 typ; 0 def)
% Number of atoms : 494 ( 130 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1153 ( 88 ~; 130 |; 0 &; 935 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 191 ( 0 ^; 191 !; 0 ?; 191 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a_real_number,type,
a_real_number: $i ).
thf(tp_absolute,type,
absolute: $i > $i ).
thf(tp_add,type,
add: $i > $i > $i ).
thf(tp_delta_1,type,
delta_1: $i > $i ).
thf(tp_delta_2,type,
delta_2: $i > $i ).
thf(tp_epsilon_0,type,
epsilon_0: $i ).
thf(tp_f,type,
f: $i > $i ).
thf(tp_g,type,
g: $i > $i ).
thf(tp_half,type,
half: $i > $i ).
thf(tp_less_or_equal,type,
less_or_equal: $i > $i > $o ).
thf(tp_minimum,type,
minimum: $i > $i > $i ).
thf(tp_n0,type,
n0: $i ).
thf(tp_negate,type,
negate: $i > $i ).
thf(tp_xs,type,
xs: $i > $i ).
thf(1,axiom,
! [X: $i] :
( ( less_or_equal @ X @ n0 )
| ~ ( less_or_equal @ ( half @ X ) @ n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_and_half) ).
thf(2,axiom,
! [X: $i,Z: $i,Y: $i] :
( ~ ( less_or_equal @ X @ ( half @ Z ) )
| ~ ( less_or_equal @ Y @ ( half @ Z ) )
| ( less_or_equal @ ( add @ X @ Y ) @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_sum_of_halves) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ( less_or_equal @ X @ n0 )
| ( less_or_equal @ Y @ n0 )
| ~ ( less_or_equal @ ( minimum @ X @ Y ) @ n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minimum9) ).
thf(4,axiom,
! [Z: $i,X: $i,Y: $i] :
( ~ ( less_or_equal @ Z @ ( minimum @ X @ Y ) )
| ( less_or_equal @ Z @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minimum7) ).
thf(5,axiom,
! [Z: $i,X: $i,Y: $i] :
( ~ ( less_or_equal @ Z @ ( minimum @ X @ Y ) )
| ( less_or_equal @ Z @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minimum3) ).
thf(6,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( less_or_equal @ ( add @ ( absolute @ X ) @ ( absolute @ Y ) ) @ Z )
| ( less_or_equal @ ( absolute @ ( add @ X @ Y ) ) @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absolute_sum_less_or_equal_sum_of_absolutes2) ).
thf(7,axiom,
! [Delta: $i] :
( ( less_or_equal @ Delta @ n0 )
| ( less_or_equal @ ( absolute @ ( add @ ( xs @ Delta ) @ ( negate @ a_real_number ) ) ) @ Delta ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
thf(8,axiom,
~ ( less_or_equal @ epsilon_0 @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
thf(9,axiom,
! [Epsilon: $i,Z: $i] :
( ( less_or_equal @ Epsilon @ n0 )
| ~ ( less_or_equal @ ( absolute @ ( add @ Z @ ( negate @ a_real_number ) ) ) @ ( delta_2 @ Epsilon ) )
| ( less_or_equal @ ( absolute @ ( add @ ( g @ Z ) @ ( negate @ ( g @ a_real_number ) ) ) ) @ Epsilon ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
thf(10,axiom,
! [Epsilon: $i,Z: $i] :
( ( less_or_equal @ Epsilon @ n0 )
| ~ ( less_or_equal @ ( absolute @ ( add @ Z @ ( negate @ a_real_number ) ) ) @ ( delta_1 @ Epsilon ) )
| ( less_or_equal @ ( absolute @ ( add @ ( f @ Z ) @ ( negate @ ( f @ a_real_number ) ) ) ) @ Epsilon ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
thf(11,axiom,
! [Epsilon: $i] :
( ( less_or_equal @ Epsilon @ n0 )
| ~ ( less_or_equal @ ( delta_2 @ Epsilon ) @ n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
thf(12,axiom,
! [Epsilon: $i] :
( ( less_or_equal @ Epsilon @ n0 )
| ~ ( less_or_equal @ ( delta_1 @ Epsilon ) @ n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
thf(13,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(14,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[13]) ).
