TSTP Solution File: SET820-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET820-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.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 11:54:25 EDT 2023
% Result : Unsatisfiable 3.00s 1.69s
% Output : Refutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of formulae : 20 ( 7 unt; 7 typ; 0 def)
% Number of atoms : 21 ( 2 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 80 ( 10 ~; 8 |; 0 &; 62 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 26 ( 0 ^; 26 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_P_type,type,
v_P: $i > $o ).
thf(v_a_type,type,
v_a: $i ).
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(tc_IntDef_Oint_type,type,
tc_IntDef_Oint: $i ).
thf(v_x_type,type,
v_x: $i > $i ).
thf(c_emptyset_type,type,
c_emptyset: $i ).
thf(c_insert_type,type,
c_insert: $i > $i > $i > $i ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_IntDef_Oint )
| ~ ( v_P @ ( v_x @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(9,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_IntDef_Oint )
| ~ ( v_P @ ( v_x @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
thf(12,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,negated_conjecture,
v_P @ v_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(7,plain,
v_P @ v_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_IntDef_Oint )
| ( c_in @ ( v_x @ B ) @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(8,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_IntDef_Oint )
| ( c_in @ ( v_x @ B ) @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
thf(15,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(21,plain,
$false,
inference(e,[status(thm)],[14,9,12,7,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET820-2 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n017.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 18:16:01 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.92/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/1.00 % [INFO] Parsing done (116ms).
% 1.25/1.01 % [INFO] Running in sequential loop mode.
% 1.57/1.21 % [INFO] eprover registered as external prover.
% 1.57/1.21 % [INFO] cvc4 registered as external prover.
% 1.57/1.22 % [INFO] Scanning for conjecture ...
% 1.87/1.27 % [INFO] Found a conjecture and 3 axioms. Running axiom selection ...
% 1.87/1.29 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.87/1.30 % [INFO] Problem is propositional (TPTP CNF).
% 1.87/1.30 % [INFO] Type checking passed.
% 1.87/1.30 % [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 ...
% 2.88/1.69 % External prover 'e' found a proof!
% 2.88/1.69 % [INFO] Killing All external provers ...
% 2.88/1.69 % Time passed: 1163ms (effective reasoning time: 679ms)
% 2.88/1.69 % 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)>
% 3.00/1.69 % Axioms used in derivation (3): cls_Set_OinsertCI_1, cls_Set_OemptyE_0, cls_Set_OinsertE_0
% 3.00/1.69 % No. of inferences in proof: 13
% 3.00/1.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1163 ms resp. 679 ms w/o parsing
% 3.00/1.73 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.00/1.73 % [INFO] Killing All external provers ...
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