%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ALG211+1 : TPTP v9.3.1. Released v3.1.0.
% 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 : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:08:25 AM UTC 2026
% Result : Theorem 0.07s 0.22s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 100 ( 48 unt; 0 typ; 0 def)
% Number of atoms : 649 ( 166 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 1238 ( 273 ~; 169 |; 25 &; 748 @)
% ( 3 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 250 ( 0 ^; 228 !; 22 ?; 250 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a_subset_of,type,
a_subset_of: $i > $i > $o ).
thf(tp_a_vector_space,type,
a_vector_space: $i > $o ).
thf(tp_a_vector_subspace_of,type,
a_vector_subspace_of: $i > $i > $o ).
thf(tp_basis_of,type,
basis_of: $i > $i > $o ).
thf(tp_lin_ind_subset,type,
lin_ind_subset: $i > $i > $o ).
thf(tp_sK1_W,type,
sK1_W: $i ).
thf(tp_sK2_SY17,type,
sK2_SY17: $i ).
thf(tp_sK3_SY29,type,
sK3_SY29: $i > $i ).
thf(tp_sK4_SY34,type,
sK4_SY34: $i > $i > $i > $i ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(tp_vec_to_class,type,
vec_to_class: $i > $i ).
thf(1,axiom,
! [W: $i,V: $i,E: $i] :
( ( ( a_vector_subspace_of @ W @ V )
& ( a_subset_of @ E @ ( vec_to_class @ W ) ) )
=> ( ( lin_ind_subset @ E @ W )
<=> ( lin_ind_subset @ E @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_2) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ( a_vector_subspace_of @ A @ B )
=> ( a_vector_space @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_a) ).
thf(3,axiom,
! [A: $i] :
( ( a_vector_space @ A )
=> ? [B: $i] : ( basis_of @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_remark_63_a) ).
thf(4,axiom,
! [S: $i,T: $i,V: $i] :
( ( ( lin_ind_subset @ S @ V )
& ( basis_of @ T @ V ) )
=> ? [U: $i] :
( ( a_subset_of @ U @ T )
& ( basis_of @ ( union @ S @ U ) @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_2_5) ).
thf(5,axiom,
! [B: $i,V: $i] :
( ( basis_of @ B @ V )
=> ( ( lin_ind_subset @ B @ V )
& ( a_subset_of @ B @ ( vec_to_class @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_of) ).
thf(6,conjecture,
! [W: $i,V: $i] :
( ( ( a_vector_subspace_of @ W @ V )
& ( a_vector_space @ V ) )
=> ? [E: $i,F: $i] :
( ( basis_of @ ( union @ E @ F ) @ V )
& ( basis_of @ E @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_3) ).
thf(7,negated_conjecture,
( ( ! [W: $i,V: $i] :
( ( ( a_vector_subspace_of @ W @ V )
& ( a_vector_space @ V ) )
=> ? [E: $i,F: $i] :
( ( basis_of @ ( union @ E @ F ) @ V )
& ( basis_of @ E @ W ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ! [W: $i,V: $i] :
( ( ( a_vector_subspace_of @ W @ V )
& ( a_vector_space @ V ) )
=> ? [E: $i,F: $i] :
( ( basis_of @ ( union @ E @ F ) @ V )
& ( basis_of @ E @ W ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [W: $i,V: $i,E: $i] :
( ( ( a_vector_subspace_of @ W @ V )
& ( a_subset_of @ E @ ( vec_to_class @ W ) ) )
=> ( ( lin_ind_subset @ E @ W )
<=> ( lin_ind_subset @ E @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [A: $i,B: $i] :
( ( a_vector_subspace_of @ A @ B )
=> ( a_vector_space @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ! [A: $i] :
( ( a_vector_space @ A )
=> ? [B: $i] : ( basis_of @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [S: $i,T: $i,V: $i] :
( ( ( lin_ind_subset @ S @ V )
& ( basis_of @ T @ V ) )
=> ? [U: $i] :
( ( a_subset_of @ U @ T )
& ( basis_of @ ( union @ S @ U ) @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ! [B: $i,V: $i] :
( ( basis_of @ B @ V )
=> ( ( lin_ind_subset @ B @ V )
& ( a_subset_of @ B @ ( vec_to_class @ V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ! [SY17: $i] :
( ( ( a_vector_subspace_of @ sK1_W @ SY17 )
& ( a_vector_space @ SY17 ) )
=> ? [SY18: $i,SY19: $i] :
( ( basis_of @ ( union @ SY18 @ SY19 ) @ SY17 )
& ( basis_of @ SY18 @ sK1_W ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(15,plain,
( ( ( ( a_vector_subspace_of @ sK1_W @ sK2_SY17 )
& ( a_vector_space @ sK2_SY17 ) )
=> ? [SY20: $i,SY21: $i] :
( ( basis_of @ ( union @ SY20 @ SY21 ) @ sK2_SY17 )
& ( basis_of @ SY20 @ sK1_W ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(16,plain,
( ( a_vector_subspace_of @ sK1_W @ sK2_SY17 )
= $true ),
inference(standard_cnf,[status(thm)],[15]) ).
