TSTP Solution File: SET863-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET863-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.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 11:54:42 EDT 2023
% Result : Unsatisfiable 3.10s 1.70s
% Output : Refutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 31
% Syntax : Number of formulae : 46 ( 13 unt; 17 typ; 0 def)
% Number of atoms : 67 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 476 ( 34 ~; 38 |; 0 &; 404 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 17 usr; 8 con; 0-3 aty)
% Number of variables : 62 ( 0 ^; 62 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(v_c_type,type,
v_c: $i ).
thf(c_Zorn_Omaxchain_type,type,
c_Zorn_Omaxchain: $i > $i > $i ).
thf(v_S_type,type,
v_S: $i ).
thf(t_a_type,type,
t_a: $i ).
thf(tc_set_type,type,
tc_set: $i > $i ).
thf(c_Zorn_Ochain_type,type,
c_Zorn_Ochain: $i > $i > $i ).
thf(v_x_type,type,
v_x: $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(v_y_type,type,
v_y: $i ).
thf(v_xa_type,type,
v_xa: $i ).
thf(c_Main_OsubsetI__1_type,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_Zorn_Ochain__extend__1_type,type,
c_Zorn_Ochain__extend__1: $i > $i > $i > $i ).
thf(c_union_type,type,
c_union: $i > $i > $i > $i ).
thf(c_insert_type,type,
c_insert: $i > $i > $i > $i ).
thf(c_emptyset_type,type,
c_emptyset: $i ).
thf(c_Zorn_Omaxchain__super__lemma__1_type,type,
c_Zorn_Omaxchain__super__lemma__1: $i > $i > $i > $i ).
thf(8,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)],[8]) ).
thf(3,negated_conjecture,
c_in @ v_x @ v_S @ ( tc_set @ t_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(20,plain,
c_in @ v_x @ v_S @ ( tc_set @ t_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,negated_conjecture,
c_in @ v_c @ ( c_Zorn_Ochain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(18,plain,
c_in @ v_c @ ( c_Zorn_Ochain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
c_in @ v_c @ ( c_Zorn_Omaxchain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(16,plain,
c_in @ v_c @ ( c_Zorn_Omaxchain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,negated_conjecture,
c_in @ v_xa @ v_x @ t_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(15,plain,
c_in @ v_xa @ v_x @ t_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ B @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ B @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,negated_conjecture,
c_lessequals @ v_y @ v_x @ ( tc_set @ t_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(21,plain,
c_lessequals @ v_y @ v_x @ ( tc_set @ t_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,negated_conjecture,
~ ( c_in @ v_xa @ v_y @ t_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(17,plain,
~ ( c_in @ v_xa @ v_y @ t_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ~ ( c_in @ D @ ( c_Zorn_Ochain @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ D @ A @ C ) @ A @ ( tc_set @ C ) )
| ( c_in @ ( c_union @ ( c_insert @ A @ c_emptyset @ ( tc_set @ C ) ) @ D @ ( tc_set @ C ) ) @ ( c_Zorn_Ochain @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_1) ).
thf(32,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ~ ( c_in @ D @ ( c_Zorn_Ochain @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ D @ A @ C ) @ A @ ( tc_set @ C ) )
| ( c_in @ ( c_union @ ( c_insert @ A @ c_emptyset @ ( tc_set @ C ) ) @ D @ ( tc_set @ C ) ) @ ( c_Zorn_Ochain @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(13,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ D @ ( c_Zorn_Omaxchain @ E @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ B @ c_emptyset @ ( tc_set @ C ) ) @ D @ ( tc_set @ C ) ) @ ( c_Zorn_Ochain @ E @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_in @ A @ F @ C )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ D @ F @ C ) @ D @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_0) ).
thf(34,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ D @ ( c_Zorn_Omaxchain @ E @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ B @ c_emptyset @ ( tc_set @ C ) ) @ D @ ( tc_set @ C ) ) @ ( c_Zorn_Ochain @ E @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_in @ A @ F @ C )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ D @ F @ C ) @ D @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(14,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ D @ ( c_Zorn_Omaxchain @ E @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ B @ c_emptyset @ ( tc_set @ C ) ) @ D @ ( tc_set @ C ) ) @ ( c_Zorn_Ochain @ E @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ D @ F @ C ) @ F @ ( tc_set @ C ) )
| ( c_in @ A @ F @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_1) ).
thf(36,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ D @ ( c_Zorn_Omaxchain @ E @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ B @ c_emptyset @ ( tc_set @ C ) ) @ D @ ( tc_set @ C ) ) @ ( c_Zorn_Ochain @ E @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ D @ F @ C ) @ F @ ( tc_set @ C ) )
| ( c_in @ A @ F @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ~ ( c_in @ D @ ( c_Zorn_Ochain @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_in @ ( c_Zorn_Ochain__extend__1 @ D @ A @ C ) @ D @ ( tc_set @ C ) )
| ( c_in @ ( c_union @ ( c_insert @ A @ c_emptyset @ ( tc_set @ C ) ) @ D @ ( tc_set @ C ) ) @ ( c_Zorn_Ochain @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_0) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ~ ( c_in @ D @ ( c_Zorn_Ochain @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_in @ ( c_Zorn_Ochain__extend__1 @ D @ A @ C ) @ D @ ( tc_set @ C ) )
| ( c_in @ ( c_union @ ( c_insert @ A @ c_emptyset @ ( tc_set @ C ) ) @ D @ ( tc_set @ C ) ) @ ( c_Zorn_Ochain @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(7,negated_conjecture,
! [A: $i] :
( ( c_lessequals @ A @ v_y @ ( tc_set @ t_a ) )
| ~ ( c_in @ A @ v_c @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_7) ).
thf(19,plain,
! [A: $i] :
( ( c_lessequals @ A @ v_y @ ( tc_set @ t_a ) )
| ~ ( c_in @ A @ v_c @ ( tc_set @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(41,plain,
$false,
inference(e,[status(thm)],[24,20,18,16,26,15,28,21,17,32,34,36,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : SET863-2 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n006.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 19:15:52 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.99/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.14/1.03 % [INFO] Parsing done (137ms).
% 1.40/1.04 % [INFO] Running in sequential loop mode.
% 1.74/1.23 % [INFO] eprover registered as external prover.
% 1.79/1.24 % [INFO] cvc4 registered as external prover.
% 1.79/1.24 % [INFO] Scanning for conjecture ...
% 1.79/1.30 % [INFO] Found a conjecture and 7 axioms. Running axiom selection ...
% 2.00/1.33 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.00/1.35 % [INFO] Problem is propositional (TPTP CNF).
% 2.00/1.35 % [INFO] Type checking passed.
% 2.00/1.35 % [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 ...
% 3.10/1.70 % External prover 'e' found a proof!
% 3.10/1.70 % [INFO] Killing All external provers ...
% 3.10/1.70 % Time passed: 1180ms (effective reasoning time: 659ms)
% 3.10/1.70 % 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)>
% 3.10/1.70 % Axioms used in derivation (7): cls_Set_OsubsetI_1, cls_Zorn_Ochain__extend_0, cls_Zorn_Omaxchain__super__lemma_0, cls_Set_OsubsetI_0, cls_Set_OsubsetD_0, cls_Zorn_Omaxchain__super__lemma_1, cls_Zorn_Ochain__extend_1
% 3.10/1.70 % No. of inferences in proof: 29
% 3.10/1.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1180 ms resp. 659 ms w/o parsing
% 3.41/1.79 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.41/1.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------