%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT269-2 : 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 : n020.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 07:46:53 AM UTC 2026
% Result : Unsatisfiable 3.02s 7.28s
% Output : Refutation 3.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of formulae : 13 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 6 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 164 ( 10 ~; 8 |; 0 &; 146 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 11 con; 0-5 aty)
% Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(c_Tarski_Opotype_Opotype__ext_decl,type,
c_Tarski_Opotype_Opotype__ext: $i > $i > $i > $i > $i > $i ).
thf(v_intY1_decl,type,
v_intY1: $i ).
thf(c_Tarski_Oinduced_decl,type,
c_Tarski_Oinduced: $i > $i > $i > $i ).
thf(v_r_decl,type,
v_r: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(c_Product__Type_OUnity_decl,type,
c_Product__Type_OUnity: $i ).
thf(tc_Product__Type_Ounit_decl,type,
tc_Product__Type_Ounit: $i ).
thf(c_Tarski_OCompleteLattice_decl,type,
c_Tarski_OCompleteLattice: $i ).
thf(tc_Tarski_Opotype_Opotype__ext__type_decl,type,
tc_Tarski_Opotype_Opotype__ext__type: $i > $i > $i ).
thf(c_Tarski_OTop_decl,type,
c_Tarski_OTop: $i > $i > $i ).
thf(v_cl_decl,type,
v_cl: $i ).
thf(v_A_decl,type,
v_A: $i ).
thf(c_Tarski_Ointerval_decl,type,
c_Tarski_Ointerval: $i > $i > $i > $i > $i ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(c_Tarski_Olub_decl,type,
c_Tarski_Olub: $i > $i > $i > $i ).
thf(v_Y_decl,type,
v_Y: $i ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( ( t_a @ ( A @ ( B @ ( v_r @ c_Tarski_Ointerval ) ) ) )
= c_emptyset )
| ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( tc_Product__Type_Ounit @ ( t_a @ ( c_Product__Type_OUnity @ ( t_a @ ( v_r @ ( t_a @ ( A @ ( B @ ( v_r @ c_Tarski_Ointerval ) ) ) @ c_Tarski_Oinduced ) ) @ ( t_a @ ( A @ ( B @ ( v_r @ c_Tarski_Ointerval ) ) ) @ c_Tarski_Opotype_Opotype__ext ) ) ) ) @ c_in ) ) )
| ~ ( t_a @ ( v_A @ ( B @ c_in ) ) )
| ~ ( t_a @ ( v_A @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_Aa2_A_58_AA_59_Ab2_A_58_AA_59_Ainterval_Ar_Aa2_Ab2_A_126_61_A_123_125_A_124_93_A_61_61_62_A_I_124_Apset_A_61_Ainterval_Ar_Aa2_Ab2_M_Aorder_A_61_Ainduced_A_Iinterval_Ar_Aa2_Ab2_J_Ar_A_124_J_A_58_ACompleteLattice_A_61_61_ATrue_0) ).
thf(10,plain,
! [B: $i,A: $i] :
( ( ( t_a @ ( A @ ( B @ ( v_r @ c_Tarski_Ointerval ) ) ) )
= c_emptyset )
| ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( tc_Product__Type_Ounit @ ( t_a @ ( c_Product__Type_OUnity @ ( t_a @ ( v_r @ ( t_a @ ( A @ ( B @ ( v_r @ c_Tarski_Ointerval ) ) ) @ c_Tarski_Oinduced ) ) @ ( t_a @ ( A @ ( B @ ( v_r @ c_Tarski_Ointerval ) ) ) @ c_Tarski_Opotype_Opotype__ext ) ) ) ) @ c_in ) ) )
| ~ ( t_a @ ( v_A @ ( B @ c_in ) ) )
| ~ ( t_a @ ( v_A @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,axiom,
t_a @ ( v_A @ ( t_a @ ( v_cl @ c_Tarski_OTop ) @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OTop_Acl_A_58_AA_A_61_61_ATrue_0) ).
thf(9,plain,
t_a @ ( v_A @ ( t_a @ ( v_cl @ c_Tarski_OTop ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
( v_intY1
= ( t_a @ ( t_a @ ( v_cl @ c_Tarski_OTop ) @ ( t_a @ ( v_cl @ ( v_Y @ c_Tarski_Olub ) ) @ ( v_r @ c_Tarski_Ointerval ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OintY1_A_61_61_Ainterval_Ar_A_Ilub_AY_Acl_J_A_ITop_Acl_J_0) ).
