%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG211+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:46:18 AM UTC 2026
% Result : Theorem 2.53s 1.44s
% Output : Refutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of formulae : 14 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 128 ( 2 ~; 0 |; 15 &; 95 @)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 38 ( 0 ^; 28 !; 10 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_vector_subspace_of_decl,type,
a_vector_subspace_of: $i > $i > $o ).
thf(a_vector_space_decl,type,
a_vector_space: $i > $o ).
thf(basis_of_decl,type,
basis_of: $i > $i > $o ).
thf(union_decl,type,
union: $i > $i > $i ).
thf(lin_ind_subset_decl,type,
lin_ind_subset: $i > $i > $o ).
thf(a_subset_of_decl,type,
a_subset_of: $i > $i > $o ).
thf(vec_to_class_decl,type,
vec_to_class: $i > $i ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ a_vector_subspace_of ) )
=> ( A @ a_vector_space ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_a) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ a_vector_subspace_of ) )
=> ( A @ a_vector_space ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ basis_of ) )
=> ( ( B @ vec_to_class @ ( A @ a_subset_of ) )
& ( B @ ( A @ lin_ind_subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_of) ).
thf(14,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ basis_of ) )
=> ( ( B @ vec_to_class @ ( A @ a_subset_of ) )
& ( B @ ( A @ lin_ind_subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ basis_of ) )
& ( C @ ( A @ lin_ind_subset ) ) )
=> ? [D: $i] :
( ( C @ ( D @ ( A @ union ) @ basis_of ) )
& ( B @ ( D @ a_subset_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_2_5) ).
thf(18,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ basis_of ) )
& ( C @ ( A @ lin_ind_subset ) ) )
=> ? [D: $i] :
( ( C @ ( D @ ( A @ union ) @ basis_of ) )
& ( B @ ( D @ a_subset_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( B @ a_vector_space )
& ( B @ ( A @ a_vector_subspace_of ) ) )
=> ? [C: $i,D: $i] :
( ( A @ ( C @ basis_of ) )
& ( B @ ( D @ ( C @ union ) @ basis_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_3) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( B @ a_vector_space )
& ( B @ ( A @ a_vector_subspace_of ) ) )
=> ? [C: $i,D: $i] :
( ( A @ ( C @ basis_of ) )
& ( B @ ( D @ ( C @ union ) @ basis_of ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [A: $i,B: $i] :
( ( ( B @ a_vector_space )
& ( B @ ( A @ a_vector_subspace_of ) ) )
=> ? [C: $i,D: $i] :
( ( A @ ( C @ basis_of ) )
& ( B @ ( D @ ( C @ union ) @ basis_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ a_vector_space )
=> ? [B: $i] : ( A @ ( B @ basis_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_remark_63_a) ).
thf(22,plain,
! [A: $i] :
( ( A @ a_vector_space )
=> ? [B: $i] : ( A @ ( B @ basis_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ vec_to_class @ ( C @ a_subset_of ) )
& ( B @ ( A @ a_vector_subspace_of ) ) )
=> ( ( A @ ( C @ lin_ind_subset ) )
<=> ( B @ ( C @ lin_ind_subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_2) ).
thf(27,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ vec_to_class @ ( C @ a_subset_of ) )
& ( B @ ( A @ a_vector_subspace_of ) ) )
=> ( ( ( B @ ( C @ lin_ind_subset ) )
=> ( A @ ( C @ lin_ind_subset ) ) )
& ( ( A @ ( C @ lin_ind_subset ) )
=> ( B @ ( C @ lin_ind_subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(34,plain,
$false,
inference(e,[status(thm)],[24,14,18,8,22,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG211+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.41 % Computer : n016.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 21:31:17 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.69/0.72 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.91/0.81 % [INFO] Parsing done (91ms).
% 0.91/0.82 % [INFO] Running in sequential loop mode.
% 1.09/1.01 % [INFO] eprover registered as external prover.
% 1.09/1.02 % [INFO] Scanning for conjecture ...
% 1.39/1.06 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 1.39/1.08 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.39/1.09 % [INFO] Problem is first-order (TPTP FOF).
% 1.39/1.09 % [INFO] Type checking passed.
% 1.39/1.10 % [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 ...
% 2.53/1.44 % External prover 'e' found a proof!
% 2.53/1.44 % [INFO] Killing All external provers ...
% 2.53/1.44 % Time passed: 929ms (effective reasoning time: 616ms)
% 2.53/1.44 % 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)>
% 2.53/1.44 % Axioms used in derivation (5): bg_remark_63_a, bg_2_2_5, bg_2_4_a, bg_2_4_2, basis_of
% 2.53/1.44 % No. of inferences in proof: 14
% 2.53/1.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 929 ms resp. 616 ms w/o parsing
% 2.53/1.46 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.53/1.46 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------