thf(15,negated_conjecture,
! [Delta: $i] :
( ( less_or_equal @ Delta @ n0 )
| ~ ( less_or_equal @ ( absolute @ ( add @ ( add @ ( f @ ( xs @ Delta ) ) @ ( negate @ ( f @ a_real_number ) ) ) @ ( add @ ( g @ ( xs @ Delta ) ) @ ( negate @ ( g @ a_real_number ) ) ) ) ) @ epsilon_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7_1) ).
thf(16,plain,
$false = $false,
inference(unfold_def,[status(thm)],[14]) ).
thf(17,plain,
( ( ! [X: $i] :
( ( less_or_equal @ X @ n0 )
| ~ ( less_or_equal @ ( half @ X ) @ n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(18,plain,
( ( ! [X: $i,Z: $i,Y: $i] :
( ~ ( less_or_equal @ X @ ( half @ Z ) )
| ~ ( less_or_equal @ Y @ ( half @ Z ) )
| ( less_or_equal @ ( add @ X @ Y ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(19,plain,
( ( ! [X: $i,Y: $i] :
( ( less_or_equal @ X @ n0 )
| ( less_or_equal @ Y @ n0 )
| ~ ( less_or_equal @ ( minimum @ X @ Y ) @ n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( less_or_equal @ Z @ ( minimum @ X @ Y ) )
| ( less_or_equal @ Z @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(21,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( less_or_equal @ Z @ ( minimum @ X @ Y ) )
| ( less_or_equal @ Z @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(22,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( less_or_equal @ ( add @ ( absolute @ X ) @ ( absolute @ Y ) ) @ Z )
| ( less_or_equal @ ( absolute @ ( add @ X @ Y ) ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(23,plain,
( ( ! [Delta: $i] :
( ( less_or_equal @ Delta @ n0 )
| ( less_or_equal @ ( absolute @ ( add @ ( xs @ Delta ) @ ( negate @ a_real_number ) ) ) @ Delta ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(24,plain,
( ( ~ ( less_or_equal @ epsilon_0 @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(25,plain,
( ( ! [Epsilon: $i,Z: $i] :
( ( less_or_equal @ Epsilon @ n0 )
| ~ ( less_or_equal @ ( absolute @ ( add @ Z @ ( negate @ a_real_number ) ) ) @ ( delta_2 @ Epsilon ) )
| ( less_or_equal @ ( absolute @ ( add @ ( g @ Z ) @ ( negate @ ( g @ a_real_number ) ) ) ) @ Epsilon ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(26,plain,
( ( ! [Epsilon: $i,Z: $i] :
( ( less_or_equal @ Epsilon @ n0 )
| ~ ( less_or_equal @ ( absolute @ ( add @ Z @ ( negate @ a_real_number ) ) ) @ ( delta_1 @ Epsilon ) )
| ( less_or_equal @ ( absolute @ ( add @ ( f @ Z ) @ ( negate @ ( f @ a_real_number ) ) ) ) @ Epsilon ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(27,plain,
( ( ! [Epsilon: $i] :
( ( less_or_equal @ Epsilon @ n0 )
| ~ ( less_or_equal @ ( delta_2 @ Epsilon ) @ n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(28,plain,
( ( ! [Epsilon: $i] :
( ( less_or_equal @ Epsilon @ n0 )
| ~ ( less_or_equal @ ( delta_1 @ Epsilon ) @ n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(29,plain,
( ( ! [Delta: $i] :
( ( less_or_equal @ Delta @ n0 )
