TSTP Solution File: LAT381+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT381+1 : TPTP v8.1.2. Released v4.0.0.
% 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 11:28:13 EDT 2023
% Result : Theorem 3.89s 2.07s
% Output : Refutation 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 28
% Syntax : Number of formulae : 44 ( 8 unt; 14 typ; 0 def)
% Number of atoms : 136 ( 5 equ; 0 cnn)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 363 ( 5 ~; 0 |; 39 &; 252 @)
% ( 6 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 64 ( 0 ^; 61 !; 3 ?; 64 :)
% 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(xT_type,type,
xT: $i ).
thf(xS_type,type,
xS: $i ).
thf(15,axiom,
( ( aSupremumOfIn0 @ xu @ xS @ xT )
& ( aSupremumOfIn0 @ xv @ xS @ xT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__744) ).
thf(74,plain,
( ( aSupremumOfIn0 @ xu @ xS @ xT )
& ( aSupremumOfIn0 @ xv @ xS @ xT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',mDefSup) ).
thf(65,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)],[14]) ).
thf(10,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
thf(53,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,conjecture,
xu = xv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
xu != xv,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
xu != xv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( isEmpty0 @ A )
<=> ~ ? [B: $i] : ( aElementOf0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmpty) ).
thf(42,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)],[8]) ).
thf(6,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/sandbox/benchmark/theBenchmark.p',mDefUB) ).
thf(25,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)],[6]) ).
thf(4,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mARefl) ).
thf(21,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,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/sandbox/benchmark/theBenchmark.p',mDefInf) ).
thf(33,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)],[7]) ).
thf(9,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
<=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
thf(45,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)],[9]) ).
thf(13,axiom,
aSubsetOf0 @ xS @ xT,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__725_01) ).
thf(64,plain,
aSubsetOf0 @ xS @ xT,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(12,axiom,
aSet0 @ xT,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__725) ).
thf(63,plain,
aSet0 @ xT,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aElement0 @ B ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mASymm) ).
thf(18,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)],[3]) ).
thf(11,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/sandbox/benchmark/theBenchmark.p',mDefLB) ).
thf(55,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)],[11]) ).
thf(5,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/sandbox/benchmark/theBenchmark.p',mTrans) ).
thf(23,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)],[5]) ).
thf(77,plain,
$false,
inference(e,[status(thm)],[74,65,53,16,42,25,21,33,45,64,63,18,55,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT381+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n017.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 13:48:01 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.87/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/0.97 % [INFO] Parsing done (124ms).
% 1.17/0.98 % [INFO] Running in sequential loop mode.
% 1.74/1.28 % [INFO] eprover registered as external prover.
% 1.74/1.28 % [INFO] cvc4 registered as external prover.
% 1.74/1.29 % [INFO] Scanning for conjecture ...
% 1.93/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.93/1.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.93/1.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.93/1.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.93/1.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.93/1.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.13/1.37 % [INFO] Found a conjecture and 16 axioms. Running axiom selection ...
% 2.13/1.42 % [INFO] Axiom selection finished. Selected 13 axioms (removed 3 axioms).
% 2.13/1.43 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.13/1.43 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.13/1.43 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.13/1.43 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.13/1.44 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.13/1.44 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.13/1.44 % [INFO] Problem is first-order (TPTP FOF).
% 2.13/1.45 % [INFO] Type checking passed.
% 2.13/1.45 % [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 ...
% 3.59/2.07 % External prover 'e' found a proof!
% 3.59/2.07 % [INFO] Killing All external provers ...
% 3.59/2.07 % Time passed: 1549ms (effective reasoning time: 1087ms)
% 3.59/2.07 % 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)>
% 3.59/2.07 % Axioms used in derivation (13): mDefSup, mDefUB, mTrans, mARefl, mDefLB, mDefInf, m__744, mASymm, mDefSub, m__725_01, m__725, mEOfElem, mDefEmpty
% 3.59/2.07 % No. of inferences in proof: 30
% 3.89/2.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1549 ms resp. 1087 ms w/o parsing
% 3.98/2.13 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.98/2.13 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------