TSTP Solution File: NUM534+2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM534+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 3.68s 1.87s
% Output : Refutation 4.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 30
% Syntax : Number of formulae : 51 ( 11 unt; 11 typ; 0 def)
% Number of atoms : 197 ( 34 equ; 0 cnn)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 469 ( 18 ~; 9 |; 75 &; 294 @)
% ( 10 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 64 ( 0 ^; 61 !; 3 ?; 64 :)
% 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(aElement0_type,type,
aElement0: $i > $o ).
thf(sdtpldt0_type,type,
sdtpldt0: $i > $i > $i ).
thf(sdtmndt0_type,type,
sdtmndt0: $i > $i > $i ).
thf(xS_type,type,
xS: $i ).
thf(xx_type,type,
xx: $i ).
thf(isFinite0_type,type,
isFinite0: $i > $o ).
thf(isCountable0_type,type,
isCountable0: $i > $o ).
thf(4,axiom,
aSet0 @ xS,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__617) ).
thf(46,plain,
aSet0 @ xS,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
thf(116,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElement0 @ B ) )
=> ! [C: $i] :
( ( C
= ( sdtmndt0 @ A @ B ) )
<=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
<=> ( ( aElement0 @ D )
& ( aElementOf0 @ D @ A )
& ( D != B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
thf(60,plain,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElement0 @ B ) )
=> ! [C: $i] :
( ( ( C
= ( sdtmndt0 @ A @ B ) )
=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aElement0 @ D )
& ( aElementOf0 @ D @ A )
& ( D != B ) ) )
& ( ( ( aElement0 @ D )
& ( aElementOf0 @ D @ A )
& ( D != B ) )
=> ( aElementOf0 @ D @ C ) ) ) ) )
& ( ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aElement0 @ D )
& ( aElementOf0 @ D @ A )
& ( D != B ) ) )
& ( ( ( aElement0 @ D )
& ( aElementOf0 @ D @ A )
& ( D != B ) )
=> ( aElementOf0 @ D @ C ) ) ) )
=> ( C
= ( sdtmndt0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,conjecture,
( ( ( aSet0 @ ( sdtmndt0 @ xS @ xx ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtmndt0 @ xS @ xx ) )
<=> ( ( aElement0 @ A )
& ( aElementOf0 @ A @ xS )
& ( A != xx ) ) ) )
=> ( ( ( aSet0 @ ( sdtpldt0 @ ( sdtmndt0 @ xS @ xx ) @ xx ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtpldt0 @ ( sdtmndt0 @ xS @ xx ) @ xx ) )
<=> ( ( aElement0 @ A )
& ( ( aElementOf0 @ A @ ( sdtmndt0 @ xS @ xx ) )
| ( A = xx ) ) ) ) )
=> ( ( sdtpldt0 @ ( sdtmndt0 @ xS @ xx ) @ xx )
= xS ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ( aSet0 @ ( sdtmndt0 @ xS @ xx ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtmndt0 @ xS @ xx ) )
<=> ( ( aElement0 @ A )
& ( aElementOf0 @ A @ xS )
& ( A != xx ) ) ) )
=> ( ( ( aSet0 @ ( sdtpldt0 @ ( sdtmndt0 @ xS @ xx ) @ xx ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtpldt0 @ ( sdtmndt0 @ xS @ xx ) @ xx ) )
<=> ( ( aElement0 @ A )
& ( ( aElementOf0 @ A @ ( sdtmndt0 @ xS @ xx ) )
| ( A = xx ) ) ) ) )
=> ( ( sdtpldt0 @ ( sdtmndt0 @ xS @ xx ) @ xx )
= xS ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ( ( ( aSet0 @ ( sdtmndt0 @ xS @ xx ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( sdtmndt0 @ xS @ xx ) )
=> ( ( aElement0 @ A )
& ( aElementOf0 @ A @ xS )
& ( A != xx ) ) )
& ( ( ( aElement0 @ A )
& ( aElementOf0 @ A @ xS )
& ( A != xx ) )
=> ( aElementOf0 @ A @ ( sdtmndt0 @ xS @ xx ) ) ) ) )
=> ( ( ( aSet0 @ ( sdtpldt0 @ ( sdtmndt0 @ xS @ xx ) @ xx ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( sdtpldt0 @ ( sdtmndt0 @ xS @ xx ) @ xx ) )
=> ( ( aElement0 @ A )
& ( ( aElementOf0 @ A @ ( sdtmndt0 @ xS @ xx ) )
| ( A = xx ) ) ) )
& ( ( ( aElement0 @ A )
& ( ( aElementOf0 @ A @ ( sdtmndt0 @ xS @ xx ) )
| ( A = xx ) ) )
=> ( aElementOf0 @ A @ ( sdtpldt0 @ ( sdtmndt0 @ xS @ xx ) @ xx ) ) ) ) )
=> ( ( sdtpldt0 @ ( sdtmndt0 @ xS @ xx ) @ xx )
= xS ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,axiom,
! [A: $i] :
( ( A = slcrc0 )
<=> ( ( aSet0 @ A )
& ~ ? [B: $i] : ( aElementOf0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
thf(97,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)],[14]) ).