thf(17,plain,
( ( a_vector_space @ sK2_SY17 )
= $true ),
inference(standard_cnf,[status(thm)],[15]) ).
thf(18,plain,
( ( ? [SY20: $i,SY21: $i] :
( ( basis_of @ ( union @ SY20 @ SY21 ) @ sK2_SY17 )
& ( basis_of @ SY20 @ sK1_W ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[15]) ).
thf(19,plain,
( ( ~ ? [SY20: $i,SY21: $i] :
( ( basis_of @ ( union @ SY20 @ SY21 ) @ sK2_SY17 )
& ( basis_of @ SY20 @ sK1_W ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(20,plain,
( ( ! [B: $i,V: $i] :
( ( basis_of @ B @ V )
=> ( ( lin_ind_subset @ B @ V )
& ( a_subset_of @ B @ ( vec_to_class @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(21,plain,
( ( ! [S: $i,T: $i,V: $i] :
( ( ( lin_ind_subset @ S @ V )
& ( basis_of @ T @ V ) )
=> ? [U: $i] :
( ( a_subset_of @ U @ T )
& ( basis_of @ ( union @ S @ U ) @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(22,plain,
( ( ! [A: $i] :
( ( a_vector_space @ A )
=> ? [B: $i] : ( basis_of @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(23,plain,
( ( ! [A: $i,B: $i] :
( ( a_vector_subspace_of @ A @ B )
=> ( a_vector_space @ A ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(24,plain,
( ( ! [W: $i,V: $i,E: $i] :
( ( ( a_vector_subspace_of @ W @ V )
& ( a_subset_of @ E @ ( vec_to_class @ W ) ) )
=> ( ( lin_ind_subset @ E @ W )
<=> ( lin_ind_subset @ E @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(25,plain,
( ( a_vector_space @ sK2_SY17 )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(26,plain,
( ( a_vector_subspace_of @ sK1_W @ sK2_SY17 )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(27,plain,
( ( ~ ? [SY20: $i,SY21: $i] :
( ( basis_of @ ( union @ SY20 @ SY21 ) @ sK2_SY17 )
& ( basis_of @ SY20 @ sK1_W ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(28,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( basis_of @ SX0 @ SX1 )
| ~ ( ~ ( lin_ind_subset @ SX0 @ SX1 )
| ~ ( a_subset_of @ SX0 @ ( vec_to_class @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(29,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ( basis_of @ ( union @ SX0 @ SX1 ) @ sK2_SY17 )
| ~ ( basis_of @ SX0 @ sK1_W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(30,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( lin_ind_subset @ SX0 @ SX2 )
| ~ ( basis_of @ SX1 @ SX2 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( a_subset_of @ SX3 @ SX1 )
| ~ ( basis_of @ ( union @ SX0 @ SX3 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(31,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( a_vector_subspace_of @ SX0 @ SX1 )
| ~ ( a_subset_of @ SX2 @ ( vec_to_class @ SX0 ) ) )
| ~ ( ~ ( ~ ( lin_ind_subset @ SX2 @ SX0 )
| ( lin_ind_subset @ SX2 @ SX1 ) )
| ~ ( ~ ( lin_ind_subset @ SX2 @ SX1 )
| ( lin_ind_subset @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(32,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( a_vector_subspace_of @ SX0 @ SX1 )