| ~ ( less_or_equal @ ( absolute @ ( add @ ( add @ ( f @ ( xs @ Delta ) ) @ ( negate @ ( f @ a_real_number ) ) ) @ ( add @ ( g @ ( xs @ Delta ) ) @ ( negate @ ( g @ a_real_number ) ) ) ) ) @ epsilon_0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(30,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(31,plain,
( ( ! [X: $i,Z: $i] :
( ~ ( less_or_equal @ X @ ( half @ Z ) )
| ! [Y: $i] :
( ~ ( less_or_equal @ Y @ ( half @ Z ) )
| ( less_or_equal @ ( add @ X @ Y ) @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(32,plain,
( ( ! [X: $i] :
( ( less_or_equal @ X @ n0 )
| ! [Y: $i] :
( ( less_or_equal @ Y @ n0 )
| ~ ( less_or_equal @ ( minimum @ X @ Y ) @ n0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(33,plain,
( ( ! [Z: $i,X: $i] :
( ! [Y: $i] :
~ ( less_or_equal @ Z @ ( minimum @ X @ Y ) )
| ( less_or_equal @ Z @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(34,plain,
( ( ! [Epsilon: $i] :
( ( less_or_equal @ Epsilon @ n0 )
| ! [Z: $i] :
( ~ ( less_or_equal @ ( absolute @ ( add @ Z @ ( negate @ a_real_number ) ) ) @ ( delta_2 @ Epsilon ) )
| ( less_or_equal @ ( absolute @ ( add @ ( g @ Z ) @ ( negate @ ( g @ a_real_number ) ) ) ) @ Epsilon ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(35,plain,
( ( ! [Epsilon: $i] :
( ( less_or_equal @ Epsilon @ n0 )
| ! [Z: $i] :
( ~ ( less_or_equal @ ( absolute @ ( add @ Z @ ( negate @ a_real_number ) ) ) @ ( delta_1 @ Epsilon ) )
| ( less_or_equal @ ( absolute @ ( add @ ( f @ Z ) @ ( negate @ ( f @ a_real_number ) ) ) ) @ Epsilon ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(36,plain,
( ( ! [Delta: $i] :
( ( less_or_equal @ Delta @ n0 )
| ~ ( less_or_equal @ ( absolute @ ( add @ ( add @ ( f @ ( xs @ Delta ) ) @ ( negate @ ( f @ a_real_number ) ) ) @ ( add @ ( g @ ( xs @ Delta ) ) @ ( negate @ ( g @ a_real_number ) ) ) ) ) @ epsilon_0 ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(37,plain,
( ( ! [Epsilon: $i] :
( ( less_or_equal @ Epsilon @ n0 )
| ~ ( less_or_equal @ ( delta_1 @ Epsilon ) @ n0 ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(38,plain,
( ( ! [Epsilon: $i] :
( ( less_or_equal @ Epsilon @ n0 )
| ~ ( less_or_equal @ ( delta_2 @ Epsilon ) @ n0 ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(39,plain,
( ( ! [Epsilon: $i] :
( ( less_or_equal @ Epsilon @ n0 )
| ! [Z: $i] :
( ~ ( less_or_equal @ ( absolute @ ( add @ Z @ ( negate @ a_real_number ) ) ) @ ( delta_1 @ Epsilon ) )
| ( less_or_equal @ ( absolute @ ( add @ ( f @ Z ) @ ( negate @ ( f @ a_real_number ) ) ) ) @ Epsilon ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(40,plain,
( ( ! [Epsilon: $i] :
( ( less_or_equal @ Epsilon @ n0 )
| ! [Z: $i] :
( ~ ( less_or_equal @ ( absolute @ ( add @ Z @ ( negate @ a_real_number ) ) ) @ ( delta_2 @ Epsilon ) )
| ( less_or_equal @ ( absolute @ ( add @ ( g @ Z ) @ ( negate @ ( g @ a_real_number ) ) ) ) @ Epsilon ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(41,plain,
( ( ~ ( less_or_equal @ epsilon_0 @ n0 ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(42,plain,
( ( ! [Delta: $i] :
( ( less_or_equal @ Delta @ n0 )
