TSTP Solution File: SET852-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET852-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.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 11:54:39 EDT 2023
% Result : Unsatisfiable 2.12s 1.40s
% Output : Refutation 2.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 16
% Syntax : Number of formulae : 23 ( 5 unt; 10 typ; 0 def)
% Number of atoms : 29 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 220 ( 10 ~; 16 |; 0 &; 194 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 10 usr; 5 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(c_Union_type,type,
c_Union: $i > $i > $i ).
thf(v_Y_type,type,
v_Y: $i ).
thf(tc_set_type,type,
tc_set: $i > $i ).
thf(t_a_type,type,
t_a: $i ).
thf(v_m_type,type,
v_m: $i ).
thf(c_Zorn_Osucc_type,type,
c_Zorn_Osucc: $i > $i > $i > $i ).
thf(v_S_type,type,
v_S: $i ).
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(c_Zorn_OUnion__lemma0__1_type,type,
c_Zorn_OUnion__lemma0__1: $i > $i > $i > $i > $i ).
thf(3,negated_conjecture,
! [A: $i] :
( ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ v_m @ t_a ) @ A @ ( tc_set @ ( tc_set @ t_a ) ) )
| ( c_lessequals @ A @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) )
| ~ ( c_in @ A @ v_Y @ ( tc_set @ ( tc_set @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(9,plain,
! [A: $i] :
( ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ v_m @ t_a ) @ A @ ( tc_set @ ( tc_set @ t_a ) ) )
| ( c_lessequals @ A @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) )
| ~ ( c_in @ A @ v_Y @ ( tc_set @ ( tc_set @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Zorn_OUnion__lemma0__1 @ A @ B @ C @ D ) @ C @ ( tc_set @ D ) )
| ( c_lessequals @ B @ ( c_Union @ C @ D ) @ ( tc_set @ D ) )
| ( c_lessequals @ ( c_Union @ C @ D ) @ A @ ( tc_set @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_0) ).
thf(13,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Zorn_OUnion__lemma0__1 @ A @ B @ C @ D ) @ C @ ( tc_set @ D ) )
| ( c_lessequals @ B @ ( c_Union @ C @ D ) @ ( tc_set @ D ) )
| ( c_lessequals @ ( c_Union @ C @ D ) @ A @ ( tc_set @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_Zorn_OUnion__lemma0__1 @ B @ A @ C @ D ) @ ( tc_set @ D ) )
| ( c_lessequals @ A @ ( c_Union @ C @ D ) @ ( tc_set @ D ) )
| ( c_lessequals @ ( c_Union @ C @ D ) @ B @ ( tc_set @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_2) ).
thf(17,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_Zorn_OUnion__lemma0__1 @ B @ A @ C @ D ) @ ( tc_set @ D ) )
| ( c_lessequals @ A @ ( c_Union @ C @ D ) @ ( tc_set @ D ) )
| ( c_lessequals @ ( c_Union @ C @ D ) @ B @ ( tc_set @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,negated_conjecture,
~ ( c_lessequals @ ( c_Union @ v_Y @ ( tc_set @ t_a ) ) @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(7,plain,
~ ( c_lessequals @ ( c_Union @ v_Y @ ( tc_set @ t_a ) ) @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,negated_conjecture,
~ ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ v_m @ t_a ) @ ( c_Union @ v_Y @ ( tc_set @ t_a ) ) @ ( tc_set @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(8,plain,
~ ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ v_m @ t_a ) @ ( c_Union @ v_Y @ ( tc_set @ t_a ) ) @ ( tc_set @ ( tc_set @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Zorn_OUnion__lemma0__1 @ A @ B @ C @ D ) @ A @ ( tc_set @ D ) )
| ( c_lessequals @ B @ ( c_Union @ C @ D ) @ ( tc_set @ D ) )
| ( c_lessequals @ ( c_Union @ C @ D ) @ A @ ( tc_set @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_1) ).
thf(15,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Zorn_OUnion__lemma0__1 @ A @ B @ C @ D ) @ A @ ( tc_set @ D ) )
| ( c_lessequals @ B @ ( c_Union @ C @ D ) @ ( tc_set @ D ) )
| ( c_lessequals @ ( c_Union @ C @ D ) @ A @ ( tc_set @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,plain,
$false,
inference(e,[status(thm)],[9,13,17,7,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.08 % Problem : SET852-2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.10 % Command : run_Leo-III %s %d
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Thu May 18 18:59:35 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.68/0.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.94/0.82 % [INFO] Parsing done (107ms).
% 0.94/0.82 % [INFO] Running in sequential loop mode.
% 1.19/1.03 % [INFO] eprover registered as external prover.
% 1.19/1.03 % [INFO] cvc4 registered as external prover.
% 1.19/1.03 % [INFO] Scanning for conjecture ...
% 1.45/1.09 % [INFO] Found a conjecture and 3 axioms. Running axiom selection ...
% 1.45/1.11 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.45/1.12 % [INFO] Problem is propositional (TPTP CNF).
% 1.45/1.12 % [INFO] Type checking passed.
% 1.45/1.13 % [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 ...
% 2.12/1.40 % External prover 'e' found a proof!
% 2.12/1.40 % [INFO] Killing All external provers ...
% 2.12/1.40 % Time passed: 1003ms (effective reasoning time: 572ms)
% 2.12/1.40 % 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)>
% 2.12/1.40 % Axioms used in derivation (3): cls_Zorn_OUnion__lemma0_0, cls_Zorn_OUnion__lemma0_2, cls_Zorn_OUnion__lemma0_1
% 2.12/1.40 % No. of inferences in proof: 13
% 2.12/1.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1003 ms resp. 572 ms w/o parsing
% 2.34/1.43 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.34/1.43 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------