| ( a_vector_space @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(33,plain,
( ( ! [SX0: $i] :
( ~ ( a_vector_space @ SX0 )
| ~ ! [SX1: $i] :
~ ( basis_of @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(34,plain,
! [SV1: $i] :
( ( ! [SY22: $i] :
( ~ ( basis_of @ SV1 @ SY22 )
| ~ ( ~ ( lin_ind_subset @ SV1 @ SY22 )
| ~ ( a_subset_of @ SV1 @ ( vec_to_class @ SY22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(35,plain,
( ( ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ( basis_of @ ( union @ SX0 @ SX1 ) @ sK2_SY17 )
| ~ ( basis_of @ SX0 @ sK1_W ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV2: $i] :
( ( ! [SY23: $i,SY24: $i] :
( ~ ~ ( ~ ( lin_ind_subset @ SV2 @ SY24 )
| ~ ( basis_of @ SY23 @ SY24 ) )
| ~ ! [SY25: $i] :
~ ~ ( ~ ( a_subset_of @ SY25 @ SY23 )
| ~ ( basis_of @ ( union @ SV2 @ SY25 ) @ SY24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV3: $i] :
( ( ! [SY26: $i,SY27: $i] :
( ~ ~ ( ~ ( a_vector_subspace_of @ SV3 @ SY26 )
| ~ ( a_subset_of @ SY27 @ ( vec_to_class @ SV3 ) ) )
| ~ ( ~ ( ~ ( lin_ind_subset @ SY27 @ SV3 )
| ( lin_ind_subset @ SY27 @ SY26 ) )
| ~ ( ~ ( lin_ind_subset @ SY27 @ SY26 )
| ( lin_ind_subset @ SY27 @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV4: $i] :
( ( ! [SY28: $i] :
( ~ ( a_vector_subspace_of @ SV4 @ SY28 )
| ( a_vector_space @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(39,plain,
! [SV5: $i] :
( ( ~ ( a_vector_space @ SV5 )
| ~ ! [SY29: $i] :
~ ( basis_of @ SY29 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(40,plain,
! [SV6: $i,SV1: $i] :
( ( ~ ( basis_of @ SV1 @ SV6 )
| ~ ( ~ ( lin_ind_subset @ SV1 @ SV6 )
| ~ ( a_subset_of @ SV1 @ ( vec_to_class @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(41,plain,
( ( ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ( basis_of @ ( union @ SX0 @ SX1 ) @ sK2_SY17 )
| ~ ( basis_of @ SX0 @ sK1_W ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(42,plain,
! [SV7: $i,SV2: $i] :
( ( ! [SY30: $i] :
( ~ ~ ( ~ ( lin_ind_subset @ SV2 @ SY30 )
| ~ ( basis_of @ SV7 @ SY30 ) )
| ~ ! [SY31: $i] :
~ ~ ( ~ ( a_subset_of @ SY31 @ SV7 )
| ~ ( basis_of @ ( union @ SV2 @ SY31 ) @ SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(43,plain,
! [SV8: $i,SV3: $i] :
( ( ! [SY32: $i] :
( ~ ~ ( ~ ( a_vector_subspace_of @ SV3 @ SV8 )
| ~ ( a_subset_of @ SY32 @ ( vec_to_class @ SV3 ) ) )
| ~ ( ~ ( ~ ( lin_ind_subset @ SY32 @ SV3 )
| ( lin_ind_subset @ SY32 @ SV8 ) )
| ~ ( ~ ( lin_ind_subset @ SY32 @ SV8 )
| ( lin_ind_subset @ SY32 @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ( a_vector_subspace_of @ SV4 @ SV9 )
| ( a_vector_space @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(45,plain,
! [SV5: $i] :
( ( ( ~ ( a_vector_space @ SV5 ) )
= $true )
| ( ( ~ ! [SY29: $i] :
~ ( basis_of @ SY29 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(46,plain,
! [SV6: $i,SV1: $i] :
( ( ( ~ ( basis_of @ SV1 @ SV6 ) )
= $true )
| ( ( ~ ( ~ ( lin_ind_subset @ SV1 @ SV6 )