| ( less_or_equal @ ( absolute @ ( add @ ( xs @ Delta ) @ ( negate @ a_real_number ) ) ) @ Delta ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(43,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( less_or_equal @ ( add @ ( absolute @ X ) @ ( absolute @ Y ) ) @ Z )
| ( less_or_equal @ ( absolute @ ( add @ X @ Y ) ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(44,plain,
( ( ! [Z: $i,X: $i] :
( ! [Y: $i] :
~ ( less_or_equal @ Z @ ( minimum @ X @ Y ) )
| ( less_or_equal @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(45,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( less_or_equal @ Z @ ( minimum @ X @ Y ) )
| ( less_or_equal @ Z @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(46,plain,
( ( ! [X: $i] :
( ( less_or_equal @ X @ n0 )
| ! [Y: $i] :
( ( less_or_equal @ Y @ n0 )
| ~ ( less_or_equal @ ( minimum @ X @ Y ) @ n0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(47,plain,
( ( ! [X: $i,Z: $i] :
( ~ ( less_or_equal @ X @ ( half @ Z ) )
| ! [Y: $i] :
( ~ ( less_or_equal @ Y @ ( half @ Z ) )
| ( less_or_equal @ ( add @ X @ Y ) @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(48,plain,
( ( ! [X: $i] :
( ( less_or_equal @ X @ n0 )
| ~ ( less_or_equal @ ( half @ X ) @ n0 ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(49,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[30]) ).
thf(50,plain,
! [SV1: $i] :
( ( ( less_or_equal @ SV1 @ n0 )
| ~ ( less_or_equal @ ( absolute @ ( add @ ( add @ ( f @ ( xs @ SV1 ) ) @ ( negate @ ( f @ a_real_number ) ) ) @ ( add @ ( g @ ( xs @ SV1 ) ) @ ( negate @ ( g @ a_real_number ) ) ) ) ) @ epsilon_0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(51,plain,
! [SV2: $i] :
( ( ( less_or_equal @ SV2 @ n0 )
| ~ ( less_or_equal @ ( delta_1 @ SV2 ) @ n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(52,plain,
! [SV3: $i] :
( ( ( less_or_equal @ SV3 @ n0 )
| ~ ( less_or_equal @ ( delta_2 @ SV3 ) @ n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(53,plain,
! [SV4: $i] :
( ( ( less_or_equal @ SV4 @ n0 )
| ! [SY23: $i] :
( ~ ( less_or_equal @ ( absolute @ ( add @ SY23 @ ( negate @ a_real_number ) ) ) @ ( delta_1 @ SV4 ) )
| ( less_or_equal @ ( absolute @ ( add @ ( f @ SY23 ) @ ( negate @ ( f @ a_real_number ) ) ) ) @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(54,plain,
! [SV5: $i] :
( ( ( less_or_equal @ SV5 @ n0 )
| ! [SY24: $i] :
( ~ ( less_or_equal @ ( absolute @ ( add @ SY24 @ ( negate @ a_real_number ) ) ) @ ( delta_2 @ SV5 ) )
| ( less_or_equal @ ( absolute @ ( add @ ( g @ SY24 ) @ ( negate @ ( g @ a_real_number ) ) ) ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(55,plain,
( ( less_or_equal @ epsilon_0 @ n0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(56,plain,
! [SV6: $i] :
( ( ( less_or_equal @ SV6 @ n0 )
| ( less_or_equal @ ( absolute @ ( add @ ( xs @ SV6 ) @ ( negate @ a_real_number ) ) ) @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(57,plain,
! [SV7: $i] :
( ( ! [SY25: $i,SY26: $i] :
( ~ ( less_or_equal @ ( add @ ( absolute @ SV7 ) @ ( absolute @ SY25 ) ) @ SY26 )
