TSTP Solution File: LAT276-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT276-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.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 11:27:17 EDT 2023
% Result : Unsatisfiable 3.26s 1.81s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 28
% Syntax : Number of formulae : 41 ( 7 unt; 16 typ; 0 def)
% Number of atoms : 59 ( 4 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 464 ( 30 ~; 34 |; 0 &; 400 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 8 con; 0-4 aty)
% Number of variables : 24 ( 0 ^; 24 !; 0 ?; 24 :)
% 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(c_Pair_type,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(v_xa_type,type,
v_xa: $i ).
thf(c_Tarski_Opotype_Oorder_type,type,
c_Tarski_Opotype_Oorder: $i > $i > $i > $i ).
thf(v_cl_type,type,
v_cl: $i ).
thf(tc_Product__Type_Ounit_type,type,
tc_Product__Type_Ounit: $i ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(c_Tarski_Olub_type,type,
c_Tarski_Olub: $i > $i > $i > $i ).
thf(c_Tarski_Opotype_Opset_type,type,
c_Tarski_Opotype_Opset: $i > $i > $i > $i ).
thf(v_r_type,type,
v_r: $i ).
thf(v_sko__4mP_type,type,
v_sko__4mP: $i > $i > $i > $i ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(14,plain,
c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ v_A @ t_a )
| ~ ( c_lessequals @ B @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ B @ v_cl @ t_a ) @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mP @ A @ B @ v_r ) @ B @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_0) ).
thf(28,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ v_A @ t_a )
| ~ ( c_lessequals @ B @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ B @ v_cl @ t_a ) @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( v_sko__4mP @ A @ B @ v_r ) @ B @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,negated_conjecture,
( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(13,plain,
( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,negated_conjecture,
( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ v_xa @ v_S @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(18,plain,
( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ v_xa @ v_S @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,negated_conjecture,
! [A: $i] :
( ( c_in @ ( c_Pair @ A @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ A @ v_S @ t_a )
| ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_10) ).
thf(16,plain,
! [A: $i] :
( ( c_in @ ( c_Pair @ A @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ A @ v_S @ t_a )
| ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
( v_A
= ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
thf(26,plain,
( v_A
= ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mP @ A @ B @ v_r ) @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_lessequals @ B @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ B @ v_cl @ t_a ) @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_1) ).
thf(30,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ v_A @ t_a )
| ~ ( c_in @ ( c_Pair @ ( v_sko__4mP @ A @ B @ v_r ) @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_lessequals @ B @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ B @ v_cl @ t_a ) @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,negated_conjecture,
! [A: $i] :
( ( c_in @ ( c_Pair @ A @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ A @ v_S @ t_a )
| ( c_in @ v_xa @ v_S @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_9) ).
thf(15,plain,
! [A: $i] :
( ( c_in @ ( c_Pair @ A @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ A @ v_S @ t_a )
| ( c_in @ v_xa @ v_S @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,negated_conjecture,
( ( c_in @ v_xa @ ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ t_a )
| ( c_in @ v_xa @ v_S @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(17,plain,
( ( c_in @ v_xa @ ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ t_a )
| ( c_in @ v_xa @ v_S @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ t_a )
| ~ ( c_lessequals @ B @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ A @ ( c_Tarski_Olub @ B @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Alub_AS1_Acl_J_A_58_Ar_A_61_61_ATrue_0) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ t_a )
| ~ ( c_lessequals @ B @ v_A @ ( tc_set @ t_a ) )
| ( c_in @ ( c_Pair @ A @ ( c_Tarski_Olub @ B @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
thf(34,plain,
( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(36,plain,
$false,
inference(e,[status(thm)],[24,14,28,13,18,16,26,30,15,17,32,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LAT276-2 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.14 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n003.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 14:19:01 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.94/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.30/0.98 % [INFO] Parsing done (120ms).
% 1.30/0.99 % [INFO] Running in sequential loop mode.
% 1.80/1.27 % [INFO] eprover registered as external prover.
% 1.80/1.28 % [INFO] cvc4 registered as external prover.
% 1.80/1.28 % [INFO] Scanning for conjecture ...
% 1.97/1.37 % [INFO] Found a conjecture and 6 axioms. Running axiom selection ...
% 2.06/1.40 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.06/1.41 % [INFO] Problem is propositional (TPTP CNF).
% 2.06/1.42 % [INFO] Type checking passed.
% 2.06/1.42 % [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 ...
% 3.26/1.81 % External prover 'e' found a proof!
% 3.26/1.81 % [INFO] Killing All external provers ...
% 3.26/1.81 % Time passed: 1304ms (effective reasoning time: 820ms)
% 3.26/1.81 % 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)>
% 3.26/1.81 % Axioms used in derivation (6): cls_Tarski_OA_A_61_61_Apset_Acl_0, cls_Set_OsubsetD_0, cls_Tarski_Or_A_61_61_Aorder_Acl_0, cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_0, cls_Tarski_O_91_124_AS1_A_60_61_AA_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Alub_AS1_Acl_J_A_58_Ar_A_61_61_ATrue_0, cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_1
% 3.26/1.81 % No. of inferences in proof: 25
% 3.26/1.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1304 ms resp. 820 ms w/o parsing
% 3.44/1.89 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.44/1.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------