| ~ ( a_subset_of @ SV1 @ ( vec_to_class @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(47,plain,
! [SV10: $i] :
( ( ~ ~ ! [SY33: $i] :
~ ~ ( ~ ( basis_of @ ( union @ SV10 @ SY33 ) @ sK2_SY17 )
| ~ ( basis_of @ SV10 @ sK1_W ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(48,plain,
! [SV7: $i,SV11: $i,SV2: $i] :
( ( ~ ~ ( ~ ( lin_ind_subset @ SV2 @ SV11 )
| ~ ( basis_of @ SV7 @ SV11 ) )
| ~ ! [SY34: $i] :
~ ~ ( ~ ( a_subset_of @ SY34 @ SV7 )
| ~ ( basis_of @ ( union @ SV2 @ SY34 ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(49,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ~ ~ ( ~ ( a_vector_subspace_of @ SV3 @ SV8 )
| ~ ( a_subset_of @ SV12 @ ( vec_to_class @ SV3 ) ) )
| ~ ( ~ ( ~ ( lin_ind_subset @ SV12 @ SV3 )
| ( lin_ind_subset @ SV12 @ SV8 ) )
| ~ ( ~ ( lin_ind_subset @ SV12 @ SV8 )
| ( lin_ind_subset @ SV12 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(50,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( a_vector_subspace_of @ SV4 @ SV9 ) )
= $true )
| ( ( a_vector_space @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(51,plain,
! [SV5: $i] :
( ( ( a_vector_space @ SV5 )
= $false )
| ( ( ~ ! [SY29: $i] :
~ ( basis_of @ SY29 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(52,plain,
! [SV6: $i,SV1: $i] :
( ( ( basis_of @ SV1 @ SV6 )
= $false )
| ( ( ~ ( ~ ( lin_ind_subset @ SV1 @ SV6 )
| ~ ( a_subset_of @ SV1 @ ( vec_to_class @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(53,plain,
! [SV10: $i] :
( ( ~ ! [SY33: $i] :
~ ~ ( ~ ( basis_of @ ( union @ SV10 @ SY33 ) @ sK2_SY17 )
| ~ ( basis_of @ SV10 @ sK1_W ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(54,plain,
! [SV7: $i,SV11: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( lin_ind_subset @ SV2 @ SV11 )
| ~ ( basis_of @ SV7 @ SV11 ) ) )
= $true )
| ( ( ~ ! [SY34: $i] :
~ ~ ( ~ ( a_subset_of @ SY34 @ SV7 )
| ~ ( basis_of @ ( union @ SV2 @ SY34 ) @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(55,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( a_vector_subspace_of @ SV3 @ SV8 )
| ~ ( a_subset_of @ SV12 @ ( vec_to_class @ SV3 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( lin_ind_subset @ SV12 @ SV3 )
| ( lin_ind_subset @ SV12 @ SV8 ) )
| ~ ( ~ ( lin_ind_subset @ SV12 @ SV8 )
| ( lin_ind_subset @ SV12 @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV9: $i,SV4: $i] :
( ( ( a_vector_subspace_of @ SV4 @ SV9 )
= $false )
| ( ( a_vector_space @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(57,plain,
! [SV5: $i] :
( ( ( ! [SY29: $i] :
~ ( basis_of @ SY29 @ SV5 ) )
= $false )
| ( ( a_vector_space @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(58,plain,
! [SV6: $i,SV1: $i] :
( ( ( ~ ( lin_ind_subset @ SV1 @ SV6 )
| ~ ( a_subset_of @ SV1 @ ( vec_to_class @ SV6 ) ) )
= $false )
| ( ( basis_of @ SV1 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(59,plain,
! [SV10: $i] :
( ( ! [SY33: $i] :