| ( less_or_equal @ ( absolute @ ( add @ SV7 @ SY25 ) ) @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(58,plain,
! [SV8: $i] :
( ( ! [SY27: $i] :
( ! [SY28: $i] :
~ ( less_or_equal @ SV8 @ ( minimum @ SY27 @ SY28 ) )
| ( less_or_equal @ SV8 @ SY27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(59,plain,
! [SV9: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ~ ( less_or_equal @ SV9 @ ( minimum @ SY29 @ SY30 ) )
| ( less_or_equal @ SV9 @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(60,plain,
! [SV10: $i] :
( ( ( less_or_equal @ SV10 @ n0 )
| ! [SY31: $i] :
( ( less_or_equal @ SY31 @ n0 )
| ~ ( less_or_equal @ ( minimum @ SV10 @ SY31 ) @ n0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(61,plain,
! [SV11: $i] :
( ( ! [SY32: $i] :
( ~ ( less_or_equal @ SV11 @ ( half @ SY32 ) )
| ! [SY33: $i] :
( ~ ( less_or_equal @ SY33 @ ( half @ SY32 ) )
| ( less_or_equal @ ( add @ SV11 @ SY33 ) @ SY32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(62,plain,
! [SV12: $i] :
( ( ( less_or_equal @ SV12 @ n0 )
| ~ ( less_or_equal @ ( half @ SV12 ) @ n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(63,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(64,plain,
! [SV1: $i] :
( ( ( less_or_equal @ SV1 @ n0 )
= $true )
| ( ( ~ ( less_or_equal @ ( absolute @ ( add @ ( add @ ( f @ ( xs @ SV1 ) ) @ ( negate @ ( f @ a_real_number ) ) ) @ ( add @ ( g @ ( xs @ SV1 ) ) @ ( negate @ ( g @ a_real_number ) ) ) ) ) @ epsilon_0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(65,plain,
! [SV2: $i] :
( ( ( less_or_equal @ SV2 @ n0 )
= $true )
| ( ( ~ ( less_or_equal @ ( delta_1 @ SV2 ) @ n0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(66,plain,
! [SV3: $i] :
( ( ( less_or_equal @ SV3 @ n0 )
= $true )
| ( ( ~ ( less_or_equal @ ( delta_2 @ SV3 ) @ n0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(67,plain,
! [SV4: $i] :
( ( ( less_or_equal @ SV4 @ n0 )
= $true )
| ( ( ! [SY23: $i] :
( ~ ( less_or_equal @ ( absolute @ ( add @ SY23 @ ( negate @ a_real_number ) ) ) @ ( delta_1 @ SV4 ) )
| ( less_or_equal @ ( absolute @ ( add @ ( f @ SY23 ) @ ( negate @ ( f @ a_real_number ) ) ) ) @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(68,plain,
! [SV5: $i] :
( ( ( less_or_equal @ SV5 @ n0 )
= $true )
| ( ( ! [SY24: $i] :
( ~ ( less_or_equal @ ( absolute @ ( add @ SY24 @ ( negate @ a_real_number ) ) ) @ ( delta_2 @ SV5 ) )
| ( less_or_equal @ ( absolute @ ( add @ ( g @ SY24 ) @ ( negate @ ( g @ a_real_number ) ) ) ) @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(69,plain,
! [SV6: $i] :
( ( ( less_or_equal @ SV6 @ n0 )
= $true )
| ( ( less_or_equal @ ( absolute @ ( add @ ( xs @ SV6 ) @ ( negate @ a_real_number ) ) ) @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(70,plain,
! [SV13: $i,SV7: $i] :
( ( ! [SY34: $i] :
( ~ ( less_or_equal @ ( add @ ( absolute @ SV7 ) @ ( absolute @ SV13 ) ) @ SY34 )
| ( less_or_equal @ ( absolute @ ( add @ SV7 @ SV13 ) ) @ SY34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(71,plain,
