%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT268-10 : TPTP v9.3.1. Released v7.5.0.
% 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 : n005.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 3.99s 2.24s
% Output : Refutation 3.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 12
% Syntax : Number of formulae : 25 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 24 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 282 ( 2 ~; 0 |; 0 &; 280 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 11 con; 0-4 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $i ).
thf(v_S_decl,type,
v_S: $i ).
thf(v_A_decl,type,
v_A: $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(true_decl,type,
true: $i ).
thf(c_in_decl,type,
c_in: $i > $i > $i > $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(c_Pair_decl,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(c_Tarski_Oglb_decl,type,
c_Tarski_Oglb: $i > $i > $i > $i ).
thf(v_cl_decl,type,
v_cl: $i ).
thf(v_r_decl,type,
v_r: $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(ifeq_decl,type,
ifeq: $i > $i > $i > $i > $i ).
thf(c_Tarski_Opotype_Opset_decl,type,
c_Tarski_Opotype_Opset: $i > $i > $i > $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_OPartialOrder_decl,type,
c_Tarski_OPartialOrder: $i ).
thf(c_Tarski_Olub_decl,type,
c_Tarski_Olub: $i > $i > $i > $i ).
thf(c_Tarski_Opotype_Oorder_decl,type,
c_Tarski_Opotype_Oorder: $i > $i > $i > $i ).
thf(c_Tarski_Odual_decl,type,
c_Tarski_Odual: $i > $i > $i ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( true @ ( C @ ( C @ tc_prod ) @ ( tc_Product__Type_Ounit @ ( C @ ( B @ c_Tarski_Opotype_Oorder ) ) @ ( C @ ( C @ ( C @ ( B @ ( A @ c_Tarski_Olub ) ) @ ( D @ c_Pair ) ) ) @ c_in ) ) @ ( true @ ( C @ ( A @ ( D @ c_in ) ) @ ifeq ) ) ) @ ( true @ ( tc_Product__Type_Ounit @ ( C @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( B @ c_in ) ) @ ifeq ) ) ) @ ( true @ ( tc_Product__Type_Ounit @ ( C @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( B @ c_in ) ) @ ifeq ) ) ) @ ( true @ ( C @ tc_set @ ( tc_Product__Type_Ounit @ ( C @ ( B @ c_Tarski_Opotype_Opset ) ) @ ( A @ c_lessequals ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OCL_Olub__upper_0) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( true @ ( C @ ( C @ tc_prod ) @ ( tc_Product__Type_Ounit @ ( C @ ( B @ c_Tarski_Opotype_Oorder ) ) @ ( C @ ( C @ ( C @ ( B @ ( A @ c_Tarski_Olub ) ) @ ( D @ c_Pair ) ) ) @ c_in ) ) @ ( true @ ( C @ ( A @ ( D @ c_in ) ) @ ifeq ) ) ) @ ( true @ ( tc_Product__Type_Ounit @ ( C @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( B @ c_in ) ) @ ifeq ) ) ) @ ( true @ ( tc_Product__Type_Ounit @ ( C @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( B @ c_in ) ) @ ifeq ) ) ) @ ( true @ ( C @ tc_set @ ( tc_Product__Type_Ounit @ ( C @ ( B @ c_Tarski_Opotype_Opset ) ) @ ( A @ c_lessequals ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(2,negated_conjecture,
( ( t_a @ ( v_S @ ( v_x @ c_in ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(14,plain,
( ( t_a @ ( v_S @ ( v_x @ c_in ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( t_a @ ( v_cl @ c_Tarski_Odual ) @ c_in ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0) ).
thf(28,plain,
( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( t_a @ ( v_cl @ c_Tarski_Odual ) @ c_in ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
( ( t_a @ tc_set @ ( v_A @ ( v_S @ c_lessequals ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(13,plain,
( ( t_a @ tc_set @ ( v_A @ ( v_S @ c_lessequals ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,axiom,
( v_A
= ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Opset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
thf(22,plain,
( v_A
= ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Opset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( C @ tc_prod ) @ ( tc_Product__Type_Ounit @ ( C @ ( D @ c_Tarski_Opotype_Oorder ) ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) @ ( true @ ( C @ ( C @ tc_prod ) @ ( tc_Product__Type_Ounit @ ( C @ ( C @ ( D @ c_Tarski_Odual ) @ c_Tarski_Opotype_Oorder ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0) ).
thf(26,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( C @ tc_prod ) @ ( tc_Product__Type_Ounit @ ( C @ ( D @ c_Tarski_Opotype_Oorder ) ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) @ ( true @ ( C @ ( C @ tc_prod ) @ ( tc_Product__Type_Ounit @ ( C @ ( C @ ( D @ c_Tarski_Odual ) @ c_Tarski_Opotype_Oorder ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,negated_conjecture,
( ( t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_x @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_Pair ) ) ) @ c_in ) ) )
!= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(15,plain,
( ( t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_x @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_Pair ) ) ) @ c_in ) ) )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Tarski_Oglb ) ) )
= ( C @ ( C @ ( B @ c_Tarski_Odual ) @ ( A @ c_Tarski_Olub ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Oglb__dual__lub_0) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Tarski_Oglb ) ) )
= ( C @ ( C @ ( B @ c_Tarski_Odual ) @ ( A @ c_Tarski_Olub ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( tc_Product__Type_Ounit @ ( B @ ( B @ ( A @ c_Tarski_Odual ) @ c_Tarski_Opotype_Opset ) ) )
= ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Opset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( tc_Product__Type_Ounit @ ( B @ ( B @ ( A @ c_Tarski_Odual ) @ c_Tarski_Opotype_Opset ) ) )
= ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Opset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
( v_r
= ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Oorder ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
thf(36,plain,
( v_r
= ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Oorder ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( t_a @ ( v_cl @ c_Tarski_Odual ) @ c_in ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_APartialOrder_0) ).
thf(30,plain,
( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( t_a @ ( v_cl @ c_Tarski_Odual ) @ c_in ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(41,plain,
$false,
inference(e,[status(thm)],[24,14,20,28,13,22,26,15,32,34,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT268-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % 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
% 0.12/0.39 % Computer : n005.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Fri Sep 25 20:22:03 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.96/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.54/1.21 % [INFO] Parsing done (222ms).
% 1.54/1.22 % [INFO] Running in sequential loop mode.
% 2.20/1.56 % [INFO] eprover registered as external prover.
% 2.20/1.57 % [INFO] Scanning for conjecture ...
% 2.46/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 2.46/1.69 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 2.70/1.72 % [INFO] Problem is propositional (TPTP CNF).
% 2.70/1.74 % [INFO] Type checking passed.
% 2.70/1.74 % [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 ...
% 3.99/2.23 % External prover 'e' found a proof!
% 3.99/2.23 % [INFO] Killing All external provers ...
% 3.99/2.23 % Time passed: 1626ms (effective reasoning time: 1005ms)
% 3.99/2.23 % Axioms used in derivation (9): cls_Tarski_OCL_Olub__upper_0, ifeq_axiom, cls_Tarski_OA_A_61_61_Apset_Acl_0, cls_Tarski_Oglb__dual__lub_0, cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0, cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0, cls_Tarski_Odual_Acl_A_58_APartialOrder_0, cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0, cls_Tarski_Or_A_61_61_Aorder_Acl_0
% 3.99/2.23 % No. of inferences in proof: 25
% 3.99/2.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1626 ms resp. 1005 ms w/o parsing
% 3.99/2.26 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.99/2.26 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------