~ ~ ( ~ ( basis_of @ ( union @ SV10 @ SY33 ) @ sK2_SY17 )
| ~ ( basis_of @ SV10 @ sK1_W ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(60,plain,
! [SV7: $i,SV11: $i,SV2: $i] :
( ( ( ~ ( ~ ( lin_ind_subset @ SV2 @ SV11 )
| ~ ( basis_of @ SV7 @ SV11 ) ) )
= $false )
| ( ( ~ ! [SY34: $i] :
~ ~ ( ~ ( a_subset_of @ SY34 @ SV7 )
| ~ ( basis_of @ ( union @ SV2 @ SY34 ) @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(61,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( ~ ( a_vector_subspace_of @ SV3 @ SV8 )
| ~ ( a_subset_of @ SV12 @ ( vec_to_class @ SV3 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( lin_ind_subset @ SV12 @ SV3 )
| ( lin_ind_subset @ SV12 @ SV8 ) )
| ~ ( ~ ( lin_ind_subset @ SV12 @ SV8 )
| ( lin_ind_subset @ SV12 @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(62,plain,
! [SV5: $i] :
( ( ( ~ ( basis_of @ ( sK3_SY29 @ SV5 ) @ SV5 ) )
= $false )
| ( ( a_vector_space @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[57]) ).
thf(63,plain,
! [SV6: $i,SV1: $i] :
( ( ( ~ ( lin_ind_subset @ SV1 @ SV6 ) )
= $false )
| ( ( basis_of @ SV1 @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(64,plain,
! [SV6: $i,SV1: $i] :
( ( ( ~ ( a_subset_of @ SV1 @ ( vec_to_class @ SV6 ) ) )
= $false )
| ( ( basis_of @ SV1 @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(65,plain,
! [SV13: $i,SV10: $i] :
( ( ~ ~ ( ~ ( basis_of @ ( union @ SV10 @ SV13 ) @ sK2_SY17 )
| ~ ( basis_of @ SV10 @ sK1_W ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(66,plain,
! [SV7: $i,SV11: $i,SV2: $i] :
( ( ( ~ ( lin_ind_subset @ SV2 @ SV11 )
| ~ ( basis_of @ SV7 @ SV11 ) )
= $true )
| ( ( ~ ! [SY34: $i] :
~ ~ ( ~ ( a_subset_of @ SY34 @ SV7 )
| ~ ( basis_of @ ( union @ SV2 @ SY34 ) @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(67,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( a_vector_subspace_of @ SV3 @ SV8 )
| ~ ( a_subset_of @ SV12 @ ( vec_to_class @ SV3 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( lin_ind_subset @ SV12 @ SV3 )
| ( lin_ind_subset @ SV12 @ SV8 ) )
| ~ ( ~ ( lin_ind_subset @ SV12 @ SV8 )
| ( lin_ind_subset @ SV12 @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(68,plain,
! [SV5: $i] :
( ( ( basis_of @ ( sK3_SY29 @ SV5 ) @ SV5 )
= $true )
| ( ( a_vector_space @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(69,plain,
! [SV6: $i,SV1: $i] :
( ( ( lin_ind_subset @ SV1 @ SV6 )
= $true )
| ( ( basis_of @ SV1 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(70,plain,
! [SV6: $i,SV1: $i] :
( ( ( a_subset_of @ SV1 @ ( vec_to_class @ SV6 ) )
= $true )
| ( ( basis_of @ SV1 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(71,plain,
! [SV13: $i,SV10: $i] :
( ( ~ ( ~ ( basis_of @ ( union @ SV10 @ SV13 ) @ sK2_SY17 )
| ~ ( basis_of @ SV10 @ sK1_W ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(72,plain,
! [SV7: $i,SV11: $i,SV2: $i] :
( ( ( ~ ( lin_ind_subset @ SV2 @ SV11 ) )
= $true )
