TSTP Solution File: LAT382+3 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT382+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.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 11:28:13 EDT 2023
% Result : Theorem 3.72s 1.87s
% Output : Refutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 32
% Syntax : Number of formulae : 52 ( 9 unt; 14 typ; 0 def)
% Number of atoms : 203 ( 7 equ; 0 cnn)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 544 ( 5 ~; 4 |; 70 &; 374 @)
% ( 6 <=>; 85 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 90 ( 0 ^; 87 !; 3 ?; 90 :)
% Comments :
%------------------------------------------------------------------------------
thf(aSet0_type,type,
aSet0: $i > $o ).
thf(isEmpty0_type,type,
isEmpty0: $i > $o ).
thf(aElementOf0_type,type,
aElementOf0: $i > $i > $o ).
thf(aSubsetOf0_type,type,
aSubsetOf0: $i > $i > $o ).
thf(aLowerBoundOfIn0_type,type,
aLowerBoundOfIn0: $i > $i > $i > $o ).
thf(sdtlseqdt0_type,type,
sdtlseqdt0: $i > $i > $o ).
thf(aUpperBoundOfIn0_type,type,
aUpperBoundOfIn0: $i > $i > $i > $o ).
thf(aInfimumOfIn0_type,type,
aInfimumOfIn0: $i > $i > $i > $o ).
thf(aSupremumOfIn0_type,type,
aSupremumOfIn0: $i > $i > $i > $o ).
thf(xu_type,type,
xu: $i ).
thf(xv_type,type,
xv: $i ).
thf(aElement0_type,type,
aElement0: $i > $o ).
thf(xS_type,type,
xS: $i ).
thf(xT_type,type,
xT: $i ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessRel) ).
thf(77,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(10,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( isEmpty0 @ A )
<=> ~ ? [B: $i] : ( aElementOf0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmpty) ).
thf(54,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( ( isEmpty0 @ A )
=> ~ ? [B: $i] : ( aElementOf0 @ B @ A ) )
& ( ~ ? [B: $i] : ( aElementOf0 @ B @ A )
=> ( isEmpty0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,axiom,
aSet0 @ xT,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__773) ).
thf(76,plain,
aSet0 @ xT,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
thf(72,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(19,axiom,
( ( aElementOf0 @ xu @ xT )
& ( aElementOf0 @ xu @ xT )
& ! [A: $i] :
( ( aElementOf0 @ A @ xS )
=> ( sdtlseqdt0 @ xu @ A ) )
& ( aLowerBoundOfIn0 @ xu @ xS @ xT )
& ! [A: $i] :
( ( ( ( aElementOf0 @ A @ xT )
& ! [B: $i] :
( ( aElementOf0 @ B @ xS )
=> ( sdtlseqdt0 @ A @ B ) ) )
| ( aLowerBoundOfIn0 @ A @ xS @ xT ) )
=> ( sdtlseqdt0 @ A @ xu ) )
& ( aInfimumOfIn0 @ xu @ xS @ xT )
& ( aElementOf0 @ xv @ xT )
& ( aElementOf0 @ xv @ xT )
& ! [A: $i] :
( ( aElementOf0 @ A @ xS )
=> ( sdtlseqdt0 @ xv @ A ) )
& ( aLowerBoundOfIn0 @ xv @ xS @ xT )
& ! [A: $i] :
( ( ( ( aElementOf0 @ A @ xT )
& ! [B: $i] :
( ( aElementOf0 @ B @ xS )
=> ( sdtlseqdt0 @ A @ B ) ) )
| ( aLowerBoundOfIn0 @ A @ xS @ xT ) )
=> ( sdtlseqdt0 @ A @ xv ) )
& ( aInfimumOfIn0 @ xv @ xS @ xT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__792) ).