thf(3,axiom,
isFinite0 @ slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEmpFin) ).
thf(45,plain,
isFinite0 @ slcrc0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ( A != slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin_01) ).
thf(49,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ( A != slcrc0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,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(108,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)],[15]) ).
thf(19,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ~ ( isFinite0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin) ).
thf(154,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ~ ( isFinite0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(9,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(55,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)],[9]) ).
thf(5,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSort) ).
thf(47,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(20,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( aSubsetOf0 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
thf(156,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( aSubsetOf0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(8,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ( isFinite0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubFSet) ).
thf(53,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ( isFinite0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
aElementOf0 @ xx @ xS,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__617_02) ).
thf(59,plain,
aElementOf0 @ xx @ xS,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( isCountable0 @ A )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCntRel) ).
thf(118,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(6,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetSort) ).
thf(48,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B )
& ( aSet0 @ C ) )
=> ( ( ( aSubsetOf0 @ A @ B )
& ( aSubsetOf0 @ B @ C ) )
=> ( aSubsetOf0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubTrans) ).
thf(95,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B )
& ( aSet0 @ C ) )
=> ( ( ( aSubsetOf0 @ A @ B )
& ( aSubsetOf0 @ B @ C ) )
=> ( aSubsetOf0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElement0 @ B ) )
=> ! [C: $i] :
( ( C
= ( sdtpldt0 @ A @ B ) )
<=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
<=> ( ( aElement0 @ D )
& ( ( aElementOf0 @ D @ A )
| ( D = B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefCons) ).
thf(119,plain,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElement0 @ B ) )
=> ! [C: $i] :
( ( ( C
= ( sdtpldt0 @ A @ B ) )
=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aElement0 @ D )
& ( ( aElementOf0 @ D @ A )
| ( D = B ) ) ) )
& ( ( ( aElement0 @ D )
& ( ( aElementOf0 @ D @ A )
| ( D = B ) ) )
=> ( aElementOf0 @ D @ C ) ) ) ) )
& ( ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aElement0 @ D )
& ( ( aElementOf0 @ D @ A )
| ( D = B ) ) ) )
& ( ( ( aElement0 @ D )
& ( ( aElementOf0 @ D @ A )
| ( D = B ) ) )
=> ( aElementOf0 @ D @ C ) ) ) )
=> ( C
= ( sdtpldt0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( isFinite0 @ A )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFinRel) ).
thf(58,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(158,plain,
$false,
inference(cvc4,[status(thm)],[46,116,60,21,97,45,49,108,154,55,47,156,53,59,118,48,95,119,58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM534+2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n022.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 17:29:33 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.88/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.96 % [INFO] Parsing done (123ms).
% 1.21/0.97 % [INFO] Running in sequential loop mode.
% 1.55/1.16 % [INFO] eprover registered as external prover.
% 1.55/1.16 % [INFO] cvc4 registered as external prover.
% 1.55/1.17 % [INFO] Scanning for conjecture ...
% 1.76/1.20 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.76/1.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.76/1.22 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.76/1.22 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.89/1.24 % [INFO] Found a conjecture and 18 axioms. Running axiom selection ...
% 1.89/1.29 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 1.89/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.89/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.89/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.13/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.13/1.30 % [INFO] Problem is first-order (TPTP FOF).
% 2.13/1.31 % [INFO] Type checking passed.
% 2.13/1.31 % [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 ...
% 3.68/1.87 % External prover 'cvc4' found a proof!
% 3.68/1.87 % [INFO] Killing All external provers ...
% 3.68/1.87 % Time passed: 1354ms (effective reasoning time: 896ms)
% 3.68/1.87 % 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)>
% 3.68/1.87 % Axioms used in derivation (18): mCountNFin, mDefEmp, mDefDiff, mSetSort, m__617_02, mFinRel, mDefCons, mCountNFin_01, mEmpFin, mSubASymm, mDefSub, mSubTrans, mCntRel, mSubRefl, mSubFSet, mEOfElem, m__617, mElmSort
% 3.68/1.87 % No. of inferences in proof: 40
% 3.68/1.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1354 ms resp. 896 ms w/o parsing
% 4.07/1.91 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.07/1.91 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------