| ( ( ~ ( basis_of @ SV7 @ SV11 ) )
= $true )
| ( ( ~ ! [SY34: $i] :
~ ~ ( ~ ( a_subset_of @ SY34 @ SV7 )
| ~ ( basis_of @ ( union @ SV2 @ SY34 ) @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(73,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( a_vector_subspace_of @ SV3 @ SV8 ) )
= $true )
| ( ( ~ ( a_subset_of @ SV12 @ ( vec_to_class @ SV3 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( lin_ind_subset @ SV12 @ SV3 )
| ( lin_ind_subset @ SV12 @ SV8 ) )
| ~ ( ~ ( lin_ind_subset @ SV12 @ SV8 )
| ( lin_ind_subset @ SV12 @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(74,plain,
! [SV13: $i,SV10: $i] :
( ( ~ ( basis_of @ ( union @ SV10 @ SV13 ) @ sK2_SY17 )
| ~ ( basis_of @ SV10 @ sK1_W ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(75,plain,
! [SV7: $i,SV11: $i,SV2: $i] :
( ( ( lin_ind_subset @ SV2 @ SV11 )
= $false )
| ( ( ~ ( basis_of @ SV7 @ SV11 ) )
= $true )
| ( ( ~ ! [SY34: $i] :
~ ~ ( ~ ( a_subset_of @ SY34 @ SV7 )
| ~ ( basis_of @ ( union @ SV2 @ SY34 ) @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(76,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ( a_vector_subspace_of @ SV3 @ SV8 )
= $false )
| ( ( ~ ( a_subset_of @ SV12 @ ( vec_to_class @ SV3 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( lin_ind_subset @ SV12 @ SV3 )
| ( lin_ind_subset @ SV12 @ SV8 ) )
| ~ ( ~ ( lin_ind_subset @ SV12 @ SV8 )
| ( lin_ind_subset @ SV12 @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(77,plain,
! [SV13: $i,SV10: $i] :
( ( ( ~ ( basis_of @ ( union @ SV10 @ SV13 ) @ sK2_SY17 ) )
= $true )
| ( ( ~ ( basis_of @ SV10 @ sK1_W ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(78,plain,
! [SV2: $i,SV11: $i,SV7: $i] :
( ( ( basis_of @ SV7 @ SV11 )
= $false )
| ( ( lin_ind_subset @ SV2 @ SV11 )
= $false )
| ( ( ~ ! [SY34: $i] :
~ ~ ( ~ ( a_subset_of @ SY34 @ SV7 )
| ~ ( basis_of @ ( union @ SV2 @ SY34 ) @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(79,plain,
! [SV8: $i,SV3: $i,SV12: $i] :
( ( ( a_subset_of @ SV12 @ ( vec_to_class @ SV3 ) )
= $false )
| ( ( a_vector_subspace_of @ SV3 @ SV8 )
= $false )
| ( ( ~ ( ~ ( ~ ( lin_ind_subset @ SV12 @ SV3 )
| ( lin_ind_subset @ SV12 @ SV8 ) )
| ~ ( ~ ( lin_ind_subset @ SV12 @ SV8 )
| ( lin_ind_subset @ SV12 @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(80,plain,
! [SV13: $i,SV10: $i] :
( ( ( basis_of @ ( union @ SV10 @ SV13 ) @ sK2_SY17 )
= $false )
| ( ( ~ ( basis_of @ SV10 @ sK1_W ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(81,plain,
! [SV11: $i,SV2: $i,SV7: $i] :
( ( ( ! [SY34: $i] :
~ ~ ( ~ ( a_subset_of @ SY34 @ SV7 )
| ~ ( basis_of @ ( union @ SV2 @ SY34 ) @ SV11 ) ) )
= $false )
| ( ( lin_ind_subset @ SV2 @ SV11 )
= $false )
| ( ( basis_of @ SV7 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(82,plain,
! [SV8: $i,SV3: $i,SV12: $i] :
( ( ( ~ ( ~ ( lin_ind_subset @ SV12 @ SV3 )
| ( lin_ind_subset @ SV12 @ SV8 ) )
| ~ ( ~ ( lin_ind_subset @ SV12 @ SV8 )
