TSTP Solution File: NUM533+2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM533+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.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 11:41:01 EDT 2023
% Result : Theorem 3.19s 1.74s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 25
% Syntax : Number of formulae : 42 ( 7 unt; 10 typ; 0 def)
% Number of atoms : 113 ( 7 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 236 ( 9 ~; 3 |; 31 &; 146 @)
% ( 2 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 43 ( 0 ^; 40 !; 3 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(slcrc0_type,type,
slcrc0: $i ).
thf(aSet0_type,type,
aSet0: $i > $o ).
thf(aElementOf0_type,type,
aElementOf0: $i > $i > $o ).
thf(aSubsetOf0_type,type,
aSubsetOf0: $i > $i > $o ).
thf(xA_type,type,
xA: $i ).
thf(xB_type,type,
xB: $i ).
thf(xC_type,type,
xC: $i ).
thf(aElement0_type,type,
aElement0: $i > $o ).
thf(isFinite0_type,type,
isFinite0: $i > $o ).
thf(isCountable0_type,type,
isCountable0: $i > $o ).
thf(11,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ~ ( isFinite0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin) ).
thf(52,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ~ ( isFinite0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(6,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSort) ).
thf(46,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( aSubsetOf0 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
thf(60,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( aSubsetOf0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,axiom,
( ( aSet0 @ xA )
& ( aSet0 @ xB )
& ( aSet0 @ xC ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__522) ).
thf(65,plain,
( ( aSet0 @ xA )
& ( aSet0 @ xB )
& ( aSet0 @ xC ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(9,axiom,
isFinite0 @ slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEmpFin) ).
thf(50,plain,
isFinite0 @ slcrc0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
<=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
thf(26,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( ( aSubsetOf0 @ B @ A )
=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ A ) ) ) )
& ( ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ A ) ) )
=> ( aSubsetOf0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ( isFinite0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubFSet) ).
thf(58,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ( isFinite0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( isCountable0 @ A )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCntRel) ).
thf(51,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [A: $i] :
( ( A = slcrc0 )
<=> ( ( aSet0 @ A )
& ~ ? [B: $i] : ( aElementOf0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
thf(34,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)],[4]) ).
thf(5,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetSort) ).
thf(45,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
( ( ! [A: $i] :
( ( aElementOf0 @ A @ xA )
=> ( aElementOf0 @ A @ xB ) )
& ( aSubsetOf0 @ xA @ xB )
& ! [A: $i] :
( ( aElementOf0 @ A @ xB )
=> ( aElementOf0 @ A @ xC ) )
& ( aSubsetOf0 @ xB @ xC ) )
=> ( ! [A: $i] :
( ( aElementOf0 @ A @ xA )
=> ( aElementOf0 @ A @ xC ) )
| ( aSubsetOf0 @ xA @ xC ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i] :
( ( aElementOf0 @ A @ xA )
=> ( aElementOf0 @ A @ xB ) )
& ( aSubsetOf0 @ xA @ xB )
& ! [A: $i] :
( ( aElementOf0 @ A @ xB )
=> ( aElementOf0 @ A @ xC ) )
& ( aSubsetOf0 @ xB @ xC ) )
=> ( ! [A: $i] :
( ( aElementOf0 @ A @ xA )
=> ( aElementOf0 @ A @ xC ) )
| ( aSubsetOf0 @ xA @ xC ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(17,plain,
~ ( ( ! [A: $i] :
( ( aElementOf0 @ A @ xA )
=> ( aElementOf0 @ A @ xB ) )
& ( aSubsetOf0 @ xA @ xB )
& ! [A: $i] :
( ( aElementOf0 @ A @ xB )
=> ( aElementOf0 @ A @ xC ) )
& ( aSubsetOf0 @ xB @ xC ) )
=> ( ! [A: $i] :
( ( aElementOf0 @ A @ xA )
=> ( aElementOf0 @ A @ xC ) )
| ( aSubsetOf0 @ xA @ xC ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ( A != slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin_01) ).
thf(54,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ( A != slcrc0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(8,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( isFinite0 @ A )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFinRel) ).
thf(49,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
thf(47,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B ) )
=> ( ( ( aSubsetOf0 @ A @ B )
& ( aSubsetOf0 @ B @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubASymm) ).
thf(62,plain,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B ) )
=> ( ( ( aSubsetOf0 @ A @ B )
& ( aSubsetOf0 @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(72,plain,
$false,
inference(cvc4,[status(thm)],[52,46,60,65,50,26,58,51,34,45,17,54,49,47,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM533+2 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n024.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 17:00:52 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.95/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/0.95 % [INFO] Parsing done (119ms).
% 1.23/0.96 % [INFO] Running in sequential loop mode.
% 1.63/1.15 % [INFO] eprover registered as external prover.
% 1.63/1.15 % [INFO] cvc4 registered as external prover.
% 1.63/1.16 % [INFO] Scanning for conjecture ...
% 1.74/1.19 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.74/1.20 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.74/1.22 % [INFO] Found a conjecture and 14 axioms. Running axiom selection ...
% 1.88/1.25 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 1.88/1.25 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.88/1.25 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.93/1.26 % [INFO] Problem is first-order (TPTP FOF).
% 1.93/1.27 % [INFO] Type checking passed.
% 1.93/1.27 % [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 ...
% 3.19/1.74 % External prover 'cvc4' found a proof!
% 3.19/1.74 % [INFO] Killing All external provers ...
% 3.19/1.74 % Time passed: 1225ms (effective reasoning time: 776ms)
% 3.19/1.74 % 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)>
% 3.19/1.74 % Axioms used in derivation (14): mCountNFin, mDefEmp, mSetSort, mFinRel, m__522, mCountNFin_01, mEmpFin, mSubASymm, mElmSort, mDefSub, mCntRel, mSubRefl, mSubFSet, mEOfElem
% 3.19/1.74 % No. of inferences in proof: 32
% 3.19/1.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1225 ms resp. 776 ms w/o parsing
% 3.46/1.78 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.46/1.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------