thf(87,plain,
( ( aElementOf0 @ xu @ xT )
& ( aElementOf0 @ xu @ xT )
& ! [A: $i] :
( ( aElementOf0 @ A @ xS )
=> ( sdtlseqdt0 @ xu @ A ) )
& ( aLowerBoundOfIn0 @ xu @ xS @ xT )
& ! [A: $i] :
( ( ( ( aElementOf0 @ A @ xT )
& ! [B: $i] :
( ( aElementOf0 @ B @ xS )
=> ( sdtlseqdt0 @ A @ B ) ) )
| ( aLowerBoundOfIn0 @ A @ xS @ xT ) )
=> ( sdtlseqdt0 @ A @ xu ) )
& ( aInfimumOfIn0 @ xu @ xS @ xT )
& ( aElementOf0 @ xv @ xT )
& ( aElementOf0 @ xv @ xT )
& ! [A: $i] :
( ( aElementOf0 @ A @ xS )
=> ( sdtlseqdt0 @ xv @ A ) )
& ( aLowerBoundOfIn0 @ xv @ xS @ xT )
& ! [A: $i] :
( ( ( ( aElementOf0 @ A @ xT )
& ! [B: $i] :
( ( aElementOf0 @ B @ xS )
=> ( sdtlseqdt0 @ A @ B ) ) )
| ( aLowerBoundOfIn0 @ A @ xS @ xT ) )
=> ( sdtlseqdt0 @ A @ xv ) )
& ( aInfimumOfIn0 @ xv @ xS @ xT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(4,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetSort) ).
thf(23,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ! [C: $i,D: $i] :
( ( ( aSupremumOfIn0 @ C @ B @ A )
& ( aSupremumOfIn0 @ D @ B @ A ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSupUn) ).
thf(24,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ! [C: $i,D: $i] :
( ( ( aSupremumOfIn0 @ C @ B @ A )
& ( aSupremumOfIn0 @ D @ B @ A ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ! [C: $i] :
( ( aUpperBoundOfIn0 @ C @ B @ A )
<=> ( ( aElementOf0 @ C @ A )
& ! [D: $i] :
( ( aElementOf0 @ D @ B )
=> ( sdtlseqdt0 @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefUB) ).
thf(37,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ! [C: $i] :
( ( ( aUpperBoundOfIn0 @ C @ B @ A )
=> ( ( aElementOf0 @ C @ A )
& ! [D: $i] :
( ( aElementOf0 @ D @ B )
=> ( sdtlseqdt0 @ D @ C ) ) ) )
& ( ( ( aElementOf0 @ C @ A )
& ! [D: $i] :
( ( aElementOf0 @ D @ B )
=> ( sdtlseqdt0 @ D @ C ) ) )
=> ( aUpperBoundOfIn0 @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,conjecture,
xu = xv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
xu != xv,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(20,plain,
xu != xv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
( ( aSet0 @ xS )
& ! [A: $i] :
( ( aElementOf0 @ A @ xS )
=> ( aElementOf0 @ A @ xT ) )
& ( aSubsetOf0 @ xS @ xT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__773_01) ).
thf(57,plain,
( ( aSet0 @ xS )
& ! [A: $i] :
( ( aElementOf0 @ A @ xS )
=> ( aElementOf0 @ A @ xT ) )
& ( aSubsetOf0 @ xS @ xT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(18,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ! [C: $i] :
( ( aSupremumOfIn0 @ C @ B @ A )
<=> ( ( aElementOf0 @ C @ A )
& ( aUpperBoundOfIn0 @ C @ B @ A )
& ! [D: $i] :
( ( aUpperBoundOfIn0 @ D @ B @ A )
=> ( sdtlseqdt0 @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSup) ).
thf(78,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ! [C: $i] :
( ( ( aSupremumOfIn0 @ C @ B @ A )
=> ( ( aElementOf0 @ C @ A )
& ( aUpperBoundOfIn0 @ C @ B @ A )
& ! [D: $i] :
( ( aUpperBoundOfIn0 @ D @ B @ A )
=> ( sdtlseqdt0 @ C @ D ) ) ) )
& ( ( ( aElementOf0 @ C @ A )
& ( aUpperBoundOfIn0 @ C @ B @ A )
& ! [D: $i] :
( ( aUpperBoundOfIn0 @ D @ B @ A )
=> ( sdtlseqdt0 @ C @ D ) ) )
=> ( aSupremumOfIn0 @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(7,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ! [C: $i] :
( ( aLowerBoundOfIn0 @ C @ B @ A )
<=> ( ( aElementOf0 @ C @ A )
& ! [D: $i] :
( ( aElementOf0 @ D @ B )
=> ( sdtlseqdt0 @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLB) ).
