TSTP Solution File: SET865-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET865-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.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 11:54:43 EDT 2023
% Result : Unsatisfiable 2.61s 1.54s
% Output : Refutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 18
% Syntax : Number of formulae : 27 ( 5 unt; 10 typ; 0 def)
% Number of atoms : 35 ( 4 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 206 ( 20 ~; 18 |; 0 &; 168 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(c_Union_type,type,
c_Union: $i > $i > $i ).
thf(t_a_type,type,
t_a: $i ).
thf(v_S_type,type,
v_S: $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 > $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Zorn_OHausdorff__1_type,type,
c_Zorn_OHausdorff__1: $i > $i > $i ).
thf(c_Zorn_Omaxchain_type,type,
c_Zorn_Omaxchain: $i > $i > $i ).
thf(2,negated_conjecture,
! [A: $i] :
( ( c_in @ ( v_x @ A ) @ v_S @ ( tc_set @ t_a ) )
| ~ ( c_in @ A @ v_S @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(10,plain,
! [A: $i] :
( ( c_in @ ( v_x @ A ) @ v_S @ ( tc_set @ t_a ) )
| ~ ( c_in @ A @ v_S @ ( tc_set @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Zorn_Omaxchain @ A @ B ) @ ( c_Zorn_Ochain @ A @ B ) @ ( tc_set @ ( tc_set @ ( tc_set @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__subset__chain_0) ).
thf(24,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Zorn_Omaxchain @ A @ B ) @ ( c_Zorn_Ochain @ A @ B ) @ ( tc_set @ ( tc_set @ ( tc_set @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Zorn_OHausdorff__1 @ A @ B ) @ ( c_Zorn_Omaxchain @ A @ B ) @ ( tc_set @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OHausdorff_0) ).
thf(20,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Zorn_OHausdorff__1 @ A @ B ) @ ( c_Zorn_Omaxchain @ A @ B ) @ ( tc_set @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ~ ( c_in @ D @ ( c_Zorn_Omaxchain @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_lessequals @ ( c_Union @ D @ C ) @ A @ ( tc_set @ C ) )
| ( ( c_Union @ D @ C )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__Zorn_0) ).
thf(21,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ~ ( c_in @ D @ ( c_Zorn_Omaxchain @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_lessequals @ ( c_Union @ D @ C ) @ A @ ( tc_set @ C ) )
| ( ( c_Union @ D @ C )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ( c_in @ ( c_Union @ A @ t_a ) @ v_S @ ( tc_set @ t_a ) )
| ~ ( c_in @ A @ ( c_Zorn_Ochain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(9,plain,
! [A: $i] :
( ( c_in @ ( c_Union @ A @ t_a ) @ v_S @ ( tc_set @ t_a ) )
| ~ ( c_in @ A @ ( c_Zorn_Ochain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,negated_conjecture,
! [A: $i] :
( ( A
!= ( v_x @ A ) )
| ~ ( c_in @ A @ v_S @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(12,plain,
! [A: $i] :
( ( A
!= ( v_x @ A ) )
| ~ ( c_in @ A @ v_S @ ( tc_set @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,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(18,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)],[5]) ).
thf(3,negated_conjecture,
! [A: $i] :
( ( c_lessequals @ A @ ( v_x @ A ) @ ( tc_set @ t_a ) )
| ~ ( c_in @ A @ v_S @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(11,plain,
! [A: $i] :
( ( c_lessequals @ A @ ( v_x @ A ) @ ( tc_set @ t_a ) )
| ~ ( c_in @ A @ v_S @ ( tc_set @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(25,plain,
$false,
inference(cvc4,[status(thm)],[10,24,20,21,9,12,18,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET865-2 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 18:48:04 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.91/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/0.94 % [INFO] Parsing done (110ms).
% 1.22/0.95 % [INFO] Running in sequential loop mode.
% 1.59/1.14 % [INFO] eprover registered as external prover.
% 1.59/1.14 % [INFO] cvc4 registered as external prover.
% 1.59/1.14 % [INFO] Scanning for conjecture ...
% 1.68/1.20 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 1.68/1.23 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.85/1.23 % [INFO] Problem is propositional (TPTP CNF).
% 1.85/1.24 % [INFO] Type checking passed.
% 1.85/1.24 % [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 ...
% 2.61/1.54 % External prover 'cvc4' found a proof!
% 2.61/1.54 % [INFO] Killing All external provers ...
% 2.61/1.54 % Time passed: 1034ms (effective reasoning time: 591ms)
% 2.61/1.54 % 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)>
% 2.61/1.54 % Axioms used in derivation (4): cls_Zorn_Omaxchain__subset__chain_0, cls_Zorn_OHausdorff_0, cls_Zorn_Omaxchain__Zorn_0, cls_Set_OsubsetD_0
% 2.61/1.54 % No. of inferences in proof: 17
% 2.61/1.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1034 ms resp. 591 ms w/o parsing
% 2.77/1.58 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.77/1.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------