TSTP Solution File: SET845-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET845-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n031.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 11:54:35 EDT 2023
% Result : Unsatisfiable 2.79s 1.88s
% Output : Refutation 3.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 16
% Syntax : Number of formulae : 24 ( 9 unt; 9 typ; 0 def)
% Number of atoms : 23 ( 6 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 134 ( 10 ~; 8 |; 0 &; 116 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 24 ( 0 ^; 24 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(v_m_type,type,
v_m: $i ).
thf(c_Zorn_OTFin_type,type,
c_Zorn_OTFin: $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_Union_type,type,
c_Union: $i > $i > $i ).
thf(c_Zorn_Osucc_type,type,
c_Zorn_Osucc: $i > $i > $i > $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(3,negated_conjecture,
( v_m
!= ( c_Zorn_Osucc @ v_S @ v_m @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(10,plain,
( v_m
!= ( c_Zorn_Osucc @ v_S @ v_m @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ A @ ( c_Union @ B @ C ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__upper_0) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ A @ ( c_Union @ B @ C ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_in @ ( c_Zorn_Osucc @ B @ A @ C ) @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin_OsuccI_0) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_in @ ( c_Zorn_Osucc @ B @ A @ C ) @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2,negated_conjecture,
( v_m
= ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(9,plain,
( v_m
= ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,negated_conjecture,
c_in @ v_m @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(8,plain,
c_in @ v_m @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Zorn_Osucc @ B @ A @ C ) @ ( tc_set @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Zorn_Osucc @ B @ A @ C ) @ ( tc_set @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,plain,
$false,
inference(e,[status(thm)],[10,14,20,9,16,8,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET845-2 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n031.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Thu May 18 19:44:11 EDT 2023
% 0.17/0.37 % CPUTime :
% 1.01/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/1.06 % [INFO] Parsing done (152ms).
% 1.26/1.06 % [INFO] Running in sequential loop mode.
% 1.68/1.39 % [INFO] eprover registered as external prover.
% 1.68/1.39 % [INFO] cvc4 registered as external prover.
% 1.80/1.39 % [INFO] Scanning for conjecture ...
% 1.80/1.46 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 1.99/1.48 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.99/1.49 % [INFO] Problem is propositional (TPTP CNF).
% 1.99/1.49 % [INFO] Type checking passed.
% 1.99/1.50 % [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 ...
% 2.79/1.88 % External prover 'e' found a proof!
% 2.79/1.88 % [INFO] Killing All external provers ...
% 2.79/1.88 % Time passed: 1352ms (effective reasoning time: 812ms)
% 2.79/1.88 % 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)>
% 2.79/1.88 % Axioms used in derivation (4): cls_Set_OUnion__upper_0, cls_Zorn_OTFin_OsuccI_0, cls_Set_Osubset__antisym_0, cls_Zorn_OAbrial__axiom1_0
% 2.79/1.88 % No. of inferences in proof: 15
% 2.79/1.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1352 ms resp. 812 ms w/o parsing
% 3.05/1.92 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.05/1.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------