! [SV14: $i,SV8: $i] :
( ( ! [SY35: $i] :
~ ( less_or_equal @ SV8 @ ( minimum @ SV14 @ SY35 ) )
| ( less_or_equal @ SV8 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(72,plain,
! [SV15: $i,SV9: $i] :
( ( ! [SY36: $i] :
( ~ ( less_or_equal @ SV9 @ ( minimum @ SV15 @ SY36 ) )
| ( less_or_equal @ SV9 @ SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(73,plain,
! [SV10: $i] :
( ( ( less_or_equal @ SV10 @ n0 )
= $true )
| ( ( ! [SY31: $i] :
( ( less_or_equal @ SY31 @ n0 )
| ~ ( less_or_equal @ ( minimum @ SV10 @ SY31 ) @ n0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(74,plain,
! [SV16: $i,SV11: $i] :
( ( ~ ( less_or_equal @ SV11 @ ( half @ SV16 ) )
| ! [SY37: $i] :
( ~ ( less_or_equal @ SY37 @ ( half @ SV16 ) )
| ( less_or_equal @ ( add @ SV11 @ SY37 ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(75,plain,
! [SV12: $i] :
( ( ( less_or_equal @ SV12 @ n0 )
= $true )
| ( ( ~ ( less_or_equal @ ( half @ SV12 ) @ n0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(76,plain,
! [SV1: $i] :
( ( ( less_or_equal @ ( absolute @ ( add @ ( add @ ( f @ ( xs @ SV1 ) ) @ ( negate @ ( f @ a_real_number ) ) ) @ ( add @ ( g @ ( xs @ SV1 ) ) @ ( negate @ ( g @ a_real_number ) ) ) ) ) @ epsilon_0 )
= $false )
| ( ( less_or_equal @ SV1 @ n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(77,plain,
! [SV2: $i] :
( ( ( less_or_equal @ ( delta_1 @ SV2 ) @ n0 )
= $false )
| ( ( less_or_equal @ SV2 @ n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(78,plain,
! [SV3: $i] :
( ( ( less_or_equal @ ( delta_2 @ SV3 ) @ n0 )
= $false )
| ( ( less_or_equal @ SV3 @ n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(79,plain,
! [SV4: $i,SV17: $i] :
( ( ( ~ ( less_or_equal @ ( absolute @ ( add @ SV17 @ ( negate @ a_real_number ) ) ) @ ( delta_1 @ SV4 ) )
| ( less_or_equal @ ( absolute @ ( add @ ( f @ SV17 ) @ ( negate @ ( f @ a_real_number ) ) ) ) @ SV4 ) )
= $true )
| ( ( less_or_equal @ SV4 @ n0 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(80,plain,
! [SV5: $i,SV18: $i] :
( ( ( ~ ( less_or_equal @ ( absolute @ ( add @ SV18 @ ( negate @ a_real_number ) ) ) @ ( delta_2 @ SV5 ) )
| ( less_or_equal @ ( absolute @ ( add @ ( g @ SV18 ) @ ( negate @ ( g @ a_real_number ) ) ) ) @ SV5 ) )
= $true )
| ( ( less_or_equal @ SV5 @ n0 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(81,plain,
! [SV19: $i,SV13: $i,SV7: $i] :
( ( ~ ( less_or_equal @ ( add @ ( absolute @ SV7 ) @ ( absolute @ SV13 ) ) @ SV19 )
| ( less_or_equal @ ( absolute @ ( add @ SV7 @ SV13 ) ) @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(82,plain,
! [SV14: $i,SV8: $i] :
( ( ( ! [SY35: $i] :
~ ( less_or_equal @ SV8 @ ( minimum @ SV14 @ SY35 ) ) )
= $true )
| ( ( less_or_equal @ SV8 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(83,plain,
! [SV20: $i,SV15: $i,SV9: $i] :
( ( ~ ( less_or_equal @ SV9 @ ( minimum @ SV15 @ SV20 ) )
| ( less_or_equal @ SV9 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(84,plain,
! [SV10: $i,SV21: $i] :
( ( ( ( less_or_equal @ SV21 @ n0 )