thf(29,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ! [C: $i] :
( ( ( aLowerBoundOfIn0 @ C @ B @ A )
=> ( ( aElementOf0 @ C @ A )
& ! [D: $i] :
( ( aElementOf0 @ D @ B )
=> ( sdtlseqdt0 @ C @ D ) ) ) )
& ( ( ( aElementOf0 @ C @ A )
& ! [D: $i] :
( ( aElementOf0 @ D @ B )
=> ( sdtlseqdt0 @ C @ D ) ) )
=> ( aLowerBoundOfIn0 @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mASymm) ).
thf(61,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(15,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mARefl) ).
thf(74,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(9,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ! [C: $i] :
( ( aInfimumOfIn0 @ C @ B @ A )
<=> ( ( aElementOf0 @ C @ A )
& ( aLowerBoundOfIn0 @ C @ B @ A )
& ! [D: $i] :
( ( aLowerBoundOfIn0 @ D @ B @ A )
=> ( sdtlseqdt0 @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefInf) ).
thf(45,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ! [C: $i] :
( ( ( aInfimumOfIn0 @ C @ B @ A )
=> ( ( aElementOf0 @ C @ A )
& ( aLowerBoundOfIn0 @ C @ B @ A )
& ! [D: $i] :
( ( aLowerBoundOfIn0 @ D @ B @ A )
=> ( sdtlseqdt0 @ D @ C ) ) ) )
& ( ( ( aElementOf0 @ C @ A )
& ( aLowerBoundOfIn0 @ C @ B @ A )
& ! [D: $i] :
( ( aLowerBoundOfIn0 @ D @ B @ A )
=> ( sdtlseqdt0 @ D @ C ) ) )
=> ( aInfimumOfIn0 @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,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(64,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)],[13]) ).
thf(3,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSort) ).
thf(22,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aElement0 @ C ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ C ) )
=> ( sdtlseqdt0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTrans) ).
thf(27,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B )
& ( aElement0 @ C ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ C ) )
=> ( sdtlseqdt0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(109,plain,
$false,
inference(cvc4,[status(thm)],[77,54,76,72,87,23,24,37,20,57,78,29,61,74,45,64,22,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT382+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n010.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 14:03:58 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.84/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/0.95 % [INFO] Parsing done (126ms).
% 1.26/0.96 % [INFO] Running in sequential loop mode.
% 1.56/1.16 % [INFO] eprover registered as external prover.
% 1.56/1.16 % [INFO] cvc4 registered as external prover.
% 1.56/1.16 % [INFO] Scanning for conjecture ...
% 1.72/1.20 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.80/1.20 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.80/1.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.80/1.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.80/1.22 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.80/1.22 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.92/1.24 % [INFO] Found a conjecture and 17 axioms. Running axiom selection ...
% 1.92/1.28 % [INFO] Axiom selection finished. Selected 17 axioms (removed 0 axioms).
% 1.92/1.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.92/1.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.92/1.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.92/1.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.92/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.92/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.92/1.31 % [INFO] Problem is first-order (TPTP FOF).
% 1.92/1.31 % [INFO] Type checking passed.
% 1.92/1.32 % [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 ...
% 3.72/1.87 % External prover 'cvc4' found a proof!
% 3.72/1.87 % [INFO] Killing All external provers ...
% 3.72/1.87 % Time passed: 1366ms (effective reasoning time: 906ms)
% 3.72/1.87 % 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)>
% 3.72/1.87 % Axioms used in derivation (17): mDefSup, mDefUB, mTrans, mARefl, mDefLB, mDefInf, mLessRel, m__773_01, mASymm, m__773, mElmSort, mDefSub, mSupUn, mEOfElem, mDefEmpty, m__792, mSetSort
% 3.72/1.87 % No. of inferences in proof: 38
% 3.72/1.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1366 ms resp. 906 ms w/o parsing
% 3.97/1.92 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.97/1.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------