| ( lin_ind_subset @ SV12 @ SV3 ) ) )
= $false )
| ( ( a_vector_subspace_of @ SV3 @ SV8 )
= $false )
| ( ( a_subset_of @ SV12 @ ( vec_to_class @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(83,plain,
! [SV13: $i,SV10: $i] :
( ( ( basis_of @ SV10 @ sK1_W )
= $false )
| ( ( basis_of @ ( union @ SV10 @ SV13 ) @ sK2_SY17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(84,plain,
! [SV7: $i,SV2: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( a_subset_of @ ( sK4_SY34 @ SV11 @ SV2 @ SV7 ) @ SV7 )
| ~ ( basis_of @ ( union @ SV2 @ ( sK4_SY34 @ SV11 @ SV2 @ SV7 ) ) @ SV11 ) ) )
= $false )
| ( ( lin_ind_subset @ SV2 @ SV11 )
= $false )
| ( ( basis_of @ SV7 @ SV11 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[81]) ).
thf(85,plain,
! [SV8: $i,SV3: $i,SV12: $i] :
( ( ( ~ ( ~ ( lin_ind_subset @ SV12 @ SV3 )
| ( lin_ind_subset @ SV12 @ SV8 ) ) )
= $false )
| ( ( a_vector_subspace_of @ SV3 @ SV8 )
= $false )
| ( ( a_subset_of @ SV12 @ ( vec_to_class @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(86,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ( ~ ( ~ ( lin_ind_subset @ SV12 @ SV8 )
| ( lin_ind_subset @ SV12 @ SV3 ) ) )
= $false )
| ( ( a_vector_subspace_of @ SV3 @ SV8 )
= $false )
| ( ( a_subset_of @ SV12 @ ( vec_to_class @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(87,plain,
! [SV7: $i,SV2: $i,SV11: $i] :
( ( ( ~ ( ~ ( a_subset_of @ ( sK4_SY34 @ SV11 @ SV2 @ SV7 ) @ SV7 )
| ~ ( basis_of @ ( union @ SV2 @ ( sK4_SY34 @ SV11 @ SV2 @ SV7 ) ) @ SV11 ) ) )
= $true )
| ( ( lin_ind_subset @ SV2 @ SV11 )
= $false )
| ( ( basis_of @ SV7 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(88,plain,
! [SV8: $i,SV3: $i,SV12: $i] :
( ( ( ~ ( lin_ind_subset @ SV12 @ SV3 )
| ( lin_ind_subset @ SV12 @ SV8 ) )
= $true )
| ( ( a_vector_subspace_of @ SV3 @ SV8 )
= $false )
| ( ( a_subset_of @ SV12 @ ( vec_to_class @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(89,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ( ~ ( lin_ind_subset @ SV12 @ SV8 )
| ( lin_ind_subset @ SV12 @ SV3 ) )
= $true )
| ( ( a_vector_subspace_of @ SV3 @ SV8 )
= $false )
| ( ( a_subset_of @ SV12 @ ( vec_to_class @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(90,plain,
! [SV7: $i,SV2: $i,SV11: $i] :
( ( ( ~ ( a_subset_of @ ( sK4_SY34 @ SV11 @ SV2 @ SV7 ) @ SV7 )
| ~ ( basis_of @ ( union @ SV2 @ ( sK4_SY34 @ SV11 @ SV2 @ SV7 ) ) @ SV11 ) )
= $false )
| ( ( lin_ind_subset @ SV2 @ SV11 )
= $false )
| ( ( basis_of @ SV7 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(91,plain,
! [SV8: $i,SV3: $i,SV12: $i] :
( ( ( ~ ( lin_ind_subset @ SV12 @ SV3 ) )
= $true )
| ( ( lin_ind_subset @ SV12 @ SV8 )
= $true )
| ( ( a_vector_subspace_of @ SV3 @ SV8 )
= $false )
| ( ( a_subset_of @ SV12 @ ( vec_to_class @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(92,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ( ~ ( lin_ind_subset @ SV12 @ SV8 ) )
