TSTP Solution File: LAT268-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT268-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:27:13 EDT 2023
% Result : Unsatisfiable 2.75s 1.69s
% Output : Refutation 3.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 31
% Syntax : Number of formulae : 43 ( 19 unt; 20 typ; 0 def)
% Number of atoms : 33 ( 8 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 254 ( 12 ~; 10 |; 0 &; 232 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 10 con; 0-4 aty)
% Number of variables : 26 ( 0 ^; 26 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(v_S_type,type,
v_S: $i ).
thf(v_A_type,type,
v_A: $i ).
thf(tc_set_type,type,
tc_set: $i > $i ).
thf(t_a_type,type,
t_a: $i ).
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(v_x_type,type,
v_x: $i ).
thf(c_Pair_type,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(c_Tarski_Oglb_type,type,
c_Tarski_Oglb: $i > $i > $i > $i ).
thf(v_cl_type,type,
v_cl: $i ).
thf(v_r_type,type,
v_r: $i ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(c_Tarski_Opotype_Opset_type,type,
c_Tarski_Opotype_Opset: $i > $i > $i > $i ).
thf(tc_Product__Type_Ounit_type,type,
tc_Product__Type_Ounit: $i ).
thf(c_Tarski_OCompleteLattice_type,type,
c_Tarski_OCompleteLattice: $i ).
thf(tc_Tarski_Opotype_Opotype__ext__type_type,type,
tc_Tarski_Opotype_Opotype__ext__type: $i > $i > $i ).
thf(c_Tarski_OPartialOrder_type,type,
c_Tarski_OPartialOrder: $i ).
thf(c_Tarski_Olub_type,type,
c_Tarski_Olub: $i > $i > $i > $i ).
thf(c_Tarski_Opotype_Oorder_type,type,
c_Tarski_Opotype_Oorder: $i > $i > $i > $i ).
thf(c_Tarski_Odual_type,type,
c_Tarski_Odual: $i > $i > $i ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Tarski_Oglb @ A @ B @ C )
= ( c_Tarski_Olub @ A @ ( c_Tarski_Odual @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Oglb__dual__lub_0) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Tarski_Oglb @ A @ B @ C )
= ( c_Tarski_Olub @ A @ ( c_Tarski_Odual @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,negated_conjecture,
~ ( c_in @ ( c_Pair @ ( c_Tarski_Oglb @ v_S @ v_cl @ t_a ) @ v_x @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(14,plain,
~ ( c_in @ ( c_Pair @ ( c_Tarski_Oglb @ v_S @ v_cl @ t_a ) @ v_x @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ D @ C ) @ C @ tc_Product__Type_Ounit ) @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Tarski_Opotype_Oorder @ D @ C @ tc_Product__Type_Ounit ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/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(20,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ D @ C ) @ C @ tc_Product__Type_Ounit ) @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Tarski_Opotype_Oorder @ D @ C @ tc_Product__Type_Ounit ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
thf(28,plain,
( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,negated_conjecture,
c_in @ v_x @ v_S @ t_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(13,plain,
c_in @ v_x @ v_S @ t_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
c_in @ ( c_Tarski_Odual @ v_cl @ t_a ) @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0) ).
thf(22,plain,
c_in @ ( c_Tarski_Odual @ v_cl @ t_a ) @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,negated_conjecture,
c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(12,plain,
c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ D @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ C @ tc_Product__Type_Ounit ) )
| ~ ( c_in @ D @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ C @ tc_Product__Type_Ounit ) )
| ~ ( c_lessequals @ B @ ( c_Tarski_Opotype_Opset @ D @ C @ tc_Product__Type_Ounit ) @ ( tc_set @ C ) )
| ( c_in @ ( c_Pair @ A @ ( c_Tarski_Olub @ B @ D @ C ) @ C @ C ) @ ( c_Tarski_Opotype_Oorder @ D @ C @ tc_Product__Type_Ounit ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OCL_Olub__upper_0) ).
thf(18,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ D @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ C @ tc_Product__Type_Ounit ) )
| ~ ( c_in @ D @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ C @ tc_Product__Type_Ounit ) )
| ~ ( c_lessequals @ B @ ( c_Tarski_Opotype_Opset @ D @ C @ tc_Product__Type_Ounit ) @ ( tc_set @ C ) )
| ( c_in @ ( c_Pair @ A @ ( c_Tarski_Olub @ B @ D @ C ) @ C @ C ) @ ( c_Tarski_Opotype_Oorder @ D @ C @ tc_Product__Type_Ounit ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
( v_A
= ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
thf(16,plain,
( v_A
= ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( c_Tarski_Opotype_Opset @ ( c_Tarski_Odual @ A @ B ) @ B @ tc_Product__Type_Ounit )
= ( c_Tarski_Opotype_Opset @ A @ B @ tc_Product__Type_Ounit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( c_Tarski_Opotype_Opset @ ( c_Tarski_Odual @ A @ B ) @ B @ tc_Product__Type_Ounit )
= ( c_Tarski_Opotype_Opset @ A @ B @ tc_Product__Type_Ounit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
c_in @ ( c_Tarski_Odual @ v_cl @ t_a ) @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_APartialOrder_0) ).
thf(23,plain,
c_in @ ( c_Tarski_Odual @ v_cl @ t_a ) @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(32,plain,
$false,
inference(e,[status(thm)],[24,14,20,28,13,22,12,18,16,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT268-2 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n025.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 14:14:49 EDT 2023
% 0.15/0.36 % CPUTime :
% 1.00/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.30/1.03 % [INFO] Parsing done (136ms).
% 1.30/1.04 % [INFO] Running in sequential loop mode.
% 1.73/1.23 % [INFO] eprover registered as external prover.
% 1.73/1.24 % [INFO] cvc4 registered as external prover.
% 1.73/1.24 % [INFO] Scanning for conjecture ...
% 1.73/1.30 % [INFO] Found a conjecture and 8 axioms. Running axiom selection ...
% 1.73/1.32 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 1.99/1.33 % [INFO] Problem is propositional (TPTP CNF).
% 1.99/1.34 % [INFO] Type checking passed.
% 1.99/1.34 % [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 ...
% 2.75/1.69 % External prover 'e' found a proof!
% 2.75/1.69 % [INFO] Killing All external provers ...
% 2.75/1.69 % Time passed: 1179ms (effective reasoning time: 648ms)
% 2.75/1.69 % 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)>
% 2.75/1.69 % Axioms used in derivation (8): cls_Tarski_OCL_Olub__upper_0, 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
% 2.75/1.69 % No. of inferences in proof: 23
% 2.75/1.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1179 ms resp. 648 ms w/o parsing
% 3.12/1.77 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.12/1.77 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------