| ~ ( less_or_equal @ ( minimum @ SV10 @ SV21 ) @ n0 ) )
= $true )
| ( ( less_or_equal @ SV10 @ n0 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(85,plain,
! [SV16: $i,SV11: $i] :
( ( ( ~ ( less_or_equal @ SV11 @ ( half @ SV16 ) ) )
= $true )
| ( ( ! [SY37: $i] :
( ~ ( less_or_equal @ SY37 @ ( half @ SV16 ) )
| ( less_or_equal @ ( add @ SV11 @ SY37 ) @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(86,plain,
! [SV12: $i] :
( ( ( less_or_equal @ ( half @ SV12 ) @ n0 )
= $false )
| ( ( less_or_equal @ SV12 @ n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(87,plain,
! [SV4: $i,SV17: $i] :
( ( ( ~ ( less_or_equal @ ( absolute @ ( add @ SV17 @ ( negate @ a_real_number ) ) ) @ ( delta_1 @ SV4 ) ) )
= $true )
| ( ( less_or_equal @ ( absolute @ ( add @ ( f @ SV17 ) @ ( negate @ ( f @ a_real_number ) ) ) ) @ SV4 )
= $true )
| ( ( less_or_equal @ SV4 @ n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(88,plain,
! [SV5: $i,SV18: $i] :
( ( ( ~ ( less_or_equal @ ( absolute @ ( add @ SV18 @ ( negate @ a_real_number ) ) ) @ ( delta_2 @ SV5 ) ) )
= $true )
| ( ( less_or_equal @ ( absolute @ ( add @ ( g @ SV18 ) @ ( negate @ ( g @ a_real_number ) ) ) ) @ SV5 )
= $true )
| ( ( less_or_equal @ SV5 @ n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(89,plain,
! [SV19: $i,SV13: $i,SV7: $i] :
( ( ( ~ ( less_or_equal @ ( add @ ( absolute @ SV7 ) @ ( absolute @ SV13 ) ) @ SV19 ) )
= $true )
| ( ( less_or_equal @ ( absolute @ ( add @ SV7 @ SV13 ) ) @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(90,plain,
! [SV22: $i,SV14: $i,SV8: $i] :
( ( ( ~ ( less_or_equal @ SV8 @ ( minimum @ SV14 @ SV22 ) ) )
= $true )
| ( ( less_or_equal @ SV8 @ SV14 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(91,plain,
! [SV20: $i,SV15: $i,SV9: $i] :
( ( ( ~ ( less_or_equal @ SV9 @ ( minimum @ SV15 @ SV20 ) ) )
= $true )
| ( ( less_or_equal @ SV9 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(92,plain,
! [SV10: $i,SV21: $i] :
( ( ( less_or_equal @ SV21 @ n0 )
= $true )
| ( ( ~ ( less_or_equal @ ( minimum @ SV10 @ SV21 ) @ n0 ) )
= $true )
| ( ( less_or_equal @ SV10 @ n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(93,plain,
! [SV16: $i,SV11: $i] :
( ( ( less_or_equal @ SV11 @ ( half @ SV16 ) )
= $false )
| ( ( ! [SY37: $i] :
( ~ ( less_or_equal @ SY37 @ ( half @ SV16 ) )
| ( less_or_equal @ ( add @ SV11 @ SY37 ) @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(94,plain,
! [SV4: $i,SV17: $i] :
( ( ( less_or_equal @ ( absolute @ ( add @ SV17 @ ( negate @ a_real_number ) ) ) @ ( delta_1 @ SV4 ) )
= $false )
| ( ( less_or_equal @ ( absolute @ ( add @ ( f @ SV17 ) @ ( negate @ ( f @ a_real_number ) ) ) ) @ SV4 )
= $true )
| ( ( less_or_equal @ SV4 @ n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(95,plain,
! [SV5: $i,SV18: $i] :
( ( ( less_or_equal @ ( absolute @ ( add @ SV18 @ ( negate @ a_real_number ) ) ) @ ( delta_2 @ SV5 ) )
= $false )
| ( ( less_or_equal @ ( absolute @ ( add @ ( g @ SV18 ) @ ( negate @ ( g @ a_real_number ) ) ) ) @ SV5 )
