TSTP Solution File: NUM531+2 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM531+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.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 11:41:00 EDT 2023
% Result : Theorem 2.53s 1.60s
% Output : Refutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 15
% Syntax : Number of formulae : 26 ( 7 unt; 6 typ; 0 def)
% Number of atoms : 50 ( 6 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 86 ( 13 ~; 0 |; 12 &; 43 @)
% ( 1 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 0 ^; 15 !; 6 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(slcrc0_type,type,
slcrc0: $i ).
thf(aSet0_type,type,
aSet0: $i > $o ).
thf(aElementOf0_type,type,
aElementOf0: $i > $i > $o ).
thf(isCountable0_type,type,
isCountable0: $i > $o ).
thf(aElement0_type,type,
aElement0: $i > $o ).
thf(isFinite0_type,type,
isFinite0: $i > $o ).
thf(5,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSort) ).
thf(29,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ~ ( isFinite0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin) ).
thf(35,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ~ ( isFinite0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ~ ( ~ ? [B: $i] : ( aElementOf0 @ B @ A )
& ( A = slcrc0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ~ ( ~ ? [B: $i] : ( aElementOf0 @ B @ A )
& ( A = slcrc0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ~ ( ~ ? [B: $i] : ( aElementOf0 @ B @ A )
& ( A = slcrc0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
thf(30,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSetSort) ).
thf(28,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
isFinite0 @ slcrc0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEmpFin) ).
thf(33,plain,
isFinite0 @ slcrc0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: $i] :
( ( A = slcrc0 )
<=> ( ( aSet0 @ A )
& ~ ? [B: $i] : ( aElementOf0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
thf(17,plain,
! [A: $i] :
( ( ( A = slcrc0 )
=> ( ( aSet0 @ A )
& ~ ? [B: $i] : ( aElementOf0 @ B @ A ) ) )
& ( ( ( aSet0 @ A )
& ~ ? [B: $i] : ( aElementOf0 @ B @ A ) )
=> ( A = slcrc0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( isFinite0 @ A )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFinRel) ).
thf(32,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( isCountable0 @ A )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCntRel) ).
thf(34,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(41,plain,
$false,
inference(cvc4,[status(thm)],[29,35,11,30,28,33,17,32,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM531+2 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n006.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 17:25:07 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.94/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.96 % [INFO] Parsing done (108ms).
% 1.18/0.97 % [INFO] Running in sequential loop mode.
% 1.62/1.17 % [INFO] eprover registered as external prover.
% 1.62/1.17 % [INFO] cvc4 registered as external prover.
% 1.62/1.18 % [INFO] Scanning for conjecture ...
% 1.71/1.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.79/1.23 % [INFO] Found a conjecture and 8 axioms. Running axiom selection ...
% 1.79/1.25 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 1.79/1.26 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.79/1.26 % [INFO] Problem is first-order (TPTP FOF).
% 1.79/1.27 % [INFO] Type checking passed.
% 1.79/1.27 % [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 ...
% 2.53/1.59 % External prover 'cvc4' found a proof!
% 2.53/1.59 % [INFO] Killing All external provers ...
% 2.53/1.59 % Time passed: 1061ms (effective reasoning time: 621ms)
% 2.53/1.59 % 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)>
% 2.53/1.59 % Axioms used in derivation (8): mCountNFin, mDefEmp, mEOfElem, mSetSort, mFinRel, mEmpFin, mElmSort, mCntRel
% 2.53/1.59 % No. of inferences in proof: 20
% 2.53/1.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1061 ms resp. 621 ms w/o parsing
% 2.82/1.68 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.82/1.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------