thf(13,plain,
( v_intY1
= ( t_a @ ( t_a @ ( v_cl @ c_Tarski_OTop ) @ ( t_a @ ( v_cl @ ( v_Y @ c_Tarski_Olub ) ) @ ( v_r @ c_Tarski_Ointerval ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,negated_conjecture,
~ ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( tc_Product__Type_Ounit @ ( t_a @ ( c_Product__Type_OUnity @ ( t_a @ ( v_r @ ( v_intY1 @ c_Tarski_Oinduced ) ) @ ( v_intY1 @ c_Tarski_Opotype_Opotype__ext ) ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(7,plain,
~ ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( tc_Product__Type_Ounit @ ( t_a @ ( c_Product__Type_OUnity @ ( t_a @ ( v_r @ ( v_intY1 @ c_Tarski_Oinduced ) ) @ ( v_intY1 @ c_Tarski_Opotype_Opotype__ext ) ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [A: $i] :
( ( ( t_a @ ( t_a @ ( v_cl @ c_Tarski_OTop ) @ ( A @ ( v_r @ c_Tarski_Ointerval ) ) ) )
!= c_emptyset )
| ~ ( t_a @ ( v_A @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Ox1_A_58_AA_A_61_61_62_Ainterval_Ar_Ax1_A_ITop_Acl_J_A_61_A_123_125_A_61_61_AFalse_0) ).
thf(16,plain,
! [A: $i] :
( ( ( t_a @ ( t_a @ ( v_cl @ c_Tarski_OTop ) @ ( A @ ( v_r @ c_Tarski_Ointerval ) ) ) )
!= c_emptyset )
| ~ ( t_a @ ( v_A @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_Y @ c_Tarski_Olub ) ) @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Olub_AY_Acl_A_58_AA_A_61_61_ATrue_0) ).
thf(15,plain,
t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_Y @ c_Tarski_Olub ) ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,plain,
$false,
inference(e,[status(thm)],[10,9,13,7,16,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT269-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % 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
% 0.13/5.41 % Computer : n020.cluster.edu
% 0.13/5.41 % Model : x86_64 x86_64
% 0.13/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.41 % Memory : 8046.5625MB
% 0.13/5.41 % OS : Linux 6.8.0-71-generic
% 0.13/5.41 % CPULimit : 300
% 0.13/5.41 % WCLimit : 300
% 0.13/5.41 % DateTime : Fri Sep 25 20:23:11 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.41 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
% 0.18/6.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/6.19 % [INFO] Parsing done (182ms).
% 1.33/6.20 % [INFO] Running in sequential loop mode.
% 1.89/6.60 % [INFO] eprover registered as external prover.
% 1.89/6.61 % [INFO] Scanning for conjecture ...
% 2.05/6.70 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.05/6.74 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.05/6.76 % [INFO] Problem is propositional (TPTP CNF).
% 2.05/6.76 % [INFO] Type checking passed.
% 2.05/6.77 % [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 ...
% 3.02/7.28 % External prover 'e' found a proof!
% 3.02/7.28 % [INFO] Killing All external provers ...
% 3.02/7.28 % Time passed: 1726ms (effective reasoning time: 1074ms)
% 3.02/7.28 % Axioms used in derivation (5): cls_Tarski_Ox1_A_58_AA_A_61_61_62_Ainterval_Ar_Ax1_A_ITop_Acl_J_A_61_A_123_125_A_61_61_AFalse_0, cls_Tarski_Olub_AY_Acl_A_58_AA_A_61_61_ATrue_0, cls_Tarski_OTop_Acl_A_58_AA_A_61_61_ATrue_0, cls_Tarski_OintY1_A_61_61_Ainterval_Ar_A_Ilub_AY_Acl_J_A_ITop_Acl_J_0, cls_Tarski_O_91_124_Aa2_A_58_AA_59_Ab2_A_58_AA_59_Ainterval_Ar_Aa2_Ab2_A_126_61_A_123_125_A_124_93_A_61_61_62_A_I_124_Apset_A_61_Ainterval_Ar_Aa2_Ab2_M_Aorder_A_61_Ainduced_A_Iinterval_Ar_Aa2_Ab2_J_Ar_A_124_J_A_58_ACompleteLattice_A_61_61_ATrue_0
% 3.02/7.28 % No. of inferences in proof: 13
% 3.02/7.28 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1726 ms resp. 1074 ms w/o parsing
% 3.26/7.32 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.26/7.32 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------