= $true )
| ( ( less_or_equal @ SV5 @ n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(96,plain,
! [SV19: $i,SV13: $i,SV7: $i] :
( ( ( less_or_equal @ ( add @ ( absolute @ SV7 ) @ ( absolute @ SV13 ) ) @ SV19 )
= $false )
| ( ( less_or_equal @ ( absolute @ ( add @ SV7 @ SV13 ) ) @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(97,plain,
! [SV22: $i,SV14: $i,SV8: $i] :
( ( ( less_or_equal @ SV8 @ ( minimum @ SV14 @ SV22 ) )
= $false )
| ( ( less_or_equal @ SV8 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(98,plain,
! [SV20: $i,SV15: $i,SV9: $i] :
( ( ( less_or_equal @ SV9 @ ( minimum @ SV15 @ SV20 ) )
= $false )
| ( ( less_or_equal @ SV9 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(99,plain,
! [SV21: $i,SV10: $i] :
( ( ( less_or_equal @ ( minimum @ SV10 @ SV21 ) @ n0 )
= $false )
| ( ( less_or_equal @ SV21 @ n0 )
= $true )
| ( ( less_or_equal @ SV10 @ n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(100,plain,
! [SV11: $i,SV16: $i,SV23: $i] :
( ( ( ~ ( less_or_equal @ SV23 @ ( half @ SV16 ) )
| ( less_or_equal @ ( add @ SV11 @ SV23 ) @ SV16 ) )
= $true )
| ( ( less_or_equal @ SV11 @ ( half @ SV16 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(101,plain,
! [SV11: $i,SV16: $i,SV23: $i] :
( ( ( ~ ( less_or_equal @ SV23 @ ( half @ SV16 ) ) )
= $true )
| ( ( less_or_equal @ ( add @ SV11 @ SV23 ) @ SV16 )
= $true )
| ( ( less_or_equal @ SV11 @ ( half @ SV16 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(102,plain,
! [SV11: $i,SV16: $i,SV23: $i] :
( ( ( less_or_equal @ SV23 @ ( half @ SV16 ) )
= $false )
| ( ( less_or_equal @ ( add @ SV11 @ SV23 ) @ SV16 )
= $true )
| ( ( less_or_equal @ SV11 @ ( half @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(103,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[55,102,99,98,97,96,95,94,86,78,77,76,69,63]) ).
thf(104,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ANA004-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Oct 6 18:15:31 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.17
% 0.07/0.17 No.of.Axioms: 13
% 0.07/0.17
% 0.07/0.17 Length.of.Defs: 0
% 0.07/0.17
% 0.07/0.17 Contains.Choice.Funs: false
% 0.07/0.17 ...
% 0.07/0.17
% 0.07/0.17 ********************************
% 0.07/0.17 * All subproblems solved! *
% 0.07/0.17 ********************************
% 0.07/0.17 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:13,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:103,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.07/0.17
% 0.07/0.17 %**** Beginning of derivation protocol ****
% 0.07/0.17 % SZS output start CNFRefutation
% See solution above
% 0.07/0.17
% 0.07/0.17 %**** End of derivation protocol ****
% 0.07/0.17 %**** no. of clauses in derivation: 104 ****
% 0.07/0.17 %**** clause counter: 103 ****
% 0.07/0.17
% 0.07/0.17 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:13,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:103,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------