TSTP Solution File: SET839-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET839-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.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 11:54:33 EDT 2023
% Result : Unsatisfiable 2.27s 1.45s
% Output : Refutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 14
% Syntax : Number of formulae : 21 ( 5 unt; 8 typ; 0 def)
% Number of atoms : 25 ( 2 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 134 ( 12 ~; 12 |; 0 &; 110 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 30 ( 0 ^; 30 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(v_S_type,type,
v_S: $i ).
thf(c_insert_type,type,
c_insert: $i > $i > $i > $i ).
thf(c_emptyset_type,type,
c_emptyset: $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_Main_OsubsetI__1_type,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(5,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(14,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)],[5]) ).
thf(4,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(12,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)],[4]) ).
thf(1,negated_conjecture,
! [A: $i] :
~ ( c_lessequals @ v_S @ ( c_insert @ A @ c_emptyset @ ( tc_set @ t_a ) ) @ ( tc_set @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(7,plain,
! [A: $i] :
~ ( c_lessequals @ v_S @ ( c_insert @ A @ c_emptyset @ ( tc_set @ 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 @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/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)],[6]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,negated_conjecture,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_set @ t_a ) )
| ~ ( c_in @ B @ 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(8,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_set @ t_a ) )
| ~ ( c_in @ B @ 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(19,plain,
$false,
inference(e,[status(thm)],[14,12,7,16,11,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SET839-2 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.14 % Command : run_Leo-III %s %d
% 0.14/0.33 % Computer : n023.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Thu May 18 19:23:45 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.89/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/0.91 % [INFO] Parsing done (100ms).
% 1.23/0.92 % [INFO] Running in sequential loop mode.
% 1.54/1.10 % [INFO] eprover registered as external prover.
% 1.54/1.10 % [INFO] cvc4 registered as external prover.
% 1.54/1.11 % [INFO] Scanning for conjecture ...
% 1.54/1.16 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 1.78/1.18 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.78/1.19 % [INFO] Problem is propositional (TPTP CNF).
% 1.78/1.19 % [INFO] Type checking passed.
% 1.78/1.19 % [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 ...
% 2.27/1.45 % External prover 'e' found a proof!
% 2.27/1.45 % [INFO] Killing All external provers ...
% 2.27/1.45 % Time passed: 959ms (effective reasoning time: 529ms)
% 2.27/1.45 % 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)>
% 2.27/1.45 % Axioms used in derivation (4): cls_Set_OsubsetI_1, cls_Set_OsubsetI_0, cls_Set_Osubset__antisym_0, cls_Set_OinsertCI_1
% 2.27/1.45 % No. of inferences in proof: 13
% 2.27/1.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 959 ms resp. 529 ms w/o parsing
% 2.58/1.48 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.58/1.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------