= $true )
| ( ( lin_ind_subset @ SV12 @ SV3 )
= $true )
| ( ( a_vector_subspace_of @ SV3 @ SV8 )
= $false )
| ( ( a_subset_of @ SV12 @ ( vec_to_class @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(93,plain,
! [SV7: $i,SV2: $i,SV11: $i] :
( ( ( ~ ( a_subset_of @ ( sK4_SY34 @ SV11 @ SV2 @ SV7 ) @ SV7 ) )
= $false )
| ( ( lin_ind_subset @ SV2 @ SV11 )
= $false )
| ( ( basis_of @ SV7 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(94,plain,
! [SV7: $i,SV11: $i,SV2: $i] :
( ( ( ~ ( basis_of @ ( union @ SV2 @ ( sK4_SY34 @ SV11 @ SV2 @ SV7 ) ) @ SV11 ) )
= $false )
| ( ( lin_ind_subset @ SV2 @ SV11 )
= $false )
| ( ( basis_of @ SV7 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(95,plain,
! [SV8: $i,SV3: $i,SV12: $i] :
( ( ( lin_ind_subset @ SV12 @ SV3 )
= $false )
| ( ( lin_ind_subset @ SV12 @ SV8 )
= $true )
| ( ( a_vector_subspace_of @ SV3 @ SV8 )
= $false )
| ( ( a_subset_of @ SV12 @ ( vec_to_class @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(96,plain,
! [SV3: $i,SV8: $i,SV12: $i] :
( ( ( lin_ind_subset @ SV12 @ SV8 )
= $false )
| ( ( lin_ind_subset @ SV12 @ SV3 )
= $true )
| ( ( a_vector_subspace_of @ SV3 @ SV8 )
= $false )
| ( ( a_subset_of @ SV12 @ ( vec_to_class @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(97,plain,
! [SV7: $i,SV2: $i,SV11: $i] :
( ( ( a_subset_of @ ( sK4_SY34 @ SV11 @ SV2 @ SV7 ) @ SV7 )
= $true )
| ( ( lin_ind_subset @ SV2 @ SV11 )
= $false )
| ( ( basis_of @ SV7 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(98,plain,
! [SV7: $i,SV11: $i,SV2: $i] :
( ( ( basis_of @ ( union @ SV2 @ ( sK4_SY34 @ SV11 @ SV2 @ SV7 ) ) @ SV11 )
= $true )
| ( ( lin_ind_subset @ SV2 @ SV11 )
= $false )
| ( ( basis_of @ SV7 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(99,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,98,97,96,95,83,70,69,68,56,26]) ).
thf(100,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG211+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n002.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 18:09:12 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.22
% 0.07/0.22 No.of.Axioms: 5
% 0.07/0.22
% 0.07/0.22 Length.of.Defs: 0
% 0.07/0.22
% 0.07/0.22 Contains.Choice.Funs: false
% 0.07/0.22 ..
% 0.07/0.22
% 0.07/0.22 ********************************
% 0.07/0.22 * All subproblems solved! *
% 0.07/0.22 ********************************
% 0.07/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:99,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.22
% 0.07/0.22 %**** Beginning of derivation protocol ****
% 0.07/0.22 % SZS output start CNFRefutation
% See solution above
% 0.07/0.22
% 0.07/0.22 %**** End of derivation protocol ****
% 0.07/0.22 %**** no. of clauses in derivation: 100 ****
% 0.07/0.22 %**** clause counter: 99 ****
% 0.07/0.22
% 0.07/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:99,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------